Showing papers in "Journal of Computational Neuroscience in 2003"

Dynamics of spiking neurons connected by both inhibitory and electrical coupling.

Abstract: We study the dynamics of a pair of intrinsically oscillating leaky integrate-and-fire neurons (identical and noise-free) connected by combinations of electrical and inhibitory coupling. We use the theory of weakly coupled oscillators to examine how synchronization patterns are influenced by cellular properties (intrinsic frequency and the strength of spikes) and coupling parameters (speed of synapses and coupling strengths). We find that, when inhibitory synapses are fast and the electrotonic effect of the suprathreshold portion of the spike is large, increasing the strength of weak electrical coupling promotes synchrony. Conversely, when inhibitory synapses are slow and the electrotonic effect of the suprathreshold portion of the spike is small, increasing the strength of weak electrical coupling promotes antisynchrony (see Fig. 10). Furthermore, our results indicate that, given a fixed total coupling strength, either electrical coupling alone or inhibition alone is better at enhancing neural synchrony than a combination of electrical and inhibitory coupling. We also show that these results extend to moderate coupling strengths.

Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics.

Abstract: Behavior of a network of neurons is closely tied to the properties of the individual neurons. We study this relationship in models of layer II stellate cells (SCs) of the medial entorhinal cortex. SCs are thought to contribute to the mammalian theta rhythm (4-12 Hz), and are notable for the slow ionic conductances that constrain them to fire at rates within this frequency range. We apply "spike time response" (STR) methods, in which the effects of synaptic perturbations on the timing of subsequent spikes are used to predict how these neurons may synchronize at theta frequencies. Predictions from STR methods are verified using network simulations. Slow conductances often make small inputs "effectively large"; we suggest that this is due to reduced attractiveness or stability of the spiking limit cycle. When inputs are (effectively) large, changes in firing times depend nonlinearly on synaptic strength. One consequence of nonlinearity is to make a periodically firing model skip one or more beats, often leading to the elimination of the anti-synchronous state in bistable models. Biologically realistic membrane noise makes such "cycle skipping" more prevalent, and thus can eradicate bistability. Membrane noise also supports "sparse synchrony," a phenomenon in which subthreshold behavior is uncorrelated, but there are brief periods of synchronous spiking.

New roles for the gamma rhythm: population tuning and preprocessing for the Beta rhythm.

Abstract: Gamma (30-80 Hz) and beta (12-30 Hz) oscillations such as those displayed by in vitro hippocampal (CA1) slice preparations and by in vivo neocortical EEGs often occur successively, with a spontaneous transition between them. In the gamma rhythm, pyramidal cells fire together with the interneurons, while in the beta rhythm, pyramidal cells fire on a subset of cycles of the interneurons. It is shown that gamma and beta rhythms have different properties with respect to creation of cell assemblies. In the presence of heterogeneous inputs to the pyramidal cells, the gamma rhythm creates an assembly of firing pyramidal cells from cells whose drive exceeds a threshold. During the gamma to beta transition, a slow outward potassium current is activated, and as a result the cell assembly vanishes. The slow currents make each of the pyramidal cells fire with a beta rhythm, but the field potential of the network still displays a gamma rhythm. Hebbian changes of connections among the pyramidal cells give rise to a beta rhythm, and the cell assemblies are recovered with a temporal separation between cells firing in different cycles. We present experimental evidence showing that such a separation can occur in hippocampal slices.

Tuning neocortical pyramidal neurons between integrators and coincidence detectors.

Abstract: Do cortical neurons operate as integrators or as coincidence detectors? Despite the importance of this question, no definite answer has been given yet, because each of these two views can find its own experimental support. Here we investigated this question using models of morphologically-reconstructed neocortical pyramidal neurons under in vivo like conditions. In agreement with experiments we find that the cell is capable of operating in a continuum between coincidence detection and temporal integration, depending on the characteristics of the synaptic inputs. Moreover, the presence of synaptic background activity at a level comparable to intracellular measurements in vivo can modulate the operating mode of the cell, and act as a switch between temporal integration and coincidence detection. These results suggest that background activity can be viewed as an important determinant of the integrative mode of pyramidal neurons. Thus, background activity not only sharpens cortical responses but it can also be used to tune an entire network between integration and coincidence detection modes.

