Progressive alignment of inhibitory and excitatory delay may drive a rapid developmental switch in cortical network dynamics.

Nervous system maturation occurs on multiple levels-synaptic, circuit, and network-at divergent timescales. For example, many synaptic properties mature gradually, whereas emergent network dynamics can change abruptly. Here we combine experimental and theoretical approaches to investigate a sudden transition in spontaneous and sensory evoked thalamocortical activity necessary for the development of vision. Inspired by in vivo measurements of timescales and amplitudes of synaptic currents, we extend the Wilson and Cowan model to take into account the relative onset timing and amplitudes of inhibitory and excitatory neural population responses. We study this system as these parameters are varied within amplitudes and timescales consistent with developmental observations to identify the bifurcations of the dynamics that might explain the network behaviors in vivo. Our findings indicate that the inhibitory timing is a critical determinant of thalamocortical activity maturation; a gradual decay of the ratio of inhibitory to excitatory onset time drives the system through a bifurcation that leads to a sudden switch of the network spontaneous activity from high-amplitude oscillations to a nonoscillatory active state. This switch also drives a change from a threshold bursting to linear response to transient stimuli, also consistent with in vivo observation. Thus we show that inhibitory timing is likely critical to the development of network dynamics and may underlie rapid changes in activity without similarly rapid changes in the underlying synaptic and cellular parameters.NEW & NOTEWORTHY Relying on a generalization of the Wilson-Cowan model, which allows a solid analytic foundation for the understanding of the link between maturation of inhibition and network dynamics, we propose a potential explanation for the role of developing excitatory/inhibitory synaptic delays in mediating a sudden switch in thalamocortical visual activity preceding vision onset.

Reduced Efficacy of the KCC2 Cotransporter Promotes Epileptic Oscillations in a Subiculum Network Model.

Pharmacoresistant epilepsy is a chronic neurological condition in which a basal brain hyperexcitability results in paroxysmal hypersynchronous neuronal discharges. Human temporal lobe epilepsy has been associated with dysfunction or loss of the potassium-chloride cotransporter KCC2 in a subset of pyramidal cells in the subiculum, a key structure generating epileptic activities. KCC2 regulates intraneuronal chloride and extracellular potassium levels by extruding both ions. Absence of effective KCC2 may alter the dynamics of chloride and potassium levels during repeated activation of GABAergic synapses due to interneuron activity. In turn, such GABAergic stress may itself affect Cl- regulation. Such changes in ionic homeostasis may switch GABAergic signaling from inhibitory to excitatory in affected pyramidal cells and also increase neuronal excitability. Possibly these changes contribute to periodic bursting in pyramidal cells, an essential component in the onset of ictal epileptic events. We tested this hypothesis with a computational model of a subicular network with realistic connectivity. The pyramidal cell model explicitly incorporated the cotransporter KCC2 and its effects on the internal/external chloride and potassium levels. Our network model suggested the loss of KCC2 in a critical number of pyramidal cells increased external potassium and intracellular chloride concentrations leading to seizure-like field potential oscillations. These oscillations included transient discharges leading to ictal-like field events with frequency spectra as in vitro Restoration of KCC2 function suppressed seizure activity and thus may present a useful therapeutic option. These simulations therefore suggest that reduced KCC2 cotransporter activity alone may underlie the generation of ictal discharges. SIGNIFICANCE STATEMENT: Ion regulation in the brain is a major determinant of neural excitability. Intracellular chloride in neurons, a partial determinant of the resting potential and the inhibitory reversal potentials, is regulated together with extracellular potassium via kation chloride cotransporters. During temporal lobe epilepsy, the homeostatic regulation of intracellular chloride is impaired in pyramidal cells, yet how this dysregulation may lead to seizures has not been explored. Using a realistic neural network model describing ion mechanisms, we show that chloride homeostasis pathology provokes seizure activity analogous to recordings from epileptogenic brain tissue. We show that there is a critical percentage of pathological cells required for seizure initiation. Our model predicts that restoration of the chloride homeostasis in pyramidal cells could be a viable antiepileptic strategy.

Inverse Stochastic Resonance in Cerebellar Purkinje Cells.

