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Christian Leibold

Publications and source records attributed to Christian Leibold.

7 recordsLinked to original sources
PubMed2007

Generation of theta oscillations by weakly coupled neural oscillators in the presence of noise.

Neuronal oscillations are a robust phenomenon occurring in a variety of brain regions despite considerable amounts of noise. In this article classical phase-response theory is generalized to the case of noisy weak-coupling regimes by deriving an iterated map for the asynchrony of spikes in an oscillation cycle. Two criteria are introduced to check the validity of our approximations: One criterion tests the assumption that all neurons fire exactly once per cycle, the other criterion tests for linearity. The framework is applied to stellate cells of the medial entorhinal cortex layer II. We find that rhythmogenesis is more robust in the case of excitatory noise as compared to inhibitory noise. It is shown that a network of stellate cells can also act as a generator of theta if the neurons are connected via a fast-oscillating network of inhibitory interneurons.

Action Potentials↗
PubMed2006

Memory capacity for sequences in a recurrent network with biological constraints.

The CA3 region of the hippocampus is a recurrent neural network that is essential for the storage and replay of sequences of patterns that represent behavioral events. Here we present a theoretical framework to calculate a sparsely connected network's capacity to store such sequences. As in CA3, only a limited subset of neurons in the network is active at any one time, pattern retrieval is subject to error, and the resources for plasticity are limited. Our analysis combines an analytical mean field approach, stochastic dynamics, and cellular simulations of a time-discrete McCulloch-Pitts network with binary synapses. To maximize the number of sequences that can be stored in the network, we concurrently optimize the number of active neurons, that is, pattern size, and the firing threshold. We find that for one-step associations (i.e., minimal sequences), the optimal pattern size is inversely proportional to the mean connectivity c, whereas the optimal firing threshold is independent of the connectivity. If the number of synapses per neuron is fixed, the maximum number P of stored sequences in a sufficiently large, nonmodular network is independent of its number N of cells. On the other hand, if the number of synapses scales as the network size to the power of 3/2, the number of sequences P is proportional to N. In other words, sequential memory is scalable. Furthermore, we find that there is an optimal ratio r between silent and nonsilent synapses at which the storage capacity alpha = P//[c(1 + r)N] assumes a maximum. For long sequences, the capacity of sequential memory is about one order of magnitude below the capacity for minimal sequences, but otherwise behaves similar to the case of minimal sequences. In a biologically inspired scenario, the information content per synapse is far below theoretical optimality, suggesting that the brain trades off error tolerance against information content in encoding sequential memories.

Hippocampus↗
PubMed2005

Spiking neurons learning phase delays: how mammals may develop auditory time-difference sensitivity.

Time differences between the two ears are an important cue for animals to azimuthally locate a sound source. The first binaural brainstem nucleus, in mammals the medial superior olive, is generally believed to perform the necessary computations. Its cells are sensitive to variations of interaural time differences of about 10 micros. The classical explanation of such a neuronal time-difference tuning is based on the physical concept of delay lines. Recent data, however, are inconsistent with a temporal delay and rather favor a phase delay. By means of a biophysical model we show how spike-timing-dependent synaptic learning explains precise interplay of excitation and inhibition and, hence, accounts for a physical realization of a phase delay.

Action Potentials↗
PubMed2004

Stability analysis of asynchronous states in neuronal networks with conductance-based inhibition.

Oscillations in networks of inhibitory interneurons have been reported at various sites of the brain and are thought to play a fundamental role in neuronal processing. This Letter provides a self-contained analytical framework that allows numerically efficient calculations of the population activity of a network of conductance-based integrate-and-fire neurons that are coupled through inhibitory synapses. Based on a normalization equation this Letter introduces a novel stability criterion for a network state of asynchronous activity and discusses its perturbations. The analysis shows that, although often neglected, the reversal potential of synaptic inhibition has a strong influence on the stability as well as the frequency of network oscillations.

Membrane Potentials↗
PubMed2004

Structure-function analysis of the cysteine string protein in Drosophila: cysteine string, linker and C terminus.

Cysteine string proteins (CSPs) are conserved secretory vesicle proteins involved in regulating neurotransmitter and peptide release. While the function of the J-domain has been studied in detail, little is known about other conserved regions. We have constructed mutant genes coding for proteins with modified cysteine string, linker region or C terminus and transformed them into Csp null-mutant Drosophila: In the living animal, mutated CSP lacking all cysteines fails to associate with membranes, does not concentrate in synaptic terminals, and cannot rescue adult temperature-sensitive paralysis and short life span, both prominent null mutant phenotypes. A mutant protein with 5 instead of 11 string cysteines appears to be normally targeted but cannot rescue paralysis at 37 degrees C. We propose that the cysteine string, in addition to its role in targeting, may be essential for a function of CSP that is dependent on the number of cysteines in the string. A deletion in the linker region or the C terminus does not affect CSP targeting, and function in adults is only marginally impaired.

Amino Acid Sequence↗
PubMed2002

How spiking neurons give rise to a temporal-feature map: from synaptic plasticity to axonal selection.

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells' synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity.

Journal Article↗