In contrast to the limited response properties observed under normal experimental conditions, spinal motoneurons generate complex firing patterns, such as Ca2+-dependent regenerative spiking and plateaus, in the presence of certain neurotransmitters and ion-channel blockers. We have developed a quantitative motoneuron model, based on turtle motoneuron data, toinvestigate the roles of specific ionic currents and the effects of their soma and dendritic distribution in generating these complex firing patterns. In addition, the model is used to explore the effects of multiple ion channel blockers and neurotransmitters that are known to modulate motoneuron firing patterns. To represent the distribution of ionic currents across the soma and dendrites, the model contains two compartments. The soma compartment, representing the soma and proximal dendrites, contains Hodgkin-Huxley-like sodium (INa) and delayed rectifier K+ (IK-dr) currents, an N-like Ca2+ current (ICa-N), and a calcium-dependent K+ current [IK(Ca)]. The dendritic compartment, representing the lumped distal dendrites, contains, in addition to ICa-N and IK(Ca) as in the soma, a persistent L-like calcium current (ICa-L). We determined kinetic parameters for INa, IK-dr, ICa-N, and IK(Ca) in order to reproduce normal action-potential firing observed in turtle spinal motoneurons, including fast and slow afterhyperpolarizations (AHPs) and a linear steady-state frequency-current relation. With this parameter set as default, a sequence of pharmacological manipulations were systematically simulated. A small reduction of IK-dr [mimicking the experimental effect of tetraethylammonium (TEA) in low concentration] enhanced the slow AHP and caused calcium spiking (mediated by ICa-N) when INa was blocked. Firing patterns observed experimentally in high TEA [and tetrodotoxin (TTX)], namely calcium spikes riding on a calcium plateau, were reproduced only when both IK-dr and IK(Ca) were reduced. Dendritic plateau potentials, mediated by ICa-L, were reliably unmasked when IK(Ca) was reduced, mimicking the experimental effect of the bee venom apamin. The effect of 5-HT, which experimentally induces the ability to generate calcium-dependent plateau potentials but not calcium spiking, was reproduced in the model by reducing IK(Ca) alone. The plateau threshold current level, however, was reduced substantially if a simultaneous increase in ICa-L was simulated, suggesting that serotonin (5-HT) induces plateau potentials by regulating more than one conductance. The onset of the plateau potential showed significant delays in response to near-threshold, depolarizing current steps. In addition, the delay times were sensitive to the current step amplitude. The delay and its sensitivity were explained by examining the model's behavior near the threshold for plateau onset. This modeling study thus accurately accounts for the basic firing behavior of vertebrate motoneurons as well as a range of complex firing patterns invoked by ion-channel blockers and 5-HT. In addition, our computational...

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.

Diniz Behn CG, Booth V. Simulating microinjection experiments in a novel model of the rat sleep-wake regulatory network. J Neurophysiol 103: 1937-1953, 2010. First published January 27, 2010 doi:10.1152/jn.00795.2009. 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 sleepwake regulatory network.

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.

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We describe a low-dimensional relation and demonstrate its use in reducing model complexity for coupled oscillator systems.

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 AutoScorer, for manual and automated scoring. Auto-Scorer is a logic-based program that displays power spectral densities of an electromyographic signal and σ, δ, and θ frequency bands of an electroencephalographic signal, along with the δ/θ ratio and σ ×θ, 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 autoscored the 12 files into 4 states (waking, non-REM, transitionto-REM, and REM sleep) in ¼ 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.

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.