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Macroscopic and microscopic properties of fullerene (C60)–cis-polyisoprene (cis-PI) composites at varying fullerene concentrations were investigated using atomistic molecular dynamics (MD) simulations over microsecond time scales. Results show that the introduction of fullerenes into a polymer matrix increases density, bulk modulus and heat capacity while thermal expansivity decreases. The presence of fullerenes slowed the diffusion of both C60 and cis-PI. Moreover, increasing fullerene concentration results in ordering of the cis-PI chains at the cis-PI–fullerene interfaces and shrinking of bulk PI regions. Free energy calculations of fullerene dimerization suggest that fullerenes disperse at low and aggregate at high fullerene concentrations. Our multi-scaled analysis approach demonstrates the role of ‘ordered’ regions adjacent to the interface between cis-PI and fullerene in controlling the level of order and mobility of the cis-PI chains. The relationship between the microscopic behavior and the changes in mechanical and thermal properties are discussed. Our study is beneficial for further studies and development of advanced rubber technology for novel, cost-effective, material with very high stiffness and thermal endurance with optimizing conditions of filler contents.

The specific adsorption of alkali ions, Li + , Na + , K + , and Cs + , in electrolyte solutions on Prussian blue (PB) is investigated by using the three-dimensional (3D) reference interaction site-model (RISM) theory. The results from 3D-RISM show dramatically different adsorption sites between large ions (K + and Cs + ) and small ions (Li + and Na + ). The small ions are adsorbed at the channel entrance sites without the water–ion exchange mechanism. In contrast, the large ions are adsorbed in PB by the water–ion exchange mechanism, and the adsorption site of large ions is located at the center of the cage or at the interstitial site.

Ferric hexacyanoferrate (FeHCF) or Prussian blue (PB) exhibits selective alkali ion adsorption and has great potential for use in various applications. In the present work, alkali ion (Li+, Na+, K+, and Cs+) and water configurations in defective PB (d-PB) were studied by using the statistical mechanics of molecular liquids. The three-dimensional (3D) distribution functions of the ions and water were determined by solving the 3D-reference interaction site model (RISM) equation of systems of a unit lattice of d-PB in electrolyte solutions, i.e., LiCl, NaCl, KCl, and CsCl. The results show the difference in the ion-water configurations and distributions between small (Li+ and Na+) and large ions (K+ and Cs+). The adsorption sites of Li+ and Na+ are located off-center and lie on the diagonal axis. By contrast, the larger ions, K+ and Cs+, are adsorbed at the center of the unit cell. The degree of dehydration due to the adsorption of alkali ions indicates that there was no water exchange during Li+ and Na+ adsorption, whereas two and three water molecules were removed after adsorption of K+ or Cs+ in the unit cell.

The potassium channel is highly selective for K + over other monovalent cations, and the narrow pore structure with 3 A in diameter named the selectivity filter (SF) is responsible for the selective permeation. Here we applied the statistical mechanics of liquids called three-dimensional reference interaction site model (3D-RISM) theory, and the binding configurations of the monovalent cations, Li + , Na + and K + , with special attention on the contribution of water in the KcsA potassium channel were examined. All the three types of cations are bound in the open SF with high affinity, but with different binding coordinations: the in-cage configuration by eight carbonyl oxygens for K + , and the in-plane configuration by four carbonyl oxygens for Li + , whereas both configurations are allowed for Na + . In each case, water contributes an integral part of the ion coordination. In the case of Li + , a linear water-Li + -water complex is settled into two adjacent cages with the Li + centered at the in-plane site. Positions of water around Na + are more flexible, which may allow a transition between in-plane and in-cage configurations. K + stably occupied in-cage configuration, and water occupies adjacent cages. The results provide the distinct configuration of ion and water in the SF, and serves clues for elementary process of selectivity.

Molecular recognition (MR) is an essential elementary process allowing biomolecules to perform their function. MR can be defined as a molecular process in which one or several guest molecules are bound with a high probability at a particular site such as a cleft or a cavity, of a host molecule in a particular orientation. It is a thermodynamic process which is characterised by the difference of the free energies between two states of a host–guest system, bound and unbound. The process features an extremely heterogeneous atomic-environment around binding sites, which has turned away challenges by the conventional statistical mechanics of liquids, e.g. a mean field theory. We have been developing a new theory for MR in biomolecular systems, based on the statistical mechanics of liquids, or the 3D-reference interaction site model (RISM)/RISM theory. The theory has demonstrated its amazing capability of predicting the process from the first principle. In this article, we review our recent works on MR concerni...

