Sensitive and selective polymer condensation at membrane surface driven by positive co-operativity.

Biomolecular phase separation has emerged as an essential mechanism for cellular organization. How cells respond to environmental stimuli in a robust and sensitive manner to build functional condensates at the proper time and location is only starting to be understood. Recently, lipid membranes have been recognized as an important regulatory center for biomolecular condensation. However, how the interplay between the phase behaviors of cellular membranes and surface biopolymers may contribute to the regulation of surface condensation remains to be elucidated. Using simulations and a mean-field theoretical model, we show that two key factors are the membrane's tendency to phase-separate and the surface polymer's ability to reorganize local membrane composition. Surface condensate forms with high sensitivity and selectivity in response to features of biopolymer when positive co-operativity is established between coupled growth of the condensate and local lipid domains. This effect relating the degree of membrane-surface polymer co-operativity and condensate property regulation is shown to be robust by different ways of tuning the co-operativity, such as varying membrane protein obstacle concentration, lipid composition, and the affinity between lipid and polymer. The general physical principle emerged from the current analysis may have implications in other biological processes and beyond.

Importance of feature construction in machine learning for phase transitions.

Machine learning is an important tool in the study of the phase behavior from molecular simulations. In this work, we use un-supervised machine learning methods to study the phase behavior of two off-lattice models, a binary Lennard-Jones (LJ) mixture and the Widom-Rowlinson (WR) non-additive hard-sphere mixture. The majority of previous work has focused on lattice models, such as the 2D Ising model, where the values of the spins are used as the feature vector that is input into the machine learning algorithm, with considerable success. For these two off-lattice models, we find that the choice of the feature vector is crucial to the ability of the algorithm to predict a phase transition, and this depends on the particular model system being studied. We consider two feature vectors, one where the elements are distances of the particles of a given species from a probe (distance-based feature) and one where the elements are +1 if there is an excess of particles of the same species within a cut-off distance and -1 otherwise (affinity-based feature). We use principal component analysis and t-distributed stochastic neighbor embedding to investigate the phase behavior at a critical composition. We find that the choice of the feature vector is the key to the success of the unsupervised machine learning algorithm in predicting the phase behavior, and the sophistication of the machine learning algorithm is of secondary importance. In the case of the LJ mixture, both feature vectors are adequate to accurately predict the critical point, but in the case of the WR mixture, the affinity-based feature vector provides accurate estimates of the critical point, but the distance-based feature vector does not provide a clear signature of the phase transition. The study suggests that physical insight into the choice of input features is an important aspect for implementing machine learning methods.

Chemically realistic coarse-grained models for polyelectrolyte solutions.

Polyelectrolyte solutions are of considerable scientific and practical importance. One of the most widely studied polymer is polystyrene sulfonate (PSS), which has a hydrophobic backbone with pendant charged groups. A polycation with similar chemical structure is poly(vinyl benzyltri methyl) ammonium (PVBTMA). In this work, we develop coarse-grained (CG) models for PSS and PVBTMA with explicit CG water and with sodium and chloride counterions, respectively. We benchmark the CG models via a comparison with atomistic simulations for single chains. We find that the choice of the topology and the partial charge distribution of the CG model, both play a crucial role in the ability of the CG model to reproduce results from atomistic simulations. There are dramatic consequences, e.g., collapse of polyions, with injudicious choices of the local charge distribution. The polyanions and polycations exhibit a similar conformational and dynamical behavior, suggesting that the sign of the polyion charge does not play a significant role.

Fast estimation of ion-pairing for screening electrolytes: A cluster can approximate a bulk liquid.

