Multivalent ions and biomolecules: Attempting a comprehensive perspective

Abstract

Ions are ubiquitous in nature. They play a key role for many biological processes on the molecular scale, from molecular interactions, to mechanical properties, to folding, to self‐organisation and assembly, to reaction equilibria, to signalling, to energy and material transport, to recognition etc. Going beyond monovalent ions to multivalent ions, the effects of the ions are frequently not only stronger (due to the obviously higher charge), but qualitatively different. A typical example is the process of binding of multivalent ions, such as Ca²⁺, to a macromolecule and the consequences of this ion binding such as compaction, collapse, potential charge inversion and precipitation of the macromolecule. Here we review these effects and phenomena induced by multivalent ions for biological (macro)molecules, from the “atomistic/molecular” local picture of (potentially specific) interactions to the more global picture of phase behaviour including, e. g., crystallisation, phase separation, oligomerisation etc. Rather than attempting an encyclopedic list of systems, we rather aim for an embracing discussion using typical case studies. We try to cover predominantly three main classes: proteins, nucleic acids, and amphiphilic molecules including interface effects. We do not cover in detail, but make some comparisons to, ion channels, colloidal systems, and synthetic polymers. While there are obvious differences in the behaviour of, and the relevance of multivalent ions for, the three main classes of systems, we also point out analogies. Our attempt of a comprehensive discussion is guided by the idea that there are not only important differences and specific phenomena with regard to the effects of multivalent ions on the main systems, but also important similarities. We hope to bridge physico‐chemical mechanisms, concepts of soft matter, and biological observations and connect the different communities further.

Ions play an important role for a large variety of biological processes. Compared to monovalent ions, the effects of multivalent ions are often qualitatively different and can include complex phenomena such as charge inversion and precipitation of macromolecules. In this article, we review the effects of multivalent ions on biological (macro)molecules from the molecular to the global level. Our hope is to bridge physico‐chemical, soft matter and biological aspects, thereby stimulating discussions between these scientific communities.

1. Introduction, motivation and scope

In this review, we will focus on effects induced in biological and chemical systems by multivalent ions. While general overviews of the influences of electrostatics on soft matter are given, e. g., in Refs. [1–3], it is generally accepted that the effects of multivalent ions go beyond such considerations.4, 5, 6 We will include different types of ions into our discussion: mono‐atomic ions, such as Na⁺ and Mg²⁺; multi‐atom ions (e. g., ${\mathrm{NH}}_4^{+}$ or spermidine); nano‐ions (such as polyoxometalates), and larger ions, e. g., oligo‐arginine. We note that the classification of ions does not only depend on their net charge, but also on their other characteristics such as their (in)organic nature. The main aspects of this review are the charge‐mediated effects of these ions whereas their other properties play a less important role. We note that specific interactions of monovalent ions with biomolecules, such as that between Ag⁺ and DNA,7 have also been shown, implying that the role of monovalent ions can go beyond that of purely inert electrolytes. However, such interactions are not the main focus of this review.

Generally, ions are present ubiquitously and are therefore of fundamental interest for a large variety of topics and research areas. Starting from biology and physiology, the importance of ions becomes apparent immediately. A typical animal or human cell contains approximately 130 mM K⁺ and 10–20 mM Na⁺ cations and relies on an active ion exchange with its surroundings to maintain its electrochemical potential.8 Similarly, the signal transduction activity of neurons depends on charge exchange mechanisms.9 Inside the nucleus, the highly negative charge of nucleic acids (DNA and RNA) implies that ions – most frequently, Mg²⁺ – are required to screen their charges, thus enabling, e.g., nucleic acid‐protein interactions.9

Several other biological aspects depend on ions. For example, many enzymes host metal cations such as Ca²⁺ and Zn²⁺ in their catalytic centers; muscle contraction is made possible via myosin‐Ca²⁺ interactions; and oxygen transport by hemoglobin is facilitated through Fe²⁺/Fe³⁺ ions.10 Generally, iron metabolism, storage and transport in mammals is a complex issue and involves, apart from hemoglobin, the proteins myoglobin, ferritin10 and lactoferrin.10, 11 Divalent ions such as Ca²⁺ and Mg²⁺ have furthermore been shown to be present at the interfaces between virus particle subunits (see Ref. [12] and refs. therein), presumably fulfilling also structurally important roles in viruses. Investigations of silk feedstock indicated that the viscosity of the latter is strongly influenced by the type and valency of the cation present. Whereas the divalent Ca²⁺ increases the viscosity by bridging acidic amino acids, the monovalent K⁺ reduces viscosity due to competition for binding to these types of residues.13

Given the prominent role of ions in physiology, it is obvious that biological and biotechnological experiments need to consider the native environment of the biomolecules they investigate. Thus, the success of ex vivo and in vitro experiments with, e. g. enzymes, strongly depends on the (ionic) composition of buffer solutions used.

The strong dependence of biological processes on ions can lead to peculiar evolution processes. As an example, due to low Zn²⁺ levels in the deep sea, a certain diatom species relies on Cd²⁺ instead14 – a heavy metal cation known to be toxic for many land‐borne creatures. Another dependence on seemingly less physiologically relevant ions has been observed in M. fumariolicum SolV, an extremophilic microbe native to Italian volcanic mudpots. This bacterium utilises lanthanide cations to catalyse methane‐based metabolic pathways.15

From ecologic and ecotoxicologic points of view, ions play significant roles as fertilisers. A large amount of fertilisers is phosphate‐based,16 but lanthanides are also known to be used in agriculture.17 In industrial settings, polyanions such as polyacrylate can be used to prevent CaCO₃ precipitation (i. e., as scale inhibitors) due to their specific interactions with Ca²⁺ in pipelines.18

At the same time, ions can be successfully employed to manipulate macromolecules in biotechnology, e. g. as crystallisation agents. This can be demonstrated in the case of negatively charged proteins where multivalent cations have been shown to promote crystallisation.19, 20, 21, 22, 23, 24, 25, 26, 27 In addition, a purification protocol using Zn²⁺ ions has recently been established for recombinant antibodies.28

Here, we first introduce the theoretical aspects of charge‐mediated interactions. We then summarise the current knowledge regarding the role of charges in (bio)(macro)molecules including DNA, surfactants, interfaces and proteins. We focus especially on charge‐mediated modifications of static, dynamic or thermodynamic properties of the macromolecules in questions, including the intriguing possibilities to rationally tune (bio)molecular interactions. Finally, we briefly cover other systems such as ion channels and synthetic polymers. We mention experimental methods where necessary, but do not consider them the main subject of this review.

Through this review, we aim to provide a comprehensive overview of the manifold ways in which charges can influence the behaviour of macromolecules. By emphasising how physical concepts can be used to understand biological and soft matter systems, our goal is to enhance mutual understanding and communication between different scientific communities tackling manifold questions. We hope to stimulate further discussion and inspire both experimental and theoretical investigations of these complex aspects. We will mostly focus on the static/equilibrium behaviour, but we note that there are of course also interesting multivalent ion‐mediated effects on the dynamics, kinetics, and viscosity of (biological) soft matter.29, 30

2. Background and theoretical concepts

In this section (partly based on Ref. [31] and Ref. 39), we provide an overview of the theoretical concepts behind ion‐related interactions of soft matter. In particular, we focus on charge effects as accounted for in mean‐field, Poisson‐Boltzmann and Derjaguin‐Landau, Verwey‐Overbeek (DLVO)32, 33 theories, outlining their strengths and shortcomings especially in the context of ion‐specific effects and multivalent ions. The two latter aspects are then outlined in more detail using the Hofmeister series as an example. We note that for a detailed review on polyelectrolytes and, inter alia, their interactions with counterions, the interested reader is referred to Ref. [2]. In the following, we will describe mean‐field and beyond‐mean‐field approaches to ion condensation. As a very general principle, we shall briefly mention here that the two main parameters governing the interaction of ions and (macro)molecules are the enthalpic contributions of their electrostatic interactions and the loss of the ions’ conformational entropy upon binding to the molecules, the former compensating the latter.3, 34

2.1. Mean‐field theory of charged matter: Poisson‐Boltzmann theory

Ion Distribution and Charge Screening: Poisson‐Boltzmann and DLVO Theory

Considering a charged object in a solution with ions, the Poisson‐Boltzmann (PB) theory provides a basic mean‐field approach to describe the ion distribution. This approach combines the exact Poisson equation with a mean‐field relation between the electrostatic potential and the potential of mean force on the ions.1, 35, 36 The resulting ion distribution around charged objects forms the so‐called electrostatic double‐layer that causes a screening of charges in electrolyte solutions, over the Debye screening length

$${\displaystyle \begin{array}{c}{\lambda }_D={\left(\frac{{ϵ}_0{ϵ}_r{k}_{B}T}{2000e^{2}I}\right)}^{-1/2}={\left(\frac{1}{8000\pi I{\lambda }_B}\right)}^{-1/2}\end{array}}$$ (1)

where ϵ ₀ is the vacuum permittivity, ϵ_r is the relative permittivity of the sample, k_B is the Boltzmann constant, and T the temperature. The Bjerrum length, λ_B, quantifies the distance on which the interaction between two elementary charges equals k_BT:1, 3, 37

$${\displaystyle \begin{array}{c}{\lambda }_B=\frac{e^2}{4\pi {ϵ}_0{ϵ}_r{k}_{B}T}\end{array}}$$ (2)

which, in water at room temperature, is approximately equal to 0.72 nm.37 Given a solution of several ions with molar concentration n_i and valency Z_i, the ionic strength

$${\displaystyle \begin{array}{c}I=\frac{1}{2}\sum _i{n}_i{Z}_i^2\end{array}}$$ (3)

provides a valency‐squared‐weighted concentration of ions, implying that even in the mean‐field approach multivalent ions have a stronger effect compared to monovalent ions.

The decay of the double‐layer potential described by the Poisson equation has been historically rationalised by different approaches. The Helmholtz theory disregards thermal motion of the counterions, assuming an unrealistic rigidity of the counterion layer.38 This drawback is addressed in the Gouy‐Chapman model which pictures the counterion layer as diffuse, but has the shortcoming of assuming that the charges in question are point‐like. Rigid and diffuse models are combined in the Stern model (Figure 1), resulting in a more comprehensive and realistic description of the interactions between charged surfaces and counterions.38

Figure 1.

Stern model combining the rigid (Helmholtz) and diffuse (Gouy‐Chapman) double layer models. The grey shaded area represents a surface immersed into bulk liquid (blue continuum). The red circles on the shaded area represent negatively charged particles, the green circles illustrate positively charged ones. The potential ψ decays linearly between the surface (ψ_S) and the outer Helmholtz layer (ψ _o.H. at a distance d_H). At d_H, the diffuse double‐layer begins and ψ decays exponentially, asymptotically approaching a value ψ_A at long distances from the charged surface. The thickness of the diffuse double‐layer corresponds to the Debye screening length (eqn. 1). Figure reproduced and adapted from Refs. [38] and [39].

The PB theory and its linearised version, the Debye‐Hückel theory,40 provide a very useful and important framework for the understanding of electrostatic phenomena in soft matter. PB theory has been fairly successful in describing, e. g., distributions of mono‐ and divalent ions around DNA,41, 42, 43 although it is well‐known that PB theory cannot fully describe the effects of multivalent ions.

One very important consequence of the PB approach is the DLVO theory. In the DLVO potential, screened Coulomb interaction and van der Waals attraction are combined to explain the charge stabilisation of solutions with charged solutes (Figure 2). With increasing ionic strength, the charge screening decreases the electrostatic repulsion more efficiently and on shorter ranges, and finally the van der Waals attraction causes aggregation and precipitation.

Figure 2.

DLVO potential for varying salt concentration c_s. With increasing c_s, the potential changes from repulsive to attractive. The aggregation barrier reflects the charge stabilisation behaviour that becomes weaker due to charge screening.

Van der Waals forces (for a detailed description, the reader is referred to Ref. [44]) account for attractive interactions arising from interactions between permanent and induced dipoles, and their azimuthal orientation and range depend on the macromolecular structure. An essential aspect is the fact that the attraction decays on shorter length scales than electrostatics.44 While not a part of the initial DLVO theory, we remark that in practice an attraction induced, e. g., by depletion or hydration can produce qualitatively similar effects, so that experimental interpretations using DLVO theory should not solely be attributed to van der Waals interactions .

The PB theory is based on strong assumptions. In particular it ignores ion–ion correlations, arising e. g. due to excluded volume and electrostatics. Furthermore, other ion properties such as polarisability and hydration effects are not included, but can actually cause significant effects. On the one hand, it is interesting that PB and DLVO theories perform so well in many cases, providing approximate theoretical predictions when a full description of the system is out of reach even with elaborate and costly computer simulations. On the other hand, it is not surprising that various ion effects have been observed that cannot be explained by PB DLVO theories.1, 45, 46

2.2. Charge effects beyond mean field: counterion condensation and ion‐ion correlations

Very importantly, while in principle PB theory allows for Z>1, there are effects not contained in the PB picture. The most obvious of these is probably the possibility of charge inversion and like‐charge attraction. We will briefly elaborate on these phenomena in the following.

