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Growth in bacterial populations generally depends on the environment (availability and quality of nutrients, presence of a toxic inhibitor, product inhibition..). Here, we build a general model to describe the action of a bacteriostatic antibiotic, assuming that this drug inhibits essential autocatalytic cycles involved in the cell metabolism. The model can describe various types of antibiotics and confirms the existence of two distinct regimes of growth-dependent susceptibility, previously identified only for ribosome targeting antibiotics. Interestingly, below a certain threshold, a coexistence of two values of the growth rate is possible, which has also been observed experimentally., Comment: 6 pages, 3 figures for the main. 16 pages, 6 figures for the supplemental

We present an improvement of the Gillespie Exact Stochastic Simulation Algorithm, which leverages a bitwise representation of variables to perform independent simulations in parallel. We show that the subsequent gain in computational yield is significant, and it may allow to perform simulations of non-well mixed chemical systems. We illustrate this idea with simulations of Frank model, originally introduced to explain the emergence of homochirality in prebiotic systems.

RNA in extant biological systems is homochiral; it consists exclusively of D-ribonucleotides rather than L-ribonucleotides. How the homochirality of RNA emerged is not known. Here, we use stochastic simulations to quantitatively explore the conditions for RNA homochirality to emerge in the prebiotic scenario of an RNA reactor, in which RNA strands react in a non-equilibrium environment. These reactions include the hybridization, dehybridization, template-directed ligation, and cleavage of RNA strands. The RNA reactor is either closed, with a finite pool of ribonucleotide monomers of both chiralities (D and L), or the reactor is open, with a constant inflow of a racemic mixture of monomers. For the closed reactor, we also consider the interconversion between D and L monomers via a racemization reaction. We first show that template-free polymerization is unable to reach a high degree of homochirality, due to the lack of autocatalytic amplification. In contrast, in the presence of template-directed ligation, with base pairing and stacking between bases of the same chirality thermodynamically favored, a high degree of homochirality can arise and be maintained, provided the non equilibrium environment overcomes product inhibition, for instance via temperature cycling. Furthermore, if the experimentally observed kinetic stalling of ligation after chiral mismatches is also incorporated, the RNA reactor can evolve towards a fully homochiral state, in which one chirality is entirely lost. This is possible because the kinetic stalling after chiral mismatches effectively implements a chiral cross-inhibition process. Taken together, our model supports a scenario where the emergence of homochirality is assisted by template-directed ligation and polymerization in a non equilibrium RNA reactor.

Autocatalytic chemical networks play a predominant role in a large number of natural systems such as in metabolic pathways and in ecological networks. Despite recent efforts, the precise impact of thermodynamic constraints on these networks remains elusive. In this work, we present a theoretical framework that allows determining bounds on the thermodynamic affinity and on the concentrations of autocatalysts in mass-action autocatalytic networks. These bounds can be obtained solely from the stoichiometry of the underlying chemical reaction network, and are independent from the numerical values of kinetic parameters. This property holds in the specific regime where all the fluxes of the network are tightly coupled and maximal. Our method is applicable to large networks, and can be used to complement constraints-based modeling methods of metabolic networks, which typically do not provide predictions about thermodynamic properties or concentration ranges of metabolites, Comment: 27 pages, 5 figures, 1 table

Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate or the population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete lineages that do not survive until the end of the experiment? Here, we develop a model-independent theoretical framework to address this issue. We show how to quantify fitness landscape, survivor bias and selection for arbitrary cell traits from cell lineage statistics in the presence of death, and we test this method using an experimental data set in which a cell population is exposed to a drug that kills a large fraction of the population. This analysis reveals that failing to properly account for dead lineages can lead to misleading fitness estimations. For simple trait dynamics, we prove and illustrate numerically that the fitness landscape and the survivor bias can in addition be used for the non-parametric estimation of the division and death rates, using only lineage histories. Our framework provides universal bounds on the population growth rate, and a fluctuation-response relation which quantifies the reduction of population growth rate due to the variability in death rate. Further, in the context of cell size control, we obtain generalizations of Powell's relation that link the distributions of generation times with the population growth rate, and show that the survivor bias can sometimes conceal the adder property, namely the constant increment of volume between birth and division.