The propensity for ion-pairing can often dictate the thermodynamic and kinetic properties of electrolyte solutions. Fast and accurate estimates of ion-pairing can thus be extremely valuable for supplementing design and screening efforts for novel electrolytes. We introduce an efficient cluster model to estimate the local ion-pair potential-of-mean-force between ionic solutes in electrolytes. The model incorporates an ion-pair and a few layers of explicit solvent in a gas-phase cluster and leverages an enhanced sampling approach to achieve high efficiency and accuracy. We employ harmonic restraints to prevent solvent escape from the cluster and restrict sampling of large inter-ion distances. We develop a cluster ion-pair sampling tool that implements our cluster model and demonstrate its potential utility for screening simple and poly-electrolyte systems.

Effect of diffusion constant on the morphology of dendrite growth in lithium metal batteries.

Lithium dendrites can lead to a short circuit and battery failure, and developing strategies for their suppression is of considerable importance. In this work, we study the growth of dendrites in a simple model system where the solvent is a continuum and the lithium ions are hard spheres that can deposit by sticking to existing spheres or the electrode surface. Using stochastic dynamics simulations, we investigate the effect of applied voltage and diffusion constant on the growth of dendrites. We find that the diffusion constant is the most significant factor, and the inhomogeneity of the electric field does not play a significant role. The growth is most pronounced when the applied voltage and diffusion constant are both low. We observe a structural change from broccoli to cauliflower shape as the diffusion constant is increased. The simulations suggest that a control of electrolyte parameters that impact lithium diffusion might be an attractive route to controlling dendrite growth.

Deep Eutectic Solvents: Molecular Simulations with a First-Principles Polarizable Force Field.

The unique properties of deep eutectic solvents make them useful in a variety of applications. In this work we develop a first-principles force field for reline, which is composed of choline chloride and urea in the molar ratio 1:2. We start with the symmetry adapted perturbation theory (SAPT) protocol and then make adjustments to better reproduce the structure and dynamics of the liquid when compared to first-principles molecular dynamics (FPMD) simulations. The resulting force field is in good agreement with experiments in addition to being consistent with the FPMD simulations. The simulations show that primitive molecular clusters are preferentially formed with choline-chloride ionic pairs bound with a hydrogen bond in the hydroxyl group and that urea molecules coordinate the chloride mainly via the trans-H chelating hydrogen bonds. Incorporating polarizability qualitatively influences the radial distributions and lifetimes of hydrogen bonds and affects long-range structural order and dynamics. The polarizable force field predicts a diffusion constant about an order of magnitude larger than the nonpolarizable force field and is therefore less computationally intensive. We hope this study paves the way for studying complex hydrogen-bonding liquids from a first-principles approach.

Why Lithium Ions Stick to Some Anions and Not Others.

Designing battery electrolytes for lithium-ion batteries has been a topic of extensive research for decades. The ideal electrolyte must have a large conductivity as well as high Li+ transference number. The conductivity is very sensitive to the nature of the anions and dynamical correlations between ions. For example, lithium bis(trifluoromethane)sulfonimide (LiTFSI) has a large conductivity, but the chemically similar lithium trifluoromethanesulfonate (LiOTf) shows poor conductivity. In this work, we study the binding of Li+ to these anions in an ethylene carbonate (EC) solvent using enhanced sampling metadynamics. The evaluated free energies display a large dissociation barrier for LiOTf compared to LiTFSI, suggesting long-lived ion-pair formation in the former but not the latter. We probe these observations via unbiased molecular dynamics simulations and metadynamics simulations of TFSI with a hypothetical OTF-like partial charge model indicating an electrostatic origin for those differences. Our results highlight the deleterious impact of sulfonate groups in lithium-ion battery electrolytes and provide a new basis for the assessment of electrolyte designs.

Liquid-Liquid Phase Separation As the Second Step of Complex Coacervation.

Liquid-liquid phase separation (LLPS) between tyrosine- and arginine-rich peptides are of biological importance. To understand the interactions between proteins in the condensed phase in close analogy to complex coacervation, we run multiple umbrella calculations between oligomers containing tyrosine (pY) and arginine (pR). We find pR-pY complexation to be energetically driven. Metadynamics simulations on monomers suggest that this energy of complexation is correlated with the number of π-cation bonds. Free energy calculations for the binding between pairs of poly glutamate-pR dimers show striking similarities between this process and LLPS. These calculations suggest that proteins containing arginine and tyrosine residues do not undergo complexation followed by coacervation. The mechanism, rather, is akin to phase separation of neutral polyion pairs.

