Interplay between the electrostatic membrane potential and conformational changes in membrane proteins

Abstract

Transmembrane electrostatic membrane potential is a major energy source of the cell. Importantly, it determines the structure as well as function of charge‐carrying membrane proteins. Here, we discuss the relationship between membrane potential and membrane proteins, in particular whether the conformation of these proteins is integrally connected to the membrane potential. Together, these concepts provide a framework for rationalizing the types of conformational changes that have been observed in membrane proteins and for better understanding the electrostatic effects of the membrane potential on both reversible as well as unidirectional dynamic processes of membrane proteins.

Abbreviation and symbols

ΔΨ

electrostatic membrane potential

E_Ψ

electric field of the membrane potential

GPCR

G‐protein coupled receptor

HMF

hydrophobic mismatch force

MFS

major facilitator superfamily (transporter)

MP

(integral) membrane protein

PMF

proton motive force

TM

transmembrane

VGIC

voltage‐gated ion channel

Membrane Potential Is Essential to the Cell

Cells are the basic units of life on Earth. From a structural point of view, cells are bounded by membranes and communicate with their environment through integral membrane proteins (MPs). MPs are responsible for material transport, signal transduction, energy conversion as well as membrane biogenesis, all processes that sustain thermodynamic non‐equilibria that keep a cell alive and fully functional.

From an energetic point of view, redox potential, phosphorylation, and transmembrane (TM) electrochemical potential are the three major interchangeable forms of energy available to living cells.1 While ATP is the most commonly used energy form present in the cytosol, the TM electrochemical potential is arguably the most important energy source for most MPs that are not directly involved in biogenesis of an electrochemical potential. Firstly, ΔΨ is generated and maintained through hydrolysis of ATP. Astonishingly, up to 60% of cellular energy originating from ATP hydrolysis can be consumed to maintain the ΔΨ of a cell.2 In turn, ΔΨ powers many TM signaling and transporting processes through ion channels and secondary active transporters. ΔΨ is present across the cytoplasmic membrane as well as in membrane‐bounded organelles such as mitochondria,3 lysosomes,4 and likely the endoplasmic reticulum.5 For a given membrane system (e.g., the sealed cytoplasma membrane), the TM electrochemical potential includes components of both concentration gradient‐related chemical potentials from individual types of substances and overall electrostatic potential (ΔΨ, i.e., a net‐charge gradient). Since each type of ion may both affect and be affected by the ΔΨ, the existence of ΔΨ provides an information hub between different types of ions, together functioning as a cellular information network.6

In animal cells, the negative‐inside ΔΨ of the resting‐state cytoplasma membrane usually ranges from −40 to −80 mV. In plant cells, ΔΨ of the cytoplasma membrane reaches −200 mV;7 and in fungi, ΔΨ can be as strong as −300 mV.8 In animal neurons, muscle, and endocrine cells, ΔΨ is highly dynamic, participating in information receiving, processing, and propagation.9 During development, ΔΨ provides direct cues to instruct pattern formation among non‐excitable cells.10 More generally, bioelectrical signaling is becoming recognized as an important dimension of the phase space that encompasses the various physiological states of a cell.6 In particular, by controlling intracellular secondary messengers (e.g., Ca²⁺), the network centered at ΔΨ is likely to be intimately intertwined with the biochemical and genetic networks of the cell.

ΔΨ not only provides energy for large conformational changes of MPs (e.g., in secondary active transporters11) but also affects their orientations and equilibrium positions relative to the lipid bilayer, as exemplified by the “positive‐inside rule” of MP assembly12 and the voltage‐gated operation of ion channels and certain membrane‐anchored enzymes.13, 14 Therefore, ΔΨ plays a unique, indispensable role in controlling the functions of MPs – a view that remains to be widely appreciated, especially in the main stream of the MP structural biology.