If the charge density in the system is strong, significantly modified ion distributions are obtained compared to the mean‐field PB approach. Manning et al.47 found a condensation of counterions on surfaces as long as the surface charge density is higher than a critical value which depends on the surface geometry and counterion valence. Generally, the Manning condensation model was introduced to obtain an estimate of the number of counterions condensing onto polyelectrolytes. The model assumes an idealised polyelectrolyte via an infinitely long, charged line. For simplification, interactions between these idealised polyelectrolytes are ignored and the dielectric constant of the surrounding medium is assumed to be that of the bulk solvent.3, 47 In addition, Olvera de la Cruz48 observed a precipitation of polyelectrolytes induced by tri‐ and tetravalent salts in a computational study, accounting for the probability of the binding of a condensed ion layer by PB theory with cylindrical geometry.

A general overview on ion‐ion correlations has been given by Jönsson and Wennerström.4 More recently, statistically advanced approaches accounting for ion–ion correlations due to strong Coulomb coupling have found counterion condensation at strongly charged surfaces as well as ion distributions that depend on the valence and size of the counterions.1, 49, 50, 51, 52 In this case, ion–ion correlations cause an inversion of the surface charge.51, 53, 54, 55 Theoretical approaches even predict a so‐called “giant overcharging”56 due to increasing monovalent salt content, while simulations suggest a lower reversed charge for these conditions.57

The effects of ion–ion correlations are, in general, expected to be small compared to specific interactions between ions and surfaces.54 While ion–ion correlations might add a finite contribution to the protein–ion interaction, other more specific effects appear to be more relevant.58

An interesting point concerns competing‐ion and co‐ion effects, both for different multivalent ions as well as for a given species of multivalent ions59 in the presence of a monovalent ion.60 We shall mention that ion effects and in particular multivalent effects are also connected with the pH of the system, but unless explicitly stated otherwise, the effects we are discussing are dominated by the charge itself, and the pH is a secondary (although quantitatively important) effect. The effects of both ionic strength and pH (pD) has been studied for lysozyme by Kundu et al.61 For information on the quantitative modelling of the coupling of charge state and pH in the context of multivalent ions we refer to Ref. [62].

2.3. Ion‐specific effects: hydration, Hofmeister, coordinative binding

While DLVO theory performs well for dilute monovalent ionic systems, a classical DLVO approach to biological systems fails due to the fact that it is no longer applicable at physiologically relevant ionic strengths above 0.1 M, as elaborated by Boström et al.46 In addition, Boström et al. point out that in order to allow for an appropriate comparison between theory and experiments, dispersion forces strongly depending on ion‐specific effects need to be taken into account.46 Such effects include ion size, electronic structure, charge density and the resulting polarisability. Moreover, given that an overwhelming majority of biological and physiological processes take place in aqueous environments, the hydration properties of ions are of particular importance.

Systematic reviews of ion‐specific effects and properties have been published, e. g., by Kunz.5, 6 Detailed theoretical and simulation studies have been described, e. g., by Lund et al., Jungwirth et al., Kalcher et al., Moreira et al., Schwierz et al., Lenz et al., Kunz et al., Smiatek et al., Lesch et al. and Kalayan et al.49, 57, 63, 64, 65, 66, 67, 68, 69, 70 We will not review the results here, but instead refer the interested reader to the corresponding publications.

In the following, we will briefly indicate the current state of rationalisation of the Hofmeister series. We will then focus our discussion on ion‐specific effects and those mediated by multivalent ions in protein systems.

The study of salt‐induced phase behaviour in protein solutions ranges back to the Hofmeister series on protein solubility in the presence of different salts71 and the related salting‐in and salting‐out behaviour.72 Figure 3 shows part of the Hofmeister series for anions and cations. The combination of cations and anions strongly affects the ability of the salt to precipitate (“salt out”) or stabilise (“salt in”) colloidal solutions.73 These variations of the phase behaviour cannot be explained by the DLVO theory and imply that the protein–ion interactions vary considerably beyond Poisson‐Boltzmann theory due to ion‐specific effects.

Figure 3.

Part of the Hofmeister series for anions and cations. Ions on the left hand side of the series destabilise solutions and “salt out” solutes, whereas ions on the right stabilise (“salt in”) solutions.

A comprehensive molecular understanding of ion‐specific effects is a challenge for theory,5 although it is clear that water‐mediated effects are a key ingredient. Baldwin74 argues that the Hofmeister effect can be understood considering the two competing abilities of ions to “salt out” nonpolar functional groups and “salt in” the polar peptide group.

A prominent theme for the molecular origin of the Hofmeister effect is the propensity of ions to change the water structure, i. e. the ion hydration.75, 76, 77 If certain ions – so‐called “kosmotropes” – interact with water strongly, the surrounding water is aligned relative to the ion, and thus additional water structure is formed. Ions with weak interaction and inappropriate size – so‐called “chaotropes” – are not able to induce any water structure and even distort the bulk structure. Kosmotropic cations are also referred to as “soft” and large with a low charge density and weak hydration while the opposite is true for kosmotropic anions which are considered “hard”, strongly hydrated and assumed to have a high charge density. In turn, chaotropic cations are considered “hard” and are strongly hydrated and chaotropic anions are “soft” and weakly hydrated.5, 6 This concept of “hard” and “soft” ions has important implications for the formation of ion pairs in aqueous solutions. One possible interpretation of this phenomenon has been given by Collins76, 78 who formulated the “law of matching water affinities”. This law approximates ions as spheres with point charges. In the case of small, “hard” ions, their hydration shell is strongly bound; the hydration shells of large, “soft” ions, however, are only loosely associated to the ions. Collins assumes that two “hard” ions of opposite charge experience a strong mutual attraction and, upon approaching each other, their strong attraction will allow them to shed their hydration shells and form an ion pair. Two “soft” ions with opposite charges will experience a much weaker mutual attraction than two “hard” ions, but their weakly associated hydration shells are readily shed, allowing them to pair up with each other easily.5, 78 Another theme involves the change of the dielectric constant at the protein–water interface, which allows non‐localised adsorption of polarisable ions at non‐polar, hydrophobic areas of the protein surface,64, 79, 80 representing another possible mechanism for the Hofmeister effect via dispersion forces.81, 82, 83

Finally, the interfacial tension of the protein–water interface has been linked to the Hofmeister series.84 Interestingly, Okur et al.85 emphasise that Hofmeister cations and anions may follow different trends depending on the part of the protein they interact with. Potentially, the typical Hofmeister trend can even be reversed, an observation corroborated by Schwierz et al.66, 82 Thus, although of practical importance and known for over a century, the Hofmeister effect, and salt effects on protein solutions in general, remain an interesting and challenging field of research. While the multivalent ion effects discussed in the remainder of this review go beyond the Hofmeister effects, some of the ingredients at least for ion‐specific effects (ionic radius, polarisability etc.) are similar.

In Sec. 2.4, we will provide a brief summary of selected physiochemical aspects of ions in solution before focusing on specific types of (biological) (macro)molecules and describing their interactions with multivalent cations in Sec. 3.

2.4. Physicochemical aspects of ions in solution

In the following, we will summarise selected physico‐chemical properties of some ions of particular relevance in biological and soft matter systems. Table 1 provides an overview on the ionic radii, hydration numbers and electron configurations. We note that in the case of the binding of transition metals (especially, but not only lanthanides) to biomolecules, their electronic configurations and particularly the presence of f‐orbitals, is likely to play a highly complex role at the quantum chemical level. Non‐trivial trends in the protein binding behaviour of lanthanide and yttrium cations have been observed, e. g., by Gomez et al.,86 Mulqueen et al.87 and the authors of this review.59 These effects can be tentatively attributed to the particular electron configurations of these ions and other highly complex properties of transition elements (polarisability, relativistic effects, anisotropic binding to biomolecules). A detailed discussion of these effects is beyond the scope of this review.

Table 1.

Selected ion properties. Unless indicated otherwise, the ionic radii are taken from Table 2.2 in Ref. 88. ^a indicates an approximate value,88 ^b from Ref. 89; ^c from Ref. 90; ^d from Ref. 91 ^e from Ref. 92.

Ion	Radius in solution (nm)	Hydration number	Electron configuration
Na+	0.102	3.5	[Ne] 3s0
K+	0.138	2.6	[Ar] 4s0
Mg2+	0.072	10.0	[Ne] 3s0
Ca2+	0.100	7.2	[Ar] 4s0
Fe3+	0.065	6.0e	[Ar] 3d5
Y3+	0.102b	8.0d	[Kr] 4p0 5s0
La3+	0.125c	10.3	[Xe] 4f0
(CH3)4N+	0.280	1.3	–
Cl−	0.181	2.0	[Ne] 3s2 3p6
F−	0.133	2.7	[He] 2s2 2p6
CO${}_3^{2-}$	0.178a	4.0
SO${}_4^{2-}$	0.230	3.1
PO${}_4^{3-}$	0.238	4.5

In the context of the hydration numbers given in Table 1, it is of interest to briefly mention the general effect that solutes such as ions can have on water structure. According to Marcus,88 a highly suitable strategy to quantify ion‐mediated effects on water structure is to determine the change of the average number of hydrogen bonds of the ion‐water structures. This parameter can be quantified by exploiting the fact that hydrogen bonds in heavy water (D₂O) are stronger than those in light water (H₂O). The experimental determination of D₂O‐ and H₂O‐specific parameters thus helps quantify the effect of solute molecules such as ions on water.88, 93

When considering the binding of (multivalent) ions to macromolecules, an obvious question concerns the influence of the co‐ions associated to the ions in question. While we note that a detailed discussion of this question is beyond the scope of this review, it is important to keep in mind that co‐ions can have dramatic effects on ion adsorption to macromolecules. This has been shown for colloidal solutions, e. g., by Alfridsson et al.94 and Karaman et al.95 and for protein phase behaviour.96 Importantly, in addition to unexpectedly specific co‐ion adsorption, Karaman et al. found that gas dissolved in the solutions played an important role in the context of emulsion stabilities, with implications even for highly complex phenomena such as enzymatic catalysis.95

It is furthermore important to mention that, in solution, different ion hydroxide and oxide complexes can be formed. This is especially well‐known in the case of iron97 and implies that the ions can no longer be considered as single‐atom ions. Iron is generally known to induce strong water protolysis, thereby acidifying aqueous iron solutions. In biological systems where pH regulation is essential for the functionality of biomolecules, the intricate interplay between the formation of such hydroxide complexes and pH effects62 needs to be considered on a case‐to‐case basis for different ions.

3. Proteins

The interior of living cells features a high ionic strength with typical intracellular concentrations of Na⁺ and K⁺ being 12 and 140 mM, respectively.9 These ions are of vital importance for, inter alia, maintaining a physiological osmotic pressure in living tissues and signal transduction in neurons. In addition to the ubiquitously present monovalent ions mentioned above, multivalent ions play equally crucial roles in ensuring the stability and functionality of different proteins. In this section, we focus on the interactions of multivalent cations with proteins as a specific example of biological soft matter. We describe the molecular mechanisms by which cations bind to proteins as well as the physiological effects these cation‐protein interactions have. Finally, we give an overview on the physico‐chemical effects of cation‐protein associations by describing phase diagrams of protein‐multivalent cation systems. Remarks on ion channels, a very specific subtype of proteins interacting with cations, will be provided in Section 3.2.2. Parts of this section are based on Refs. [31] and [39].

As an example, calcium (Ca²⁺) can be mentioned as a multivalent cation responsible for several phenomena related to the cytoskeleton98 and muscle cells,99 including the contraction of heart muscle cells.100 In addition, Ca²⁺ is involved in the formation of protein aggregates of relevance for the food industry.101, 102, 103 Crucially, the (dis)assembly of viruses features a pronounced dependence on Ca²⁺.104, 105, 106, 107, 108

Further multivalent ions of physiological relevance for proteins include Zn²⁺, which is a cofactor of several enzymes9, 109, as well as iron (Fe²⁺ and Fe³⁺) being an integral part of a variety of so‐called heme proteins.110 These and other multivalent ions playing important roles in the context of physiology are discussed in more detail in Sec. 3.1.

There are some interesting aspects of physiological relevance of elements not occuring as natural constituents of living cells. Artificially introducing such elementary metals or their ions or their complexes into the human body is common practice in the field of medical imaging. For example, tumours and abscesses can be imaged by intravenously administering gallium ⁶⁷Ga‐citrate.111 The gamma radiation energies emitted by ⁶⁷Ga and suitable for imaging are 93, 184, 296 and 388 keV.112 Animal studies showed ⁶⁷Ga‐citrate to bind exclusively to transferrin and to be transported inside the body by the latter.111 Another radioactive element, ¹⁶⁶Ho, has been shown to efficiently label chelate‐conjugated antibodies,113 which offers a valuable method to trace the uptake and distribution of antibody‐based therapeutics.

Barium (Ba) and gadolinium (Gd) are often used as contrast agents for X‐ray scans and for magnetic resonance imaging (MRI). The respective advantageous properties for the techniques in question are a high atomic number and therefore X‐ray contrast enhancement (Ba) as well as an increase of the local longitudinal and transverse water proton relaxation rates.114 Similarly, neodymium cations (Nd³⁺) have been used for an investigation of histidine in aqueous solution115 using nuclear magnetic resonance (NMR). Further information on lanthanides in structural biology can be found, e. g., in Refs. [116–118]. Metals and metal cations can also find applications in, e.g., cancer therapy. For example, attempts have been made to selectively target cancerous liver tissue by microspheres containing ⁹⁰Y.119, 120

Apart from these obviously beneficial, albeit not side effect‐ or risk‐free, interactions between proteins and ions, attention needs to be drawn to the potential toxicity of ions. Amongst other pathways, the latter can be mediated by ion‐protein interactions. Poisoning due to an ingestion of, or exposure to, pathologic concentrations or levels of mercury (Hg), lead (Pb) or cadmium (Cd) are a well‐known danger. Further metals with potentially toxic properties are copper (Cu) and aluminium (Al). Copper poisoning primarily affects the liver121 with possible damage being inflicted to the kidneys and the brain as well.122 Aluminium (Al) concentrations >0.1 mg/ml in drinking water have been associated with a potentially elevated risk of developing dementia and Alzheimer's disease.123, 124 In addition, Mn²⁺ has recently been proposed to be involved in neurotoxic effects in the context of parkinsonianism.125

3.1. Local picture of cation binding sites of proteins

Given the obvious importance of protein‐ion interactions under both physiological and pathological conditions in medical and biological contexts, much research effort has been invested into studying these interactions from the chemical and physical points of view. A necessary step to investigate proteins the functionality of which depends on ions was to determine and characterise their ion binding sites.