Phase Behavior of Poly(ethylene oxide) in Room Temperature Ionic Liquids: A Molecular Simulation and Deep Neural Network Study.

The phase behavior of polymers in room temperature ionic liquids is a topic of considerable interest. In this work we study the phase diagram of poly(ethylene oxide) in four imidazolium ionic liquids (ILs) using molecular simulation. We develop united atom models for 1-butyl-2,3-dimethylimidazolium ([BMMIM]), 1-ethyl-2,3-dimethylimidazolium ([EMMIM]), and 1-ethyl-3-methylimidazolium ([EMIM]) in an analogous fashion to previously developed models for 1-butyl-3-methylimidazolium ([BMIM]) and tetrafluoroborate ([BF4]) using symmetry-adapted perturbation theory. At high temperatures we obtain the coexistence concentrations using an interface method where the polymer and IL are simulated in a large elongated box, and an interface between coexisting phases is formed. At lower temperatures we use a deep neural network (DNN) method. The input descriptors for the DNN are the cohesive energy of mixing, the volume change of mixing, and the coordination numbers between cation and polymer, all of which are obtained from simulations of mixed systems at a series of temperatures. The DNN is trained by using the phase-separated systems at high temperatures and a mixed phase at low temperatures. The method predicts a lower critical solution temperature which decreases as the alkyl chain length on the cation is decreased, consistent with experiment. The simulations show that methylation of the cation has little effect on the phase diagram. This is in contrast to what is seen in experiments but could be because the polymer chains in the simulations are too short. At low temperatures the chains display two conformational motifs, namely a crown ether conformation and a ring conformation, each of which can wrap the chain around a single cation. This provides the entropic penalty for mixing and a reason for demixing as the temperature is raised. Such conformations might not be possible for longer chains. The combination of data-driven techniques and molecular simulation shows promise in the study of the phase behavior and physical properties of complex fluids.

A Transferable Polarizable Force Field for Urea Crystals and Aqueous Solutions.

Urea is an important chemical with many biological and industrial applications. In this work, we develop a first-principles polarizable force field for urea crystals and aqueous solutions within the symmetry-adapted perturbation theory (SAPT) protocol with the SWM4-NDP model for water. We make three adjustments to the SAPT force field protocol: We augment the carbonyl oxygen atom of urea with additional interaction sites in order to address the "chelated" bent double hydrogen bonds in urea, we reduce the polarizability of urea by a factor of 0.70 to reproduce experimental in-crystal dipole moments, and we re-fit atomic pre-exponential parameters to correct the predicted liquid structure. We find that the resulting force field is in good agreement for the static and dynamic properties of aqueous urea solutions when compared to experiment or first-principles molecular dynamics simulations. The polarizable urea model accurately reproduces the crystal-solution phase diagram in the temperature range of 261 to 310 K; for which, it is superior to non-polarizable models. We expect that this force field will be useful in the modeling of complex biomolecular systems and enable studies of polarizability effects of solid-liquid phase behavior of complex fluids.

Solvation Induced Ring Puckering Effect in Fluorinated Prolines and Its Inclusion in Classical Force Fields.

Strategic incorporation of fluorinated prolines can accelerate folding and increase thermal stability of proteins. It has been suggested that this behavior emerges from puckering effects induced by fluorination of the proline ring. We use electronic structure calculations to characterize the potential energy surface (PES) along puckering coordinates for a simple dipeptide model of proline and its fluorinated derivatives. Significant shifts in puckering trends between gas phase and implicit solvent calculations shed light on the effect of solvation on electronic structure and conformational preferences of the ring. This solvation induced puckering effect is previously unknown in the context of prolines. The PES based on implicit solvent is then utilized to construct a correction for a classical force field. The corrected force field accurately captures the experimental conformational equilibrium including the coupling between ring puckering and cis-trans isomerism in fluorinated prolines. This method can be extended to other rings and substituents besides fluorine.

