Wave nucleation rate in excitable systems in the low noise limit

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential pair of equations driven by thermal (i.e. white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other non-equilibrium pattern-forming processes

Mechanisms of Induction and Maintenance of Spike-Timing Dependent Plasticity in Biophysical Synapse Models

We review biophysical models of synaptic plasticity, with a focus on spike-timing dependent plasticity (STDP). The common property of the discussed models is that synaptic changes depend on the dynamics of the intracellular calcium concentration, which itself depends on pre- and postsynaptic activity. We start by discussing simple models in which plasticity changes are based directly on calcium amplitude and dynamics. We then consider models in which dynamic intracellular signaling cascades form the link between the calcium dynamics and the plasticity changes. Both mechanisms of induction of STDP (through the ability of pre/postsynaptic spikes to evoke changes in the state of the synapse) and of maintenance of the evoked changes (through bistability) are discussed

Cellular and nuclear morphology…and calcium signaling: revealing the interplay between structure and function

Poster presentation: Calcium plays a pivotal role in relaying electrical signals of the cell to subcellular compartments, such as the nucleus. Since this one ion type is used by the cell for many processes a neuron needs to establish finely tuned calcium pathways in order to be able to differentiate multiple tasks, [1-3]. While it is known that neurons can actively change their shape upon neuronal activity, [4-7], we here present novel findings of activity-regulated nuclear morphology, [8,9]. With the help of an experimental and computational modeling approach, we show that hippocampal neurons can change the previously spherical shape of their nuclei to complex and infolded morphologies. This morphology regulation is demonstrated to be regulated by NMDA-receptor gated calcium, while synaptic and extra-synaptic NMDA-receptors elicit opposing effects on nuclear morphology, [8]. The structural alterations of the cell nucleus have significant effects on nuclear calcium dynamics. Compartmentalization of the nucleus, due to membrane infoldings, changes calcium frequencies, amplitudes and spatial distributions, [8,10]. Since these parameters have been shown to control downstream events towards gene transcription, [11,12], the results elucidate the cellular control of nuclear function with the help of morphology modulation. With respect to processes downstream of calcium, we show that histone H3 phosphorylation is closely linked to nuclear morphology. Investigating the nuclear morphologies of hippocampal neurons, two major classes were identified [9,10]. One class contains non-infolded nuclei that have the function of calcium signal integrators, while the other class contains highly infolded nuclei, which function as frequency detectors of nuclear calcium, [10]. Extending this interdisciplinary approach of investigating structure/function relationships in neurons, the effects of cellular morphology – as well as the morphology of the endoplasmic reticulum and other organelles – on neuronal calcium signals is currently being investigated. This endeavor makes use of highly detailed, three-dimensional models of neuronal calcium dynamics, including the three-dimensional morphology of the cell and its organelles

Using Delay-Differential Equations for Modeling Calcium Cycling in Cardiac Myocytes

The cycling of calcium at the intracellular level of cardiac cells plays a key role in the excitation-contraction process. The interplay between ionic currents, buffering agents, and calcium release from the sarcoplasmic reticulum (SR) is a complex system that has been shown experimentally to exhibit complex dynamics including period-2 states (alternans) and higher-order rhythms. Many of the calcium cycling activities involve the sensing, binding, or diffusion of calcium between intracellular compartments; these are physical processes that take time and typically are modeled by “relaxation” equations where the steady-state value and time course of a particular variable are specified through an ordinary differential equation (ODE) with a time constant. An alternative approach is to use delay-differential equations (DDEs), where the delays in the system correspond to non-instantaneous events. In this thesis, we present a thorough overview of results from calcium cycling experiments and proposed intracellular calcium cycling models, as well as the context of alternans and delay-differential equations in cardiac modeling. We utilize a DDE to model the diffusion of calcium through the SR by replacing the relaxation ODE typically used for this process. The relaxation time constant τa is replaced by a delay δj, which could also be interpreted as the refractoriness of ryanodine receptor channels after releasing calcium from the sarcoplasmic reticulum. This is the first application of delay-differential equations to modeling calcium cycling dynamics, and to modeling cardiac systems at the cellular level. We analyzed the dynamical behaviors of the system and focus on the factors that have been shown to produce alternans and irregular dynamics in experiments and models with cardiac myocytes. We found that chaotic calcium dynamics could occur even for a more physiologically revelant SR calcium release slope than comparable ODE models. Increasing the SR release slope did not affect the calcium dynamics, but only shifted behavior down to lower values of the delay, allowing alternans, higher-order behavior, and chaos to occur for smaller delays than in simulations with a normal SR release slope. For moderate values of the delay, solely alternans and 1:1 steady-state behavior were observed. Above a particular threshold value for the delay, chaos appeared in the dynamics and further increasing the delay caused the system to destabilize under broader ranges of periods. We also compare our results with other models of intracellular calcium cycling and suggest promising avenues for further development of our preliminary work

