A theory of plasma membrane calcium pump stimulation and activity

Influence of T-Bar on Calcium Concentration Impacting Release Probability

The relation of form and function, namely the impact of the synaptic anatomy on calcium dynamics in the presynaptic bouton, is a major challenge of present (computational) neuroscience at a cellular level. The Drosophila larval neuromuscular junction (NMJ) is a simple model system, which allows studying basic effects in a rather simple way. This synapse harbors several special structures. In particular, in opposite to standard vertebrate synapses, the presynaptic boutons are rather large, and they have several presynaptic zones. In these zones, different types of anatomical structures are present. Some of the zones bear a so-called T-bar, a particular anatomical structure. The geometric form of the T-bar resembles the shape of the letter “T” or a table with one leg. When an action potential arises, calcium influx is triggered. The probability of vesicle docking and neurotransmitter release is superlinearly proportional to the concentration of calcium close to the vesicular release site. It is tempting to assume that the T-bar causes some sort of calcium accumulation and hence triggers a higher release probability and thus enhances neurotransmitter exocytosis. In order to study this influence in a quantitative manner, we constructed a typical T-bar geometry and compared the calcium concentration close to the active zones (AZs). We compared the case of synapses with and without T-bars. Indeed, we found a substantial influence of the T-bar structure on the presynaptic calcium concentrations close to the AZs, indicating that this anatomical structure increases vesicle release probability. Therefore, our study reveals how the T-bar zone implies a strong relation between form and function. Our study answers the question of experimental studies (namely “Wichmann and Sigrist, Journal of neurogenetics 2010”) concerning the sense of the anatomical structure of the T-bar.

Calcium modeling of spine apparatus-containing human dendritic spines demonstrates an “all-or-nothing” communication switch between the spine head and dendrite

Dendritic spines are highly dynamic neuronal compartments that control the synaptic transmission between neurons. Spines form ultrastructural units, coupling synaptic contact sites to the dendritic shaft and often harbor a spine apparatus organelle, composed of smooth endoplasmic reticulum, which is responsible for calcium sequestration and release into the spine head and neck. The spine apparatus has recently been linked to synaptic plasticity in adult human cortical neurons. While the morphological heterogeneity of spines and their intracellular organization has been extensively demonstrated in animal models, the influence of spine apparatus organelles on critical signaling pathways, such as calcium-mediated dynamics, is less well known in human dendritic spines. In this study we used serial transmission electron microscopy to anatomically reconstruct nine human cortical spines in detail as a basis for modeling and simulation of the calcium dynamics between spine and dendrite. The anatomical study of reconstructed human dendritic spines revealed that the size of the postsynaptic density correlates with spine head volume and that the spine apparatus volume is proportional to the spine volume. Using a newly developed simulation pipeline, we have linked these findings to spine-to-dendrite calcium communication. While the absence of a spine apparatus, or the presence of a purely passive spine apparatus did not enable any of the reconstructed spines to relay a calcium signal to the dendritic shaft, the calcium-induced calcium release from this intracellular organelle allowed for finely tuned “all-or-nothing” spine-to-dendrite calcium coupling; controlled by spine morphology, neck plasticity, and ryanodine receptors. Our results suggest that spine apparatus organelles are strategically positioned in the neck of human dendritic spines and demonstrate their potential relevance to the maintenance and regulation of spine-to-dendrite calcium communication.

During the past decade it has become increasingly clear that abnormal synaptic plasticity is a major hallmark of neurological and cognitive disorders. Developing a better understanding of the synaptic plasticity process, which describes the ability of neurons to adapt their contacts in an activity-dependent manner, will lead to improved treatment of many neurological and cognitive disorders. It is known that calcium-dependent events such as synaptic transmission, intracellular calcium release, and calcium wave propagation, are required for many types of synaptic plasticity expression. However, the biological significance of these processes in neurons of the adult human cortex remains unknown. Due to technical limitations and ethical concerns, experimental data addressing this biologically and clinically relevant topic are not available. Therefore, we have implemented a computational model to study the intracellular calcium dynamics in realistic human dendritic spines based on detailed morphological reconstructions. With our model and simulations, we have established the morphological and biological requirements for the propagation of calcium from spines into the dendrites. Our results suggest a critical role for the calcium-storing spine apparatus organelle in regulating calcium homeostasis and propagation in human dendritic spines.