On the protein surface, numerous side chains with different physico‐chemical properties are exposed to the solvent. As a first consequence, in aqueous solutions charge regulation of the protein surface occurs. Functional surface groups – basic (Lys, Arg) and acidic (Glu, Asp, His) amino acid side chains and the carboxy and amino termini of the protein – are (de)protonated depending on the pH and the charges in the environment,126, 127 thus coupling pH to protein surface charge.

As a second and indeed key effect in the context of this review, also ions other than the hydronium ion, in particular multivalent ones, interact with functional groups. Numerous studies report equilibrium constants for the binding of multivalent counterions to proteins specialised in metal storage and transport.128, 129, 130, 131, 132

Moreover, models for ion binding have been developed in order to understand the interactions of proteins with ions and ligands.133, 134, 135, 136 On the molecular level, amino acids with carboxylate, hydroxyl, thiol, thioether, and imidazole side chain groups bind transition metal ions coordinatively.19, 137, 138, 139, 140, 141, 142, 143 In fact, the binding of the potentially toxic heavy metal ions Cd²⁺ and Cr³⁺ to the cysteine‐rich protein Cry has been suggested to be an environmentally friendly method of eliminating said cations from water.144

The binding of ions is enhanced at hydrophilic sites surrounded by hydrophobic surface areas.145 The overall ubiquity of these surface groups suggests that the association of salt counterions with side chains of the opposite charge at the protein surface is at the heart of the model for the interaction of ions and proteins.64 This notion has been explicitly supported for a study on the oligopeptide tetra‐aspartate. Kubíčková et al.146 observed a charge inversion both experimentally and by molecular dynamics simulations for tetra‐aspartate with trivalent cations. Mono‐ and divalent ions also decreased the overall charge, but did not overcome the initial negative protein charge. As the basic mechanism, the ion binding to carboxylic acids is evidenced by radial distribution functions that also show the different behaviour of multi‐ and monovalent cations.146

As will be discussed in the following, this type of multidentate coordination of multivalent cations by negatively charged or polar residues is observed in many proteins. Nevertheless, other cation‐binding mechanisms shall also be briefly mentioned here. As an example, the side chains of aromatic amino acids such as tyrosine, phenylalanine or tryptophan feature π electron systems which have been shown to undergo so‐called cation‐π interactions.147, 148 According to Dougherty,148 all kinds of cations can be part of this type of interaction. Given the hydrophobic nature of π‐electron systems, however, they may be more likely to occur between π systems and hydrophobic cations such as quaternary ammonium ions or even the protonated guanidino group of the amino acid arginine.148

We shall briefly note here that binding of (monovalent) anions to nonpolar surface patches has been observed in molecular dynamics simulations.149 This phenomenon has been traced back to solvent‐assisted attraction of the ion to the protein surface.

Having outlined general characteristics of cation binding sites on the protein surface, we will discuss specific examples of protein‐cation systems in the following.

Calcium. In the human body, calcium is involved in a variety of processes in living cells, including cytoskeleton mobility, muscle contraction, bone formation, blood coagulation and hormone‐mediated metabolism regulation9, 10, 109 (for a detailed description, see also the review by Kretsinger99). In fact, Ca²⁺ is often referred to as a so‐called “second messenger” due to its ubiquity in physiological processes.10, 99 Thus, it is of particular physiological relevance to consider different Ca²⁺‐binding proteins. Amongst these, a specific helix‐loop‐helix motif referred to as the “EF‐hand” is a commonly shared feature.150, 151, 152, 153 Examples of proteins containing an EF‐hand motif are calbindin, myosin, troponin, calmodulin and parvalbumin (see Ref. [150] and refs. therein). The Ca²⁺ ion is usually coordinated by aspartic acid, asparagine or serine150 (see visualisation in Figure 4). Experimental studies have shown that the affinity of the EF‐hand motif for Mg²⁺ can be increased while decreasing that for Ca²⁺ by residue‐specific mutations,154 implying that subtle effects are important in determining the cation specificity of EF‐hands.

Figure 4.

Binding sites of multivalent ions in proteins (see text for details). The image illustrates the pivotal roles of negatively charged amino acid residues in coordinating the respective ions. As opposed to the Y³⁺ cations bound by BLG (b) and the Ca²⁺ ions bound by calbindin (c), binding of Fe³⁺ requires carbonate ions in addition to the protein residues coordinating the ion (seen on the right side of the orange sphere representing Fe³⁺ in (a)). The structures were visualised using UCSF Chimera164 based on PDB IDs 1SUV, 3PH5 and 6FIE.

In addition to the EF‐hand protein family, Ca²⁺ interacts with actin (see, e. g., the review by Janmey155) and gelsolin156, 157 or both actin and gelsolin simultaneously.157 These Ca²⁺‐protein interactions are involved in the regulation of cytoskeletal motility. According to Robinson et al.,157 both actin and gelsolin bind Ca²⁺ ions via aspartate and glutamate residues. Osteopontin, a protein abundantly present in the bone and teeth matrices, binds calcium in an inorganic form (hydroxyapatite) through phosphorylated serine and threonine residues as well as polyaspartate sequences.158 The physiological role of osteopontin is briefly discussed in Sec. 3.2.1. Interestingly, in osteocalcin (another important protein in bone tissue), Ca²⁺ cations are bound by γ‐carboxyglutamic acid residues,159 a rarely occuring version of glutamic acid.9 The tripeptide peptide Tyr‐Asp‐Thr with a very high Ca²⁺ chelating propensity has been isolated from whey protein,160 evidencing the cooperative effect of several amino acids for binding of Ca²⁺.

For more detailed and elaborate discussions on the binding of calcium ions to proteins, we refer the reader to Ref. [99]. Protein self‐assembly in the presence of Ca²⁺ is discussed in Sec. 3.2.1.

Iron. In mammal physiology, iron is known particularly well for its role in protein‐mediated oxygen homeostasis and is often found in a coordination complex with porphyrin structures. This iron‐porphyrin complex is referred to as a “heme group” and is present as a prosthetic group in a variety of proteins such as myoglobin, hemoglobin, plant leghemoglobin and cytochromes (proteins involved in electron transport processes of the cellular respiratory chain)109 as well as catalases, peroxidases, and mono‐ and dioxygenases110 (enzymes catalysing redox reactions). For an overview of iron binding, the reader is also referred to Ref. [161].

The structure of myoglobin has been extensively studied, providing detailed insights into the local environment of the Fe²⁺ cation bound to the heme. The latter is located in a pocket‐like structure of myoglobin, thus being protected from the surrounding solvent. Importantly, this steric protection prevents the Fe²⁺ ions from being oxidised to Fe³⁺, which is not able to bind oxygen.9

Iron metabolism in mammals furthermore involves the non‐heme proteins ferritin,10 lactoferrin10, 11 and transferrin with its corresponding receptor protein.162 As an example, one of the two iron‐binding sites of transferrin consists of two tyrosines, a histidine and an aspartate residue and involves a carbonate anion162 (Figure 4). Several so‐called iron‐sulfur proteins can furthermore bind Fe ions via cysteine side chains.9 Moreover, while the ionic form of iron is clearly an important factor in the physiological context, it can also interact with proteins in other forms. Prominent examples are other types of iron‐sulfur proteins, namely those hosting inorganic iron‐sulfur (FeS) clusters. Those are, for example, found in the protein ferredoxin of the bacterium Anabaena. A particularly curious use of inorganic iron structures are so‐called magnetosomes (inorganic, iron‐containing crystals such as Fe₃O₄ crystals) providing bacteria with the ability to orient themselves along magnetic fields (for an overview on this interesting phenomenon, see Ref. [163] and refs. therein).

The iron‐ and calcium‐binding sites mentioned above share a common feature – the multivalent cations bound to the respective proteins are complexed by charged and/or polar amino acid residues such as aspartate and tyrosine. Some examples of such binding sites are shown in Figure 4.

Magnesium. Mg²⁺ cations are known to play an important role in enzymatic reactions catalysing the cleavage of phosphate bonds. This can be especially relevant in sugar metabolism and nucleic acid (RNA and DNA) degradation. The latter is often catalysed by so‐called nucleases such as ribonuclease H. Generally, magnesium ions are coordinated octahedrally.165 In the active centre of the ribonuclease RNase H, Mg²⁺ ions are also surrounded by hydration shells (see Ref. [166] and refs. therein as well as Ref. [167]). As opposed to other alkaline metals, Mg²⁺ appears to have a particularly strong affinity to water molecules in its inner coordination shell,166 making water an important constituent of catalytically active Mg²⁺‐enzyme complexes. In addition to these in vivo roles of Mg²⁺, a very interesting magnesium‐mediated transition from binary to unitary protein structures has been demonstrated by Künzle et al.168

Zinc. A crucial physiological role of zinc is its stabilisation of insulin microcrystals in the pancreas,169, 170 with obvious implications for diabetes. Zinc is furthermore known to be involved as a cofactor in several enzymes. Examples include carboanhydrase,109 several proteases10 and alcohol dehydrogenase.9 In numerous proteins, Zn²⁺ ions are coordinated by a so‐called zinc finger motif consisting of cysteine and histidine residues (“Cys₂His₂”).171

Copper. In physiology, the most prominent role of copper is the electron transport in the respiratory chain. Here, it is bound to sulfhydryl groups of the protein cytochrome oxidase.9 It is important to note that the oxidation state of the copper ions involved in the reduction of oxygen to water changes throughout the catalysis.172 Interestingly, the enzyme copper‐zinc superoxide dismutase – which catalyses the reaction of superoxide radicals to hydrogen peroxide and molecular oxygen – uses both copper and zinc for said catalysis.173 Structural studies reveal that the ions are coordinated by histidine and aspartate (Zn) and histidine and arginine residues (Cu).173

Molybdenum and vanadium. In plant metabolism, molybdenum (Mo), together with iron, plays an important role as a cofactor in the enzyme dinitrogenase. In addition, Mo is part of the active centre of the enzyme nitrogenase from Azotobacter vinelandii.174 Interestingly, some dinitrogenase versions contain vanadium (V) instead of Mo.9 Furthermore, vanadium is of great importance for the biosynthesis of halogenated products by marine organisms.175

Cobalt. A Co³⁺ ion is complexed by the corrin ring of coenzyme B12, a slightly modified form of vitamin B12. The latter is, inter alia, a cofactor of the enzyme methyl malonyl‐CoA mutase which catalyses a step of a complex metabolic process referred to as β‐oxidation of fatty acids. Importantly, the cobalt ion allows the reaction to proceed via an extremely unusual intermediate step involving a hydrogen radical9 by undergoing a change in oxidation state from +2 to +3.

Lanthanides. Complexes of lanthanide ions and some organic ligands possess several favourable fluorescence properties such as long fluorescence lifetimes, strong Stokes shifts and distinct emission peaks;176 depending on the choice of the ligand, the fluorescence can be enhanced.177 Thus, lanthanides proved valuable structural probes to tackle questions related to cation binding sites of proteins. As an example, Harris and co‐workers178, 179, 180, 181, 182 examined the binding of various non‐ferrous cations to human transferrin and lactoferrin, notably including the lanthanides Lu³⁺, Er³⁺, Ho³⁺, Tb³⁺, Gd³⁺, Sm³⁺, Nd³⁺ and Pr³⁺. The authors report two lanthanide binding sites involving tyrosine residues183 and a decrease in the number of cations bound with increasing cation radius.180 Here, we remind the reader of the phenomenon of lanthanide contraction,184 another important property of lanthanides in addition to those mentioned above. Lanthanide contraction describes the continuous decrease of the ionic radii from lanthanum (La) to hafnium (Hf) due to the successive increase in the occupation of the 4f orbitals and the simultaneous increase of the nuclear charge.184

Apart from purely structural studies, the influence of lanthanides on biological protein activities has been investigated as well. Smolka et al.185 analysed the consequences of replacing calcium by trivalent lanthanides and Y³⁺ in the calcium‐dependent enzyme α‐amylase. This study suggests an inverse linear proportionality of the enzyme efficiency on cation radius, underlining cation‐specific effects. No strong structural changes of the protein were observed. A similar study replacing Ca²⁺ by lanthanides in trypsinogen and evaluating the respective efficiencies of the cations in catalysing the conversion to trypsin was conducted by Gomez et al.86 The dependence of the conversion rate efficiency is non‐linear, but also inversely proportional to the cation radius. Interestingly, Nd³⁺ and Pr³⁺ were shown to be even better trypsinogen‐trypsin conversion activators than Ca²⁺, which was ascribed to their higher charge.86

The study conducted by Gomez et al. highlights an important property of lanthanides. With their radii being similar to that of Ca²⁺, they can replace Ca²⁺ not only in vitro, but also in vivo, being of toxicological relevance.128, 186

Lanthanides as well as yttrium are usually found in the form of trivalent cations that strongly interact with binding sites formed by carboxylic residues. This coordinative binding of Y³⁺ is apparent from protein crystals, where the cations bridge different protein molecules.19 Importantly, the driving force for this binding is not enthalpy alone, but hydration entropy. In particular, a physicochemical characterisation of the binding reveals a lower critical solution temperature,187 and the water coordination around Y³⁺ is reduced upon binding to the protein,188 both of which evidence the release of hydration water molecules with substantial related entropy gains. Finally, we refer the interested reader to a recent overview on the roles of lanthanides in biochemistry by Daumann.189

Other cations. There are, of course, many other cations that could be mentioned here, but a full list would be beyond the scope of this review. We therefore refer the reader to the detailed works by Lipfert,190 Permyakov,128 Frausto da Silva and Williams191 and Evans.192 The above should suffice to indicate the main phenomena and concepts.

