Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporally Resolved Virus Replication Dynamics.

Advanced methods of treatment are needed to fight the threats of virus-transmitted diseases and pandemics. Often, they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the hepatitis C virus (HCV) proceeds under the influence of nonstructural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5A protein. The diffusion of NSPs has been studied by in vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDEs). Previous work estimated the diffusion coefficient of the NS5A protein by minimizing the discrepancy between an extended set of sufPDE simulations and experimental FRAP time-series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region to its contour length. The quality of this estimate is explored by a comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

Complex networks of interacting stochastic tipping elements: Cooperativity of phase separation in the large-system limit.

Tipping elements in the Earth system have received increased scientific attention over recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are subdominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks of different size and with different coupling parameters.

Dose-response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study.

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other non-linear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose-response functions and hypothesis testing using surrogate data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study. This data set provides a physically-close-contact network between several hundreds of university students participating in the study over the course of 3 months. We study the potential spreading dynamics of the health-related behaviour "regularly going to the fitness studio" on this network. Based on a hierarchy of surrogate data models, we find that our method neither provides significant evidence for an influence of a dose-response-type network spreading process in this data set, nor significant evidence for homophily. The empirical dynamics in exercise behaviour are likely better described by individual features such as the disposition towards the behaviour, and the persistence to maintain it, as well as external influences affecting the whole group, and the non-trivial network structure. The proposed methodology is generic and promising also for applications to other temporal network data sets and traits of interest.

Hybrid sideways/longitudinal swimming in the monoflagellate Shewanella oneidensis: from aerotactic band to biofilm.

Shewanella oneidensis MR-1 are facultative aerobic electroactive bacteria with an appealing potential for sustainable energy production and bioremediation. They gather around air sources, forming aerotactic bands and biofilms. Here, we experimentally follow the evolution of the band around an air bubble, and we find good agreement with the numerical solutions of the pertinent transport equations. Video microscopy reveals a transition between motile and non-motile MR-1 upon oxygen depletion, preventing further development of the biofilm. We discover that MR-1 can alternate between longitudinal fast and sideways slow swimming. The resulting bimodal velocity distributions change in response to different oxygen concentrations and gradients, supporting the biological functions of aerotaxis and confinement.

Fluctuating currents in stochastic thermodynamics. I. Gauge invariance of asymptotic statistics.

Stochastic thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication.

Fluctuating currents in stochastic thermodynamics. II. Energy conversion and nonequilibrium response in kinesin models.

Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational states of these biological macromolecules. A recently developed theoretical framework [A. Wachtel, J. Vollmer, and B. Altaner, Phys. Rev. E 92, 042132 (2015)] provides a simple algorithm for the determination of macroscopic currents and correlation integrals of arbitrary fluctuating currents. Here we use it to discuss energy conversion and nonequilibrium response in different models for the molecular motor kinesin. Methodologically, our results demonstrate the effectiveness of the algorithm in dealing with parameter-dependent stochastic models. For the concrete biophysical problem our results reveal two interesting features in experimentally accessible parameter regions: the validity of a nonequilibrium Green-Kubo relation at mechanical stalling as well as a negative differential mobility for superstalling forces.

Granular Brownian motors: role of gas anisotropy and inelasticity.

We investigate the motion of a two-dimensional wedge-shaped object (a granular Brownian motor), which is restricted to move along the x axis and cannot rotate as gas particles collide with it. We show that its steady-state drift, resulting from inelastic gas-motor collisions, is dramatically affected by anisotropy in the velocity distribution of the gas. We identify the dimensionless parameter providing the dependence of this drift on shape, masses, inelasticity, and anisotropy: The anisotropy leads to dramatically enhanced drift of the motor, which should easily be visible in experimental realizations.

Flow-induced shear instabilities of cohesive granulates.

In this work we use a multiscale framework to calculate the fluidization threshold of three-dimensional cohesive granulates under shear forces exerted by a creeping flow. A continuum model of flow through porous media provides an analytical expression for the average drag force on a single grain. The balance equation for the forces and a force propagation model are then used to investigate the effects of porosity and packing structure on the stability of the pile. We obtain a closed-form expression for the instability threshold of a regular packing of monodisperse frictionless cohesive spherical grains in a planar fracture. Our result quantifies the compound effect of structural (packing orientation and porosity) and dynamical properties of the system on its stability.

Breath figures: nucleation, growth, coalescence, and the size distribution of droplets.

The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth mechanisms of the droplets. This finding establishes a gateway connecting nucleation and growth of the smallest droplets on surfaces to gross features of the evolution of the droplet size distribution.

Fluctuation-preserving coarse graining for biochemical systems.

Finite stochastic Markov models play a major role in modeling biological systems. Such models are a coarse-grained description of the underlying microscopic dynamics and can be considered mesoscopic. The level of coarse-graining is to a certain extent arbitrary since it depends on the resolution of accommodating measurements. Here we present a systematic way to simplify such stochastic descriptions which preserves both the meso-micro and the meso-macro connections. The former is achieved by demanding locality, the latter by considering cycles on the network of states. Our method preserves fluctuations of observables much better than naïve approaches.

Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations.

We have examined the effects of current and conductance noise in a single-neuron model which can generate a variety of physiologically important impulse patterns. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Additive Gaussian white noise which is implemented as conductance noise appears in the voltage equations as an additive and a multiplicative term. Moreover, the originally white noise is turned into colored noise. The noise correlation time is a function of the system's control parameters which may explain the different effects of current and conductance noise in different dynamic states. We have found the most significant, qualitative differences between different noise implementations in a pacemaker-like, tonic firing regime at the transition to chaotic burst discharges. This reflects a dynamic state of high physiological relevance.

Statistical analysis of coherent structures in transitional pipe flow.

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about Re=2200 , and it decreases to about 20% for Re=2500 . The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.

Minimal model for phase separation under slow cooling.

Inducing phase separation by a sustained change of temperature often induces repeated waves of nucleation. As demonstrated in an accompanying movie, these oscillations can easily be demonstrated in the classroom by slowly cooling raw spirit (i.e., ethanol) and vegetable oil. In the present communication we suggest a minimal theoretical model predicting that they are of thermodynamic origin. Their frequency depends on the diffusion constant and ramp rate, and is not affected by the overall composition and sample geometry. Our experimental data support this model.

Vortex formation by active agents as a model for Daphnia swarming.

We propose a self-propelled particle model for the swarming of Daphnia that takes into account mutual repulsion and attraction to a center. Surprisingly, a vortex is formed only for an intermediate strength of propulsion. The phase diagram and the transitions between states with and without a vortex are analyzed, and the nature of the phase boundaries is discussed based on a linear stability analysis of the motion of individual swimmers. This allows us to identify various key parameters determining the characteristic features of the collective motion.

Oscillatory instabilities in phase separation of binary mixtures: fixing the thermodynamic driving.

Binary liquid mixtures can show pronounced oscillations in the differential scanning calorimeter signal for the specific heat and in the turbidity when phase separation is induced by continuously ramping the temperature. For a fixed ramp rate, i.e., a linear temporal drift of temperature, only a small number of oscillations have been observed. In the present manuscript we describe an experimental setup where simultaneous video-microscopy and shadow-graph measurements can be performed on mixtures subjected to an arbitrary temporal temperature evolution. In particular, it can be adjusted to fix the thermodynamic driving force, which characterizes the rate of change of the composition of the coexisting phases. With this novel technique both the number of oscillations and the temperature interval where oscillations are observed increase significantly. This technique can easily be applied to a great variety of binary mixtures, permitting detailed investigations of their phase-separation kinetics under slowly ramping temperature.

Electrolyte diodes and hydrogels: determination of concentration and pK value of fixed acidic groups in a weakly charged hydrogel.

Current-voltage (CV) characteristics of polyvinyl alcohol (PVA)-glutardialdehyde hydrogel cylinders were measured in aqueous KCl solutions. To this end a new special apparatus was constructed where the gel cylinder connects two electrolyte reservoirs. The measured quantities are the electric current flowing through the gel and the potential difference between the two reservoirs. Concentration polarization near the gel-liquid interfaces is decreased considerably by applying an intense mechanical stirring in both reservoirs. Under these conditions below 1 V concentration polarization is negligible, and the CV curves are nearly straight lines. It was found that the gel applied here is a weakly charged anionic hydrogel. Concentration of fixed anions was determined from the slope of these lines measured in 0.001 and 0.01 molar KCl solutions. Fixed anion concentration of the same piece of gel was measured also with a different method, when the gel was used in an acid-base diode. In this case one reservoir contained 0.1 molar HCl, and the other 0.1 molar KOH. From the results of the two measurements, the concentration (4.45 x 10(-3) M) and the pK value (4.03) of the fixed acid groups responsible for the anionic character of the gel was calculated. The pK value is compatible with fixed carboxylic acid groups contaminating the PVA gel. Furthermore, concentration polarization phenomena in the boundary layers nearby the gel were studied in 0.001 M KCl solutions, measuring the diodelike CV characteristic of a gel cylinder, when stirring was applied only at one side of the gel. Boundary layers facing the cathode or the anode responded in a different way to stirring. The difference cannot be explained completely with the hypothesis of electroconvection suggested previously.

Entropy balance, time reversibility, and mass transport in dynamical systems.

We review recent results concerning entropy balance in low-dimensional dynamical systems modeling mass (or charge) transport. The key ingredient for understanding entropy balance is the coarse graining of the local phase-space density. It mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected up to a finite resolution. In addition, we derive a new relation for the rate of irreversible entropy production in steady states of dynamical systems: It is proportional to the average growth rate of the local phase-space density. Previous results for the entropy production in steady states of thermostated systems without density gradients and of Hamiltonian systems with density gradients are recovered. As an extension we derive the entropy balance of dissipative systems with density gradients valid at any instant of time, not only in stationary states. We also find a condition for consistency with thermodynamics. A generalized multi-Baker map is used as an illustrative example. (c) 1998 American Institute of Physics.