Organisms that grow and survive in uncertain environments may need to change their physiological state as the environment changes. When the environment is uncertain, one strategy known as bet-hedging is to make these changes randomly and independently of the environment, to ensure that at least part of the population is well adapted. Organisms that collect information from their environment may also use this information to modulate their changes of physiological states. We review these different strategies and point out parallels with the theory of optimal financial investments.

We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. A known asymptotic scaling for the difference between the growth rate of the gambler and the optimal growth rate, known as the gambler'sregret, is recovered. We show how this adaptive strategy is related to the universal portfolio strategy, and we build improved adaptive strategies in which the gambler exploits information contained in the bookmaker odds distribution to reduce his/her initial loss of the capital during the learning phase., Comment: 13 pages, 8 figures

We study the Stochastic Thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to an identical copy of itself, and resetting, by which some properties of the daughter cells (such as their size or age) are reset to new values following division. We derive the first and second laws of Stochastic Thermodynamics for this process, and identify separate contributions due to branching and resetting. We apply our framework to well-known models of cell size control, such as the sizer, the timer, and the adder. We show that the entropy production of resetting is negative and that of branching is positive for these models in the regime of exponential growth of the colony. This property suggests an analogy between our model for cell growth and division and heat engines, and the introduction of a thermodynamic efficiency, which quantifies the conversion of one form of entropy production to another.

Homochirality, i.e. the dominance across all living matter of one enantiomer over the other among chiral molecules, is thought to be a key step in the emergence of life. Building on ideas put forward by Frank and many others, we proposed recently one such mechanism in G. Laurent et al., PNAS (2021) based on the properties of large out of equilibrium chemical networks. We showed that in such networks, a phase transition towards an homochiral state is likely to occur as the number of chiral species in the system becomes large or as the amount of free energy injected into the system increases. This paper aims at clarifying some important points in that scenario, not covered by our previous work. We first analyze the various conventions used to measure chirality, introduce the notion of chiral symmetry of a network, and study its implications regarding the relative chiral signs adopted by different groups of molecules. We then propose a generalization of Frank's model for large chemical networks, which we characterize completely using methods of random matrices. This analysis can be extended to sparse networks, which shows that the emergence of homochirality is a robust transition.

The selection of a single molecular handedness, or homochirality across all living matter, is a mystery in the origin of life. Frank's seminal model showed in the fifties how chiral symmetry breaking can occur in non-equilibrium chemical networks. However, an important shortcoming in this classic model is that it considers a small number of species, while there is no reason for the prebiotic system, in which homochirality first appeared, to have had such a simple composition. Furthermore, this model does not provide information on what could have been the size of the molecules involved in this homochiral prebiotic system. Here, we show that large molecular systems are likely to undergo a phase transition towards a homochiral state, as a consequence of the fact that they contain a large number of chiral species. Using chemoinformatics tools, we quantify how abundant are chiral species in the chemical universe of all possible molecules of a given length. Then, we propose that Frank's model should be extended to include a large number of species, in order to possess the transition towards homochirality as confirmed by numerical simulations. Finally, using random matrix theory, we prove that large non-equilibrium reaction networks possess a generic and robust phase transition towards a homochiral state.

We obtain general inequalities constraining the difference between the average of an arbitrary function of a phenotypic trait, which includes the fitness landscape of the trait itself, in the presence or in the absence of natural selection. These inequalities imply bounds on the strength of selection, which can be measured from the statistics of trait values and divisions along lineages. The upper bound is related to recent generalizations of linear response relations in Stochastic Thermodynamics, and shares common features with Fisher's fundamental theorem of natural selection, and with its generalization by Price, although they define different measures of selection. The lower bound follows from recent improvements on Jensen's inequality, and both bounds depend on the variability of the fitness landscape. We illustrate our results using numerical simulations of growing cell colonies and with experimental data of time-lapse microscopy experiments of bacteria cell colonies.

