<title>Stochastic cluster dynamics of macromolecules</title>

Abstract

The issues about the behaviour of variant test particles (TP) in 2D potential field with complex relief are studied. The cases with time-dependent parameters of potential field are considered. In particular the mathematical models that are discussed in this paper can describe either the process of penetration of TP (ligand) in active site of the enzyme or proton's transition from one potential pit to another.The study ofthe transition of a multistable system from one stable to another traces back to L.Pontryagm, A. Andronov and A.Vitt (1933). In the recent years new problems emerged in the studies of complex vibrational systems. These problems deal with the transitions of a TP in the 2D potential relieves with the fluctuating or periodically changmg parameters. As a complex relief is a variant of Sinai billiard, the motions of TP therein become stochastic even without any external action. The examples of the cluster dynamics of macromolecules are considered. The dependencies are established ofthe time oftransition of a TP from the area of one minimum to the zone of attraction of another one on the frequency of the periodic changes of the parameters of the potential relief.The finite sizes of TPs are taken into account. The study of these processes will allow us to get closer to the comprehension ofprinciples ofmolecular machines. This paper is based on ideas formulated in Ref. 1-3 and continues our preceding papers Ref 4-9. 3. BASIC TWO-DIMENSIONAL (2D) MODEL Let us consider the equations of motion of a TP in the potential field U (here and hereinafter all values are non-dimensional): 54 SPIE Vol. 3053 • 0277-786X/97/$10.00 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/22/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx