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. 2024 Apr 5;15(15):4047–4055. doi: 10.1021/acs.jpclett.3c03421

Entropy Tug-of-War Determines Solvent Effects in the Liquid–Liquid Phase Separation of a Globular Protein

Saumyak Mukherjee †, Sashary Ramos ‡, Simone Pezzotti ‡, Abhishek Kalarikkal , Tobias M Prass †, Laura Galazzo , Dominik Gendreizig §, Natercia Barbosa §, Enrica Bordignon §,, Martina Havenith ‡,*, Lars V Schäfer †,*
PMCID: PMC11033941  PMID: 38580324

Abstract

graphic file with name jz3c03421_0006.jpg

Liquid–liquid phase separation (LLPS) plays a key role in the compartmentalization of cells via the formation of biomolecular condensates. Here, we combined atomistic molecular dynamics (MD) simulations and terahertz (THz) spectroscopy to determine the solvent entropy contribution to the formation of condensates of the human eye lens protein γD-Crystallin. The MD simulations reveal an entropy tug-of-war between water molecules that are released from the protein droplets and those that are retained within the condensates, two categories of water molecules that were also assigned spectroscopically. A recently developed THz-calorimetry method enables quantitative comparison of the experimental and computational entropy changes of the released water molecules. The strong correlation mutually validates the two approaches and opens the way to a detailed atomic-level understanding of the different driving forces underlying the LLPS.

Recent developments have extended our understanding of the mechanisms of cellular compartmentalization and the associated biological functions: Biomolecular condensates can constitute membraneless organelles and organelle subdomains in biological cells.1−6 These condensates are dense liquid droplets composed of proteins, RNA, and other (bio)molecules, which exhibit dynamic properties and facilitate efficient molecular interactions crucial for specific biochemical processes.7−11 Many biomolecular condensates are formed via liquid–liquid phase separation (LLPS), which has been implicated in the regulation of various cellular processes and also in the formation of pathological aggregates associated with certain diseases.4,12 Condensates formed through LLPS may act as nucleation points for protein aggregates linked to neurodegenerative diseases such as amyotrophic lateral sclerosis, Alzheimer’s, and Parkinson’s.13,14

LLPS research has predominantly focused on elucidating protein–protein and protein–crowder interactions.15 However, many studies have emphasized the significance of water in biomolecular systems.16−18 The interplay between biological macromolecules and water is a mechanistic principle governing many processes, including protein folding, oligomerization, aggregation, ligand binding, and many more.19−24 Therefore, it is highly desirable to gain a comprehensive understanding of the different thermodynamic contributions to biomolecular processes, including those related to solvation.

Hydration thermodynamics have been highlighted as a driving force of LLPS, which leads to the formation of dense protein condensates.25−28Figure 1 schematically illustrates a phase diagram in temperature and protein concentration of a solution with an upper critical solution temperature. Above that temperature, the solution is homogeneous, and the proteins are, on average, uniformly distributed and solvated. Upon a temperature drop down into the coexistence region of the phase diagram (depicted as the yellow dome in Figure 1), the system separates into two phases with different protein concentrations. Consequently, the hydration of the proteins changes, as well. Proteins are in closer proximity in the condensate, and hence, LLPS is associated with the liberation of at least some of the water molecules in the hydration layers of the proteins. These water molecules exit the condensate and are released into the dilute phase. At the same time, a significant fraction of hydration water remains retained in the condensates, where the water molecules experience increasingly strong confinement in the dense environment formed by the proteins (Figure 1).

Figure 1.

Figure 1

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Schematic illustration of liquid–liquid phase separation (LLPS) in a temperature–concentration phase diagram (top). Upon cooling the homogeneous protein solution (green arrow), the yellow region resembling a dome enters and the system phase-separates into two phases, a condensed and a dilute phase. This process involves the release of a portion of hydration water (red) into the dilute phase, while another portion is retained within the protein condensates (blue). The plot at the bottom displays a THz difference spectrum acquired during LLPS. Two distinct spectroscopic signatures emerge, HB-wrap water (depicted in red) at lower frequencies and bound water (shown in blue) at higher frequencies, which are assigned to the released (HB-wrap) and retained (bound) waters, respectively. The amplitude of the signal is employed to quantify the HB-wrap water, while the slope of the curve between 450 and 650 cm–1 is utilized to quantify the bound water.

