Non-affine deformation analysis and 3D packing defects: A new way to probe membrane heterogeneity in molecular simulations.

Here, we discuss a new framework developed over the last 5 years in our group to probe nanoscale membrane heterogeneity. The framework is based on the idea of characterizing lateral heterogeneity through non-affine deformation (NAD) measurements, transverse heterogeneity through three dimensional (3D) lipid packing defects, and using these approaches to formalize the seemingly trivial correlation between lateral organization and lipid packing in biological membranes. We find that measurements from NAD analysis, a prescription which is borrowed from Physics of glasses and granular material, can faithfully distinguish between liquid-ordered and disordered phases in membranes at molecular length scales and, can also be used to identify phase boundaries with high precision. Concomitantly, 3D-packing defects can not only distinguish between the two co-existing fluid phases based on their molecular scale packing (or membrane free volume), but also provide a route to connect the membrane domains to their functionality, such as exploring the molecular origins of inter-leaflet domain registration and peptide partitioning. The correlation between lateral membrane order and transverse packing presents novel molecular design-level features that can explain functions such as protein/peptide partitioning and small-molecule permeation dynamics in complex and heterogeneous membranes with high-fidelity. The framework allows us to explore the nature of lateral organization and molecular packing as a manifestation of intricate molecular interactions among a chemically rich variety of lipids and other molecules in a membrane with complex membrane composition and asymmetry across leaflets.

Interactions of adsorbing cosolutes with hydrophobic hydration shells.

The analysis of water density fluctuations in the hydration shell of nonpolar solutes provides insights into water-mediated interactions, especially hydrophobic interactions. These fluctuations are sensitive to small perturbations due to changes in thermodynamic conditions, such as temperature and pressure, but also to the presence of cosolutes, such as salts or small organic molecules. Herein, we investigate the effect of two classes of adsorbing cosolutes, using urea and methanol as representatives, on the fluctuations in energy and solvent density within the solvation shell of a model extended hydrophobic solute. We focus on the interactions of the cosolutes with the hydrophobic hydration shell, rather than with the solute itself, which though important remain largely unexplored. We calculate and analyze the interfacial partial molar energy of the cosolute, using a methodology based on the small system method. This approach provides correlated solvent density and energy fluctuations and allows us to decompose them into contributions due to interactions between the different components present in the solvation shell of the solute. The results show that adsorbed urea molecules interact more favorably with water than nonadsorbed urea molecules, which leads to the attenuation of interfacial density fluctuations and thus to the stabilization of the solvation shell. By contrast, the adsorbed methanol molecules interact preferably with other methanol molecules in the solvation shell, leading to a nano-phase segregated structure, which enhances interfacial fluctuations.

Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms.

Salts reduce the pKa of weak acids by a mechanism sensitive to ion identity and concentration via charge screening of the deprotonated state. In this study, we utilize constant pH molecular dynamics simulations to understand the molecular mechanism behind the salt-dependent dissociation of aspartic acid (Asp). We calculate the pKa of Asp in the presence of a monovalent salt and investigate Hofmeister ion effects by systematically varying the ionic radii. We observe that increasing the anion size leads to a monotonic decrease in Asp pKa. Conversely, the cation size affects the pKa nonmonotonically, interpretable in the context of the law of matching water affinity. The net effect of salt on Asp acidity is governed by an interplay of solvation and competing ion interactions. The proposed mechanism is rather general and can be applicable to several problems in Hofmeister ion chemistry, such as pH effects on protein stability and soft matter interfaces.

Dynamical coarse-grained models of molecular liquids and their ideal and non-ideal mixtures.