Purkinje neurons play an important role in cerebellar computation since their axons are the only projection from the cerebellar cortex to deeper cerebellar structures. They have complex internal dynamics, which allow them to fire spontaneously, display bistability, and also to be involved in network phenomena such as high frequency oscillations and travelling waves. Purkinje cells exhibit type II excitability, which can be revealed by a discontinuity in their f-I curves. We show that this excitability mechanism allows Purkinje cells to be efficiently inhibited by noise of a particular variance, a phenomenon known as inverse stochastic resonance (ISR). While ISR has been described in theoretical models of single neurons, here we provide the first experimental evidence for this effect. We find that an adaptive exponential integrate-and-fire model fitted to the basic Purkinje cell characteristics using a modified dynamic IV method displays ISR and bistability between the resting state and a repetitive activity limit cycle. ISR allows the Purkinje cell to operate in different functional regimes: the all-or-none toggle or the linear filter mode, depending on the variance of the synaptic input. We propose that synaptic noise allows Purkinje cells to quickly switch between these functional regimes. Using mutual information analysis, we demonstrate that ISR can lead to a locally optimal information transfer between the input and output spike train of the Purkinje cell. These results provide the first experimental evidence for ISR and suggest a functional role for ISR in cerebellar information processing.

Dopamine Neurons Change the Type of Excitability in Response to Stimuli.

The dynamics of neuronal excitability determine the neuron's response to stimuli, its synchronization and resonance properties and, ultimately, the computations it performs in the brain. We investigated the dynamical mechanisms underlying the excitability type of dopamine (DA) neurons, using a conductance-based biophysical model, and its regulation by intrinsic and synaptic currents. Calibrating the model to reproduce low frequency tonic firing results in N-methyl-D-aspartate (NMDA) excitation balanced by γ-Aminobutyric acid (GABA)-mediated inhibition and leads to type I excitable behavior characterized by a continuous decrease in firing frequency in response to hyperpolarizing currents. Furthermore, we analyzed how excitability type of the DA neuron model is influenced by changes in the intrinsic current composition. A subthreshold sodium current is necessary for a continuous frequency decrease during application of a negative current, and the low-frequency "balanced" state during simultaneous activation of NMDA and GABA receptors. Blocking this current switches the neuron to type II characterized by the abrupt onset of repetitive firing. Enhancing the anomalous rectifier Ih current also switches the excitability to type II. Key characteristics of synaptic conductances that may be observed in vivo also change the type of excitability: a depolarized γ-Aminobutyric acid receptor (GABAR) reversal potential or co-activation of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) leads to an abrupt frequency drop to zero, which is typical for type II excitability. Coactivation of N-methyl-D-aspartate receptors (NMDARs) together with AMPARs and GABARs shifts the type I/II boundary toward more hyperpolarized GABAR reversal potentials. To better understand how altering each of the aforementioned currents leads to changes in excitability profile of DA neuron, we provide a thorough dynamical analysis. Collectively, these results imply that type I excitability in dopamine neurons might be important for low firing rates and fine-tuning basal dopamine levels, while switching excitability to type II during NMDAR and AMPAR activation may facilitate a transient increase in dopamine concentration, as type II neurons are more amenable to synchronization by mutual excitation.

Implications of cellular models of dopamine neurons for disease.

This review addresses the present state of single-cell models of the firing pattern of midbrain dopamine neurons and the insights that can be gained from these models into the underlying mechanisms for diseases such as Parkinson's, addiction, and schizophrenia. We will explain the analytical technique of separation of time scales and show how it can produce insights into mechanisms using simplified single-compartment models. We also use morphologically realistic multicompartmental models to address spatially heterogeneous aspects of neural signaling and neural metabolism. Separation of time scale analyses are applied to pacemaking, bursting, and depolarization block in dopamine neurons. Differences in subpopulations with respect to metabolic load are addressed using multicompartmental models.

Flexible frequency control of cortical oscillations enables computations required for working memory.

Cognitive effort leads to a seeming cacophony of brain oscillations. For example, during tasks engaging working memory (WM), specific oscillatory frequency bands modulate in space and time. Despite ample data correlating such modulation to task performance, a mechanistic explanation remains elusive. We propose that flexible control of neural oscillations provides a unified mechanism for the rapid and controlled transitions between the computational operations required by WM. We show in a spiking network model that modulating the input oscillation frequency sets the network in different operating modes: rapid memory access and load is enabled by the beta-gamma oscillations, maintaining a memory while ignoring distractors by the theta, rapid memory clearance by the alpha. The various frequency bands determine the dynamic gating regimes enabling the necessary operations for WM, whose succession explains the need for the complex oscillatory brain dynamics during effortful cognition.

