Simple Mechanism for the Observed Breakdown of the Nernst-Einstein Relation for Ions in Carbon Nanotubes.

In this Letter, we present a simple mechanism that explains the recent experimental observation of the breakdown of the Nernst-Einstein (NE) relation for an ion moving in a carbon nanotube of subnanometer diameter. We argue that the friction acting on the ion is largely independent of the ion velocity, i.e., dry friction, and demonstrate, based on the Langevin equation for a particle subject to both dry and viscous friction, that the NE relation is violated when dry friction dominates. We predict that the ratio of the diffusion constant to the mobility of the ion is a few orders of magnitude smaller than the value predicted by the NE relation, in quantitative agreement with experiment.

Computational modeling predicts ephemeral acidic microdomains in the glutamatergic synaptic cleft.

At chemical synapses, synaptic vesicles release their acidic contents into the cleft, leading to the expectation that the cleft should acidify. However, fluorescent pH probes targeted to the cleft of conventional glutamatergic synapses in both fruit flies and mice reveal cleft alkalinization rather than acidification. Here, using a reaction-diffusion scheme, we modeled pH dynamics at the Drosophila neuromuscular junction as glutamate, ATP, and protons (H+) were released into the cleft. The model incorporates bicarbonate and phosphate buffering systems as well as plasma membrane calcium-ATPase activity and predicts substantial cleft acidification but only for fractions of a millisecond after neurotransmitter release. Thereafter, the cleft rapidly alkalinizes and remains alkaline for over 100 ms because the plasma membrane calcium-ATPase removes H+ from the cleft in exchange for calcium ions from adjacent pre- and postsynaptic compartments, thus recapitulating the empirical data. The extent of synaptic vesicle loading and time course of exocytosis have little influence on the magnitude of acidification. Phosphate but not bicarbonate buffering is effective at suppressing the magnitude and time course of the acid spike, whereas both buffering systems are effective at suppressing cleft alkalinization. The small volume of the cleft levies a powerful influence on the magnitude of alkalinization and its time course. Structural features that open the cleft to adjacent spaces appear to be essential for alleviating the extent of pH transients accompanying neurotransmission.

Neuronal Glutamatergic Synaptic Clefts Alkalinize Rather Than Acidify during Neurotransmission.

The dogma that the synaptic cleft acidifies during neurotransmission is based on the corelease of neurotransmitters and protons from synaptic vesicles, and is supported by direct data from sensory ribbon-type synapses. However, it is unclear whether acidification occurs at non-ribbon-type synapses. Here we used genetically encoded fluorescent pH indicators to examine cleft pH at conventional neuronal synapses. At the neuromuscular junction of female Drosophila larvae, we observed alkaline spikes of over 1 log unit during fictive locomotion in vivo. Ex vivo, single action potentials evoked alkalinizing pH transients of only ∼0.01 log unit, but these transients summated rapidly during burst firing. A chemical pH indicator targeted to the cleft corroborated these findings. Cleft pH transients were dependent on Ca2+ movement across the postsynaptic membrane, rather than neurotransmitter release per se, a result consistent with cleft alkalinization being driven by the Ca2+/H+ antiporting activity of the plasma membrane Ca2+-ATPase at the postsynaptic membrane. Targeting the pH indicators to the microenvironment of the presynaptic voltage gated Ca2+ channels revealed that alkalinization also occurred within the cleft proper at the active zone and not just within extrasynaptic regions. Application of the pH indicators at the mouse calyx of Held, a mammalian central synapse, similarly revealed cleft alkalinization during burst firing in both males and females. These findings, made at two quite different non-ribbon type synapses, suggest that cleft alkalinization during neurotransmission, rather than acidification, is a generalizable phenomenon across conventional neuronal synapses.SIGNIFICANCE STATEMENT Neurotransmission is highly sensitive to the pH of the extracellular milieu. This is readily evident in the neurological symptoms that accompany systemic acid/base imbalances. Imaging data from sensory ribbon-type synapses show that neurotransmission itself can acidify the synaptic cleft, likely due to the corelease of protons and glutamate. It is not clear whether the same phenomenon occurs at conventional neuronal synapses due to the difficulties in collecting such data. If it does occur, it would provide for an additional layer of activity-dependent modulation of neurotransmission. Our findings of alkalinization, rather than acidification, within the cleft of two different neuronal synapses encourages a reassessment of the scope of activity-dependent pH influences on neurotransmission and short-term synaptic plasticity.

Charge regulation of a surface immersed in an electrolyte solution.

