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.

Anionic Phospholipids Stabilize RecA Filament Bundles in Escherichia coli.

We characterize the interaction of RecA with membranes in vivo and in vitro and demonstrate that RecA binds tightly to the anionic phospholipids cardiolipin (CL) and phosphatidylglycerol (PG). Using computational models, we identify two regions of RecA that interact with PG and CL: (1) the N-terminal helix and (2) loop L2. Mutating these regions decreased the affinity of RecA to PG and CL in vitro. Using 3D super-resolution microscopy, we demonstrate that depleting Escherichia coli PG and CL altered the localization of RecA foci and hindered the formation of RecA filament bundles. Consequently, E. coli cells lacking aPLs fail to initiate a robust SOS response after DNA damage, indicating that the membrane acts as a scaffold for nucleating the formation of RecA filament bundles and plays an important role in the SOS response.

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.

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.

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.

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.

Cavity hydration dynamics in cytochrome c oxidase and functional implications.

Cytochrome c oxidase (CcO) is a transmembrane protein that uses the free energy of O2 reduction to generate the proton concentration gradient across the membrane. The regulation of competitive proton transfer pathways has been established to be essential to the vectorial transport efficiency of CcO, yet the underlying mechanism at the molecular level remains lacking. Recent studies have highlighted the potential importance of hydration-level change in an internal cavity that connects the proton entrance channel, the site of O2 reduction, and the putative proton exit route. In this work, we use atomistic molecular dynamics simulations to investigate the energetics and timescales associated with the volume fluctuation and hydration-level change in this central cavity. Extensive unrestrained molecular dynamics simulations (accumulatively [Formula: see text]4 [Formula: see text]s) and free energy computations for different chemical states of CcO support a model in which the volume and hydration level of the cavity are regulated by the protonation state of a propionate group of heme a3 and, to a lesser degree, the redox state of heme a and protonation state of Glu286. Markov-state model analysis of [Formula: see text]2-[Formula: see text]s trajectories suggests that hydration-level change occurs on the timescale of 100-200 ns before the proton-loading site is protonated. The computed energetic and kinetic features for the cavity wetting transition suggest that reversible hydration-level change of the cavity can indeed be a key factor that regulates the branching of proton transfer events and therefore contributes to the vectorial efficiency of proton transport.

Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity.

Supramolecular self-assembly enables access to designer soft materials that typically exhibit high-symmetry packing arrangements, which optimize the interactions between their mesoscopic constituents over multiple length scales. We report the discovery of an ionic small molecule surfactant that undergoes water-induced self-assembly into spherical micelles, which pack into a previously unknown, low-symmetry lyotropic liquid crystalline Frank-Kasper σ phase. Small-angle X-ray scattering studies reveal that this complex phase is characterized by a gigantic tetragonal unit cell, in which 30 sub-2-nm quasispherical micelles of five discrete sizes are arranged into a tetrahedral close packing, with exceptional translational order over length scales exceeding 100 nm. Varying the relative concentrations of water and surfactant in these lyotropic phases also triggers formation of the related Frank-Kasper A15 sphere packing as well as a common body-centered cubic structure. Molecular dynamics simulations reveal that the symmetry breaking that drives the formation of the σ and A15 phases arises from minimization of local deviations in surfactant headgroup and counterion solvation to maintain a nearly spherical counterion atmosphere around each micelle, while maximizing counterion-mediated electrostatic cohesion among the ensemble of charged particles.

A simulation method for the phase diagram of complex fluid mixtures.

The phase behavior of complex fluid mixtures is of continuing interest, but obtaining the phase diagram from computer simulations can be challenging. In the Gibbs ensemble method, for example, each of the coexisting phases is simulated in a different cell, and ensuring the equality of chemical potentials of all components requires the transfer of molecules from one cell to the other. For complex fluids such as polymers, successful insertions are rare. An alternative method is to simulate both coexisting phases in a single simulation cell, with an interface between them. The challenge here is that the interface position moves during the simulation, making it difficult to determine the concentration profile and coexisting concentrations. In this work, we propose a new method for single cell simulations that uses a spatial concentration autocorrelation function to (spatially) align instantaneous concentration profiles from different snapshots. This allows one to obtain average concentration profiles and hence the coexisting concentrations. We test the method by calculating the phase diagrams of two systems: the Widom-Rowlinson model and the symmetric blends of freely jointed polymer molecules for which phase diagrams from conventional methods are available. Excellent agreement is found, except in the neighborhood of the critical point where the interface is broad and finite size effects are important. The method is easy to implement and readily applied to any mixture of complex fluids.

