William W. Lytton

Computer modelling of epilepsy

Epilepsy is a complex set of disorders that can involve many areas of the cortex, as well as underlying deep-brain systems. The myriad manifestations of seizures, which can be as varied as déjà vu and olfactory hallucination, can therefore give researchers insights into regional functions and relations. Epilepsy is also complex genetically and pathophysiologically: it involves microscopic (on the scale of ion channels and synaptic proteins), macroscopic (on the scale of brain trauma and rewiring) and intermediate changes in a complex interplay of causality. It has long been recognized that computer modelling will be required to disentangle causality, to better understand seizure spread and to understand and eventually predict treatment efficacy. Over the past few years, substantial progress has been made in modelling epilepsy at levels ranging from the molecular to the socioeconomic. We review these efforts and connect them to the medical goals of understanding and treating the disorder.

Attention-Like Modulation of Hippocampus Place Cell Discharge

Hippocampus place cell discharge is an important model system for understanding cognition, but evidence is missing that the place code is under the kind of dynamic attentional control characterized in primates as selective activation of one neural representation and suppression of another, competing representation. We investigated the apparent noise (“overdispersion”) in the CA1 place code, hypothesizing that overdispersion results from discharge fluctuations as spatial attention alternates between distal cues and local/self-motion cues. The hypothesis predicts that: (1) preferential use of distal cues will decrease overdispersion; (2) global, attention-like states can be decoded from ensemble discharge such that both the discharge rates and the spatial firing patterns of individual cells will be distinct in the two states; (3) identifying attention-like states improves reconstructions of the rats path from ensemble discharge. These predictions were confirmed, implying that a covert, dynamic attention-like process modulates discharge on a ∼1 s time scale. We conclude the hippocampus place code is a dynamic representation of the spatial information in the immediate focus of attention.

Unmasking the CA1 Ensemble Place Code by Exposures to Small and Large Environments: More Place Cells and Multiple, Irregularly Arranged, and Expanded Place Fields in the Larger Space

In standard experimental environments, a constant proportion of CA1 principal cells are place cells, each with a spatial receptive field called a place field. Although the properties of place cells are a basis for understanding the mammalian representation of spatial knowledge, there is no consensus on which of the two fundamental neural-coding hypotheses correctly accounts for how place cells encode spatial information. Within the dedicated-coding hypothesis, the current activity of each cell is an independent estimate of the location with respect to its place field. The average of the location estimates from many cells represents current location, so a dedicated place code would degrade if single cells had multiple place fields. Within the alternative, ensemble-coding hypothesis, the concurrent discharge of many place cells is a vector that represents current location. An ensemble place code is not degraded if single cells have multiple place fields as long as the discharge vector at each location is unique. Place cells with multiple place fields might be required to represent the substantially larger space in more natural environments. To distinguish between the dedicated-coding and ensemble-coding hypotheses, we compared the characteristics of CA1 place fields in a standard cylinder and an approximately six times larger chamber. Compared with the cylinder, in the chamber, more CA1 neurons were place cells, each with multiple, irregularly arranged, and enlarged place fields. The results indicate that multiple place fields is a fundamental feature of CA1 place cell activity and that, consequently, an ensemble place code is required for CA1 discharge to accurately signal location.

