Infinitely Dilute Partial Molar Properties of Proteins from Computer Simulation

Abstract

A detailed understanding of temperature and pressure effects on an infinitely dilute protein’s conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method’s feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.

Particle and Energy Pair and Triplet Correlations in Liquids and Liquid Mixtures from Experiment and Simulation

“…More importantly, the bulk system equations are approximate when applied to proteins at infinite dilution, while the FST based equations are exact. 64 For example, even if one defined an instantaneous protein volume by V = −[N 1 − ⟨N 1 ⟩ 0 ]V 1°, as suggested by eq 10, and whose average is the thermodynamically correct protein volume, the fluctuations in this quantity are not simply the fluctuations provided by eqs 12 and 13, as suggested by several studies. 79 In fact, the quantity ⟨δVδV⟩ N = ⟨δN 1 δN 1 ⟩ N (V 1°) 2 is even extensive in nature.…”

“…This is in good agreement with our earlier study of the second derivatives using other approaches. 64 …”

Determination of partial molar volumes from free energy perturbation theory

“…16,23–29 Each method has its advantages. 30 SPT yields an expression for the work of cavitation in hard sphere and real fluids, 31 and KBT can probe the local environment around a solute, giving insight into preferential solvation and solute–solvent interactions.…”

“…16 Others have employed this method to study thermodynamic properties of small proteins. 26,29 $$V°=\langle V_{\mathrm{N},\mathrm{A}}\rangle -\langle V_{\mathrm{normalN}}\rangle +k_{\mathrm{b}}T{\kappa }_{\mathrm{T}}$$ $$V°=\langle V_{\mathrm{N}+\mathrm{A}}\rangle -\langle V_{\mathrm{normalN}}\rangle$$…”

Simulated pressure denaturation thermodynamics of ubiquitin

“…As we have recently reviewed [2], most previous approaches to obtain the thermodynamic properties of a protein are subjective. The enhanced sampling technique of replica exchange molecular dynamics (REMD) is an exception, because it does provide rigorous thermodynamic properties [3].…”