Nonequilibrium Strategy for Fast Target Search on the Genome.

Vital biological processes such as genome repair require fast and efficient binding of selected proteins to specific target sites on DNA. Here we propose an active target search mechanism based on "chromophoresis," the dynamics of DNA-binding proteins up or down gradients in the density of epigenetic marks, or colors (biochemical tags on the genome). We focus on a set of proteins that deposit marks from which they are repelled-a case which is only encountered away from thermodynamic equilibrium. For suitable ranges of kinetic parameter values, chromophoretic proteins can perform undirectional motion and are optimally redistributed along the genome. Importantly, they can also locally unravel a region of the genome which is collapsed due to self-interactions and "dive" deep into its core, for a striking enhancement of the efficiency of target search on such an inaccessible substrate. We discuss the potential relevance of chromophoresis for DNA repair.

Efficiency of one-dimensional active transport conditioned on motility.

By conditioning a stochastic process on the value of an observable, one obtains a new stochastic process with different properties. We apply this idea in the context of active matter and condition interacting self-propelled particles on their individual motility. Using the effective process formalism from dynamical large deviations theory, we derive the interactions that actuate the imposed mobility against jamming interactions in two toy models-the totally asymmetric exclusion process and run-and-tumble particles, in the case of two or three particles. We provide a framework which takes into account the energy-consumption required for self-propulsion and address the question of how energy-efficient the emergent interactions are. Upon conditioning, run-and-tumble particles develop an alignment interaction and achieve a higher gain in efficiency than TASEP particles. A point of diminishing returns in efficiency is reached beyond a certain level of conditioning. With recourse to a general formula for the change in energy efficiency upon conditioning, we conclude that the most significant gains occur when there are large fluctuations in mobility to exploit. From a detailed comparison of the emergent effective interaction in a two- versus a three-body scenario, we discover evidence of a screening effect which suggests that conditioning can produce topological rather than metric interactions.

Statistical mechanics of a single active slider on a fluctuating interface.

We study the statistical mechanics of a single active slider on a fluctuating interface, by means of numerical simulations and theoretical arguments. The slider, which moves by definition towards the interface minima, is active as it also stimulates growth of the interface. Even though such a particle has no counterpart in thermodynamic systems, active sliders may provide a simple model for ATP-dependent membrane proteins that activate cytoskeletal growth. We find a wide range of dynamical regimes according to the ratio between the timescales associated with the slider motion and the interface relaxation. If the interface dynamics is slow, the slider behaves like a random walker in a random environment, which, furthermore, is able to escape environmental troughs by making them grow. This results in different dynamic exponents to the interface and the particle: the former behaves as an Edward-Wilkinson surface with dynamic exponent 2, whereas the latter has dynamic exponent 3/2. When the interface is fast, we get sustained ballistic motion with the particle surfing a membrane wave created by itself. However, if the interface relaxes immediately (i.e., it is infinitely fast), particle motion becomes symmetric and goes back to diffusive. Due to such a rich phenomenology, we propose the active slider as a toy model of fundamental interest in the field of active membranes and, generally, whenever the system constituent can alter the environment by spending energy.

Active Growth and Pattern Formation in Membrane-Protein Systems.

Inspired by recent experimental observations of patterning at the membrane of a living cell, we propose a generic model for the dynamics of a fluctuating interface driven by particlelike inclusions which stimulate its growth. We find that the coupling between interfacial and inclusions dynamics yields microphase separation and the self-organization of traveling waves. These patterns are strikingly similar to those detected in experiments on biological membranes. Our results further show that the active growth kinetics do not fall into the Kardar-Parisi-Zhang universality class for growing interfaces, displaying instead a novel superposition of scaling and sustained oscillations.

Large Fluctuations and Dynamic Phase Transition in a System of Self-Propelled Particles.

We study the statistics, in stationary conditions, of the work W_{τ} done by the active force in different systems of self-propelled particles in a time τ. We show the existence of a critical value W_{τ}^{†} such that fluctuations with W_{τ}>W_{τ}^{†} correspond to configurations where interaction between particles plays a minor role whereas those with W_{τ}