Biomedical subjects

D Holcman

Publications and source records attributed to D Holcman.

5 recordsLinked to original sources

PubMed2005

Stochastic chemical reactions in microdomains.

Traditional chemical kinetics may be inappropriate to describe chemical reactions in microdomains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a master-diffusion equation for the joint probability density of a mobile reactant and the number of bound substrate in a confined domain. We use the equation to calculate the fluctuations in the number of bound substrate molecules as a function of initial reactant distribution. A second model is presented based on a Markov description of the binding and unbinding and on the mean first passage time of a molecule to a small portion of the boundary. These models can be used for the description of noise due to gating of ionic channels by random binding and unbinding of ligands in biological sensor cells, such as olfactory cilia, photoreceptors, hair cells in the cochlea.

Journal Article↗

PubMed2005

Modeling the spontaneous activity of the auditory cortex.

We present a rate model of the spontaneous activity in the auditory cortex, based on synaptic depression. A Stochastic integro-differential system of equations is derived and the analysis reveals two main regimes. The first regime corresponds to a normal activity. The second regime corresponds to epileptic spiking. A detailed analysis of each regime is presented and we prove in particular that synaptic depression stabilizes the global cortical dynamics. The transition between the two regimes is induced by a change in synaptic connectivity: when the overall connectivity is strong enough, an epileptic activity is spontaneously generated. Numerical simulations confirm the predictions of the theoretical analysis. In particular, our results explain the transition from normal to epileptic regime which can be induced in rats auditory cortex, following a specific pairing protocol. A change in the cortical maps reorganizes the synaptic connectivity and this transition between regimes is accounted for by our model. We have used data from recording experiments to fit synaptic weight distributions. Simulations with the fitted distributions are qualitatively similar to the real EEG recorded in vivo during the experiments. We conclude that changes in the synaptic weight function in our model, which affects excitatory synapses organization and reproduces the changes in cortical map connectivity can be understood as the main mechanism to explain the transitions of the EEG from the normal to the epileptic regime in the auditory cortex.

Algorithms↗

PubMed2005

Calcium dynamics in dendritic spines, modeling and experiments.

Dendritic spines are microstructures, about one femtoliter in volume, where excitatory synapses are made with incoming afferents, in most neurons of the vertebrate brain. The spine contains all the molecular constituents of the postsynaptic side of the synapse, as well as a contractile element that can cause its movement in space. It also contains calcium handling machineries to allow fast buffering of excess calcium that influx through voltage and NMDA gated channels. The spine is connected to the dendrite through a thin neck that serves as a variable barrier between the spine head and the parent dendrite. We review a novel modeling approach that is more suitable for the accurate description of the stochastic behavior of individual molecules in microstructures. Using this approach, we predict the calcium handling ability of the spine in complex situations associated with synaptic activity, spine motility and plasticity.

Animals↗

PubMed2004

Calcium dynamics in dendritic spines and spine motility.

A dendritic spine is an intracellular compartment in synapses of central neurons. The role of the fast twitching of spines, brought about by a transient rise of internal calcium concentration above that of the parent dendrite, has been hitherto unclear. We propose an explanation of the cause and effect of the twitching and its role in the functioning of the spine as a fast calcium compartment. Our molecular model postulates that rapid spine motility is due to the concerted contraction of calcium-binding proteins. The contraction induces a stream of cytoplasmic fluid in the direction of the dendritic shaft, thus speeding up the time course of spine calcium dynamics, relative to pure diffusion. Simulations indicate that chemical reaction rate theory at the molecular level can explain spine motility. They reveal two time periods in calcium dynamics, as measured recently by other researchers. It appears that rapid motility in dendritic spines increases the efficiency of calcium conduction to the dendrite and speeds up the emptying of the spine. This could play a major role in the induction of synaptic plasticity. A prediction of the model is that alteration of spine motility will modify the time course of calcium in the dendritic spine and could be tested experimentally.

Animals↗

PubMed1999

Statistical evaluation of clusters derived by nonlinear mapping of EEG spatial patterns.

New methods were devised to improve the discrimination of EEG spatial amplitude patterns recorded from arrays of 64 electrodes placed on visual, auditory or somatic cortex. The 64 traces shared a spatially coherent, aperiodic carrier wave with a spatial pattern of amplitude modulation (AM). Previous observations on AM patterns from rabbits trained to discriminate conditioned stimuli with reinforcement (CS+) and without (CS-) had revealed epochs between the CS and the CR in which AM patterns on CS+ trials could be distinguished from AM patterns on CS- trials. The AM patterns were expressed by points in 64-space that formed clusters. Levels of CS-/CS+ pattern separation were quantified by a pair-wise Euclidean distance method with cross-validation. The present study documents use of the technique for nonlinear mapping (NLM) to project the 64-dimensional structure onto a plane while preserving the relative distances between all points. The goodness of classification by the Euclidean distance measure was the same or improved after projection. Whereas the Euclidean distance measure only gave pair-wise classifications, the planar displays showed the patterns for multiple clusters simultaneously. These NLM-based methods revealed previously unrecognized structures within distributions of AM patterns in sensory cortices in the time period between the CS and CR.

Animals↗