Summary.The rotatory motor of bacterial flagella is driven by a transmembrane electrochemical gradient of protons. A model of the flagellar motor is analysed, which is based on the notion that protons passing through the motor use a channel-like pathway formed by ligand groups located partly on the rotor, partly on the stator. Proton translocation is linked to the displacement of stator elements which are elastically bound to the cell wall. The model is described by a cyclic sequence of translocation steps and proton binding and release reactions. Stochastic simulations of the model are carried out in which transitions between the states of the reaction cycle are treated as random events. In this way the rotation frequency can be predicted as a function of experimental variables such as driving force and viscous load. Furthermore, the effects of microscopic parameters such as the transition frequencies of stator elements and the force constant of elastic coupling on the dynamic properties of the motor can be studied. The model allows for intrinsic uncoupling ("slippage") resulting from translocation steps without associated rotational movement. It is shown that mechanistic information can be obtained by studying random fluctuations of rotational speed.

Some years ago a theory of non-equilibrium voltage fluctuations in biological membranes was developed (Frehland and Solleder 1985, 1986) under a linearisation condition which is valid for a great number of transport units. In order to get an insight into the stochastic behaviour of such systems, consisting of small numbers of transport units, we carried out Monte-Carlo-simulations and compared the mean voltage course and the spectral density with the results of the previous theory. Under parameter conditions of biological relevance no significant differences from the behaviour of systems with large numbers, as predicted from the earlier theory, could be found in the case of rigid pores and ion carriers. However, in the case of small numbers, channels with open-closed-kinetics showed great deviation. With increasing number of transport units agreement with the previous theory was obtained.

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