Coarse-grained (CG) simulation models of condensed-phase systems can be derived with well-established methods that perform coarse-graining in space and provide an effective Hamiltonian with which some of the structural and thermodynamic properties of the underlying fine-grained (FG) reference system can be represented. Coarse-graining in time potentially provides CG models that furthermore represent dynamic properties. However, systematic efforts in this direction have so far been limited, especially for moderately coarse-grained, chemistry-specific systems with complicated conservative interactions. With the aim of representing structural, thermodynamic, and dynamic properties in CG simulations of multi-component molecular systems, we investigated a recently introduced method in which the force on a CG particle originates from conservative interactions with surrounding particles and non-Markovian dissipative interactions, the latter introduced by means of a colored-noise thermostat. We examined two different methods to derive isotropic memory kernels required for integrating the corresponding generalized Langevin equation (GLE) of motion, based on the orthogonal dynamics of the FG forces and on an iterative optimization scheme. As a proof of concept, we coarse-grain single-component molecular liquids (cyclohexane, tetrachloromethane) and ideal and non-ideal binary mixtures of cyclohexane/tetrachloromethane and ethanol/tetrachloromethane, respectively. We find that for all systems, the FG single particle velocity auto-correlation functions and, consequently, both the short time and long time diffusion coefficients can be quantitatively reproduced with the CG-GLE models. We furthermore demonstrate that the present GLE-approach leads to an improved description of the rate with which the spatial correlations decay, which is artificially accelerated in the absence of dissipation.

Lipid packing in biological membranes governs protein localization and membrane permeability.

Plasma membrane (PM) heterogeneity has long been implicated in various cellular functions. However, mechanistic principles governing functional regulations of lipid environment are not well understood due to the inherent complexities associated with the relevant length and timescales that limit both direct experimental measurements and their interpretation. In this context, computer simulations hold immense potential to investigate molecular-level interactions and mechanisms that lead to PM heterogeneity and its functions. Herein, we investigate spatial and dynamic heterogeneity in model membranes with coexisting liquid ordered and liquid disordered phases and characterize the membrane order in terms of the local topological changes in lipid environment using the nonaffine deformation framework. Furthermore, we probe the packing defects in these membranes, which can be considered as the conjugate of membrane order assessed in terms of the nonaffine parameter. In doing so, we formalize the connection between membrane packing and local membrane order and use that to explore the mechanistic principles behind their functions. Our observations suggest that heterogeneity in mixed phase membranes is a consequence of local lipid topology and its temporal evolution, which give rise to disparate lipid packing in ordered and disordered domains. This in turn governs the distinct nature of packing defects in these domains that can play a crucial role in preferential localization of proteins in mixed phase membranes. Furthermore, we observe that lipid packing also leads to contrasting distribution of free volume in the membrane core region in ordered and disordered membranes, which can lead to distinctive membrane permeability of small molecules. Our results, thus, indicate that heterogeneity in mixed phase membranes closely governs the membrane functions that may emerge from packing-related basic design principles.

Protein as evolvable functionally constrained amorphous matter.

We explore current ideas around the representation of a protein as an amorphous material, in turn represented by an abstract graph G with edges weighted by elastic stiffnesses. By embedding this graph in physical space, we can map every graph to a spectrum of conformational fluctuations and responses (as a result of, say, ligandbinding). This sets up a 'genotype-phenotype' map, which we use to evolve the amorphous material to select for fitness. Using this, we study the emergence of allosteric interaction, hinge joint, crack formation and a slide bolt in functional proteins such as adenylate kinase, HSP90, calmodulin and GPCR proteins. We find that these emergent features are associated with specific geometries and mode spectra of floppy or liquid-like regions. Our analysis provides insight into understanding the architectural demands on a protein that enable a prescribed function and its stability to mutations.

How Does Temperature Affect the Dynamics of SARS-CoV-2 M Proteins? Insights from Molecular Dynamics Simulations.