3.2. Physico‐chemical and global effects of protein‐cation interactions

In this section, we will discuss the global, physico‐chemical behaviour of several systems composed of proteins and multivalent cations. We will explain the phase behaviour of several selected systems and discuss their respective origins. A particular focus will be on the role of the multivalent cations and their interactions with the proteins in question. We remark that we intentionally limit ourselves to a few examples of systems, and related implications, as a complete review of protein‐cation interactions would be too voluminous for this review. In this context, we aim for a balanced account of basic references and new studies evidencing ongoing work.

3.2.1. Calcium‐induced effects on protein assembly

Calcium represents one of the most common multivalent cations, which is why we dedicate an extra paragraph to it. It has effects on protein systems exploited both in nature (e. g. in blood coagulation, for viral assembly, and bone formation), as well as in nano‐ and biotechnological contexts such as food engineering. In the following paragraphs, we will outline a few examples to show the various functions and structures that are controlled by calcium ions.

Milk proteins. As one well‐studied example in food science, milk proteins represent calcium‐controlled molecules which significantly contribute to the calcium intake into the human body. The presence of calcium strongly affects the aggregation of whey protein,193 and the resulting gel structure.194, 195 As a particular example, calcium has a dramatic effect on the speed of the gelation of whey aggregates, and mildly strengthens the resulting gels.196, 197 These structural variations have been shown e. g., to regulate the release of drugs from whey hydrogels.198

The second protein source in milk, casein, is also strongly affected by Ca²⁺ and calcium‐phosphate clusters. The calcium effects range from changing the micellar structure of casein,199, 200, 201 over varied aggregates after thermal denaturation,202 to macroscopic effects such as the texture of milk‐derived products, e. g. yoghurt.203, 204 For a detailed overview of the functionality, association and aggregation of caseins, we refer to Ref. [205].

Fibrin clot formation. Calcium is an essential cofactor in the initial step of blood coagulation, i. e., fibrin clot formation. Fibrin clots are the organism's immediate response to injury in order to prevent excessive blood loss, and fibrin assembly thus has fundamental as well as applied relevance e. g. for drug carriers and fibrin sealants. Ca²⁺ controls the cross‐linking of fibrin protofibrils into fibers and hydrogel structures.206 In particular, Ca²⁺ tunes the fibrin cross‐linking rate,207 resulting in values ranging from seconds to tens of minutes depending on the overall conditions of the fibrin solutions.208 In this context, Ca²⁺ also affects the resulting gel structure, thereby generally enhancing the elasticity209 and non‐monotonically adapting the gel permeability.210 Consequently, calcium is a very common additive in fibrin sealants, as well as in applications for drug delivery and bone tissue engineering.211, 212, 213

Inhibition of calcium crystal growth by osteopontin. Osteopontin is known to be an important constituent of body fluids with a high calcium content, such as milk and urine. It is therefore assumed that it is involved in the prevention of calcium salt precipitation (reviewed in Ref. [158]). Indeed, amongst its other roles (reviewed in Ref. [214]), e. g., in bone tissue homeostasis, osteopontin has been shown to inhibit the nucleation and growth of calcium oxalate.215, 216, 217 A study combining molecular modelling and atomic force microscopy (AFM)218 revealed that osteopontin strongly changed the morphology and growth of calcium oxalate crystals. Interestingly, the strength of these effects were pronounced to different degrees for different crystal faces of calcium oxalate crystals, indicating a strong interaction specificity between osteopontin and oxalate.218

Virus assembly. A crucial role of Ca²⁺ has been found for a large range of viruses. Early findings reported already that most plant viruses rely on correct Ca²⁺ binding for controlled structural assembly.219 Similar indications were found for the bacteriophage PM2 and papillomaviruses, where Ca²⁺ was found to be essential for viral reassembly in vitro and during infection.106, 220 In the case of PM2, Ca²⁺ was hypothesised to stabilise the lipid bilayer of the virus before the protein outer layer is deposited on top of the lipid structure.106 For bovine papillomavirus, the role of Ca²⁺ appeared to be to stabilise the protein capsid.220 A recent study reports the requirement of Ca²⁺ for Rubella virus infections, as well as viral fusion and liposome insertion,221 evidencing that Ca²⁺ enables virus function via structural adaption of the virus.

For simian virus 40 (SV40), Ca²⁺, along with pH effects,222 was found to be important for the accuracy of the assembled structure, and appropriate affinities of the viral protein capsid to Ca²⁺ regulate assembly and disassembly of the virus.104 The presence of Ca²⁺ also proved relevant for the cell and nuclear entry during infection with simian virus 40, and Ca²⁺ was proposed to not only change the assembly state, but also the flexibility of the capsid.105 Related to this, SAXS investigations showed that chelating Ca²⁺ caused a uniform swelling of SV40,223 stressing the role of Ca²⁺ in regulating the virus structure.

A comparable picture is found for the hepatitis B virus (HBV), where calcium signalling plays an important role for DNA replication.224 Again, Ca²⁺ was found to be important for the HBV core assembly.108 Importantly, the knowledge on the Ca²⁺ effects for virus assembly even translates into nanotechnology. As an example besides the more general establishment of purification schemes,219 an encapsulation system based on the hepatitis B virus allows to adapt the affinity to the cargo molecule via the Ca²⁺ concentration.225

Lipoprotein metabolism. Calcium has been found to be effective in regulating the low‐density lipoprotein receptor (LDLR), which controls the body's cholesterol homeostasis. Indeed, a relation between calcium intake and the lipoprotein metabolism has been suggested.226 On a molecular level, a recent study suggests that LDLR senses Ca²⁺ and unfolds partially,227 thereby providing an alternative route for triggering of LDL release apart from the acidic‐induced release.228 Similar strong binding affinity of Ca²⁺ is found in a LDLR related protein abundant in the liver.229 Furthermore, calcium also acts on the lipoprotein metabolism by assembling the lipoprotein lipase into its functional dimeric structure.230

3.2.2. Ion Channels

While ion channels are a specific type of proteins, they represent a slightly different topic in the context of this review, one particular characteristic being the fact that they are transmembrane proteins. We shall therefore limit ourselves to a few comments here.

The main functions of ion channels include the maintenance of physiological ionic strengths inside cells and the transduction of electrochemical signals along neurons. Prominent examples of ion channels include the Na⁺ K⁺ ATPase antiporter and the SERCA pumps (sarco/endoplasmic reticulum Ca²⁺ ATPase).231, 232 The function of the latter is to transport Ca²⁺ ions across the membrane of the sarco/endoplasmic reticulum. Thereby, SERCA pumps maintain an intracellular Ca²⁺ storage and also terminate Ca²⁺‐mediated signalling. Just as is the case for the EF‐hand motif in proteins, SERCA proteins coordinate the Ca²⁺ ions via glutamate residues. In addition, glutamine and asparagine residues are involved (reviewed in Ref. [233]).

The functionality of ion channels relies on their selective permittivity with respect to different ion types. Indeed, the uptake of the “wrong” type of ions such as La³⁺ instead of Ca²⁺ can have drastic toxicological consequences.128, 186 Similar effects have been demonstrated for Gd³⁺.234

On the other hand, ion selectivity can also be used to prevent cell death caused by toxic ion channels. This has been shown by Menestrina235 in a study of the α‐toxin of S. aureus. This toxin binds to the cell membrane, inserts itself into the membrane and forms ion channels, thus causing K⁺ leakage, which results in an osmotic shock and, ultimately, cell death.236 Menestrina demonstrated that the channels formed by S. aureus α‐toxin, which are open in a KCl solution, can be closed ‐ and their function thus inhibited ‐ by multivalent cations. The inhibition efficiency was shown to be

$${\displaystyle {\mathrm{Zn}}^{2+}>{\mathrm{Tb}}^{3+}>{\mathrm{Ca}}^{2+}>{\mathrm{Mg}}^{2+}>{\mathrm{Ba}}^{2+}.}$$ (4)

Menestrina provides a mathematical model to quantify the multivalent cation‐mediated inhibition of the channel in which it is assumed that one multivalent cation binds to the channel in its open and one in its closed state. In addition, Menestrina suggests that a carboxyl group is involved in the binding of the cations,235 which is consistent with the mechanisms described in Sec. 3.1. Similarly, Döbereiner et al.237 observed an inhibition of the conductance of ion channels formed by α‐hemolysin (HlyA) from E. coli 238 upon addition of multivalent cations. Here, the divalent cations Sr²⁺ and Ba²⁺ were able to induce HlyA‐mediated erythrocyte hemolysis, albeit less efficiently than Ca²⁺. Mg²⁺, Cu²⁺, Mn²⁺, Zn²⁺ and Pb²⁺ did not lead to hemolysis; neither did the trivalent cations Fe³⁺ and La³⁺. In addition, Mg²⁺, Ca²⁺, Sr²⁺ and Ba²⁺ inhibited HlyA conductance; Fe³⁺ and La³⁺ did so with greater efficiency. Döbereiner et al.237 suggest that the cation radius plays an important role in cation recognition by HlyA.237

In order to better understand the selectivity of ion channels, Kumpf and Dougherty239 performed computational studies on the affinity of Li⁺, Na⁺, K⁺ and Rb⁺ to benzene. The latter was chosen as a model of the hydrophobic core of a specific type of K⁺ channel. Their results demonstrate a preference of benzene for K⁺ and indicate that so‐called cation‐π interactions – that is, interactions of cations with delocalised π electron ring systems, of which benzene is representative – appear to occur in hydrophobic regions of ion channels. In particular, these interactions could give a hint towards the ion selectivity of ion channels. More information on this intriguing subject is found in Ref. [240].

3.2.3. Lanthanide‐induced phase behaviour in protein solutions

Apart from their roles as structural probes and in medical imaging, lanthanide ions can be used to tune the phase behaviour of protein solutions, including the rational induction of protein crystal growth.

The local interactions of multivalent ions with proteins have profound consequences for the global behaviour, qualitatively different from, say, Na⁺. Here, we discuss the phase behaviour and related collective phenomena of protein systems. Special attention will be paid to those types of phase behaviour induced by multivalent ions in negatively charged proteins.

Generally, a rich phase behaviour has been found in protein solutions, including liquid−liquid phase separation (LLPS), the formation of protein clusters, and crystallisation as well as other aggregates such as fibers. The nucleation kinetics differ considerably for different phases, which allows for metastable phases such as LLPS or clusters as precursor structures during crystallisation, as well as arrested phases such as gels to occur.241, 242 In this section, we provide an overview of the different phenomena that also play an important role in the present context.

Protein Surface Charge and Ion‐Induced Charge Inversion. Charges on the protein surface are an important feature ensuring stability and functionality of proteins.243, 244, 245 Charge patterns lead to anisotropic interaction patches that affect the phase behaviour of protein solutions246, 247, 248, 249 as well as pathways for aggregation and crystallisation.250, 251, 252

Protein–protein interactions are linked to charge regulation, which is, in turn, a complex process depending on system geometry and ion specific effects like binding or condensation. A comprehensive understanding of charge regulation at the protein surface is also needed in order to account for ion‐specific effects such as binding and condensation as well as for the system geometry, e. g. the proximity of a wall.245, 253

A special case is charge inversion, i. e., overcompensation, of surfaces in the presence of counterions. A comprehensive understanding of charge inversion has to account for both local ion binding and non‐local contributions such as ion–ion correlations and hydrophobic effects.254, 255 Charge inversion has been observed for a broad range of systems such as silica spheres,54 insoluble oxides254 and also biological systems such as DNA.56 The latter is discussed in more detail in Sec. 4.