While the TM electrostatic potential is conceptually simple and fully described by using a single variable, ΔΨ, the spatial distribution of its vectorial electric field, E _Ψ(x) (≡ ∇[ΔΨ]), may vary spatially and temporally_, especially when a dynamically charged MP is involved. For a given configuration of the MP‐membrane system, the Poisson‐Boltzmann equation is commonly used to determine the E _Ψ(x), with ΔΨ defining the boundary condition of the solution. ΔΨ is usually contributed to by multiple TM ion‐gradients established through facilitating ATP‐driven pumps (e.g., P‐type ATPases15, 16). Applying ΔΨ as the boundary condition of the Poisson–Boltzmann equation implies a mean‐field approximation in which the structural fluctuations of the target system are significantly slower than the movements of the contributing ions. Thus, these ions form rapidly equilibrated clouds on both sides of the membrane, establishing a mesoscopic ΔΨ. In addition, electrically charged head‐groups of lipid molecules as well as their surrounding counter ions superimpose their local electric fields onto the mesoscopic ΔΨ.

One simplified yet useful model of the membrane potential is the parallel‐plate capacitor model,9 in which the lipid bilayer acts as a thin‐layer medium (of uniform thickness, d) that insulates opposite electric charges on the two sides of the membrane, thus maintaining a uniform electric field (E _Ψ = ΔΨ/d) inside the membrane. The opposite charges of the ion clouds are attracted toward each other near the surface of the insulating medium and exponentially decay on both sides, with a decay rate (termed Debye length) of ~0.7 nm.9 Outside this Debye length, the E _Ψ becomes negligibly small. Inside the membrane bilayer, the force lines of E _Ψ are, by‐definition, perpendicular to the contour surfaces of the ΔΨ, and point from the positive side to the negative side of the ΔΨ.

To illustrate how the capacitor model is applied to a lipid bilayer, let us assume that ΔΨ possesses a value of 100‐mV, with the membrane thickness (d) being 3‐nm and a dielectric constant (ε) of 1. The charge density (εε₀ΔΨ/d) on each side of the membrane is estimated as ~0.02 e₀ per 1000 A² surface (which is equivalent to the cross‐sectional area of a typical membrane protein). This rather low “basal” value of the average density of the net‐charge clouds suggests that the “incidental” binding of an electrically charged ligand to the MP (or a charge‐altering mutation) is likely to have drastic effects on the local E _Ψ as well as on the target MP immersed in this field. A fundamental question to be addressed regarding ΔΨ is under what condition and to what extent ΔΨ affects the MP.

The Electrostatic Force Originating from the Charge Gradient Is Biologically Relevant

TM electrostatic potential, ΔΨ, exerts a force on any charged particle immersed in its electric field, E _Ψ. Movement of the charged particle along the force lines of E _Ψ converts the electrostatic potential energy of the charge into mechanical energy. For instance, in the capacitor model, a proton carrying a unitary electric charge (e ₀) is subject to a force of ~5 pN. Its translocation across the membrane, if allowed, would release energy of 10 kJ/mol (or ~4RT; assuming ΔpH = 0). This level of force is considered large for a MP floating in the lipid bilayer, and is comparable to those observed in typical molecular events within the cell.17, 18, 19, 20 Interestingly, the electrostatic force of the ΔΨ exerted on negatively charged residues in a nascent polypeptide chain traversing the Escherichia coli inner membrane has been detected experimentally.21 Therefore, it is highly probable that both the conformation and function of a charge‐carrying MP are strongly influenced by the existence and/or change of ΔΨ, provided that the protein is able to move relative to E _Ψ.