Due to the complexity of the LLPS process, it is necessary to develop experimental and theoretical tools that can quantitatively probe such changes in hydration water properties upon LLPS. Difference terahertz (THz) spectroscopy is a sensitive and robust tool to study the effect of the hydration water upon LLPS in real-time, as has been shown in the studies of the proteins FUS and elastin.26−28 At the same time, advancements in molecular dynamics (MD) simulations fostered their applications to support experiments and, in many cases, aid their interpretation at the microscopic level, especially also concerning (local) solvation contributions.21,29−32 However, due to the size and complexity of the simulation systems and the associated large computational effort, fully atomistic simulations of biomolecular condensates are scarce and have so far focused on intrinsically disordered proteins (IDPs), as multivalent interactions between such IDPs often drive LLPS.25,33−38

In this work, γD-Crystallin, a globular protein from a family of mammalian proteins that are highly concentrated in the cytoplasm of eye lens cells and are known to undergo LLPS,39−42 is used as a model system to quantify the water entropy involved in LLPS. The experimental THz spectroscopy results are reconciled with the predictions from all-atom MD simulations. The experiments and simulations show a high degree of correlation and support the notion of solvent entropy change as an important thermodynamic contribution for LLPS. A physical model is proposed that explains this contribution, which needs to be considered when aiming to manipulate biomolecular condensation processes.

To comprehensively understand the molecular thermodynamics governing LLPS, it is essential to characterize the water molecules involved in this process (Figure 1). All-atom molecular dynamics (MD) simulations with explicit solvent are a powerful tool to do so, as they enable one to track the motions of individual water molecules with precise spatial and temporal resolution. However, the time scales accessible in MD simulations are significantly shorter than those required to capture the slow LLPS process, thus rendering it impractical to simulate the complete process at the atomistic level.

The objective of this work is to gain insight into the changes in the solvation entropy during LLPS of human γD-Crystallin. As entropy is a state function, it suffices to determine the initial and final states, while characterizing the progression along specific pathways of the transition is not required. Therefore, we carried out MD simulations of multiple homogeneous protein solutions, spanning a concentration range from the dilute phase (25 mg mL–1) to the condensate phase (420 mg mL–1 and beyond, Figure 2). The approach used to estimate the concentrations of the dilute and condensate phases from published experimental data43,44 is outlined in the Supporting Information (SI, Figure S1).

Figure 2.

Figure 2

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Snapshots from MD simulations of γD-Crystallin systems with different concentrations. The systems at 25 mg mL–1 and 420 mg mL–1 are the dilute and condensate phases, respectively.

Figure 3A shows variation in the number of water molecules present in the first protein hydration layer (PHL) as a function of the protein concentration (ρ). The number of PHL water molecules decreases as ρ increases, indicating the release of water from the protein surfaces. Interestingly, at the condensate concentration of 420 mg mL–1, 90% of the PHL is still retained, contributing to the dynamic “liquid-like” nature of the droplets.

Figure 3.

Figure 3

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(A) The number of water molecules in the protein hydration layer (PHL) per protein molecule is plotted as a function of protein concentration, ρ. The PHL is defined as the region within 4 Å of the protein surface. (B) Molar entropy of water in the protein solutions as a function of protein concentration. In A and B, the dilute (ρdil = 25 mg mL–1) and the condensate (ρcond = 420 mg mL–1) phases are indicated by arrows. (C) Number of water molecules released (red squares) and retained (blue circles) per protein molecule in the process of LLPS starting from different initial protein concentrations. (D) Free energy differences, −TΔS (at 273 K), due to water entropy changes associated with γD-Crystallin condensate formation as a function of protein concentration. The red circles and blue hexagons represent contributions from released and retained waters, respectively. The total entropy change is plotted as gray squares (zoom-in shown in the inset). In all panels, the error bars indicate the standard deviations of the three independent trajectories (in some cases, the error bars are smaller than the size of the dots).

