Nobuhiro Gō

Protein Folding as a Stochastic Process

In physiological conditions globular protein molecules assume a specific native conformation uniquely determined by its amino acid sequence. Upon environmental changes the protein molecules undergo reversible unfolding (order losing) and folding (order gaining) transitions, which is similar to the first-order phase transition. Pathways of folding have been intensively studied in the hope of deciphering the code that amino acid sequences carry as to the threedimensional structure of proteins. A strongly simplifiedlattice model of proteins has been found to be a powerful theoretical tool to simulate the dynamic process of the folding and unfolding transitions. The results of the simulation indicate the existence of stochastic pathways of folding.

Conformations and CD curves of cyclo(L- or D-Phe-L-Pro-Aca): cyclized models for specific types of β-bends

β‐Bend CD Measurement Conformational energy calculation Cyclic peptide Gramicidin S NMR measurement

MONTE CARLO SIMULATION STUDY OF THERMAL FLUCTUATIONS AND CONFORMATIONAL ENERGY SURFACE OF A SMALL PROTEIN, BASIC PANCREATIC TRYPSIN INHIBITOR

The conformation energy surface of a small protein, basic pancreatic trypsin inhibitor, is studied to characterize small-amplitude thermal fluctuations in the protein molecule. In order to see the shape of the conformational energy surface near the energy minimum point, the thermal equilibrium of the molecule is stimulated by the Monte Carlo method of Metropolis et al. From the sample of the equilibrium population, which reflects the shape of the energy surface, orthogonal directions are generated in the conformational space, and the conformational energy is actually calculated along these directions. All energy profiles along these directions are found to be approximately a parabola within the range of thermal fluctuations, which suggests the possibility of harmonic approximation to the conformational energy surface of the globular protein.

Statistical error in time correlation functions from computer experiments on approximately two‐state processes

Statistical error due to finite time averaging in the calculation of the time correlation function from a computer experiment is analyzed in cases when a record of a computer experiment is approximately a Poisson process. The result indicates that the computer time in units of the main relaxation time can be shorter in these cases by a factor of 2 than in the cases studied by Zwanzig and Ailawadi, i.e., when a record of a computer experiment is approximately a Gaussian process. (AIP)

Regulatory Functions of Allosteric Enzymes in Far-from-Equilibrium Systems

Abstract A theoretical study is made on catalytic activities of allosteric enzymes in non-equilibrium systems. It is demonstrated that the amount of chemical flow catalyzed by allosteric enzymes in systems maintained far-from-equilibrium can be qualitatively different from that familiar in the near-equilibrium situations. To be more specific, a study is made of a system containing two chemical species, S and P , and an allosteric enzyme, E , which catalyzes the reaction of the interconversion between them. This system interacts with its environment in a way characterized by a set of controlled parameters. By this interaction the system is maintained far-from-equilibrium. More than one steady state is possible for a certain range of controlled parameters. For continuous changes of the controlled parameters, discontinuous transitions between the multiple steady states can occur. This new aspect of the enzyme kinetics of allosteric proteins may play a role in the regulation of metabolic flows within living cells.

Mathematical analysis of the mutarotation of sugars

Abstract The tautomerism of sugars showing complex mutarotation has been analyzed mathematically based on a scheme of three components. More-complete but complex schemes are shown to be reducible to the three-component scheme, because the supposed intermediates of interconversion can be neglected in the kinetics when their equilibrium contents are very small and because two furanose tautomers can be regarded as one component under appropriate conditions. The kinetics of the three-component scheme have been fully studied and are shown to explain successfully the tautomerism of most of the sugars. The tautomerism of D -galactose has been analyzed in especial detail. From the polarimetric data and the equilibrium content of α-pyranose, the kinetic rate-constants for D -galactose were determined and found consistent with all other experimental data. The slow and fast processes of complex mutarotation of D -galactose are shown to correspond approximately to pyranose-pyranose and pyranose-furanose interconversions, respectively.

Solitary wave and spatially locked solitary pattern in a chemical reaction system.

We investigate the behavior of a one-dimensional two component dynamical system. The dynamical equations are obtained by extracting an essence out of equations which describe the behavior of a biochemical reaction catalyzed by an allosteric protein. The obtained dynamical equations are similar to van der Pol equations. The dynamical equations are solved numerically. In the continuous system, a solitary wave is found to occur in certain ranges of the parameter space. The condition of occurrence of the solitary wave is investigated. The solitary wave can be induced by various initial perturbations, including rectangular ones with space-wise length longer than a certain critical value. The property of the solitary wave is similar to that of the impulses in nervous systems. In the discrete system, a spatially locked solitary pattern is found to occur in certain ranges of the parameter space.

Behavior of chemical reaction catalyzed by allosteric enzyme: Threshold phenomena and discontinuous transition to oscillatory state

Abstract A theoretical study is made on a chemical reaction system catalyzed by an allosteric protein, especially on its behavior in far-from-equilibrium situations. The reaction system, which was introduced in a previous paper, consists of two chemical species, S and P , and an allosteric enzyme, E , which catalyzes the reaction of interconversion between them. This system is kept far-from-equilibrium by an interaction with its environment. This interaction is characterized by four parameters. For certain values of the parameters, the system was previously shown to have multiple steady states. In the present paper it is shown that a sustained oscillation takes place in a certain region of the control-parameter space. On one part of the boundary of this region, the system undergoes a discontinuous transition from a steady state to a state oscillating with finite amplitude, while on the other part of the boundary the amplitude of oscillation is vanishingly small right after the transition. It is also shown that this system exhibits a threshold phenomenon. A few possible mechanisms are discussed by which the assumed interaction of the system with its environment can be realized.