The basal ganglia (BG), and more specifically the striatum, have long been proposed to play an essential role in action-selection based on a reinforcement learning (RL) paradigm. However, some recent findings, such as striatal spike-timing-dependent plasticity (STDP) or striatal lateral connectivity, require further research and modelling as their respective roles are still not well understood. Theoretical models of spiking neurons with homeostatic mechanisms, lateral connectivity, and reward-modulated STDP have demonstrated a remarkable capability to learn sensorial patterns that statistically correlate with a rewarding signal. In this article, we implement a functional and biologically inspired network model of the striatum, where learning is based on a previously proposed learning rule called spike-timing-dependent eligibility (STDE), which captures important experimental features in the striatum. The proposed computational model can recognize complex input patterns and consistently choose rewarded actions to respond to such sensorial inputs. Moreover, we assess the role different neuronal and network features, such as homeostatic mechanisms and lateral inhibitory connections, play in action-selection with the proposed model. The homeostatic mechanisms make learning more robust (in terms of suitable parameters) and facilitate recovery after rewarding policy swapping, while lateral inhibitory connections are important when multiple input patterns are associated with the same rewarded action. Finally, according to our simulations, the optimal delay between the action and the dopaminergic feedback is obtained around 300 ms, as demonstrated in previous studies of RL and in biological studies.

Motivation: Dynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis (GSA) in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as to give guidance on parameters that are essential in distinguishing different qualitative output behaviours. Results: We used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a GSA was performed on the predictions using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions. This approach is useful both for experimental design as well as model building. Availability and implementation: Source code is freely available at https://github.com/alexjau/uqsa. Supplementary information: Supplementary data are available at Bioinformatics online.

Long-term potentiation and depression of synaptic activity in response to stimuli is a key factor in reinforcement learning. Strengthening of the corticostriatal synapses depends on the second messenger cAMP, whose synthesis is catalysed by the enzyme adenylyl cyclase 5 (AC5), which is itself regulated by the stimulatory Gαolf and inhibitory Gαi proteins. AC isoforms have been suggested to act as coincidence detectors, promoting cellular responses only when convergent regulatory signals occur close in time. However, the mechanism for this is currently unclear, and seems to lie in their diverse regulation patterns. Despite attempts to isolate the ternary complex, it is not known if Gαolf and Gαi can bind to AC5 simultaneously, nor what activity the complex would have. Using protein structure-based molecular dynamics simulations, we show that this complex is stable and inactive. These simulations, along with Brownian dynamics simulations to estimate protein association rates constants, constrain a kinetic model that shows that the presence of this ternary inactive complex is crucial for AC5's ability to detect coincident signals, producing a synergistic increase in cAMP. These results reveal some of the prerequisites for corticostriatal synaptic plasticity, and explain recent experimental data on cAMP concentrations following receptor activation. Moreover, they provide insights into the regulatory mechanisms that control signal processing by different AC 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.

In reward learning, the integration of NMDA-dependent calcium and dopamine by striatal projection neurons leads to potentiation of corticostriatal synapses through CaMKII/PP1 signaling. In order to elicit the CaMKII/PP1-dependent response, the calcium and dopamine inputs should arrive in temporal proximity and must follow a specific (dopamine after calcium) order. However, little is known about the cellular mechanism which enforces these temporal constraints on the signal integration. In this computational study, we propose that these temporal requirements emerge as a result of the coordinated signaling via two striatal phosphoproteins, DARPP-32 and ARPP-21. Specifically, DARPP-32-mediated signaling could implement an input-interval dependent gating function, via transient PP1 inhibition, thus enforcing the requirement for temporal proximity. Furthermore, ARPP-21 signaling could impose the additional input-order requirement of calcium and dopamine, due to its Ca2+/calmodulin sequestering property when dopamine arrives first. This highlights the possible role of phosphoproteins in the temporal aspects of striatal signal transduction.