Combining Diffusion NMR and Small-Angle Neutron Scattering Enables Precise Measurements of Polymer Chain Compression in a Crowded Environment.

The effect of particles on the behavior of polymers in solution is important in a number of important phenomena such as the effect of "crowding" proteins in cells, colloid-polymer mixtures, and nanoparticle "fillers" in polymer solutions and melts. In this Letter, we study the effect of spherical inert nanoparticles (which we refer to as "crowders") on the diffusion coefficient and radius of gyration of polymers in solution using pulsed-field-gradient NMR and small-angle neutron scattering (SANS), respectively. The diffusion coefficients exhibit a plateau below a characteristic polymer concentration, which we identify as the overlap threshold concentration c^{⋆}. Above c^{⋆}, in a crossover region between the dilute and semidilute regimes, the (long-time) self-diffusion coefficients are found, universally, to decrease exponentially with polymer concentration at all crowder packing fractions, consistent with a structural basis for the long-time dynamics. The radius of gyration obtained from SANS in the crossover regime changes linearly with an increase in polymer concentration, and must be extrapolated to c^{⋆} in order to obtain the radius of gyration of an individual polymer chain. When the polymer radius of gyration and crowder size are comparable, the polymer size is very weakly affected by the presence of crowders, consistent with recent computer simulations. There is significant chain compression, however, when the crowder size is much smaller than the polymer radius gyration.

The effect of crowder charge in a model polymer-colloid system for macromolecular crowding: Polymer structure and dynamics.

We have examined the effect of crowder particle charge on macromolecular structure, studied via small-angle neutron scattering, and translational dynamics, studied via pulsed-field gradient NMR, in addition to bulk viscosity measurements, in a polymer macromolecule (polyethylene glycol)-nanoparticle crowder (polysucrose, Ficoll70) model system, in the case where polymer size and crowder size are comparable. While there are modest effects of crowder charge on polymer dynamics at relatively low packing fractions, there is only a tiny effect at the high packing fractions that represent the limit of molecular crowding. We find, via different measures of macromolecular mobility, that the mobility of the flexible polymer in the crowding limit is 10-100 times larger than that of the compact, spherical crowder in spite of their similar size, implying that the flexible polymer chain is able to squeeze through crowder interstices.

Water Dynamics in Gyroid Phases of Self-Assembled Gemini Surfactants.

Water-mediated ion transport through functional nanoporous materials depends on the dynamics of water confined within a given nanostructured morphology. Here, we investigate H-bonding dynamics of interfacial water within a "normal" (Type I) lyotropic gyroid phase formed by a gemini dicarboxylate surfactant self-assembly using a combination of 2DIR spectroscopy and molecular dynamics simulations. Experiments and simulations demonstrate that water dynamics in the normal gyroid phase is 1 order of magnitude slower than that in bulk water, due to specific interactions between water, the ionic surfactant headgroups, and counterions. Yet, the dynamics of water in the normal gyroid phase are faster than those of water confined in a reverse spherical micelle of a sulfonate surfactant, given that the water pool in the reverse micelle and the water pore in the gyroid phase have roughly the same diameters. This difference in confined water dynamics likely arises from the significantly reduced curvature-induced frustration at the convex interfaces of the normal gyroid, as compared to the concave interfaces of a reverse spherical micelle. These detailed insights into confined water dynamics may guide the future design of artificial membranes that rapidly transport protons and other ions.

Dynamics of water confined in lyotropic liquid crystals: Molecular dynamics simulations of the dynamic structure factor.

