Arun Yethiraj

We introduce a structural order parameter to determine phase diagrams in complex fluids without particle insertion or specialized simulation ensembles. The order parameter, termed the mean local affinity, is based on the local composition or density surrounding each particle and measures whether a particle resides in a locally homogeneous or heterogeneous environment. We validate the approach on three systems: the Widom–Rowlinson mixture, a symmetric polymer blend, and the Lennard-Jones fluid. In all cases, the mean local affinity exhibits finite-size scaling and yields phase diagrams consistent with established methods. The method relies only on structural information and can therefore be applied as a post-processing tool for complex macromolecular systems where conventional approaches are difficult to implement.

Active particles convert stored energy into directed motion and can display complex emergent behavior arising from non-equilibrium effects. In many cases, e.g., living cells, the environment is complex and heterogeneous. In this work, we investigate a two-dimensional system of soft active Brownian particles (ABPs) in quenched matrices. The matrix induces a clustering of the particles even at low density and activity. However, the nature of clustering is different in regimes of low and high activity. For low activity (Peclet number less than 10), the number of clusters increases with increasing activity and the size of the clusters decreases. The opposite is true for high activity (Peclet number greater than 50). We perform a percolation analysis using a Voronoi construction where the connectedness of empty space depends on the activity. As expected, the percolation threshold is higher for active particles (compared to passive counterparts) because they can push through the matrix. For a fixed time slice, a fraction of particles satisfy all four diagnostic criteria consistent with genuine fractional Brownian motion (FBM), including scale-free velocity correlations. Analysis of long trajectories shows that single particles display FBM-like dynamics for some stretches. Such a behavior is absent for passive particles in a matrix and for active particles without a matrix and suggests a possible physical origin for the particle-to-particle variability observed in single-particle tracking experiments in cellular environments. Polydispersity in the matrix particle size has a quantitative but not qualitative effect on the properties of the ABPs.

A simple mechanism is suggested for the segregation of lipid domains to the poles of bacterial cells. The cell is modeled as a capsule (or spherocylinder), and the lipids are particles that are confined to the surface of the capsule. The lipid particles interact via a short-ranged Lennard-Jones interaction, and single particles are not curvature sensing in any way. When the temperature is decreased, liquid clusters nucleate on the surface. These domains then segregate to the spherical caps of the capsule. The segregation is scale invariant, i.e., it happens whether the capsule is large, of the order or micrometers, or of the order of tens of nanometers, for particles of size ∼1 nm. We propose that the slight energetic preference for the curved regions between next nearest neighbors is sufficient to promote a large scale segregation. The phenomenon is general, i.e., as long as lipids make domains, e.g., rafts, they are predicted to be preferentially found at the poles.

Lithium ion batteries are important in a number of applications, and the demand for Lithium is expected to increase. In typical industrial Li⁺ extraction, brine is pumped to the surface of large reservoirs, followed by chemical treatment. This method requires large quantities of water and can pollute groundwater. There has been considerable interest in developing membranes that can be used for preferential Lithium recovery. It has been suggested that para-toluene sulfonate (PTS) can preferentially bind Li⁺ over other cations. In this work, we study the physical chemistry of Li⁺, Na⁺, and K⁺ binding to solutes in an aqueous solution via combined classical and ab initio molecular dynamics simulations. The solutes we consider are PTS, a trimer of PTS, and 4-(trifluoromethyl)benzenesulfonate (TBS). From the analysis of radial distribution functions and the potential of mean force (PMF), we find that the sulfonate group in the cations has the strongest spatial correlation with Li⁺ followed by Na⁺ and then K⁺. The magnitude of PMF, however, is only of the order of the thermal energy. The correlation between the sulfonate group and Li⁺ can be enhanced by polymerizing the PTS molecule, providing a possible means of extracting Li⁺ from the aqueous phase. For PTS, K⁺ is more strongly correlated with the carbon atoms in the benzene ring than the sulfonate group. This might provide a resolution to the puzzling difference between the behavior of sulfonated polystyrene polymers in the presence of K⁺ and Li⁺ counterions.

Unraveling the relationship between structural information and the dynamic properties of supercooled liquids is one of the great challenges of physics. Dynamic heterogeneity, characterized by the propensity of particles, is often used as a proxy for dynamic slowing. Over the years, significant efforts have been made to capture the structural variations linked to dynamic heterogeneity in supercooled liquids. In this work, we present an innovative unsupervised machine learning protocol based on time-lagged canonical correlation analysis or time-lagged autoencoder to autonomously identify a key order parameter (OP) for the amorphous structures of the Kob-Andersen glass former. The OP is constructed by integrating numerous classical structural descriptors and represents the component with the strongest short-term correlation on a timescale thousands of times shorter than the relaxation time. Strikingly, this OP demonstrates a remarkable correlation with the propensity at long times, significantly outperforming traditional unsupervised models and rivaling supervised models. This demonstrates that fluctuations of structural descriptors contain sufficient information about the long-time dynamic heterogeneity. The most important structural features are the density distributions at mid-range. As a consequence, the OP also exhibits excellent transferability in capturing dynamic heterogeneity across a wide temperature range and greatly facilitates the evaluation of descriptor importance, highlighting its potential for broader application to other glassy systems.

Machine learning methods have been important in the study of phase transitions. Unsupervised methods are particularly attractive because they do not require prior knowledge of the existence of a phase transition. In this work we focus on the constant magnetization Ising model in two (2D) and three (3D) dimensions. While there have been many studies using machine learning for the critical behavior of these systems, we are not aware of any studies for the phase diagram at off-critical magnetizations below the critical temperature. Previous work has used the raw spins as the input feature. We show that a more robust input feature is the local affinity, where the value of the feature at each site is determined by the spin and its neighbors. When coupled with a variational autoencoder, the method is able to predict the phase behavior of the 2D and 3D Ising models (including the critical exponent β) in quantitative agreement with conventional simulations. The choice of activation functions in the autoencoder is crucial, and this requires physical insight into the nature of the phase transition. The method is general and can be applied to any lattice or off-lattice system.

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.

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.

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.