The three-deimensional distribution functions (3D-DFs) and potentials of mean force (PMFs) of small neutral molecules inside the two aquaporin channels, AQP1 and GlpF, are calculated based on the 3D-RISM theory, the statistical mechanics theory of molecular liquids, in order to investigate the permeability of those ligands through the channels. The ligands investigated are neon (Ne), carbon dioxide (CO(2)), nitric oxide (NO), ammonia (NH(3)), urea, and glycerol. Neon shows continuous distribution throughout the channel pore in AQP1 as is the case of water, although the PMF of Ne at the selective filter (SF) region is higher than that of water, indicating that the stability of molecules in the channel is determined not only by their size, but also by the charge distribution. The ligand molecules, CO(2), NO, urea, and glycerol, have a large barrier in PMF at the SF region in AQP1, indicating that the channel is not permeable by those ligands. On the other hand, NH(3) has only a small activation barrier, approximately 2.5 kJ/mol, to be overcome. Therefore, our theory predicts that a NH(3) molecule can be permeated through the AQP1 channel. In GlpF, all the ligands have negative PMF throughout the channel pore except for glycerol, which has a small barrier at the SF area, approximately 2.1 kJ/mol. The barrier can be readily overcome by the thermal motion. So, our results are quite consistent with the experiments for urea and glycerol, for which the corresponding data are available. The results obtained by the 3D-RISM theory show striking differences from those obtained by the MD simulations, especially in the case of GlpF. Possible causes of the difference in the results between the two methods are discussed.

The three dimensional (3D) distributions of sodium, chloride, and hydronium ions along with water, in two aquaporin channels, AQP1 and GlpF, were calculated using the three dimensional reference interaction site model (3D-RISM) theory. It was found from the potential of mean force (PMF) obtained from the 3D-distribution that water inside the both channels is slightly more stable than bulk, and that PMF does not have high barriers for a water molecule to cross. The results are completely in harmony with the experimental observations, while they are in accord with none of the molecular simulation studies. All the ions studied are hard to permeate through either of the channels. However, the reasons why the permeability is so low are different depending on the channels and the ions. In the AQP1 channel, the cations, or Na + and H 3 O + , are largely excluded from the channel essentially by the electrostatic repulsion due to the positively charged residues, while the Cl − ion is blocked by a high steric barrier at the selective filter (SF) region. In the GlpF, the PMFs of Na + and H 3 O + inside the channel are mostly positive, and they have three large barriers to cross, which may be preventing the ions from permeation. On the other hand, the PMF of Cl − is largely negative, but it has wide and deep well which likely prevents the ion from permeating through the channel by “trapping” mechanism.

The equilibrium distribution function of water in the aquaporin-Z is calculated based on the three-dimensional reference interaction site model theory. It is found that water in aquaporin-Z distributes continuously throughout the channel with the open structure, while the distribution has a conspicuous gap around the R189 side chain in the closed form. The gating mechanism of the channel is inferred from the water distribution. The method also provides information with respect to the distribution of hydrogen atoms of water inside the channel, which is important to investigate the conduction mechanism of molecules including protons in the channel.

Selective ion binding by human lysozyme and its mutants is probed with the three-dimensional interaction site model theory which is the statistical mechanical integral equation theory. Preliminary and partial results of the study have been already published (Yoshida, N. et al. J. Am. Chem. Soc. 2006, 128, 12042-12043). The calculation was carried out for aqueous solutions of three different electrolytes, CaCl2, NaCl, and KCl, and for four different mutants of the human lysozyme: wild type, Q86D, A92D, and Q86D/A92D, which have been studied experimentally. The discussion of this article focuses on the cleft that consists of amino acid residues from Q86 to A92. For the wild type of protein in the aqueous solutions of all the electrolytes studied, there are no distributions observed for the ions inside the cleft. The Q86D mutant shows essentially the same behavior with that of the wild type. The A92D mutant shows strong binding ability to Na+ in the recognition site, which is in accord with the experimental results. There are two isomers of the Q86D/A92D mutant, e.g., apo-Q86D/A92D and holo-Q86D/A92D. Although both isomers exhibit the binding ability to the Na+ and Ca2+ ions, the holo isomer shows much greater affinity compared with the apo isomer. Regarding the selective ion binding of the holo-Q86D/A92D mutant, it shows greater affinity to Ca2+ than to Na+, which is also consistent with the experimental observation.

Recent progress in the theory of molecular recognition in biomolecules is reviewed, which has been made based on the statistical mechanics of liquids or the RISM/3D-RISM theory during the last five years in the authors' group. The method requires just the structure of protein and the potential energy parameters for the biomolecules and solutions as inputs. The calculation is carried out in two steps. The first step is to obtain the pair correlation functions for solutions consisting of water and ligands based on the RISM theory. Then, given the pair correlation functions prepared in the first step, we calculate the 3D-distribution functions of water and ligands around and inside protein based on the 3D-RISM theory. The molecular recognition of a ligand by the protein is realized by the 3D-distribution functions: if one finds some conspicuous peaks in the distribution of a ligand inside protein, then the ligand is regarded as "recognized" by the protein. Some biochemical processes are investigated, which are intimately related to the molecular recognition of small ligands including water, noble gases, and ions by a protein.