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Complexity and limited knowledge render it impractical to write down the equations describing a cellular system completely. Cellular biophysics uses hypotheses-based modelling instead. How can we set up models with predictive power beyond the experimental examples used to develop them? The two textbook systems of cellular biophysics, Ca(2+) signalling and neuronal membrane potential dynamics, both face this question. Both systems also have a non-equilibrium feature in common: on different time scales and for different observables, they exhibit stochastic spiking, i.e., sequences of stereotypical events that are separated by statistically distributed intervals, the interspike intervals (ISI). Here we review recent progress on the description of Ca(2+) spikes in terms of blips, puffs and cellular Ca(2+) spikes and focus on stochastic models that can explain the statistics of the single ISIs, in particular its mean and variance and the cell-to-cell variability of these statistics. We also review models of the stochastic integrate-and-fire type and measures like the spike-train power spectrum or the serial correlation coefficient that are used to describe neuronal spike trains. These concepts from computational neuroscience might be applicable for understanding long-term memory effects in Ca(2+) spiking that extend beyond a single ISI, such as cumulative refractoriness.

Calcium (Ca(2+)) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression (LTD) and long-term potentiation (LTP) at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP(3)) induced Ca(2+) release. These Ca(2+) transients happen in response to stimuli from parallel fibers (PF) from granule cells and climbing fibers (CF) from the inferior olivary nucleus. These events occur at low numbers of free Ca(2+) requiring stochastic single particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca(2+) transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum (ER), several Ca(2+) transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca(2+) transients in different dynamical situations. We test two different models of the IP(3) receptor (IP3R). The model with non-linear concentration response of binding of activating Ca(2+) reproduces experimental results better than the model with linear response due to the filtering of noise. Our results also suggest that Ca(2+) dependent inhibition of the IP3R needs to be slow in order to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli to arise from the relative timing of CF influx of Ca(2+) and IP(3) production sensitizing IP3R for Ca(2+) induced Ca(2+) release. We also model Ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca2+ transients. Finally, we propose possible ways of recovering Ca(2+) transients under Ataxia.

AIMS: Heart failure with preserved ejection fraction (HFpEF) is increasingly common but there is currently no established pharmacological therapy. We hypothesized that ORM-11035, a novel specific Na(+)/Ca(2+) exchanger (NCX) inhibitor, improves cardiac function and remodelling independent of effects on arterial blood pressure in a model of cardiorenal HFpEF. METHODS AND RESULTS: Rats were subjected to subtotal nephrectomy (NXT) or sham operation. Eight weeks after intervention, treatment for 16 weeks with ORM-11035 (1 mg/kg body weight) or vehicle was initiated. At 24 weeks, blood pressure measurements, echocardiography and pressure-volume loops were performed. Contractile function, Ca(2+) transients and NCX-mediated Ca(2+) extrusion were measured in isolated ventricular cardiomyocytes. NXT rats (untreated) showed a HFpEF phenotype with left ventricular (LV) hypertrophy, LV end-diastolic pressure (LVEDP) elevation, increased brain natriuretic peptide (BNP) levels, preserved ejection fraction and pulmonary congestion. In cardiomyocytes from untreated NXT rats, early relaxation was prolonged and NCX-mediated Ca(2+) extrusion was decreased. Chronic treatment with ORM-11035 significantly reduced LV hypertrophy and cardiac remodelling without lowering systolic blood pressure. LVEDP [14 ± 3 vs. 9 ± 2 mmHg; NXT (n = 12) vs. NXT + ORM (n = 12); P = 0.0002] and BNP levels [71 ± 12 vs. 49 ± 11 pg/mL; NXT (n = 12) vs. NXT + ORM (n = 12); P

First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under an exponential transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent ν depends on the chain length N like ν=-N/(N+1) to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy and are closely related to the timing of repetitive excitations, coherence resonance, and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission.

Membrane waves propagating along the cell circumference in a top down view have been observed with several eukaryotic cells (Döbereiner et al 2006 Phys. Rev. Lett. 97 10; Machacek and Danuser 2006 Biophys. J. 90 1439–52). We present a mathematical model reproducing these traveling membrane undulations during lamellipodial motility of cells on flat substrates. The model describes the interplay of pushing forces exerted by actin polymerization on the membrane, pulling forces of attached actin filaments on the cell edge, contractile forces powered by molecular motors across the actin gel and resisting membrane tension. The actin filament network in the bulk of lamellipodia obeys gel flow equations. We investigated in particular the dependence of wave properties on gel parameters and found that inhibition of myosin motors abolishes waves in some cells but not in others in agreement with experimental observations. The model provides a unifying mechanism explaining the dynamics of actin-based motility in a variety of systems.

The behavior of biological systems is determined by the properties of their component molecules, but the interactions are usually too complex to understand fully how molecular behavior generates cellular behavior. Ca(2+) signaling by inositol trisphosphate receptors (IP(3)R) offers an opportunity to understand this relationship because the cellular behavior is defined largely by Ca(2+)-mediated interactions between IP(3)R. Ca(2+) released by a cluster of IP(3)R (giving a local Ca(2+) puff) diffuses and ignites the behavior of neighboring clusters (to give repetitive global Ca(2+) spikes). We use total internal reflection fluorescence microscopy of two mammalian cell lines to define the temporal relationships between Ca(2+) puffs (interpuff intervals, IPI) and Ca(2+) spikes (interspike intervals) evoked by flash photolysis of caged IP(3). We find that IPI are much shorter than interspike intervals, that puff activity is stochastic with a recovery time that is much shorter than the refractory period of the cell, and that IPI are not periodic. We conclude that Ca(2+) spikes do not arise from oscillatory dynamics of IP(3)R clusters, but that repetitive Ca(2+) spiking with its longer timescales is an emergent property of the dynamics of the whole cluster array.

We present a model for actin-based motility that combines the dynamics of the semiflexible region at the leading edge of the lamellipodium with actomyosin gel properties in the bulk described by the theory of active polar gels. We calculate the velocity of the lamellipodium determined by the interaction of the gel and adhesion with forces in the semiflexible region. The stationary concave force-velocity relation of the model reproduces experimental results. We suggest that it is determined by retrograde flow at small forces and gel formation and retrograde flow at large ones. The variety of dynamic regimes of the semiflexible region reproducing experimentally observed morphodynamics is conserved when we couple the leading edge to the gel.

This is an electronic version of the paper presented at the 5th Joint Symposium on Neural Computation, held in California on 1998, The role that subcellular processes play in the firing properties of individual neurons and circuit activity is no yet fully understood. We have built a two-compartment model of stomatogastric motor neuron to study synchronization, chaotic and regularization phenomena observed in real circuits. It is observed experimentally that two stomatogastric bursting neurons with natural electrical coupling can synchronize the slow voltage oscillations but not the more rapid spiking activity. We have studied the mechanism underlying these synchronized chaotic oscillaions using two LP model neurons coupled electrically. The effect of changing the coupling conductance and the role of calcium dynamics in the generation of the chaos and the regularization of the bursting behavior are discussed in this paper., This work has been supported by grants from ORD (H. D. I. A.), DOE (H. D. I. A., M. I. R.) and Universidad de Granada (J. J. T.)