Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism

LTP regulates burst initiation and frequency at mossy fiber-granule cell synapses of rat cerebellum: experimental observations and theoretical predictions

Long-term potentiation (LTP) is a synaptic change supposed to provide the cellular basis for learning and memory in brain neuronal circuits. Although specific LTP expression mechanisms could be critical to determine the dynamics of repetitive neurotransmission, this important issue remained largely unexplored. In this paper, we have performed whole cell patch-clamp recordings of mossy fiber-granule cell LTP in acute rat cerebellar slices and studied its computational implications with a mathematical model. During LTP, stimulation with short impulse trains at 100 Hz revealed earlier initiation of granule cell spike bursts and a smaller nonsignificant spike frequency increase. In voltage-clamp recordings, short AMPA excitatory postsynaptic current (EPSC) trains showed short-term facilitation and depression and a sustained component probably generated by spillover. During LTP, facilitation disappeared, depression accelerated, and the sustained current increased. The N-methyl-d-aspartate (NMDA) current also increased. In agreement with a presynaptic expression caused by increased release probability, similar changes were observed by raising extracellular [Ca(2+)]. A mathematical model of mossy fiber-granule cell neurotransmission showed that increasing release probability efficiently modulated the first-spike delay. Glutamate spillover, by causing tonic NMDA and AMPA receptor activation, accelerated excitatory postsynaptic potential (EPSP) temporal summation and maintained a sustained spike discharge. The effect of increasing neurotransmitter release could not be replicated by increasing receptor conductance, which, like postsynaptic manipulations enhancing intrinsic excitability, proved very effective in raising granule cell output frequency. Independent regulation of spike burst initiation and frequency during LTP may provide mechanisms for temporal recoding and gain control of afferent signals at the input stage of cerebellar cortex.

Feedback Inhibition and Throughput Properties of an Integrate-and-Fire-or-Burst Network Model of Retinogeniculate Transmission

Computational modeling has played an important role in the dissection of the biophysical basis of rhythmic oscillations in thalamus that are associated with sleep and certain forms of epilepsy. In contrast, the dynamic filter properties of thalamic relay nuclei during states of arousal are not well understood. Here we present a modeling and simulation study of the throughput properties of the visually driven dorsal lateral geniculate nucleus (dLGN) in the presence of feedback inhibition from the perigeniculate nucleus (PGN). We employ thalamocortical (TC) and thalamic reticular (RE) versions of a minimal integrate-and-fire-or-burst type model and a one-dimensional, two-layered network architecture. Potassium leakage conductances control the neuromodulatory state of the network and eliminate rhythmic bursting in the presence of spontaneous input (i.e., wake up the network). The aroused dLGN/PGN network model is subsequently stimulated by spatially homogeneous spontaneous retinal input or spatio-temporally patterned input consistent with the activity of X-type retinal ganglion cells during full-field or drifting grating visual stimulation. The throughput properties of this visually-driven dLGN/PGN network model are characterized and quantified as a function of stimulus parameters such as contrast, temporal frequency, and spatial frequency. During low-frequency oscillatory full-field stimulation, feedback inhibition from RE neurons often leads to TC neuron burst responses, while at high frequency tonic responses dominate. Depending on the average rate of stimulation, contrast level, and temporal frequency of modulation, the TC and RE cell bursts may or may not be phase-locked to the visual stimulus. During drifting-grating stimulation, phase-locked bursts often occur for sufficiently high contrast so long as the spatial period of the grating is not small compared to the synaptic footprint length, i.e., the spatial scale of the network connectivity.

Phase Dependent Sign Changes of GABAergic Synaptic Input Explored In-Silicio and In-Vitro

Inhibitory interactions play a crucial role in the synchronization of neuronal activity. Here we investigate the effect of GABAergic PSPs on spike timing in cortical neurons that exhibit an oscillatory modulation of their membrane potential. To this end we combined numerical simulations with in-vitro patch-clamp recordings from layer II/III pyramidal cells of the rat visual cortex. Special emphasis was placed on exploring how the reversal potential of the GABAergic synaptic currents (EGABA) and the phase relations of the PSPs relative to the oscillation cycles affect the timing of spikes riding on the depolarizing peaks of the oscillations. The simulations predicted: (1) With EGABA more negative than the oscillation minima PSPs are hyperpolarizing at all phases and thus delay or prevent spikes. (2) With EGABA being more positive than the oscillation maxima PSPs are depolarizing in a phase-independent way and lead to a phase advance of spikes. (3) In the intermediate case where EGABA lies within oscillation maxima and minima PSPs are either hyper- or depolarizing depending on their phase relations to the V(m) oscillations and can therefore either delay or advance spikes. Experiments conducted in this most interesting last configuration with biphasic PSPs agreed with the model predictions. Additional theoretical investigations revealed the effect of these PSP induced shifts in spike timing on synchronization in neuronal circuits. The results suggest that GABAergic mechanisms can assume highly specific timing functions in oscillatory networks.

Fast odor learning improves reliability of odor responses in the locust antennal lobe

Recordings in the locust antennal lobe (AL) reveal activity-dependent, stimulus-specific changes in projection neuron (PN) and local neuron response patterns over repeated odor trials. During the first few trials, PN response intensity decreases, while spike time precision increases, and coherent oscillations, absent at first, quickly emerge. We examined this "fast odor learning" with a realistic computational model of the AL. Activity-dependent facilitation of AL inhibitory synapses was sufficient to simulate physiological recordings of fast learning. In addition, in experiments with noisy inputs, a network including synaptic facilitation of both inhibition and excitation responded with reliable spatiotemporal patterns from trial to trial despite the noise. A network lacking fast plasticity, however, responded with patterns that varied across trials, reflecting the input variability. Thus, our study suggests that fast olfactory learning results from stimulus-specific, activity-dependent synaptic facilitation and may improve the signal-to-noise ratio for repeatedly encountered odor stimuli.