While analytical methods are applicable for determining the entropy of solids and gases, no such accurate analytical approach currently exists for the entropy of liquids. Lin et al. introduced the 2-phase-thermodynamics (2PT) method,45 which describes the spectral density of a liquid by a linear combination of a harmonic oscillator component, as applicable to solids, and a hard sphere/rigid rotor component, as applicable to gases. Initially used for liquid argon,45 the 2PT method has since been extended and employed to various liquid systems, including water,46 where 2PT was shown to provide accurate bulk liquid entropies that are in agreement with estimates from rigorous free energy perturbation (FEP) calculations.25,46 Beyond pure water, this method has proven successful in providing quantitative entropy values for a wide range of aqueous systems under diverse conditions.31,47−53 Here, the 2PT method was used to compute the entropy of water in the simulated γD-Crystallin solutions.

Figure 3B shows that the molar entropy of water decreases with an increasing protein concentration. This entropy loss is attributed to the crowded and confined environment encountered by the water molecules at higher concentrations, where the densely packed proteins form a “matrix” that restricts the configuration space volume available to the retained water molecules. Figure 3B may give the fallacious impression that approaching the condensate phase is increasingly disfavored in terms of solvent entropy. However, focusing solely on the entropy of only the retained water provides an incomplete picture as the entropy gain of the water molecules that are released from the condensate into the dilute phase also needs to be considered.

To include the contribution of the released water, the number of water molecules that are released and retained were counted. The number of retained water molecules is constant and defined by the given concentration of the condensate (ρcond = 420 mg mL–1),

graphic file with name jz3c03421_m001.jpg 1

The number of released waters (ΔNreleW) depends on the “initial” protein concentration (ρ), that is, the protein concentration of the (hypothetical) homogeneous solution prior to LLPS (green arrow in Figure 1). To reach the dense phase from a given initial concentration, a number of water molecules are released, corresponding to the difference between the number of waters in the initial system and that in the condensate,

graphic file with name jz3c03421_m002.jpg 2

The concentration dependence of these two categories of water molecules (normalized with respect to the number of protein molecules, NP) is plotted in Figure 3C. While the number of released water molecules decreases with an increasing initial protein concentration, the number of retained waters is constant. Combining these numbers with the molar water entropy values described above yields the solvent entropy changes associated with the release (“rele”) and retention (“reta”)

graphic file with name jz3c03421_m003.jpg 3

In eqs 3, S(ρ) denotes the molar entropy of water in a solution with protein concentration ρ. By construction, ΔSrele(ρ = ρdil) is zero when the (hypothetical) process starts from a protein concentration that corresponds to that of the dilute phase. Likewise, if the phase separation process would start from a protein concentration that already corresponds to that of the condensate phase, no water would be released (ΔNreleW(ρ = ρcond) = 0), and thus ΔSrele = 0 at this concentration as well. In contrast, ΔSreta is zero only for ρ = ρcond. To get the total solvent entropy change, these two individual contributions are summed (eq 4)

graphic file with name jz3c03421_m004.jpg 4

The entropy changes are plotted in Figure 3D. The red curve represents the free energy contribution linked to the entropy change of released water, −TΔSrele(ρ). It is negative (favorable) because upon release into the dilute phase, the water molecules are on average further away from the protein surfaces, where the environment is more bulk-like. This change is determined by a competition between the change in molar entropy (that is, per water molecule) and the number of water molecules released. The maximum in the curve results from these two having opposite trends as a function of protein concentration.

The blue line in Figure 3D shows the contribution due to the retention of water in the condensate. This change is positive (unfavorable) because the water molecules in the condensates experience an increasingly confined environment. Since the number of retained waters is constant, −TΔSreta(ρ) monotonically decreases with increasing protein concentration.

The statistical uncertainties of the computed solvent entropy (error bars in Figure 3D) result from averaging over the large number of water molecules present in the systems, whose dynamics are very fast (in the picosecond range) and thus are fully sampled in the MD simulations. Therefore, the water entropies are obtained under quasi-equilibrium conditions also for the intermediate protein concentrations (Figure 2) that are in the two-phase regime and would slowly undergo phase separation on much longer time scales because the drift during the relatively short simulations is negligible.

One might wonder whether the precise details of the protein arrangement, that is, their orientations and distances, could have an influence on the dynamics of the water molecules and, therefore, on the solvent entropy. The orientational tumbling and translational diffusion of proteins are very slow, especially under high-concentration conditions, and extremely long MD simulations (at the microsecond time scale and beyond) are necessary to capture them.54−59 Here, we have carried out several repeat simulations, each starting from a different random initial arrangement of the protein molecules in the simulation box (see the Computational Methods in SI). While the motions of an individual water molecule might depend on its precise position at a distinct protein interface, such effects are expected to average out when considering the total solvent properties. In this sense, the main global determinant of the solvent entropy is the degree of confinement, as defined by the protein concentration. This expectation is supported by our data, which show that the variation among the three different repeats, each initiated from a different random protein arrangement, is relatively small (error bars in Figure 3).