A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During a particular phase of the retina development (stage II) these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. The underlying mechanisms of the spontaneous bursting and the transient excitability of immature SACs are not completely clear yet. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing V-gated calcium channels and hyperpolarizing V-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.

P2Y1 receptor inhibits GABA transport through a calcium signalling-dependent mechanism in rat cortical astrocytes

Astrocytes express a variety of purinergic (P2) receptors, involved in astrocytic communication through fast increases in [Ca(2+) ]i . Of these, the metabotropic ATP receptors (P2Y) regulate cytoplasmic Ca(2+) levels through the PLC-PKC pathway. GABA transporters are a substrate for a number of Ca(2+) -related kinases, raising the possibility that calcium signalling in astrocytes impact the control of extracellular levels of the major inhibitory transmitter in the brain. To access this possibility we tested the influence of P2Y receptors upon GABA transport into astrocytes. Mature primary cortical astroglial-enriched cultures expressed functional P2Y receptors, as evaluated through Ca(2+) imaging, being P2Y1 the predominant P2Y receptor subtype. ATP (100 μM, for 1 min) caused an inhibition of GABA transport through either GAT-1 or GAT-3 transporters, decreasing the Vmax kinetic constant. ATP-induced inhibition of GATs activity was still evident in the presence of adenosine deaminase, precluding an adenosine-mediated effect. This, was mimicked by a specific agonist for the P2Y1,12,13 receptor (2-MeSADP). The effect of 2-MeSADP on GABA transport was blocked by the P2 (PPADS) and P2Y1 selective (MRS2179) receptor antagonists, as well as by the PLC inhibitor (U73122). 2-MeSADP failed to inhibit GABA transport in astrocytes where intracellular calcium had been chelated (BAPTA-AM) or where calcium stores were depleted (α-cyclopiazonic acid, CPA). In conclusion, P2Y1 receptors in astrocytes inhibit GABA transport through a mechanism dependent of P2Y1 -mediated calcium signalling, suggesting that astrocytic calcium signalling, which occurs as a consequence of neuronal firing, may operate a negative feedback loop to enhance extracellular levels of GABA.

A mathematical model of T lymphocyte calcium dynamics derived from single transmembrane protein properties

Fate decision processes of T lymphocytes are crucial for health and disease. Whether a T lymphocyte is activated, divides, gets anergic, or initiates apoptosis depends on extracellular triggers and intracellular signaling. Free cytosolic calcium dynamics plays an important role in this context. The relative contributions of store-derived calcium entry and calcium entry from extracellular space to T lymphocyte activation are still a matter of debate. Here we develop a quantitative mathematical model of T lymphocyte calcium dynamics in order to establish a tool which allows to disentangle cause-effect relationships between ion fluxes and observed calcium time courses. The model is based on single transmembrane protein characteristics which have been determined in independent experiments. This reduces the number of unknown parameters in the model to a minimum and ensures the predictive power of the model. Simulation results are subsequently used for an analysis of whole cell calcium dynamics measured under various experimental conditions. The model accounts for a variety of these conditions, which supports the suitability of the modeling approach. The simulation results suggest a model in which calcium dynamics dominantly relies on the opening of channels in calcium stores while calcium entry through calcium-release activated channels (CRAC) is more associated with the maintenance of the T lymphocyte calcium levels and prevents the cell from calcium depletion. Our findings indicate that CRAC guarantees a long-term stable calcium level which is required for cell survival and sustained calcium enhancement.

