Pritam Ganguly

Systematic coarse-graining methods for soft matter simulations - a review

Multiscale modelling of soft matter is an emerging field that has made rapid progress in the past decade. Several methods for systematic coarse-graining of molecular liquids and soft matter systems have been proposed in recent years. Herein, we review these methods and discuss a selected number of applications as well as limitations of the models and remaining challenges in developing representative and transferable pair potentials.

Convergence of Sampling Kirkwood-Buff Integrals of Aqueous Solutions with Molecular Dynamics Simulations.

We discuss two methods for calculating Kirkwood-Buff integrals (KBIs) of aqueous cosolvent solutions from molecular simulations. The first method is based on computing running integrals over radial distribution functions obtained from NVT or NpT simulations. The second, more recent method, originally introduced by Schnell et al. (J. Phys. Chem. B2011, 115, 10911), obtains the KBIs from direct analysis of particle number fluctuations in small, open subvolumes embedded in a larger reservoir as provided by the NVT (NpT) simulation cell. The thermodynamic limit is taken in the first method by using the plateau-values of the running KBIs for large distances, while in the second method an analytical finite-size scaling relation is applied to the KBIs of subvolumes of variable size. We find that direct analysis of particle number fluctuations at small scales provides more precise estimates of KBIs for methanol-water and urea-water solutions. Converged KBIs could, however, not be obtained from nanosecond time scale molecular dynamics simulations with either of the two methods. Based on 0.1 μs simulation trajectories of small and large system sizes time-converged KBIs were obtained with both methods. The running integral method suffers, however, from stronger finite-size artifacts than the sub-box method, also when empirical finite-size tail corrections are applied to the radial distribution functions.

Kirkwood–Buff Coarse-Grained Force Fields for Aqueous Solutions

We present an approach to systematically coarse-grain liquid mixtures using the fluctuation solution theory of Kirkwood and Buff in conjunction with the iterative Boltzmann inversion method. The approach preserves both the liquid structure at pair level and the dependence of solvation free energies on solvent composition within a unified coarse-graining framework. To test the robustness of our approach, we simulated urea-water and benzene-water systems at different concentrations. For urea-water, three different coarse-grained potentials were developed at different urea concentrations, in order to extend the simulations of urea-water mixtures up to 8 molar urea concentration. In spite of their inherent state point dependence, we find that the single-site models for urea and water are transferable in concentration windows of approximately 2 M. We discuss the development and application of these solvent models in coarse-grained biomolecular simulations.

Mutual Exclusion of Urea and Trimethylamine N-Oxide from Amino Acids in Mixed Solvent Environment.

We study the solvation of amino acids in pure-osmolyte and mixed-osmolyte urea and trimethylamine N-oxide (TMAO) solutions using molecular dynamics simulations. Analysis of Kirkwood-Buff integrals between the solution components provides evidence that in the mixed osmolytic solution, both urea and TMAO are mutually excluded from the amino acid surface, accompanied by an increase in osmolyte-osmolyte aggregation. Similar observations are made in simulations of a model protein backbone, represented by triglycine, and suggest that TMAO stabilizes proteins under urea denaturation conditions by effectively removing urea from the protein surface. The effects of the mixed osmolytes on the solvation of the amino acids and the backbone are found to be highly nonlinear in terms of the effects of the individual osmolytes and independent of differences in the strength of the TMAO-water interactions, as observed with different TMAO force fields.

Ion Pairing in Aqueous Electrolyte Solutions with Biologically Relevant Anions

We performed molecular simulations to study ion pairing in aqueous solutions. Our results indicate that ion specific interactions of Li(+), Na(+), and K(+) with the dimethyl phosphate anion are solvent-mediated. The same mechanism applies to carboxylate ions, as has been illustrated in earlier simulations of aqueous alkali acetate solutions. Contact ion pairs play only a minor role--or no role at all--in determining the solution structure and ion specific thermodynamics of these systems. On the basis of the Kirkwood-Buff theory of solution we furthermore show that the well-known reversal of the Hofmeister series of salt activity coefficients, comparing chloride or bromide with dimethyl phosphate or acetate, is caused by changing from a contact pairing mechanism in the former system to a solvent-mediated interaction mechanism in the latter system.

Tau Assembly: The Dominant Role of PHF6 (VQIVYK) in Microtubule Binding Region Repeat R3

Self-aggregation of the microtubule-binding protein Tau reduces its functionality and is tightly associated with Tau-related diseases, termed tauopathies. Tau aggregation is also strongly associated with two nucleating six-residue segments, namely PHF6 (VQIVYK) and PHF6* (VQIINK). In this paper, using experiments and computational modeling, we study the self-assembly of individual and binary mixtures of Tau fragments containing PHF6* (R2/wt; (273)GKVQIINKKLDL(284)) and PHF6 (R3/wt; (306)VQIVYKPVDLSK(317)) and a mutant R2/ΔK280 associated with a neurodegenerative tauopathy. The initial stage of aggregation is probed by ion-mobility mass spectrometry, the kinetics of aggregation monitored with Thioflavin T assays, and the morphology of aggregates visualized by transmission electron microscopy. Insights into the structure of early aggregates and the factors stabilizing the aggregates are obtained from replica exchange molecular dynamics simulations. Our data suggest that R3/wt has a much stronger aggregation propensity than either R2/wt or R2/ΔK280. Heterodimers containing R3/wt are less stable than R3/wt homodimers but much more stable than homodimers of R2/wt and R2/ΔK280, suggesting a possible role of PHF6*-PHF6 interactions in initiating the aggregation of full-length Tau. Lastly, R2/ΔK280 binds more strongly to R3/wt than R2/wt, suggesting a possible mechanism for a pathological loss of normal Tau function.

