Modelling motor protein systems

Abstract

Motor proteins are the cell’s workforce. They are specialized molecules which convert chemical energy to mechanical work, thereby generating force and directional motion. In some situations motor proteins act individually, but more commonly they cooperate in large ensembles to accomplish cellular functions. How do molecular motors work? And how do they work together? This lecture course recounts theoretical approaches to these questions, which complement the experimental investigations of motor protein systems described in Jonathon Howard’s course. The methods of non-equilibrium statistical mechanics permit a general analysis of how chemical energy can most effectively be used to generate the movement of an individual motor. The class of models known as “isothermal ratchets”, in particular, is a powerful tool for discussing the principles of energy transduction. More specific kinetic models, such as the “swinging lever-arm” model which is based on the known structure and chemistry of the myosin protein, indicate how these molecules are designed to work efficiently together to drive the contraction of muscle. Both classes of model indicate what types of collective effects can arise when many molecules operate in concert. Cooperative interactions within a team of motor proteins may lead to dynamical instabilities and hysteretic behaviour, which can be exploited to generate oscillations. Physiological processes which may rely on such instabilities include the vibration of insect flight muscle and the undulation of spermatozoid flagella. Motor proteins also play functional roles in sensory systems — hearing being a particularly intriguing example. Hair bundles, which are the mechano-sensors that detect motion in the inner ear, have been found to vibrate spontaneously. Motor proteins appear to play a role either in generating the oscillations, or in maintaining the bundles at the threshold of the oscillatory instability. Poised on the verge of vibrating, they are especially responsive to faint sounds.