A review of methods for identifying stochastic resonance in simulations of single neuron models.

Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed on real neural systems. Despite the ubiquity of biophysical sources of stochastic noise in the nervous system, however, it has not yet been established whether neuronal computation mechanisms involved in performance of specific functions such as perception or learning might exploit such noise as an integral component, such that removal of the noise would diminish performance of these functions. In this paper we revisit the methods used to demonstrate stochastic resonance in models of single neurons. This includes a previously unreported observation in a multicompartmental model of a CA1-pyramidal cell. We also discuss, as a contrast to these classical studies, a form of 'stochastic facilitation', known as inverse stochastic resonance. We draw on the reviewed examples to argue why new approaches to studying 'stochastic facilitation' in neural systems need to be developed.

Impact of prefrontal cortex in nicotine-induced excitation of ventral tegmental area dopamine neurons in anesthetized rats.

Systemic administration of nicotine increases dopaminergic (DA) neuron firing in the ventral tegmental area (VTA), which is thought to underlie nicotine reward. Here, we report that the medial prefrontal cortex (mPFC) plays a critical role in nicotine-induced excitation of VTA DA neurons. In chloral hydrate-anesthetized rats, extracellular single-unit recordings showed that VTA DA neurons exhibited two types of firing responses to systemic nicotine. After nicotine injection, the neurons with type-I response showed a biphasic early inhibition and later excitation, whereas the neurons with type-II response showed a monophasic excitation. The neurons with type-I, but not type-II, response exhibited pronounced slow oscillations (SOs) in firing. Pharmacological or structural mPFC inactivation abolished SOs and prevented systemic nicotine-induced excitation in the neurons with type-I, but not type-II, response, suggesting that these VTA DA neurons are functionally coupled to the mPFC and nicotine increases firing rate in these neurons in part through the mPFC. Systemic nicotine also increased the firing rate and SOs in mPFC pyramidal neurons. mPFC infusion of a non-α7 nicotinic acetylcholine receptor (nAChR) antagonist mecamylamine blocked the excitatory effect of systemic nicotine on the VTA DA neurons with type-I response, but mPFC infusion of nicotine failed to excite these neurons. These results suggest that nAChR activation in the mPFC is necessary, but not sufficient, for systemic nicotine-induced excitation of VTA neurons. Finally, systemic injection of bicuculline prevented nicotine-induced firing alterations in the neurons with type-I response. We propose that the mPFC plays a critical role in systemic nicotine-induced excitation of VTA DA neurons.

Recurring Cholinergic Inputs Induce Local Hippocampal Plasticity through Feedforward Disinhibition.

The CA1 pyramidal neurons are embedded in an intricate local circuitry that contains a variety of interneurons. The roles these interneurons play in the regulation of the excitatory synaptic plasticity remains largely understudied. Recent experiments showed that recurring cholinergic activation of α7 nACh receptors expressed in oriens-lacunosum-moleculare (OLMα2) interneurons can directly induce LTP in Schaffer collateral (SC)-CA1 synapses. Here, we pair in vitro studies with biophysically based modeling to uncover the underlying mechanisms. According to our model, α7 nAChR activation increases OLM GABAergic activity. This results in the inhibition of the fast-spiking interneurons that provide feedforward inhibition onto CA1 pyramidal neurons. This disinhibition, paired with tightly timed SC stimulation, can induce potentiation at the excitatory synapses of CA1 pyramidal neurons. Our work details the role of cholinergic modulation in disinhibition-induced hippocampal plasticity. It relates the timing of cholinergic pairing found experimentally in previous studies with the timing between disinhibition and hippocampal stimulation necessary to induce potentiation and suggests the dynamics of the involved interneurons play a crucial role in determining this timing.Significance StatementWe use a combination of experiments and mechanistic modeling to uncover the key role for cholinergic neuromodulation of feedforward disinhibitory circuits in regulating hippocampal plasticity. We found that cholinergic activation of α7 nAChR on α7 nACh receptors expressed in oriens-lacunosum-moleculare interneurons, when tightly paired with stimulation of the Schaffer collaterals, can cancel feedforward inhibition onto CA1 pyramidal cells, enabling the potentiation of the SC-CA1 synapse. Our work details how cholinergic action on GABAergic interneurons can tightly regulate the excitability and plasticity of the hippocampal network, unraveling the intricate interplay of the hierarchal inhibitory circuitry and cholinergic neuromodulation as a mechanism for hippocampal plasticity.

