Quelques Problèmes de Cinétique Conformationnelle de Systèmes Coopératifs

Résumé

Ayant souligné l’importance de la coopérativité en biologie, on restreint le sujet à la cinétique des transconformations coopératives de macromolécules. Le problème théorique est alors celui de la cinétique du modèle d’Ising à une dimension.

Deux solutions sont résumées (cas des chaînes longues; cas de réduction à un modèle séquentiel).

La cinétique de l’isomérisation cis-trans de la poly-L-proline illustre certains aspects de la théorie, tandis que des mesures nouvelles de l’absorption des ultrasons dans des solutions d’acides poly-L- glutamique montrent l’importance des fluctuations du nombre de séquences hélice (ou pelote) ininterrompues.

Des modèles simples, illustrés par leurs applications, sont finalement passés en revue (modèle par tout ou rien utilisé par Eigen et Pörschke dans l’étude cinétique de l’appariement des bases des oligonucléotides; un modèle non-arrhénien à deux états; un modèle à trois états conduisant à interpréter certaines expériences de saut de température lent pour des solutions de protéines pancréatiques par l’existence d’une conformation intermédiaire).

Summary

While the utmost importance of cooperativity in biological processes is underlined, the subject is restricted to linear chain molecules and the kinetics of their transconformations, such as the helix-coil transition of polypeptides and of oligonucleotides, and protein unfolding and refolding.

The theoretical problem is connected with the kinetics of a linear Ising lattice. An exact solution for long chains, based on the triplet closure approximation, is reviewed, as well as an early calculation giving the initial change with time of the helicity, after a sudden perturbation, in terms of a mean relaxation time.

As an illustration of the latter theoretical results, experiments on the poly-L-proline cis-trans isomerization are briefly described. On the other hand, new ultrasonic studies of the kinetics of the helix-coil transition of poly-L-glutamic acid are reported, showing that fluctuations of the number of uninterrupted helix (or coil) sequences contribute to the ultrasonic absorption.

An important case of reduction of the general (Ising) problem is that of sequential processes. An example is described, for which the eigenvalues of the transition rate matrix can be obtained easily, thus leading to an exact solution.

Simple models can be quite successful in treating kinetic problems of cooperative systems. An example is provided by the all-or-none model used by Eigen and Pörschke in their investigation of the oligoribouridylic-oligoriboadenylic acid system. The nucleation process was shown to involve three A.U base pairs, as in the codon-anticodon interaction, and the activation enthalpy was found to be negative.

A non-Arrhenius two-state model, adequate for studying the kinetics of cooperative processes of the type considered, is described; it leads also to a negative activation enthalpy, in a somewhat different way.

Analysis of the kinetics of proteins unfolding and refolding, using three-state models, is finally reviewed. The values of the relaxation amplitudes show that a three-state system can exhibit one relaxation time only. Thus, with the aid of certain assumptions, one can interpret in terms of an intermediate state slow T-jump measurements on pancreatic proteins as a function of temperature. The intermediate state must then have a nonnegligible population at certain temperatures. A simple model, with two identical steps, leads to satisfactory agreement for chymotrypsin-α, thus suggesting the reality of the postulated intermediate state.