Victoria Booth

A Temporal Mechanism for Generating the Phase Precession of Hippocampal Place Cells

The phase relationship between the activity of hippocampal place cells and the hippocampal theta rhythm systematically precesses as the animal runs through the region in an environment called the place field of the cell. We present a minimal biophysical model of the phase precession of place cells in region CA3 of the hippocampus. The model describes the dynamics of two coupled point neurons—namely, a pyramidal cell and an interneuron, the latter of which is driven by a pacemaker input. Outside of the place field, the network displays a stable, background firing pattern that is locked to the theta rhythm. The pacemaker input drives the interneuron, which in turn activates the pyramidal cell. A single stimulus to the pyramidal cell from the dentate gyrus, simulating entrance into the place field, reorganizes the functional roles of the cells in the network for a number of cycles of the theta rhythm. In the reorganized network, the pyramidal cell drives the interneuron at a higher frequency than the theta frequency, thus causing a systematic precession relative to the theta input. The frequency of the pyramidal cell can vary to account for changes in the animals running speed. The transient dynamics end after up to 360 degrees of phase precession when the pacemaker input to the interneuron occurs at a phase to return the network to the stable background firing pattern, thus signaling the end of the place field. Our model, in contrast to others, reports that phase precession is a temporally, and not spatially, controlled process. We also predict that like pyramidal cells, interneurons phase precess. Our model provides a mechanism for shutting off place cell firing after the animal has crossed the place field, and it explains the observed nearly 360 degrees of phase precession. We also describe how this model is consistent with a proposed autoassociative memory role of the CA3 region.

A minimal, compartmental model for a dendritic origin of bistability of motoneuron firing patterns

Various nonlinear regenerative responses, including plateau potentials and bistable repetitive firing modes, have been observed in motoneurons under certain conditions. Our simulation results support the hypothesis that these responses are due to plateau-generating currents in the dendrites, consistent with a major role for a noninactivating calcium L-type current as suggested by experiments. Bistability as observed in the soma of low- and higher-frequency spiking or, under TTX, of near resting and depolarized plateau potentials, occurs because the dendrites can be in a near resting or depolarized stable steady state. We formulate and study a two-compartment minimal model of a motoneuron that segregates currents for fast spiking into a soma-like compartment and currents responsible for plateau potentials into a dendrite-like compartment. Current flows between compartments through a coupling conductance, mimicking electrotonic spread. We use bifurcation techniques to illuminate how the coupling strength affects somatic behavior. We look closely at the case of weak coupling strength to gain insight into the development of bistable patterns. Robust somatic bistability depends on the electrical separation since it occurs only for weak to moderate coupling conductance. We also illustrate that hysteresis of the two spiking states is a natural consequence of the plateau behavior in the dendrite compartment.

Interaction of Cellular and Network Mechanisms in Spatiotemporal Pattern Formation in Neuronal Networks

Spatiotemporal patterning of neuronal activity is considered to be an important feature of cognitive processing in the brain as well as pathological brain states, such as seizures. Here, we investigate complex interactions between intrinsic properties of neurons and network structure in the generation of network spatiotemporal patterning in the context of seizure-like synchrony. We show that membrane excitability properties have differential effects on network activity patterning for different network topologies. We consider excitatory networks consisting of neurons with excitability properties varying between type I and type II that exhibit significantly different spike frequency responses to external current stimulation, especially at firing threshold. We find that networks with type II-like neurons show higher synchronization and bursting capacity across a range of network topologies than corresponding networks with type I-like neurons. These differences in activity patterning are persistent across different network sizes, connectivity strengths, magnitudes of random external input, and the addition of inhibitory interneurons to the network, making them highly likely to be relevant to brain function. Furthermore, we show that heterogeneous networks of mixed cell types show emergent dynamical patterns even for very low mixing ratios. Specifically, the addition of a small percentage of type II-like cells into a network of type I-like cells can markedly change the patterning of network activity. These findings suggest that cellular as well as network mechanisms can go hand in hand, leading to the generation of seizure-like discharges, suggesting that a single ictogenic mechanism alone may not be responsible for seizure generation.