In contrast to the electrostatic force, the hydrophobic mismatch force (HMF) is a major factor acting to keep the MP static in the lipid bilayer.22 While hydrophobic interaction is the driving force for the folding of MPs, the HMF relates to the compatibility of the TM hydrophobic surface of the folded MP with its surrounding lipid bilayer. The structural and functional properties of MPs are often implied as being dictated solely by HMF; we will argue, instead, that such an assumption is likely to be incomplete or misleading. Like electrostatic force originating from multiple electric charges embedded within the MP, the HMF is the collective name for all hydrophobic forces distributed in the MP–membrane interface. Unlike electrostatic forces, however, the HMF would increase drastically upon a perpendicular displacement of the MP relative to the membrane, consistent with the steep barrier in the energy landscape of MP unfolding.23

A charge‐carrying MP maintains its equilibrium position and conformation by adjusting the HMF to balance forces from the ΔΨ. In particular, one of these equilibrium conformations (e.g., the resting state) is often taken as the reference point, at which all pre‐existing forces are balanced against each other. All effects of altered electric forces are then evaluated relative to this reference point. This methodological treatment is of fundamental importance to the following simplified models of MPs. During a ΔΨ‐driven conformational change, a change of electric charges (ΔQ) at a fixed ΔΨ is thermodynamically equivalent to a change of ΔΨ (denoted as ΔΔΨ) that acts on a fixed set of electric charges in the MP. The former is exemplified by protonation/deprotonation in the proton motive force (PMF)‐driven transporter, lactose permease,11 or by binding of an ionic ligand,24, 25 and the latter by the voltage sensors of voltage‐gated ion channels (VGICs).13 Thus, most of the following discussion is likely applicable to both situations. Together with HMF, the electrostatic force exerted by ΔΨ on a MP is likely to have a strong effect on both the equilibrium properties as well as the functions of such a MP.

Is the Charge Gradient Connected to the Membrane or the Membrane Protein?

Under certain strict conditions, however, a MP appears not to be able to sense the existence of ΔΨ. To illustrate such a possibility, let us first consider a thought experiment illustrated in Figure 1. In Figure 1(A), MP is represented by a flat, rigid‐body cylinder, floating in the lipid bilayer. Its height perfectly matches the thickness of the membrane, with its diameter longer than its height. This will serve as our reference configuration. At time zero, this cylinder captures a positive charge at its mass center, which becomes the acting point of the ΔΨ. One might anticipate that an electrostatic force will act on the cylindrical MP, and the latter will move translationally toward the negative side of the ΔΨ. If the ΔΨ is exceedingly strong compared to the HMF, would such a cylindrical MP be ejected from the membrane, like the abovementioned proton? Surprisingly, the answer may actually be “No.” It appears from our model that the MP is not able to sense any force originating from the interaction between its carried charge and ΔΨ. The reason is that, in the discussion above on the membrane‐permeable proton, an unconscious assumption is made that ΔΨ remains static relative to the membrane, analogous to how the gravitational field of Earth acts on a freely dropping object. For a MP immersed in the ΔΨ, however, this assumption is often proven incorrect. Both the geometrical shape and the electric‐charge constellation of the MP influence the distribution of ion clouds on both sides of membrane, thus affecting the spatial distribution of E _Ψ. Because of the particular shape of our cylinder model, E _Ψ can be considered as being integrally connected to the MP in such a way that any small translation of the cylinder would be accompanied by the same movement of E _Ψ. Since it is embedded in the rigid body, the electric charge of interest cannot move relative to the cylinder, and thus cannot move relative to the E _Ψ. Consequently, this charge will not move along the force lines of the E _Ψ and thus not utilize the ΔΨ energy to fuel its movement. According to the principle of virtual work, the net force applied on the charged group is zero, and thus the model MP stays static in the membrane. For a similar reason, the electric field originating from a charge bound to the rigid‐body MP per se (i.e., in the absence of external ΔΨ) will not affect the equilibrium position of the MP in the membrane.

Figure 1.

Membrane protein and ΔΨ. The darker‐blue shapes represent proteins of different shape embedded in a membrane: (A) flat cylinder, (B) long cylinder, (C) sphere, and (D) protein with a cleft. The contour surfaces of ΔΨ are represented by green lines, and the electric charge is marked as δ⁺. The initial level of the membrane protein corresponding to the extracellular surface of the membrane is marked by the red line. Overall hydrophobic mismatch forces (HMF) and electrostatic forces are represented by orange and blue open arrows, respectively. Directions of conformational changes are depicted as yellow solid arrows. Only in panel A is the ΔΨ integrally connected to the membrane protein.