Representability and Transferability of Kirkwood-Buff Iterative Boltzmann Inversion Models for Multicomponent Aqueous Systems.

We discuss the application of the Kirkwood-Buff iterative Boltzmann inversion (KB-IBI) method for molecular coarse-graining (Ganguly et al. J. Chem. Theory Comput. 2012, 8, 1802) to multicomponent aqueous mixtures. Using a fixed set of effective single-site solvent-solvent potentials previously derived for binary urea-water systems, solute-solvent and solute-solute KB-IBI coarse-grained (CG) potentials have been derived for benzene in urea-water mixtures. Preferential solvation and salting-in coefficients of benzene are reproduced in quantitative agreement with the atomistic force field model. The transferability of the CG models is discussed, and it is shown that free energies of formation of hydrophobic benzene clusters obtained from simulations with the CG model are in good agreement with results obtained from all-atom simulations. The state-point representability of the CG models is discussed with respect to reproducing thermodynamic quantities such as pressure, isothermal compressibility, and preferential solvation. Combined use of KB-IBI and pressure corrections in deriving single-site CG models for pure-water, binary mixtures of urea and water, and ternary mixtures of benzene in urea-water at infinite benzene dilution provides an improved scheme to representing the atomistic pressure and the preferential solvation between the solution components. It is also found that the application of KB-IBI leads to a faster and improved convergence of the pressure and potential energy compared to the IBI method.

Hydrophobic Association in Mixed Urea–TMAO Solutions

The formation of a hydrophobic core is key to the folding and resulting function of most proteins in the cell. In several organisms, as well as in many in vitro experiments, protein folding is modulated by the presence of osmolytes, but the mechanism by which hydrophobic association occurs is not well understood. We present a study of the solvation thermodynamics of hydrophobic self-association in mixed-osmolyte urea-TMAO solutions, with neopentane as a model hydrophobic molecule. Using molecular dynamics simulations and the Kirkwood-Buff theory of solutions, we show that a sensitive balance between the TMAO-water and the TMAO-urea interactions governs the osmolyte-induced changes in hydrophobic association in mixed urea-TMAO solutions. This balance must be correctly incorporated in force-field parametrization because hydrophobic association can be either enhanced or prevented all together by slightly increasing or decreasing the osmolyte-water affinity and osmolyte-osmolyte self-affinity of TMAO molecules.

Enthalpy–Entropy of Cation Association with the Acetate Anion in Water

Negatively charged carboxylate and phosphate groups on biomolecules have different affinity for Na(+) and K(+) ions. We performed molecular simulations and studied the pair potential of mean force between monovalent cations and the carboxylate group of the acetate anion in aqueous solution at 298 K. The simulations indicate that a larger affinity of Na(+) over K(+) in the contact ion pair (CIP) state is of entropic origin with the CIP state becoming increasingly populated at higher temperature. Differences between the osmotic activities of these two ions are however governed by interactions with acetate in the solvent-shared ion pair (SIP) state as was previously shown (Hess, B.; van der Vegt, N. F. A. Proc. Natl. Acad. Sci. U.S.A.2009, 106, 13296). SIP states with Na(+) are slightly more stable than SIP states with K(+), resulting in a smaller osmotic activity of sodium. We discuss the different affinities of Na(+) and K(+) in the SIP state in terms of an enthalpy-entropy reinforcement mechanism which involves a water-mediated hydrogen-bonding interaction between the oppositely charged ions. SIP states are enthalpically favorable and become decreasingly populated at higher temperature.

Signature of an aggregation-prone conformation of tau

The self-assembly of the microtubule associated tau protein into fibrillar cell inclusions is linked to a number of devastating neurodegenerative disorders collectively known as tauopathies. The mechanism by which tau self-assembles into pathological entities is a matter of much debate, largely due to the lack of direct experimental insights into the earliest stages of aggregation. We present pulsed double electron-electron resonance measurements of two key fibril-forming regions of tau, PHF6 and PHF6*, in transient as aggregation happens. By monitoring the end-to-end distance distribution of these segments as a function of aggregation time, we show that the PHF6(*) regions dramatically extend to distances commensurate with extended β-strand structures within the earliest stages of aggregation, well before fibril formation. Combined with simulations, our experiments show that the extended β-strand conformational state of PHF6(*) is readily populated under aggregating conditions, constituting a defining signature of aggregation-prone tau, and as such, a possible target for therapeutic interventions.