Energie Transfer and Chaotic Oscillations in Enzyme Catalysis

Introduction to the reaction theory and cluster dynamics of enzymes

“…We observe here a mode coupling of the linear modes of the second oscillator on the modes of the first oscillator [Ebeling & Romanovsky, 1985;Ebeling & Jenssen, 1988;Hesse &;Schimansky-Geier, 1991]. Of special interest is the case k < 0, k' -0, k" > 0 corresponding to a the bistable potential shown in Fig.…”

“…The simplest case is the coupling of a nonlinear oscillator in a;-direction with a linear oscillator in y-direction through a mixed quadratic and cubic coupling term. The energy transfer between the modes has been proposed as a simple model for the processes in enzyme catalysis [Ebeling, 1985;Ebeling & Romanovsky, 1985]. The hamiltonian dynamics of the systems is defined by the potential U{x, y) = \kx 2 + \k'x 3 + ]k"x* -exy + \K V 2 + rjxy 2 ( 1.43) with K > 0 and k" > 0.…”

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

“…Here: U = U0 {(arctg(r1b)arctg(r1 + b)) + (arctg(r2b)arctg(r2 + b))} +Cr2 + UL, (2) = +(xg)2, = +(x + g)2, r = + where U0, c, b, g, x, Yc , d, r0 are free constants; x, y are Cartesian coordinates; ULJ is a Lennard-Jones potential. By varying the coefficients we can easily change a location of potential pits, their depths, as well as a height of bamer between them.…”

“…By varying the coefficients we can easily change a location of potential pits, their depths, as well as a height of bamer between them. RESULTS OF CALCULATIONS 1 . The process of stochastization of oscillations of a particle in a conservative system depending on initial conditions was studied (see (2) without ULJ). The behavior on infinity is similar to Lennard-Jones potential behavior.…”

“…Such a large range of eigen frequencies is explained by essential nonlinear behavior of functions in (2). Depending on the initial position of the particle and the direction of its initial velocity vector the particle can either overcome the potential barrier and make a turn in the vicinity of the other minimum, or not overcome it.…”