Enveloped viruses, in general, have several transmembrane proteins and glycoproteins, which assist the virus in entry and attachment onto the host cells. These proteins also play a significant role in determining the shape and size of the newly formed virus particles. The lipid membrane and the embedded proteins affect each other in non-trivial ways during the course of the viral life cycle. Unraveling the nature of the protein-protein and protein-lipid interactions, under various environmental and physiological conditions, could therefore prove to be crucial in development of therapeutics. Here, we study the M protein of SARS-CoV-2 to understand the effect of temperature on the properties of the protein-membrane system. The membrane-embedded dimeric M proteins were studied using atomistic and coarse-grained molecular dynamics simulations at temperatures ranging between 10 and 50 °C. While temperature-induced fluctuations are expected to be monotonic, we observe a steady rise in the protein dynamics up to 40 °C, beyond which it surprisingly reverts back to the low-temperature behavior. Detailed investigation reveals disordering of the membrane lipids in the presence of the protein, which induces additional curvature around the transmembrane region. Coarse-grained simulations indicate temperature-dependent aggregation of M protein dimers. Our study clearly indicates that the dynamics of membrane lipids and integral M protein of SARS-CoV-2 enables it to better associate and aggregate only at a certain temperature range (i.e., ~ 30-40 °C). This can have important implications in the protein aggregation and subsequent viral budding/fission processes.

Solvation shell thermodynamics of extended hydrophobic solutes in mixed solvents.

The ability of various cosolutes and cosolvents to enhance or quench solvent density fluctuations at solute-water interfaces has crucial implications on the conformational equilibrium of macromolecules such as polymers and proteins. Herein, we use an extended hydrophobic solute as a model system to study the effect of urea and methanol on the density fluctuations in the solute's solvation shell and the resulting thermodynamics. On strengthening the solute-water/cosolute repulsive interaction, we observe distinct trends in the mutual affinities between various species in, and the thermodynamic properties of, the solvation shell. These trends strongly follow the respective trends in the preferential adsorption of urea and methanol: solute-water/cosolute repulsion strengthens, urea accumulation decreases, and methanol accumulation increases. Preferential accumulation of urea is found to quench the density fluctuations around the extended solute, leading to a decrease in the compressibility of the solvation shell. In contrast, methanol accumulation enhances the density fluctuations, leading to an increase in the compressibility. The mode of action of urea and methanol seems to be strongly coupled to their hydration behavior. The observations from this simple model is discussed in relation to urea driven swelling and methanol induced collapse of some well-known thermo-responsive polymers.

Introducing Memory in Coarse-Grained Molecular Simulations.

Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

Three-Dimensional Packing Defects in Lipid Membrane as a Function of Membrane Order.

Lipid membrane packing defects are considered to be an essential parameter that regulates specific membrane binding of several peripheral proteins. In the absence of direct experimental characterization, lipid packing defects and their role in the binding of peripheral proteins are generally investigated through computational studies, which have been immensely successful in unraveling the key steps of the membrane-binding process. However, packing defects are calculated using two-dimensional (2D) projections and the crucial information on their depths is generally overlooked. Here, we present a simple yet computationally efficient algorithm, which identifies these defects in three dimensions. We validate the algorithm on a number of model membrane systems that are previously studied using 2D defect calculations and find that the defect size and the defect depth may not always be directly correlated. We employ the algorithm to understand the nature of packing defects in flat bilayer membranes exhibiting liquid-ordered (Lo), liquid-disordered (Ld), and co-existing (Lo/Ld) phases. Our results indicate the presence of shallower, smaller, and spatially localized defects in the Lo phase membranes as compared to the defects in Ld and mixed Lo/Ld phase membranes. Such analyses can elucidate the molecular-scale mechanisms that drive the preferential localization of certain proteins to either of the liquid phases or their interface. We also analyze the membrane sensing and anchoring process of a peptide in terms of the three-dimensional defects, which provides additional insights into the process with respect to depth distributions across the bilayer leaflets.

Characterizing Polymer Hydration Shell Compressibilities with the Small-System Method.

The small-system method (SSM) exploits the unique feature of finite-sized open systems, whose thermodynamic quantities scale with the inverse system size. This scaling enables the calculation of properties in the thermodynamic limit of macroscopic systems based on computer simulations of finite-sized systems. We herein extend the SSM to characterize the hydration shell compressibility of a generic hydrophobic polymer in water. By systematically increasing the strength of polymer-water repulsion, we find that the excess inverse thermodynamic correction factor (Δ1/Γs∞) and compressibility (Δχs) of the first hydration shell change sign from negative to positive. This occurs with a concurrent decrease in water hydrogen bonding and local tetrahedral order of the hydration shell water. The crossover lengthscale corresponds to an effective polymer bead diameter of 0.7 nm and is consistent with previous works on hydration of small and large hydrophobic solutes. The crossover lengthscale in polymer hydration shell compressibility, herein identified with the SSM approach, relates to hydrophobic interactions and macromolecular conformational equilibria in aqueous solution. The SSM approach may further be applied to study thermodynamic properties of polymer solvation shells in mixed solvents.

Preferential solvation of p-nitroaniline in a binary mixture of chloroform and hydrogen bond acceptor solvents: the role of specific solute-solvent hydrogen bonding.

Preferential solvation of solvatochromic probe p-nitroaniline (PNA) has been studied in binary mixtures of chloroform with different hydrogen bond acceptor (HBA) solvents using the spectroscopic transition energy (ET). Analyses of the solvatochromic shifts of the absorption spectra of PNA in different neat solvents as a function of the solvent polarity parameters reveal the major contribution from the solvent dipolarity/polarizability and HBA basicity in the solvation of PNA. The event of preferential solvation in the chloroform-HBA binary mixtures and the preference of one solvent above the other in the solvation shell have been attributed to the hydrogen bond donor and acceptor ability of the solvent mixtures. HBA solvents form a strong hydrogen bond with the amino group while chloroform forms a hydrogen bond with the nitro group of PNA. This specific functional group recognition increases the local concentration at specific sites resulting in location specific preferential solvation and synergistic preferential solvation. Solvents with comparable polarity have been found to show significant synergistic behavior as a result of the formation of stronger solvent-solvent hydrogen bonded S1-S2 species. These propositions were found to be supported by theoretical solvation models, calculated HOMO-LUMO energy gaps, the effect of deuterated solvent on the extent of PS, and 1H NMR spectral analyses.

Fluid Phase Coexistence in Biological Membrane: Insights from Local Nonaffine Deformation of Lipids.

Lateral heterogeneities in biomembranes play a crucial role in various physiological functions of the cell. Such heterogeneities lead to demixing of lipid constituents and formation of distinct liquid domains in the membrane. We study lateral heterogeneities in terms of topological rearrangements of lipids to identify the liquid-liquid phase coexistence in model membranes. Using ideas from the physics of amorphous systems and glasses, we calculate the degree of nonaffine deformation associated with individual lipids to characterize the liquid-ordered (Lo) and liquid-disordered (Ld) regions in model lipid bilayers. We explore the usage of this method on all-atom and coarse-grained lipid bilayer trajectories. This method is helpful in defining the instantaneous Lo-Ld domain boundaries in complex multicomponent bilayer systems. The characterization is also used to highlight the effect of line-active molecules on the phase boundaries and domain mixing. Overall, we propose a framework to explore the molecular origin of spatial and dynamical heterogeneity in biomembrane systems, which can be exploited not only in computer simulations but also in experiments.

Molecular Structuring and Percolation Transition in Hydrated Sulfonated Poly(ether ether ketone) Membranes.

The extent of phase separation and water percolation in sulfonated membranes are the key to their performance in fuel cells. Toward this, the effect of hydration on the morphology and transport characteristics of sulfonated poly(ether ether ketone), sPEEK, membrane is investigated using atomistic molecular dynamics simulation at various hydration levels(λ: number of water molecules per sulfonate group). The evolution of local morphology is investigated using structural correlations and minimum pair distances. Transport properties are probed using mean squared displacements and diffusion coefficients. The water-sulfonate interaction in sPEEK is found to be stronger than that in Nafion, as observed in experiments. Analyses indicate the presence of narrow connected path of water and hydronium at λ = 4 and large domains, spanning half the simulation box, at λ = 15. The behavior of membrane water remains far from bulk as indicated by its diffusion coefficient. The persistence of small isolated water clusters demonstrates the extent of phase separation in sPEEK to be lesser than that in Nafion. Analyses at molecular and collective levels suggest the occurrence of a percolation transition between λ = 8 and 10, which leads to a connected network of water channels in the membrane, thereby boosting the hydronium mobility.