Journal of Computational Neuroscience

The extent of anoxic depolarization (AD), the initial electrophysiological event during ischemia, determines the degree of brain region–specific neuronal damage. Neurons in higher brain regions exhibiting nonreversible, strong AD are more susceptible to ischemic injury as compared to cells in lower brain regions that exhibit reversible, weak AD. While the contrasting ADs in different brain regions in response to oxygen–glucose deprivation (OGD) is well established, the mechanism leading to such differences is not clear. Here we use computational modeling to elucidate the mechanism behind the brain region–specific recovery from AD. Our extended Hodgkin–Huxley (HH) framework consisting of neural spiking dynamics, processes of ion accumulation, and ion homeostatic mechanisms unveils that glial–vascular K+ clearance and Na+/K+–exchange pumps are key to the cell’s recovery from AD. Our phase space analysis reveals that the large extracellular space in the upper brain regions leads to impaired Na+/K+–exchange pumps so that they function at lower than normal capacity and are unable to bring the cell out of AD after oxygen and glucose is restored.

A large body of experimental and theoretical work on neural coding suggests that the information stored in brain circuits is represented by time-varying patterns of neural activity. Reservoir computing, where the activity of a recurrently connected pool of neurons is read by one or more units that provide an output response, successfully exploits this type of neural activity. However, the question of system robustness to small structural perturbations, such as failing neurons and synapses, has been largely overlooked. This contrasts with well-studied dynamical perturbations that lead to divergent network activity in the presence of chaos, as is the case for many reservoir networks. Here, we distinguish between two types of structural network perturbations, namely local (e.g., individual synaptic or neuronal failure) and global (e.g., network-wide fluctuations). Surprisingly, we show that while global perturbations have a limited impact on the ability of reservoir models to perform various tasks, local perturbations can produce drastic effects. To address this limitation, we introduce a new architecture where the reservoir is driven by a layer of oscillators that generate stable and repeatable trajectories. This model outperforms previous implementations while being resistant to relatively large local and global perturbations. This finding has implications for the design of reservoir models that capture the capacity of brain circuits to perform cognitively and behaviorally relevant tasks while remaining robust to various forms of perturbations. Further, our work proposes a novel role for neuronal oscillations found in cortical circuits, where they may serve as a collection of inputs from which a network can robustly generate complex dynamics and implement rich computations.

Particle swarm optimization (PSO) has gained widespread use as a general mathematical programming paradigm and seen use in a wide variety of optimization and machine learning problems. In this work, we introduce a new variant on the PSO social network and apply this method to the inverse problem of input parameter selection from recorded auditory neuron tuning curves. The topology of a PSO social network is a major contributor to optimization success. Here we propose a new social network which draws influence from winner-take-all coding found in visual cortical neurons. We show that the winner-take-all network performs exceptionally well on optimization problems with greater than 5 dimensions and runs at a lower iteration count as compared to other PSO topologies. Finally we show that this variant of PSO is able to recreate auditory frequency tuning curves and modulation transfer functions, making it a potentially useful tool for computational neuroscience models.

We introduce the concept of “type I burst excitability”, which is a generalization of the “normal” excitability that is well-known in cardiac and neural systems. We demonstrate this type of burst excitability in a specific model system, a pyramidal cell from the electrosensory lateral line lobe of the weakly electric fish Apteronotus leptorhynchus. As depolarizing current is increased, a saddle-node bifurcation of periodic orbits occurs, which separates tonic and burst activity. This bifurcation is responsible for the excitable nature of the system, and is the basis for the “type I” designation. We verify the existence of this transition from in vitro recordings of a number of actual pyramidal cells. A scaling relationship between the magnitude and duration of a current pulse required to induce a burst is derived. We also observe this type of burst excitability and the scaling relationships in a multicompartmental model that is driven by realistic stochastic synaptic inputs mimicking sensory input. We conclude by discussing the relevance of burst excitability to communication between weakly electric fish.

The stochastic integrate and fire neuron is one of the most commonly used stochastic models in neuroscience. Although some cases are analytically tractable, a full analysis typically calls for numerical simulations. We present a fast and accurate finite volume method to approximate the solution of the associated Fokker-Planck equation. The discretization of the boundary conditions offers a particular challenge, as standard operator splitting approaches cannot be applied without modification. We demonstrate the method using stationary and time dependent inputs, and compare them with Monte Carlo simulations. Such simulations are relatively easy to implement, but can suffer from convergence difficulties and long run times. In comparison, our method offers improved accuracy, and decreases computation times by several orders of magnitude. The method can easily be extended to two and three dimensional Fokker-Planck equations.