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 cell's 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.

Maintenance and termination of neocortical oscillations by dynamic modulation of intrinsic and synaptic excitability

Mechanisms underlying seizure cessation remain elusive. The Lennox-Gastaut syndrome, a severe childhood epileptic disorder, is characterized by episodes of seizure with alternating epochs of spike-wave and fast run discharges. In a detailed computational model that incorporates extracellular potassium dynamics, we studied the dynamics of these state transitions between slow and fast oscillations. We show that dynamic modulation of synaptic transmission can cause termination of paroxysmal activity. An activity-dependent shift in the balance between synaptic excitation and inhibition towards more excitation caused seizure termination by favoring the slow oscillatory state, which permits recovery of baseline extracellular potassium concentration. We found that slow synaptic depression and change in chloride reversal potential can have similar effects on the seizure dynamics. Our results indicate a novel role for synaptic dynamics during epileptic neural activity patterns.

Whole cell stochastic model reproduces the irregularities found in the membrane potential of bursting neurons

Irregular intrinsic behavior of neurons seems ubiquitous in the nervous system. Even in circuits specialized to provide periodic and reliable patterns to control the repetitive activity of muscles, such as the pyloric central pattern generator (CPG) of the crustacean stomatogastric ganglion (STG), many bursting motor neurons present irregular activity when deprived from synaptic inputs. Moreover, many authors attribute to these irregularities the role of providing flexibility and adaptation capabilities to oscillatory neural networks such as CPGs. These irregular behaviors, related to nonlinear and chaotic properties of the cells, pose serious challenges to developing deterministic Hodgkin-Huxley-type (HH-type) conductance models. Only a few deterministic HH-type models based on experimental conductance values were able to show such nonlinear properties, but most of these models are based on slow oscillatory dynamics of the cytosolic calcium concentration that were never found experimentally in STG neurons. Based on an up-to-date single-compartment deterministic HH-type model of a STG neuron, we developed a stochastic HH-type model based on the microscopic Markovian states that an ion channel can achieve. We used tools from nonlinear analysis to show that the stochastic model is able to express the same kind of irregularities, sensitivity to initial conditions, and low dimensional dynamics found in the neurons isolated from the STG. Without including any nonrealistic dynamics in our whole cell stochastic model, we show that the nontrivial dynamics of the membrane potential naturally emerge from the interplay between the microscopic probabilistic character of the ion channels and the nonlinear interactions among these elements. Moreover, the experimental irregular behavior is reproduced by the stochastic model for the same parameters for which the membrane potential of the original deterministic model exhibits periodic oscillations.

Extracting information from the power spectrum of synaptic noise

In cortical neurons, synaptic "noise" is caused by the nearly random release of thousands of synapses. Few methods are presently available to analyze synaptic noise and deduce properties of the underlying synaptic inputs. We focus here on the power spectral density (PSD) of several models of synaptic noise. We examine different classes of analytically solvable kinetic models for synaptic currents, such as the "delta kinetic models," which use Dirac delta functions to represent the activation of the ion channel. We first show that, for this class of kinetic models, one can obtain an analytic expression for the PSD of the total synaptic conductance and derive equivalent stochastic models with only a few variables. This yields a method for constraining models of synaptic currents by analyzing voltage-clamp recordings of synaptic noise. Second, we show that a similar approach can be followed for the PSD of the the membrane potential (Vm) through an effective-leak approximation. Third, we show that this approach is also valid for inputs distributed in dendrites. In this case, the frequency scaling of the Vm PSD is preserved, suggesting that this approach may be applied to intracellular recordings of real neurons. In conclusion, using simple mathematical tools, we show that Vm recordings can be used to constrain kinetic models of synaptic currents, as well as to estimate equivalent stochastic models. This approach, therefore, provides a direct link between intracellular recordings in vivo and the design of models consistent with the dynamics and spectral structure of synaptic noise.

Dynamic modeling of biochemical reactions with application to signal transduction: principles and tools using Mathematica

Modeling of biochemical phenomena is based on formal reaction kinetics. This requires the translation of the original reaction systems into sets of differential equations expressing the effects of the various reaction steps. The temporal behavior of the system is obtained by solving the differential equations. We present the main concepts on which the formal approach of these two problems is based and we show how the amount of work needed to treat them can be significantly reduced by using a mathematical program package (Mathematica). Symbolic and numerical calculations can be performed with the programs presented and graphic presentations of the behavior of the system be obtained. The basic ideas are illustrated with three examples taken from the area of signal transduction and ion signaling.

Intrinsic and circuit properties favor coincidence detection for decoding oscillatory input

In the insect olfactory system the antennal lobe generates oscillatory synchronization of its output as a framework for coincidence detection by its target, the mushroom body (MB). The intrinsic neurons of the MB (Kenyon cells, KCs) are thus a good model system in which to investigate the functional relevance of oscillations and neural synchronization. We combine electrophysiological and modeling approaches to examine how intrinsic and circuit properties might contribute to the preference of KCs for coincident input and how their decoding of olfactory information is affected by the absence of oscillatory synchronization in their input. We show that voltage-dependent subthreshold properties of KCs bring about a supralinear summation of their inputs, favoring responses to coincident EPSPs. Abolishing oscillatory synchronization weakens the preference of KCs for coincident input and causes a large reduction in their odor specificity. Finally, we find that a decoding strategy that is based on coincidence detection enhances both noise tolerance and input discriminability by KCs.

