Measuring the Limping of Processive Motor Proteins

The cells of all living creatures rely on a host of molecular scale machines to perform vital tasks. In the spirit of this special issue of J. Stat. Phys., we describe briefly the background concerning one class of these machines, namely, processive motor proteins such as, specifically, conventional kinesin, myosin V, and cytoplasmic dynein. These single-molecule motors tow cellular cargoes under load along oriented linear molecular tracks within the cell taking many hundreds of consecutive discrete steps. Experiments aimed at understanding the mechanism of the stepping process have recently led to observations of ‘‘limping” in which alternate steps are found to be slow or fast, respectively. Reliable experimental measurements of the ‘‘true” or intrinsic limping factor, L ₀, understood as the ideal overall ratio of the longer dwell times prior to one set of steps to the shorter times for the interlaced steps, provide a route to improving appropriate biomechanochemical models. These, in turn, may help reveal and quantify details of the underlying asymmetric walking mechanisms. However, a difficulty is posed in measuring L ₀ by the inescapable thermal fluctuations that act on an individual motor molecule that takes only a finite number, say, n odd and n even steps under fixed load, etc. Accordingly, we treat the stochastic issues theoretically for some basic kinetic motor models and experimental procedures, obtaining various exact bounds and explicit results for distributions and their moments. Typically for n?10 the observed mean values, 〈L _n 〉, significantly overestimate L ₀. However, the medians and rescaled means, \({\overline{L}}_{n}^{\, *}=\langle L_{n}\rangle(n-1)/n\), provide better guides to the value of L ₀ provided it is not too close to unity. Separately, we present figures, a table, and approximate formulas intended to assist practically those designing, undertaking, and assessing experiments on limping.