Nobuhiko Saitô

The Statistical Mechanical Theory of Stiff Chains

The statistical mechanical theory of stiff chains which can be represented by differentiable space curves is developed by the analogy of the path integral formulation in quantum mechanics. The second and fourth moments of end-to-end distance of the chain are calculated. The stretching and contraction of the chain are also taken into account. The Brownian motion of the stiff chain is discussed, and some statistical properties, especially the correlation function of random forces, are determined.

Tertiary Structure of Proteins. I. Representation and Computation of the Conformations

A protein conformation can be computed by connecting peptide units of usual trans-planar structure successively with a given set of dihedral angles ϕ and ψ. It is, however, not easy to generate the native conformations such as myoglobin and lysozyme by the computation. In order to show the discrepancy between the native conformation and the computed one, we have introduced a map, where the mutual distance between C α -atoms of i -th and j -th residue , r i j , is listed against the residue number, in row and column. This map represents a tertiary structure of the protein (e. g. α-helix, β-structure) as the characteristic patterns. It becomes possible to estimate the difference of the computed conformation from the native one numerically by comparing the corresponding maps. The improvement of the dihedral angles, ϕ and ψ, as made by minimizing the deviation of the computed map from the native one on both myoglobin and lysozyme.

Statistical Mechanical Theory of the Protein Conformation. II. Folding Pathway for Protein

The theory of a one-dimensional lattice gas with long-range many-body interactions is applied to the folding pathways of proteins. This model presents the quantitative informations about the order of inter-residue interactions, the location of nucleation and so on. Three typical proteins are cited as examples and their folding pathways are traced according to the computation of some useful properties.

Statistical mechanical theory of the protein conformation. I. General considerations and the application to homopolymers

A one-dimensional lattice gas with long-range many-body interactions is studied by a matrix method for the model of the transition between native and denatured states of globular proteins. The interactions in our model have the nature that two particles situated on two different sites can interact with each other only when all sites between them are occupied by other particles, or in other words, only when they are in a same island which is formed by particles situated side by side. In this system a phase transition occurs in the limit of the infinite long-range interaction and under certain potential functions. The sharpness and the all-or-none type property of the transitions are discussed from the nature of interaction.

Spectral Distribution of the Light Scattered from Rodlike Macromolecules in Solution

Rodlike macromolecules in solution undergo translational and rotatory Brownian motions. These motions are not independent, since the translational mobility is anisotropic, and the components are orientation-dependent. By taking this fact into consideration, the space-time correlation function of density is calculated to obtain the spectral intensity of the Rayleigh scattered light. Extra terms are found to exist in the expression of spectral intensity in addition to the main term which comes from the translational and rotatory diffusions assumed independent of each other. This may provide a method to measure separately the principal values of the mobility tensor of rodlike macromolecule.

A Remark on the Hydrodynamical Theory of the Viscosity of Solutions of Macromolecules

The hydrodynamical problem of many particles interacting in a laminar flow is discussed on the basis of Stokes approximation. Two methods of approximation are introduced in order to derive the concentration dependence of the viscosity of solutions of rigid spheres. In any case an improper integral is involved which can be evaluated to be of different values according to different ways of integration. This physically absurd result comes from Stokes approximation. A new fundamental equation is proposed for the problems in a laminar flow from an analogous reasoning given by Oseen for the case of uniform flow.

Time delays and chaos in two competing species

Abstract The logistic equation describing the population of a species with time delayed saturation effect can be generalized to the ones describing two competing species with the same effects. These equations display various dynamical behaviors, e.g., periodic solutions and nonperiodic or chaotic solutions. The trajectories of these solutions do not intersect with themeselves in an appropriate 3-dimensional space.

On the stability of isolating integrals. I. Effect of the perturbation in the potential function

The stability of isolating integrals against the perturbation of potential function was studied by the method of surface of section in the classical dynamical system of two degrees of freedom with the hamiltonian, \begin{aligned} H{=}\frac{1}{2}\left(\dot{x}^{2}+\dot{y}^{2}+x^{2}+y^{2}+2x^{2}y+\frac{2}{3}y^{3}-\frac{4}{3}\varepsilon y^{3}\right), \end{aligned} in the range -1< e <1. This system has isolating integrals in this range. Their structure is found to change discontinuously at e =-1/2 and e =0.

Statistical mechanical treatment of α-helices and extended structures in proteins with inclusion of short- and medium-range interactions

A statistical mechanical model of protein conformation with medium-range interactions between theith and (i+k)th residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interactionk; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameterss and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as inall empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.

The Light Scattering by Non-Spherical Particles in Solutions

The angular distribution of the intensity of light scattered by macromolecules in solution has been calculated numerically, assuming these molecules as ellipsoids of revolution and cylinders whose dielectric constant is slightly different from that of the solvent. The results are given in graphs and they will be useful for the determination of the shapes of large protein molecules such as vaccinia virus.