Reconstructing the three-dimensional GABAergic microcircuit of the striatum

A system's wiring constrains its dynamics, yet modelling of neural structures often overlooks the specific networks formed by their neurons. We developed an approach for constructing anatomically realistic networks and reconstructed the GABAergic microcircuit formed by the medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs) of the adult rat striatum. We grew dendrite and axon models for these neurons and extracted probabilities for the presence of these neurites as a function of distance from the soma. From these, we found the probabilities of intersection between the neurites of two neurons given their inter-somatic distance, and used these to construct three-dimensional striatal networks. The MSN dendrite models predicted that half of all dendritic spines are within 100 mu m of the soma. The constructed networks predict distributions of gap junctions between FSI dendrites, synaptic contacts between MSNs, and synaptic inputs from FSIs to MSNs that are consistent with current estimates. The models predict that to achieve this, FSIs should be at most 1% of the striatal population. They also show that the striatum is sparsely connected: FSI-MSN and MSN-MSN contacts respectively form 7% and 1.7% of all possible connections. The models predict two striking network properties: the dominant GABAergic input to a MSN arises from neurons with somas at the edge of its dendritic field; and FSIs are interconnected on two different spatial scales: locally by gap junctions and distally by synapses. We show that both properties influence striatal dynamics: the most potent inhibition of a MSN arises from a region of striatum at the edge of its dendritic field; and the combination of local gap junction and distal synaptic networks between FSIs sets a robust input-output regime for the MSN population. Our models thus intimately link striatal micro-anatomy to its dynamics, providing a biologically grounded platform for further study

Adaptive and Phase Selective Spike Timing Dependent Plasticity in Synaptically Coupled Neuronal Oscillators

We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits

The Effects of NMDA Subunit Composition on Calcium Influx and Spike Timing-Dependent Plasticity in Striatal Medium Spiny Neurons

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

Soft-bound synaptic plasticity increases storage capacity

Accurate models of synaptic plasticity are essential to understand the adaptive properties of the nervous system and for realistic models of learning and memory. Experiments have shown that synaptic plasticity depends not only on pre- and post-synaptic activity patterns, but also on the strength of the connection itself. Namely, weaker synapses are more easily strengthened than already strong ones. This so called soft-bound plasticity automatically constrains the synaptic strengths. It is known that this has important consequences for the dynamics of plasticity and the synaptic weight distribution, but its impact on information storage is unknown. In this modeling study we introduce an information theoretic framework to analyse memory storage in an online learning setting. We show that soft-bound plasticity increases a variety of performance criteria by about 18% over hard-bound plasticity, and likely maximizes the storage capacity of synapses

Longitudinal neuronal organization and coordination in a simple vertebrate: a continuous, semi-quantitative computer model of the central pattern generator for swimming in young frog tadpoles

When frog tadpoles hatch their swimming requires co-ordinated contractions of trunk muscles, driven by motoneurons and controlled by a Central Pattern Generator (CPG). To study this co-ordination we used a 3.5 mm long population model of the young tadpole CPG with continuous distributions of neurons and axon lengths as estimated anatomically. We found that: (1) alternating swimming-type activity fails to self-sustain unless some excitatory interneurons have ascending axons, (2) a rostro-caudal (R-C) gradient in the distribution of excitatory premotor interneurons with short axons is required to obtain the R-C gradient in excitation and resulting progression of motoneuron firing necessary for forward swimming, (3) R-C delays in motoneuron firing decrease if excitatory motoneuron to premotor interneuron synapses are present, (4) these feedback connections and the electrical synapses between motoneurons synchronise motoneuron discharges locally, (5) the above findings are independent of the detailed membrane properties of neurons

Colocalization of Protein Kinase A with Adenylyl Cyclase Enhances Protein Kinase A Activity during Induction of Long-Lasting Long-Term-Potentiation

The ability of neurons to differentially respond to specific temporal and spatial input patterns underlies information storage in neural circuits. One means of achieving spatial specificity is to restrict signaling molecules to particular subcellular compartments using anchoring molecules such as A-Kinase Anchoring Proteins (AKAPs). Disruption of protein kinase A (PKA) anchoring to AKAPs impairs a PKA-dependent form of long term potentiation (LTP) in the hippocampus. To investigate the role of localized PKA signaling in LTP, we developed a stochastic reaction-diffusion model of the signaling pathways leading to PKA activation in CA1 pyramidal neurons. Simulations investigated whether the role of anchoring is to locate kinases near molecules that activate them, or near their target molecules. The results show that anchoring PKA with adenylyl cyclase (which produces cAMP that activates PKA) produces significantly greater PKA activity, and phosphorylation of both inhibitor-1 and AMPA receptor GluR1 subunit on S845, than when PKA is anchored apart from adenylyl cyclase. The spatial microdomain of cAMP was smaller than that of PKA suggesting that anchoring PKA near its source of cAMP is critical because inactivation by phosphodiesterase limits diffusion of cAMP. The prediction that the role of anchoring is to colocalize PKA near adenylyl cyclase was confirmed by experimentally rescuing the deficit in LTP produced by disruption of PKA anchoring using phosphodiesterase inhibitors. Additional experiments confirm the model prediction that disruption of anchoring impairs S845 phosphorylation produced by forskolin-induced synaptic potentiation. Collectively, these results show that locating PKA near adenylyl cyclase is a critical function of anchoring

A Diffusive Homeostatic Signal Maintains Neural Heterogeneity and Responsiveness in Cortical Networks

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

Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus

Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 \ub5M gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10 3690] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)