,.~" .~ t. ~,- ELSEVIER 21 March 1997 Chemical Physics Letters 267 (1997) 234-243 CHEMICAL PHYSICS LETTERS Hierarchically constrained dynamics of the configurational coordinate for rate processes in complex systems Yuri A. Berlin 1, Alexander L. Burin 2 Technische Universit~t Mrmchen, Physik Department T-38, D-85748 Garching, Germany Received 1 November 1996; in final form 1 January 1997 Abstract A class of models has been proposed for the dynamics of the local configurational changes governing rate processes in complex systems. Models that fall into this class are based on a hierarchical picture of a complex object. In addition, they include constraints in order to take into account the coupling between local and global configurational rearrangements of a complex object. Using the simplest formulation possible, we have shown that the net effect of global modes on the dynamics of the configuration coordinate is the anomalous time-dependent diffusivity. The latter arises only below a certain temperature prescribed by the energy distribution of configurational substates. 1. Introduction Configurational rearrangements of the reactant surroundings often accompany rate processes in complex molecular objects, such as polymers [1,2] and biomolecules [3-13]. Detailed experimental studies of ligand binding reactions [4,9,13-16] and electron transfer processes in proteins [3,17] show that these rearrangements can be triggered by the formation of reactants inside complex objects due to their excitation, for instance, by a short laser flash. As a result, the reactant surroundings undergo relaxation from the initial non-equilibrium configuration towards the final equilibrium configurational state. For complex objects, the latter process proceeds along many degrees of freedom and on a large number of timescales. Since at least several of the coordinates specifying the relaxing degrees of freedom also define the height of the reaction barrier, the rate process turns out to be coupled to the changes in configuration of the complex molecular system where the chemical transformation occurs. In this case reaction dynamics can be described in terms of a non-equilibrium barrier crossing, frequently discussed in the literature [6,11,12,18-20] using the model proposed by Agmon and Hopfieid [21]. On leave from N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, ulitsa Kossygina 4, 117334 Moscow, Russian Federation. 2 Current address: Department of Physics, City College of the City University of New York, 138th Street at Convent Avenue, 10031 New York, USA. 0009-2614/97/$17.00 Copyright © 1997 Published by Elsevier Science B.V. All rights reserved PH S0009-2614(97)00101-2