No abstract

A diffusion-reaction model for the growth of bacterial colonies is presented. The often observed cooperative behavior developed by bacteria which increases their motility in adverse growth conditions is here introduced as a nonlinear diffusion term. The presence of this mechanism depends on a response which can present hysteresis. By changing only the concentrations of agar and initial nutrient, numerical integration of the proposed model reproduces the different patterns shown by Bacillus subtilis OG-01.

Despite the important role of electromechanical alternans in cardiac arrhythmogenesis, its molecular origin is not well understood. The appearance of calcium alternans has often been associated to fluctuations in the sarcoplasmic reticulum (SR) Ca loading. However, cytosolic calcium alternans observed without concurrent oscillations in the SR Ca content suggests an alternative mechanism related to a dysfunction in the dynamics of the ryanodine receptor (RyR2). We have investigated the effect of SR release refractoriness in the appearance of alternans, using a mathematical model of a single human atrial cell, based on the model by Nygren et al. (30), where we modified the dynamics of the RyR2 and of SR Ca release. The genesis of calcium alternans was studied stimulating the cell for different periods and values of the RyR2 recovery time from inactivation. At fast rates cytosolic calcium alternans were obtained without concurrent SR Ca content fluctuations. A transition from regular response to alternans was also observed, changing the recovery time from inactivation of the RyR2. This transition was found to be hysteretic, so for a given set of parameters different responses were observed. We then studied the relevance of RyR2 refractoriness for the generation of alternans, reproducing the same protocols as in recent experiments. In particular, restitution of Ca release during alternans was studied with a S1S2 protocol, obtaining a different response if the S2 stimulation was given after a long or a short release. We show that the experimental results can be explained by RyR2 refractoriness, arising from a slow RyR2 recovery from inactivation, stressing the role of the RyR2 in the genesis of alternans.

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low-or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of ͑low-field͒ dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features ͑maxima, minima, plateaus, etc.͒ and several critical currents ͑which depend on the values of the contact parameters͒. Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation. ͓S1063-651X͑97͒04708-9͔ PACS number͑s͒: 05.45.ϩb, 72.20.Ht, 85.30.Fg

BackgroundRapid pacing rates induce alternations in the cytosolic calcium concentration caused by fluctuations in calcium released from the sarcoplasmic reticulum (SR). However, the relationship between calcium alternans and refractoriness of the SR calcium release channel (RyR2) remains elusive.Methodology/Principal FindingsTo investigate how ryanodine receptor (RyR2) refractoriness modulates calcium handling on a beat-to-beat basis using a numerical rabbit cardiomyocyte model. We used a mathematical rabbit cardiomyocyte model to study the beat-to-beat calcium response as a function of RyR2 activation and inactivation. Bi-dimensional maps were constructed depicting the beat-to-beat response. When alternans was observed, a novel numerical clamping protocol was used to determine whether alternans was caused by oscillations in SR calcium loading or by RyR2 refractoriness. Using this protocol, we identified regions of RyR2 gating parameters where SR calcium loading or RyR2 refractoriness underlie the induction of calcium alternans, and we found that at the onset of alternans both mechanisms contribute. At low inactivation rates of the RyR2, calcium alternans was caused by alternation in SR calcium loading, while at low activation rates it was caused by alternation in the level of available RyR2s.Conclusions/SignificanceWe have mapped cardiomyocyte beat-to-beat responses as a function of RyR2 activation and inactivation, identifying domains where SR calcium load or RyR2 refractoriness underlie the induction of calcium alternans. A corollary of this work is that RyR2 refractoriness due to slow recovery from inactivation can be the cause of calcium alternans even when alternation in SR calcium load is present.