In summary, the entropy gain of the released water molecules is favorable for the process of condensate formation via LLPS, which is counteracted by the entropy loss of the water molecules that are retained inside the condensate. The net entropy change resulting from this tug-of-war is shown by the gray line in Figure 3D. The −TΔS contribution is favorable above a threshold concentration, which is roughly 120 mg mL–1. At lower concentrations, that is, closer to the dilute phase, the entropy penalty experienced by the retained waters dominates over the entropy gain of the released ones and the solvent entropy change becomes unfavorable. This concentration cannot be interpreted as a threshold for LLPS to be observed because in addition to the solvent entropy contribution, also other important thermodynamic contributions, such as changes in protein–protein interaction energy, protein conformational entropy, etc., also play a role.25 When interpreting the calculated entropy changes in terms of free energy contributions, it is important to consider that the values reported here include both the contributions from protein–water (PW) and from water–water (WW) interactions, ΔS = ΔSPW + ΔSWW. This facilitates the comparison with THz spectroscopy, which probes the total solvent response and cannot distinguish between PW and WW contributions. As originally shown by Ben-Naim,60 only the TΔSPW term contributes to the total ΔG because the energy and entropy terms involving water reorganization compensate each other, ΔEWW – TΔSWW = 0. However, as shown and discussed in our previous work,25 taking the compensating terms into account does not change the sign of the TΔS contributions. Thus, the reported −TΔSrele and −TΔSreta contributions can be interpreted as favorable and unfavorable, respectively.

The distinct hydration populations underlying the entropy tug-of-war predicted by the simulations can be directly probed experimentally via vibrational THz spectroscopy—denoted as THz calorimetry—using a recently introduced ATR spectroscopic sedimentation assay.26,28,61 In a nutshell, difference THz spectra upon LLPS of γD-Crystallin at distinct temperatures were acquired (Figure 4). The protein undergoes temperature-induced LLPS; see the wide field microscopy images of γD-Crystallin at two different temperatures (before and after droplet formation) in Figure S2. We started with a dilute protein solution at a given temperature. Within a period of 1 h, protein condensates form, sink, and cover the ATR crystal. THz difference spectra at a given temperature in Figure 4 show the subsequent changes in absorption between the formed protein condensates which increasingly cover the ATR crystal and the initial solution; see refs (26−28) for more details. Two distinct spectral features are observed in the THz Δα spectra (Figure 4), which are the signatures of two distinct hydration water populations.27,28,61 The first is a decrease in absorption, that is, a negative Δα at ∼150 cm–1, referred to as loss of “cavity-wrap” or “HB-wrap” hydration water contribution. This 150 cm–1 band is a spectroscopic fingerprint of the cavity at hydrophobic patches, that is, the 2-dim H-bond network imposed to make space for the solute. This 2-dim cavity forming hydration bond network has a red-shifted HB stretching frequency compared to the 3-dim bulk network from ∼190 cm–1 (bulk value) to ∼150 cm–1. This partial contribution is an intrinsic part of the solvation process of any solute but is often associated with hydrophobic solvation because cavity formation dominates the free energy cost to solvate hydrophobic molecules. The negative amplitude of the 150 cm–1 band indicates a release of a corresponding population of water molecules into the dilute phase upon LLPS, as also shown in our MD simulations.

Figure 4.

Figure 4

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THz difference spectra generated by the subtraction of the absorption coefficient (α) of the first γD-Crystallin spectrum acquired from that of the final γD-Crystallin spectrum acquired, Δα = αfinal(ν) – αinitial(ν), at each experimental temperature. Evolution of the cavity-wrap water band at 150 cm–1 and in the bound water (slope between 450 and 650 cm–1) is observed with changes in temperature. The spectra shown are averages of at least three independent experiments; the error shown is the standard deviation. The raw absorption spectra for 283 K are shown in Figure S3.