Depolarization-dependent outward currents were analyzed using the single-electrode voltage clamp technique in the dendritic membrane of an identified nonspiking interneuron (LDS interneuron) in situ in the terminal abdominal ganglion of crayfish. When the membrane was depolarized by more than 20 mV from the resting potential (65.0 ± 5.7 mV), a transient outward current was observed to be followed by a sustained outward current. Pharmacological experiments revealed that these outward currents were composed of 3 distinct components. A sustained component (I s) was activated slowly (half rise time > 5 msec) and blocked by 20 mM TEA. A transient component (I t1) that was activated and inactivated very rapidly (peak time < 2.5 msec, half decay time < 1.2 msec) was also blocked by 20 mM TEA. Another transient component (I t2) was blocked by 100 μM 4AP, activated rapidly (peak time < 10.0 msec) and inactivated slowly (half decay time > 131.8 msec). Two-step pulse experiments have revealed that both sustained and transient components are not inactivated at the resting potential: the half-maximal inactivation was attained at −21.0 mV in I t1, and −38.0 mV in I t2. I s showed no noticeable inactivation. When the membrane was initially held at the resting potential level and clamped to varying potential levels, the half-maximal activation was attained at −36.0 mV in I s, −31.0 mV in I t1 and −40.0 mV in I t2. The activation and inactivation time constants were both voltage dependent. A mathematical model of the LDS interneuron was constructed based on the present electrophysiological records to simulate the dynamic interaction of outward currents during membrane depolarization. The results suggest that those membrane conductances found in this study underlie the outward rectification of the interneuron membrane as well as depolarization-dependent shaping of the excitatory synaptic potential observed in current-clamp experiments.

Contrast enhancement via lateral inhibitory circuits is a common mechanism in sensory systems. We here employ a computational model to show that, in addition to shaping experimentally observed molecular receptive fields in the olfactory bulb, functionally lateral inhibitory circuits can also mediate the elemental and configurational properties of odor mixture perception. To the extent that odor perception can be predicted by slow-timescale neural activation patterns in the olfactory bulb, and to the extent that interglomerular inhibitory projections map onto a space of odorant similarity, the model shows that these inhibitory processes in the olfactory bulb suffice to generate the behaviorally observed inverse relationship between two odorants' perceptual similarities and the perceptual similarities between either of these same odorants and their binary mixture.

A model of columnar networks of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others, randomly chosen. Any module encodes and stores a number of elementary percepts, or features. Memory items, or patterns, are peculiar combinations of features sparsely distributed over the multi-modular network. Any feature stored in any module can be involved in several of the stored patterns; feature-sharing is in fact source of local ambiguities and, consequently, a potential cause of erroneous memory retrieval spreading through the model network in pattern completion tasks. The memory retrieval dynamics of the large modular autoassociator is investigated by combining mathematical analysis and numerical simulations. An oscillatory retrieval process is proposed that is very efficient in overcoming feature-sharing drawbacks; it requires a mechanism that modulates the robustness of local attractors to noise, and neuronal activity sparseness such that quiescent and active modules are about equally noisy to any post-synaptic module. Moreover, it is shown that statistical correlation between ‘kinds’ of features across the set of memory patterns can be exploited to obtain a more efficient achievement of memory retrieval capabilities. It is also shown that some spots of the network cannot be reached by retrieval activity spread if they are not directly cued by the stimulus. The locations of these activity isles depend on the pattern to retrieve, while their extension only depends (in large networks) on statistics of inter-modular connections and stored patterns. The existence of activity isles determines an upper-bound to retrieval quality that does not depend on the specific retrieval dynamics adopted, nor on whether feature-sharing is permitted. The oscillatory retrieval process nearly saturates this bound.

Serotonin (5-HT) applied to the exposed but otherwise intact nervous system results in enhanced excitability of Hermissenda type-B photoreceptors. Several ion currents in the type-B photoreceptors are modulated by 5-HT, including the A-type K+ current (IK,A), sustained Ca2+ current (ICa,S), Ca-dependent K+ current (IK,Ca), and a hyperpolarization-activated inward rectifier current (Ih). In this study, we developed a computational model that reproduces physiological characteristics of type B photoreceptors, e.g. resting membrane potential, dark-adapted spike activity, spike width, and the amplitude difference between somatic and axonal spikes. We then used the model to investigate the contribution of different ion currents modulated by 5-HT to the magnitudes of enhanced excitability produced by 5-HT. Ion currents were systematically varied within limits observed experimentally, both individually and in combinations. A reduction of IK,A or IK,Ca, or an increase in Ih enhanced excitability by 20–50%. Decreasing ICa,S produced a dramatic decrease in excitability. Reductions of IK,V produced only minimal increases in excitability, suggesting that IK,V probably plays a minor role in 5-HT induced enhanced excitability. Combinations of changes in IK,A, IK,Ca, Ih and ICa,S produced increases in excitability comparable to experimental observations. After 5-HT application, the cell's depolarization force is shifted from the Ih–ICa,S combination to predominantly Ih.