Nematic ordering of hard rods under strong confinement in a dense array of nanoposts.

The effect of confinement on the behavior of liquid crystals is interesting from a fundamental and practical standpoint. In this work, we report Monte Carlo simulations of hard rods in an array of hard nanoposts, where the surface-to-surface separations between nanoposts are comparable to or less than the length of hard rods. This particular system shows promise as a means of generating large-scale organization of the nematic liquid by introducing an entropic external field set by the alignment of nanoposts. The simulations show that nematic ordering of hard rods is enhanced in the nanopost arrays compared with that in bulk, in the sense that the nematic order is significant even at low concentrations at which hard rods remain isotropic in bulk, and the enhancement becomes more significant as the passage width between two nearest nanoposts decreases. An analysis of local distribution of hard-rod orientations at low concentrations with weak nematic ordering reveals that hard rods are preferentially aligned along nanoposts in the narrowing regions between two curved surfaces of nearest nanoposts; hard rods are less ordered in the passages and in the centers of interpost spaces. It is concluded that at low concentrations the confinement in a dense array of nanoposts induces the localized nematic order first in the narrowing regions and, as the concentration further increases, the nematic order spreads over the whole region. The formation of a well-ordered phase at low concentrations of hard rods in a dense array of nanoposts can provide a new route to the low-concentration preparation of nematic liquid crystals that can be used as anisotropic dispersion media.

Driving Force for the Complexation of Charged Polypeptides.

The phase separation of oppositely charged polyelectrolytes in solution is of current interest. In this work, we study the driving force for polyelectrolyte complexation using molecular dynamics simulations. We calculate the potential of mean force between poly(lysine) and poly(glutamate) oligomers using three different force fields, an atomistic force field and two coarse-grained force fields. There is qualitative agreement between all force fields, i.e., the sign and magnitude of the free energy and the nature of the driving force are similar, which suggests that the molecular nature of water does not play a significant role. For fully charged peptides, we find that the driving force for association is entropic in all cases when small ions either neutralize the poly ions, or are in excess. The removal of all counterions switches the driving force, making complexation energetic. This suggests that the entropy of complexation is dominated by the counterions. When only 6 residues of a 11-mer are charged, however, the driving force is energetic in the abscence of excess salt. The simulations shed insight into the mechanism of complex coacervation and the importance of realistic models for the polyions.

Phase behavior of continuous-space systems: A supervised machine learning approach.

The phase behavior of complex fluids is a challenging problem for molecular simulations. Supervised machine learning (ML) methods have shown potential for identifying the phase boundaries of lattice models. In this work, we extend these ML methods to continuous-space systems. We propose a convolutional neural network model that utilizes grid-interpolated coordinates of molecules as input data of ML and optimizes the search for phase transitions with different filter sizes. We test the method for the phase diagram of two off-lattice models, namely, the Widom-Rowlinson model and a symmetric freely jointed polymer blend, for which results are available from standard molecular simulations techniques. The ML results show good agreement with results of previous simulation studies with the added advantage that there is no critical slowing down. We find that understanding intermediate structures near a phase transition and including them in the training set is important to obtain the phase boundary near the critical point. The method is quite general and easy to implement and could find wide application to study the phase behavior of complex fluids.

Proper Thermal Equilibration of Simulations with Drude Polarizable Models: Temperature-Grouped Dual-Nosé-Hoover Thermostat.

