Biomedical subjects

Carlo R Laing

Publications and source records attributed to Carlo R Laing.

7 recordsLinked to original sources

PubMed2006

On the application of "equation-free modelling" to neural systems.

"Equation-free modelling" is a recently-developed technique for bridging the gap between detailed, microscopic descriptions of systems and macroscopic descriptions of their collective behaviour. It uses short, repeated bursts of simulation of the microscopic dynamics to analyse the effective macroscopic equations, even though such equations are not directly available for evaluation. This paper demonstrates these techniques on a variety of networks of model neurons, and discusses the advantages and limitations of such an approach. New results include an understanding of the effects of including gap junctions in a model capable of sustaining spatially localised "bumps" of activity, and an investigation of a network of coupled bursting neurons.

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PubMed2004

Spiral waves in disinhibited mammalian neocortex.

Spiral waves are a basic feature of excitable systems. Although such waves have been observed in a variety of biological systems, they have not been observed in the mammalian cortex during neuronal activity. Here, we report stable rotating spiral waves in rat neocortical slices visualized by voltage-sensitive dye imaging. Tissue from the occipital cortex (visual) was sectioned parallel to cortical lamina to preserve horizontal connections in layers III-V (500-mum-thick, approximately 4 x 6 mm(2)). In such tangential slices, excitation waves propagated in two dimensions during cholinergic oscillations. Spiral waves occurred spontaneously and alternated with plane, ring, and irregular waves. The rotation rate of the spirals was approximately 10 turns per second, and the rotation was linked to the oscillations in a one-cycle- one-rotation manner. A small (<128 mum) phase singularity occurred at the center of the spirals, about which were observed oscillations of widely distributed phases. The phase singularity drifted slowly across the tissue ( approximately 1 mm/10 turns). We introduced a computational model of a cortical layer that predicted and replicated many of the features of our experimental findings. We speculate that rotating spiral waves may provide a spatial framework to organize cortical oscillations.

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PubMed2003

Periodic forcing of a model sensory neuron.

We study the effects of sinusoidally modulating the current injected into a model sensory neuron from the weakly electric fish Apteronotus leptorhynchus. This neuron's behavior is known to switch from quiescence to periodic firing to bursting as the injected current is increased. The bifurcation separating periodic from bursting behavior is a saddle-node bifurcation of periodic orbits, and it has been shown previously that there is "type-I burst excitability" associated with this bifurcation, similar to the usual excitability associated with the transition from quiescence to periodic firing. Here we show numerically that sinusoidal modulation of the dc current injected into the model neuron can switch it from periodic to burst firing, or vice versa, depending on the frequency of modulation and the distance to the burst excitability threshold. This is explained by mapping resonance tongues in parameter space. We also show that such a model neuron can undergo stochastic resonance near the transition from periodic to burst firing, as a result of the burst excitability, regardless of the location (soma or dendrite) of the signal and noise. The novelty is that the "output event" is now a burst rather than a single action potential, and the neuron returns to almost periodic firing between bursts, rather than to the vicinity of a fixed point. Since the neuron under study is a sensory neuron that must encode signals with varying temporal structure in the presence of considerable intrinsic noise, these aspects are of potential importance to electrosensory processing and also to other bursting neurons that have periodic input.

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PubMed2003

Dynamics of deterministic and stochastic paired excitatory-inhibitory delayed feedback.

We examine the effects of paired delayed excitatory and inhibitory feedback on a single integrate-and-fire neuron with reversal potentials embedded within a feedback network. These effects are studied using bifurcation theory and numerical analysis. The feedback occurs through modulation of the excitatory and inhibitory conductances by the previous firing history of the neuron; as a consequence, the feedback also modifies the membrane time constant. Such paired feedback is ubiquitous in the nervous system. We assume that the feedback dynamics are slower than the membrane time constant, which leads to a rate model formulation. Our article provides an extensive analysis of the possible dynamical behaviors of such simple yet realistic neural loops as a function of the balance between positive and negative feedback, with and without noise, and offers insight into the potential behaviors such loops can exhibit in response to time-varying external inputs. With excitatory feedback, the system can be quiescent, can be periodically firing, or can exhibit bistability between these two states. With inhibitory feedback, quiescence, oscillatory firing rates, and bistability between constant and oscillatory firing-rate solutions are possible. The general case of paired feedback exhibits a blend of the behaviors seen in the extreme cases and can produce chaotic firing. We further derive a condition for a dynamically balanced paired feedback in which there is neither bistability nor oscillations. We also show how a biophysically plausible smoothing of the firing function by noise can modify the existence and stability of fixed points and oscillations of the system. We take advantage in our mathematical analysis of the existence of an invariant manifold, which reduces the dimensionality of the dynamics, and prove the stability of this manifold. The novel computational challenges involved in analyzing such dynamics with and without noise are also described. Our results demonstrate that a paired delayed feedback loop can act as a sophisticated computational unit, capable of switching between a variety of behaviors depending on the input current, the relative strengths and asymmetry of the two parallel feedback pathways, and the delay distributions and noise level.

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PubMed2002

A two-variable model of somatic-dendritic interactions in a bursting neuron.

We present a two-variable delay-differential-equation model of a pyramidal cell from the electrosensory lateral line lobe of a weakly electric fish that is capable of burst discharge. It is a simplification of a six-dimensional ordinary differential equation model for such a cell whose bifurcation structure has been analyzed (Doiron et al., J. Comput. Neurosci., 12, 2002). We have modeled the effects of back-propagating action potentials by a delay, and use an integrate-and-fire mechanism for action potential generation. The simplicity of the model presented here allows one to explicitly derive a two-dimensional map for successive interspike intervals, and to analytically investigate the effects of time-dependent forcing on such a model neuron. Some of the effects discussed include 'burst excitability', the creation of resonance tongues under periodic forcing, and stochastic resonance. We also investigate the effects of changing the parameters of the model.

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PubMedDate not supplied

A spiking neuron model for binocular rivalry.

We present a biologically plausible model of binocular rivalry consisting of a network of Hodgkin-Huxley type neurons. Our model accounts for the experimentally and psychophysically observed phenomena: (1) it reproduces the distribution of dominance durations seen in both humans and primates, (2) it exhibits a lack of correlation between lengths of successive dominance durations, (3) variation of stimulus strength to one eye influences only the mean dominance duration of the contralateral eye, not the mean dominance duration of the ipsilateral eye, (4) increasing both stimuli strengths in parallel decreases the mean dominance durations. We have also derived a reduced population rate model from our spiking model from which explicit expressions for the dependence of the dominance durations on input strengths are analytically calculated. We also use this reduced model to derive an expression for the distribution of dominance durations seen within an individual.

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PubMedDate not supplied

Type I burst excitability.

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.

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