福田 育夫

Ligand-receptor docking simulation is difficult when the biomolecules have high intrinsic flexibility. If some knowledge on the ligand-receptor complex structure or inter-molecular contact sites are presented in advance, the difficulty of docking problem considerably decreases. This paper proposes a generalized-ensemble method "cartesian-space division mD-VcMD" (or CSD-mD-VcMD), which calculates stable complex structures without assist of experimental knowledge on the complex structure. This method is an extension of our previous method that requires the knowledge on the ligand-receptor complex structure in advance. Both the present and previous methods enhance the conformational sampling, and finally produce a binding free-energy landscape starting from a completely dissociated conformation, and provide a free-energy landscape. We applied the present method to same system studied by the previous method: A ligand (ribocil A or ribocil B) binding to an RNA (the aptamer domain of the FMN riboswitch). The two methods produced similar results, which explained experimental data. For instance, ribocil B bound to the aptamer's deep binding pocket more strongly than ribocil A did. However, this does not mean that two methods have a similar performance. Note that the present method did not use the experimental knowledge of binding sites although the previous method was supported by the knowledge. The RNA-ligand binding site could be a cryptic site because RNA and ligand are highly flexible in general. The current study showed that CSD-mD-VcMD is actually useful to obtain a binding free-energy landscape of a flexible system, i.e., the RNA-ligand interacting system.

We introduce a simple cutoff-based method for precise electrostatic energy calculations in the molecular dynamics (MD) simulations of point-particle systems. Our method employs a theoretically derived smooth pair potential function to define electrostatic energy, offering stability and computational efficiency in MD simulations. Instead of imposing specific physical conditions, such as dielectric environments or charge neutrality, we focus on the relationship represented by a single summation formula of charge-weighted pair potentials. This approach allows an accurate energy approximation for each particle, enabling a straightforward error analysis. The resulting particle-dependent pair potential captures the charge distribution information, making it suitable for heterogeneous systems and ensuring an enhanced accuracy through distant information inclusion. Numerical investigations of the Madelung constants of crystalline systems validate the method's accuracy.

A small and flexible molecule, ribocil A (non-binder) or B (binder), binds to the deep pocket of the aptamer domain of the FMN riboswitch, which is an RNA molecule. This binding was studied by mD-VcMD, which is a generalized-ensemble simulation method. Ribocil A and B are structurally similar because they are optical isomers to each other. In the initial conformation of simulation, the ligands and the aptamer were completely dissociated in explicit solvent. The aptamer-ribocil B binding was stronger than the aptamer-ribocil A binding, which agrees with experiments. The computed free-energy landscape for the aptamer-ribocil B binding was funnel-like, whereas that for the aptamer-ribocil A binding was rugged. When passing through the gate (named "front gate") of the binding pocket, each ligand interacted with bases of the riboswitch by non-native π-π stackings, and the stackings restrained the ligand's orientation to be advantageous to reach the binding site smoothly. When the ligands reached the binding site in the pocket, the non-native stackings were replaced by the native stackings. The ligand's orientation restriction is discussed referring to a selection mechanism reported in an earlier work on a drug-GPCR interaction. The present simulation showed another pathway leading the ligands to the binding site. The gate ("rear gate") for this pathway was located completely opposite to the front gate on the aptamer's surface. However, the approach from the rear gate required overcoming a free-energy barrier regarding ligand's rotation before reaching the binding site.

In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cutoff-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology. In particular, we take into account the reaction field (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cutoff-based methods are based on different physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cutoff region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the artificial effects, generated near the boundary, from the cutoff sphere. Nonetheless, we find physical and/or mathematical similarities between these methods. In particular, the modified RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.