Is it possible, then, that if we alter these restrictions, the E _Ψ will become independent of movement of the MP? The answer is likely to be “Yes.” One such an example is that in which the MP cylinder becomes very long in the direction perpendicular to the membrane [Fig. 1(B)] (i.e., significantly longer than the Debye length at both extra‐membranous ends). In fact, Type‐I receptors (each containing a single TM helix) fit this description well. In this case, a small translational movement of the MP perpendicular to the membrane has nearly no effect on the E _Ψ. Once it becomes MP‐independent, ΔΨ should be considered as being integrally connected to the membrane.

From the above model MPs, two extreme scenarios can be envisaged:

1. The E _Ψ is virtually bound with the rigid‐body MP, and thus the protein cannot sense the electrostatic force.

2. The E _Ψ is totally independent of the movement of the MP. Such a charge‐carrying MP will be able to sense the full electrostatic force from ΔΨ.

An early bioinformatic analysis on MPs suggested that helix‐bundle MPs come in two flavors: those with many TM segments and short connecting loops; and those with few TM segments and large extra‐membranous domains.26 Whether these two groups of MPs respond differently to the ΔΨ remains to be an unanswered question. In addition, many MPs form oligomers that possess a laterally extended, often rather flat, rigid core structure (e.g., the photosynthesis system II,27 TRIC channels,24 and glutamate transporters28). Such an oligomeric core is likely to be resistant to the influence of ΔΔΨ, and thus provides a stable platform for surrounding structural elements to carry out their functionally required conformational changes in addition to promoting co‐operativity. Of course, the categorization based on simplified rigid‐body models should not be taken as a rule. Instead, a real MP is more likely approximated as behaving somewhere between the two extreme scenarios. Importantly, the more flat and more rigid the MP (complex), the more weakly it responses to ΔΨ.

By stating that “a rigid‐body MP cannot sense an electrostatic force,” we do not claim that the electric charge carried by the MP is able to escape the surveillance of the E _Ψ; rather, we aim to emphasize that this interaction cannot cause the entire MP to move as a rigid body along the force lines of E _Ψ. Undoubtedly, an electric field exerts forces on any immersed charges. Each force equals the product of the amount of the charges and the local strength of the electric field (i.e., QE _Ψ). However, because the MP directly affects the E _Ψ, the electrostatic force may be considered as an internal force of the combined ΔΨ‐MP‐charge system. For a rigid body, this extra force must be balanced by other internal forces (including the network of thousands of covalent and non‐covalent bonds); otherwise, the MP would not remain as a rigid body. In addition, a rigid body is an extreme abstraction for the MP, as if the deformation in response to any external force was infinitesimally small. In contrast, a real MP can be assumed to substantially deviate from ideal, rigid‐body behavior. More specifically, the electrostatic force sensed by the embedded charges will most likely cause a certain degree of deformation in the MP. The direction of the conformational change is consistent with a reduction of the potential of the immersed charged group(s): i.e., a positively charged group tends to move toward the negative side of ΔΨ, and a negatively charged group does the opposite. Any mechanism that prohibits ΔΨ‐driven movements will inevitably generate internal stress inside the MP. Such stress is likely to change in both magnitude and distribution with either ΔQ or ΔΔΨ. When the mechanical stress is sufficiently small, the structural deformation can be described using Hook's law, and the overall deformation energy is the integration of local deformation energy over the entire MP.9 In principle, the distribution of deformation energy can be analyzed by using molecular‐dynamics simulation. Similar to the finite element analysis in civil engineering, such analysis of the MP should be able to highlight those “hot” regions likely to undergo rearrangements in response to external forces. Taken together, the interaction between an embedded charge and external ΔΨ is translated into a stress‐causing, internal interaction between the charge‐carrying structural component(s) and the remainder of the MP that integrally connected with ΔΨ.