Ca2+-Mg2+-dependent ATP-ase activity and calcium homeostasis in children with chronic kidney disease

Extracellular calcium concentrations in humans are thousands times higher than within cells. Maintenance of such gradient requires specific regulation including intracellular stores, Ca binding proteins and transmembrane protein systems. The aim of the study was to estimate PMCA (plasma membrane Ca-transporting adenosine triphosphatase; ATPase 3.6.1.38) activity and calcium homeostasis in erythrocytes of children with chronic kidney disease (CKD). Twenty-one children wth CKD stages 1-3 (group I) and 18 healthy children (group II) were examined. Group I was divided into two subgroups: Ia (8 patients with normal intact parathyroid hormone, iPTH, serum levels) and Ib (13 patients with increased iPTH). iPTH, urea, creatinine, inorganic phosphorus, cytosolic Ca2+ in red blood cells (R-Ca), and PMCA were determined. Significantly elevated R-Ca levels were observed in children from subgroup Ib in comparison with group II and subgroup Ia. The lowest activity of PMCA was found in subgroup Ia and Ib in comparison with group II. There was a negative correlation between PMCA and R-Ca in group Ia and Ib (r=-0.8, r=-0.9, respectively). In children with CKD treated conservatively, activity of PMCA in erythrocytes is disturbed. An increase in R-Ca and decrease in PMCA activity are also observed.

Dynamics of Calcium Fluxes in Nonexcitable Cells: Mathematical Modeling

Mathematical models simulating the dynamics of calcium redistribution (elicited by experimental interference with the pathways of calcium fluxes) in cellular compartments have been developed, based on a minimal scheme of the pathways of calcium fluxes in nonexcitable cells suspended in calcium-free medium. The models are consistent with available experimental data. All parameters are quantitatively related to the intrinsic properties of calcium adenosine triphosphatases (ATPases) and cellular membranes; there is no interdependence between the parameters. The models can be used as the basis for quantitative analysis and interpretation of experimental data. The activities of plasma membrane and sarcoendoplasmic reticulum calcium ATPases (PMCA and SERCAs) are governed by different mechanisms. PMCA is likely to undergo transitions from inactive to active to "dormant" (not identical to the initial) and back to inactive states, the mean duration of the cycle lasting for minutes or longer. The sequence of the transitions is initiated, presumably, by an increase in cytosolic calcium concentration. The transition of PMCA from inactive to active (at least at low rates of increase in cytosolic calcium concentration) is likely to be slower than that from active to dormant. SERCA, presumably, transits from inactive to active state in response to increases in calcium leakage from calcium stores. Whereas PMCA extrudes excess calcium (a definite quantity of it) in a short pulse, SERCA retakes calcium back into the stores permanently at a high rate. The models presented here may be the best means for the moment to quantitatively relate the dynamics of calcium fluxes in nonexcitable cells with known or putative properties of the mechanisms underlying activation of calcium ATPases.

ON THE INTEGRATION OF PHYSIOLOGICAL MECHANISMS IN THE NERVOUS TISSUE USING THE MTIP: SYNAPTIC PLASTICITY DEPENDING ON NEURONS-ASTROCYTES-CAPILLARIES INTERACTIONS

The objective in this work is twofold: (i) to illustrate the use of the Mathematical Theory of Integrative Physiology (MTIP) [13], that is a general theory and practical method for the systematic and progressive mathematical integration of physiological mechanisms; (ii) to study a complex neurobiological system taken as an example, i.e., the synaptic plasticity depending on brain activity, on astrocytic and neuronal metabolism, and on brain hemodynamics. The functional organization of the nervous tissue is presented in the framework of the MTIP, the ultimate objective being the study of learning and memory by coupling the three networks of neurons, astrocytes and capillaries. Specifically in this paper, we study the influence of the variation of capillaries arterial oxygen on the induction of LTP/LTD by coupling validated mathematical models of AMPA, NMDA, VDCC channels, calcium current in the dendritic spine, vesicular glutamate dynamics in the presynaptic bouton derived from glycolysis and neuronal glucose, mitochondrial respiration, Ca/Na pumps, glycolysis, and calcium dynamics in the astrocytes, hemodynamics of the capillaries. The integration of all these models is discussed by claiming the advantages of using a common framework and a specific dedicated computing system, PhysioMatica.