A Learning Rule for Local Synaptic Interactions Between Excitation and Shunting Inhibition

The basic requirement for direction selectivity is a nonlinear interaction between two different inputs in space-time. In some models, the interaction is hypothesized to occur between excitation and inhibition of the shunting type in the neuron's dendritic tree. How can the required spatial specificity be acquired in an unsupervised manner? We here propose an activity-based, local learning model that can account for direction selectivity in visual cortex based on such a local veto operation and that depends on synaptically induced changes in intracellular calcium concentration. Our biophysical simulations suggest that a model cell with our learning algorithm can develop direction selectivity organically after unsupervised training. The learning rule is also applicable to a neuron with multiple-direction-selective subunits and to a pair of cells with opposite-direction selectivities and is stable under different starting conditions, delays, and velocities.

Estimation of multiscale neurophysiologic parameters by electroencephalographic means

It is shown that new model-based electroencephalographic (EEG) methods can quantify neurophysiologic parameters that underlie EEG generation in ways that are complementary to and consistent with standard physiologic techniques. This is done by isolating parameter ranges that give good matches between model predictions and a variety of experimental EEG-related phenomena simultaneously. Resulting constraints range from the submicrometer synaptic level to length scales of tens of centimeters, and from timescales of around 1 ms to 1 s or more, and are found to be consistent with independent physiologic and anatomic measures. In the process, a new method of obtaining model parameters from the data is developed, including a Monte Carlo implementation for use when not all input data are available. Overall, the approaches used are complementary to other methods, constraining allowable parameter ranges in different ways and leading to much tighter constraints overall. EEG methods often provide the most restrictive individual constraints. This approach opens a new, noninvasive window on quantitative brain analysis, with the ability to monitor temporal changes, and the potential to map spatial variations. Unlike traditional phenomenologic quantitative EEG measures, the methods proposed here are based explicitly on physiology and anatomy.

Membrane bistability in thalamic reticular neurons during spindle oscillations

The thalamic reticular (RE) nucleus is a major source of inhibition in the thalamus. It plays a crucial role in regulating the excitability of thalamocortical networks and in generating some sleep rhythms. Current-clamp intracellular recordings of RE neurons in cats under barbiturate anesthesia revealed the presence of membrane bistability in approximately 20% of neurons. Bistability consisted of two alternate membrane potentials, separated by approximately 17-20 mV. While non-bistable (common) RE neurons fired rhythmic spike-bursts during spindles, bistable RE neurons fired tonically, with burst modulation, throughout spindle sequences. Bistability was strongly voltage dependent and only expressed under resting conditions (i.e. no current injection). The transition from the silent to the active state was a regenerative event that could be activated by brief depolarization, whereas brief hyperpolarizations could switch the membrane potential from the active to the silent state. These effects outlasted the current pulses. Corticothalamic stimulation could also switch the membrane potential from silent to active states. Addition of QX-314 in the recording micropipette either abolished or disrupted membrane bistability, suggesting I(Na(p)) to be responsible for its generation. Thalamocortical cells presented various patterns of spindling that reflected the membrane bistability in RE neurons. Finally, experimental data and computer simulations predicted a role for RE neurons' membrane bistability in inducing various patterns of spindling in target thalamocortical cells. We conclude that membrane bistability of RE neurons is an intrinsic property, likely generated by I(Na(p)) and modulated by cortical influences, as well as a factor that determines different patterns of spindle rhythms in thalamocortical neurons.

An improved non-linear thermodynamic model of voltage-dependent ionic currents

Thermodynamic models of ionic currents are used to deduce exact functional form of rate constant. It is first assumed that free energy depends linearly on voltage. A major criticism of this approach is that time constant can reach arbitrarily small values resulting in an aberrant behavior. Recently, non-linear effects of electric field on the free energy were considered to solve this problem based on T-type calcium channel. In this study, we show that the current model approximately captures the voltage-dependence of the time constant only in a specific range of voltage and does not provide saturation of the time constant outside this range. Then, we propose an improved non-linear thermodynamic model and illustrate its applicability based on T-type calcium channel.

Potassium model for slow (2-3 Hz) in vivo neocortical paroxysmal oscillations

In slow neocortical paroxysmal oscillations, the de- and hyperpolarizing envelopes in neocortical neurons are large compared with slow sleep oscillations. Increased local synchrony of membrane potential oscillations during seizure is reflected in larger electroencephalographic oscillations and the appearance of spike- or polyspike-wave complex recruitment at 2- to 3-Hz frequencies. The oscillatory mechanisms underlying this paroxysmal activity were investigated in computational models of cortical networks. The extracellular K(+) concentration ([K(+)](o)) was continuously computed based on neuronal K(+) currents and K(+) pumps as well as glial buffering. An increase of [K(+)](o) triggered a transition from normal awake-like oscillations to 2- to 3-Hz seizure-like activity. In this mode, the cells fired periodic bursts and nearby neurons oscillated highly synchronously; in some cells depolarization led to spike inactivation lasting 50-100 ms. A [K(+)](o) increase, sufficient to produce oscillations could result from excessive firing (e.g., induced by external stimulation) or inability of K(+) regulatory system (e.g., when glial buffering was blocked). A combination of currents including high-threshold Ca(2+), persistent Na(+) and hyperpolarization-activated depolarizing (I(h)) currents was sufficient to maintain 2- to 3-Hz activity. In a network model that included lateral K(+) diffusion between cells, increase of [K(+)](o) in a small region was generally sufficient to maintain paroxysmal oscillations in the whole network. Slow changes of [K(+)](o) modulated the frequency of bursting and, in some case, led to fast oscillations in the 10- to 15-Hz frequency range, similar to the fast runs observed during seizures in vivo. These results suggest that modifications of the intrinsic currents mediated by increase of [K(+)](o) can explain the range of neocortical paroxysmal oscillations in vivo.

