Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

Abstract

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-ofthe-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

On the interactions of the receptor-binding domain of SARS-CoV-1 and SARS-CoV-2 spike proteins with monoclonal antibodies and the receptor ACE2

“…A large diversity of models is available for MD and MC molecular simulations. 38,[49][50][51][52] The need to repeat the calculations on several different physical chemical conditions and to obtain free energy of interactions at them drives the options to the so-called cost-effective coarse-grained (CG) models. These CG models offer the possibility to explore the main physical features of a system with a reduced number of parameters and lower computational costs.…”

“…This additional approximation is justified by the prohibitive computational costs of constant-pH methods with pH-dependent conformational changes. 52,56,57 Moreover, it is known that SARS-CoV-1 S protein does not exhibit large conformational changes upon the binding to ACE2 at least. 58 Each group of atoms that define an amino acid is converted in a single charged Lennard-Jones (LJ) sphere of radius (Ri) and valence zi.…”

“…The valences of all ionizable residues are a function of the solution pH. The fast proton titration scheme (FPTS) 40,41,52 was employed both to initially assign these valences zi´s for the amino acids and to let them vary during the simulation sampling at a given pH. This method has proved to predict pKa´s with a very good accuracy at low computational costs.…”

“…41 The fundamental physical chemical basis of this titration scheme, its numerical implementation, benchmarks, discussions related to its approximations, pros and cons can be found in previous publications. 40,41,52,59 As illustrated in Figure 4, two proteins are placed in an electroneutral open cylindrical simulation box, and free to translate back and forward along the axis in which their centers are laying, rotate in any direction and titrate. In this example, these two proteins are the modeled three dimensional structure of the SARS-CoV-2 S RBD and the crystallographic structure of the fragment of the mAb 80R.…”

Grand-Reaction Method for Simulations of Ionization Equilibria and Ion Partitioning in a Broad Range of pH and Ionic Strength

“…This approximation inherently neglects some correlations but at the same time it makes the computational cost relatively insensitive to the actual number of particles in the studied system. Such approach has been applied to study various systems in equilibrium with a bulk solution, such as proteins treated as rigid objects 14,15 , flexible star-like polymers [16][17][18][19][20] , or planar systems, such as a polyelectrolyte brush grafted to a surface [21][22][23][24][25] . Polyelectrolyte hydrogels have been studied using a similar approach [26][27][28] .…”