A computational model of spatio-temporal cardiac intracellular calcium handling with realistic structure and spatial flux distribution from sarcoplasmic reticulum and t-tubule reconstructions

Intracellular calcium cycling is a vital component of cardiac excitation-contraction coupling. The key structures responsible for controlling calcium dynamics are the cell membrane (comprising the surface sarcolemma and transverse-tubules), the intracellular calcium store (the sarcoplasmic reticulum), and the co-localisation of these two structures to form dyads within which calcium-induced-calcium-release occurs. The organisation of these structures tightly controls intracellular calcium dynamics. In this study, we present a computational model of intracellular calcium cycling in three-dimensions (3-D), which incorporates high resolution reconstructions of these key regulatory structures, attained through imaging of tissue taken from the sheep left ventricle using serial block face scanning electron microscopy. An approach was developed to model the sarcoplasmic reticulum structure at the whole-cell scale, by reducing its full 3-D structure to a 3-D network of one-dimensional strands. The model reproduces intracellular calcium dynamics during control pacing and reveals the high-resolution 3-D spatial structure of calcium gradients and intracellular fluxes in both the cytoplasm and sarcoplasmic reticulum. We also demonstrated the capability of the model to reproduce potentially pro-arrhythmic dynamics under perturbed conditions, pertaining to calcium-transient alternans and spontaneous release events. Comparison with idealised cell models emphasised the importance of structure in determining calcium gradients and controlling the spatial dynamics associated with calcium-transient alternans, wherein the probabilistic nature of dyad activation and recruitment was constrained. The model was further used to highlight the criticality in calcium spark propagation in relation to inter-dyad distances. The model presented provides a powerful tool for future investigation of structure-function relationships underlying physiological and pathophysiological intracellular calcium handling phenomena at the whole-cell. The approach allows for the first time direct integration of high-resolution images of 3-D intracellular structures with models of calcium cycling, presenting the possibility to directly assess the functional impact of structural remodelling at the cellular scale

Automated optimization of a reduced layer 5 pyramidal cell model based on experimental data.

The construction of compartmental models of neurons involves tuning a set of parameters to make the model neuron behave as realistically as possible. While the parameter space of single-compartment models or other simple models can be exhaustively searched, the introduction of dendritic geometry causes the number of parameters to balloon. As parameter tuning is a daunting and time-consuming task when performed manually, reliable methods for automatically optimizing compartmental models are desperately needed, as only optimized models can capture the behavior of real neurons. Here we present a three-step strategy to automatically build reduced models of layer 5 pyramidal neurons that closely reproduce experimental data. First, we reduce the pattern of dendritic branches of a detailed model to a set of equivalent primary dendrites. Second, the ion channel densities are estimated using a multi-objective optimization strategy to fit the voltage trace recorded under two conditions - with and without the apical dendrite occluded by pinching. Finally, we tune dendritic calcium channel parameters to model the initiation of dendritic calcium spikes and the coupling between soma and dendrite. More generally, this new method can be applied to construct families of models of different neuron types, with applications ranging from the study of information processing in single neurons to realistic simulations of large-scale network dynamics

Spontaneous Calcium Release in Cardiac Myocytes: Store Overload and Electrical Dynamics

Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca2+) mishandling in cardiac muscle cells. We adapt Izu\u27s et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes implemented by Gobbert, and analyzed in Coulibaly et al. to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca2+ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with known biological models and principles, giving us a thorough understanding of several factors that influence Ca2+ dynamics in cardiac myocytes. Specifically, dynamic calcium store will cap previous calcium blow-up seen in the model. Calcium channels located in spatial opposition of calcium release units produce more predictable intracellular calcium propagation. And we used multi-parametric calcium dynamics tables, which act as a multidimensional bifurcation diagram, to visualize parameter boundaries between different biophysical dynamics