Dynamics of active membranes with internal noise

We study the time-dependent height fluctuations of an active membrane containing energy-dissipating pumps that drive the membrane out of equilibrium. Unlike previous investigations based on models that neglect either curvature couplings or random fluctuations in pump activities, our formulation explores two new models that take both of these effects into account. In the first model, the magnitude of the nonequilibrium forces generated by the pumps is allowed to fluctuate temporally. In the second model, the pumps are allowed to switch between "on" and "off" states. We compute the mean squared displacement of a membrane point for both models, and show that they exhibit distinct dynamical behaviors from previous models, and in particular, a superdiffusive regime specifically arising from the shot noise.Comment: 7 pages, 4 figure

Nonequilibrium Fluctuations, Travelling Waves, and Instabilities in Active Membranes

The stability of a flexible fluid membrane containing a distribution of mobile, active proteins (e.g. proton pumps) is shown to depend on the structure and functional asymmetry of the proteins. A stable active membrane is in a nonequilibrium steady state with height fluctuations whose statistical properties are governed by the protein activity. Disturbances are predicted to travel as waves at sufficiently long wavelength, with speed set by the normal velocity of the pumps. The unstable case involves a spontaneous, pump-driven undulation of the membrane, with clumping of the proteins in regions of high activity.Comment: 4 two-column pages, two .eps figures included, revtex, uses eps

Fluctuations in active membranes

Active contributions to fluctuations are a direct consequence of metabolic energy consumption in living cells. Such metabolic processes continuously create active forces, which deform the membrane to control motility, proliferation as well as homeostasis. Membrane fluctuations contain therefore valuable information on the nature of active forces, but classical analysis of membrane fluctuations has been primarily centered on purely thermal driving. This chapter provides an overview of relevant experimental and theoretical approaches to measure, analyze and model active membrane fluctuations. In the focus of the discussion remains the intrinsic problem that the sole fluctuation analysis may not be sufficient to separate active from thermal contributions, since the presence of activity may modify membrane mechanical properties themselves. By combining independent measurements of spontaneous fluctuations and mechanical response, it is possible to directly quantify time and energy-scales of the active contributions, allowing for a refinement of current theoretical descriptions of active membranes.Comment: 38 pages, 9 figures, book chapte

Simulating counting oracles with cooperation

We prove that monodirectional shallow chargeless P systems with active membranes and minimal cooperation working in polynomial time precisely characterise P#P k , the complexity class of problems solved in polynomial time by deterministic Turing machines with a polynomial number of parallel queries to an oracle for a counting problem

A Toolbox for Simpler Active Membrane Algorithms

We show that recogniser P systems with active membranes can be augmented with a priority over their set of rules and any number of membrane charges without loss of generality, as they can be simulated by standard P systems with active membranes, in particular using only two charges. Furthermore, we show that more general accepting conditions, such as sending out several, possibly contradictory results and keeping only the first one, or rejecting by halting without output, are also equivalent to the standard accepting conditions. The simulations we propose are always without significant loss of efficiency, and thus the results of this paper can hopefully simplify the design of algorithms for P systems with active membranes

P Systems with Active Membranes and Separation Rules

The P systems are a class of distributed parallel computing devices of a biochemical type. In this paper, a new de¯nition of separation rules in P systems with active membranes is given. Under the new de¯nition, the e±ciency and universality of P systems with active membranes and separation rules instead of division are investigated

Complete Problems for a Variant of P Systems with Active Membranes

We identify a family of decision problems that are hard for some complexity classes defined in terms of P systems with active membranes working in polynomial time. Furthermore, we prove the completeness of these problems in the case where the systems are equipped with a form of priority that linearly orders their rules. Finally, we highlight some possible connections with open problems related to the computational complexity of P systems with active membranes

Tissue P Systems with Cell Division

In tissue P systems several cells (elementary membranes) commu- nicate through symport/antiport rules, thus carrying out a computation. We add to such systems the basic feature of (cell) P systems with active membranes { the possibility to divide cells. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computa- tionally hard problems in polynomial time; we illustrate this possibility with SAT problem.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

Tissue P systems with cell division

In tissue P systems several cells (elementary membranes) communicate through symport/antiport rules, thus carrying out a computation. We add to such systems the basic feature of (cell–like) P systems with active membranes – the possibility to divide cells. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time; we illustrate this possibility with SAT problem.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58