We investigate theoretically the violations of Einstein and Onsager relations and the thermodynamic efficiency for a single processive motor operating far from equilibrium using an extension of the two-state model introduced by Kafri et al. [Biophys. J. 86, 3373 (2004)10.1529/biophysj.103.036152]. With the aid of the Fluctuation Theorem, we analyze the general features of these violations and this efficiency and link them to mechanochemical couplings of motors. In particular, an analysis of the experimental data of kinesin using our framework leads to interesting predictions that may serve as a guide for future experiments.

Uncovering mechanisms that control the dynamics of microtubules is fundamental for our understanding of multiple cellular processes such as chromosome separation and cell motility. Building on previous theoretical work on the dynamic instability of microtubules, we propose here a stochastic model that includes all relevant biochemical processes that affect the dynamics of microtubule plus-end, namely, the binding of GTP-bound monomers, unbinding of GTP- and GDP-bound monomers, and hydrolysis of GTP monomers. The inclusion of dissociation processes, present in our approach but absent from many previous studies, is essential to guarantee the thermodynamic consistency of the model. Our theoretical method allows us to compute all dynamic properties of microtubules explicitly. Using experimentally determined rates, it is found that the cap size is ∼3.6 layers, an estimate that is compatible with several experimental observations. In the end, our model provides a comprehensive description of the dynamic instability of microtubules that includes not only the statistics of catastrophes but also the statistics of rescues.

We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a minimal ratchet model. We extend our previous work on this model, by further investigating the constraints imposed by the fluctuation theorem on the operation of a molecular motor far from equilibrium. In this work, we show the connections between different formulations of the fluctuation theorem. One formulation concerns the generating function of the currents while another one concerns the corresponding large deviation function, which we have calculated exactly for this model. A third formulation concerns the ratio of the probability of observing a velocity v to the same probability of observing a velocity -v . Finally, we show that all the formulations of the fluctuation theorem can be understood from the notion of entropy production.

Autocatalysis is essential for the origin of life and chemical evolution. However, the lack of a unified framework so far prevents a systematic study of autocatalysis. Here, we derive, from basic principles, general stoichiometric conditions for catalysis and autocatalysis in chemical reaction networks. This allows for a classification of minimal autocatalytic motifs called cores. While all known autocatalytic systems indeed contain minimal motifs, the classification also reveals hitherto unidentified motifs. We further examine conditions for kinetic viability of such networks, which depends on the autocatalytic motifs they contain and is notably increased by internal catalytic cycles. Finally, we show how this framework extends the range of conceivable autocatalytic systems, by applying our stoichiometric and kinetic analysis to autocatalysis emerging from coupled compartments. The unified approach to autocatalysis presented in this work lays a foundation toward the building of a systems-level theory of chemical evolution.