A quantitative model for presynaptic free Ca2+ dynamics during different stimulation protocols

Monomeric α-synuclein activates the plasma membrane calcium pump

Alpha-synuclein (aSN) is a membrane-associated and intrinsically disordered protein, well known for pathological aggregation in neurodegeneration. However, the physiological function of aSN is disputed. Pull-down experiments have pointed to plasma membrane Ca2+ -ATPase (PMCA) as a potential interaction partner. From proximity ligation assays, we find that aSN and PMCA colocalize at neuronal synapses, and we show that calcium expulsion is activated by aSN and PMCA. We further show that soluble, monomeric aSN activates PMCA at par with calmodulin, but independent of the autoinhibitory domain of PMCA, and highly dependent on acidic phospholipids and membrane-anchoring properties of aSN. On PMCA, the key site is mapped to the acidic lipid-binding site, located within a disordered PMCA-specific loop connecting the cytosolic A domain and transmembrane segment 3. Our studies point toward a novel physiological role of monomeric aSN as a stimulator of calcium clearance in neurons through activation of PMCA.

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.

Neuron-Glia Interactions and Brain Circuits

Recent evidence suggests that glial cells take an active role in a number of brain functions that were previously attributed solely to neurons. For example, astrocytes, one type of glial cells, have been shown to promote coordinated activation of neuronal networks, modulate sensory-evoked neuronal network activity, and influence brain state transitions during development. This reinforces the idea that astrocytes not only provide the "housekeeping" for the neurons, but that they also play a vital role in supporting and expanding the functions of brain circuits and networks. Despite this accumulated knowledge, the field of computational neuroscience has mostly focused on modeling neuronal functions, ignoring the glial cells and the interactions they have with the neurons. In this chapter, we introduce the biology of neuron-glia interactions, summarize the existing computational models and tools, and emphasize the glial properties that may be important in modeling brain functions in the future.

Transient reversal of the sodium/calcium exchanger boosts presynaptic calcium and synaptic transmission at a cerebellar synapse

The sodium/calcium exchanger (NCX) is a widespread transporter that exchanges sodium and calcium ions across excitable membranes. Normally, NCX mainly operates in its "forward" mode, harnessing the electrochemical gradient of sodium ions to expel calcium. During membrane depolarization or elevated internal sodium levels, NCX can instead switch the direction of net flux to expel sodium and allow calcium entry. Such "reverse"-mode NCX operation is frequently implicated during pathological or artificially extended periods of depolarization, not during normal activity. We have used fast calcium imaging, mathematical simulation, and whole cell electrophysiology to study the role of NCX at the parallel fiber-to-Purkinje neuron synapse in the mouse cerebellum. We show that nontraditional, reverse-mode NCX activity boosts the amplitude and duration of parallel fiber calcium transients during short bursts of high-frequency action potentials typical of their behavior in vivo. Simulations, supported by experimental manipulations, showed that accumulation of intracellular sodium drove NCX into reverse mode. This mechanism fueled additional calcium influx into the parallel fibers that promoted synaptic transmission to Purkinje neurons for up to 400 ms after the burst. Thus we provide the first functional demonstration of transient and fast NCX-mediated calcium entry at a major central synapse. This unexpected contribution from reverse-mode NCX appears critical for shaping presynaptic calcium dynamics and transiently boosting synaptic transmission, and is likely to optimize the accuracy of cerebellar information transfer.

A mathematical model of the tripartite synapse: astrocyte-induced synaptic plasticity

In this paper, we present a biologically detailed mathematical model of tripartite synapses, where astrocytes modulate short-term synaptic plasticity. The model consists of a pre-synaptic bouton, a post-synaptic dendritic spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca(2 + ) dynamics inside the synaptic bouton. This in turn controls glutamate release dynamics in the cleft. As a consequence of this, glutamate concentration in the cleft has been modeled, in which glutamate reuptake by astrocytes has also been incorporated. Finally, dendritic spine-head dynamics has been modeled. As an application, this model clearly shows synaptic potentiation in the hippocampal region, i.e., astrocyte Ca(2 + ) mediates synaptic plasticity, which is in conformity with the majority of the recent findings (Perea and Araque (Science 317, 1083-1086, 2007); Henneberger et al. (Nature 463, 232-236, 2010); Navarrete et al. (PLoS Biol. 10, e1001259, 2012)).