Ketamine Disrupts Theta Modulation of Gamma in a Computer Model of Hippocampus

Abnormalities in oscillations have been suggested to play a role in schizophrenia. We studied theta-modulated gamma oscillations in a computer model of hippocampal CA3 in vivo with and without simulated application of ketamine, an NMDA receptor antagonist and psychotomimetic. Networks of 1200 multicompartment neurons [pyramidal, basket, and oriens-lacunosum moleculare (OLM) cells] generated theta and gamma oscillations from intrinsic network dynamics: basket cells primarily generated gamma and amplified theta, while OLM cells strongly contributed to theta. Extrinsic medial septal inputs paced theta and amplified both theta and gamma oscillations. Exploration of NMDA receptor reduction across all location combinations demonstrated that the experimentally observed ketamine effect occurred only with isolated reduction of NMDA receptors on OLMs. In the ketamine simulations, lower OLM activity reduced theta power and disinhibited pyramidal cells, resulting in increased basket cell activation and gamma power. Our simulations predict the following: (1) ketamine increases firing rates; (2) oscillations can be generated by intrinsic hippocampal circuits; (3) medial-septum inputs pace and augment oscillations; (4) pyramidal cells lead basket cells at the gamma peak but lag at trough; (5) basket cells amplify theta rhythms; (6) ketamine alters oscillations due to primary blockade at OLM NMDA receptors; (7) ketamine alters phase relationships of cell firing; (8) ketamine reduces network responsivity to the environment; (9) ketamine effect could be reversed by providing a continuous inward current to OLM cells. We suggest that this last prediction has implications for a possible novel treatment for cognitive deficits of schizophrenia by targeting OLM cells.

Synaptic information transfer in computer models of neocortical columns

Understanding the direction and quantity of information flowing in neuronal networks is a fundamental problem in neuroscience. Brains and neuronal networks must at the same time store information about the world and react to information in the world. We sought to measure how the activity of the network alters information flow from inputs to output patterns. Using neocortical column neuronal network simulations, we demonstrated that networks with greater internal connectivity reduced input/output correlations from excitatory synapses and decreased negative correlations from inhibitory synapses, measured by Kendall’s τ correlation. Both of these changes were associated with reduction in information flow, measured by normalized transfer entropy (nTE). Information handling by the network reflected the degree of internal connectivity. With no internal connectivity, the feedforward network transformed inputs through nonlinear summation and thresholding. With greater connectivity strength, the recurrent network translated activity and information due to contribution of activity from intrinsic network dynamics. This dynamic contribution amounts to added information drawn from that stored in the network. At still higher internal synaptic strength, the network corrupted the external information, producing a state where little external information came through. The association of increased information retrieved from the network with increased gamma power supports the notion of gamma oscillations playing a role in information processing.

Emergence of Physiological Oscillation Frequencies in a Computer Model of Neocortex

Coordination of neocortical oscillations has been hypothesized to underlie the “binding” essential to cognitive function. However, the mechanisms that generate neocortical oscillations in physiological frequency bands remain unknown. We hypothesized that interlaminar relations in neocortex would provide multiple intermediate loops that would play particular roles in generating oscillations, adding different dynamics to the network. We simulated networks from sensory neocortex using nine columns of event-driven rule-based neurons wired according to anatomical data and driven with random white-noise synaptic inputs. We tuned the network to achieve realistic cell firing rates and to avoid population spikes. A physiological frequency spectrum appeared as an emergent property, displaying dominant frequencies that were not present in the inputs or in the intrinsic or activated frequencies of any of the cell groups. We monitored spectral changes while using minimal dynamical perturbation as a methodology through gradual introduction of hubs into individual layers. We found that hubs in layer 2/3 excitatory cells had the greatest influence on overall network activity, suggesting that this subpopulation was a primary generator of theta/beta strength in the network. Similarly, layer 2/3 interneurons appeared largely responsible for gamma activation through preferential attenuation of the rest of the spectrum. The network showed evidence of frequency homeostasis: increased activation of supragranular layers increased firing rates in the network without altering the spectral profile, and alteration in synaptic delays did not significantly shift spectral peaks. Direct comparison of the power spectra with experimentally recorded local field potentials from prefrontal cortex of awake rat showed substantial similarities, including comparable patterns of cross-frequency coupling.

Optimizing synaptic conductance calculation for network simulations

High computational requirements in realistic neuronal network simulations have led to attempts to realize implementation efficiencies while maintaining as much realism as possible. Since the number of synapses in a network will generally far exceed the number of neurons, simulation of synaptic activation may be a large proportion of total processing time. We present a consolidating algorithm based on a recent biophysically-inspired simplified Markov model of the synapse. Use of a single lumped state variable to represent a large number of converging synaptic inputs results in substantial speed-ups.

