Force and Motion Generation of Molecular Motors: A Generic Description

We review the properties of biological motor proteins which move along linear filaments that are polar and periodic. The physics of the operation of such motors can be described by simple stochastic models which are coupled to a chemical reaction. We analyze the essential features of force and motion generation and discuss the general properties of single motors in the framework of two-state models. Systems which contain large numbers of motors such as muscles and flagella motivate the study of many interacting motors within the framework of simple models. In this case, collective effects can lead to new types of behaviors such as dynamic instabilities of the steady states and oscillatory motion.Comment: 29 pages, 9 figure

The relationship between the intracellular Ca2+ transient and the isometric twitch force in frog muscle fibres

The calcium-sensitive fluorescent indicator fluo-3 was used to monitor the intracellular free calcium concentration ([Ca2+]i) during isometric twitches in twenty-nine single muscle fibres from the anterior tibialis muscle of Rana temporaria (sarcomere length, 2.2 microns; 2-4 degrees C). The transient change in [Ca2+]i in response to a single stimulus was very brief. The time to peak and the duration of the Ca2+ signal, measured at 50% of the peak amplitude, were 8.3 +/- 0.2 and 22.1 +/- 1.4 ms (mean +/- S.E.M., n = 29), respectively. The mean peak amplitude of the Ca2+ transient was 3.2 +/- 0.1 microM, ranging from 2.46 to 3.92 microM among the different fibres. The isometric force started to rise 2.5 ms before [Ca2+]i reached its maximum value. When peak twitch force was attained, [Ca2+]i had already declined to approximately 10% of its maximum value. The peak force produced during a twitch was closely related to the decay phase of the Ca2+ transient, a slower decay of [Ca2+]i being associated with a greater amplitude of the twitch. The amplitude and duration of the Ca2+ transient varied in a systematic way relative to one another in different fibres, in that a greater amplitude was associated with a more rapid decay of the Ca2+ transient. NO3- and Zn2+ added to the external medium greatly enhanced the peak twitch force without markedly affecting the amplitude of the Ca2+ transient. However, both agents delayed the decay of [Ca2+]i. It is concluded that the decay phase of the Ca2+ transient is a more important determinant of the mechanical response during an isometric twitch than is the peak amplitude of the transient.Peer reviewe

A dynamic model of the head acceleration associated with heading a soccer ball

This study develops a dynamic model of head acceleration, which incorporates physiologically related neck muscle contributions, to further the understanding of the mechanical behaviour of the head-neck system during soccer heading. An inverted pendulum is combined with a linear visco-elastic element to model the head-neck system following a half-sine input force. Model parameter values were varied to obtain agreement with previously published experimental data (Naunheimet al., 2003), and were subsequently compared to literature values. The model predicted the same mechanical angular kinematics as observed experimentally both during and post impact. The greatest acceleration was in the anterior direction at the instant the ball left the head, attributed to the elastic stiffness of the neck musculature. The head-neck stiffness and damping coefficients determined from the model (350 N m rad-1 and 4 N m s rad-1, respectively) were similar to those reported elsewhere when subjects were asked to resist maximally. The model may be subsequently used to investigate differences in technique and ability with respect to the salient model parameters to further our biomechanical understanding of soccer heading