Solvent plays a significant role in mediating the structural dynamics of biological macromolecules and their assemblies. A variety of approaches based on 1D and 3D RISM have been used to study different solvent and co-solute effects on conformational and configurational transitions in biomolecules. The earliest of these studies used single point calculations of solvation free energies and solvent structure to determine the most stable members of preselected sets of molecular confor- mations/configurations. More recently, however, dynamic systems have been studied using 1D and 3D RISM coupled with geometry optimization, normal mode analysis, MD and MC simulations, to provide a more realistic description of their dynamics. Furthermore, RISM has recently been employed to develop multi-scale quantum-mechanics/molecular mechanics (QM/MM) methods to study biological macromolecules.7,340,341 In this approach, a selected region of the solute (e.g. an enzyme active site) is treated by quantum mechanics, the surrounding region of the biomolecule is modeled at the molecular mechanics level, and the solvent effects are incorporated by RISM (see Figure 17). Such multiscale methods are excellent approaches to model quantum-level effects of biological macromolecules that are too large to treat with a pure quantum mechanics approaches.
ferred conformations of the Met-enkephalin peptide (Tyr-Gly-Gly-Phe-Met) in different solvents. It was shown that the conformation space of Met-enkephalin peptide could be sampled in fewer steps in aqueous solvent than in simple non-aqueous solvents because in the former many con- formers were found to be too high in energy to be observed at biological temperatures. The authors speculate that this focusing of peptide conformations in water might go some way to address the paradox related to protein folding noted by Levinthal, who pointed out that the time for a random search of all possible conformations would be unrealistically long even for a relatively small pep- tide/protein. Similarly, Kinoshita et al185used 1D RISM to study the influence of water, methanol and ethanol solvents on four selected conformations of Met-enkephalin peptide (Tyr-Gly-Gly-Phe- Met) and two selected conformations of a peptide from ribonuclease A (Lys-Glu-Thr-Ala-Ala-Ala- Lys-Phe-Leu-Arg-Gln-His-Met). The total solvation free energy was shown to vary less between different peptide conformations in alcohols than in water, which was rationalised by partitioning the solvation free energy calculated by 1D RISM into contributions from individual solvophilic and solvophobic atoms. In alcohol, solvophobic atoms were shown to be less solvophobic than in water, and solvophilic atoms were found to be less solvophilic. Consequently, in alcohol where the solvation free energy varies less between different conformers, the peptides tend to adopt con- formers that have the lowest internal energies (i.e. α-helix for Met-enkephalin peptide and the C-peptide tested in this paper, but alcohol is also observed to stabiliseβ-sheet structures in some peptides).
Kitao et al.342studied the effects of (pure) aqueous solvent on the conformation and collective motions of the small protein melittin (26 amino acids and 436 atoms) using both explicit solvent molecular dynamics and XRISM theory. The conformational energy profiles along the two lowest frequency normal modes of the protein were calculated as ∆F = ∆GXRISM + ∆Econf, where ∆GXRISM is the hydration free energy calculated by XRISM and∆Econf is the internal confor- mational energy of the protein. Maruyama et al.343 used geometry optimization coupled with 3D RISM to study the preferred conformations of human telomere in different electrolyte solutions (pure water, 0.1M NaCl, 0.1M KCl). In agreement with experiment, the calculations predict that
the preferred conformation of the telomere is different in 0.1M NaCl (”basket” conformation) than in pure water (”chair” conformation). Yamazaki et al.344 studied the self-assembly and stability of organic rosette nanotubes (RNT) from monomers comprised of guanine - cytosine blocks dec- orated with 4-aminobenzo-18-crown-6-ether. A putative self-assembly process was proposed and shown by 3D RISM calculations to be thermodynamically favorable. The salt-induced conforma- tional change of the DNA oligomer d(5’CGCGCGCGCGCG3’) from B-form to Z-form has been rationalized by Maruyama et al345 on the basis of 3D RISM calculations. The conformational stability of the DNA oligomers was interpreted on the basis of Coulombic interactions between neighboring phosphate groups and counter-ions. In low salt concentrations, Coulombic repulsions between phosphate groups mean that the B-form is more favorable than the Z-form, primarily be- cause the latter has a shorter interphosphate distance. In high salt concentrations, however, the counter-ions effectively screen the phosphate groups reversing the relative stabilities of the two forms. The results do not support the hypothesis of Saenger at al.346
The essential elements of life (self-replication, information processing, metabolism) occur largely by specific interaction between biological molecules. Understanding how two molecules recognize each other in biological environments is thus one of the fundamental issues in the biomolecular sciences. It is also of great importance in many areas of industrial research including the pharmaceutical industry, where predictions of the binding modes of small molecules (e.g. wa- ters, ions, drugs) to biological macromolecules (e.g. proteins, DNA) are used to help design new pharmaceuticals. The key thermodynamic parameter characterizing the binding of a ligand (L) by a receptor (R) is the binding free energy (∆Gbind ) for the processR + L → RL.
Since the solvent phase plays an important role in mediating many molecular recognition events in biological systems, it is vital that computational methods to model biomolecular recognition in- corporate an adequate molecular-scale model of solvent. Several methods to compute absolute or relative binding free energies using molecular integral equation theory have been proposed. Genheden et al. computed the binding free energies of seven biotin analogues to avidin using both MM-PBSA and MM-3DRISM methods.101Blinov et al. used the MM-3DRISM method to
Figure 18: Correlation between the error in the HFEs calculated by the 3D RISM with the PLHNC closure using the GF free energy expression: ∆GGF
hyd− ∆G exp
hyd, and the DPMV,ρ ¯V . Red crosses are small organic molecules; black dots are druglike solutes. The pharmaceutical molecules lie on the line-of-best-fit calculated for simple organic molecules (the solid red line). Reprinted with permission from Ref.329Copyright 2011 American Chemical Society.
compute the binding thermodynamics of amyloid fibrils.310 The association free energy of small β-sheet oligomers was observed to increase approximately linearly with the number of peptides in the complex. Palmer et al. performed computational alanine scanning calculations of the bovine chymosin – bovineκ-casein complex using MM-3DRISM to probe the contribution of individual residues to the overall binding free energy.102The complex is of industrial interest because bovine chymosin is widely-used to cleave bovineκ-casein and to initiate milk clotting in the manufactur- ing of processed dairy products.347–349