AHP's, HAP's and DAP's: how potassium currents regulate the excitability of rat supraoptic neurones.

Abstract: We have constructed mathematical models of the electrical activity of two hypothalamic supraoptic neuro-secretory cell-types, and we support our models with new calcium imaging and in vitro electrophysiological data. These cells are neurones that project to the pituitary gland and secrete either of two hormones, oxytocin or vasopressin, into the blood from their axonal terminals. Oxytocin-secreting and vasopressin-secreting cells are closely related and physically they differ only subtly, however when physiologically stressed their discharge patterns are dramatically distinct. We first show how each potassium current contributes to the action-potentials and after-potentials observed in these cells, and we show how these after-potentials are correlated to intra-cellular calcium elevations. We then show how these currents regulate the excitability of these cells and consequently shape their discharge pattern.

Spike generating dynamics and the conditions for spike-time precision in cortical neurons.

Abstract: Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.

Stimulus-invariant processing and spectrotemporal reverse correlation in primary auditory cortex

Abstract: The spectrotemporal receptive field (STRF) provides a versatile and integrated, spectral and temporal, functional characterization of single cells in primary auditory cortex (AI) In this paper, we explore the origin of, and relationship between, different ways of measuring and analyzing an STRF We demonstrate that STRFs measured using a spectrotemporally diverse array of broadband stimuli—such as dynamic ripples, spectrotemporally white noise, and temporally orthogonal ripple combinations (TORCs)—are very similar, confirming earlier findings that the STRF is a robust linear descriptor of the cell We also present a new deterministic analysis framework that employs the Fourier series to describe the spectrotemporal modulations contained in the stimuli and responses Additional insights into the STRF measurements, including the nature and interpretation of measurement errors, is presented using the Fourier transform, coupled to singular-value decomposition (SVD), and variability analyses including bootstrap The results promote the utility of the STRF as a core functional descriptor of neurons in AI

Presynaptic frequency- and pattern-dependent filtering.

Abstract: Dual intracellular recordings from pairs of synaptically connected neurones have demonstrated that the frequency-dependent pattern of transmitter release varies dramatically between different classes of connections. Somewhat surprisingly, these patterns are not determined by the class of neurone supplying the axon alone, but to a large degree by the class of postsynaptic neurone. A wide range of presynaptic mechanisms, some that depress the release of transmitter and others that enhance release have been identified. It is the selective expression of these different mechanisms that determines the unique frequency- and pattern-dependent properties of each class of connection. Although the molecular interactions underlying these several mechanisms have yet to be fully identified, the wealth and complexity of the protein-protein and protein-lipid interactions that have been shown to control the release of transmitter suggest many ways in which the properties of a synapse may be tuned to respond to particular patterns and frequencies.

Propagating waves in visual cortex: a large-scale model of turtle visual cortex.

Abstract: This article describes a large-scale model of turtle visual cortex that simulates the propagating waves of activity seen in real turtle cortex. The cortex model contains 744 multicompartment models of pyramidal cells, stellate cells, and horizontal cells. Input is provided by an array of 201 geniculate neurons modeled as single compartments with spike-generating mechanisms and axons modeled as delay lines. Diffuse retinal flashes or presentation of spots of light to the retina are simulated by activating groups of geniculate neurons. The model is limited in that it does not have a retina to provide realistic input to the geniculate, and the cortex and does not incorporate all of the biophysical details of real cortical neurons. However, the model does reproduce the fundamental features of planar propagating waves. Activation of geniculate neurons produces a wave of activity that originates at the rostrolateral pole of the cortex at the point where a high density of geniculate afferents enter the cortex. Waves propagate across the cortex with velocities of 4 μm/ms to 70 μm/ms and occasionally reflect from the caudolateral border of the cortex.

How does connectivity between cortical areas depend on brain size? Implications for efficient computation

Abstract: A formula for an average connectivity between cortical areas in mammals is derived. Based on comparative neuroanatomical data, it is found, surprisingly, that this connectivity is either only weakly dependent or independent of brain size. It is discussed how this formula can be used to estimate the average length of axons in white matter. Other allometric relations, such as cortical patches and area sizes vs. brain size, are also provided. Finally, some functional implications, with an emphasis on efficient cortical computation, are discussed as well.

On the Integration of Subthreshold Inputs from Perforant Path and Schaffer Collaterals in Hippocampal CA1 Pyramidal Neurons

Abstract: Using a realistic model of a CA1 hippocampal pyramidal neuron, we make experimentally testable predictions on the roles of the non-specific cation current, Ih, and the A-type Potassium current, I A, in modulating the temporal window for the integration of the two main excitatory afferent pathways of a CA1 neuron, the Schaffer Collaterals and the Perforant Path. The model shows that the experimentally observed increase in the dendritic density of Ih and I A could have a major role in constraining the temporal integration window for these inputs, in such a way that a somatic action potential (AP) is elicited only when they are activated with a relative latency consistent with the anatomical arrangement of the hippocampal circuitry.

Estimating the strength and direction of functional coupling in the lamprey spinal cord.

Abstract: A method of estimating coupling strength between two neural oscillators based on their spikes trains (Kiemel and Cohen, J. Comput. Neurosci. 5: 267–284, 1998) is tested using simulated data and then applied to experimental data from the central pattern generator (CPG) for swimming in the lamprey. The method is tested using a model of two connectionist oscillators and a model of two endogenously bursting cells. For both models, the method provides useful estimates of the relative strength of coupling in each direction, as well as estimates of total strength. The method is applied to pairs of motor-nerve recordings from isolated 50-segment pieces of spinal cords from adult silver lampreys (Ichthyomyzon unicuspus). The strength and direction of coupling is estimated under control conditions and conditions in which intersegmental coupling between the two recording locations is weakened by hemisections of the spinal cords and/or chambers containing an inhibitory solution that blocks firing in postsynaptic cells. The relevance of these measures in constraining models of the CPG is discussed.

Type I burst excitability.

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

Analysis of state-dependent transitions in frequency and long-distance coordination in a model oscillatory cortical circuit.

Abstract: Changes in behavioral state are typically accompanied by changes in the frequency and spatial coordination of rhythmic activity in the neocortex. In this article, we analyze the effects of neuromodulation on ionic conductances in an oscillating cortical circuit model. The model consists of synaptically-coupled excitatory and inhibitory neurons and supports rhythmic activity in the alpha, beta, and gamma ranges. We find that the effects of neuromodulation on ionic conductances are, by themselves, sufficient to induce transitions between synchronous gamma and beta rhythms and asynchronous alpha rhythms. Moreover, these changes are consistent with changes in behavioral state, with the rhythm transitioning from the slower alpha to the faster gamma and beta as arousal increases. We also observe that it is the same set of underlying intrinsic and network mechanisms that appear to be simultaneously responsible for both the observed transitions between the rhythm types and between their synchronization properties. Spike time response curves (STRCs) are used to study the relationship between the transitions in rhythm and the underlying biophysics.

Linear and nonlinear measures and seizure anticipation in temporal lobe epilepsy.

Abstract: In a recent paper, we showed that the value of a nonlinear quantity computed from scalp electrode data was correlated with the time to a seizure in patients with temporal lobe epilepsy. In this paper we study the relationship between the linear and nonlinear content and analyses of the scalp data. We do this in two ways. First, using surrogate data methods, we show that there is important nonlinear structure in the scalp electrode data to which our methods are sensitive. Second, we study the behavior of some simple linear metrics on the same set of scalp data to see whether the nonlinear metrics contain additional information not carried by the linear measures. We find that, while the nonlinear measures are correlated with time to seizure, the linear measures are not, over the time scales we have defined. The linear and nonlinear measures are themselves apparently linearly correlated, but that correlation can be ascribed to the influence of a small set of outliers, associated with muscle artifact. A remaining, more subtle relation between the variance of the values of a nonlinear measure and the expectation value of a linear measure persists. Implications of our observations are discussed.

No parallel fiber volleys in the cerebellar cortex: evidence from cross-correlation analysis between Purkinje cells in a computer model and in recordings from anesthetized rats.

Abstract: Purkinje cells aligned on the medio-lateral axis share a large proportion of their ∼175,000 parallel fiber inputs. This arrangement has led to the hypothesis that movement timing is coded in the cerebellum by beams of synchronously active parallel fibers. In computer simulations I show that such synchronous activation leads to a narrow spike cross-correlation between pairs of Purkinje cells. This peak was completely absent when shared parallel fiber input was active in an asynchronous mode. To determine the presence of synchronous parallel fiber beams {in vivo} I recorded from pairs of Purkinje cells in crus IIa of anesthetized rats. I found a complete absence of precise spike synchronization, even when both cells were strongly modulated in their spike rate by trains of air-puff stimuli to the face. These results indicate that Purkinje cell spiking is not controlled by volleys of synchronous parallel fiber inputs in the conditions examined. Instead, the data support a model by which granule cells primarily control Purkinje cell spiking via dynamic population rate changes.

Design parameters of the fan-out phase of sensory systems.

Abstract: This paper focuses on the calculation of boundary values for the design parameters in the fan-out phase of the olfactory system of insects. Three main criteria are taken into account to determine the boundaries of the parameters: (i) information conservation, (ii) low energy costs and (iii) full involvement of all the neurons. These criteria serve to determine the structural parameters that produce a sufficient minimal response. Analytical calculations lead to a few general expressions which show how the main internal parameters can be obtained for any system with similar characteristics. We calculate the optimal threshold for coincidence detection, connectivity and output activity values that verify criteria (i), (ii) and (iii). The range of parameter values obtained by these calculations include those observed in the olfactory system of the locust.

Early cortical orientation selectivity: how fast inhibition decodes the order of spike latencies.

Abstract: Following a flashed stimulus, I show that a simple neurophysiological mechanism in the primary visual system can generate orientation selectivity based on the first incoming spikes. A biological model of the lateral geniculate nucleus generates an asynchronous wave of spikes, with the most strongly activated neurons firing first. Geniculate activation leads to both the direct excitation of a cortical pyramidal cell and disynaptic feed-forward inhibition. The mechanism provides automatic gain control, so the cortical neurons respond over a wide range of stimulus contrasts. It also demonstrates the biological plausibility of a new computationally efficient neural code: latency rank order coding.

Noise, not stimulus entropy, determines neural information rate.

Abstract: In the quest for deciphering the neural code, theoretical advances were made which allow for the determination of the information rate inherent in the spike trains of nerve cells. However, up to now, the dependence of the information rate on stimulus parameters has not been studied in any neuron in a systematic way. Here, I investigate the information carried by the spike trains of H1, a motion-sensitive visual interneuron of the blowfly (Calliphora vicina) using a moving grating as a stimulus. Stimulus parameters fall in two classes: those that have only a minor effect on the information rate like increasing the frequency bandwidth or the maximum amplitude of the stimulus velocity, and those which dramatically affect the neural information rate, like varying the spatial size or the contrast of the visual pattern being moved. It appears that, for a broad range of complex stimuli, the neuron covers the stimulus with its whole response repertoire regardless of the stimulus entropy, with the information rate being limited by the noise of the stimulus and the neural hardware.

Mathematical models of cochlear nucleus onset neurons: I. Point neuron with many weak synaptic inputs.

Abstract: The cochlear nucleus (CN) presents a unique opportunity for quantitatively studying input-output transformations by neurons because it gives rise to a variety of different response types from a relatively homogeneous input source, the auditory nerve (AN). Particularly interesting among CN neurons are Onset (On) neurons, which have a prominent response to the onset of sustained sounds followed by little or no response in the steady-state. On neurons contrast sharply with their AN inputs, which respond vigorously throughout stimuli. On neurons can entrain to stimuli (firing once per cycle of a periodic stimulus) at up to 1000 Hz, unlike their AN inputs. To understand the mechanisms underlying these response patterns, we tested whether an integrate-to-threshold point-neuron model with a fixed refractory period can account for On discharge patterns for tones, systematically examining the effect of membrane time constant and the number and strength of the exclusively excitatory AN synaptic inputs. To produce both onset responses to high-frequency tone bursts and entrainment to a broad range of low-frequency tones, the model must have a short time constant (≈0.125 ms) and a large number (>100) of weak synaptic inputs, properties that are consistent with the electrical properties and anatomy of On-responding cells. With these parameters, the model acts like a coincidence detector with a threshold-like relationship between the instantaneous discharge rates of the output and the inputs. Onset responses to high-frequency tone bursts result because the threshold effect enhances the initial response of the AN inputs and suppresses their relatively lower sustained response. However, when the model entrains across a broad range of frequencies, it also produces short interspike intervals at the onset of high-frequency tone bursts, a response pattern not found in all types of On neurons. These results show a tradeoff, that may be a general property of many neurons, between following rapid stimulus fluctuations and responding without short interspike intervals at the onset of sustained stimuli.

An analysis of the reliability phenomenon in the FitzHugh-Nagumo model.

Abstract: The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes—the excitable, bistable, and oscillatory ones. We use tools from the random dynamical systems theory, such as the pullbacks and the estimation of the Lyapunov exponents and rotation number. The results show that for most stimulus intensities, trajectories converge to a single stochastic equilibrium point, and the leading Lyapunov exponent is negative. Consequently, in these regimes the discharge times are reliable in the sense that repeated presentation of the same aperiodic input segment evokes similar firing times after some transient time. Surprisingly, for a certain range of stimulus intensities, unreliable firing is observed due to the onset of stochastic chaos, as indicated by the estimated positive leading Lyapunov exponents. For this range of stimulus intensities, stochastic chaos occurs in the bistable regime and also expands in adjacent parts of the excitable and oscillating regimes. The obtained results are valuable in the explanation of experimental observations concerning the reliability of neurons stimulated with broad-band Gaussian inputs. They reveal two distinct neuronal response types. In the regime where the first Lyapunov has negative values, such inputs eventually lead neurons to reliable firing, and this suggests that any observed variance of firing times in reliability experiments is mainly due to internal noise. In the regime with positive Lyapunov exponents, the source of unreliable firing is stochastic chaos, a novel phenomenon in the reliability literature, whose origin and function need further investigation.

Decoding Temporal Information Through Slow Lateral Excitation in the Olfactory System of Insects

Abstract: Sensory information is represented in a spatio-temporal code in the antennal lobe, the first processing stage of the olfactory system of insects We propose a novel mechanism for decoding this information in the next processing stage, the mushroom body The Kenyon cells in the mushroom body of insects exhibit lateral excitatory connections at their axons We demonstrate that slow lateral excitation between Kenyon cells allows one to decode sequences of activity in the antennal lobe We are thus able to clarify the role of the existing connections as well as to demonstrate a novel mechanism for decoding temporal information in neuronal systems This mechanism complements the variety of existing temporal decoding schemes It seems that neuronal systems not only have a rich variety of code types but also quite a diversity of algorithms for transforming different codes into each other

Computational Constraints that may have Favoured the Lamination of Sensory Cortex

Abstract: At the transition from early reptilian ancestors to primordial mammals, the areas of sensory cortex that process topographic modalities acquire the laminar structure of isocortex A prominent step in lamination is granulation, whereby the formerly unique principal layer of pyramidal cells is split by the insertion of a new layer of excitatory, but intrinsic, granule cells, layer IV I consider the hypothesis that granulation, and the differentiation between supra- and infra-granular pyramidal layers, may be advantageous to support fine topography in their sensory maps Fine topography implies a generic distinction between "where" information, explicitly mapped on the cortical sheet, and "what" information, represented in a distributed fashion as a distinct firing pattern across neurons These patterns can be stored on recurrent collaterals in the cortex, and such memory can help substantially in the analysis of current sensory input The simulation of a simplified network model demonstrates that a non-laminated patch of cortex must compromise between transmitting "where" information or retrieving "what" information The simulation of a modified model including differentiation of a granular layer shows a modest but significant quantitative advantage, expressed as a less severe trade-off between "what" and "where" The further connectivity differentiation between infra-granular and supra-granular pyramidal layers is shown to match the mix of "what" and "where" information optimal for their respective target structures

Dendritic Synchrony and Transient Dynamics in a Coupled Oscillator Model of the Dopaminergic Neuron

Abstract: Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.

The Influences of I h on Temporal Summation in Hippocampal CA1 Pyramidal Neurons: A Modeling Study

Abstract: Recent experimental and theoretical studies have found that active dendritic ionic currents can compensate for the effects of electrotonic attenuation In particular, temporal summation, the percentage increase in peak somatic voltage responses invoked by a synaptic input train, is independent of location of the synaptic input in hippocampal CA1 pyramidal neurons under normal conditions This independence, known as normalization of temporal summation, is destroyed when the hyperpolarization-activated current, I h, is blocked [Magee JC (1999a), Nature Neurosci 2: 508–514] Using a compartmental model derived from morphological recordings of hippocampal CA1 pyramidal neurons, we examined the hypothesis that I h was primarily responsible for normalization of temporal summation We concluded that this hypothesis was incomplete With a model that included I h, the persistent Na+ current (I NaP), and the transient A-type K+ current (I A), however, we observed normalization of temporal summation across a wide range of synaptic input frequencies, in keeping with experimental observations

A cooperation and competition based simple cell receptive field model and study of feed-forward linear and nonlinear contributions to orientation selectivity.

Abstract: We present a model for development of orientation selectivity in layer IV simple cells. Receptive field (RF) development in the model, is determined by diffusive cooperation and resource limited competition guided axonal growth and retraction in geniculocortical pathway. The simulated cortical RFs resemble experimental RFs. The receptive field model is incorporated in a three-layer visual pathway model consisting of retina, LGN and cortex. We have studied the effect of activity dependent synaptic scaling on orientation tuning of cortical cells. The mean value of hwhh (half width at half the height of maximum response) in simulated cortical cells is 58° when we consider only the linear excitatory contribution from LGN. We observe a mean improvement of 22.8° in tuning response due to the non-linear spiking mechanisms that include effects of threshold voltage and synaptic scaling factor.

Spike-based synaptic plasticity and the emergence of direction selective simple cells: mathematical analysis.

Abstract: In the companion paper we presented extended simulations showing that the recently observed spike-timing dependent synaptic plasticity can explain the development of simple cell direction selectivity (DS) when simultaneously modifying the synaptic strength and the degree of synaptic depression. Here we estimate the spatial shift of the simple cell receptive field (RF) induced by the long-term synaptic plasticity, and the temporal phase advance caused by the short-term synaptic depression in response to drifting grating stimuli. The analytical expressions for this spatial shift and temporal phase advance lead to a qualitative reproduction of the frequency tuning curves of non-directional and directional simple cells. In agreement with in vivo recordings, the acquired DS is strongest for test gratings with a temporal frequency around 1–4 Hz. In our model this best frequency is determined by the width of the learning function and the time course of depression, but not by the temporal frequency of the ‘training’ stimuli. The analysis further reveals the instability of the initially symmetric RF, and formally explains why direction selectivity develops from a non-directional cell in a natural, directionally unbiased stimulation scenario.

Clustering in small networks of excitatory neurons with heterogeneous coupling strengths.

