Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion

In this chapter we describe a continuum model for the cortex that includes both axon-to-dendrite chemical synapses and direct neuron-to-neuron gap-junction diffusive synapses. The effectiveness of chemical synapses is determined by the voltage of the receiving dendrite V relative to its Nernst reversal potential Vrev. Here we explore two alternative strategies for incorporating dendritic reversal potentials, and uncover surprising differences in their stability properties and model dynamics. In the “slow-soma” variant, the (Vrev - V) weighting is applied after the input flux has been integrated at the dendrite, while for “fast-soma”, the weighting is applied directly to the input flux, prior to dendritic integration. For the slow-soma case, we find that–-provided the inhibitory diffusion (via gap-junctions) is sufficiently strong–-the cortex generates stationary Turing patterns of cortical activity. In contrast, the fast-soma destabilizes in favor of standing-wave spatial structures that oscillate at low-gamma frequency ( 30-Hz); these spatial patterns broaden and weaken as diffusive coupling increases, and disappear altogether at moderate levels of diffusion. We speculate that the slow- and fast-soma models might correspond respectively to the idling and active modes of the cortex, with slow-soma patterns providing the default background state, and emergence of gamma oscillations in the fast-soma case signaling the transition into the cognitive state

Dopaminergic and Non-Dopaminergic Value Systems in Conditioning and Outcome-Specific Revaluation

Animals are motivated to choose environmental options that can best satisfy current needs. To explain such choices, this paper introduces the MOTIVATOR (Matching Objects To Internal Values Triggers Option Revaluations) neural model. MOTIVATOR describes cognitiveemotional interactions between higher-order sensory cortices and an evaluative neuraxis composed of the hypothalamus, amygdala, and orbitofrontal cortex. Given a conditioned stimulus (CS), the model amygdala and lateral hypothalamus interact to calculate the expected current value of the subjective outcome that the CS predicts, constrained by the current state of deprivation or satiation. The amygdala relays the expected value information to orbitofrontal cells that receive inputs from anterior inferotemporal cells, and medial orbitofrontal cells that receive inputs from rhinal cortex. The activations of these orbitofrontal cells code the subjective values of objects. These values guide behavioral choices. The model basal ganglia detect errors in CS-specific predictions of the value and timing of rewards. Excitatory inputs from the pedunculopontine nucleus interact with timed inhibitory inputs from model striosomes in the ventral striatum to regulate dopamine burst and dip responses from cells in the substantia nigra pars compacta and ventral tegmental area. Learning in cortical and striatal regions is strongly modulated by dopamine. The model is used to address tasks that examine food-specific satiety, Pavlovian conditioning, reinforcer devaluation, and simultaneous visual discrimination. Model simulations successfully reproduce discharge dynamics of known cell types, including signals that predict saccadic reaction times and CS-dependent changes in systolic blood pressure.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Institutes of Health (R29-DC02952, R01-DC007683); National Science Foundation (IIS-97-20333, SBE-0354378); Office of Naval Research (N00014-01-1-0624

Spike Train Auto-Structure Impacts Post-Synaptic Firing and Timing-Based Plasticity

Cortical neurons are typically driven by several thousand synapses. The precise spatiotemporal pattern formed by these inputs can modulate the response of a post-synaptic cell. In this work, we explore how the temporal structure of pre-synaptic inhibitory and excitatory inputs impact the post-synaptic firing of a conductance-based integrate and fire neuron. Both the excitatory and inhibitory input was modeled by renewal gamma processes with varying shape factors for modeling regular and temporally random Poisson activity. We demonstrate that the temporal structure of mutually independent inputs affects the post-synaptic firing, while the strength of the effect depends on the firing rates of both the excitatory and inhibitory inputs. In a second step, we explore the effect of temporal structure of mutually independent inputs on a simple version of Hebbian learning, i.e., hard bound spike-timing-dependent plasticity. We explore both the equilibrium weight distribution and the speed of the transient weight dynamics for different mutually independent gamma processes. We find that both the equilibrium distribution of the synaptic weights and the speed of synaptic changes are modulated by the temporal structure of the input. Finally, we highlight that the sensitivity of both the post-synaptic firing as well as the spike-timing-dependent plasticity on the auto-structure of the input of a neuron could be used to modulate the learning rate of synaptic modification

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of Computational Neuroscience, in press (2007

Modeling Rhythm Generation in Swim Central Pattern Generator of Melibe Leonina

Central pattern generators (CPGs) are neural networks to produce a rich multiplicity of rhythmic activity types like walking, breathing and swim locomotion. Basis principles of the underlying mechanisms of rhythm generation in CPGs remain yet insufficiently understood. Interactive pairing experimental and modeling studies have proven to be vital to unlocking insights into operational and dynamical principles of CPGs and support the consensus that the most of essential structural and functional elements in vertebrate and invertebrate nervous systems are shared. We have developed a family of highly-detailed, biologically plausible CPG models using the extensive data intracellularly recorded from constituent interneurons of the swim CPG of the sea slug {\it Melibe leonina}. We also have deduced fundamental properties needed for the devised Hodgkin-Huxley type neuronal models with specific slow-fast dynamics to become qualitatively and quantitatively similar to biological CPG interneurons and their responses to parameter and external perturbations. We have studied the onset and robustness of rhythmogenesis of network bursting the CPG circuits comprised of tonic spiking interneurons coupled with mixed inhibitory/excitatory, slow chemical synapses. We have shown that the mathematical CPG model can be reduced functionally from an 8-cell circuit to a 4-cell one using the calibration of timing and weights of synaptic coupling between CPG core interneurons. We demonstrate that the developed mathematical network meets all the experimental fact-checks obtained for the biological Melibe swim CPG from a variety of state-of-the-art experimental studies including dynamic-clamp recordings, external pulses perturbations as well as from its forced behaviors under applications of neuro-blockers such as curare and TTX. Our model and developed mathematical approaches and computational methodology allow for laying down theoretical foundations necessary for devising new detailed and phenomenological models of neural circuits and for making testable predictions of dynamics of rhythmic neural networks from diverse species

