The statistics of calcium-mediated focal excitations on a one-dimensional cable.

It is well known that various cardiac arrhythmias are initiated by an ill-timed excitation that originates from a focal region of the heart. However, up to now, it is not known what governs the timing, location, and morphology of these focal excitations. Recent studies have shown that these excitations can be caused by abnormalities in the calcium (Ca) cycling system. However, the cause-and-effect relationships linking subcellular Ca dynamics and focal activity in cardiac tissue is not completely understood. In this article, we present a minimal model of Ca-mediated focal excitations in cardiac tissue. This model accounts for the stochastic nature of spontaneous Ca release on a one-dimensional cable of cardiac cells. Using this model, we show that the timing of focal excitations is equivalent to a first passage time problem in a spatially extended system. In particular, we find that for a short cable the mean first passage time increases exponentially with the number of cells in tissue, and is critically dependent on the ratio of inward to outward currents near the threshold for an action potential. For long cables excitations occurs due to ectopic foci that occur on a length scale determined by the minimum length of tissue that can induce an action potential. Furthermore, we find that for long cables the mean first passage time decreases as a power law in the number cells. These results provide precise criteria for the occurrence of focal excitations in cardiac tissue, and will serve as a guide to determine the propensity of Ca-mediated triggered arrhythmias in the heart.

Exploring the dynamics of dimer crossing over a Kramers type potential.

We explore the escape rate of a dimer crossing a potential barrier using both analytical and numerical approaches. We find that for small coupling strength k, the barrier hopping can be well approximated by a two step reaction scheme where one monomer hops over the barrier and is then followed by the other. In this regime the escape rate increases with k showing that the cooperativity between monomers enhances the crossing rate. However, in the limit of large coupling strength, applying the method of adiabatic elimination, we find that the escape rate is a decreasing function of k. Thus, we find that the escape rate is a non-monotonic function of the spring constant which is peaked at an optimal coupling strength. Furthermore, in the presence of a weak periodic signal, we show that the system response to the periodic signal is pronounced at a particular spring constant showing the dimer can be transported rapidly across the reaction coordinate in a half period.

Adhesion-induced lateral phase separation of multicomponent membranes: the effect of repellers and confinement.

We present a theoretical study of adhesion-induced lateral phase separation for a membrane with short stickers, long stickers, and repellers confined between two hard walls. The effects of confinement and repellers on lateral phase separation are investigated. We find that the critical potential depth of the stickers for lateral phase separation increases as the distance between the hard walls decreases. This suggests confinement-induced or force-induced mixing of stickers. We also find that repellers with stronger repulsive potential tend to enhance, while repellers with weaker repulsive potential tend to suppress adhesion-induced lateral phase separation.

Energetics of a simple microscopic heat engine.

We model a microscopic heat engine as a particle hopping on a one-dimensional lattice in a periodic sawtooth potential, with or without load, assisted by the thermal kicks it gets from alternately placed hot and cold thermal baths. We find analytic expressions for current and rate of heat flow when the engine operates at steady state. Three regions are identified where the model acts either as a heat engine or as a refrigerator or as neither of the two. At the quasistatic limit both efficiency of the engine and coefficient of performance of the refrigerator go to that for Carnot engine and Carnot refrigerator, respectively. We investigate efficiency of the engine at two operating conditions (at maximum power and at optimum value with respect to energy and time) and compare them with those of the endoreversible and Carnot engines.

Thermodynamic feature of a Brownian heat engine operating between two heat baths.

A generalized theory of nonequilibrium thermodynamics for a Brownian motor operating between two different heat baths is presented. Via a simple paradigmatic model, we not only explore the thermodynamic feature of the engine in the regime of the nonequilibrium steady state but also study the short time behavior of the system for either the isothermal case with load or, in general, the nonisothermal case with or without load. Many elegant thermodynamic theories can be checked via the present model. Furthermore the dependence of the velocity, the efficiency, and the performance of the refrigerator on time t is examined. Our study reveals a current reversal due to time t. In the early system relaxation period, the model works neither as a heat engine nor as a refrigerator and only after a certain period of time does the model start functioning as a heat engine or as a refrigerator. The performance of the engine also improves with time and at steady state the engine manifests a higher efficiency or performance as a refrigerator. Furthermore the effect of energy exchange via the kinetic energy on the performance of the heat engine is explored.

The timing statistics of spontaneous calcium release in cardiac myocytes.

A variety of cardiac arrhythmias are initiated by a focal excitation that disrupts the regular beating of the heart. In some cases it is known that these excitations are due to calcium (Ca) release from the sarcoplasmic reticulum (SR) via propagating subcellular Ca waves. However, it is not understood what are the physiological factors that determine the timing of these excitations at both the subcellular and tissue level. In this paper we apply analytic and numerical approaches to determine the timing statistics of spontaneous Ca release (SCR) in a simplified model of a cardiac myocyte. In particular, we compute the mean first passage time (MFPT) to SCR, in the case where SCR is initiated by spontaneous Ca sparks, and demonstrate that this quantity exhibits either an algebraic or exponential dependence on system parameters. Based on this analysis we identify the necessary requirements so that SCR occurs on a time scale comparable to the cardiac cycle. Finally, we study how SCR is synchronized across many cells in cardiac tissue, and identify a quantitative measure that determines the relative timing of SCR in an ensemble of cells. Using this approach we identify the physiological conditions so that cell-to-cell variations in the timing of SCR is small compared to the typical duration of an SCR event. We argue further that under these conditions inward currents due to SCR can summate and generate arrhythmogenic triggered excitations in cardiac tissue.

Exploring the elastic features of spherically shaped biological assemblies and soft matter systems.

Using a numerical simulation, we study the elastic features of biological assemblies (e.g. viruses and bacteria) and soft matter systems (e.g. colloidosomes and nanoparticle covered droplets) that possess a spherical shape in which the proteins (particles) on the colloidosomes or virus shells are mechanically linked to form a stress-bearing spherical structure that may dramatically enhance the surface rigidity. The dependence of the rigidity enhancement upon the density of the cross-linked proteins situated on the surface of the virus is explored. We determine the percolation threshold P(ce) by considering bond percolation on the spherical elastic networks involving nearest neighbor forces. The percolation threshold of such networks is very different from that of a two-dimensional triangular lattice due to the topological effect. We find that the threshold probability for the spherical elastic network is considerably smaller than for an unwrapped network, which reveals that the spherical topology induces more rigidity to the network.

Thermally activated barrier crossing and stochastic resonance of a flexible polymer chain in a piecewise linear bistable potential.

We study the stochastic resonance of a flexible polymer chain crossing over a piecewise linear bistable potential. The dependence of signal to noise ratio SNR on noise intensity D , coupling constant k , and polymer length N is studied via two-state approximation. We find that the response of signal to the background noise strength is significant at optimum values of D{opt} , k{opt} , and N{opt} which suggests a means of manipulating proteins or vesicles. Furthermore, the thermally activated barrier crossing rate r{k} for the flexible polymer chain is studied. We find that the crossing rate r{k} exhibits an optimal value at an optimal coupling constant k{opt} ; k{opt} decreases with N . As the chain length N increases, the escape rate for the center of mass r{k} monotonously decreases. On the other hand, the crossing rate for the portion of polymer segment r{s} increases and saturates to a constant rate as N steps up.