We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called fluctuation relation relates these two samplings, independently of the model used to generate divisions and growth in the cell population. These relations lead to estimators of the population growth rate, which can be very efficient as we demonstrate by an analysis of a set of mother machine data. These fluctuation relations lead to general and important inequalities between the mean number of divisions and the doubling time of the population. We also study the fitness landscape, a concept based on the two samplings mentioned above, which quantifies the correlations between a phenotypic trait of interest and the number of divisions. We obtain explicit results when the trait is the age or the size, for age and size-controlled models.

In this paper, we derive a number of inequalities which express power-efficiency trade-offs that hold generally for thermodynamic machines operating in non-equilibrium stationary states. One of these inequalities concerns the output power, which is bounded by a quadratic function of the thermodynamic efficiency multiplied by a factor. Different factors can be obtained according to the level of knowledge one has about the underlying dynamics of the machine, they can depend for instance on the covariance of the input flux, the dynamical activity, or the non-equilibrium conductance., Comment: 18 pages, 3 figures

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. While these inequalities have been derived before for age controlled models with negligible mother-daughter correlations, we show that they also hold for a broad class of size-controlled models. We discuss the implications of this result for the interpretation of a recent experiment in which the growth of bacteria strains has been probed at the single cell level., Comment: 13 pages, 5 figures

Can prelife proceed without cell division? A recently proposed mechanism suggests that transient compartmentalization could have preceded cell division in prebiotic scenarios. Here, we study transient compartmentalization dynamics in the presence of mutations and noise in replication, as both can be detrimental the survival of compartments. Our study comprises situations where compartments contain uncoupled autocatalytic reactions feeding on a common resource, and systems based on RNA molecules copied by replicases, following a recent experimental study. Using the theory of branching processes, we show analytically that two regimes are possible. In the diffusion-limited regime, replication is asynchronous which leads to a large variability in the composition of compartments. In contrast, in a replication-limited regime, the growth is synchronous and thus the compositional variability is low. Typically, simple autocatalysts are in the former regime, while polymeric replicators can access the latter. For deterministic growth dynamics, we introduce mutations that turn functional replicators into parasites. We derive the phase boundary separating coexistence or parasite dominance as a function of relative growth, inoculation size and mutation rate. We show that transient compartmentalization allows coexistence beyond the classical error threshold, above which the parasite dominates. Our findings invite to revisit major prebiotic transitions, notably the transitions towards cooperation, complex polymers and cell division., Comment: 37 pages, 13 figures

The mobility of membrane proteins controls many biological functions. The application of the model of Saffman and Delbr\"uck to the diffusion of membrane proteins does not account for all the experimental measurements. These discrepancies have triggered a lot of studies on the role of the mechanical factors in the mobility. After a short review of the Saffman and Delbr\"uck model and of some key experiments, we explore the various ways to incorporate the effects of the different mechanical factors. Our approach focuses on the coupling of the protein to the membrane, which is the central element in the modelling. We present a general, polaron-like model, its recent application to the mobility of a curvature sensitive protein, and its various extensions to other couplings that may be relevant in future experiments., Comment: To appear as a Chapter in "Physics of Biological Membranes", edited by Dr. Patricia Bassereau & Dr. Pierre Sens, Springer Nature Switzerland

Kinetic theory and thermodynamics of reaction networks are extended to the out-of-equilibrium dynamics of continuous-flow stirred tank reactors (CSTR) and serial transfers. On the basis of their stoichiometry matrix, the conservation laws and the cycles of the network are determined for both dynamics. It is shown that the CSTR and serial transfer dynamics are equivalent in the limit where the time interval between the transfers tends to zero proportionally to the ratio of the fractions of fresh to transferred solutions. These results are illustrated with finite cross-catalytic reaction network and an infinite reaction network describing mass exchange between polymers. Serial transfer dynamics is typically used in molecular evolution experiments in the context of research on the origins of life. The present study is shedding a new light on the role played by serial transfer parameters in these experiments., Comment: 11 pages, 7 figures

Transient compartments have been recently shown to be able to maintain functional replicators in the context of prebiotic studies. Motivated by this experiment, we show that a broad class of selection dynamics is able to achieve this goal. We identify two key parameters, the relative amplification of non-active replicators (parasites) and the size of compartments. Since the basic ingredients of our model are the competition between a host and its parasite, and the diversity generated by small size compartments, our results are relevant to various phage-bacteria or virus-host ecology problems., Comment: 11 pages, 10 figures