Single-neuron discharge properties and network activity in dissociated cultures of neocortex

Cultures of neurons from rat neocortex exhibit spontaneous, temporally patterned, network activity. Such a distributed activity in vitro constitutes a possible framework for combining theoretical and experimental approaches, linking the single-neuron discharge properties to network phenomena. In this work, we addressed the issue of closing the loop, from the identification of the single-cell discharge properties to the prediction of collective network phenomena. Thus, we compared these predictions with the spontaneously emerging network activity in vitro, detected by substrate arrays of microelectrodes. Therefore, we characterized the single-cell discharge properties to Gauss-distributed noisy currents, under pharmacological blockade of the synaptic transmission. Such stochastic currents emulate a realistic input from the network. The mean (m) and variance (s(2)) of the injected current were varied independently, reminiscent of the extended mean-field description of a variety of possible presynaptic network organizations and mean activity levels, and the neuronal response was evaluated in terms of the steady-state mean firing rate (f). Experimental current-to-spike-rate responses f(m, s(2)) were similar to those of neurons in brain slices, and could be quantitatively described by leaky integrate-and-fire (IF) point neurons. The identified model parameters were then used in numerical simulations of a network of IF neurons. Such a network reproduced a collective activity, matching the spontaneous irregular population bursting, observed in cultured networks. We finally interpret such a collective activity and its link with model details by the mean-field theory. We conclude that the IF model is an adequate minimal description of synaptic integration and neuronal excitability, when collective network activities are considered in vitro.

Cellular effects of deep brain stimulation: model-based analysis of activation and inhibition

Deep brain stimulation (DBS) is an effective therapy for medically refractory movement disorders. However, fundamental questions remain about the effects of DBS on neurons surrounding the electrode. Experimental studies have produced apparently contradictory results showing suppression of activity in the stimulated nucleus, but increased inputs to projection nuclei. We hypothesized that cell body firing does not accurately reflect the efferent output of neurons stimulated with high-frequency extracellular pulses, and that this decoupling of somatic and axonal activity explains the paradoxical experimental results. We studied stimulation using the combination of a finite-element model of the clinical DBS electrode and a multicompartment cable model of a thalamocortical (TC) relay neuron. Both the electric potentials generated by the electrode and a distribution of excitatory and inhibitory trans-synaptic inputs induced by stimulation of presynaptic terminals were applied to the TC relay neuron. The response of the neuron to DBS was primarily dependent on the position and orientation of the axon with respect to the electrode and the stimulation parameters. Stimulation subthreshold for direct activation of TC relay neurons caused suppression of intrinsic firing (tonic or burst) activity during the stimulus train mediated by activation of presynaptic terminals. Suprathreshold stimulation caused suppression of intrinsic firing in the soma, but generated efferent output at the stimulus frequency in the axon. This independence of firing in the cell body and axon resolves the apparently contradictory experimental results on the effects of DBS. In turn, the results of this study support the hypothesis of stimulation-induced modulation of pathological network activity as a therapeutic mechanism of DBS.

Active dendrites and spike propagation in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneurons

It is well known that interneurons are heterogeneous in their morphologies, biophysical properties, pharmacological sensitivities and electrophysiological responses, but it is unknown how best to understand this diversity. Given their critical roles in shaping brain output, it is important to try to understand the functionality of their computational characteristics. To do this, we focus on specific interneuron subtypes. In particular, it has recently been shown that long-term potentiation is induced specifically on oriens-lacunosum/moleculare (O-LM) interneurons in hippocampus CA1 and that the same cells contain the highest density of dendritic sodium and potassium conductances measured to date. We have created multi-compartment models of an O-LM hippocampal interneuron using passive properties, channel kinetics, densities and distributions specific to this cell type, and explored its signalling characteristics. We found that spike initiation depends on both location and amount of input, as well as the intrinsic properties of the interneuron. Distal synaptic input always produces strong back-propagating spikes whereas proximal input could produce both forward- and back-propagating spikes depending on the input strength. We speculate that the highly active dendrites of these interneurons endow them with a specialized function within the hippocampal circuitry by allowing them to regulate direct and indirect signalling pathways within the hippocampus.

Dynamical Consequences of Fast-Rising, Slow-Decaying Synapses in Neuronal Networks

Synapses that rise quickly but have long persistence are shown to have certain computational advantages. They have some unique mathematical properties as well and in some instances can make neurons behave as if they are weakly coupled oscillators. This property allows us to determine their synchronization properties. Furthermore, slowly decaying synapses allow recurrent networks to maintain excitation in the absence of inputs, whereas faster decaying synapses do not. There is an interaction between the synaptic strength and the persistence that allows recurrent networks to fire at low rates if the synapses are sufficiently slow. Waves and localized structures are constructed in spatially extended networks with slowly decaying synapses.

Decoding of synaptic voltage waveforms by specific classes of recombinant high-threshold Ca(2+) channels

Studies suggest that the preferential role of L-type voltage-sensitive Ca(2+) channels (VSCCs) in coupling strong synaptic stimulation to transcription is due to their selective activation of local chemical events. However, it is possible that selective activation of the L-type channel by specific voltage waveforms also makes a contribution. To address this issue we have examined the response of specific Ca(2+) channel types to simulated complex voltage waveforms resembling those encountered during synaptic plasticity (gamma and theta firing frequency). L-, P/Q- and N-type VSCCs (alpha1C, alpha1A, alpha1B/beta1B/alpha2delta, respectively) were all similarly activated by brief action potential (AP) waveforms or sustained step depolarization. When complex waveforms containing large excitatory postsynaptic potentials (EPSPs), APs and spike accommodation were applied under voltage clamp we found that the integrated L-type VSCC current was approximately three times larger than that produced by the P/Q- or N-type Ca(2+) channels (gamma frequency 1 s stimulation). For P/Q- or N-type channels the complex waveforms led to a smaller current than that expected from the response to a simple 1 s step depolarization to 0 or +20 mV. EPSPs present in the waveforms favoured the inactivation of P/Q- and N-type channels. In contrast, activation of the L-type channel was dependent on both EPSP- and AP-mediated depolarization. Expression of P/Q-type channels with reduced voltage-dependent inactivation (alpha1A/beta2A/alpha2delta) or the use of hyperpolarized intervals between AP stimuli greatly increased their response to complex voltage stimuli. We propose that in response to complex synaptic voltage waveforms P/Q- and N-type channels can undergo selective voltage-dependent inactivation leading to a Ca(2+) current mediated predominantly by L-type channels.