The properties of water under confinement are of practical and fundamental interest. In this work, we study the properties of water in the self-assembled lyotropic phases of Gemini surfactants with a focus on testing the standard analysis of quasi-elastic neutron scattering (QENS) experiments. In QENS experiments, the dynamic structure factor is measured and fit to models to extract the translational diffusion constant, D(T), and rotational relaxation time, τ(R). We test this procedure by using simulation results for the dynamic structure factor, extracting the dynamic parameters from the fit as is typically done in experiments, and comparing the values to those directly measured in the simulations. We find that the de-coupling approximation, where the intermediate scattering function is assumed to be a product of translational and rotational contributions, is quite accurate. The jump-diffusion and isotropic rotation models, however, are not accurate when the degree of confinement is high. In particular, the exponential approximations for the intermediate scattering function fail for highly confined water and the values of D(T) and τ(R) can differ from the measured value by as much as a factor of two. Other models have more fit parameters, however, and with the range of energies and wave-vectors accessible to QENS, the typical analysis appears to be the best choice. In the most confined lamellar phase, the dynamics are sufficiently slow that QENS does not access a large enough time scale.

Importance of hydrophobic traps for proton diffusion in lyotropic liquid crystals.

The diffusion of protons in self-assembled systems is potentially important for the design of efficient proton exchange membranes. In this work, we study proton dynamics in a low-water content, lamellar phase of a sodium-carboxylate gemini surfactant/water system using computer simulations. The hopping of protons via the Grotthuss mechanism is explicitly allowed through the multi-state empirical valence bond method. We find that the hydronium ion is trapped on the hydrophobic side of the surfactant-water interface, and proton diffusion then proceeds by hopping between surface sites. The importance of hydrophobic traps is surprising because one would expect the hydronium ions to be trapped at the charged headgroups. The physics illustrated in this system should be relevant to the proton dynamics in other amphiphilic membrane systems, whenever there exist exposed hydrophobic surface regions.

Dynamics of two-dimensional and quasi-two-dimensional polymers.

The dynamic properties of dense two-dimensional (2D) polymer melts are studied using discontinuous molecular dynamics simulations. Both strictly 2D and quasi-2D systems are investigated. The strictly 2D model system consists of a fluid of freely jointed tangent hard disc chains. The translational diffusion coefficient, D, is strongly system size dependent with D ∼ ln L where L is the linear dimension of the square simulation cell. The rotational correlation time, τrot, is, however, independent of system size. The dynamics is consistent with Rouse behavior with D∕ln L ∼ N(-1) and τrot ∼ N(2) for all area fractions. Analysis of the intermediate scattering function, Fs(k, t), shows that the dynamics becomes slow for N = 256 and the area fraction of 0.454 and that there might be a glass transition for long polymers at sufficiently high area fractions. The polymer mobility is not correlated with the conformation of the molecules. In the quasi-2D system hard sphere chains are confined between corrugated surfaces so that chains cannot go over each other or into the surfaces. The conformational properties are identical to the 2D case, but D and τrot are independent of system size. The scaling of D and τrot with N is similar to that of strictly 2D systems. The simulations suggest that 2D polymers are never entangled and follow Rouse dynamics at all densities.

Effect of polydispersity on diffusion in random obstacle matrices.

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D~(φ(c)-φ(m))(µ-ß) for all values of the polydispersity, where φ(m) is the area fraction and φ(c) is the value of φ(m) at the percolation threshold.

Effect of secondary structure on the self-assembly of amphiphilic molecules: a multiscale simulation study.

The self-assembly of amphiphilic molecules is of interest from a fundamental and practical standpoint. There has been recent interest in a class of molecules made from ß-amino acids (which contain an additional backbone carbon atom when compared with natural amino acids). Block copolymers of ß-peptides, where one block is hydrophobic and the other is hydrophilic, self-assemble into micelles. In this work, we use computer simulations to provide insight into the effect of secondary structure on the self-assembly of these molecules. Atomistic simulations for the free energy of association of a pair of molecules show that a homochiral hydrophobic block promotes self assembly compared to a heterochiral hydrophobic block, consistent with experiment. Simulations of a coarse-grained model show that these molecules spontaneously form spherical micelles.