In particular, charge inversion has been observed in solutions of globular, negatively charged proteins with multivalent cations.58, 256, 257 The lower charge density of the protein surface speak against ion–ion correlations being the main cause of charge inversion. Instead, Zhang et al.19 support the notion of a charge inversion due to ion binding to acidic residues on the protein surface, based on information from crystal structures. Note that not only cations, but also negatively charged molecular complexes have been shown to interact specifically with net negatively charged proteins, as demonstrated for human and bovine serum albumin.258 Remarkably, a protein crystallisation strategy similar to the one demonstrated by Zhang et al.19 has been pursued using negative multivalent ion complexes.24, 25, 26, 259

Reentrant Condensation. The inversion of the surface charge is related to a specific phase behaviour called reentrant condensation known from polyelectrolytes (see, e. g., Ref.260), which has been observed in aqueous solutions of negatively charged proteins with trivalent58, 256, 261 and tetravalent cations,262 as illustrated schematically in Figure 5. At a given protein concentration c_p and a low salt concentration c_s, the system is a homogeneous liquid (Regime I), charge‐stabilised by the initially net protein charge. A continuous increase in c_s, while keeping c_p constant, decreases the negative surface charge of the protein and eventually condenses the protein molecules in solution into cluster‐like structures. This condensed state is referred to as Regime II, the entrance into which is marked by a critical salt concentration, c*. A further increase of salt concentration leads to overcharging of the protein, and the clusters redissolve upon surpassing a second critical salt concentration, c** (Regime III), stabilised by the reversed charge of the protein‐cation complex. Computer simulations confirmed the reentrant behavior in the protein‐protein potential of mean force,263 and support a picture of very directional interaction due to binding of multivalent ions.264, 265

Although induced by salts, this phenomenon is clearly beyond the usual salting‐in and salting‐out behaviour of proteins and needs an individual explanation linked to the ion binding to proteins. We remark that a macroscopically similar phenomenon is observed for DNA, but arises from a different microscopic driving force (see Sec. 4.3).

Liquid−Liquid Phase Separation (LLPS). Under certain conditions within the condensed regime II of the reentrant condensation (see paragraph above and Figure 5), a liquid‐liquid phase separation (LLPS) into a protein‐rich and a protein‐poor liquid phase is observed.257, 266

Figure 5.

Phase diagram showing regimes I, II and III, reentrant condensation and LLPS. See text for details.

In general, LLPS was found in several protein systems, first in mammalian eye lenses267, 268 with implications for cataract269, 270 and exemplifying critical phenomena in a biological model system.271, 272, 273, 274, 275 A metastable LLPS in hemoglobin solutions has been found to be the primary event of sickle cell anemia.276

In addition to the above examples, LLPS is a process which is often invoked to explain how living cells regulate signal transduction pathways and organise their interior. This organisation often occurs via the formation of membraneless organelles, e. g., so‐called P granules, which feature liquid‐like properties.277 Such organelles can consist of different types of proteins and RNA molecules. The proteins driving phase separation in cells are in many cases so‐called intrinsically disordered proteins (IDPs).278, 279, 280, 281 The propensity of IDPs to undergo LLPS is strongly influenced by their molecular interactions, which are, in turn, determined by properties such as net charge and hydrophobicity. It is known that IDPs are often enriched in aromatic, polar, and positively and negatively charged amino acids.282, 283, 284, 285, 286 This implies that salt/ion effects are an important factor capable of influencing the behaviour of IDPs.280 Indeed, theoretical studies of block polyampholytes containing positive and negative charges as IDP models287 have shown that divalent ions decrease the width of the coexistence region of high‐ and low‐polymer density phases of the symmetric block polyampholytes, but only have a weak influence on the coexisting concentrations. Trivalent ions have a stronger effect, significantly shifting the dense branch of the binodal to lower concentrations.287 This study thus demonstrates how ions can influence the phase behaviour of IDPs.

While condensed structures formed by IDPs are often functional and physiologically relevant, they can also play a role in several pathologies such as Alzheimer's and Huntington's diseases.278, 288 This can be due to the formation of aggregates which perturb the physiological processes of cells. Interestingly, this aggregation process can be enhanced by metal ions, e. g. if these allow IDPs to populate certain conformations prone to aggregation (see Ref. [289] for a detailed overview). As an example, the fibrillation kinetics of α‐synuclein, an IDP involved in the pathogenesis of Parkinson's disease, has been shown to be strongly enhanced in the presence of Cu²⁺, Fe³⁺, Co³⁺ and Mn²⁺.290

Experimental results confirmed the metastability of the LLPS with respect to the crystal phase291 as theoretically expected for an attraction that is short‐ranged compared to the protein size.292, 293, 294 Interestingly, such a short‐ranged attraction can be introduced into protein solutions by multivalent cations that induce cation‐activated attractive patches.265 Multivalent cations such as Y³⁺ are able to form cation bridges between negatively charged areas on protein molecules,19 thus introducing an effective short‐ranged attraction between the proteins. Interestingly, under appropriate experimental conditions, LLPS occurs257, 266 with a lower critical solution temperature (LCST‐LLPS), i. e., representing an entropy‐driven transition,187 most likely related to the release of hydration water around the multivalent cation. Given that entropic considerations usually favour phase separation for globular, folded proteins upon a temperature decrease,295 this behaviour is rather unusual and most likely linked to release of hydration water.187 It also provides clues regarding the water‐ion interactions and entropic contributions (cf. Ref. [188])

The width of the reentrant regimes, the lower critical transition temperature as well as the overall strength of the interaction can be strongly influenced by the type of multivalent cation.59 Pronounced anion as well as solvent isotope effects on the phase behaviour of protein‐multivalent salt systems have also been shown.96, 296

Generally, metastable LLPS in protein solutions is of specific interest due to its connection to protein crystallisation. In this context, control of the phase behaviour is essential to optimise nucleation conditions for high‐quality protein crystals (see below).

Additives in protein solutions such as PEG, glycerol, monovalent salts or a second protein species have been found to shift the coexistence curve of protein solutions in temperature.297, 298, 299, 300, 301, 302, 303, 304, 305 Theoretical studies have reproduced these shifts based on colloidal models and nonspecific interactions between proteins and additives.246, 247, 248, 305, 306, 307, 308 More information on how multivalent cations can be used to induce protein crystallisation can be found in Section 3.2.3.5.

Cluster Formation. The formation of equilibrium clusters in solutions of charged particles has been predicted by a simple argument:309, 310, 311 if particles exhibit a short‐ranged attraction and a long‐ranged (Coulomb) repulsion, monomers attach due to the attraction until the repulsion of the entire cluster grows strong enough to destabilise further attachment. Indeed, transient clusters, potentially of this type, were observed e. g. for solutions of lysozyme,312, 313, 314, 315 β‐lactoglobulin,316, 317 hemoglobin,318 and lumazine synthase.319 Reversible cluster formation in protein solutions is not only of fundamental, but also of practical interest, since it would be promising for drug delivery at high antibody volume fractions and moderate viscosity.320

An ion‐induced short‐range attraction via bridges of multivalent cation is also expected to stabilise protein clusters.265 Soraruf et al.321 studied the formation of multivalent cation‐induced cluster formation in bovine serum albumin, as evidenced by an increased structural correlation length and significantly slowed down diffusion. In addition, the slowing down of the diffusion with increasing salt concentration was found to depend mainly of the ratio of cations per protein, consistent with the ion‐bridge picture.322

The presence of flexible clusters might affect pathways of protein crystallisation, as will be discussed in the following.

Protein Crystallisation and Nucleation Pathways. The lack of a systematic and general procedure to obtain high‐quality protein crystals has inspired numerous studies on the connection of phase behaviour and crystal nucleation as well as the control of optimum conditions for protein crystallisation.

George and Wilson323 suggested the so‐called crystallisation slot for the protein attraction. While for too weak attractive interaction the nucleation is very slow, too strong attraction causes multiple nucleation events and irregular and arrested assembly of proteins. Vliegenthart and Lekkerkerker324 explain optimum crystallisation conditions by two effects: nucleation rates can be enhanced by the proximity to the critical point of a metastable LLPS, or the presence of small dense droplets325, 326 or clusters,327 both of which have indeed been found in experiments.298, 328

Both conditions proposed represent multi‐step nucleation pathways in the sense that the two order parameters density and structure, which are coupled in classical nucleation theory, are separated and develop independently. In a first step, the solution forms a dense precursor which then reorders to a structured crystal nucleus.329 The exact nature of the precursor in protein solutions remains unclear and is, most likely, not a general feature.330

Notably, cation‐mediated bridging of negatively charged protein molecules can promote the nucleation and growth of protein crystals,19, 331, 332 thus allowing for a controlled growth of crystals which is considered a major obstacle in protein crystallography. Intriguingly, the location of the samples in the protein‐salt phase diagram, i. e., their composition, determines their crystallisation pathways. Using β‐lactoglobulin (BLG) and YCl₃ as an example, classical nucleation dominates at low salt concentrations,21 while a two‐step mechanism can be observed at high salt concentrations.22 For an overview of non‐classical protein crystallisation, we refer to Ref. [332]. The ion‐mediated approach has also been successfully applied to positively charged proteins using polyoxometallates (POMs), a specific type of anions.24, 25, 26, 333

Arrested Phases: Gels and Amorphous Aggregates. Besides the equilibrium properties, also kinetic pathways matter for the observed phase behaviour. In systems with short‐ranged attractions, arrested phases such as gels and glasses311, 334, 335 are observed in colloidal systems. For the case of proteins, the gel formation has been related to an arrested metastable LLPS242 and the formation of clusters.336, 337, 338 Poon339 argues that the arrested LLPS might be the reason that crystals cannot grow at high attraction strength.

In the case of cation‐induced LLPS, arrested states are also possible. The LCST‐LLPS of BSA‐YCl₃ systems has been shown to occur via spinodal decomposition and the kinetics of the latter have been studied using ultra small‐angle scattering.340 It was found that the characteristic length ξ of the respective systems grows as a function of time t as $\xi \sim t^{1/3}$ for T<45 °C. For T<45 °C and at t>30 s, the growth of ξ slows down. At even higher temperatures, arrest is observed as indicated by constant values of ξ until protein denaturing interferes with further investigations above 55 °C. Interestingly, the kinetics of LCST‐LLPS samples as well as the onset of arrest can be strongly influenced by the choice of multivalent cations used. Matsarskaia et al.341 studied arrested states in systems consisting of BSA and varying mixtures of HoCl₃ and LaCl₃, finding that higher HoCl₃ concentrations progressively lower the temperature of the onset of arrest. These results indicate that Ho³⁺ induces stronger interprotein attractions than La³⁺.

4. Nucleic Acids (DNA and RNA)

DNA and RNA are the two most commonly known dominant types of nucleic acids and play pivotal roles in cell division, protein biosynthesis and the regulation of various cell signaling pathways.9 Similarly to the primary structures of proteins, they are also chain‐like, but do not undergo an equally elaborate folding process, although especially RNA is known to form different secondary and tertiary structures.10, 342 Nucleic acids also exhibit a charge pattern on their “surface“ and are therefore also classified as polyelectrolytes.343 However, as opposed to proteins, the net charge of nucleic acids is typically dominated by the negative charge of their phosphate backbones. Not surprisingly, charge‐driven or charge‐mediated interactions therefore play a key role in DNA/RNA research and several strategies have been employed to control and manipulate their interactions with charges. The vital involvement of DNA in cell proliferation implies its role as a target in chemotherapy via different, specific types of interactions, which will be briefly explained.

In the following, we will first discuss the local picture of the ion distribution around DNA and RNA, and then focus on the resulting more macroscopic ion effects in these systems.

4.1. Local picture: ion distribution and binding

Given the high charge density of DNA and RNA, the ion distribution around the nucleic acids is dominated by electrostatic interactions. The regularity of DNA furthermore provides an interesting experimental test case for validation of theoretical assumptions.

In particular, several experimental studies contributed to a detailed characterisation of ion clouds around DNA by exploiting the anomalous X‐ray scattering around the absorption edges of the counterions Rb⁺, Sr²⁺ and (Co(NH₃)₆)³⁺. Interestingly, both monovalent and divalent salts show quantitative agreement with predictions based on atomic scale non‐linear Poisson–Boltzmann theory (NLPB).42 ASAXS difference spectra characterising the DNA‐ion spatial correlations show ion distributions which are more extended for monovalent ions (decay length 4.2 Å) than divalent ions (2.9 Å), as expected theoretically.42 Furthermore, the number of ions per base pair was obtained, yielding 1.36 monovalent and 0.76 divalent cations per base pair, in good agreement with NLPB predictions for excess ions of 1.43 and 0.85, respectively.344

As another test of NLPB, Andresen et al.41 performed an experiment on mixed cation solutions where monovalent and divalent cation compete. As predicted, the shape of the ionic clouds remained invariant, and the ratio of surface‐close monovalent to divalent cations follows a simple Boltzmann relation,41 overall preferring divalent ions to be bound.

Even for trivalent cations, NLPB predictions were valid up to a critical threshold beyond which DNA condensation sets in.345 The authors speculated that, at these low ion concentrations, the ion‐ion correlations might not be strong enough to significantly vary the profiles. For competition between mono‐ and trivalent ions, NLPB had to be corrected for effects of finite ion size.345

For RNA, a study combining anomalous small‐angle X‐ray scattering (ASAXS) with MD simulations provides a consistent picture on the ion distribution around a more flexible RNA segment.346

Recent computer simulations for cations around DNA and RNA suggest that tighly bound divalent Mg²⁺ ions can occur in two different surface areas with different binding distances, as opposed to tight binding of monovalent ions in one broad population.347 Figure 6 shows a schematic representation of ion binding to a DNA molecule as well as condensation and charge inversion of DNA molecules induced by ion‐ion correlation effects.

Figure 6.