Submillisecond precision of the input-output transformation function mediated by fast sodium dendritic spikes in basal dendrites of CA1 pyramidal neurons

The ability of cortical neurons to perform temporally accurate computations has been shown to be important for encoding of information in the cortex; however, cortical neurons are expected to be imprecise temporal encoders because of the stochastic nature of synaptic transmission and ion channel gating, dendritic filtering, and background synaptic noise. Here we show for the first time that fast local spikes in basal dendrites can serve to improve the temporal precision of neuronal output. Integration of coactivated, spatially distributed synaptic inputs produces temporally imprecise output action potentials within a time window of several milliseconds. In contrast, integration of closely spaced basal inputs initiates local dendritic spikes that amplify and sharpen the summed somatic potential. In turn, these fast basal spikes allow precise timing of output action potentials with submillisecond temporal jitter over a wide range of activation intensities and background synaptic noise. Our findings indicate that fast spikes initiated in individual basal dendrites can serve as precise "timers" of output action potentials in various network activity states and thus may contribute to temporal coding in the cortex.

The impact of corticothalamic feedback on the output dynamics of a thalamocortical neurone model: the role of synapse location and metabotropic glutamate receptors

The spatio-temporal integration of cortical excitatory postsynaptic potentials was investigated in a multi-compartment model of a thalamocortical neurone. Consistent with experimental data, cortical excitatory postsynaptic potentials contained a metabotropic glutamate receptor-mediated component and were generated by synapses located on distal dendrites. Within this framework, three synaptic distributions (each with equal maximal synaptic conductances) were compared: symmetric, with synapses distributed equally between all dendritic trees, single-dendrite, where synapses were allocated on all distal segments of one dendrite, and single-segment, which comprised one synapse on a single dendritic compartment. We addressed three main issues: (1) the propagation of cortical excitatory postsynaptic potentials to the soma, (2) the interaction of cortical excitatory postsynaptic potentials with proximally generated retinal excitatory postsynaptic potentials, and (3) the effectiveness of cortical excitatory postsynaptic potentials in entraining and perturbing the delta oscillation. The somatic and dendritic amplitudes of the cortical excitatory postsynaptic potentials depended on the distribution of the synapses, being largest and smallest, respectively, for the symmetric distribution, and smallest and largest, respectively, for the single-segment distribution. When a retinal excitatory postsynaptic potential followed a subthreshold cortical excitatory postsynaptic potential with a short (2-200 ms) delay, its ability to evoke action potentials was increased, with single-segment cortical excitatory postsynaptic potentials having the longest-lasting facilitatory effect. When a retinal excitatory postsynaptic potential arrived with a longer delay (210-400 ms), the effect of the cortical excitatory postsynaptic potential was to decrease the number of retinally evoked action potentials. These facilitatory and depressant effects of the cortical excitatory postsynaptic potentials were dependent on the presence of their metabotropic glutamate receptor, and were enhanced by increasing the strength of this glutamate receptor component. Axial resistivity and distal dendritic A-type current had little qualitative effect on these modulatory actions of the cortical excitatory postsynaptic potential. Cortical excitatory postsynaptic potentials were more effective than retinal excitatory postsynaptic potentials in perturbing the phase of the delta oscillation, indicating that they are ideally suited to entraining this form of rhythmic activity. Again, this effect was closely dependent on the presence of metabotropic glutamate receptor but was largely independent of synapse distribution. These results indicate that the distribution of activated synapses and the presence of metabotropic glutamate receptor are crucial factors in determining the effect of cortical feedback excitation on thalamocortical neurons. Moreover, the distinct postsynaptic receptor composition of cortical inputs renders them ideally suited to synchronising low-frequency oscillatory activity in thalamocortical neurons.

Dynamic balance of metabotropic inputs causes dorsal horn neurons to switch functional states

Sensory relay structures in the spinal cord dorsal horn are now thought to be active processing structures that function before supraspinal sensory integration. Dorsal horn neurons directly receive nociceptive (pain) signals from the periphery, express a high degree of functional plasticity and are involved in long-term sensitization and chronic pain. We show here that deep dorsal horn neurons (DHNs) in Wistar rats can switch their intrinsic firing properties from tonic to plateau or endogenous bursting patterns, depending upon the balance of control by metabotropic glutamate (mGlu) and GABA(B) receptors. We further show that this modulation acts on at least one common target, the inwardly rectifying potassium channel (Kir3). Finally, we found that these firing modes correspond to specific functional states of information transfer in which dorsal horn neurons can faithfully transmit, greatly enhance or block the transfer of nociceptive information.