Activity-dependent intracellular chloride accumulation and diffusion controls GABA(A) receptor-mediated synaptic transmission.

In the CNS, prolonged activation of GABA(A) receptors (GABA(A)Rs) has been shown to evoke biphasic postsynaptic responses, consisting of an initial hyperpolarization followed by a depolarization. A potential mechanism underlying the depolarization is an acute chloride (Cl(-)) accumulation resulting in a shift of the GABA(A) reversal potential (E(GABA)). The amount of GABA-evoked Cl(-) accumulation and accompanying depolarization depends on presynaptic and postsynaptic properties of GABAergic transmission, as well as on cellular morphology and regulation of Cl(-) intracellular concentration ([Cl(-)](i)). To analyze the influence of these factors on the Cl(-) and voltage behavior, we studied spatiotemporal dynamics of activity-dependent [Cl(-)](i) changes in multicompartmental models of hippocampal cells based on realistic morphological data. Simulated Cl(-) influx through GABA(A) Rs was able to exceed physiological Cl(-) extrusion rates thereby evoking HCO(3)(-) -dependent E(GABA) shift and depolarizing responses. Depolarizations were observed in spite of GABA(A) receptor desensitization. The amplitude of the depolarization was frequency-dependent and determined by intracellular Cl(-) accumulation. Changes in the dendritic diameter and in the speed of GABA clearance in the synaptic cleft were significant sources of depolarization variability. In morphologically reconstructed granule cells subjected to an intense GABAergic background activity, dendritic inhibition was more affected by accumulation of intracellular Cl(-) than somatic inhibition. Interestingly, E(GABA) changes induced by activation of a single dendritic synapse propagated beyond the site of Cl(-) influx and affected neighboring synapses. The simulations suggest that E(GABA) may differ even along a single dendrite supporting the idea that it is necessary to assign E(GABA) to a given GABAergic input and not to a given neuron.

The role of ongoing dendritic oscillations in single-neuron dynamics.

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.

The effects of cholinergic neuromodulation on neuronal phase-response curves of modeled cortical neurons.

The response of an oscillator to perturbations is described by its phase-response curve (PRC), which is related to the type of bifurcation leading from rest to tonic spiking. In a recent experimental study, we have shown that the type of PRC in cortical pyramidal neurons can be switched by cholinergic neuromodulation from type II (biphasic) to type I (monophasic). We explored how intrinsic mechanisms affected by acetylcholine influence the PRC using three different types of neuronal models: a theta neuron, single-compartment neurons and a multi-compartment neuron. In all of these models a decrease in the amount of a spike-frequency adaptation current was a necessary and sufficient condition for the shape of the PRC to change from biphasic (type II) to purely positive (type I).

Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise.

The effects of noise on neuronal dynamical systems are of much current interest. Here, we investigate noise-induced changes in the rhythmic firing activity of single Hodgkin-Huxley neurons. With additive input current, there is, in the absence of noise, a critical mean value mu=mu(c) above which sustained periodic firing occurs. With initial conditions as resting values, for a range of values of the mean micro near the critical value, we have found that the firing rate is greatly reduced by noise, even of quite small amplitudes. Furthermore, the firing rate may undergo a pronounced minimum as the noise increases. This behavior has the opposite character to stochastic resonance and coherence resonance. We found that these phenomena occurred even when the initial conditions were chosen randomly or when the noise was switched on at a random time, indicating the robustness of the results. We also examined the effects of conductance-based noise on Hodgkin-Huxley neurons and obtained similar results, leading to the conclusion that the phenomena occur across a wide range of neuronal dynamical systems. Further, these phenomena will occur in diverse applications where a stable limit cycle coexists with a stable focus.

Cortical pyramidal cells as non-linear oscillators: experiment and spike-generation theory.

