Peter H. Richter

Diffusion controlled reaction rates in spheroidal geometry: Application to repressor-operator association and membrane bound enzymes

Abstract The von Smoluchowski-Debye formulae for diffusion controlled reaction rates are extended to the more general case of spheroidal geometry. Their application to the association of represser and operator is thoroughly discussed in the light of recent experiments on the lac system by Riggs et al. The conclusions suggest that the surprisingly high association rate is not essentially due to electrostatic attraction but rather to unspecific binding of represser to nonoperator DNA with subsequent diffusion along the chain.

Rate enhancement by guided diffusion. Chain length dependence of repressor-operator association rates.

Association rates are calculated for cases where one reaction partner belongs to a chain that has an unspecific affinity to the other. Provided that the unspecific attachment does not completely suppress diffusion along the chain, this channeling may considerably speed up the association. Explicit formulae are derived to show how this effect depends on the chain length and other parameters. The influence of electrostatic forces and reaction barriers is discussed. Time dependent solutions of the diffusion equations are analyzed in order to test the usual steady state assumptions. Experiments on the repressor-operator system seem to be in good agreement with our theory.

Fluctuations in spatially homogeneous chemical steady states

The investigation of the properties of small fluctuations serves as a basis for the generalization of equilibrium and irreversible thermodynamics, to encompass all spatially homogeneous situations of stable chemical steady states. In terms of a Gibbs ensemble picture, the reactants are coupled to particle reservoirs, often in a more intriguing way than in usual grand canonical statistics. It is shown how these couplings can be represented as generalized forces, by postulating an equipartition theorem. Response functions connected with the action of external forces are introduced, and the fluctuation–dissipation theorem is derived as a consequence of the proper definition of forces. The symmetry properties of the systems, with respect to time reversal, provide a classification scheme for the large body of possible steady states.

On the structure of rotational discontinuities with large phase angles

Abstract Using hybrid simulations (particle ions and electron fluid) we have investigated the stability of rotational discontinuities. A density increase builds up at the position of the rotational discontinuity. The final density structure of the rotational discontinuity develops independently of the initial phase angle φ and of the half width D . Only minor differences occur for different senses of rotation, i.e. for a rotational discontinuity exhibiting an ion sense or an electron sense of rotation, respectively. However the structure of the magnetic field, B, strongly depends on the phase as shown by simulations of rotational discontinuities with 270° phase angle. Rotational discontinutiies with 270° phase develop independently of the initial sense of rotation into structures with 90°-rotation.

Stochastic theory of a selection game

The stochastic theory of a nonlinear game is presented which incorporates some of the essential properties of living systems: metabolism, reproduction and mutability. The steady state distribution function as well as the complete time development are given explicitly. The second law of thermodynamics is generalized to a certain class of nonequilibrium systems. An order parameter is introduced as a measure of the systems internal organization. From the point of view of phase transition theory, the model exhibits a transition at the absolute zero of temperature, with critical behaviour showing up in the low temperature region.