Synaptic background noise controls the input/output characteristics of single cells in an in vitro model of in vivo activity

In vivo, in vitro and computational studies were used to investigate the impact of the synaptic background activity observed in neocortical neurons in vivo. We simulated background activity in vitro using two stochastic Ornstein-Uhlenbeck processes describing glutamatergic and GABAergic synaptic conductances, which were injected into a cell in real time using the dynamic clamp technique. With parameters chosen to mimic in vivo conditions, layer 5 rat prefrontal cortex cells recorded in vitro were depolarized by about 15 mV, their membrane fluctuated with a S.D. of about 4 mV, their input resistances decreased five-fold, their spontaneous firing had a high coefficient of variation and an average firing rate of about 5-10 Hz. Brief changes in the variance of the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synaptic conductance fluctuations induced time-locked spiking without significantly changing the average membrane potential of the cell. These transients mimicked increases in the correlation of excitatory inputs. Background activity was highly effective in modulating the firing-rate/current curve of the cell: the variance of the simulated gamma-aminobutyric acid (GABA) and AMPA conductances individually set the input/output gain, the mean excitatory and inhibitory conductances set the working point, and the mean inhibitory conductance controlled the input resistance. An average ratio of inhibitory to excitatory mean conductances close to 4 was optimal in generating membrane potential fluctuations with high coefficients of variation. We conclude that background synaptic activity can dynamically modulate the input/output properties of individual neocortical neurons in vivo.

Detectability of excitatory versus inhibitory drive in an integrate-and-fire-or-burst thalamocortical relay neuron model

Although inhibitory inputs are often viewed as equal but opposite to excitatory inputs, excitatory inputs may alter the firing of postsynaptic cells more effectively than inhibitory inputs. This is because spike cancellation produced by an inhibitory input requires coincidence in time, whereas an excitatory input can add spikes with less temporal constraint. To test for such potential differences, especially in the context of the function of thalamocortical (TC) relay nuclei, we used a stochastic "integrate-and-fire-or-burst" TC neuron model to quantify the detectability of excitatory and inhibitory drive in the presence and absence of the low-threshold Ca2+ current, I(T), and the hyperpolarization-activated cation conductance, I(sag). We find that excitatory inputs are generally superior drivers compared with inhibitory inputs in part because spontaneous activity of a postsynaptic neuron is not required in the case of excitatory drive. Interestingly, the presence of the low-threshold Ca2+ current, I(T) in a postsynaptic neuron allows the robust detection of inhibitory drive over a certain range of spontaneous and driven activity, a range that can be extended by the presence of the hyperpolarization-activated cation conductance, I(sag). These simulations suggest a possible reinterpretation of the role of inhibitory inputs, such as those to the thalamus.

NEUROFIT: software for fitting Hodgkin-Huxley models to voltage-clamp data

I introduce publicly available software for accurate fitting of Hodgkin-Huxley models to voltage-clamp data. I describe the model and non-linear fitting procedure employed by the software and compare its results with the usual method of fitting such models using potassium A-current data from a pyloric dilator cell of the lobster Panulirus interruptus and sodium current data from an electrocyte cell of the electric fish Sternopygus macrurus. The set of parameter values for the model determined by this software yield current traces that are substantially closer to the observed data than those determined from the usual fitting method. This improvement is due to the fact that the software fits all of the parameters simultaneously utilizing all of the data rather than fitting steady-state and time constant parameters disjointly using peak currents and portions of the rising and falling phases. I analyze the convergence properties of the software's fitting algorithm using simulated data showing that accurate parameter values are obtained for most of the parameters using any reasonable initial values. The software also incorporates a linear pre-estimation procedure to help in determining reasonable initial values for the full non-linear algorithm. I illustrate and discuss some of the inadequacies of voltage-clamp data.

Model of thalamocortical slow-wave sleep oscillations and transitions to activated States

During natural slow-wave sleep (SWS) in nonanesthetized cats, silent (down) states alternate with active (up) states; the down states are absent during rapid-eye-movement sleep and waking. Oscillations (<1 Hz) in SWS and transformation to an activated awake state were investigated with intracellular recordings in vivo and with computational models of the corticothalamic system. Occasional summation of the miniature EPSPs during the hyperpolarized (silent) phase of SWS oscillation activated the persistent sodium current and depolarized the membrane of cortical pyramidal (PY) cells sufficiently for spike generation. In the model, this triggered the active phase, which was maintained by lateral PY-PY excitation and persistent sodium current. Progressive depression of the excitatory interconnections and activation of Ca2+-dependent K+ current led to termination of the 20-25 Hz activity after 500-1000 msec. Including thalamocortical (TC) and thalamic reticular neurons in the model increased the duration of the active epochs up to 1-1.5 sec and introduced waning spindle sequences. An increase in acetylcholine activity, which is associated with activated states, was modeled by the reduction in the K+ leak current in PY and TC cells and by a decrease in intracortical PY-PY synaptic conductances. These changes eliminated the hyperpolarizing phases of network activity and transformed cortical neurons to tonic firing at 15-20 Hz. During the transition from SWS to the activated state, the input resistance of cortical neurons gradually increased and, in a fully activated state, reached the same or even higher values as during silent phases of SWS oscillations. The model describes many essential features of SWS and activated states in the thalamocortical system as well as the transition between them.

Modelling large scale neuronal networks using 'average neurones'

Large scale neuronal network models have become important tools in studying the information transmission within the CNS. In most cases, these models use simplifying assumptions because of unavailable data (e.g. unknown exact network connectivity), and for technical reasons (to preserve numerical stability of the model). Here, we present a novel approach, based on a probabilistic connectivity principle, to this modelling problem for which no knowledge of the exact network connectivity is required. This principle makes it sufficient to compute only the typical neuronal behaviour, represented by 'average neurones', in the network. As a consequence, detailed neurone models can be employed without seriously compromising computational efficiency. Our model thus provides a viable alternative to deterministic models.

