A semi‐implicit solvent model for the simulation of peptides and proteins

Abstract

We present a new model of biomolecules hydration based on macroscopic electrostatic theory, that can both describe the microscopic details of solvent-solute interactions and allow for an efficient evaluation of the electrostatic hydration free energy. This semi-implicit model considers the solvent as an ensemble of polarizable pseudoparticles whose induced dipole describe both the electronic and orientational solvent polarization. In the presented version of the model, there is no mutual dipolar interaction between the particles, and they only interact through short-ranged Lennard-Jones interactions. The model has been integrated into a molecular dynamics code, and offers the possibility to simulate efficiently the conformational evolution of biomolecules. It is able to provide estimations of the electrostatic solvation free energy within short time windows during the simulation. It has been applied to the study of two small peptides, the octaalanine and the N-terminal helix of ribonuclease A, and two proteins, the bovine pancreatic trypsin inhibitor and the B1 immunoglobin-binding domain of streptococcal protein G. Molecular dynamics simulations of these biomolecules, using a slightly modified Amber force field, provide stable and meaningful trajectories in overall agreement with experiments and all-atom simulations. Correlations with respect to Poisson-Boltzmann electrostatic solvation free energies are also presented to discuss the parameterization of the model and its consequences.

Biomolecular electrostatics and solvation: a computational perspective

“…An interesting particle-based macroscopic solvent model, which represents electronic and oriental polarization of water molecules by an ensemble of polarizable pseudo-particles (PPP) (Basdevant et al, 2004; Basdevant et al, 2006) in a framework that bears some similarity to the polarizable Langevin dipoles of Warshel (Papazyan & Warshel, 1997; Papazyan & Warshel, 1998) has recently been proposed. In this approach, the solute electric field induces dipoles at the centers of the solvent PPPs which, in turn, interact with the solute charge distribution.…”

Coarse-grained molecular models of water: a review

“…Borgis and coworkers [38–40] developed the so-called polarizable pseudo-particle (PPP) model for water that retains accurate hydrodynamics and solvation, whilst minimizing simulation time and speed up of diffusion for similar reasons as stated for the DSRI method [31] discussed above. Originally [38], the model used a 12-6 Lennard-Jones (LJ) potential, $$V_{\text{italicLJ}}(r)=4{\epsilon }_{\text{italicij}}true[{\left(\frac{{\sigma }_{\mathit{\text{ij}}}}{r}\right)}^{12}-{\left(\frac{{\sigma }_{\mathit{\text{ij}}}}{r}\right)}^{6}true],$$ with ε ij equal to the interaction strength and σ ij equal to the diameter between sites i and j , but many properties, including density and vaporization enthalpy, were inaccurate.…”

“…Borgis and coworkers [38–40] developed the so-called polarizable pseudo-particle (PPP) model for water that retains accurate hydrodynamics and solvation, whilst minimizing simulation time and speed up of diffusion for similar reasons as stated for the DSRI method [31] discussed above. Originally [38], the model used a 12-6 Lennard-Jones (LJ) potential, $$V_{\text{italicLJ}}(r)=4{\epsilon }_{\text{italicij}}true[{\left(\frac{{\sigma }_{\mathit{\text{ij}}}}{r}\right)}^{12}-{\left(\frac{{\sigma }_{\mathit{\text{ij}}}}{r}\right)}^{6}true],$$ with ε ij equal to the interaction strength and σ ij equal to the diameter between sites i and j , but many properties, including density and vaporization enthalpy, were inaccurate. To overcome these problems Masella et al [40], refined the original potential by adding a sum of Gaussian functions, $$U_{\mathit{\text{pp}}}^{\mathit{\text{corr}}}={\displaystyle \sum _{i=1}^N}{\displaystyle \sum _{j>i}^N}{\displaystyle \sum _{k=1}^3}{\epsilon }_{\text{italicpp}}^k\text{exp}true(\frac{-{(r_{\mathit{\text{ij}}}-r_k)}^2}{{\gamma }_k}true),$$ where ε is an energy term, r k is the Gaussian center, and γ k is the width of the Gaussian peak and a density energy term (used to maintain the local solvent density near a particle), $$n_i^k={\displaystyle \sum _{i=1,i\ne j}^N}{f}_{k}false(r_{\text{italicij}}false),$$ $$f_{0}false(r_{\text{italicij}}false)={\varphi }_{0}false(r_{\text{italicij}}false),f_{k>0}false(r_{\text{italicij}}false)={\varphi }_{\mathrm{k...}}$$…”

New Strategies for Integrative Dynamic Modeling of Macromolecular Assembly

“…Sansom and coworkers have used the same approach to study the self-assembly of cohesin and dockerin, demonstrating that CG models are even able to capture the influence of point mutations affecting binding (Hall & Sansom, 2009), maintaing a good agreement with experimental results (Parton, Kilngelhoefer, & Sansom, 2011;Scott et al, 2008). Scorpion, another CG force field of this mapping class and featuring an explicit solvent model, allows to simulate solvated protein complexes (Basdevant, Borgis, & Ha-Duong, 2004;Ha-Duong, 2009;Ha-Duong, Basdevant, & Borgis, 2009). In the case of the barnase-barstar, self-assembled structures were closely resembling the known target complex (Basdevant, Borgis, & Ha-Duong, 2013).…”

“…In our model, the solvation effects can be treated both implicitly and explicitly (Spiga et al, 2013). The implicit solvent model consists of a distance-dependent dielectric constant (Rubinstein & Sherman, 2004;Spiga et al, 2013), whereas the explicit solvent model is based on the work of Warshel (Florian & Warshel, 1997) and Borgis (Basdevant et al, 2004(Basdevant et al, , 2013Ha-Duong et al, 2009;Ha-Duong, Phan, Marchi, & Borgis, 2002). We showed earlier that the explicit introduction of electrostatic dipolar terms (Cascella et al, 2008) contributes to enhance the stability of secondary structure elements without the use of ad hoc bias potentials (Alemani et al, 2010).…”