A topologically sealed membrane is both necessary to maintain the ΔΨ as well as to provide a stage for the MP to perform its function. If ΔΨ is virtually fixed with the membrane (i.e., fully independent of movement of the MP), the requirement of keeping the MP static in the membrane becomes equivalent to an assumption that the electrostatic force is perfectly balanced by the HMF. Only in this case can a charge‐carrying MP be properly described as being immersed in a static field of the E _Ψ, analogous to a floating boat in the ocean in the presence of a gravitational field. In general, however, the balance to the electrostatic force is shared by both the HMF and the internal rigidity of the MP. In other words, the electrostatic force exerted on a given charged group can be conceptually partitioned into two parts: One part is associated with the MP‐dependent ΔΨ and causes internal stress or conformational change inside the host MP. The other part is associated with the MP‐independent ΔΨ, and propagates to the surrounding protein–membrane interface. The existence of internal stress raises a practical concern to a molecular dynamic simulation: If an external electric force is explicitly applied to a charged particle in the MP by using a mean‐field approximation, balanced counter forces must be distributed over the remainder of the simulated MP‐membrane system; otherwise, an unrealistic systematic drift of the whole system would occur. Furthermore, a certain long‐range correlation between a force on a charged group and distal conformational changes within a MP is probably achieved through propagation of such internal stress. For instance, when introducing a single‐point double‐charge substitution, Lys‐to‐Glu, in the extracellular‐side selectivity‐filter region of the Na⁺ channel rNa_V1.4, the gating property in the cytosolic‐side activation‐gate region changes, presumably by pulling the protein toward the extracellular side.29, 30

In general, ΔΨ‐induced deformation in a non‐rigid MP, whether a large or subtle conformational change, is likely to alter its properties such as ligand binding31 and/or enzyme activity.32 In turn, changes of these properties may show complex effects on the overall function of the MP, by either reinforcing or canceling each other. Even for MPs from the same family, the net results of the electrostatic effects can be drastically different from protein to protein. For instance, the G‐protein coupled receptor (GPCR) M₂R showed decreased affinity to its agonist acetylcholine upon depolarization of the ΔΨ, whereas its homolog M₁R appeared to behave in an opposite manner.33 This difference is likely to be (at least partially) caused by an electrostatic force that acts on a cytosolic loop of M₂R containing additional positive charges, toward the cytosolic direction in the presence of a negative‐inside ΔΨ. Such an inward electrostatic force would favor a conformation promoting G‐protein binding and thus enhance the agonist binding. Depolarization would reverse this tendency. Taken together, interactions between the ΔΨ and immersed electric charges are to be assumed to represent a universal phenomenon across all charge‐carrying non‐rigid MPs.

ΔΨ does not rotate with the MP

Another example of MP‐independent ΔΨ is a scenario whereby E _Ψ is integrally connected with the membrane but the MP is able to rotate around an axis not parallel to the membrane normal [Fig. 1(C)]. For simplicity, assuming that the MP is a uniform, isotropic, perfect sphere, the E _Ψ will become completely independent of the orientation of the MP. Because of this dissociation of E _Ψ from the MP, a charged group additionally embedded in the MP (but not at the center) will sense the force from the E _Ψ, which is not aligned co‐linearly with the overall HMF. Together, the two forces generate a torque to rotate the MP until the two forces become co‐linear (i.e., zero torque). Therefore, provided that a MP (or its parts) is able to rotate relative to the E _Ψ, its carried electric charge will be able to convert electrostatic energy into mechanical movement.