In this paper, we introduce a real symmetric and positive semi-definite matrix, which we call the non-equilibrium conductance matrix, and which generalizes the Onsager response matrix for a system in a non-equilibrium stationary state. We then express the thermodynamic efficiency in terms of the coefficients of this matrix using a parametrization similar to the one used near equilibrium. This framework, then valid arbitrarily far from equilibrium allows to set bounds on the thermodynamic efficiency by a universal function depending only on the degree of coupling between input and output currents. It also leads to new general power-efficiency trade-offs valid for macroscopic machines that are compared to trade-offs previously obtained from uncertainty relations. We illustrate our results on an unicycle heat to heat converter and on a discrete model of molecular motor., Comment: 24 pages, 5 figures

Inferring the directionality of interactions between cellular processes is a major challenge in systems biology. Time-lagged correlations allow to discriminate between alternative models, but they still rely on assumed underlying interactions. Here, we use the transfer entropy (TE), an information-theoretic quantity that quantifies the directional influence between fluctuating variables in a model-free way. We present a theoretical approach to compute the transfer entropy, even when the noise has an extrinsic component or in the presence of feedback. We re-analyze the experimental data from Kiviet et al. (2014) where fluctuations in gene expression of metabolic enzymes and growth rate have been measured in single cells of E. coli. We confirm the formerly detected modes between growth and gene expression, while prescribing more stringent conditions on the structure of noise sources. We furthermore point out practical requirements in terms of length of time series and sampling time which must be satisfied in order to infer optimally transfer entropy from times series of fluctuations., Comment: 24 pages, 7 figures

We describe the kinetics and thermodynamics of copolymers undergoing recombination reactions, which are important for prebiotic chemistry. We use two approaches: the first one, based on chemical rate equations and the mass-action law describes the infinite size limit, while the second one, based on the chemical master equation, describes systems of finite size. We compare the predictions of both approaches for the relaxation of thermodynamic quantities towards equilibrium. We find that for some choice of initial conditions, the entropy of the sequence distribution can be lowered at the expense of increasing the entropy of the length distribution. We consider mainly energetically neutral reactions, except for one simple case of non-neutral reactions., Comment: 15 pages, 6 figures and 1 table

Fluctuation theorems have become an important tool in single molecule biophysics to measure free energy differences from non-equilibrium experiments. When significant coarse-graining or noise affect the measurements, the determination of the free energies becomes challenging. In order to address this thermodynamic inference problem, we propose improved estimators of free energy differences based on fluctuation theorems, which we test on a number of examples. The effect of the noise can be described by an effective temperature, which only depends on the signal to noise ratio, when the work is Gaussian distributed and uncorrelated with the error made on the work. The notion of effective temperature appears less useful for non-Gaussian work distributions or when the error is correlated with the work, but nevertheless, as we show, improved estimators can still be constructed for such cases. As an example of non-trivial correlations between the error and the work, we also consider measurements with delay, as described by linear Langevin equations., Comment: 19 pages, 8 figures. Submitted to Phys. Rev. E

Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues obtained for non-equilibrium systems where the broken symmetry is time reversal. At equilibrium, these relations show that the ratio of the probabilities of opposite fluctuations goes exponentially with the symmetry-breaking external field and the magnitude of the fluctuations. These relations are applied to the Curie-Weiss, Heisenberg, and $XY$~models of magnetism where the continuous rotational symmetry is broken, as well as to the $q$-state Potts model and the $p$-state clock model where discrete symmetries are broken. Broken symmetries are also considered in the anisotropic Curie-Weiss model. For infinite systems, the results are calculated using large-deviation theory. The relations are also applied to mean-field models of nematic liquid crystals where the order parameter is tensorial. Moreover, their extension to quantum systems is also deduced., Comment: 34 pages, 14 figures

We describe the oligosaccharides-exchange dynamics performed by so-called D-enzymes on polysaccharides. To mimic physiological conditions, we treat this process as an open chemical network by assuming some of the polymer concentrations fixed (chemostatting). We show that three different long-time behaviors may ensue: equilibrium states, nonequilibrium steady states, and continuous growth states. We dynamically and thermodynamically characterize these states and emphasize the crucial role of conservation laws in identifying the chemostatting conditions inducing them., Comment: 12 pages, 9 figures and 1 table