Schematic of DNA‐ion correlations at different ion concentrations. (a): Cation binding to minor and major grooves (inspired by Refs. [347] and [348]). (b) Condensation and charge inversion of DNA molecules induced by ion‐ion‐correlation. The circles on the DNA molecules indicate the net charge of the latter (red: net negative; turquoise: net neutral; green: net positive). Figure was rendered using UCSF chimera164 and Avogadro.349

4.2. Structural stabilisation by cations

DNA and RNA fulfil different functions in the cell,9 but their chemical compositions are rather similar. Indeed, their interactions with cations also feature similarities,350, 351 including the fact that both types of nucleic acids can be stabilised by delocalised as well as site‐specific cation interactions.352

In the case of RNA, it is interesting to note that this type of nucleic acid can, starting from an initially rather simple linear structure, proceed to form more complex structures. This phenomenon, also known as RNA folding, is particularly important in the case of transfer RNA (tRNA) which is involved in cellular protein synthesis.10 Since the formation of such structures involves a compaction of the negatively charged RNA phosphate backbone, inorganic cations are required to screen these charges and facilitate the compaction process.353, 354 Both mono‐ and divalent cations can fulfil this role355, 356 and the melting temperature of tertiary RNA structures has been shown to have a non‐monotonous dependence on dehydrated monovalent cation radii352 with the effectiveness of stabilisation indicated as

$${\displaystyle {\mathrm{Li}}^{+}\approx {\mathrm{Na}}^{+}<{\mathrm{K}}^{+}\ll {\mathrm{NH}}_4^{+}\gg {\mathrm{Rb}}^{+}>{\mathrm{Cs}}^{+}}$$

In addition to inorganic ones, Heerschap et al.357 tested organic cations and found the following order of stabilisation for a certain type of tRNA:

$${\displaystyle \mathrm{spermine}>\mathrm{spermidine}>\mathrm{putrescine}>{\mathrm{Na}}^{+}\approx {\mathrm{NH}}_4^{+}}$$

Divalent cations are more efficient in stabilising RNA structures than monovalent ones,356 as exemplified by the prominent role of Mg²⁺ in tRNA folding.358 NLPB theory‐based calculations show that, in an RNA solution with a constant monovalent ionic strength mediated by NaCl, the addition of MgCl₂ stabilises the folded RNA conformation.359 This is traced back to the entropically favourable release of roughly 2 Na⁺ ions per Mg²⁺ binding event.359 In addition, due to their higher charge density, half as many divalent cations are needed to neutralise RNA phosphate backbone charges upon folding and subsequent compaction. Hence, the entropically unfavourable decrease in conformational space of the cations is less thermodynamically relevant than in the case of monovalent cations.356

Importantly, for Mg²⁺ ions bound to RNA, the cation‐mediated effects go beyond pure electrostatics, and include polarisation and charge transfer.353 Along these lines, the intricate interplay between the hydration shell of the cation and its interaction with the phosphate residues of the RNA need to be considered.353

How strongly cations influence RNA structure depends on the type of their interaction with RNA. The latter can be classified on a scale from “chelated” to “free in bulk”353 and those classified as “chelated” (i. e., coordinated and fully dehydrated) are the ones of greatest structural significance. Moreover, the more RNA ligands a cation coordinates in its first shell, the more it contributes to RNA folding.353 A clear prediction for structural changes of RNA in the presence of cations is challenging, and clear differences exist between the structure of RNA in KCl and MgCl₂ solutions.347 Interestingly, for both salts, the RNA structure deviates also significantly from the assumed canonical A‐form of RNA.347

Interestingly and potentially counterintuitively, quasi‐elastic neutron scattering (QENS) measurements have shown RNA folding to go along with an increased flexibility of its backbone as is reflected, inter alia, in an increased mean‐squared displacement and mobile atom fraction.360 The authors of Ref. [360] propose that the diffusion of hydrated cations close to the RNA molecules lead to stronger electrostatic fluctuations. Another possible explanation involves more strongly fluctuating hydrogen bonds between hydration shell water molecules and the RNA backbone screened by Mg²⁺ cations.360 For a more comprehensive discussion of RNA folding in the presence of metal ions we refer to the review by Woodson.361

In addition to electrostatic interactions between the RNA phosphate backbone and cations, both mono‐ and divalent cations have also been shown to interact with DNA bases through cation‐π interactions as well as through the first hydration shell water molecules of the cations.362 These types of interactions can lead to an enhanced stabilisation of certain DNA binding motifs, thus playing a role in cellular processes relying on, e. g., protein‐DNA binding.362

Because of its crucial role in cell proliferation, DNA is an obvious target for cancer treatment. In the context of this review, the chemotherapeutic cisplatin needs to be emphasised. Once inside a cell, cisplatin is hydrolysed, yielding the charged complex [Pt(NH₃)₂ClH₂O]⁺. Importantly, this cation undergoes a very specific coordinative reaction to a guanine or adenine base, enabling an interaction between the cisplatin‐DNA complex and DNA repair proteins.363 A different approach to cancer treatment involves the direct suppression of the production of a cancer‐promoting protein in vivo. Such an approach involved the targeted delivery of small interfering RNA (siRNA) molecules using the large organic cation oligo‐arginine has been described by Cantini et al.364

4.3. Reentrant condensation of DNA by multivalent ions

Reentrant condensation of DNA macromolecules by multivalent cations, particularly spermine, has been studied intensively. In this system, the stability of DNA solutions is determined by two transition concentrations of multivalent cations. At low cation concentrations, the DNA solution is stable. Crossing the condensation cation concentration, DNA condenses and precipitation sets in. Beyond the second reentrant transition concentration, the DNA solution is stable again.365, 366, 367

The phenomenon of reentrant condensation in DNA can be explained by a charge inversion55 and like‐charge attractions368 of DNA molecules induced by ion−ion correlations of multivalent counterions.51, 53, 369, 370 Similarly to the question on ion distributions (see above), DNA again provided a well‐characterised experimental system with a surface‐charge density sufficiently high to allow the observation of clear effects beyond PB theory. These observations inspired the further development of theories and simulation approaches, also accounting for ion–ion correlation effects. Ion–ion correlations in the strong‐coupling limit induce a rather ordered distribution of condensed ions over the surface, which leads to both overcharging and like‐charge attraction without the need for specific interactions.51

The effect of competing monovalent salt represents a debated topic. Experimentally, monovalent cations induce an increase of the condensation concentration of multivalent cations, whereas the reentrant transition remains constant.365, 371 From analytical theory, a so‐called giant charge inversion, i. e. a larger reverted positive charge than the initial negative charge, was predicted at large monovalent cation concentrations,56 but not observed in simulations.57 Burak et al.43 concluded that the actual number of condensed multivalent ions depends on the choice of short‐range interactions, and thus has to be salt and model‐dependent.43 Indeed, the structure of multivalent cations has been found to affect DNA condensation and condensates,372 which was traced back to a non‐specific recognition process of complex cations to DNA.373 On a finer structural level, it was suggested that DNA condensation is connected to ion condensation in the major groove of DNA which depends on ionic properties and also allows for a temperature‐driven transition due to entropic effects.374 Recent simulations indeed found that aggregation of DNA and RNA induced by multivalent ions depends on the helical structure (A or B form), suggesting a critical role of the condensation area of the ions.375

In the context of the relevance of local structure, it is helpful to contrast the different pictures for reentrant condensation in DNA and proteins. Proteins provide a very irregular condensation pattern, as both charges are distributed irregularly on the surface, and local binding sites have different geometries, making solvation effects very dependent on the specific surface area. As a result, proteins typically have few strong interaction sites with multivalent ions, which dominate the binding and require a more local picture of cross‐linking as the main cause of attraction. By contrast, DNA provides a fairly regular structure with repeating condensation areas, which allowed initial approaches based on uniformly charged cylinders to recapitulate the overall effects due to ion–ion correlations. Even when considering the atomic picture, ion distributions are more uniform along the full chain, and attraction due to ion–ion correlations can thus still be expected to play a major role.

4.4. DNA: stiffness, kinks, and persistence length

There have been very intense and detailed studies of the mechanical properties of DNA,376 including in particular single‐molecule DNA. A comprehensive feature and overview was written by Bustamante et al.377 ds‐DNA is 50 times harder to bend into a circle than ss‐DNA,377 although material‐wise ds‐DNA is only two strands of ss‐DNA plus the twist. The stiffness is reflected in a rather large flexural persistence length, A, which in the worm‐like chain (WLC) model is about 50 nm (the length of roughly 150 base pairs) for dsDNA in physiological buffer.377 The phosphates in the DNA backbone make it one of the most highly charged polymers known.377 As a result, its structure is “pre‐stressed” by electrostatic self‐repulsion.

Thus, we can expect that charges can provoke a strong response of DNA. Other charged macromolecules, such as DNA‐binding proteins, can, provided a suitable charge pattern, effectively associate with DNA and even bend DNA.377 Interestingly, even enantiospecific kinking of DNA by a partially intercalating metal complex was reported.378

A landmark study on “ionic effects on the elasticity of single DNA molecules”379 reported several effects of ions, some of which were unexpected based on macroscopic elasticity theory. While details of the analysis of the elasticity of DNA (with in fact three different elastic regimes, and some effects opposite to what would be expected from macroscopic elasticity theory) are beyond the scope of this review, it was clearly shown that multivalent ions can have a much stronger effect on the persistence length than monovalent ions for the same nominal ionic strength379 (cf. quadratic functionality of valency Z in Eq. 3). For further work in the context of mechanical properties of DNA and charges, see, e. g., Refs. [380–384].

Generally, we can expect that the mechanical properties of DNA impact biologically relevant reactions, and vice versa, i. e. the impact of other biomolecules attached to DNA have an impact on the mechanical properties, which means that the latter can be used as a sensor for the former.

We remark that in addition to its biological relevance, DNA is also employed in nanoscience and nanoengineering applications including, e. g., “DNA origami”.385 These are beyond our scope here, but we note that of course also for these systems charges typically play a key role for the interactions and the resulting behaviour.

5. Amphiphilic molecules and interfaces

Amphiphilic molecules assembled at interfaces are excellent model systems. They can be found as monolayers or bilayers, the latter serving, e. g., to mimic biomembranes. This is especially important given the crucial role of cations, including divalent ones, in different processes involving cellular membranes such as signal transduction.

Amphiphilic molecules in general typically exhibit a hydrophilic and, in some cases, charged head and a hydrophobic tail. They play a key role as constituents of bilayer structures and biological membranes such as those surrounding cells. Given that they can be used in vitro as model systems mimicking cell membranes, they are thus also of relevance for pharmaceutical research.

In addition, amphiphilic molecules are essential ingredients of everyday consumer products such as cosmetics or detergents. In this context, also terms such as “surfactants” and “tensides” are used.386 These are not the main focus of this review, but we wish to point out some of their properties with special attention being paid to those involving multivalent cations. Importantly, there are ionic surfactants and especially these (but not only these) are subject to various ion‐mediated effects. In this section, we shall organise the material according to their nature, e. g. interface layers and micelles or, more generally, interface and bulk behaviour, respectively. We shall also comment on ion effects at interfaces, including those occuring in the absence of amphiphilic molecules, as model studies. We note that the distinction between interfaces and bulk is not always sharp since the bulk can also involve internal interfaces that may be formed in solution.

5.1. Monolayers and remarks on the local picture

A general overview on phase behaviour of monolayers, including lipids, is found in Ref. [388]. A general schematic of ions and amphiphilic molecules in an aqueous solvent is shown in Figure 7. Here, we begin our discussion with lipid monolayers, which are also very suitable to study local ion‐lipid interactions.

Figure 7.

Schematic representation of the arrangement of cations in the bulk solution and near a monolayer of amphiphilic molecules. Image inspired by Ref. [387].

Bu et al.389 used X‐ray spectroscopy to investigate a Langmuir monolayer of dihexadecyl phosphate on a cesium iodide (CsI) solution. The experiments showed that the monovalent Cs⁺ ions form a diffuse Gouy‐Chapman layer on the surface of the monolayer. With 0.58 Cs⁺ ions per lipid molecule, the cations were found to be surrounded by oxygens from the aqueous solution as well as from the dihexadecyl phosphate head groups. The counterions (I⁻), on the other hand, appeared to be depleted from the monolayer‐water interface.389 Moreover, the pathologically relevant divalent cation Be²⁺ has been shown to cross‐link and thereby compact phosphatidylserine (PS, an anionic lipid) monolayers.390 The authors also showed that Be²⁺ was able to displace Ca²⁺ from PS, indicating a potential mechanism behind the pathological condition berylliosis.390

A powerful technique to study the local distribution of ions around amphiphilic molecules is X‐ray reflectivity. In a very elegant XRR experiment exploiting anomalous scattering, Vaknin et al.387 characterised in detail the ion distribution at biomimetic membranes, specifically Ba²⁺, near DMPA (1,2‐dimyristoyl‐sn‐glycero‐3‐phosphatidic acid). They found an unexpectedly large concentration of barium at the interface, 1.5 per DMPA, forming a Stern layer of bound ions and a cloud of less densely bound ions near the lipid headgroups.387

Interestingly, in the case of divalent cation mixtures (Ba²⁺ and Ca²⁺), DMPA was found to exhibit a strong preference for Ca²⁺ with the ratio of Ca²⁺ : Ba²⁺ at the DMPA‐water interface being roughly 4 : 1 even though theoretical predictions based on cation hydration behaviour suggest the opposite.391 In addition, the fact that more than the one Ca²⁺ ion required for charge neutralisation is bound to the DMPA surface suggests that charge inversion of DMPA occurs upon Ca²⁺ binding. Similarly to the study by Bu et al.,389 no accumulation of I⁻ ions at the interface was observed here and, also similarly, some hydroxide species (Ca(OH)²⁺) are assumed to be present. The fact that this preferential binding of Ca²⁺ is in stark contrast with data obtained using a different surfactant392 underlines the strong molecular specificity of cation‐surfactant interactions.391