Abstract: Excitatory coupling with a slow rise time destabilizes synchrony between coupled neurons. Thus, the fully synchronous state is usually unstable in networks of excitatory neurons. Phase-clustered states, in which neurons are divided into multiple synchronized clusters, have also been found unstable in numerical studies of excitatory networks in the presence of noise. The question arises as to whether synchrony is possible in networks of neurons coupled through slow, excitatory synapses. In this paper, we show that robust, synchronous clustered states can occur in such networks. The effects of non-uniform distributions of coupling strengths are explored. Conditions for the existence and stability of clustered states are derived analytically. The analysis shows that a multi-cluster state can be stable in excitatory networks if the overall interactions between neurons in different clusters are stabilizing and strong enough to counter-act the destabilizing interactions between neurons within each cluster. When heterogeneity in the coupling strengths strengthens the stabilizing inter-cluster interactions and/or weakens the destabilizing in-cluster interactions, robust clustered states can occur in excitatory networks of all known model neurons. Numerical simulations were carried out to support the analytical results.

Mathematical models of cochlear nucleus onset neurons: II. model with dynamic spike-blocking state.

Abstract: Onset (On) neurons in the cochlear nucleus (CN), characterized by their prominent response to the onset followed by little or no response to the steady-state of sustained stimuli, have a remarkable ability to entrain (firing 1 spike per cycle of a periodic stimulus) to low-frequency tones up to 1000 Hz. In this article, we present a point-neuron model with independent, excitatory auditory-nerve (AN) inputs that accounts for the ability of On neurons to both produce onset responses for high-frequency tone bursts and entrain to a wide range of low-frequency tones. With a fixed-duration spike-blocking state after a spike (an absolute refractory period), the model produces entrainment to a broad range of low-frequency tones and an On response with short interspike intervals (chopping) for high-frequency tone bursts. To produce On response patterns with no chopping, we introduce a novel, more complex, active membrane model in which the spike-blocking state is maintained until the instantaneous membrane voltage falls below a transition voltage. During the sustained depolarization for a high-frequency tone burst, the new model does not chop because it enters a spike-blocking state after the first spike and fails to leave this state until the membrane voltage returns toward rest at the end of the stimulus. The model entrains to low-frequency tones because the membrane voltage falls below the transition voltage on every cycle when the AN inputs are phase-locked. With the complex membrane model, On response patterns having moderate steady-state activity for high-frequency tone bursts (On-L) are distinguished from those having no steady-state activity (On-I) by requiring fewer AN inputs. Voltage-gated ion channels found in On-responding neurons of the CN may underlie the hypothesized dynamic spike-blocking state. These results provide a mechanistic rationale for distinguishing between the different physiological classes of CN On neurons.

Coordinated motor activity in simulated spinal networks emerges from simple biologically plausible rules of connectivity.

Abstract: The spinal motor circuits of the Xenopus embryo have been simulated in a 400-neuron network. To explore the consequences of differing patterns of synaptic connectivity within the network for the generation of the motor rhythm, a system of biologically plausible rules was devised to control synapse formation by three parameters. Each neuron had an intrinsic probability of synapse formation (Psoma, specified by a space constant λ) that was a monotonically decreasing function of its soma location in the rostro-caudal axis of the simulated network. The neurons had rostral and caudal going axons of specified length (Laxon) associated with a probability of synapse formation (Paxon). The final probability of synapse formation was the product of Psoma and Paxon. Realistic coordinated activity only occurred when Laxon and the probabilities of interconnection were sufficiently high. Increasing the values of the three network parameters reduced the burst duration, cycle period, and rostro-caudal delay and increased the reliability with which the network functioned as measured by the coefficient of variance of these parameters. Whereas both Laxon and Paxon had powerful and consistent effects on network output, the effects of λ on burst duration and rostro-caudal delay were more variable and depended on the values of the other two parameters. This network model can reproduce the rostro-caudal coordination of swimming without using coupled oscillator theory. The changes in network connectivity and resulting changes in activity explored by the model mimic the development of the motor pattern for swimming in the real embryo.