Biomedical subjects

Vincent Hakim

Publications and source records attributed to Vincent Hakim.

8 recordsLinked to original sources

PubMed2006

Nonequilibrium ribbon model of twisted scroll waves.

We formulate a reduced model to analyze the motion of the core of a twisted scroll wave. The model is first shown to provide a simple description of the onset and nonlinear evolution of the helical state appearing in the sproing bifurcation of scroll waves. It then serves to examine the experimentally studied case of a medium with spatially varying excitability. The model shows the role of sproing in this more complex setting and highlights the differences between the convective and absolute sproing instabilities.

DNA↗

PubMed2005

Crack path prediction in anisotropic brittle materials.

A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure and macroscopic linear elasticity. The path is uniquely determined by the directional anisotropy of the fracture energy, independent of details of the failure process. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby's configurational forces, cohesive forces, and dissipative forces. Numerical simulations are in very good agreement with analytic predictions.

Journal Article↗

PubMed2005

Core genetic module: the mixed feedback loop.

The so-called mixed feedback loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed description of the nonlinear oscillation regime are presented and some biological examples are discussed. The results emphasize the role of protein interactions in the function of genetic modules and the usefulness of modeling RNA dynamics explicitly.

Cell Physiological Phenomena↗

PubMed2004

Optimal information storage and the distribution of synaptic weights: perceptron versus Purkinje cell.

It is widely believed that synaptic modifications underlie learning and memory. However, few studies have examined what can be deduced about the learning process from the distribution of synaptic weights. We analyze the perceptron, a prototypical feedforward neural network, and obtain the optimal synaptic weight distribution for a perceptron with excitatory synapses. It contains more than 50% silent synapses, and this fraction increases with storage reliability: silent synapses are therefore a necessary byproduct of optimizing learning and reliability. Exploiting the classical analogy between the perceptron and the cerebellar Purkinje cell, we fitted the optimal weight distribution to that measured for granule cell-Purkinje cell synapses. The two distributions agreed well, suggesting that the Purkinje cell can learn up to 5 kilobytes of information, in the form of 40,000 input-output associations.

Afferent Pathways↗

PubMed2004

Design of genetic networks with specified functions by evolution in silico.

Recent studies have provided insights into the modular structure of genetic regulatory networks and emphasized the interest of quantitative functional descriptions. Here, to provide a priori knowledge of the structure of functional modules, we describe an evolutionary procedure in silico that creates small gene networks performing basic tasks. We used it to create networks functioning as bistable switches or oscillators. The obtained circuits provide a variety of functional designs, demonstrate the crucial role of posttranscriptional interactions, and highlight design principles also found in known biological networks. The procedure should prove helpful as a way to understand and create small functional modules with diverse functions as well as to analyze large networks.

Algorithms↗

PubMed2003

Firing-rate resonance in a generalized integrate-and-fire neuron with subthreshold resonance.

Neurons that exhibit a peak at finite frequency in their membrane potential response to oscillatory inputs are widespread in the nervous system. However, the influence of this subthreshold resonance on spiking properties has not yet been thoroughly analyzed. To this end, generalized integrate-and-fire models are introduced that reproduce at the linear level the subthreshold behavior of any given conductance-based model. A detailed analysis is presented of the simplest resonant model of this kind that has two variables: the membrane potential and a supplementary voltage-gated resonant variable. The firing-rate modulation created by a noisy weak oscillatory drive, mimicking an in vivo environment, is computed numerically and analytically when the dynamics of the resonant variable is slow compared to that of the membrane potential. The results show that the firing-rate modulation is shaped by the subthreshold resonance. For weak noise, the firing-rate modulation has a minimum near the preferred subthreshold frequency. For higher noise, such as that prevailing in vivo, the firing-rate modulation peaks near the preferred subthreshold frequency.

Action Potentials↗

PubMed2002

From subthreshold to firing-rate resonance.

Many types of neurons exhibit subthreshold resonance. However, little is known about whether this frequency preference influences spike emission. Here, the link between subthreshold resonance and firing rate is examined in the framework of conductance-based models. A classification of the subthreshold properties of a general class of neurons is first provided. In particular, a class of neurons is identified in which the input impedance exhibits a suppression at a nonzero low frequency as well as a peak at higher frequency. The analysis is then extended to the effect of subthreshold resonance on the dynamics of the firing rate. The considered input current comprises a background noise term, mimicking the massive synaptic bombardment in vivo. Of interest is the modulatory effect an additional weak oscillating current has on the instantaneous firing rate. When the noise is weak and firing regular, the frequency most preferentially modulated is the firing rate itself. Conversely, when the noise is strong and firing irregular, the modulation is strongest at the subthreshold resonance frequency. These results are demonstrated for two specific conductance-based models and for a generalization of the integrate-and-fire model that captures subthreshold resonance. They suggest that resonant neurons are able to communicate their frequency preference to postsynaptic targets when the level of noise is comparable to that prevailing in vivo.

Algorithms↗

PubMed2002

Scroll waves in isotropic excitable media: linear instabilities, bifurcations, and restabilized states.

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves.

Animals↗