Pittler et al.393 extended the studies performed on DMPA and monovalent and divalent ions to the trivalent ion La³⁺. Their results showed a charge inversion of DMPA at very small LaCl₃ concentrations of 0.5 μM, much lower than those observed by other experiments investigating a silicon (Si) surface.394 The charge inversion observed is believed to be mediated by La³⁺ intercalation between the negative charges of DMPA phosphates and/or hydrogen bonds between the phosphate oxygens and La(OH)²⁺.393

5.2. Micelles and bulk behaviour

Amphiphilic molecules can, under suitable conditions, assemble into micelles,395 which may then be considered (soft) nanoparticles in solution, essentially in a colloidal sense. If these are subject to the influence of multivalent ions, they can exhibit a variety of different behaviours which we will discuss in the following.396

An intriguing approach to tuning the phase behaviour of micelles using multivalent cations was demonstrated by Carl et al.397, 398 The authors synthesised block‐copolymers consisting of polyacrylate (PA) and polystyrenesulfonate (PSS). Combining these two polyelectrolytes prevents the well‐known Ca²⁺‐induced precipitation of PA. Instead, the diblock copolymers underwent reversible micellisation which could be tuned by varying the Ca²⁺ concentration and temperature.397 In another study, the authors exploited thermodynamic differences in cation‐polymer interactions of PSS and PA and demonstrated that Ca²⁺ triggers micellisation at high temperatures, while Ba²⁺‐ and Sr²⁺‐induced micelles form at both high and low temperatures. At intermediate temperatures, single block copolymer chains are found. Importantly, the micelle structure can be inversed by changing the temperature. At low temperatures, PA forms the outer layer of the micelle; at high temperatures, the outer layer consists of PSS.398

In addition to micelle formation, the ion‐dependent behaviour of amphiphiles and lipids in bulk is also of interest. An interesting example of ion specificity on the behaviour of a lipid derivative, lecithin, has been described by Lee et al.399 The authors observed that, depending on the cation and anion added to their lecithin samples, the tendency of lecithin to form a gel can be strongly altered. Studying lecithin‐Ca²⁺ as a reference system, they established that lecithin gelation goes along with the formation of cylinder‐like structures and an increase in the viscosity of the sample. A possible application for this ion‐induced gelation is a reversible, isothermal gelification of kerosene for transport purposes.399

Similarly, the cation‐dependent bulk properties of water‐in‐oil microemulsions stabilised by the sodium salt of the surfactant bis‐2‐ethylhexylsulfosuccinate were investigated by Eastoe et al.400 The authors demonstrated the formation of rod‐shaped aggregates of the water‐oil emulsion when Na⁺ was exchanged for Co²⁺, Ni²⁺, Cu²⁺ and Zn²⁺ . Interestingly, the aggregates formed in the presence of these cations assume a spherical shape upon water addition. Spherical structures were also observed in the case of Mg²⁺ and Ca²⁺, indicating a pronounced sensitivity to ion‐specific effects of this system.

For a system with an anionic surfactant and anionic surfaces (the isoelectric point for silica is approximately pH=2) normally repulsive interactions would be expected, but divalent ions (Ca²⁺) can form bridges between the negatively charged surfactant and surface, thus enabling their binding.401 Furthermore, the authors of this study varied the pH and compared their results to Na⁺, showing that the behaviour can be qualitatively different depending on the type and valency of the used cation. We note that Ref. [401] did not report reentrant effects, in contrast to the study of protein adsorption at solid‐liquid interfaces using trivalent ions (Y³⁺), where reentrant adsorption reflecting bulk reentrant behaviour could be observed.402

The adsorption of mono‐ and divalent anions to cetryltrimethyl ammonium (CTA) surfactant salts and the resulting effects on the surface tension of the latter was investigated by Para and Warszynski.403 The authors found that the monovalent ions Br⁻, Cl⁻ and ${\mathrm{HSO}}_4^{-}$ decrease the surface tension of CTA more efficiently than the divalent anion ${\mathrm{SO}}_4^{2-}$ . This result is traced back to a strong hydration of ${\mathrm{SO}}_4^{2-}$ anions, preventing them from penetrating the surfactant surface layer403 and it is an interesting example of non‐trivial effects as a function of charge.

An overview on the phase equilibria of selected ionic surfactants in the presence of mono‐ and divalent ions is given in Ref. [404], demonstrating ion‐specific effects on the stability of liquid crystalline phases of sodium di‐2‐ethylhexylsulphosuccinate in D₂O. In the presence of divalent cations, the water uptake of the lamellar crystalline phase of an octylsulphate‐decanol‐D₂O is reduced. Furthermore, Mg²⁺ leads to the formation of two additional liquid crystalline phases of the system.404

Surfactants at the solid‐liquid interface with divalent ions were studied in Ref. [401] using neutron reflectometry.

5.3. Bilayers: vesicles and membranes

In biology, one of the most important manifestation of lipid bilayers are membranes surrounding various cell types including cells of the human body, but also bacteria.9 An interesting example is the outer membrane of Gram‐negative bacteria. This membrane is strongly asymmetric with the inner side consisting of phospholipids, whereas the outer part contains a significant proportion of lipopolysaccharides (LPS).405 Mg²⁺ and Ca²⁺ ions are known to bridge these molecules, thereby compensating their mutual electrostatic repulsion. Clifton et al.406 demonstrated that removing these cations from a model closely mimicking the outer membrane of Gram‐negative bacteria leads to a destabilisation of membrane asymmetry and intermixing of LPS from the inner and outer parts of the membrane. This study illustrates the key role divalent cations can have especially in a biological context.

In the context of physiological relevance, pulmonary surfactants need to be mentioned. Dipalmitoylphosphatidylcholine (DPPC), which is considered the main component of lung surfactants (see, e. g., Ref. [407]), was investigated with respect to the effect of divalent cations on its structure and activity by Efrati et al.408 These authors established that, in the presence of the divalent ion‐dependent surfactant proteins SP28‐36 (which are part of the tubular myelin fraction of lung surfactants), the critical ion concentration inducing DPPC liposome aggregation decreased in the case of Ca²⁺, Ba²⁺ and Sr²⁺. Mg²⁺ and Mn²⁺, on the contrary, did not show this effect. The formation of tubular myelin structures required the presence of Ca²⁺. The authors suggest that the physiological role of Ca²⁺ is partly due to a neutralisation of the negatively charged carboxyl groups of the SP28‐36 proteins.408

An interesting approach to estimate the affinity of (multivalent) cations to membranes is to use channel proteins inserted into reconstituted lipid systems. Gurnev et al.409 employed a cation‐selective channel to estimate the extent of charge inversion of lipid membranes of multivalent cations, revealing that La³⁺ cations were more efficient at inverting membrane surface charge than hexaamminecobalt and spermidine. The effect of another trivalent cation was demonstrated by Ermakov et al.410 who showed a pronounced compaction of brain PS upon binding of Gd³⁺. Interestingly, the authors observed Gd³⁺‐mediated blocking of the large mechanosensitive channel MscL from E. coli inserted into reconstituted lipid bilayers containing PS. The authors trace this effect back to Gd³⁺‐mediated compaction of anionic lipids, which in turn exhibits pressure on the channel, thus blocking it.410 These studies thus evidence an intriguing correlation between local effects of multivalent cations translating into a large‐scale, global influence on a biological system.

Generally, just as in the case of proteins, Ca²⁺ appears to play a particularly important role for lipids, their structures and their interactions (for a detailed account, see Ref. [411] and refs. therein). Amongst other aspects, the fusion of lipid membranes during, e. g., the uptake or release of vesicles by cells, is often mediated by Ca²⁺. Churchward et al.412 demonstrated the importance of cholesterol for such Ca²⁺‐induced membrane fusion processes: removing cholesterol from model membranes significantly reduced the Ca²⁺ sensitivity of the fusion.412 A possible explanation for the importance of cholesterol is that it contributes negative curvature to the membranes (i. e., promotes the formation of concave surfaces at lipid‐water interfaces) involved in the fusion process (see Ref. [413] and refs. therein). This effect can also be mediated by other lipids the structures of which are not necessarily similar to cholesterol, but need to have a certain threshold negative curvature.414 One of the first biological systems shown to respond to Ca²⁺ were PS vesicles.411 In particular, the presence of Ca²⁺ induces the formation of dehydrated, multilamellar Ca(PS)₂ complexes from PS bilayers.415, 416 This process is referred to as a gel‐to‐liquid crystal bilayer transition and the periodicity and order of the bilayer structures were shown to differ depending on the type of cation present (Li⁺, Ca²⁺, Mg²⁺, Ba²⁺, Sr²⁺ or Pr³⁺).416

The effect of neutral lipids on this gel‐to‐liquid crystal bilayer transition was investigated by Coorssen et al.417 The neutral lipid molecules were shown to be incorporated into the dehydrated multilamellar PS bilayers. At higher concentrations of the neutral lipids, the interactions between the PS bilayers became weaker, the bilayers showed larger separations and, under certain conditions, two structures were observed.417

A further aspect of strong physiological relevance of Ca²⁺‐lipid (and Ca²⁺‐protein) interactions involves vision.418, 419 In particular, the photoresponse of rod outer segment membranes is known to depend on Ca²⁺.418 Huster et al.418 investigated the effect of unsaturated docosahexaenoic acid on the interaction between membranes and Ca²⁺. Here, the fatty acid saturation degree of the lipid membranes under study affected the Ca²⁺ affinity of the membrane. The more important factor determining Ca²⁺ affinity, however, was the content of PS.

McLaughlin et al.420 studied the effect that divalent ions (Ca²⁺, Mg²⁺, Sr²⁺, and Ba²⁺) have on the surface potential of phospholipid membranes. While no surface potential could be induced by cations in the case of an overall neutral surfactant (phosphatidylethanolamine, PE), the authors did observe a decrease of the surface potential in the case of the negatively charged surfactant phosphatidylserine (PS) upon addition of Sr²⁺ and Ba²⁺, consistent with predictions based on double layer theory. The same phenomenon was observed in the case of Ca²⁺ and Mg²⁺. Interestingly, however, smaller concentrations of the two latter cations were required in order to achieve the surface potential decrease mentioned above, implying that cation‐specific binding parameters and properties need to be taken into account.420

Vanderkooi and Martonosi421 used a dye molecule the fluorescence of which is strongly enhanced in a hydrophobic environment to investigate the influence of different parameters on lecithin microsomes (membranes). They observed that trivalent ions are more effective than mono‐ and divalent ones in enhancing the fluorescence signal. This observation was traced back to two possible reasons – a stronger hydrophobicity of the membranes induced by the cations or the cations affecting the binding of the dye to the membranes. The latter possibility was deemed more likely.421

Lis et al.422 investigated the binding of Ca²⁺ to bilayers of dipalmitoylphosphatidylcholine (DPPC) by measuring the repulsive forces between the bilayers. They found that a low concentration of Ca²⁺ leads to a strong increase of the bilayer separation distance in aqueous solution, implying that Ca²⁺ increases these repulsive forces. High Ca²⁺ concentrations had a smaller effect on the interbilayer distance. The addition of a monovalent salt (NaCl) was found to weaken this effect of Ca²⁺. Lis et al. found that pushing together the lipid monolayers forming the bilayer led to a desorption of Ca²⁺ and a decreasing surface potential. They tentatively attribute this phenomenon to the possibility of the double‐layer electric fields deforming the arrangement of polar surface groups of the bilayer, thereby altering their Ca²⁺ binding pattern. They speculate that this change in arrangement might, in turn, be due to changes in the conformations of lecithin head groups.423

The same authors then extended their studies to other surfactant bilayer systems as well as to other divalent cations.424 The order of preferential cation binding to DPPC was found to be

$${\displaystyle {\mathrm{Ca}}^{2+}\approx {\mathrm{Cd}}^{2+}\approx {\mathrm{Mn}}^{2+}>{\mathrm{Co}}^{2+}\approx {\mathrm{Mg}}^{2+}>{\mathrm{Ba}}^{2+}.}$$ (5)

Moreover, a higher density of polar groups present on the surface of the bilayer as well as a higher concentration of divalent cations invokes a higher density of cations bound. Concerning the phase behaviour of the surfactants studied, the authors found that phase separation into two different lamellar phases occured in phosphatidylcholine (PC) mixtures differing only in their hydrocarbon chain residues in the presence of Ca²⁺.424 In the context of the cation‐DPPC affinity study, it is interesting to note that McLaughlin et al.425 found the following order for divalent cation affinity to PC:

$${\displaystyle {\mathrm{Mn}}^{2+}>{\mathrm{Mg}}^{2+}>{\mathrm{Ca}}^{2+}>{\mathrm{Co}}^{2+}>{\mathrm{Ni}}^{2+}>{\mathrm{Sr}}^{2+}>{\mathrm{Ba}}^{2+}}$$ (6)

These results emphasise the importance of cation‐specific effects in the context of cation‐lipid interactions. As a general conclusion regarding the binding of divalent cations to PC, Lis et al.424 established it to be a highly sensitive and multifactorial phenomenon, depending not only on the length of the PC hydrocarbon chain, but also on the distance between the bilayers, and, importantly, the concentration and type of divalent cations used.