An explicit treatment of electronic polarization is critically important to accurate simulations of highly charged or interfacial systems. Compared to the iterative self-consistent field (SCF) scheme, extended Lagrangian approaches are computationally more efficient for simulations that employ a polarizable force field. However, an appropriate thermostat must be chosen to minimize heat flow and ensure an equipartition of kinetic energy among all unconstrained system degrees of freedom. Here we investigate the effects of different thermostats on the simulation of condensed phase systems with the Drude polarizable force field using several examples that include water, NaCl/water, acetone, and an ionic liquid (IL) BMIM+/BF4-. We show that conventional dual-temperature thermostat schemes often suffer from violations of equipartitioning and adiabatic electronic state, leading to considerable errors in both static and dynamic properties. Heat flow from the real degrees of freedom to the Drude degrees of freedom leads to a steady temperature gradient and puts the system at an incorrect effective temperature. Systems with high-frequency internal degrees of freedom such as planar improper dihedrals or C-H bond stretches are most vulnerable; this issue has been largely overlooked in the literature because of the primary focus on simulations of rigid water molecules. We present a new temperature-grouped dual-Nosé-Hoover thermostat, where the molecular center of mass translations are assigned to a temperature group separated from the rest degrees of freedom. We demonstrate that this scheme predicts correct static and dynamic properties for all the systems tested here, regardless of the thermostat coupling strength. This new thermostat has been implemented into the GPU-accelerated OpenMM simulation package and maintains a significant speedup relative to the SCF scheme.

Influence of Charge Scaling on the Solvation Properties of Ionic Liquid Solutions.

Scaled-charge force fields (FFs) are widely employed in the simulation of neat ionic liquids (ILs), where the charges on the ions are empirically scaled to approximately account for electronic polarization and/or charge transfer. Such charge scaling has been found to yield significant improvement in liquid-state thermodynamic and dynamic properties (when compared to experiment). However, the mean field approximation inherent in charge scaling becomes suspect when applied to IL mixtures or solutions. In this work, we simulate solutions of IL with various nonpolar and polar gas solutes and compare results of charge-scaled and polarizable FFs to experiment. Our results demonstrate that scaling of the Coulomb interaction inherent in scaled-charge FFs leads to an underestimation of the solute-solvent electrostatic interaction and thus also the enthalpy and free energy of solvation; this effect is particularly pronounced for polar solutes. In some cases, we find that this artificial reduction in the solute-solvent interaction can also alter the apparent phase behavior of the resulting solution. Overall, the totality of our results suggests that explicit polarization (rather than charge scaling) is likely necessary to provide high transferability to both neat IL and IL mixtures and solutions.

Understanding the Properties of Ionic Liquids: Electrostatics, Structure Factors, and Their Sum Rules.

The properties of room-temperature ionic liquids (ILs) may be viewed as resulting from a balance of electrostatic interactions that can be tuned at short range but constrained to satisfy universal, asymptotic screening conditions. Short-range interactions and ion packing provide ample opportunity for chemical tunability, while asymptotic sum rules dictate that the long-range structure and charge oscillation be similar to those of molten alkali halide salts. In this work, we study the structure factors and long-range electrostatic interactions in six ILs. The cation in all cases is 1-butyl-3-methylimidazolium (BMIM+), and we study six anions, namely, tetrafluoroborate (BF4-), hexafluorophosphate (PF6-), nitrate (NO3-), triflate (CF3SO3-), bisfluorosulfonylimide [(FSO2)2N-], and bistriflimide [(CF3SO2)2N-]. To gain insight, we perform similar computer simulations of a primitive molten salt model with and without electronic polarization. We emphasize universal similarities among ionic liquids and molten salts in the long-range ion ordering and the influence of electronic polarization on the screening conditions while also characterizing important differences in the short-range electrostatic interactions. We show that polarization systematically reduces charge oscillations by as much as ∼0.5-1 ion per radial shell, which we argue is general to all room-temperature ILs as well as molten salts. We suggest that a fundamentally important distinction among BMIM-based ionic liquids (with different anions) is the nature of the midrange, ∼1 Å-1 peak in the charge-correlation structure factor; while this correlation is straightforward to analyze in computer simulations, it may often be hidden in X-ray and/or neutron scattering structure factors.