Cortical neurons are capable of generating trains of action potentials in response to current injections. These discharges can take different forms, e.g., repetitive firing that adapts during the period of current injection or bursting behaviors. We have used a combined experimental and computational approach to characterize the dynamics leading to action potential responses in single neurons. Specifically we investigated the origin of complex firing patterns in response to sinusoidal current injections. Using a reduced model, the theta-neuron, alongside recordings from cortical pyramidal cells we show that both real and simulated neurons show phase-locking to sine wave stimuli up to a critical frequency, above which period skipping and 1-to-x phase-locking occurs. The locking behavior follows a complex "devil's staircase" phenomena, where locked modes are interleaved with irregular firing. We further show that the critical frequency depends on the time scale of spike generation and on the level of spike frequency adaptation. These results suggest that phase-locking of neuronal responses to complex input patterns can be explained by basic properties of the spike-generating machinery.

The simulation of addiction: pharmacological and neurocomputational models of drug self-administration.

In an attempt to better understand the pharmacological and neurobiological determinants of drug addiction, researchers have begun to build mathematical and computational models of drug self-administration. Quantitative pharmacological models have been developed to describe the acquisition of drug self-administration behavior and the maintenance of drug use behavior. However, models that describe behavior acquisition are unable to explain behavior maintenance, and vice versa. Recently, computational modeling has been used to develop more neurobiologically realistic models with the potential to explain drug self-administration across all major behavioral stages (i.e., initiation, escalation and maintenance)and across a wide range of reinforcement contingencies. Intrigued by the apparent irrational behavior of drug addicts, researchers from a wide range of scientific disciplines have formulated a plethora of theoretical schemes over the years to understand addiction. However, most of these models are qualitative in nature and are formulated using terms that are often ill-defined. As a result, the empirical validity of these models has been difficult to test rigorously, which has served to generate more controversy than clarity. In this context, as in other scientific fields, mathematical and computational modeling may contribute to the development of more testable and rigorous models of addiction. Recently, several researchers have begun to simulate drug self-administration behavior in an attempt to better understand the pharmacological and neurobiological determinants of drug addiction. This article stems from a 2006 College on Problems of Drug Dependence (CPDD) workshop and includes a few examples of mathematical and computational models of drug self-administration in rodents that illustrate the contribution of mathematical modeling to our understanding of the pharmacological and neurobiological factors in drug self-administration.

Misdeed of the need: towards computational accounts of transition to addiction.

Drug addiction is a complex behavioral and neurobiological disorder which, in an emergent brain-circuit view, reflects a loss of prefrontal top-down control over subcortical circuits governing drug-seeking and drug-taking. We first review previous computational accounts of addiction, focusing on cocaine addiction and on prevalent dopamine-based positive-reinforcement and negative-reinforcement computational models. Then, we discuss a recent computational proposal that the progression to addiction is unlikely to result from a complete withdrawal of the goal-oriented decision system in favor the habitual one. Rather, the transition to addiction would arise from a drug-induced alteration in the structure of organismal needs which reorganizes the goal structure, ultimately favoring predominance of drug-oriented goals. Finally, we outline unmet challenges for future computational research on addiction.

Nicotine reverses hypofrontality in animal models of addiction and schizophrenia.

The prefrontal cortex (PFC) underlies higher cognitive processes that are modulated by nicotinic acetylcholine receptor (nAChR) activation by cholinergic inputs. PFC spontaneous default activity is altered in neuropsychiatric disorders, including schizophrenia-a disorder that can be accompanied by heavy smoking. Recently, genome-wide association studies (GWAS) identified single-nucleotide polymorphisms (SNPs) in the human CHRNA5 gene, encoding the α5 nAChR subunit, that increase the risks for both smoking and schizophrenia. Mice with altered nAChR gene function exhibit PFC-dependent behavioral deficits, but it is unknown how the corresponding human polymorphisms alter the cellular and circuit mechanisms underlying behavior. Here we show that mice expressing a human α5 SNP exhibit neurocognitive behavioral deficits in social interaction and sensorimotor gating tasks. Two-photon calcium imaging in awake mouse models showed that nicotine can differentially influence PFC pyramidal cell activity by nAChR modulation of layer II/III hierarchical inhibitory circuits. In α5-SNP-expressing and α5-knockout mice, lower activity of vasoactive intestinal polypeptide (VIP) interneurons resulted in an increased somatostatin (SOM) interneuron inhibitory drive over layer II/III pyramidal neurons. The decreased activity observed in α5-SNP-expressing mice resembles the hypofrontality observed in patients with psychiatric disorders, including schizophrenia and addiction. Chronic nicotine administration reversed this hypofrontality, suggesting that administration of nicotine may represent a therapeutic strategy for the treatment of schizophrenia, and a physiological basis for the tendency of patients with schizophrenia to self-medicate by smoking.