Motivated by a recent work on the metabolism of carbohydrates in bacteria, we study the kinetics and thermodynamics of two classic models for reversible polymerization, one preserving the total polymer concentration and the other one not. The chemical kinetics is described by rate equations following the mass-action law. We consider a closed system and nonequilibrium initial conditions and show that the system dynamically evolves towards equilibrium where detailed balance is satisfied. The entropy production during this process can be expressed as the time derivative of a Lyapunov function. When the solvent is not included in the description and the dynamics conserves the total concentration of polymer, the Lyapunov function can be expressed as a Kullback-Leibler divergence between the nonequilibrium and the equilibrium polymer length distribution. The same result holds true when the solvent is explicitly included in the description and the solution is assumed dilute, whether or not the total polymer concentration is conserved. Furthermore, in this case a consistent nonequilibrium thermodynamic formulation can be established and the out-of-equilibrium thermodynamic enthalpy, entropy and free energy can be identified. Such a framework is useful in complementing standard kinetics studies with the dynamical evolution of thermodynamic quantities during polymerization.

We study the stochastic thermodynamics of an overdamped harmonic chain, which can be viewed equivalently as a 1D Rouse chain or as an approximate model of single file diffusion. We discuss mainly two levels of description of this system: the Markovian level for which the trajectories of all the particles of the chain are known and the non-Markovian level in which only the motion of a tagged particle is available. For each case, we analyze the energy dissipation and its dependence on initial conditions. Surprisingly, we find that the average coarse-grained entropy production rate can become transiently negative when an oscillating force is applied to the tagged particle. This occurs due to memory effects as shown in a framework based on path integrals or on a generalized Langevin equation., Comment: 17 pages, 7 figures, REVTeX, minor revisions

We present a general framework for systems which are prepared in a non-stationary non-equilibrium state in the absence of any perturbation, and which are then further driven through the application of a time-dependent perturbation. We distinguish two different situations depending on the way the non-equilibrium state is prepared, either it is created by some driving; or it results from a relaxation following some initial non-stationary conditions. Our approach is based on a recent generalization of the Hatano-Sasa relation for non-stationary probability distributions. We also investigate whether a form of second law holds for separate parts of the entropy production, in a way similar to the work of M. Esposito et al., Phys. Rev. Lett., 104:090601 (2010), but for a non-stationary reference process instead of a stationary one. We find that although the special structure of the theorems derived in this reference is not recovered in the general case, detailed fluctuation theorems still hold separately for parts of the entropy production in this case. These detailed fluctuation theorems lead to interesting generalizations of the second-law of thermodynamics off equilibrium., Comment: 36 pages, 4 figures

We discuss the consequences of a variant of the Hatano-Sasa relation in which a non-stationary distribution is used in place of the usual stationary one. We first show that this non-stationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and non-adiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law like inequalities for transitions between non-stationary states., Comment: 4 pages, 2 figures

In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying markovian dynamics. We show that the method to derive modified fluctuation-dissipation theorems near non-equilibrium stationary states used by J. Prost et al., PRL 103, 090601 (2009), is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano-Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy, in a way which is similar to what has been done recently in the case of MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a brownian particle in an harmonic trap submitted to a quench of temperature and to a time-dependent stiffness. The second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics., Comment: 25 pages, 4 figures

A simple stochastic model which describes microtubule dynamics and explicitly takes into account the relevant biochemical processes is presented. The model incorporates binding and unbinding of monomers and random phosphate release inside the polymer. It is shown that this theoretical approach provides a microscopic picture of the dynamic instability phenomena of microtubules. The cap size, the concentration dependence of the catastrophe times and the delay before observing catastrophes following a dilution can be quantitatively predicted by this approach in a direct and simple way. Furthermore, the model can be solved analytically to a large extend, thus offering a valuable starting point for more refined studies of microtubules dynamics., Comment: 26 pages, 8 figures