The second spectroscopic contribution, referred to as the “bound water” contribution, was previously assigned to be a signature of hydrophilic solvation and is observed in the 400 and 650 cm–1 range, and is associated with the impact on the librational water band, most sensitive to the hindered reorientation of water when forming a hydrogen bond. Here we observe an almost linear increase in absorption with increasing wavenumber. Such a linear increase was previously shown to originate from water molecules that are directly H-bonded to the protein surface and that has therefore more constrained librational motions (as compared to bulk water). It is quantified by the slope, Δα/Δν, obtained by linearly fitting the spectra in the 450 to 650 cm–1 range.61,62 A positive slope corresponds to a relative increase in the population. Upon condensation, water molecules that are interacting with the protein surface are retained as much as possible. As the protein concentration in the condensate is increased compared to the bulk the experimental observation of an increase in the higher frequency part of the librational mode reflects the retained water population found in the simulations, and specifically with the retention of about 90% of the PHL in the condensate (Figure 3A).

In the following, we leverage over a recently developed THz-calorimetry approach to experimentally quantify the entropic driving force to LLPS due to the released cavity-wrap hydration water population from the measured THz spectra.27,61,63,64 In a nutshell,

graphic file with name jz3c03421_m005.jpg 5

where Δαwrap is the amplitude of the cavity-wrap 150 cm–1 band, obtained from the fit to a damped harmonic oscillator, and ΔS̅wrap = −4.4 J ± 0.3 mol–1 K–1 cm is a linear correlation factor between the spectroscopic and thermodynamic quantities. ΔS̅wrap was previously parametrized based on a large set of solutes.61,63 As ΔS̅wrap was shown to be solute-independent, in THz-calorimetry the changes in hydration entropy are solely determined by Δαwrap. The concept behind this approach is that the variations in the hydration water network that dictate hydration entropy are encoded in the spectroscopic response of hydration water in the low-frequency THz range and not in the correlation factor. The T-dependence of the bound water signal (slope between 450–650 cm–1) is shown in Figure S4.

We focus here on the quantification of the released water contribution, ΔSwrap, which favors LLPS as predicted by the simulations. In previous THz-calorimetry studies,27,28,61 we showed (using an analogous expression to eq 5) that the bound water population that is retained upon LLPS contributes favorably to enthalpy. The entropy penalty of the bound water is ΔS̅bound < 0, in qualitative agreement with the present MD results on the entropy penalty from the retained water.

For the released wrap water, using eq 5, ΔSwrap is linearly correlated to the amplitude of the mode at 150 cm–1, that is, the cavity-wrap spectroscopic feature. We finally obtained TΔSwrap by taking the temperatures of the samples into account (Table 1). When we compare entropy differences from the simulations with the experimentally derived values, we use the concentration of the protein condensate at the given temperature (see the phase diagram in Figure S1).

Table 1. Estimation of the Wrap Water Entropy Changes from THz Spectroscopy.

Temp (K) Fit amplitudea (cm–1) TΔSb (kJ mol–1)
281 –347 ± 13 429 ± 16
283 –348 ± 14 433 ± 17
285 –401 ± 12 503 ± 15
288 –516 ± 19 654 ± 24
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a

The fit amplitudes were obtained from averaging over at least three repeat measurements.

b

Calculated from the fit amplitudes with eq 5.

The agreement between the experimentally derived entropy values and those determined from our simulations (Figure 5) is encouraging. At a quantitative level, both approaches rely on distinct approximations. On the simulation side, the 2PT method was shown in a previous study to provide solvation entropy values lower than standard calorimetry and THz-calorimetry by ∼20% for a small alcohol solute, while it could reproduce the temperature dependence with excellent agreement.64 Moreover, the water force field used is known to slightly underestimate the bulk water entropy at room temperature.25 Furthermore, as described above and detailed in the Supporting Information, we here assume a protein concentration in the condensate of 420 mg/mL, which also has some degree of uncertainty. On the experimental side, as described above (eq 5), ΔS̅wrap is obtained from Δαwrap by multiplication with a scaling factor of −4.4 J mol–1 K–1 cm. This ratio between the amplitude in the THz signature and ΔS̅ was deduced from measurements of alcohol/water mixtures in a temperature range between 270 and 320 K.61,63 It is remarkable that the same spectroscopic feature is observed for other solutes and protein condensates. As detailed in ref (28), the measured spectroscopic response at 150 cm–1 is assigned to wrap water, but there might also be contributions from bound water H-bond stretching bands due to spectral overlap. Furthermore, the coverage of the ATR crystal in our sedimentation assay with protein condensates changes the refractive index (and therefore the penetration depth), which might affect the measured absorption coefficient. The correlation between temperature and protein concentration of the condensate is extrapolated (see SI). Taken together, these factors can explain the remaining differences between THz-calorimetry and MD values. Nevertheless, the correspondence of the deduced values based on two completely independent approaches and the degree of correlation between experiment and simulation show the potential of a synergistic combination of the two methods to capture and understand hydration entropy contributions. Both, experimental and simulation show that the entropy gain due to the release of water from the protein droplets upon LLPS plays a key role in the formation of γD-Crystallin condensates.