Subcellular interactions between parallel fibre and climbing fibre signals in Purkinje cells predict sensitivity of classical conditioning to interstimulus interval

Classical conditioning of the nictitating membrane response requires a specific temporal interval between conditioned stimulus and unconditioned stimulus, and produces an increase in Protein Kinase C (PKC) activation in Purkinje cells. To evaluate whether biochemical interactions within the Purkinje cell may explain the temporal sensitivity, a model of PKC activation by Ca2+, diacylglycerol (DAG), and arachidonic acid (AA) is developed. Ca2+ elevation is due to CF stimulation and IP3 induced Ca2+ release (IICR). DAG and IP3 result from PF stimulation, while AA results from phospholipase A2 (PLA2). Simulations predict increased PKC activation when PF stimulation precedes CF stimulation by 0.1 to 3 s. The sensitivity of IICR to the temporal relation between PF and CF stimulation, together with the buffering system of Purkinje cells, significantly contribute to the temporal sensitivity.

Feedback inhibition controls spike transfer in hybrid thalamic circuits

Sensory information reaches the cerebral cortex through the thalamus, which differentially relays this input depending on the state of arousal. Such 'gating' involves inhibition of the thalamocortical relay neurons by the reticular nucleus of the thalamus, but the underlying mechanisms are poorly understood. We reconstructed the thalamocortical circuit as an artificial and biological hybrid network in vitro. With visual input simulated as retinal cell activity, we show here that when the gain in the thalamic inhibitory feedback loop is greater than a critical value, the circuit tends towards oscillations -- and thus imposes a temporal decorrelation of retinal cell input and thalamic relay output. This results in the functional disconnection of the cortex from the sensory drive, a feature typical of sleep states. Conversely, low gain in the feedback inhibition and the action of noradrenaline, a known modulator of arousal, converge to increase input output correlation in relay neurons. Combining gain control of feedback inhibition and modulation of membrane excitability thus enables thalamic circuits to finely tune the gating of spike transmission from sensory organs to the cortex.

Calcium waves and closure of potassium channels in response to GABA stimulation in Hermissenda type B photoreceptors

Classical conditioning of Hermissenda crassicornis requires the paired presentation of a conditioned stimulus (light) and an unconditioned stimulus (turbulence). Light stimulation of photoreceptors leads to production of diacylglycerol, an activator of protein kinase C, and inositol triphosphate (IP(3)), which releases calcium from intracellular stores. Turbulence causes hair cells to release GABA onto the terminal branches of the type B photoreceptor. One prior study has shown that GABA stimulation produces a wave of calcium that propagates from the terminal branches to the soma and raises the possibility that two sources of calcium are required for memory storage. GABA stimulation also causes an inhibitory postsynaptic potential (IPSP) followed by a late depolarization and increase in input resistance, whose cause has not been identified. A model was developed of the effect of GABA stimulation on the Hermissenda type B photoreceptor to evaluate the currents underlying the late depolarization and to evaluate whether a calcium wave could propagate from the terminal branches to the soma. The model included GABA(A), GABA(B), and calcium-sensitive potassium leak channels; calcium dynamics including release of calcium from intracellular stores; and the biochemical reactions leading from GABA(B) receptor activation to IP(3) production. Simulations show that it is possible for a wave of calcium to propagate from the terminal branches to the soma. The wave is initiated by IP(3)-induced calcium release but propagation requires release through the ryanodine receptor channel where IP(3) concentration is small. Wave speed is proportional to peak calcium concentration at the crest of the wave, with a minimum speed of 9 microM/s in the absence of IP(3). Propagation ceases when peak concentration drops below 1.2 microM; this occurs if the rate of calcium pumping into the endoplasmic reticulum is too large. Simulations also show that both a late depolarization and an increase in input resistance occur after GABA stimulation. The duration of the late depolarization corresponds to the duration of potassium leak channel closure. Neither the late depolarization nor the increase in input resistance are observed when a transient calcium current and a hyperpolarization-activated current are added to the model as replacement for closure of potassium leak channels. Thus the late depolarization and input resistance elevation can be explained by a closure of calcium-sensitive leak potassium currents but cannot be explained by a transient calcium current and a hyperpolarization-activated current.

Electrotonic profile and passive propagation of synaptic potentials in three subpopulations of hippocampal CA1 interneurons

To elucidate the role of dendritic morphology in signal transfer, the passive propagation of somatic and dendritic potentials was compared in multi-compartment models of three interneuron subpopulations in the CA1 region. Nine calbindin-, 15 calretinin- and 10 parvalbumin-containing cells were modelled incorporating the detailed geometry, the currents of the action potentials in the soma, and the AMPA, N-methyl-D-aspartate and GABA-B receptor-mediated postsynaptic currents in the dendrites. The cable properties show characteristic differences among the subpopulations. The morphotonic length of calbindin and calretinin cell dendrites is larger than of parvalbumin cells. Thus parvalbumin cells are more compact than calbindin or calretinin cells unless the ratio of their axial and membrane resistivities exceeds the ratios of the other two cell types by more than 33%. In calbindin cells, the distal parts of the extremely long dendrites that invade the alveus are virtually isolated from the soma for passively propagating signals. The synaptic potentials evoked at a given morphotonic distance from the soma show larger differences locally on the dendrites than on the soma in all subpopulations. Both the somatic and dendritic amplitude ratios are the smallest in PV cells. In calbindin cells the somatic amplitude of synaptic potentials evoked at the same morphotonic distance from the soma is similar regardless of the number of branchpoints along their path. In calretinin and parvalbumin cells, from dendrites with long primary segments synaptic potentials reach the soma with larger amplitude than from dendrites that are branching close to the soma. The dendrites with the larger impact on somatic membrane potential are usually the dendrites that enter the stratum lacunosum-moleculare. These results indicate that dendritic morphology plays a role in changing the effectiveness of synaptic potentials evoked at different dendritic locations, and in this way is likely to be an important factor in determining the integrative properties of the different neuron populations.

Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks

To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of postspike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate-and-fire conductance-based point neurons with all-to-all coupling. For six-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step of Delta(t) = 0.5 x 10(-3) seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10(-5) seconds or 10(-9) seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.

Model of transient oscillatory synchronization in the locust antennal lobe

Transient pairwise synchronization of locust antennal lobe (AL) projection neurons (PNs) occurs during odor responses. In a Hodgkin-Huxley-type model of the AL, interactions between excitatory PNs and inhibitory local neurons (LNs) created coherent network oscillations during odor stimulation. GABAergic interconnections between LNs led to competition among them such that different groups of LNs oscillated with periodic Ca(2+) spikes during different 50-250 ms temporal epochs, similar to those recorded in vivo. During these epochs, LN-evoked IPSPs caused phase-locked, population oscillations in sets of postsynaptic PNs. The model shows how alternations of the inhibitory drive can temporally encode sensory information in networks of neurons without precisely tuned intrinsic oscillatory properties.

Model of cellular and network mechanisms for odor-evoked temporal patterning in the locust antennal lobe

Locust antennal lobe (AL) projection neurons (PNs) respond to olfactory stimuli with sequences of depolarizing and hyperpolarizing epochs, each lasting hundreds of milliseconds. A computer simulation of an AL network was used to test the hypothesis that slow inhibitory connections between local neurons (LNs) and PNs are responsible for temporal patterning. Activation of slow inhibitory receptors on PNs by the same GABAergic synapses that underlie fast oscillatory synchronization of PNs was sufficient to shape slow response modulations. This slow stimulus- and neuron-specific patterning of AL activity was resistant to blockade of fast inhibition. Fast and slow inhibitory mechanisms at synapses between LNs and PNs can thus form dynamical PN assemblies whose elements synchronize transiently and oscillate collectively, as observed not only in the locust AL, but also in the vertebrate olfactory bulb.

Correlation detection and resonance in neural systems with distributed noise sources

We investigated the resonance behavior in model neurons receiving a large number of random synaptic inputs, whose distributed nature permits one to introduce correlations between them and investigate its effect on cellular responsiveness. A change in the strength of this background led to enhanced responsiveness, consistent with stochastic resonance. Altering the correlation revealed a type of resonance behavior in which the neuron is sensitive to statistical properties rather than the strength of the noise. Remarkably, the neuron could detect weak correlations among the distributed inputs within millisecond time scales.

Variability of excitatory currents due to single-channel noise, receptor number and morphological heterogeneity

Patch clamp recordings of excitatory postsynaptic currents (EPSCs) in central neurons reveal large fluctuations in amplitudes and decay times of AMPA-receptor-mediated EPSCs. By using Monte Carlo simulations of synaptic transmission in brainstem interneurons, we tested several hypothesis that could account for the observed variability. The coefficient of variation (CV) of 0.5 for miniature amplitudes cannot be explained by fluctuations in vesicle content or receptor distribution, but is traced to variations in receptor number, which is estimated as 77+/-39 receptors per bouton. As the variability of rise times reflects fluctuations in size of the post-synaptic density and heterogeneity of the receptor distribution, the relatively small CV=0.37 of experimentally determined values points to a homogeneous arrangement of receptors. Within our model the large variability of decay times (CV=0.49) can only be explained by fluctuations in the transmitter time course (mean residence times of 0.4+/-0.13 ms), presumably resulting from heterogeneities in synaptic morphology. Hence, our simulations indicate that different noise sources control the variability of amplitudes, rise and decay times. In particular, the distribution of decay times yields information about the synaptic transmission process, which cannot be obtained from other observables.

Computer-simulation studies on roles of potassium currents in neurotransmission of the auditory nerve

Our previous work showed that action potentials (APs) fired in spiral ganglion (SG) neurons broaden gradually as a result of cumulative inactivation of the potassium current (I(K)), or with the application of a tinnitus-inducing drug (quinine). These results led us to speculate that AP width could affect neurotransmission of the auditory nerve under both normal and pathological conditions. This study used both experimental and theoretical approaches to test this hypothesis. We first measured the effect of AP broadening on Ca2+ entry into SG neurons. The effect of pre-synaptic AP broadening on post-synaptic responses was then assessed using computer-simulations. Results showed that wider presynaptic APs augmented responses of all types of postsynaptic glutamatergic receptors mainly by amplifying responses of postsynaptic receptors whose locations were not well aligned with the presynaptic release sites. A cumulative inactivation of I(K) in SG neurons significantly enhanced the responses of kainate receptors at all spike rates, while the augmentations for the alpha-amino-3-hydroxy-5-methylisoxazole-4-propionic acid and N-methyl-D-aspartic acid receptors were most prominent below 100 spikes/s. These modeling results suggest that, in addition to the AP firing rate and timing, the width of APs could affect the neurotransmission of the auditory nerve under both normal and pathological conditions.

Differential filtering of two presynaptic depression mechanisms

The filtering of input signals carried out at synapses is key to the information processing performed by networks of neurons. Two forms of presynaptic depression, vesicle depletion and G-protein inhibition of Ca2+ channels, can play important roles in the presynaptic processing of information. Using computational models, we demonstrate that these two forms of depression filter information in very different ways. G-protein inhibition acts as a high-pass filter, preferentially transmitting high-frequency input signals to the postsynaptic cell, while vesicle depletion acts as a low-pass filter. We examine how these forms of depression separately and together affect the steady-state postsynaptic responses to trains of stimuli over a range of frequencies. Finally, we demonstrate how differential filtering permits the multiplexing of information within a single impulse train.