Stochastic thermodynamics for active matter

The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven systems that allows to define fluctuating work and heat. We apply these definitions to active matter, assuming that dissipation can be modelled by effective non-conservative forces. We show that, through the work, conjugate extensive and intensive observables can be defined even in non-equilibrium steady states lacking a free energy. As an illustration, we derive the expressions for the pressure and interfacial tension of active Brownian particles. The latter becomes negative despite the observed stable phase separation. We discuss this apparent contradiction, highlighting the role of fluctuations, and we offer a tentative explanation

Cdc6 ATPase activity disengages Cdc6 from the pre-replicative complex to promote DNA replication

© 2015, Chang et al.To initiate DNA replication, cells first load an MCM helicase double hexamer at origins in a reaction requiring ORC, Cdc6, and Cdt1, also called pre-replicative complex (pre-RC) assembly. The essential mechanistic role of Cdc6 ATP hydrolysis in this reaction is still incompletely understood. Here, we show that although Cdc6 ATP hydrolysis is essential to initiate DNA replication, it is not essential for MCM loading. Using purified proteins, an ATPase-defective Cdc6 mutant ‘Cdc6-E224Q’ promoted MCM loading on DNA. Cdc6-E224Q also promoted MCM binding at origins in vivo but cells remained blocked in G1-phase. If after loading MCM, Cdc6-E224Q was degraded, cells entered an apparently normal S-phase and replicated DNA, a phenotype seen with two additional Cdc6 ATPase-defective mutants. Cdc6 ATP hydrolysis is therefore required for Cdc6 disengagement from the pre-RC after helicase loading to advance subsequent steps in helicase activation in vivo

Shock formation for 2D2D quasilinear wave systems featuring multiple speeds: Blowup for the fastest wave, with non-trivial interactions up to the singularity

We prove a stable shock formation result for a large class of systems of quasilinear wave equations in two spatial dimensions. We give a precise description of the dynamics all the way up to the singularity. Our main theorem applies to systems of two wave equations featuring two distinct wave speeds and various quasilinear and semilinear nonlinearities, while the solutions under study are (non-symmetric) perturbations of simple outgoing plane symmetric waves. The two waves are allowed to interact all the way up to the singularity. Our approach is robust and could be used to prove shock formation results for other related systems with many unknowns and multiple speeds, in various solution regimes, and in higher spatial dimensions. However, a fundamental aspect of our framework is that it applies only to solutions in which the "fastest wave" forms a shock while the remaining solution variables do not. Our approach is based on an extended version of the geometric vectorfield method developed by D. Christodoulou in his study of shock formation for scalar wave equations as well as the framework developed in our recent joint work with J. Luk, in which we proved a shock formation result for a quasilinear wave-transport system featuring a single wave operator. A key new difficulty that we encounter is that the geometric vectorfields that we use to commute the equations are, by necessity, adapted to the wave operator of the (shock-forming) fast wave and therefore exhibit very poor commutation properties with the slow wave operator, much worse than their commutation properties with a transport operator. To overcome this difficulty, we rely on a first-order reformulation of the slow wave equation, which, though somewhat limiting in the precision it affords, allows us to avoid uncontrollable commutator terms.Comment: 117 pages, 3 figure