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Several enzymes exhibit enhanced diffusion in the presence of a substrate. One explanation of this enhancement arises from fluctuating dimer models, which suggest that enzymes have a higher diffusion constant when interacting with substrates compared to when they are free. Another possible mechanism, suggested in both experimental and theoretical studies, is that enzymes act as nanoswimmers. However, existing nanoswimmer models have struggled to account for the exceptionally high self-propulsion speeds observed in experiments, with estimated increases in diffusion due to self-propulsion found to be minimal. In this study, we model enzymes as dimers with fluctuating mobility. We show that even dimers can exhibit run-and-tumble motion when transitioning between states of varying mobility within the enzymatic cycle. By exploring a three-state enzymatic cycle, we identify the conditions under which self-propulsion speeds and increases in diffusion rate consistent with experimental observations can be achieved.

We calculate the Casimir stresses in a thin layer of active fluid with nematic order. By using a stochastic hydrodynamic approach for an active fluid layer of finite thickness $L$, we generalize the Casimir stress for nematic liquid crystals in thermal equilibrium to active systems. We show that the active Casimir stress differs significantly from its equilibrium counterpart. For contractile activity, the active Casimir stress, although attractive like its equilibrium counterpart, diverges logarithmically as $L$ approaches a threshold of the spontaneous flow instability from below. In contrast, for small extensile activity, it is repulsive, has no divergence at any $L$ and has a scaling with $L$ different from its equilibrium counterpart.

We investigate the effect of stress fluctuations on the stochastic dynamics of an inclusion embedded in a viscous gel. We show that, in non-equilibrium systems, stress fluctuations give rise to an effective attraction towards the boundaries of the confining domain, which is reminiscent of an active Casimir effect. We apply this generic result to the dynamics of deformations of the cell nucleus and we demonstrate the appearance of a fluctuation maximum at a critical level of activity, in agreement with recent experiments [E. Makhija, D. S. Jokhun, and G. V. Shivashankar, Proc. Natl. Acad. Sci. U.S.A. 113, E32 (2016)]., Comment: 12 pages, 5 figures

We study stochastic dynamics of a point and extended inclusion within a one dimensional confined active viscoelastic gel. We show that the dynamics of a point inclusion can be described by a Langevin equation with a confining potential and multiplicative noise. Using a systematic adiabatic elimination over the fast variables, we arrive at an overdamped equation with a proper definition of the multiplicative noise. To highlight various features and to appeal to different biological contexts, we treat the inclusion in turn as a rigid extended element, an elastic element and a viscoelastic (Kelvin-Voigt) element. The dynamics for the shape and position of the extended inclusion can be described by coupled Langevin equations. Deriving exact expressions for the corresponding steady state probability distributions, we find that the active noise induces an attraction to the edges of the confining domain. In the presence of a competing centering force, we find that the shape of the probability distribution exhibits a sharp transition upon varying the amplitude of the active noise. Our results could help understanding the positioning and deformability of biological inclusions, eg. organelles in cells, or nucleus and cells within tissues., Comment: 16 pages, 9 figures

The hair bundle of sensory cells in the vertebrate ear provides an example of a noisy oscillator close to a Hopf bifurcation. The analysis of the data from both spontaneous and forced oscillations shows a strong violation of the fluctuation-dissipation theorem, revealing the presence of an underlying active process that keeps the system out of equilibrium. Nevertheless, we show that a generalized fluctuation-dissipation theorem, valid for non-equilibrium steady states, is fulfilled within the limits of our experimental accuracy and computational approximations, when the adequate conjugate degrees of freedom are chosen., Comment: 5 pages, 3 figures

We show that the synchronization transition of a large number of noisy coupled oscillators is an example for a dynamic critical point far from thermodynamic equilibrium. The universal behaviors of such critical oscillators, arranged on a lattice in a $d$-dimensional space and coupled by nearest neighbors interactions, can be studied using field theoretical methods. The field theory associated with the critical point of a homogeneous oscillatory instability (or Hopf bifurcation of coupled oscillators) is the complex Ginzburg-Landau equation with additive noise. We perform a perturbative renormalization group (RG) study in a $4-\epsilon$ dimensional space. We develop an RG scheme that eliminates the phase and frequency of the oscillations using a scale-dependent oscillating reference frame. Within a Callan-Symanzik RG scheme to two-loop order in perturbation theory, we find that the RG fixed point is formally related to the one of the model $A$ dynamics of the real Ginzburg-Landau theory with an O(2) symmetry of the order parameter. Therefore, the dominant critical exponents for coupled oscillators are the same as for this equilibrium field theory. This formal connection with an equilibrium critical point imposes a relation between the correlation and response functions of coupled oscillators in the critical regime. Since the system operates far from thermodynamic equilibrium, a strong violation of the fluctuation-dissipation relation occurs and is characterized by a universal divergence of an effective temperature. The formal relation between critical oscillators and equilibrium critical points suggests that long-range phase order exists in critical oscillators above two dimensions., Comment: 24 pages, published in 2005

We study the universal thermodynamic properties of systems consisting of many coupled oscillators operating in the vicinity of a homogeneous oscillating instability. In the thermodynamic limit, the Hopf bifurcation is a dynamic critical point far from equilibrium described by a statistical field theory. We perform a perturbative renormalization group study, and show that at the critical point a generic relation between correlation and response functions appears. At the same time the fluctuation-dissipation relation is strongly violated., Comment: 10 pages, 1 figure

We introduce a general framework to study the processivity of molecular motors moving along a polar filament and discuss the average time spent attached to the filament as a function of a tangentially applied load. Our study of specific models suggests that the attachment time of a motor decreases with increasing ATP concentration and that double-headed motors such as kinesins lose their processivity under forcing conditions while processive single-headed motors are less sensitive to tangential forcing., Comment: 7 pages, 5 figures. To be published on Europhysics Letters

We present a detailed analysis of the micropipet experiments recently reported in J-B. Manneville et al., Phys. Rev. Lett. 82, 4356--4359 (1999), including a derivation of the expected behaviour of the membrane tension as a function of the areal strain in the case of an active membrane, i.e., containing a nonequilibrium noise source. We give a general expression, which takes into account the effect of active centers both directly on the membrane, and on the embedding fluid dynamics, keeping track of the coupling between the density of active centers and the membrane curvature. The data of the micropipet experiments are well reproduced by the new expressions. In particular, we show that a natural choice of the parameters quantifying the strength of the active noise explains both the large amplitude of the observed effects and its remarkable insensitivity to the active-center density in the investigated range. [Submitted to Phys Rev E, 22 March 2001], Comment: 14 pages, 5 encapsulated Postscript figures

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 epsf

We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces., Comment: 16 pages, 10 figures

We analyze a simple stochastic model to describe motor molecules which cooperate in large groups and present a physical mechanism which can lead to oscillatory motion if the motors are elastically coupled to their environment. Beyond a critical fuel concentration, the non-moving state of the system becomes unstable with respect to a mode with angular frequency omega. We present a perturbative description of the system near the instability and demonstrate that oscillation frequencies are determined by the typical timescales of the motors., Comment: 11 pages, Revtex, 4 pages Figures