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

Synaptic mechanisms of interference in working memory

Information from preceding trials of cognitive tasks can bias performance in the current trial, a phenomenon referred to as interference. Subjects performing visual working memory tasks exhibit interference in their trial-to-trial response correlations: the recalled target location in the current trial is biased in the direction of the target presented on the previous trial. We present modeling work that (a) develops a probabilistic inference model of this history-dependent bias, and (b) links our probabilistic model to computations of a recurrent network wherein short-term facilitation accounts for the dynamics of the observed bias. Network connectivity is reshaped dynamically during each trial, providing a mechanism for generating predictions from prior trial observations. Applying timescale separation methods, we can obtain a low-dimensional description of the trial-to-trial bias based on the history of target locations. The model has response statistics whose mean is centered at the true target location across many trials, typical of such visual working memory tasks. Furthermore, we demonstrate task protocols for which the plastic model performs better than a model with static connectivity: repetitively presented targets are better retained in working memory than targets drawn from uncorrelated sequences.Comment: 28 pages, 7 figure

Neuronal Synchronization Can Control the Energy Efficiency of Inter-Spike Interval Coding

The role of synchronous firing in sensory coding and cognition remains controversial. While studies, focusing on its mechanistic consequences in attentional tasks, suggest that synchronization dynamically boosts sensory processing, others failed to find significant synchronization levels in such tasks. We attempt to understand both lines of evidence within a coherent theoretical framework. We conceptualize synchronization as an independent control parameter to study how the postsynaptic neuron transmits the average firing activity of a presynaptic population, in the presence of synchronization. We apply the Berger-Levy theory of energy efficient information transmission to interpret simulations of a Hodgkin-Huxley-type postsynaptic neuron model, where we varied the firing rate and synchronization level in the presynaptic population independently. We find that for a fixed presynaptic firing rate the simulated postsynaptic interspike interval distribution depends on the synchronization level and is well-described by a generalized extreme value distribution. For synchronization levels of 15% to 50%, we find that the optimal distribution of presynaptic firing rate, maximizing the mutual information per unit cost, is maximized at ~30% synchronization level. These results suggest that the statistics and energy efficiency of neuronal communication channels, through which the input rate is communicated, can be dynamically adapted by the synchronization level.Comment: 47 pages, 14 figures, 2 Table

Neural Dynamics Underlying Impaired Autonomic and Conditioned Responses Following Amygdala and Orbitofrontal Lesions

A neural model is presented that explains how outcome-specific learning modulates affect, decision-making and Pavlovian conditioned approach responses. The model addresses how brain regions responsible for affective learning and habit learning interact, and answers a central question: What are the relative contributions of the amygdala and orbitofrontal cortex to emotion and behavior? In the model, the amygdala calculates outcome value while the orbitofrontal cortex influences attention and conditioned responding by assigning value information to stimuli. Model simulations replicate autonomic, electrophysiological, and behavioral data associated with three tasks commonly used to assay these phenomena: Food consumption, Pavlovian conditioning, and visual discrimination. Interactions of the basal ganglia and amygdala with sensory and orbitofrontal cortices enable the model to replicate the complex pattern of spared and impaired behavioral and emotional capacities seen following lesions of the amygdala and orbitofrontal cortex.National Science Foundation (SBE-0354378; IIS-97-20333); Office of Naval Research (N00014-01-1-0624); Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Institutes of Health (R29-DC02952

Synchronization in Neuronal Networks with Electrical and Chemical Coupling

Synchronized cortical activities in the central nervous systems of mammals are crucial for sensory perception, coordination, and locomotory function. The neuronal mechanisms that generate synchronous synaptic inputs in the neocortex are far from being fully understood. This thesis contributes toward an understanding of the emergence of synchronization in networks of bursting neurons as a highly nontrivial, combined effect of chemical and electrical connections. The first part of this thesis addresses the onset of synchronization in networks of bursting neurons coupled via both excitatory and inhibitory connections. We show that the addition of pairwise repulsive inhibition to excitatory networks of bursting neurons induces synchrony, in contrast to one’s expectations. Through stability analysis, we reveal the mechanism underlying this purely synergistic phenomenon and demonstrates that it originates from the transition between different types of bursting, caused by excitatory-inhibitory synaptic coupling. We also report a universal scaling law for the synchronization stability condition for large networks in terms of the number of excitatory and inhibitory inputs each neuron receives, regardless of the network size and topology. In the second part of this thesis, we show that similar effects are also observed in other models of bursting neurons, capable of switching from square-wave to plateau bursting. Finally, in the third part, we report a counterintuitive find that combined electrical and inhibitory coupling can synergistically induce robust synchronization in a range of parameters where electrical coupling alone promotes anti-phase spiking and inhibition induces anti-phase bursting. We reveal the underlying mechanism which uses a balance between hidden properties of electrical and inhibitory coupling to act together to synchronize neuronal bursting. We show that this balance is controlled by the duty cycle of the self-coupled system which governs the synchronized bursting rhythm. This work has potential implications for understanding the emergence of abnormal synchrony in epileptic brain networks. It suggests that promoting presumably desynchronizing inhibition in an attempt to prevent seizures can have a counterproductive effect and induce abnormal synchronous firing