In this paper, we investigate theoretically a model of charge regulation of a single charged planar surface immersed in an aqueous electrolyte solution. Assuming that the adsorbed ions are mobile in the charged plane, we formulate a field theory of charge regulation where the numbers of adsorbed ions can be determined consistently by equating the chemical potentials of the adsorbed ions to that of the ions in the bulk. We analyze the mean-field treatment of the model for electrolyte of arbitrary valences, and then beyond, where correlation effects are systematically taken into account in a loop expansion. In particular, we compute exactly various one-loop quantities, including electrostatic potentials, ion distributions, and chemical potentials, not only for symmetric (1, 1) electrolyte but also for asymmetric (2, 1) electrolyte, and make use of these quantities to address charge regulation at the one-loop level. We find that correlation effects give rise to various phase transitions in the adsorption of ions, and present phase diagrams for (1, 1) and (2, 1) electrolytes, whose distinct behaviors suggest that charge regulation, at the one-loop level, is no longer universal but depends crucially on the valency of the ions.

Solid friction between soft filaments.

Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments' overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes's drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament's elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials.

Theory of the force of friction acting on water chains flowing through carbon nanotubes.

A simple model for the friction experienced by the one-dimensional water chains that flow through subnanometer diameter carbon nanotubes is studied. The model is based on a lowest order perturbation theory treatment of the friction experienced by the water chains due to the excitation of phonon and electron excitations in both the nanotube and the water chain, as a result of the motion of the chain. On the basis of this model, we are able to demonstrate how the observed flow velocities of water chains through carbon nanotubes of the order of several centimeters per second can be accounted for. If the hydrogen bonds between the water molecules are broken (as would occur if there were an electric field oscillating with a frequency equal to the resonant frequency of the hydrogen bonds present), it is shown that the friction experienced by the water flowing in the tube can be much smaller.

Pulling a harmonically bound particle subjected to Coulombic friction: A nonequilibrium analysis.

We address the effects of dry friction, which has emerged only recently to play an important role in some biological systems. In particular, we investigate the nonequilibrium dynamics of a mesoscopic particle, bound to a spring being pulled at a definite speed, moving on a surface with dry friction in a noisy environment. We model the dry friction phenomenologically with a term that is proportional to the sign of the velocity, and by means of numerical simulations of a Langevin equation we show that (a) the frictional force scales with the logarithm of the pulling velocity, (b) the probability distribution function of the spatial displacement away from the potential minimum is non-Gaussian, (c) the fluctuation-dissipation theorem is violated as expected, but (d) the work function obeys the stationary fluctuation theorem, with an effective temperature related to the noise of the system.

Enhancement of the ion concentration in a salt solution near a wall due to electrical image potentials and enhancement of surface tension due to the presence of salt.

Effects of electrical image potentials on the salt ion concentration near a solid wall are studied using a one-loop approximation treatment of the grand canonical partition function, which is the Debye-Hückel approximation. Electrical image potentials resulting from both metallic and dielectric walls of dielectric constant larger than that of water near the wall are considered. Our treatment of this problem supports the conclusions of an earlier publication by one of the authors which shows that near a solid wall there should be a high concentration of ions, resulting from image potentials. We have also applied our treatment to the increase of the surface tension of a liquid that occurs when salt is dissolved in the liquid. Our treatment gives the -c_{s}log(c_{s}) dependence of the surface tension found by Onsager and Samarasa in the small c_{s} limit, where c_{s} is the salt concentration.

Fluctuating hydrodynamics and microrheology of a dilute suspension of swimming bacteria.

A bacterial bath is a model active system consisting of a population of rodlike motile or self-propelled bacteria suspended in a fluid environment. This system can be viewed as an active, nonequilibrium version of a lyotropic liquid crystal or as a generalization of a driven diffusive system. We derive a set of phenomenological equations, which include the effects of internal force generators in the bacteria, describing the hydrodynamic flow, orientational dynamics of the bacteria, and fluctuations induced by both thermal and nonthermal noises. These equations violate the fluctuation dissipation theorem and the Onsager reciprocity relations. We use them to provide a quantitative account of results from recent microrheological experiments on bacterial baths.

Fluctuation and correlation effects in a charged surface immersed in an electrolyte solution.

We explore correlation and fluctuation effects in an overall neutral system consisting of a single homogeneously charged planar surface with both the counterions and coions distributed on both sides of the surface. Using a field-theoretic formulation, we compute the one-loop correction to the electrostatic potential, to the ion densities, to the surface tension, and to the surface free energy. From the asymptotic behavior of the electrostatic potential, we obtain an exact expression for the effective surface charge density, which can become negative, indicating charge inversion. Furthermore, we find that the ion distributions can be substantially different from the mean-field ion densities. In particular, the counterion density, at high couplings, develops a minimum at some intermediate distances, larger than the Gouy-Chapman length, away from the charged surface, whereas the coion density develops a maximum, whose values can be greater than the counterion density. Therefore, the coions develop a second layer. Moreover, the one-loop correction always lowers the electrostatic contributions to the surface tension and at high couplings, the surface tension may become negative.

Fluctuation theorem and large deviation function for a solvable model of a molecular motor.

