Angelina Peñaranda

Modeling of spatiotemporal patterns in bacterial colonies.

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.

Dependency of calcium alternans on Ryanodine Receptor Refractoriness

Background Rapid 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 Findings To 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/Significance We 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.

Are SR Ca content fluctuations or SR refractoriness the key to atrial cardiac alternans?: insights from a human atrial model

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.

Reexcitation mechanisms in epicardial tissue: Role of Ito density heterogeneities and INa inactivation kinetics

Dispersion of action potential repolarization is known to be an important arrhythmogenic factor in cardiopathies such as Brugada syndrome. In this work, we analyze the effect of a variation in sodium current (I(Na)) inactivation and a heterogeneous rise of transient outward current (I(to)) in the probability of reentry in epicardial tissue. We use the Luo-Rudy model of epicardial ventricular action potential to study wave propagation in a one-dimensional fiber. Spatial dispersion in repolarization is introduced by splitting the fiber into zones with different strength of I(to). We then analyze the pro-arrhythmic effect of a variation in the relaxation time and steady-state of the sodium channel fast inactivating gate h. We quantify the probability of reentry measuring the percentage of reexcitations that occurs in 200 beats. We find that, for high stimulation rates, this percentage is negligible, but increases notably for pacing periods above 700ms. Surprisingly, with decreasing I(Na) inactivation time, the percentage of reexcitations does not grow monotonically, but presents vulnerable windows, separated by values of the I(Na) inactivation speed-up where reexcitation does not occur. By increasing the strength of L-type calcium current I(CaL) above a certain threshold, reexcitation disappears. Finally, we show the formation of reentry in stimulated two-dimensional epicardial tissue with modified I(Na) kinetics and I(to) heterogeneity. Thus, we confirm that while I(to) dispersion is necessary for phase-2 reentry, altered sodium inactivation kinetics influences the probability of reexcitation in a highly nonlinear fashion.

Cardiac dynamics: a simplified model for action potential propagation

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit’s ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.

Minimal model for calcium alternans due to SR release refractoriness

In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of the intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to (1) a strong dependence of calcium release on sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or (2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation for calcium concentration at the dyadic space, coupled to a relaxation equation for the number of recovered RyR2s. Depending on the number of RyR2s that are recovered at the beginning of a stimulation, the increase in calcium concentration may pass, or not, over an excitability threshold that limits the occurrence of a large calcium transient. When the recovery of the RyR2 is slow, this produces naturally a period doubling bifurcation, resulting in calcium alternans. We then study the effects of inactivation, calcium diffusion, and release conductance for the onset of alternans. We find that the development of alternans requires a well-defined value of diffusion while it is less sensitive to the values of inactivation or release conductance.

Influence of gap junction dynamics on the stability of reentrant waves in cardiac tissue

Constant conductances are often assumed when modeling cardiac tissue. However experimental evidences have shown that gap junctions (GJ) actually connect adjacent cardiac myocytes. These GJ are complex proteins of the connexin family (Cx40; Cx43; Cx45 are the most common in human). These GJ modify the conductances between cardiac cell through a dynamical process. The aim of this study is to develop a bidomain model of the cardiac tissue where the dynamics of the connexins is also included. In particular we will compare the differences associated with the use of a monodomain versus bidomain formulation in inducing intra-cellular conductance variations. We have found that the monodomain formulation gives conductance variations a factor four to five larger with respect to the bidomain formulation.

Green Streets for Noise Reduction

Abstract Green streets as a means to reduce urban noise are discussed in this chapter. Standard solutions used in highways or industrial environments, namely high noise barriers or wide space of dense vegetation, are frequently not feasible in urban spaces, and other solutions have to be considered. Hedges and medium-height greenery barriers can be interesting elements, due to their possibility to be placed near the noise source and the receiver. The presence of trees along the streets, and the integration of vegetation in walls, building facades and roofs increase the sound absorption, reducing the level of noise and the consequent annoyance. Furthermore, greenery elements present the advantage of landscape visual quality that physiologically affect acoustic perception, increasing the pleasantness and decreasing the annoyance impression. Findings from latest research referring to the efficacy of these kinds of barriers in main arteries of big cities are presented.

Mechanisms Underlying Electro-Mechanical Cardiac Alternans

Electro-mechanical cardiac alternans consists in beat-to-beat changes in the strength of cardiac contraction. Despite its important role 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 calcium level (SR Ca load). 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). In this chapter we review recent results regarding the relative role of SR Ca content fluctuations and SR refractoriness for the appearance of alternans in both ventricular and atrial cells.

Calcium alternans is a global order-disorder phase transition. Robustness on Ryanodine Receptor release dynamics

Electromechanical alternans is a beat-to-beat alternation in the strength of contraction of a cardiac cell which appears often due to an instability of calcium cycling. The global calcium signal in cardiomyocytes is the result of the combined effect of several thousand micron scale domains called Calcium Release Units (CaRU), coupled through diffusion, where the flow of calcium among different cell compartments is regulated by stochastic signaling involving the ryanodine receptor (RyR). Recently, numerical simulations have suggested that the transition from regular Ca cycling to alternans is an order-disorder phase transition consistent with the Ising universality class. Inside the cell, groups of CaRU form transient areas within the cell where alternans appear. However, global alternans appears only as a result of the synchronization of the oscillation phase among different subunits. We show here that this transition is indeed robust and universal upon changes in the behavior of the RyR. Using three different set of parameters for the transition rates among open, closed and inactivated states in the RyR, we show that different RyR behavior leads to the same type of order-disorder transition.