Postsynaptic Signal Transduction Models for Long-Term Potentiation and Depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models

A single Markov-type kinetic model accounting for the macroscopic currents of all human voltage-gated sodium channel isoforms

Modelling ionic channels represents a fundamental step towards developing biologically detailed neuron models. Until recently, the voltage-gated ion channels have been mainly modelled according to the formalism introduced by the seminal works of Hodgkin and Huxley (HH). However, following the continuing achievements in the biophysical and molecular comprehension of these pore-forming transmembrane proteins, the HH formalism turned out to carry limitations and inconsistencies in reproducing the ion-channels electrophysiological behaviour. At the same time, Markov-type kinetic models have been increasingly proven to successfully replicate both the electrophysiological and biophysical features of different ion channels. However, in order to model even the finest non-conducting molecular conformational change, they are often equipped with a considerable number of states and related transitions, which make them computationally heavy and less suitable for implementation in conductance-based neurons and large networks of those. In this purely modelling study we develop a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs). The model framework is detailed, unifying (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The electrophysiological data to be modelled are gathered from previously published studies on whole-cell patch-clamp experiments in mammalian cell lines heterologously expressing the human VGSC subtypes (from NaV1.1 to NaV1.9). By adopting a minimum sequence of states, and using the same state diagram for all the distinct isoforms, the model ensures the lightest computational load when used in neuron models and neural networks of increasing complexity. The transitions between the states are described by original ordinary differential equations, which represent the rate of the state transitions as a function of voltage (i.e., membrane potential). The kinetic model, developed in the NEURON simulation environment, appears to be the simplest and most parsimonious way for a detailed phenomenological description of the human VGSCs electrophysiological behaviour

Striatal Fast-Spiking Interneurons: From Firing Patterns to Postsynaptic Impact

In the striatal microcircuit, fast-spiking (FS) interneurons have an important role in mediating inhibition onto neighboring medium spiny (MS) projection neurons. In this study, we combined computational modeling with in vitro and in vivo electrophysiological measurements to investigate FS cells in terms of their discharge properties and their synaptic efficacies onto MS neurons. In vivo firing of striatal FS interneurons is characterized by a high firing variability. It is not known, however, if this variability results from the input that FS cells receive, or if it is promoted by the stuttering spike behavior of these neurons. Both our model and measurements in vitro show that FS neurons that exhibit random stuttering discharge in response to steady depolarization do not show the typical stuttering behavior when they receive fluctuating input. Importantly, our model predicts that electrically coupled FS cells show substantial spike synchronization only when they are in the stuttering regime. Therefore, together with the lack of synchronized firing of striatal FS interneurons that has been reported in vivo, these results suggest that neighboring FS neurons are not in the stuttering regime simultaneously and that in vivo FS firing variability is more likely determined by the input fluctuations. Furthermore, the variability in FS firing is translated to variability in the postsynaptic amplitudes in MS neurons due to the strong synaptic depression of the FS-to-MS synapse. Our results support the idea that these synapses operate over a wide range from strongly depressed to almost fully recovered. The strong inhibitory effects that FS cells can impose on their postsynaptic targets, and the fact that the FS-to-MS synapse model showed substantial depression over extended periods of time might indicate the importance of cooperative effects of multiple presynaptic FS interneurons and the precise orchestration of their activity

The Arbitration–Extension Hypothesis: A Hierarchical Interpretation of the Functional Organization of the Basal Ganglia

Based on known anatomy and physiology, we present a hypothesis where the basal ganglia motor loop is hierarchically organized in two main subsystems: the arbitration system and the extension system. The arbitration system, comprised of the subthalamic nucleus, globus pallidus, and pedunculopontine nucleus, serves the role of selecting one out of several candidate actions as they are ascending from various brain stem motor regions and aggregated in the centromedian thalamus or descending from the extension system or from the cerebral cortex. This system is an action-input/action-output system whose winner-take-all mechanism finds the strongest response among several candidates to execute. This decision is communicated back to the brain stem by facilitating the desired action via cholinergic/glutamatergic projections and suppressing conflicting alternatives via GABAergic connections. The extension system, comprised of the striatum and, again, globus pallidus, can extend the repertoire of responses by learning to associate novel complex states to certain actions. This system is a state-input/action-output system, whose organization enables it to encode arbitrarily complex Boolean logic rules using striatal neurons that only fire given specific constellations of inputs (Boolean AND) and pallidal neurons that are silenced by any striatal input (Boolean OR). We demonstrate the capabilities of this hierarchical system by a computational model where a simulated generic “animal” interacts with an environment by selecting direction of movement based on combinations of sensory stimuli, some being appetitive, others aversive or neutral. While the arbitration system can autonomously handle conflicting actions proposed by brain stem motor nuclei, the extension system is required to execute learned actions not suggested by external motor centers. Being precise in the functional role of each component of the system, this hypothesis generates several readily testable predictions

