The kinesin walk: a dynamic model with elastically coupled heads

Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads showing all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity which can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.Comment: 6 pages, 3 figure

Effects of intermediate bound states in dynamic force spectroscopy

We revisit here some aspects of the interpretation of dynamic force spectroscopy experiments. The standard theory predicts a typical unbinding force $f^*$ linearly proportional to the logarithm of the loading rate $r$ when a single energetical barrier controls the unbinding process; for a more complex situation of $N$ barriers, it predicts at most $N$ linear segments for the $f^*$ vs. $\log(r)$ curve, each segment characterizing a different barrier. We here extend this existing picture using a refined approximation, we provide a more general analytical formula, and show that in principle up to $N(N+1)/2$ segments can show up experimentally. As a consequence the interpretation of data can be ambiguous, for the characteristics and even the number of barriers. A further possible outcome of a multiple-barrier landscape is a bimodal or multimodal distribution of the unbinding force at a given loading rate, a feature recently observed experimentally.Comment: 7 pages, 5 figure

The maintenance of sex in bacteria is ensured by its potential to reload genes

Why sex is maintained in nature is a fundamental question in biology. Natural genetic transformation (NGT) is a sexual process by which bacteria actively take up exogenous DNA and use it to replace homologous chromosomal sequences. As it has been demonstrated, the role of NGT in repairing deleterious mutations under constant selection is insufficient for its survival, and the lack of other viable explanations have left no alternative except that DNA uptake provides nucleotides for food. Here we develop a novel simulation approach for the long-term dynamics of genome organization (involving the loss and acquisition of genes) in a bacterial species consisting of a large number of spatially distinct populations subject to independently fluctuating ecological conditions. Our results show that in the presence of weak inter-population migration NGT is able to subsist as a mechanism to reload locally lost, intermittently selected genes from the collective gene pool of the species through DNA uptake from migrants. Reloading genes and combining them with those in locally adapted genomes allow individual cells to re-adapt faster to environmental changes. The machinery of transformation survives under a wide range of model parameters readily encompassing real-world biological conditions. These findings imply that the primary role of NGT is not to serve the cell with food, but to provide homologous sequences for restoring genes that have disappeared from or become degraded in the local population.Comment: 16 pages with 3 color figures. Manuscript accepted for publication in Genetics (www.genetics.org

Fundamental statistical features and self-similar properties of tagged networks

We investigate the fundamental statistical features of tagged (or annotated) networks having a rich variety of attributes associated with their nodes. Tags (attributes, annotations, properties, features, etc.) provide essential information about the entity represented by a given node, thus, taking them into account represents a significant step towards a more complete description of the structure of large complex systems. Our main goal here is to uncover the relations between the statistical properties of the node tags and those of the graph topology. In order to better characterise the networks with tagged nodes, we introduce a number of new notions, including tag-assortativity (relating link probability to node similarity), and new quantities, such as node uniqueness (measuring how rarely the tags of a node occur in the network) and tag-assortativity exponent. We apply our approach to three large networks representing very different domains of complex systems. A number of the tag related quantities display analogous behaviour (e.g., the networks we studied are tag-assortative, indicating possible universal aspects of tags versus topology), while some other features, such as the distribution of the node uniqueness, show variability from network to network allowing for pin-pointing large scale specific features of real-world complex networks. We also find that for each network the topology and the tag distribution are scale invariant, and this self-similar property of the networks can be well characterised by the tag-assortativity exponent, which is specific to each system