Avni Jain

Inverse methods for material design

In this Perspective, we highlight several recent studies that illustrate how inverse strategies using appropriate physical models and computational methods can address complex materials design questions.

Inverse design of simple pairwise interactions with low-coordinated 3D lattice ground states

We demonstrate that inverse statistical mechanical optimization can be used to discover simple (e.g., short-range, isotropic, and convex-repulsive) pairwise interparticle potentials with three-dimensional diamond or simple cubic lattice ground states over a wide range of densities.

Structure, thermodynamics, and position-dependent diffusivity in fluids with sinusoidal density variations.

Molecular dynamics simulations and a stochastic method based on the Fokker-Planck equation are used to explore the consequences of inhomogeneous density profiles on the thermodynamic and dynamic properties of the hard-sphere fluid and supercooled liquid water. Effects of the inhomogeneity length scale are systematically considered via the imposition of sinusoidal density profiles of various wavelengths. For long-wavelength density profiles, bulk-like relationships between local structure, thermodynamics, and diffusivity are observed as expected. However, for both systems, a crossover in behavior occurs as a function of wavelength, with qualitatively different correlations between the local static and dynamic quantities emerging as density variations approach the scale of a particle diameter. Irrespective of the density variation wavelength, average diffusivities of hard-sphere fluids in the inhomogeneous and homogeneous directions are coupled and approximately correlate with the volume available for insertion of another particle. Unfortunately, a quantitatively reliable static predictor of position-dependent dynamics has yet to be identified for even the simplest of inhomogeneous fluids.

Communication: Local structure-mobility relationships of confined fluids reverse upon supercooling

We examine the structural and dynamic properties of confined binary hard-sphere mixtures designed to mimic realizable colloidal thin films. Using computer simulations, governed by either Newtonian or overdamped Langevin dynamics, together with other techniques including a Fokker-Planck equation-based method, we measure the position-dependent and average diffusivities of particles along structurally isotropic and inhomogeneous dimensions of the fluids. At moderate packing fractions, local single-particle diffusivities normal to the direction of confinement are higher in regions of high total packing fraction; however, these trends are reversed as the film is supercooled at denser average packings. Auxiliary short-time measurements of particle displacements mirror data obtained for experimental supercooled colloidal systems. We find that average dynamics can be approximately predicted based on the distribution of available space for particle insertion across orders of magnitude in diffusivity regardless of the governing microscopic dynamics.

Communication: Phase behavior of materials with isotropic interactions designed by inverse strategies to favor diamond and simple cubic lattice ground states

We use molecular simulation to construct equilibrium phase diagrams for two recently introduced model materials with isotropic, soft-repulsive pair interactions designed to favor diamond and simple cubic lattice ground states, respectively, over a wide range of densities [Jain et al., Soft Matter 9, 3866 (2013)]. We employ free energy based Monte Carlo simulation techniques to precisely trace the inter-crystal and fluid-crystal coexistence curves. We find that both model materials display rich polymorphic phase behavior featuring stable crystals corresponding to the target ground-state structures, as well as a variety of other crystalline (e.g., hexagonal and body-centered cubic) phases and multiple reentrant melting transitions.

Tuning structure and mobility of solvation shells surrounding tracer additives

Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction, and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordination-shell structure [Carmer et al., Soft Matter 8, 4083-4089 (2012)]. For the latter case, we show that the mobility of surrounding solvent particles is also increased by addition of the soft repulsive interaction, which helps to rationalize the mechanism underlying the tracers enhanced diffusivity. However, if multiple tracer surfaces are in closer proximity (as at higher tracer concentrations), similar interactions that disrupt local solvation structure instead suppress the position-dependent solvent dynamics.

Communication: Fine discretization of pair interactions and an approximate analytical strategy for predicting equilibrium behavior of complex fluids

We study whether fine discretization (i.e., terracing) of continuous pair interactions, when used in combination with first-order mean-spherical approximation theory, can lead to a simple and general analytical strategy for predicting the equilibrium structure and thermodynamics of complex fluids. Specifically, we implement a version of this approach to predict how screened electrostatic repulsions, solute-mediated depletion attractions, or ramp-shaped repulsions modify the radial distribution function and the potential energy of reference hard-sphere fluids, and we compare the predictions to exact results from molecular simulations.

