Searcharxiv⌕ Search

arXiv · q-bio/0412023

The dynamics of the min proteins of Escherichia coli under the constant external fields

Abstract

In E. coli the determination of the middle of the cell and the proper placement of the septum is essential to the division of the cell. This step depends on the proteins MinC, MinD, and MinE. Exposure to a constant external field e.g., an electric field or magnetic field may cause the bacteria cell division mechanism to change resulting in an abnormal cytokinesis. To have insight into the effects of an external field on this process, we model the process using a set of the deterministic reaction diffusion equations, which incorporate the influence of an external field, min protein reactions, and diffusion of all species. Using the numerical method, we have found some changes in the dynamics of the oscillations of the min proteins from pole to pole when compared that of without the external field. The results show some interesting effects, which are qualitatively in good agreement with some experimental results.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Paisan Kanthang, Waipot Ngamsaad, Charin Modchang, Wannapong Triampo, Narin Nuttawut, I-Ming Tang, Yongwimol Lenbury. 2004-12-13. The dynamics of the min proteins of Escherichia coli under the constant external fields. https://arxiv.org/abs/q-bio/0412023

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Tau creates spatially moving hotspots of amyloid-$β$ secondary nucleation: a reaction-diffusion model

Tau-amyloid-$β$ cross-seeding creates a spatial paradox. Bioavailable tau can promote A$β$42 nucleation, thereby increasing local fibril number and catalytic-site burden; yet the same fibrils consume the free A$β$ monomer required for homotypic secondary nucleation. The region containing the most tau or fibrillar material therefore need not be the region with the highest secondary-nucleation rate. We test this idea with a reaction-diffusion model that tracks a propagating effective tau catalyst, free A$β$ monomer, elongation-competent fibrils, fibril mass, and the catalytic sites exposed to monomer. The model reduces the spatial competition to two quantities: accessible catalytic sites and free monomer. Their balance yields an exact condition for an interior kinetic maximum: the logarithmic decrease in accessible catalytic sites must equal twice the logarithmic increase in free monomer. Two Damkohler numbers then separate the relevant competitions-elongation versus clearance, and elongation versus diffusive redistribution-while a monomer screening length sets the physical scale over which depletion can persist. Independent transport and turnover estimates place this length near 0.44-0.54 mm. Simulations show that tau first raises secondary nucleation near its source; continued fibril growth then produces a monomer-depleted wake, and the maximum shifts to a region with fewer catalytic sites but more available monomer. Oligomer transport and sustained reversible exchange can weaken or eliminate this contrast, whereas growth-history-dependent site density can strengthen it. The robust prediction is therefore a spatial separation among tau burden, fibril-mass growth, and instantaneous A$β$ secondary-nucleation activity, rather than a universal hotspot speed.

q-bio.SC↗

A Multiscale Kinetic Model of DNA Damage Signalling and Repair under Combined Proton and Nanoparticle Exposure

We present a multiscale kinetic framework for predicting the induction, processing, and biological consequences of DNA double-strand breaks (DSBs) in AG1522 human fibroblasts exposed to combined proton and 15-nm GNP irradiation. The model connects proton dose and linear energy transfer (LET), perinuclear GNP localization, secondary-electron and reactive-species production, and Poisson--Gamma-distributed lesion induction. Initial DSBs are separated into simple and complex classes and coupled to an ATM--$γ$H2AX--53BP1 signalling cascade, cell-cycle-dependent allocation among canonical non-homologous end joining, homologous recombination, alternative end joining, and single-strand annealing, and class-specific repair fidelities. The model identifies the initial complex-lesion fraction and its slower resolution, rather than post-irradiation conversion of simple DSBs, as the principal determinants of persistent damage under high-LET, GNP-enhanced irradiation. The residual-DSB results provide strong internal out-of-sample validation of the kinetic component. However, the opposing biases in correct repair and misrepair reveal an inconsistency between the class-specific fidelities and the supplied integrated-fidelity endpoint. These repair-fate predictions should therefore be regarded as model-constrained estimates pending independent measurements of correct-end joining, mutation, chromosome aberrations, and clonogenic survival.

q-bio.SC↗

Shorter but not more catalytic: an active-site-resolved model of how tau reshapes amyloid-$β$ secondary nucleation

Tau cross-seeding creates a mechanistic puzzle. Tau fibrils accelerate amyloid-$β$42 (A$β$42) nucleation and produce a larger population of shorter A$β$ fibrils, yet homotypic secondary nucleation occurs at rare catalytic sites rather than uniformly over fibril mass. Does making more, shorter fibrils make the A$β$ population more catalytic? A coupled tau-A$β$ model is extended to track fibril number, fibril mass, total active secondary-nucleation sites, and the fraction of sites exposed after plaque consolidation. The model recovers the preceding plaque-surface-limited formulation when active sites form in direct proportion to fibril mass. At matched fibril mass, shortening alone has little effect: the departure of active-site density from mass proportionality scales inversely with mean fibril size, so the extra fibrils matter only if each birth event introduces about as many sites as elongation adds over a mean-length fibril. At equal time, the sign of the homotypic response is controlled mainly by a Damkohler number comparing monomer consumption by elongation with monomer clearance. Tau coupling increases homotypic secondary nucleation while clearance controls free monomer, but suppresses it once elongation becomes the dominant monomer sink. In a composite scenario, these regimes occur in sequence. Across all cases examined, including 800 Latin-hypercube samples and simulations with mean fibril lengths of 0.3-30 $μm$, direct tau catalysis increases accumulated oligomer-equivalent exposure. The model predicts that shorter tau-seeded fibrils are not intrinsically more catalytic unless their sites are more numerous per unit mass, more active, or more exposed; matched-mass site counting and secondary-nucleation measurements can distinguish these alternatives.

q-bio.SC↗