Computational study of non-homogeneous distribution of Ca(2+) handling systems in cerebellar granule cells

Estimation of presynaptic calcium currents and endogenous calcium buffers at the frog neuromuscular junction with two different calcium fluorescent dyes

At the frog neuromuscular junction, under physiological conditions, the direct measurement of calcium currents and of the concentration of intracellular calcium buffers—which determine the kinetics of calcium concentration and neurotransmitter release from the nerve terminal—has hitherto been technically impossible. With the aim of quantifying both Ca²⁺ currents and the intracellular calcium buffers, we measured fluorescence signals from nerve terminals loaded with the low-affinity calcium dye Magnesium Green or the high-affinity dye Oregon Green BAPTA-1, simultaneously with microelectrode recordings of nerve-action potentials and end-plate currents. The action-potential-induced fluorescence signals in the nerve terminals developed much more slowly than the postsynaptic response. To clarify the reasons for this observation and to define a spatiotemporal profile of intracellular calcium and of the concentration of mobile and fixed calcium buffers, mathematical modeling was employed. The best approximations of the experimental calcium transients for both calcium dyes were obtained when the calcium current had an amplitude of 1.6 ± 0.08 pA and a half-decay time of 1.2 ± 0.06 ms, and when the concentrations of mobile and fixed calcium buffers were 250 ± 13 μM and 8 ± 0.4 mM, respectively. High concentrations of endogenous buffers define the time course of calcium transients after an action potential in the axoplasm, and may modify synaptic plasticity.

Models of calcium dynamics in cerebellar granule cells

Intracellular calcium dynamics is critical for many functions of cerebellar granule cells (GrCs) including membrane excitability, synaptic plasticity, apoptosis, and regulation of gene transcription. Recent measurements of calcium responses in GrCs to depolarization and synaptic stimulation reveal spatial compartmentalization and heterogeneity within dendrites of these cells. However, the main determinants of local calcium dynamics in GrCs are still poorly understood. One reason is that there have been few published studies of calcium dynamics in intact GrCs in their native environment. In the absence of complete information, biophysically realistic models are useful for testing whether specific Ca(2+) handling mechanisms may account for existing experimental observations. Simulation results can be used to identify critical measurements that would discriminate between different models. In this review, we briefly describe experimental studies and phenomenological models of Ca(2+) signaling in GrC, and then discuss a particular biophysical model, with a special emphasis on an approach for obtaining information regarding the distribution of Ca(2+) handling systems under conditions of incomplete experimental data. Use of this approach suggests that Ca(2+) channels and fixed endogenous Ca(2+) buffers are highly heterogeneously distributed in GrCs. Research avenues for investigating calcium dynamics in GrCs by a combination of experimental and modeling studies are proposed.

Effects of calretinin on Ca2+ signals in cerebellar granule cells: implications of cooperative Ca2+ binding

Calretinin is thought to be the main endogenous calcium buffer in cerebellar granule cells (GrCs). However, little is known about the impact of cooperative Ca(2+) binding to calretinin on highly localized and more global (regional) Ca(2+) signals in these cells. Using numerical simulations, we show that an essential property of calretinin is a delayed equilibration with Ca(2+). Therefore, the amount of Ca(2+), which calretinin can accumulate with respect to equilibrium levels, depends on stimulus conditions. Based on our simulations of buffered Ca(2+) diffusion near a single Ca(2+) channel or a large cluster of Ca(2+) channels and previous experimental findings that 150 μM 1,2-bis(o-aminophenoxy) ethane-N, N, N', N'-tetraacetic acid (BAPTA) and endogenous calretinin have similar effects on GrC excitability, we estimated the concentration of mobile calretinin in GrCs in the range of 0.7-1.2 mM. Our results suggest that this estimate can provide a starting point for further analysis. We find that calretinin prominently reduces the action potential associated increase in cytosolic free Ca(2+) concentration ([Ca(2+)]( i )) even at a distance of 30 nm from a single Ca(2+) channel. In spite of a buildup of residual Ca(2+), it maintains almost constant maximal [Ca(2+)]( i ) levels during repetitive channel openings with a frequency less than 80 Hz. This occurs because of accelerated Ca(2+) binding as calretinin binds more Ca(2+). Unlike the buffering of high Ca(2+) levels within Ca(2+) nano/microdomains sensed by large conductance Ca(2+)-activated K(+) channels, the buffering of regional Ca(2+) signals by calretinin can never be mimicked by certain concentration of BAPTA under all different experimental conditions.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

Designing dynamical output feedback controllers for store-operated Ca²+ entry

Store-operated calcium entry (SOCE) has been proposed as the main process controlling Ca²+ entry in non-excitable cells. Although recent breakthroughs in experimental studies of SOCE have been made, its mathematical modeling has not been developed. In the present work, SOCE is viewed as a feedback control system subject to an extracellular agonist disturbance and an extracellular calcium input. We then design a dynamic output feedback controller to reject the disturbance and track Ca²+ resting levels in the cytosol and the endoplasmic reticulum (ER). The constructed feedback control system is validated by published experimental data and its global asymptotic stability is proved by using the LaSalle's invariance principle. We then simulate the dynamic responses of STIM1 and Orai1, two major components in the operation of the store-operated channels, to the depletion of Ca²+ in the ER with thapsigargin, which show that: (1) Upon the depletion of Ca²+ in the ER, the concentrations of activated STIM1 and STIM1-Orai1 cluster are elevated gradually, indicating that STIM1 is accumulating in the ER-PM junctions and that the cytosolic portion of the active STIM1 is binding to Orai1 and driving the opening of CRAC channels for Ca²+ entry; (2) after the extracellular Ca²+ addition, the concentrations of both STIM1 and STIM1-Orai1 cluster decrease but still much higher than the original levels. We also simulate the system responses to the agonist disturbance, which show that, when a sequence of periodic agonist pulses is applied, the system returns to its equilibrium after each pulse. This indicates that the designed feedback controller can reject the disturbance and track the equilibrium.

Dendritic vulnerability in neurodegenerative disease: insights from analyses of cortical pyramidal neurons in transgenic mouse models

In neurodegenerative disorders, such as Alzheimer's disease, neuronal dendrites and dendritic spines undergo significant pathological changes. Because of the determinant role of these highly dynamic structures in signaling by individual neurons and ultimately in the functionality of neuronal networks that mediate cognitive functions, a detailed understanding of these changes is of paramount importance. Mutant murine models, such as the Tg2576 APP mutant mouse and the rTg4510 tau mutant mouse have been developed to provide insight into pathogenesis involving the abnormal production and aggregation of amyloid and tau proteins, because of the key role that these proteins play in neurodegenerative disease. This review showcases the multidimensional approach taken by our collaborative group to increase understanding of pathological mechanisms in neurodegenerative disease using these mouse models. This approach includes analyses of empirical 3D morphological and electrophysiological data acquired from frontal cortical pyramidal neurons using confocal laser scanning microscopy and whole-cell patch-clamp recording techniques, combined with computational modeling methodologies. These collaborative studies are designed to shed insight on the repercussions of dystrophic changes in neocortical neurons, define the cellular phenotype of differential neuronal vulnerability in relevant models of neurodegenerative disease, and provide a basis upon which to develop meaningful therapeutic strategies aimed at preventing, reversing, or compensating for neurodegenerative changes in dementia.