Simulating Microinjection Experiments in a Novel Model of the Rat Sleep-Wake Regulatory Network

This study presents a novel mathematical modeling framework that is uniquely suited to investigating the structure and dynamics of the sleep-wake regulatory network in the brain stem and hypothalamus. It is based on a population firing rate model formalism that is modified to explicitly include concentration levels of neurotransmitters released to postsynaptic populations. Using this framework, interactions among primary brain stem and hypothalamic neuronal nuclei involved in rat sleep-wake regulation are modeled. The model network captures realistic rat polyphasic sleep-wake behavior consisting of wake, rapid eye movement (REM) sleep, and non-REM (NREM) sleep states. Network dynamics include a cyclic pattern of NREM sleep, REM sleep, and wake states that is disrupted by simulated variability of neurotransmitter release and external noise to the network. Explicit modeling of neurotransmitter concentrations allows for simulations of microinjections of neurotransmitter agonists and antagonists into a key wake-promoting population, the locus coeruleus (LC). Effects of these simulated microinjections on sleep-wake states are tracked and compared with experimental observations. Agonist/antagonist pairs, which are presumed to have opposing effects on LC activity, do not generally induce opposing effects on sleep-wake patterning because of multiple mechanisms for LC activation in the network. Also, different agents, which are presumed to have parallel effects on LC activity, do not induce parallel effects on sleep-wake patterning because of differences in the state dependence or independence of agonist and antagonist action. These simulation results highlight the utility of formal mathematical modeling for constraining conceptual models of the sleep-wake regulatory network.

Open-source logic-based automated sleep scoring software using electrophysiological recordings in rats

Manual state scoring of physiological recordings in sleep studies is time-consuming, resulting in a data backlog, research delays and increased personnel costs. We developed MATLAB-based software to automate scoring of sleep/waking states in rats, potentially extendable to other animals, from a variety of recording systems. The software contains two programs, Sleep Scorer and Auto-Scorer, for manual and automated scoring. Auto-Scorer is a logic-based program that displays power spectral densities of an electromyographic (EMG) signal and sigma, delta, and theta frequency bands of an electroencephalographic (EEG) signal, along with the delta/theta ratio and sigmaxtheta, for every epoch. The user defines thresholds from the training file state definitions which the Auto-Scorer uses with logic to discriminate the state of every epoch in the file. Auto-Scorer was evaluated by comparing its output to manually scored files from 6 rats under 2 experimental conditions by 3 users. Each user generated a training file, set thresholds, and auto-scored the 12 files into 4 states (waking, non-REM, transition-to-REM, and REM sleep) in 1/4 the time required to manually score the file. Overall performance comparisons between Auto-Scorer and manual scoring resulted in a mean agreement of 80.24+/-7.87%, comparable to the average agreement among 3 manual scorers (83.03+/-4.00%). There was no significant difference between user-user and user-Auto-Scorer agreement ratios. These results support the use of our open-source Auto-Scorer, coupled with user review, to rapidly and accurately score sleep/waking states from rat recordings.

Cellularly-Driven Differences in Network Synchronization Propensity Are Differentially Modulated by Firing Frequency

Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties. The neuronal phase response curve (PRC) is an experimentally obtainable measure that characterizes the cellular response to small perturbations, and can serve as an indicator of cellular propensity for synchronization. Two broad classes of PRCs have been identified for neurons: Type I, in which small excitatory perturbations induce only advances in firing, and Type II, in which small excitatory perturbations can induce both advances and delays in firing. Interestingly, neuronal PRCs are usually attenuated with increased spiking frequency, and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region. We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval. As a result, excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs. Specifically, increased frequency induced a sharp decrease in synchrony of networks of Type II neurons, while frequency increases only minimally affected synchrony in networks of Type I neurons. These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model, as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type. These results are robust to different network structures, synaptic strengths and modes of driving neuronal activity, and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information.