Control of slow oscillations in the thalamocortical neuron: a computer model

We investigated computer models of a single thalamocortical neuron to assess the interaction of intrinsic voltage-sensitive channels and cortical synaptic input in producing the range of oscillation frequencies observed in these cells in vivo. A morphologically detailed model with Hodgkin-Huxley-like ion channels demonstrated that intrinsic properties would be sufficient to readily produce 3 to 6 Hz oscillations. Hyperpolarization of the model cell reduced its oscillation frequency monotonically whether through current injection or modulation of a potassium conductance, simulating the response to a neuromodulatory input. We performed detailed analysis of highly reduced models to determine the mechanism of this frequency control. The interburst interval was controlled by two different mechanisms depending on whether or not the pacemaker current, IH, was present. In the absence of IH, depolarization during the interburst interval occurred at the same rate with different current injections. The voltage difference from the nadir to threshold for the low-threshold calcium current, IT, determined the interburst interval. In contrast, with IH present, the rate of depolarization depended on injected current. With the full model, simulated repetitive cortical synaptic input entrained oscillations up to approximately double the natural frequency. Cortical input readily produced phase resetting as well. Our findings suggest that neither ascending brainstem control altering underlying hyperpolarization, nor descending drive by repetitive cortical inputs, would alone be sufficient to produce the range of oscillation frequencies seen in thalamocortical neurons. Instead, intrinsic neuronal mechanisms would dominate for generating the delta range (0.5-4 Hz) oscillations seen during slow wave sleep, whereas synaptic interactions with cortex and the thalamic reticular nucleus would be required for faster oscillations in the frequency range of spindling (7-14 Hz).

Independent Variable Time-Step Integration of Individual Neurons for Network Simulations

Realistic neural networks involve the coexistence of stiff, coupled, continuous differential equations arising from the integrations of individual neurons, with the discrete events with delays used for modeling synaptic connections. We present here an integration method, the local variable time-step method (lvardt), that uses separate variable-step integrators for individual neurons in the network. Cells that are undergoing excitation tend to have small time steps, and cells that are at rest with little synaptic input tend to have large time steps. A synaptic input to a cell causes reinitialization of only that cells integrator without affecting the integration of other cells. We illustrated the use of lvardt on three models: a worst-case synchronizing mutual-inhibition model, a best-case synfire chain model, and a more realistic thalamocortical network model.

Cortical plasticity induced by spike-triggered microstimulation in primate somatosensory cortex.

Electrical stimulation of the nervous system for therapeutic purposes, such as deep brain stimulation in the treatment of Parkinson’s disease, has been used for decades. Recently, increased attention has focused on using microstimulation to restore functions as diverse as somatosensation and memory. However, how microstimulation changes the neural substrate is still not fully understood. Microstimulation may cause cortical changes that could either compete with or complement natural neural processes, and could result in neuroplastic changes rendering the region dysfunctional or even epileptic. As part of our efforts to produce neuroprosthetic devices and to further study the effects of microstimulation on the cortex, we stimulated and recorded from microelectrode arrays in the hand area of the primary somatosensory cortex (area 1) in two awake macaque monkeys. We applied a simple neuroprosthetic microstimulation protocol to a pair of electrodes in the area 1 array, using either random pulses or pulses time-locked to the recorded spiking activity of a reference neuron. This setup was replicated using a computer model of the thalamocortical system, which consisted of 1980 spiking neurons distributed among six cortical layers and two thalamic nuclei. Experimentally, we found that spike-triggered microstimulation induced cortical plasticity, as shown by increased unit-pair mutual information, while random microstimulation did not. In addition, there was an increased response to touch following spike-triggered microstimulation, along with decreased neural variability. The computer model successfully reproduced both qualitative and quantitative aspects of the experimental findings. The physiological findings of this study suggest that even simple microstimulation protocols can be used to increase somatosensory information flow.