We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a minimal ratchet model. We extend our previous work on this model, by further investigating the constraints imposed by the fluctuation theorem on the operation of a molecular motor far from equilibrium. In this work, we show the connections between different formulations of the fluctuation theorem. One formulation concerns the generating function of the currents while another one concerns the corresponding large deviation function, which we have calculated exactly for this model. A third formulation concerns the ratio of the probability of observing a velocity v to the same probability of observing a velocity -v . Finally, we show that all the formulations of the fluctuation theorem can be understood from the notion of entropy production.

State-dependent diffusion: Thermodynamic consistency and its path integral formulation.

The friction coefficient of a particle can depend on its position, as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show that the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number of examples with spatially varying diffusion coefficients. We also derive a path integral representation for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

Counterion condensation and fluctuation-induced attraction.

We consider an overall neutral system consisting of two similarly charged plates and their oppositely charged counterions and analyze the electrostatic interaction between the two surfaces beyond the mean-field Poisson-Boltzmann approximation. Our physical picture is based on the fluctuation-driven counterion condensation model, in which a fraction of the counterions is allowed to "condense" onto the charged plates. In addition, an expression for the pressure is derived, which includes fluctuation contributions of the whole system. We find that for sufficiently high surface charges, the distance at which the attraction, arising from charge fluctuations, starts to dominate can be large compared to the Gouy-Chapmann length. We also demonstrate that depending on the valency, the system may exhibit a first-order binding transition at short distances.

Entropic interactions in suspensions of semiflexible rods: short-range effects of flexibility.

We compute the entropic interactions between two colloidal spheres immersed in a dilute suspension of semiflexible rods. Our model treats the semiflexible rod as a bent rod at fixed angle, set by the rod contour and persistence lengths. The entropic forces arising from this additional rotational degree of freedom are captured quantitatively by the model, and account for observations at short range in a recent experiment. Global fits to the interaction potential data suggest the persistence length of the fd virus is about two to three times smaller than the commonly used value of 2.2 microm.

Charge fluctuations and counterion condensation.

We predict a condensation phenomenon in an overall neutral system, consisting of a single charged plate and its oppositely charged counterions. Based on the "two-fluid" model, in which the counterions are divided into a "free" and a "condensed" fraction, we argue that for high surface charge, fluctuations can lead to a phase transition in which a large fraction of counterions is condensed. Furthermore, we show that depending on the valence, the condensation is either a first-order or a smooth transition.

Nonequilibrium fluctuations and mechanochemical couplings of a molecular motor.

We investigate theoretically the violations of Einstein and Onsager relations and the thermodynamic efficiency for a single processive motor operating far from equilibrium using an extension of the two-state model introduced by Kafri et al. [Biophys. J. 86, 3373 (2004)10.1529/biophysj.103.036152]. With the aid of the Fluctuation Theorem, we analyze the general features of these violations and this efficiency and link them to mechanochemical couplings of motors. In particular, an analysis of the experimental data of kinesin using our framework leads to interesting predictions that may serve as a guide for future experiments.

Fluctuations and rheology in active bacterial suspensions.

We probe nonequilibrium properties of an active bacterial bath through measurements of correlations of passive tracer particles and the response function of a driven, optically trapped tracer. These measurements demonstrate violation of the fluctuation-dissipation theorem and enable us to extract the power spectrum of the active stress fluctuations. In some cases, we observe 1/sqrt[omega] scaling in the noise spectrum which we show can be derived from a theoretical model incorporating coupled stress, orientation, and concentration fluctuations of the bacteria.

Effects of counterion fluctuations in a polyelectrolyte brush.

We investigate the effect of counterion fluctuations in a single polyelectrolyte brush in the absence of added salt by systematically expanding the counterion free energy about Poisson-Boltzmann mean-field theory. We find that for strongly charged brushes, there is a collapse regime in which the brush height decreases with increasing charge on the polyelectrolyte chains. The transition to this collapsed regime is similar to the liquid-gas transition, which has a first-order line terminating at a critical point. We find that, for monovalent counterions, the transition is discontinuous in theta solvent, while for multivalent counterions, the transition is generally continuous. For collapsed brushes, the brush height is not independent of grafting density as it is for osmotic brushes, but scales linear with it.

Phase transitions in lyotropic nematic gels.

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur.

Microrheology, stress fluctuations, and active behavior of living cells.

We report the first measurements of the intrinsic strain fluctuations of living cells using a recently developed tracer correlation technique along with a theoretical framework for interpreting such data in heterogeneous media with nonthermal driving. The fluctuations' spatial and temporal correlations indicate that the cytoskeleton can be treated as a course-grained continuum with power-law rheology, driven by a spatially random stress tensor field. Combined with recent cell rheology results, our data imply that intracellular stress fluctuations have a nearly 1/omega2 power spectrum, as expected for a continuum with a slowly evolving internal prestress.