For many biotechnological applications it would be useful to better understand the effects produced by electric fields on lipid membranes. This review discusses several aspects of the electrostatic properties of a planar lipid membrane with its surrounding electrolyte in a normal DC or AC electric field. In the planar geometry, the analysis of electrokinetic equations can be carried out quite far, allowing to characterize analytically the steady state and the dynamics of the charge accumulation in the Debye layers, which results from the application of the electric field. For a conductive membrane in an applied DC electric field, we characterize the corrections to the elastic moduli, the appearance of a membrane undulation instability and the associated flows which are built up near the membrane. For a membrane in an applied AC electric field, we analytically derive the impedance from the underlying electrokinetic equations. We discuss different relevant effects due to the membrane conductivity or due to the bulk diffusion coefficients of the ions. Of particular interest is the case where the membrane has selective conductivity for only one type of ion. These results, and future extensions thereof, should be useful for the interpretation of impedance spectroscopy data used to characterize e.g. ion channels embedded in planar bilayers., Comment: 33 pages, 7 figures

The behavior of a non-conductive quasi-planar lipid membrane in an electrolyte and in a static (DC) electric field is investigated theoretically in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to charges in the membrane lipids and in the double layers lead to corrections to the membrane elastic moduli which are analyzed here. We show that, especially in the low salt limit, i) the electrostatic contribution to the membrane's surface tension due to the Debye layers crosses over from a quadratic behavior in the externally applied voltage to a linear voltage regime. ii) the contribution to the membrane's bending modulus due to the Debye layers saturates for high voltages. Nevertheless, the membrane undulation instability due to an effectively negative surface tension as predicted by linear Debye-H\"uckel theory is shown to persist in the nonlinear, high voltage regime., Comment: 15 pages, 4 figures

The behavior of a conductive membrane in a static (DC) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Non-equilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field., Comment: 14 pages, 5 figures

We study the stochastic dynamics of growth and shrinkage of single actin filaments taking into account insertion, removal, and ATP hydrolysis of subunits either according to the vectorial mechanism or to the random mechanism. In a previous work, we developed a model for a single actin or microtubule filament where hydrolysis occurred according to the vectorial mechanism: the filament could grow only from one end, and was in contact with a reservoir of monomers. Here we extend this approach in several ways, by including the dynamics of both ends and by comparing two possible mechanisms of ATP hydrolysis. Our emphasis is mainly on two possible limiting models for the mechanism of hydrolysis within a single filament, namely the vectorial or the random model. We propose a set of experiments to test the nature of the precise mechanism of hydrolysis within actin filaments., Comment: To appear in Biophysical Journal (2010)

We study the stochastic dynamics of growth and shrinkage of single actin filaments or microtubules taking into account insertion, removal, and ATP/GTP hydrolysis of subunits. The resulting phase diagram contains three different phases: a rapidly growing phase, an intermediate phase and a bound phase. We analyze all these phases, with an emphasis on the bound phase. We also discuss how hydrolysis affects force-velocity curves. The bound phase shows features of dynamic instability, which we characterize in terms of the time needed for the ATP/GTP cap to disappear as well as the time needed for the filament to reach a length of zero, i.e., (to collapse) for the first time. We obtain exact expressions for all these quantities, which we test using Monte Carlo simulations., Comment: 34 pages

Heat-induced mobility of nucleosomes along DNA is an experimentally well-studied phenomenon. A recent experiment shows that the repositioning is modified in the presence of minor-groove binding DNA ligands. We present here a stochastic three-state model for the diffusion of a nucleosome along DNA in the presence of such ligands. It allows us to describe the dynamics and the steady state of such a motion analytically. The analytical results are in excellent agreement with numerical simulations of this stochastic process.With this model, we study the response of a nucleosome to an external force and how it is affected by the presence of ligands., Comment: 10 pages, 8 figures, submitted to Eur. Phys. J. E

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_\xi]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_\xi$, which corresponds to the area of the membrane coarse-grained at the mesh size $\xi$. We show that the meshwork modifies the membrane tension $\sigma$ both below and above the scale $\xi$, inducing a tension-jump $\Delta\sigma=dF_\mathrm{el}/dA_\xi$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane area. We also predict an observable tension jump for membranes decorated with polymer "brushes".