Spatial and reversal learning in the Morris water maze are largely resistant to six hours of REM sleep deprivation following training

This first test of the role of REM (rapid eye movement) sleep in reversal spatial learning is also the first attempt to replicate a much cited pair of papers reporting that REM sleep deprivation impairs the consolidation of initial spatial learning in the Morris water maze. We hypothesized that REM sleep deprivation following training would impair both hippocampus-dependent spatial learning and learning a new target location within a familiar environment: reversal learning. A 6-d protocol was divided into the initial spatial learning phase (3.5 d) immediately followed by the reversal phase (2.5 d). During the 6 h following four or 12 training trials/day of initial or reversal learning phases, REM sleep was eliminated and non-REM sleep left intact using the multiple inverted flowerpot method. Contrary to our hypotheses, REM sleep deprivation during four or 12 trials/day of initial spatial or reversal learning did not affect training performance. However, some probe trial measures indicated REM sleep-deprivation-associated impairment in initial spatial learning with four trials/day and enhancement of subsequent reversal learning. In naive animals, REM sleep deprivation during normal initial spatial learning was followed by a lack of preference for the subsequent reversal platform location during the probe. Our findings contradict reports that REM sleep is essential for spatial learning in the Morris water maze and newly reveal that short periods of REM sleep deprivation do not impair concurrent reversal learning. Effects on subsequent reversal learning are consistent with the idea that REM sleep serves the consolidation of incompletely learned items.

Physiologically-based modeling of sleep–wake regulatory networks

Mathematical modeling has played a significant role in building our understanding of sleep-wake and circadian behavior. Over the past 40 years, phenomenological models, including the two-process model and oscillator models, helped frame experimental results and guide progress in understanding the interaction of homeostatic and circadian influences on sleep and understanding the generation of rapid eye movement sleep cycling. Recent advances in the clarification of the neural anatomy and physiology involved in the regulation of sleep and circadian rhythms have motivated the development of more detailed and physiologically-based mathematical models that extend the approach introduced by the classical reciprocal-interaction model. Using mathematical formalisms developed in the field of computational neuroscience to model neuronal population activity, these models investigate the dynamics of proposed conceptual models of sleep-wake regulatory networks with a focus on generating appropriate sleep and wake state transition patterns as well as simulating disease states and experimental protocols. In this review, we discuss several recent physiologically-based mathematical models of sleep-wake regulatory networks. We identify common features among these models in their network structures, model dynamics and approaches for model validation. We describe how the model analysis technique of fast-slow decomposition, which exploits the naturally occurring multiple timescales of sleep-wake behavior, can be applied to understand model dynamics in these networks. Our purpose in identifying commonalities among these models is to propel understanding of both the mathematical models and their underlying conceptual models, and focus directions for future experimental and theoretical work.

Circadian regulation of sleep-wake behaviour in nocturnal rats requires multiple signals from suprachiasmatic nucleus

The dynamics of sleep and wake are strongly linked to the circadian clock. Many models have accurately predicted behaviour resulting from dynamic interactions between these two systems without specifying physiological substrates for these interactions. By contrast, recent experimental work has identified much of the relevant physiology for circadian and sleep–wake regulation, but interaction dynamics are difficult to study experimentally. To bridge these approaches, we developed a neuronal population model for the dynamic, bidirectional, neurotransmitter-mediated interactions of the sleep–wake and circadian regulatory systems in nocturnal rats. This model proposes that the central circadian pacemaker, located within the suprachiasmatic nucleus (SCN) of the hypothalamus, promotes sleep through single neurotransmitter-mediated signalling to sleep–wake regulatory populations. Feedback projections from these populations to the SCN alter SCN firing patterns and fine-tune this modulation. Although this model reproduced circadian variation in sleep–wake dynamics in nocturnal rats, it failed to describe the sleep–wake dynamics observed in SCN-lesioned rats. We thus propose two alternative, physiologically based models in which neurotransmitter- and neuropeptide-mediated signalling from the SCN to sleep–wake populations introduces mechanisms to account for the behaviour of both the intact and SCN-lesioned rat. These models generate testable predictions and offer a new framework for modelling sleep–wake and circadian interactions.

Causal entropies—A measure for determining changes in the temporal organization of neural systems

We propose a novel measure to detect temporal ordering in the activity of individual neurons in a local network, which is thought to be a hallmark of activity-dependent synaptic modifications during learning. The measure, called causal entropy, is based on the time-adaptive detection of asymmetries in the relative temporal patterning between neuronal pairs. We characterize properties of the measure on both simulated data and experimental multiunit recordings of hippocampal neurons from the awake, behaving rat, and show that the metric can more readily detect those asymmetries than standard cross correlation-based techniques, especially since the temporal sensitivity of causal entropy can detect such changes rapidly and dynamically.