A mathematical model for astrocytes mediated LTP at single hippocampal synapses

Many contemporary studies have shown that astrocytes play a significant role in modulating both short and long form of synaptic plasticity. There are very few experimental models which elucidate the role of astrocyte over Long-term Potentiation (LTP). Recently, Perea and Araque (Science 317:1083-1086, 2007) demonstrated a role of astrocytes in induction of LTP at single hippocampal synapses. They suggested a purely pre-synaptic basis for induction of this N-methyl-D-Aspartate (NMDA) Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic induction were not investigated. Here, in this article, we propose a mathematical model for astrocyte modulated LTP which successfully imitates the experimental findings of Perea and Araque (Science 317:1083-1086, 2007). Our study suggests the role of retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically modulated LTP.

The Neurobiological Basis of Cognition: Identification by Multi-Input, Multioutput Nonlinear Dynamic Modeling: A method is proposed for measuring and modeling human long-term memory formation by mathematical analysis and computer simulation of nerve-cell dynamics

The successful development of neural prostheses requires an understanding of the neurobiological bases of cognitive processes, i.e., how the collective activity of populations of neurons results in a higher level process not predictable based on knowledge of the individual neurons and/or synapses alone. We have been studying and applying novel methods for representing nonlinear transformations of multiple spike train inputs (multiple time series of pulse train inputs) produced by synaptic and field interactions among multiple subclasses of neurons arrayed in multiple layers of incompletely connected units. We have been applying our methods to study of the hippocampus, a cortical brain structure that has been demonstrated, in humans and in animals, to perform the cognitive function of encoding new long-term (declarative) memories. Without their hippocampi, animals and humans retain a short-term memory (memory lasting approximately 1 min), and long-term memory for information learned prior to loss of hippocampal function. Results of more than 20 years of studies have demonstrated that both individual hippocampal neurons, and populations of hippocampal cells, e.g., the neurons comprising one of the three principal subsystems of the hippocampus, induce strong, higher order, nonlinear transformations of hippocampal inputs into hippocampal outputs. For one synaptic input or for a population of synchronously active synaptic inputs, such a transformation is represented by a sequence of action potential inputs being changed into a different sequence of action potential outputs. In other words, an incoming temporal pattern is transformed into a different, outgoing temporal pattern. For multiple, asynchronous synaptic inputs, such a transformation is represented by a spatiotemporal pattern of action potential inputs being changed into a different spatiotemporal pattern of action potential outputs. Our primary thesis is that the encoding of short-term memories into new, long-term memories represents the collective set of nonlinearities induced by the three or four principal subsystems of the hippocampus, i.e., entorhinal cortex-to-dentate gyrus, dentate gyrus-to-CA3 pyramidal cell region, CA3-to-CA1 pyramidal cell region, and CA1-to-subicular cortex. This hypothesis will be supported by studies using in vivo hippocampal multineuron recordings from animals performing memory tasks that require hippocampal function. The implications for this hypothesis will be discussed in the context of "cognitive prostheses"-neural prostheses for cortical brain regions believed to support cognitive functions, and that often are subject to damage due to stroke, epilepsy, dementia, and closed head trauma.

The electrophysiology of the beta-cell based on single transmembrane protein characteristics

The electrophysiology of beta-cells is at the origin of insulin secretion. beta-Cells exhibit a complex behavior upon stimulation with glucose including repeated bursts and continuous spiking. Mathematical modeling is most suitable to improve knowledge about the function of various transmembrane currents provided the model is based on reliable data. This is the first attempt to build a mathematical model for the beta-cell electrophysiology in a bottom-up approach that relies on single protein conductance data. The results of previous whole-cell-based models are reconsidered. The full simulation including all prominent transmembrane proteins in beta-cells is used to provide a functional interpretation of their role in beta-cell bursting and an updated vantage point of beta-cell electrophysiology. As a result of a number of in silico knock-out and block experiments the novel model makes some unexpected predictions: single-channel conductance data imply that large-conductance calcium-gated potassium currents acquire the potential of driving oscillations at supralarge glucose levels. A more complex burst interruption model is presented. It also turns out that, depending on the species, sodium currents may be more relevant than considered so far. Experiments are proposed to verify these predictions.

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.