Computation of high-order virial coefficients in high-dimensional hard-sphere fluids by Mayer sampling

<div><p>The Mayer sampling method was used to compute the virial coefficients of high-dimensional hard-sphere fluids. The first 64 virial coefficients for dimensions 12 < <i>D</i> ⩽ 100 were obtained to high precision, and several lower dimensional virial coefficients were computed. The radii of convergence of the virial series in 13, 15, 17 and 19 dimensions agreed well with the analytical results from the Percus–Yevick closure.</p></div

Sequence Affects the Cyclization of DNA Minicircles

Understanding how the sequence of a DNA molecule affects its dynamic properties is a central problem affecting biochemistry and biotechnology. The process of cyclizing short DNA, as a critical step in molecular cloning, lacks a comprehensive picture of the kinetic process containing sequence information. We have elucidated this process by using coarse-grained simulations, enhanced sampling methods, and recent theoretical advances. We are able to identify the types and positions of structural defects during the looping process at a base-pair level. Correlations along a DNA molecule dictate critical sequence positions that can affect the looping rate. Structural defects change the bending elasticity of the DNA molecule from a harmonic to subharmonic potential with respect to bending angles. We explore the subelastic chain as a possible model in loop formation kinetics. A sequence-dependent model is developed to qualitatively predict the relative loop formation time as a function of DNA sequence

Examining the Assumptions Underlying Continuum-Solvent Models

Continuum-solvent models (CSMs) have successfully predicted many quantities, including the solvation-free energies (Δ<i>G</i>) of small molecules, but they have not consistently succeeded at reproducing experimental binding free energies (ΔΔ<i>G</i>), especially for protein–protein complexes. Several CSMs break Δ<i>G</i> into the free energy (Δ<i>G</i>_vdw) of inserting an uncharged molecule into solution and the free energy (Δ<i>G</i>_el) gained from charging. Some further divide Δ<i>G</i>_vdw into the free energy (Δ<i>G</i>_rep) of inserting a nearly hard cavity into solution and the free energy (Δ<i>G</i>_att) gained from turning on dispersive interactions between the solute and solvent. We show that for 9 protein–protein complexes neither Δ<i>G</i>_rep nor Δ<i>G</i>_vdw was linear in the solvent-accessible area <i>A</i>, as assumed in many CSMs, and the corresponding components of ΔΔ<i>G</i> were not linear in changes in <i>A</i>. We show that linear response theory (LRT) yielded good estimates of Δ<i>G</i>_att and ΔΔ<i>G</i>_att, but estimates of ΔΔ<i>G</i>_att obtained from either the initial or final configurations of the solvent were not consistent with those from LRT. The LRT estimates of Δ<i>G</i>_el differed by more than 100 kcal/mol from the explicit solvent model’s (ESM’s) predictions, and its estimates of the corresponding component (ΔΔ<i>G</i>_el) of ΔΔ<i>G</i> differed by more than 10 kcal/mol. Finally, the Poisson–Boltzmann equation produced estimates of Δ<i>G</i>_el that were correlated with those from the ESM, but its estimates of ΔΔ<i>G</i>_el were much less so. These findings may help explain why many CSMs have not been consistently successful at predicting ΔΔ<i>G</i> for many complexes, including protein–protein complexes

Solute–Solvent Energetics Based on Proximal Distribution Functions

We consider the hydration structure and thermodynamic energetics of solutes in aqueous solution. On the basis of the dominant local correlation between the solvent and the chemical nature of the solute atoms, proximal distribution functions (pDF) can be used to quantitatively estimate the hydration pattern of the macromolecules. We extended this technique to study the solute–solvent energetics including the van der Waals terms representing excluded volume and tested the method with butane and propanol. Our results indicate that the pDF-reconstruction algorithm can reproduce van der Waals solute–solvent interaction energies to useful kilocalorie per mole accuracy. We subsequently computed polyalanine–water interaction energies for a variety of conformers, which also showed agreement with the simulated values

Effects of Conformational Constraint on Peptide Solubility Limits

Liquid–liquid phase separation of proteins preferentially involves intrinsically disordered proteins or disordered regions. Understanding the solution chemistry of these phase separations is key to learning how to quantify and manipulate systems that involve such processes. Here, we investigate the effect of cyclization on the liquid–liquid phase separation of short polyglycine peptides. We simulated separate aqueous systems of supersaturated cyclic and linear GGGGG and observed spontaneous liquid–liquid phase separation in each of the solutions. The cyclic GGGGG phase separates less robustly than linear GGGGG and has a higher aqueous solubility, even though linear GGGGG has a more favorable single molecule solvation free energy. The versatile and abundant interpeptide contacts formed by the linear GGGGG stabilize the condensed droplet phase, driving the phase separation in this system. In particular, we find that van der Waals close contact interactions are enriched in the droplet phase as opposed to electrostatic interactions. An analysis of the change in backbone conformational entropy that accompanies the phase transition revealed that cyclic peptides lose significantly less entropy in this process as expected. However, we find that the enhanced interaction enthalpy of linear GGGGG in the droplet phase is enough to compensate for a larger decrease in conformational entropy

Twist-Induced Defects of the P‑SSP7 Genome Revealed by Modeling the Cryo-EM Density

We consider the consequences of assuming that DNA inside of phages can be approximated as a strongly nonlinear persistence length polymer. Recent cryo-EM experiments find a hole in the density map of P-SSP7 phage, located in the DNA segment filling the portal channel of the phage. We use experimentally derived structural constraints with coarse-grained simulation techniques to consider contrasting model interpretations of reconstructed density in the portal channel. The coarse-grained DNA models used are designed to capture the effects of torsional strain and electrostatic environment. Our simulation results are consistent with the interpretation that the vacancy or hole in the experimental density map is due to DNA strain leading to strand separation. We further demonstrate that a moderate negative twisting strain is able to account for the strand separation. This effect of nonlinear persistence length may be important in other aspects of phage DNA packing

A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies

We show that an Ng bridge function modified version of the three-dimensional reference interaction site model (3D-RISM-NgB) solvation free energy method can accurately predict the hydration free energy (HFE) of a set of 504 organic molecules. To achieve this, a single unique constant parameter was adjusted to the computed HFE of single atom Lennard-Jones solutes. It is shown that 3D-RISM is relatively accurate at predicting the electrostatic component of the HFE without correction but requires a modification of the nonpolar contribution that originates in the formation of the cavity created by the solute in water. We use a free energy functional with the Ng scaling of the direct correlation function [Ng, K. C. <i>J. Chem. Phys.</i> <b>1974</b>, <i>61</i>, 2680]. This produces a rapid, reliable small molecule HFE calculation for applications in drug design

Nonpolar Solvation Free Energy from Proximal Distribution Functions

Using precomputed near neighbor or proximal distribution functions (pDFs) that approximate solvent density about atoms in a chemically bonded context one can estimate the solvation structures around complex solutes and the corresponding solute–solvent energetics. In this contribution, we extend this technique to calculate the solvation free energies (Δ<i>G</i>) of a variety of solutes. In particular we use pDFs computed for small peptide molecules to estimate Δ<i>G</i> for larger peptide systems. We separately compute the non polar (Δ<i>G</i>_vdW) and electrostatic (Δ<i>G</i>_elec) components of the underlying potential model. Here we show how the former can be estimated by thermodynamic integration using pDF-reconstructed solute–solvent interaction energy. The electrostatic component can be approximated with Linear Response theory as half of the electrostatic solute–solvent interaction energy. We test the method by calculating the solvation free energies of butane, propanol, polyalanine, and polyglycine and by comparing with traditional free energy simulations. Results indicate that the pDF-reconstruction algorithm approximately reproduces Δ<i>G</i>_vdW calculated by benchmark free energy simulations to within ∼ kcal/mol accuracy. The use of transferable pDFs for each solute atom allows for a rapid estimation of Δ<i>G</i> for arbitrary molecular systems

Conditional Solvation Thermodynamics of Isoleucine in Model Peptides and the Limitations of the Group-Transfer Model

The hydration thermodynamics of the amino acid X relative to the reference G (glycine) or the hydration thermodynamics of a small-molecule analog of the side chain of X is often used to model the contribution of X to protein stability and solution thermodynamics. We consider the reasons for successes and limitations of this approach by calculating and comparing the conditional excess free energy, enthalpy, and entropy of hydration of the isoleucine side chain in zwitterionic isoleucine, in extended penta-peptides, and in helical deca-peptides. Butane in gauche conformation serves as a small-molecule analog for the isoleucine side chain. Parsing the hydrophobic and hydrophilic contributions to hydration for the side chain shows that both of these aspects of hydration are context-sensitive. Furthermore, analyzing the solute–solvent interaction contribution to the conditional excess enthalpy of the side chain shows that what is nominally considered a property of the side chain includes entirely nonobvious contributions of the background. The context-sensitivity of hydrophobic and hydrophilic hydration and the conflation of background contributions with energetics attributed to the side chain limit the ability of a single scaling factor, such as the fractional solvent exposure of the group in the protein, to map the component energetic contributions of the model-compound data to their value in the protein. But ignoring the origin of cancellations in the underlying components the group-transfer model may appear to provide a reasonable estimate of the free energy for a given error tolerance

Intramolecular Interactions Overcome Hydration to Drive the Collapse Transition of Gly₁₅

Simulations and experiments show oligo-glycines, polypeptides lacking any side chains, can collapse in water. We assess the hydration thermodynamics of this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here taken as the end-to-end distance (<i>r</i>) in the chain. To examine the role of the various conformations for a given <i>r</i>, we study the conditional distribution, <i>P</i>(<i>R</i>_g|<i>r</i>), of the radius of gyration for a given value of <i>r</i>. The free energy change versus <i>R</i>_g, −<i>k</i>_B<i>T</i> ln <i>P</i>(<i>R</i>_g|<i>r</i>), is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this observation within a multistate generalization of the potential distribution theorem, we calculate a tight upper bound for the hydration free energy of the peptide for a given <i>r</i>. On this basis, we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intrapeptide and hydration effects, with intrapeptide contributions favoring collapse