Dilute Vs Non-Dilute Flooding Molecular Dynamics Simulations - Where Do We Draw The Line

Computer simulation is a useful tool to predict and analyze properties of complex molecular systems. Among those, protein modulation by ligands is one of major interest to advance our current understanding of both regular and pathological biomolecular processes. Ligand-receptor interaction is traditionally investigated by means of flooding molecular dynamics (flooding-MD) simulations. The main information extracted from such simulations is the 3-dimensional distribution of ligand probability density, ρ(R). In flooding simulations, ligands sample the environment by importance at an established concentration, in such a way that high ρ(R) regions nearby the receptor encode potentially higher affinity regions, thus qualitatively solving ligand binding to protein sites. In a quantitative perspective, it is possible to map ρ(R) into n ligand occupancy probabilities of loosely-defined, independent binding-site volumes j, in order to estimate binding constants (Knj). Knowledge of Knj allows, in principle, for the reconstruction of relevant concentration-dependent properties such as average number of protein-bound ligands, binding-site occupancy probabilities, etc; for a range of concentrations distinct from the originally simulated one. Accurate quantification of Knj is convenient, since flooding-MD simulations are typically performed well above the physiological range of concentrations, thus entering a regimen where concentration effects might come into play. Aspiring to estimate such constants, we propose here a discussion about (i) the theoretical framework put forth to estimate Knj; (ii) the limits of what constitutes a diluted flooding-MD system and the accuracy of the ideality assumption frequently implied in those systems; (iii) the magnitude of the improvement in Knj calculation, brought by taking into consideration ligand-ligand interaction. We further confront these results with binding affinities (and associated binding constants) calculated for ultra-diluted conditions by means of free-energy perturbation (FEP) calculations.