In addition to the extensive studies of cation‐bilayer interactions described above, several studies were performed on the interactions between cations and vesicles. Ohki et al.426 studied the propensity of both mono‐ and divalent cations to induce aggregation of phospholipid (phosphatidylserine (PS) and ‐choline (PC)) vesicles. The effectiveness of monovalent cations to induce PS aggregation was determined to be

$${\displaystyle {\mathrm{H}}^{+}>{\mathrm{Na}}^{+}>{\mathrm{Li}}^{+}>{\mathrm{K}}^{+}>\mathrm{TMA}.}$$ (7)

where TMA is short for tetramethylammonium. The threshold concentrations of divalent cations causing PS vesicle formation were ranked in the order

$${\displaystyle {\mathrm{Mn}}^{2+}<{\mathrm{Ba}}^{2+}<{\mathrm{Ca}}^{2+}<{\mathrm{Sr}}^{2+}<{\mathrm{Mg}}^{2+}.}$$ (8)

The explanation of these observations proposed by the authors involves the surface potential and surface charge densities of the vesicles as well as the repulsive interactions between vesicles.426 We note that a detailed review on ion effects on amphiphilic molecules is provided in Ref. [427].

All of these studies underline that subtle, cation‐specific effects should not be neglected when discussing cation‐mediated phenomena.

5.4. Other interfaces

While this review is not specific for interface phenomena, they play, of course, a major role in soft and biological matter in general, not limited to surfactants. Therefore, we shall briefly comment on this issue, without claiming to be exhaustive. Obviously, simpler, non‐biological interfaces can serve as model systems, e. g., to study the charging behaviour with better spatial resolution. Examples are found, inter alia, in Ref. [428] and references therein. Furthermore, interesting and remarkably strong ion‐specific effects at interfaces were reported in Refs. [429] and [430].

An important area is that of protein adsorption at interfaces.431, 432, 433 Since proteins frequently exhibit amphiphilic properties, there are even some analogies to the surfactant systems discussed above. Importantly, in the context of this review, they usually also have a (nontrivial) charge pattern on their surface. Multivalent ions can, of course, induce a richer phenomenology, including charge inversion.402 This was demonstrated using BSA and Y³⁺ in water at SiO₂ surfaces. Depending on the salt concentration, “reentrant” effects in the adsorption were found, nicely mirroring the bulk reentrant behaviour.58, 256, 257

Other biomolecules such as DNA/RNA were, of course, also investigated with respect to their adsorption and interface behaviour.434 Several of the studies discussed in Sec. 4 were, in fact, related to interfaces, meaning that we will not further elaborate on them here.

Furthermore, we wish to mention several other systems because of their model character. As an example, the adsorption of β‐lactoglobulin to the air‐water interface was studied by Richert et al.435 in the presence of Y³⁺ and Nd³⁺ cations using a multi‐method approach including sum frequency generation (SFG) spectroscopy. Binding of the cations resulted in a reduction of the net protein charge and subsequent aggregation. Ion binding to protein residues located at the air‐water interface was concluded to mediate foam stability via structure‐property relations.

An interesting system to investigate with respect to their sensitivity to charges are polyelectrolyte brushes due to their intriguing surface geometry. Yu et al.30 studied the effect of multivalent ions on the lubricity of polystyrene sulfonate brushes. Even small concentrations of multivalent cations such as Y³⁺, Ba²⁺ and Ca²⁺ were found to strongly increase the friction between layers of the brush polyelectrolyte due to cation bridging effects. Yu et al.30 underline the significant effect of multivalent counterions on the lubricating properties of polyelectrolyte brushes, stressing the importance of this effect for applications such as biomedical devices.

6. Remarks on other systems

In addition to those described above, there are other systems in the broader area of soft and biological systems which exhibit interesting charge effects, also and in particular with multivalent ions. While we cannot discuss them in detail, we nevertheless wish to give some examples below.

6.1. Synthetic polymers

While these are not the primary scope of this review, we feel that some comments on the ion‐dependent properties of synthetic polymers are in order, since a lot can be learned from the comparison between synthetic polymers and, in particular, proteins and DNA/RNA.

It is interesting to note, for example, that the Hofmeister effect, initially described for proteins, has also been observed in systems of the polymer poly(N‐isopropylacrylamide) (PNIPAM).436 The authors of this study found that kosmotropes can polarise water molecules forming hydrogen bonds with the amide groups of the polymer and increase the surface tension of the backbone cavity, thus interfering with hydrophobic hydration of these moieties. Additionally, a direct binding of the anions to the polyamide groups of PNIPAM is possible. Those interacting directly and via the surface are classified as chaotropes; they decrease the lower critical solution temperature of the system. Those anions exhibiting mostly polarising effects represent kosmotropes.436

The multivalent ion‐driven behaviour of polyelectrolytes is a complex area of research (see, e. g., Ref. [437]). In particular, the charge‐driven interaction between polyelectrolytes (PE) and alkali cations is exploited in industrial processes where polyacrylates are frequently used as, inter alia, scale inhibitors.18 This cation‐PE interaction has been studied in detail using various scattering methods.18, 438, 439, 440, 441, 442, 443 Using anomalous small‐angle X‐ray scattering (ASAXS) on a sodium polyacrylate (NaPA)‐Sr²⁺ system, Goerigk et al.441 demonstrated that the Sr²⁺ counterions reside in spherical structures on the NaPA chains.441 Hansch et al.443 investigated the temperature‐dependent phase behaviour of sodium polysterene sulfonate (NaPSS) in the presence of Ba²⁺ and Al³⁺ cations. Interestingly, while in the presence of Al³⁺ NaPSS shrinks with increasing temperature, Ba²⁺ cations decrease the dimensions of NaPSS upon a temperature decrease. This strong difference is traced back to differences in cation binding thermodynamics and underlines the strong specificity of cation effects in macromolecular systems. As such, it is yet another example of non‐monotonic cation‐mediated effects.

In addition to inorganic cations, the influence of multivalent organic cations on PE molecules has also been investigated. Mechtaeva et al.444 observed crosslinking of polyacrylic acid by oligoethylenimines, leading to the formation of ionic complexes. The shape of the complexes formed was investigated by atomic force microscopy (AFM) and scanning electron microscopy (SEM) and found to depend on the the polyelectrolyte concentration as well as on the ratio of amine and carboxylic groups of the oligoethylenimines.444

In another study performed by Buyukdagli and Podgornik,445 it was found that PE adsorption to like‐charged membranes immersed in a monovalent salt solution was facilitated by the addition of tri‐ and tetravalent cations. The PE adsorption is traced back to a condensation of the multivalent counterions at the membrane which strengthens the monovalent salt‐mediated screening. The critical concentration of the multivalent counterions is found to decrease with increasing charge of the counterions. Additionally, an increase of monovalent salt concentration leads to polymer desorption from the membrane.445

The effect of trivalent ions on a biologically relevant PE (hyaluronic acid (HA), a charged polysaccharide) was studied by Innes‐Gold et al.446 by combining magnetic tweezers force spectroscopy as well as simulations and theory. The results indicate that in the presence of the trivalent cations hexammine cobalt (III) chloride and hexammine ruthenium (III) chloride, the system displays a remarkably decreased sensitivity to the ionic strength of its surroundings, reflected in a decreased elasticity of HA. Innes‐Gold et al.446 trace these observations back to the formation of a tight “jacket” of trivalent ions around the HA molecules.

Ion‐specific effects on hydrogels were shown by Fullenkamp et al.447 The authors synthesised these gels in order to perform model studies on the self‐repairing thread structures used by marine mussels to attach to various surfaces. In the hydrogels studied, ion binding proceeds via chelation by histidine residues. Interestingly, the different ions used by Fullenkamp et al. (Zn²⁺, Cu²⁺, Co²⁺ and Ni²⁺) lead to differences in the brittleness, self‐repair rates, gel relaxation times and colouring of the gels.447

6.2. Colloids and nanoparticles

The first experimental observations of certain phase behaviours closely reflecting those of atomic systems were made in colloidal systems.448 In particular, a seminal publication by Pusey and van Megen449 proved principles based on atomistic explanations to be able to account for phase behaviours observed experimentally for polymethylmethacrylate (PMMA) colloids. This study thus provided a strong indication that aspects of atomic systems can be applied to colloidal ones and vice versa. Colloids are hence sometimes referred to as “superatoms“.450 In fact, also the phenomenon of charge inversion has been discussed in terms of the colloidal picture.254 Thus, while colloids are obviously not “molecules” in the true sense of the word, colloidal models and model systems are frequently very useful in particular in the interpretation of observations on globular proteins. In the context of multivalent ions, the analysis of patchy colloid models provides a valuable link between simplified models and much more complex protein systems.249, 265, 451, 452, 453 The different effects of mono‐, di‐ and trivalent ions on colloidal particles has been described by Linse and Lobaskin454 using canonical Monte Carlo. In particular, the authors report decreasing intercolloid distances and a stronger tendency to aggregate with increasing counterion valency, indicating the importance of theoretical approaches rationalising high charge densities of counterions.

In addition to purely charge‐mediated effects, cation‐induced pH changes need to be considered as well. Schubert et al.455 studied the influence of metal ions and their hydroxides and the associated pH changes on NPs coated with BSA. This study reports both charge inversion of the NPs and a decrease of the solution pH upon addition of several trivalent cations, going along with the adsorption of metal hydroxide species on the NPs. Schubert et al.455 trace the charge inversion observed to these hydroxides, thus connecting pH and pure charge effects.

7. Concluding Remarks

We have attempted to provide a comprehensive perspective on multivalent ions and biological (macro)molecules.

It is rather suggestive to expect similarities in the local picture (binding and bridging) and indeed these are found, since essentially the same functional groups are involved. While the local chemistry is not in all cases fully understood in terms of a quantitative quantum‐chemical picture of the interactions of multivalent ions (in particular lanthanides) with, e. g., carboxylic acids in the presence of water, it is expected to be similar for different types of macromolecules containing similar functional groups. An interesting case in point is Ca²⁺, which appears to play a very special role in many different systems. Importantly, for most of the systems described in this review, i. e., including proteins, nucleic acids, synthetic polyelectrolytes and amphiphilic molecules, non‐trivial ion‐specific effects were found. The latter can sometimes be traced back to “simple” features such as ionic radii, but this one parameter is not always sufficient to accout for ion specificity and it is thus clear that aspects such as ion hydration properties and possibly quantum chemical effects need to be taken into account.

In terms of the overall/global picture, there are also some similarities, certainly on a qualitative level. As an example, both proteins and DNA can bind multivalent ions and, as a consequence, undergo charge inversion. However, the strong differences in charge distribution – rather homogeneous, “polymer‐like” in the case of DNA vs. typically highly inhomogeneous for proteins – will generally lead to different overall macroscopic behaviour, including the response to higher concentrations of multivalent ions. In addition, at east double‐stranded DNA is somewhat special in terms of its high stiffness and large persistence length. This leads to a rather unique response to multivalent ions.

The comparison with soft‐matter model systems, such as colloids, is in many cases fertile in terms of the overall phase diagram (most notably patchy colloid models), especially for the case of globular proteins. In particular, applying the concept of “colloids as superatoms“ greatly helps transferring the knowledge obtained on the phase behaviour of well‐controlled, colloidal systems to much more complex (bio)molecules.

For amphiphilic molecules, the presence of large, potentially bulky hydrophobic areas strongly distinguishes these from nucleic acids and proteins, as does the dominant role they play for interfaces (and vice versa). Thus, the similarities in the overall/global behaviour are limited, and usually a different approach is needed. Nevertheless, amphiphilic molecules actually offer unique opportunities to study ion effects in a very targeted way, such as exposing a specific group in a large area (at the surface of a liquid) and thus sufficient signal for a specific study of, e. g., ion association parameters. In addition, they exhibit their own very rich phase behaviour, which can be subjected to and influenced by multivalent ions.

We hope that the material compiled here and the perspective offered help to understand the effects of multivalent ions more comprehensively. We also hope that there will be some cross‐fertilisation with the areas beyond the scope of this review, covered only in passing, such as ion channels in membranes, synthetic polymers, and colloids. It may also spark new studies and inspire new discoveries by translating ideas from one field to the other.

Conflict of interest

The authors declare no conflict of interest.

Biographical Information

Dr. Olga Matsarskaia obtained her PhD on the topic of tuning protein interactions using multivalent ions in the group of Prof. Frank Schreiber (University of Tübingen, Germany) in 2018. After postdoctoral stays at the Institut Laue‐Langevin (ILL, Grenoble, France) and at the Université Grenoble‐Alpes, she is, as of February 2020, co‐responsible of the small‐angle scattering instrument D22 at the ILL. Her primary research interests consist in using physical concepts in order to understand the mechanisms underlying the functionality of soft and biological matter.

Biographical Information

Associate Senior Lecturer Dr. Felix Roosen‐Runge obtained his PhD at University of Tübingen (Germany). After postdoctoral stays at the Institut Laue‐Langevin (Grenoble, France) and Lund University (Sweden), he started as an Associate Senior Lecturer at Malmö University (Sweden) in 2019. His research interests are centered around dynamics and structure in soft and biological matter, with a special focus on the physical chemistry of proteins. He aims for an integrative picture combining in particular dynamic and static scattering techniques with coarse‐grained simulations and modeling.

Biographical Information

Professor Dr. Frank Schreiber obtained his PhD at Bochum University (Germany). He spent his postdoctoral research at Princeton University (USA) and gained his habilitation at Stuttgart University (Germany). After a three‐year period as a Lecturer at Oxford University (UK), he has been a full professor at the University of Tübingen since 2004. His research interests include the physics and physical chemistry of molecular and biological matter, including equilibrium as well as non‐equilibrium aspects. His group makes strong use of X‐ray and neutron scattering techniques.

O. Matsarskaia, F. Roosen-Runge, F. Schreiber, ChemPhysChem 2020, 21, 1742.