How Local and Average Particle Diffusivities of Inhomogeneous Fluids Depend on Microscopic Dynamics.

Computer simulations and a stochastic Fokker-Planck equation based approach are used to compare the single-particle diffusion coefficients of equilibrium hard-sphere fluids exhibiting identical inhomogeneous static structure and governed by either Brownian (i.e., overdamped Langevin) or Newtonian microscopic dynamics. The physics of inhomogeneity is explored via the imposition of one-dimensional sinusoidal density profiles of different wavelengths and amplitudes. When imposed density variations are small in magnitude for distances on the scale of a particle diameter, bulk-like average correlations between local structure and mobility are observed. In contrast, when density variations are significant on that length scale, qualitatively different structure-mobility correlations emerge that are sensitive to the governing microscopic dynamics. Correspondingly, a previously proposed scaling between long-time diffusivities for bulk isotropic fluids of particles exhibiting Brownian versus Newtonian dynamics [Pond et al. Soft Matter 2011, 7, 9859-9862] cannot be generalized to describe the position-dependent behaviors of strongly inhomogeneous fluids. While average diffusivities in the inhomogeneous and homogeneous directions are coupled, their qualitative dependencies on inhomogeneity wavelength are sensitive to the details of the microscopic dynamics. Nonetheless, average diffusivities of the inhomogeneous fluids can be approximately predicted for either type of dynamics based on knowledge of bulk isotropic fluid behavior and how inhomogeneity modifies the distribution of available volume. Analogous predictions for average diffusivities of experimental, inhomogeneous colloidal dispersions (based on known bulk behavior) suggest that they will exhibit qualitatively different trends than those predicted by models governed by overdamped Langevin dynamics that do not account for hydrodynamic interactions.

Impact of solvent granularity and layering on tracer hydrodynamics in confinement

Classic hydrodynamic arguments establish that when a spherical tracer particle is suspended between parallel walls, tracer-wall coupling mediated by the solvent will cause the tracer to exhibit position-dependent diffusivity. We investigate how the diffusivity profiles of confined tracers are impacted by the diameter size-ratio of the tracer to solvent: starting from the classic limit of infinite size-ratio (i.e., continuum solvent), we consider size-ratios of four or less to examine how hydrodynamic predictions are disrupted for systems where the tracer and solvent are of similar scale. We use computer simulations and techniques based on the Fokker-Planck formalism to calculate the diffusivity profiles of hard-sphere tracer particles in hard-sphere solvents, focusing on the dynamics perpendicular to the walls. Given wall separations of several tracer diameters, we first consider confinement between hard walls, where anisotropic structuring at the solvent lengthscale generates inhomogeneity in the tracer free-energy landscape and undermines hydrodynamic predictions locally. We then introduce confining planes that we term transparent walls, which restrict tracer and solvent center-accessibilities while completely eliminating static anisotropy, and reveal position-dependent signatures in tracer diffusivity solely attributable to confinement. With or without suppressing static heterogeneity, we find that tracer diffusivity increasingly deviates on a local basis from hydrodynamic predictions at smaller size-ratios. However, hydrodynamic theory still approximately captures spatially-averaged dynamics across the pores even for very small tracer-solvent size-ratios over a wide range of solvent densities and wall separations.

Effects of protein engineering and rational mutagenesis on crystal lattice of single chain antibody fragments

Protein crystallization is dependent upon, and sensitive to, the intermolecular contacts that assist in ordering proteins into a three‐dimensional lattice. Here we used protein engineering and mutagenesis to affect the crystallization of single chain antibody fragments (scFvs) that recognize the EE epitope (EYMPME) with high affinity. These hypercrystallizable scFvs are under development to assist difficult proteins, such as membrane proteins, in forming crystals, by acting as crystallization chaperones. Guided by analyses of intermolecular crystal lattice contacts, two second‐generation anti‐EE scFvs were produced, which bind to proteins with installed EE tags. Surprisingly, although noncomplementarity determining region (CDR) lattice residues from the parent scFv framework remained unchanged through the processes of protein engineering and rational design, crystal lattices of the derivative scFvs differ. Comparison of energy calculations and the experimentally‐determined lattice interactions for this basis set provides insight into the complexity of the forces driving crystal lattice choice and demonstrates the availability of multiple well‐ordered surface features in our scFvs capable of forming versatile crystal contacts. Proteins 2014; 82:1884–1895.