Two‐State Rigid‐Body Motion Is a Common Way to Utilize Electrostatic Energy

By using the above simplified models, we introduced two types of MP–ΔΨ relationships, namely (i) a rigid‐body MP remaining static relatively to the E _Ψ and (ii) a MP, no matter rigid or not, able to rock‐and‐roll inside the E _Ψ. In fact, many MPs have evolved to behave using both of these modes in different functional stages. In particular, a MP may exhibit two (or more) distinct states, with each state appearing as a rigid‐body structure. When the external electrostatic force exceeds a threshold value, the internal forces maintaining one state become off‐balance. Consequently, the MP experiences a rapid and large conformational change, thus switching to the other state. (From a thermodynamic point of view, whether the intermediate states consist of rigid bodies is unimportant.) In addition, the stabilizing internal forces are usually those provided by non‐covalent bonds between secondary structures and/or domains. Thus, the state‐transition is often involved in domain rearrangement. Interestingly, the electrostatic force from the ΔΨ can be sufficiently strong to break a disulfide bond, permitting a subsequent large conformational change in the MP, as shown experimentally in the VGIC.34 Recently, an artificially designed, ΔΨ‐driven molecular motor running inside a membrane‐embedded channel was reported to operate using a similar, disulfide‐bond hopping mechanism.35

Many transporters behave as a “two‐state” rigid body, following the alternating access model.36 Such a MP often possesses a surface crevice in each of the two states, and these crevices are alternatingly accessible at either side of the membrane [Fig. 1(D)], as observed in the crystal structures of transporters from the major facilitator superfamily (MFS).37, 38, 39 While the dielectric constant (ε) of the protein roughly equals 1, that of water is ~80. As a result, the E _Ψ becomes stronger in the creviced protein part while approaching zero inside the crevice. Consequently, the contour surfaces of ΔΨ (and the force lines of the E _Ψ) become condensed inside the protein part, forming a so‐called focused electric field [Fig. 1(D)].40 Related to this, a recent study showed that in a sub‐nanometer space the dielectric constant of water becomes smaller than 2 along the direction of narrowing;41 however, the resultant dielectric constant is likely to be anisotropic, and thus this observation is not in conflict with our arguments. In the presence of a crevice and thus of focused E _Ψ, a charged group captured inside the creviced protein will sense a powerful electrostatic force, which, due to reduced thickness of the insulating medium (d < < 3 nm), can become significantly stronger than the 5‐pN value estimated from a uniform E _Ψ. In turn, this transiently strengthened force drives the conformational transition between the two states of the MP. During the conformational switching, the charged group moves across ΔΨ (or a significant portion of ΔΨ), reducing its potential energy. This type of ΔΨ‐driving mechanisms has been proposed for several major families of MPs which are known to be involved in large conformational changes during their functional cycles. For instance, all PMF‐driven, multidrug resistance, secondary active exporters are hypothesized to utilize the same ΔΨ‐driving mechanism (Fig. 2),42 including those from the MFS family,43 multidrug and toxin extrusion (MATE) family,44, 45 small multidrug resistance (SMR) family,46 and resistance nodulation‐cell division (RND)/AcrB family.47 Moreover, as an example of multi‐states MPs, the PMF‐driven, F₁–F_O type of ATP synthase possesses two half‐channels connecting to opposite sides of the membrane.48 Because of the special configuration of the focused electric field between the two half‐channels located within the stator (with force lines more‐or‐less parallel to the membrane plane), the protonatible rotor is driven to rotate continuously within the membrane plane (with the rotation axis parallel to the membrane normal), converting TM electrostatic potential of protons into mechanical energy of the rotor.49, 50

Figure 2.

ΔΨ‐driven conformational changes in MPs. (A) Schematic diagram of the functional cycle of a secondary active transporter. The cationic driving substance is represented as a blue sphere (substrates are omitted for clarity). The electrostatic force (and related torques) is depicted as a blue arrow. Amphipathic helices are depicted as two‐color circles. The functional cycle is driven by alternation of the binding of electric charges, and the charge movement results in an inward activation‐current. (B) Schematic diagram of the activation mechanism of the voltage sensor in a subunit of the VGIC. The intrinsic positive charges in the sensor helix S4 are shown as blue spheres. The activation process is driven by potential depolarization, and the charge movements result in an outward gating‐current. (C) Examples of panel A: crystal structures of lactose permease (LacY) in the inward‐facing conformation and of fucose transporter (FucP) in the outward‐facing conformation. N‐ and C‐domains are in wheat and orange colors, respectively. Entries of interdomain crevices are indicated with pink triangles. Potential protonation sites are marked with red spheres. Amphipathic helices are shown in yellow‐cyan colors. (D) Examples of panel B: crystal structures of the voltage sensor domains of the voltage‐gated Na⁺ channel (Na_VAb)77 in the outward‐facing conformation and of the two‐pore channel (TPC1) in the inward‐facing conformation. S1‐S3 bundle and S4 helix are in wheat and orange colors, respectively. Crevices entries are indicated with pink triangles. Basic residues in S4 are marked with blue spheres.

