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Biomedical subjects

W Gerstner

Publications and source records attributed to W Gerstner.

26 records · Page 2Linked to original sources
PubMed1995

Intracellular Ca2+ stores can account for the time course of LTP induction: a model of Ca2+ dynamics in dendritic spines.

1. A model of Ca2+ dynamics in spines of CA1 hippocampal neurons is presented. In contrast to traditional models, which concentrate on the effects of Ca2+ influx, diffusion, buffering, and extrusion, we also consider the additional effect of intracellular Ca2+ stores. 2. It is shown that traditional models without Ca2+ stores cannot account for the time course of long-term potentiation (LTP) induction as found in recent experiments. Experimental data suggest that the intracellular Ca2+ concentration should be elevated for up to 2 s, whereas the Ca2+ concentration in standard models of Ca2+ dynamics decays much faster. 3. When intracellular Ca2+ stores are taken into account, a much slower decay is found. In particular, a model simulation with a stimulation paradigm consisting of two bursts of four impulses at 100 Hz each and variable interburst intervals can reproduce experimental results found for primed or theta-burst stimulation. 4. In our model, Ca2+ release from the store has a nonlinear, bell-shaped dependence on the intracellular Ca2+ concentration, similar to the one found for inositoltrisphosphate and ryanodine receptors. These receptors are known to control calcium release from intracellular stores. 5. Our model suggests an important role of intracellular calcium stores in the induction of LTP. The stores serve as a long-term calcium source that can sustain an intracellular Ca2+ concentration above the resting level for 1-2 s.

Animals↗
PubMed1995

Spontaneous excitations in the visual cortex: stripes, spirals, rings, and collective bursts.

As a simple model of the cortical sheet, we study a locally connected net of spiking neurons. Refractoriness, noise, axonal delays, and the time course of excitatory and inhibitory postsynaptic potentials are taken into account explicitly. In addition to a low-activity state and depending on the synaptic efficacy, four different scenarios evolve spontaneously, viz., stripes, spirals, rings, and collective bursts. Our results can be related to experimental observations of drug-induced epilepsy and hallucinations.

Action Potentials↗
PubMed1994

A biologically motivated and analytically soluble model of collective oscillations in the cortex. II. Application to binding and pattern segmentation.

Feature linking and pattern separation are shown to be performed as simultaneous processes by a highly connected auto-associative network of spiking neurons (spike response model). In principle, many (e.g., with nine) patterns can be separated, but with a biological set of parameters the number is limited to four. The patterns have been learned by an asymmetric hebbian rule that can handle a low activity which may vary from pattern to pattern (in a range between 4% and 7%). Spikes are generated by a threshold process and--with some delay--transmitted to postsynaptic neurons. There they evoke an excitatory or inhibitory postsynaptic potential (EPSP or IPSP). Spike emission is followed by an absolute refractory period (1 ms) and activates an inhibitory delay loop that prevents continuous firing. Three different network topologies are discussed, i.e., a structureless fully connected system, a network composed of two 'hemispheres', and finally a hierarchical network with four subsystems that represent different 'functions' and interact via feedforward and feedback connections. Functional feedback turns out to be essential for context-sensitive binding. The coherence between the two hemispheres is dependent on the interhemispheric delays. If these are on average too large, the two hemispheres oscillate coherently by themselves but phase-shifted by half a period with respect to each other.

Animals↗
PubMed1993

A biologically motivated and analytically soluble model of collective oscillations in the cortex. I. Theory of weak locking.

A model of an associative network of spiking neurons with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neurons spike and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. During retrieval of a pattern, all active neurons exhibit periodic spike bursts which may or may not be synchronized ('locked') into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. In a stationary retrieval state, the overlap assumes a constant value proportional to the mean firing rate of the neurons. It is argued that in a biological network an intermediate scenario of 'weak locking' is most likely.

Animals↗
PubMed1993

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns.

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runs n times as often as learned, when n is a positive integer (n > or = 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.

Animals↗
PubMed1992

Universality in neural networks: the importance of the 'mean firing rate'.

We present a general analysis of highly connected recurrent neural networks which are able to learn and retrieve a finite number of static patterns. The arguments are based on spike trains and their interval distribution and require no specific model of a neuron. In particular, they apply to formal two-state neurons as well as to more refined models like the integrate-and-fire neuron or the Hodgkin-Huxley equations. We show that the mean firing rate defined as the inverse of the mean interval length is the only relevant parameter (apart from the synaptic weights) that determines the existence of retrieval solutions with a large overlap with one of the learnt patterns. The statistics of the spiking noise (Gaussian, Poisson or other) and hence the shape of the interval distribution does not matter. Thus our unifying approach explains why, and when, all the different associative networks which treat static patterns yield basically the same results, i.e., belong to the same universality class.

Mathematics↗
PubMedDate not supplied

How the threshold of a neuron determines its capacity for coincidence detection.

Coherent oscillatory activity of a population of neurons is thought to be a vital feature of temporal coding in the brain. We focus on the question of whether a single neuron can transform a spike code into a rate code. More precisely, how does a neuron vary its mean output firing rate, if its input changes from random to coherent? We investigate the coincidence detection properties of an integrate-and-fire neuron in dependence upon internal parameters and input statistics. In particular, we show how coincidence detection depends on the membrane time constant and the threshold. Furthermore, we demonstrate that there is an optimal threshold for coincidence detection and that there is a broad range of near-optimal threshold values. Fine-tuning is not necessary.

Action Potentials↗