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The theoretical model of proteins on the two-dimensional square lattice, introduced previously, is extended to include the specific short-range interactions. Attractive long-range interactions with various specificities and non-specific repulsive long-range interactions in the form of self-avoidance of the polymer chain are also operative in the model. Dynamics of the model protein is studied by a Monte Carlo method. The short-range interactions are found to accelerate the folding and unfolding transitions. Non-specific part of the attractive long-range interactions have a competing effect of decelerating the transitions. When the short-range interactions are weighted beyond a certain extent over the attractive long-range interactions are weighted beyond a certain extent over the attractive long-range interactions, the all-or-none character of the folding and unfolding transitions is destroyed. How the destruction proceeds is quantitatively expressed in terms of the S-H curves. The limiting case of dominance of the specific short-range interactions over the attractive long-range interactions is studied in detail. The lattice polymer in this limit does not behave like a globular protein at all. This observation leads to a reexamination of the currently popular notion of the dominance of the short-range interactions. A new concept of consistency is proposed to replace it. Possible mechanisms of the acceleration of the transitions by the specific short-range interactions are discussed.

The effect of ester bond on the conformation of peptide molecule was studied by designing and synthesizing a model tetradepsipeptide cyclo(-L-Ala-L-Hmb-)2 and by analyzing the conformation both theoretically and experimentally. Theoretical analysis showed that both ester and peptide bonds in the calculated low-energy conformations within 3 kcal/mol of the global minimum take a trans but distorted configuration. The distortion is larger in ester bonds than in peptide bonds. Further, the four carbonyls project from one side of the plane of the cyclic backbone, whereas the side chains project from the other side. These results are consistent with the experimental results obtained by NMR measurement; first, the coupling constant deduced from 1H-NMR species in DMSO-d6 is consistent with the dihedral angles of the calculated low-energy conformations; second, results of NOE measurement can reproduce the calculated configuration of the carbonyls and side chains. From the consistency between theoretical and experimental results, it is concluded that this model tetradepsipeptide takes an all-trans backbone conformation in solution and this backbone conformation is stabilized by large distortion in the ester bond, which compensates the strain resulted from the 12-membered cyclic backbone structure consisting only of L-residues.

For the purpose of calculating the crystal structure of polyglycine II, a system of three parallel chains are considered. The structure obtained by the energy minimization of this system agrees well with experimentally determined crystal structure. Hydrogen bonds of the type of Cα–H. O, which are discussed in literature as existing in the crystal structure, are neglected in the calculation. The fact that the crystal structure is well reproduced by this calculation indicates that hydrogen bonds of this type, if any, are weak in this crystal structure. The relative contributions of various energy terms to the stabilization of the structure are investigated. Interchain hydrogen bonds do not play a significant role in the determination of the crystal structure, but the interchain nonbonded interactions do. Mechanical properties are studied by calculating a response to a static external force applied to the system. Young's modulus E = 4.2 times 1011-dyncm-2 and Poisson's ratio s=0.25 are obtained. Relative contributions of various energy terms to elastic properties are discussed.

A theory is developed about large-amplitude conformational fluctuations in globular proteins in their native or predenaturational state. A model is introduced, an independent fluctuating site model, in which we assume that there is more than one independent fluctuating site, each one localized in some part of a protein molecule. Without assuming any further details for each fluctuating site, the entropy S versus enthalpy H curve of this model is shown to be convex. From this fact the predenaturational excess heat capacity can be derived, as observed in recent experimental studies of a few systems of a protein in solution.

A long record of computer simulation of folding-unfolding transition in a two-dimensional lattice model of protein as monitored by one conformational order parameter was studied to see if it could be approximated by a markoffian process. For this purpose the normalized time correlation functions of the order parameter were calculated (i) directly from the record of simulation and (ii) by assuming the markoffian behavior of the record. Both of them can be well approximated by a sum of two simple exponential terms. The relaxation time of the slow relaxing term, which corresponds to the overall folding-unfolding transition, becomes very short when the markoffian assumption is made. From this observation we conclude that intermediate states defined by one more-or-less arbitrarily chosen conformational parameter are, in general, collections of very heterogeneous conformations and therefore transitions between them cannot be markoffian. This indicates the importance of multi-parameter observation of dynamic process of folding. Characteristic features of the method of trapping disulfide intermediates are discussed.

The theoretical model of proteins on the two-dimensional square lattice, introduced previously, is extended to include the hydrophobic interactions. Two proteins, whose native conformations have different folded patterns, are studied. Units in the protein chains are classified into polar units and nonpolar units. If there is a vacant lattice point next to a nonpolar unit, it is interpreted as being occupied by solvent water and the entropy of the system is assumed to decrease by a certain amount. Besides these hydrophobic free energies, the specific long-range interactions studied in previous papers are assumed to be operative in a protein chain. Equilibrium properties of the folding and unfolding transitions of the two proteins are found to be similar, even though one of them was predicted, based on the one globule model of the transitions, to unfold through a significant intermediate state (or at least to show a tendency toward such a behavior), when the hydrophobic interactions are strongly weighted. The failure of this prediction led to the development of a more refined model of transitions; a non-interacting local structure model. The hydrophobic interactions assumed here have a character of non-specific long-range interactions. Because of this character the hydrophobic interactions have the effect of decelerating the folding kinetics. The deceleration effect is less pronounced in one of the two proteins, whose native conformation is stabilized by many pairs of medium-range interactions. It is therefore inferred that the medium-range interactions have the power to cope with the decelerating effect of the non-specific hydrophobic interactions.

A theoretical method is developed by which the character of the process of protein denaturation (e.g., whether or not it is of the all-or-none type) can be discussed in terms of conformation of native proteins and the forces stabilizing it. An important role is played by a quantity S(H): entropy of a protein molecule in solution in the conformational states with a given value of enthalpy H. It is demonstrated that the all-or-none type denaturation of proteins is a rather direct consequence of the globularity and specificity of the native conformations. Denaturations with significant intermediate states are discussed. Denaturations induced by added denaturants are also discussed.