Furthermore, two subtypes of charge movements can be identified in MPs. First, charge movements that are strictly related to conformational changes are usually called gating charges, as exemplified in the voltage sensors of VGICs during response to ΔΔΨ [Fig. 2(B,D)].13 This subtype of charge movement originates from intrinsic charges (e.g., charged groups covalently attached to the MP) and is reversible when the conformation switches back and forth.51 Here, the charge movement (or gating current) is usually driven by a change of the external ΔΨ, rather than being the source of energy required for the conformational change. Based on electrophysiology experiments, the gating charges of a typical tetrameric VGIC are estimated to be ~10 e₀.52, 53 With a 50‐mV depolarization (ΔΔΨ), the four voltage‐sensor domains release total ~50‐kJ/mol electrostatic energy previously stored in the VGIC to drive the opening of the ion channel.30 Second, ion transfer driving the conformational change (which we define here as activation current) is typically irreversible during a unidirectional functional cycle [Fig. 2(A,C)]. This subtype of charge movement is exemplified by electrogenic transport of secondary transporters and was also proposed to function in the activation of class‐A GPCRs.54 (In transporters, the activation current was called pre‐steady‐state current51; in rhodopsin activation, it was called early‐receptor current.55) The number of driving ions (e.g., protons) consumed in each transport cycle may vary with the type of transporters as well as substrates,56 with each monovalent ion generating ~10‐kJ/mol energy. In principle, gating charges and an activation current may co‐exist in a given MP.

Tool Kits of Common Sensors

At least two types of ΔΨ sensors exist, respectively, based on electric charges and dipoles.57 Effects of other higher order (e.g., quadrupole) electrostatic interactions are usually weaker compared to those of the charge and dipole. In the first category, the best known inducible electric charges are proton‐titratable groups, such as in the acidic amino acids, as well as histidine and cysteine. Their pK _a values are adjustable in response to ligand binding as well as the changes of their micro‐environment, resulting in protonation or deprotonation. In particular, being approached by a negatively charged ligand, an acidic residue, or a hydrogen‐bond acceptor increases the pK _a of the target residue (see e.g., Ref. 58); in contrast, being approached by a positively charged ligand, a basic residue, or a hydrogen‐bond donor decreases the pK _a (see e.g., Refs. 54, 59). Consequently, these titratable groups can be subject to (extra) forces originating from the ΔΨ [Fig. 2(A,C)]. In principle, such proton‐titratable groups can also function as pH sensors in the presence of ΔΨ. This type of proton‐titratable residues are likely to be sensitive to point mutations to their corresponding non‐titratable analogous, namely Asp to Asn, Glu to Gln, and Cys to Ser.60, 61, 62, 63 In addition, binding of ions or charged ligands may also be sensitive to the ΔΨ, inducing conformational changes as long as the time of binding exceeds the duration of the conformation transition. Moreover, positive charges from basic residues are often found in the voltage‐sensor domains of VGICs, where they detect ΔΔΨ13, 64 [Fig. 2(B,D)].