Figure 5.

Figure 5

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Entropy change associated with the wrap waters in THz experiments plotted against the same for the released water in MD simulations (Pearson correlation coefficient RP = 0.97). The dashed line is a linear fit to the data. The experimental temperatures and corresponding condensate concentrations are given next to each data point. To map the data from the MD simulations of the different protein concentrations (Table S1 and Figure 2), which were carried out at 273 K, to the different experimental temperatures, the concentrations corresponding to the temperatures were determined from the phase diagram in Figure S1. The entropy contribution due to the released water molecules was then obtained from the set of simulated concentrations by cubic spline interpolation between the data points plotted in Figure 3D. Error bars on the abscissa indicate the standard deviation from the three MD trajectories; error bars on the ordinate are the statistical errors from at least three independent THz experiments.

In summary, we combined atomistic MD simulations and THz spectroscopy to characterize the role of water entropy as a thermodynamic contribution to the condensate formation of a globular protein, the human eye lens protein γD-Crystallin. In this respect, this work is complementary to our previous computational study of an intrinsically disordered protein, the low-complexity domain of the human fused in sarcoma (FUS) protein,25 in which the theoretical framework for MD simulation-based quantification of the different thermodynamic contributions, as used in the present study, was laid out. Both studies support the finding of a tug-of-war between two populations of water molecules. Importantly, the present study reconciles the entropies obtained from MD simulations with those from THz spectroscopy, thereby providing direct experimental support for the theoretical predictions. In our THz spectroscopy experiments, we detected two spectral features associated with the involvement of two distinct categories of hydration water in the LLPS process, “cavity-wrap” and “bound”. These spectral features were mapped to the released and retained water molecules observed in our MD simulations. The entropy tug-of-war between these two classes of hydration water plays a crucial role in the process of LLPS, whereby the released water molecules gain entropy, and the retained waters pay an entropy penalty due to increased confinement in the dense condensate phase. Overall, we find that, beyond a certain protein concentration, the entropy change of the water favors LLPS, and therefore complements additional contributions, for example, from protein–protein interactions, redistribution of ions, protein conformational entropy, and droplet surface tension, which have not been explicitly addressed in this work. The tug-of-war between retained and released water molecules upon condensate formation is demonstrated in the present work for a globular protein (γD-Crystallin) and was previously shown for α-elastin27,28 and for an IDP.25,26 It thus appears to be a rather general feature, which can be transferred to other biomolecular systems that form condensates, including more complex condensates such as protein–RNA coacervates.

Acknowledgments

We thank Benedikt König (Ruhr University Bochum) for help with the experiment and protein handling, Roland Winter (TU Dortmund University) and Matthias Heyden (Arizona State University) for useful discussions, and Prof. Takuji Adachi (University of Geneva) for microscopy support. This project received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 801459 - FP-RESOMUS and was funded by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy - EXC 2033 - 390677874 - RESOLV.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.3c03421.

  • Concentrations of the dilute and the condensate phases of γD-Crystallin from experimental phase diagrams, wide field microscopy images, computational and experimental methods. (PDF)

  • Transparent Peer Review report available (PDF)

Author Present Address

⊥ PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne University, CNRS, 75005 Paris, France

Author Contributions

∥ S.M. and S.R. contributed equally to this work.

The authors declare no competing financial interest.

Supplementary Material

jz3c03421_si_001.pdf (1MB, pdf)
jz3c03421_si_002.pdf (338.7KB, pdf)

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