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V Hakim

Publications and source records attributed to V Hakim.

At least 19 recordsLinked to original sources
PubMed2000

Linear stability of scroll waves.

A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigenmode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are found to play a dominant role. For untwisted scroll waves, modulations in the third dimension have stabilizing or destabilizing effects on the different modes depending on the parameter regimes, in partial agreement with previous predictions. The influence of twist on the different branches is investigated. In particular, the sproing instability is seen to arise from the twist-induced deformation of the translation branches above a threshold twist.

Journal Article↗
PubMed1999

Fast global oscillations in networks of integrate-and-fire neurons with low firing rates.

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons --> infinity, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regions. The results are found to be in good agreement with numerical simulations.

Algorithms↗
PubMed1999

Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications.

In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract, causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wave front slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency, (iii) drift under external actions (external field with application to axisymmetric scroll ring motion in three dimensions, and spatial- or/and time-dependent variation of excitability), and (iv) the dynamics of multiarmed spiral waves with the prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHugh-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semiquantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models.

Journal Article↗
PubMed1991

Regulation of the multiple promoters of the human aldolase A gene: response of its two ubiquitous promoters to agents promoting cell proliferation.

The human aldolase A gene is transcribed from three distinct promoters, the two ubiquitous promoters PN and PH and the muscle specific promoter PM. In the present study, we investigate further aldolase A mRNA structure and expression. We demonstrate that the upstream N-type exon is, in fact, extremely heterogeneous. RNAse H mapping experiments permit quantification of relative abundance of N, M, and H type mRNAs and show that the level of transcripts containing the downstream H-type exon is at least 30 times higher than that of those containing N exon, in all tissues tested. Aldolase A level is up-regulated in proliferating cells. Here we show that both N and H type mRNAs, although barely detectable in normal liver, are highly expressed in human hepatomas biopsies. Furthermore, in human lymphocytes, N-type mRNA level is enhanced by serum treatment, while in cultured Hep G2 cells, both N-type and H-type mRNA levels are increased by serum and by the tumor promoting agent PMA. Using CAT constructs in transfection experiments, we demonstrate that the H exon plus its upstream region can function autonomously: the 420 base pairs upstream of the H exon are sufficient to confer to promoter PH an efficiency comparable that of the complete SV40 early promoter and enhancer in two cell lines.

Base Sequence↗
PubMed1987

Characterization of three optional promoters in the 5' region of the human aldolase A gene.

We undertook cloning and sequencing of the 5' portion of the human aldolase A gene to elucidate the mechanisms that govern synthesis of its different mRNAs. The sequenced gene is the only active gene in human-rodent fibroblastic somatic hybrids, while the other aldolase A-related sequences are inactive. S1 mapping and primer extension analysis enabled us to demonstrate that three promoter regions were implicated in the initiation of different aldolase A mRNAs, differing only in their 5' non-coding extremities. A distal promoter, N (non-specific), governs the synthesis of a 5' non-coding region of 142 bases composed of two exons, N1 and N2, which are found in a variety of tissues. A median promoter, M (muscle), is only active in skeletal muscle, and initiates the transcription by a 5' non-coding exon of 45 bases. Finally, a proximal promoter, H (housekeeping), contained in a "G + C-rich island", permits transcription of three colinear mRNAs containing 172, 126 or 112 bases of 5' non-coding sequence; their expression seems ubiquitous. These three promoters are arranged in 1.5 X 10(3) base-pairs of DNA. Homologies between rat and human genomic sequences and the absence of homology between promoters or 5' non-coding exons of the same species exclude a recent duplication of the promoter regions.

Amino Acid Sequence↗