Controlling Working Memory Operations by Selective Gating: The Roles of Oscillations and Synchrony.

Working memory (WM) is a primary cognitive function that corresponds to the ability to update, stably maintain, and manipulate short-term memory (ST M) rapidly to perform ongoing cognitive tasks. A prevalent neural substrate of WM coding is persistent neural activity, the property of neurons to remain active after having been activated by a transient sensory stimulus. This persistent activity allows for online maintenance of memory as well as its active manipulation necessary for task performance. WM is tightly capacity limited. Therefore, selective gating of sensory and internally generated information is crucial for WM function. While the exact neural substrate of selective gating remains unclear, increasing evidence suggests that it might be controlled by modulating ongoing oscillatory brain activity. Here, we review experiments and models that linked selective gating, persistent activity, and brain oscillations, putting them in the more general mechanistic context of WM. We do so by defining several operations necessary for successful WM function and then discussing how such operations may be carried out by mechanisms suggested by computational models. We specifically show how oscillatory mechanisms may provide a rapid and flexible active gating mechanism for WM operations.

Mechanisms for multiple activity modes of VTA dopamine neurons.

Midbrain ventral segmental area (VTA) dopaminergic neurons send numerous projections to cortical and sub-cortical areas, and diffusely release dopamine (DA) to their targets. DA neurons display a range of activity modes that vary in frequency and degree of burst firing. Importantly, DA neuronal bursting is associated with a significantly greater degree of DA release than an equivalent tonic activity pattern. Here, we introduce a single compartmental, conductance-based computational model for DA cell activity that captures the behavior of DA neuronal dynamics and examine the multiple factors that underlie DA firing modes: the strength of the SK conductance, the amount of drive, and GABA inhibition. Our results suggest that neurons with low SK conductance fire in a fast firing mode, are correlated with burst firing, and require higher levels of applied current before undergoing depolarization block. We go on to consider the role of GABAergic inhibition on an ensemble of dynamical classes of DA neurons and find that strong GABA inhibition suppresses burst firing. Our studies suggest differences in the distribution of the SK conductance and GABA inhibition levels may indicate subclasses of DA neurons within the VTA. We further identify, that by considering alternate potassium dynamics, the dynamics display burst patterns that terminate via depolarization block, akin to those observed in vivo in VTA DA neurons and in substantia nigra pars compacta (SNc) DA cell preparations under apamin application. In addition, we consider the generation of transient burst firing events that are NMDA-initiated or elicited by a sudden decrease of GABA inhibition, that is, disinhibition.

Contribution of sublinear and supralinear dendritic integration to neuronal computations.

Nonlinear dendritic integration is thought to increase the computational ability of neurons. Most studies focus on how supralinear summation of excitatory synaptic responses arising from clustered inputs within single dendrites result in the enhancement of neuronal firing, enabling simple computations such as feature detection. Recent reports have shown that sublinear summation is also a prominent dendritic operation, extending the range of subthreshold input-output (sI/O) transformations conferred by dendrites. Like supralinear operations, sublinear dendritic operations also increase the repertoire of neuronal computations, but feature extraction requires different synaptic connectivity strategies for each of these operations. In this article we will review the experimental and theoretical findings describing the biophysical determinants of the three primary classes of dendritic operations: linear, sublinear, and supralinear. We then review a Boolean algebra-based analysis of simplified neuron models, which provides insight into how dendritic operations influence neuronal computations. We highlight how neuronal computations are critically dependent on the interplay of dendritic properties (morphology and voltage-gated channel expression), spiking threshold and distribution of synaptic inputs carrying particular sensory features. Finally, we describe how global (scattered) and local (clustered) integration strategies permit the implementation of similar classes of computations, one example being the object feature binding problem.