In the second category of sensors, a permanent and/or induced electric dipole may generate a torque in the presence of ΔΨ, thus stimulating a conformational change in the host MP.9 Furthermore, an electric dipole exists in its lowest energy state when it is aligned with the force lines of the strongest E _Ψ. Therefore, this type of sensor most likely functions in those TM regions where the E _Ψ exhibits a strong gradient. For instance, among the 20 natural amino acids, tryptophan is the most polarizable.65 It is highly abundant at the circumference of MPs near the membrane–solvent interface66, 67 where the phosphate head‐groups from the lipid molecules induce a strong non‐uniform local electric field [Fig. 3(A)]. Together with the well‐known hydrophobic interaction of tryptophan residues, the interactions between their electric dipoles and the strong gradient of the local electric field from the lipid head groups contribute to the stability of MPs. Other aromatic residues may also exhibit similar yet smaller induced electric dipole.

Figure 3.

Functional roles of electric dipoles and amphipathic helices. (A) Electric dipoles near the surface of lipid bilayer. Electric field is colored from blue (positive) to red (negative). Inducible dipoles are represented with two‐color diamond shapes. (B) Amphipathic helices on the membrane surface. This schematic diagram depicts two situations, in which either a “vertical” force or a torque may result in “horizontally” sliding movement of the amphipathic helix. Helices are represented as cylinders, and sliding hinge‐points as spheres.

In addition to ΔΨ sensors, MPs often contain a characteristic type of structural elements, namely amphipathic helices (as well as amphipathic β‐hairpins), which reinforce the HMF. Examples include GPCRs,68, 69 MFS transporters,38, 39, 70 RND/AcrB transporters,47, 71 ABC exporters,72 P‐type ATPases,73 proton pumps in respiration complex I,74 VGICs,13 mechanosensitive channels,75 and membrane integral enzymes.76 It appears, among homologous proteins, that amphipathic helices usually lack obviously conserved amino acid sequence. Instead, they maintain a conserved length and a pattern of alternating hydrophobicity in their primary sequences. Often observed on the cytosolic side, these helices are necessarily positioned in the periphery of the MP, with their hydrophobic surface being inserted into the membrane and their hydrophilic surface facing the solvent (Fig. 2). In general, an amphipathic helix will incur an energetic penalty if it moves away from the membrane surface, thus restricting the connected end of the TM helix to sliding only along the surface of the membrane. Moreover, upon applying an electrostatic force, the joint of an amphipathic helix with its connecting TM helix is likely to function as a sliding hinge‐point (or a pivotal point) [Fig. 3(B)], while other structural elements of the TM domain rotate and/or tilt relatively to the membrane. Such sliding hinges appear to be a common structural feature in MPs that require a large conformational change in their functional cycles. They are able to convert a “vertical” force into “horizontal” movements of the terminus of the attaching TM helix.

Concluding Remarks

We argue here that the mesoscopic electrostatic membrane potential ΔΨ strongly influences microscopic charge‐carrying MPs, including their orientations, equilibrium positions, internal structural stress, interdomain conformations, and thus their functions and kinetics. Therefore, drawing conclusions from experiments performed in the absence of ΔΨ, especially from those involved in analysis of kinetics of state‐transition, must be treated with caution.

The simplified rigid‐body models introduced here allow us to discuss the MP‐ΔΨ relationship (e.g., whether they are integrally connected) in more general terms, on the bases of basic principles instead of specific structural information of a given MP. Furthermore, although a real MP may carry multiple electric charges and thus be involved in complex electrostatic interactions, the existence of structurally well‐characterized equilibrium/resting states allows us to focus on a single additional charge (e.g., introduced by protonation or deprotonation) and to study the effects of its interaction with the ΔΨ on the entire MP. In particular, once one equilibrium state maintained by the balance between the electrostatic force and HMF is chosen as the reference point, the subsequent ΔΨ‐related conformational transition can often be described reasonably well using the simplified two‐state rigid‐body model. This methodology may become the basis of discussion of a variety of complex mechanisms and epitomizes the essence of the phenomena occurring during the functional cycles of MPs, which might otherwise be obscured by structural details. We hope that the present overview provides a new yet crucial perspective to better understand the nature of the structure–function relationship of all charge‐carrying MPs.

Conflict of interest

The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported.

Authors’ contribution

Both authors contributed to the research and writing.