Gaseous neurotransmitters such as nitric oxide (NO) provide a unique and often overlooked mechanism for neurons to communicate through diffusion within a network, independent of synaptic connectivity. NO provides homeostatic control of intrinsic excitability. Here we conduct a theoretical investigation of the distinguishing roles of NO-mediated diffusive homeostasis in comparison with canonical non-diffusive homeostasis in cortical networks. We find that both forms of homeostasis provide a robust mechanism for maintaining stable activity following perturbations. However, the resulting networks differ, with diffusive homeostasis maintaining substantial heterogeneity in activity levels of individual neurons, a feature disrupted in networks with non-diffusive homeostasis. This results in networks capable of representing input heterogeneity, and linearly responding over a broader range of inputs than those undergoing non-diffusive homeostasis. We further show that these properties are preserved when homeostatic and Hebbian plasticity are combined. These results suggest a mechanism for dynamically maintaining neural heterogeneity, and expose computational advantages of non-local homeostatic processes.

The convergence of corticostriatal glutamate and dopamine from the midbrain in the striatal medium spiny neurons (MSN) triggers synaptic plasticity that underlies reinforcement learning and pathological conditions such as psychostimulant addiction. The increase in striatal dopamine produced by the acute administration of psychostimulants has been found to activate not only effectors of the AC5/cAMP/PKA signaling cascade such as GluR1, but also effectors of the NMDAR/Ca(2+)/RAS cascade such as ERK. The dopamine-triggered effects on both these cascades are mediated by D1R coupled to Golf but while the phosphorylation of GluR1 is affected by reductions in the available amount of Golf but not of D1R, the activation of ERK follows the opposite pattern. This segregation is puzzling considering that D1R-induced Golf activation monotonically increases with DA and that there is crosstalk from the AC5/cAMP/PKA cascade to the NMDAR/Ca(2+)/RAS cascade via a STEP (a tyrosine phosphatase). In this work, we developed a signaling model which accounts for this segregation based on the assumption that a common pool of D1R and Golf is distributed in two D1R/Golf signaling compartments. This model integrates a relatively large amount of experimental data for neurons in vivo and in vitro. We used it to explore the crosstalk topologies under which the sensitivities of the AC5/cAMP/PKA signaling cascade to reductions in D1R or Golf are transferred or not to the activation of ERK. We found that the sequestration of STEP by its substrate ERK together with the insensitivity of STEP activity on targets upstream of ERK (i.e. Fyn and NR2B) to PKA phosphorylation are able to explain the experimentally observed segregation. This model provides a quantitative framework for simulation based experiments to study signaling required for long term potentiation in MSNs.

Calcium through NMDA receptors (NMDARs) is necessary for the long-term potentiation (LTP) of synaptic strength; however, NMDARs differ in several properties that can influence the amount of calcium influx into the spine. These properties, such as sensitivity to magnesium block and conductance decay kinetics, change the receptor's response to spike timing dependent plasticity (STDP) protocols, and thereby shape synaptic integration and information processing. This study investigates the role of GluN2 subunit differences on spine calcium concentration during several STDP protocols in a model of a striatal medium spiny projection neuron (MSPN). The multi-compartment, multi-channel model exhibits firing frequency, spike width, and latency to first spike similar to current clamp data from mouse dorsal striatum MSPN. We find that NMDAR-mediated calcium is dependent on GluN2 subunit type, action potential timing, duration of somatic depolarization, and number of action potentials. Furthermore, the model demonstrates that in MSPNs, GluN2A and GluN2B control which STDP intervals allow for substantial calcium elevation in spines. The model predicts that blocking GluN2B subunits would modulate the range of intervals that cause long term potentiation. We confirmed this prediction experimentally, demonstrating that blocking GluN2B in the striatum, narrows the range of STDP intervals that cause long term potentiation. This ability of the GluN2 subunit to modulate the shape of the STDP curve could underlie the role that GluN2 subunits play in learning and development.

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.