Transient Calcium and Dopamine Increase PKA Activity and DARPP-32 Phosphorylation

Reinforcement learning theorizes that strengthening of synaptic connections in medium spiny neurons of the striatum occurs when glutamatergic input (from cortex) and dopaminergic input (from substantia nigra) are received simultaneously. Subsequent to learning, medium spiny neurons with strengthened synapses are more likely to fire in response to cortical input alone. This synaptic plasticity is produced by phosphorylation of AMPA receptors, caused by phosphorylation of various signalling molecules. A key signalling molecule is the phosphoprotein DARPP-32, highly expressed in striatal medium spiny neurons. DARPP-32 is regulated by several neurotransmitters through a complex network of intracellular signalling pathways involving cAMP (increased through dopamine stimulation) and calcium (increased through glutamate stimulation). Since DARPP-32 controls several kinases and phosphatases involved in striatal synaptic plasticity, understanding the interactions between cAMP and calcium, in particular the effect of transient stimuli on DARPP-32 phosphorylation, has major implications for understanding reinforcement learning. We developed a computer model of the biochemical reaction pathways involved in the phosphorylation of DARPP-32 on Thr34 and Thr75. Ordinary differential equations describing the biochemical reactions were implemented in a single compartment model using the software XPPAUT. Reaction rate constants were obtained from the biochemical literature. The first set of simulations using sustained elevations of dopamine and calcium produced phosphorylation levels of DARPP-32 similar to that measured experimentally, thereby validating the model. The second set of simulations, using the validated model, showed that transient dopamine elevations increased the phosphorylation of Thr34 as expected, but transient calcium elevations also increased the phosphorylation of Thr34, contrary to what is believed. When transient calcium and dopamine stimuli were paired, PKA activation and Thr34 phosphorylation increased compared with dopamine alone. This result, which is robust to variation in model parameters, supports reinforcement learning theories in which activity-dependent long-term synaptic plasticity requires paired glutamate and dopamine inputs

AKAP79 enables calcineurin to directly suppress protein kinase A activity

Interplay between the second messengers cAMP and Ca2+ is a hallmark of dynamic cellular processes. A common motif is the opposition of the Ca2+-sensitive phosphatase calcineurin and the major cAMP receptor, protein kinase A (PKA). Calcineurin dephosphorylates sites primed by PKA to bring about changes including synaptic long-term depression (LTD). AKAP79 supports signaling of this type by anchoring PKA and calcineurin in tandem. In this study, we discovered that AKAP79 increases the rate of calcineurin dephosphorylation of type II PKA regulatory subunits by an order of magnitude. Fluorescent PKA activity reporter assays, supported by kinetic modeling, show how AKAP79-enhanced calcineurin activity enables suppression of PKA without altering cAMP levels by increasing PKA catalytic subunit capture rate. Experiments with hippocampal neurons indicate that this mechanism contributes towards LTD. This non-canonical mode of PKA regulation may underlie many other cellular processes

Roles for globus pallidus externa revealed in a computational model of action selection in the basal ganglia

The basal ganglia are considered vital to action selection - a hypothesis supported by several biologically plausible computational models. Of the several subnuclei of the basal ganglia, the globus pallidus externa (GPe) has been thought of largely as a relay nucleus, and its intrinsic connectivity has not been incorporated in significant detail, in any model thus far. Here, we incorporate newly revealed subgroups of neurons within the GPe into an existing computational model of the basal ganglia, and investigate their role in action selection. Three main results ensued. First, using previously used metrics for selection, the new extended connectivity improved the action selection performance of the model. Second, low frequency theta oscillations were observed in the subpopulation of the GPe (the TA or ‘arkypallidal’ neurons) which project exclusively to the striatum. These oscillations were suppressed by increased dopamine activity - revealing a possible link with symptoms of Parkinson’s disease. Third, a new phenomenon was observed in which the usual monotonic relationship between input to the basal ganglia and its output within an action ‘channel’ was, under some circumstances, reversed. Thus, at high levels of input, further increase of this input to the channel could cause an increase of the corresponding output rather than the more usually observed decrease. Moreover, this phenomenon was associated with the prevention of multiple channel selection, thereby assisting in optimal action selection. Examination of the mechanistic origin of our results showed the so-called ‘prototypical’ GPe neurons to be the principal subpopulation influencing action selection. They control the striatum via the arkypallidal neurons and are also able to regulate the output nuclei directly. Taken together, our results highlight the role of the GPe as a major control hub of the basal ganglia, and provide a mechanistic account for its control function