Morphogen gradient from a noisy source.

Jeremy L England; John Cardy

doi:10.1103/physrevlett.94.078101

Home/Archive/PubMed

PubMed · 15783857

Morphogen gradient from a noisy source.

Jeremy L England·John Cardy

View original source ↗Export metadata ↓

Abstract

We investigate the effect of time-dependent noise on the shape of a morphogen gradient in a developing embryo. Perturbation theory is used to calculate the deviations from deterministic behavior in a simple reaction-diffusion model of robust gradient formation, and the results are confirmed by numerical simulation. It is shown that such deviations can disrupt robustness for sufficiently high noise levels, and the implications of these findings for more complex models of gradient-shaping pathways are discussed.

Explore related subjects

Diffusion Embryonic Development Growth Substances Models, Biological Signal Transduction Journal Article Research Support, Non-U.S. Gov't

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Jeremy L England, John Cardy. 2005-02-24. Morphogen gradient from a noisy source.. https://doi.org/10.1103/physrevlett.94.078101

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

KEEP EXPLORING

Related citations

PubMed2005

Separating the contribution of translational and rotational diffusion to protein association.

The association of two proteins is preceded by a mutual diffusional search in solution. The role of translational and rotational diffusion in this process has been studied theoretically for many years. However, systematic experimental verification of theoretical results is still lacking. We report here measurements of association rates of the proteins beta-lactamase (TEM) and beta-lactamase inhibitor protein (BLIP) in solutions of glycerol and poly(ethylene glycol) of increasing viscosity. We also measured translational and rotational diffusion in the same solutions, using fluorescence correlation spectroscopy and fluorescence anisotropy, respectively. It is found that in glycerol both translational and rotational diffusion rates are inversely dependent on viscosity, as predicted by the classical Stokes-Einstein relations, while the association rate depends nonlinearly on viscosity. In contrast, the association rate depends only weakly on the viscosity of the polymer solutions, which results in a similar weak dependence of k(on) on viscosity. The data are modeled using the theory of diffusion-limited association. Deviations from the theory are explained by a short-range solute-induced repulsion between the proteins in glycerol solution and an attractive depletion interaction generated by the polymers. These results open the way to the creation of a unified framework for all nonspecific effects involved in the protein association process, as well as to better theoretical understanding of these effects. Further, they reflect on the complex factors controlling protein association within the crowded environment of cells and suggest that a high concentration of macromolecules does not significantly impede protein association.

Diffusion↗

PubMed2005

Theoretical characterization of alpha-helix and beta-hairpin folding kinetics.

By means of the conformational free energy surface and corresponding diffusion coefficients, as obtained by long time scale atomistic molecular dynamics simulations (mus time scale), we model the folding kinetics of alpha-helix and beta-hairpin peptides as a diffusive process over the free energy surface. The two model systems studied in this paper (the alpha-helical temporin L and the beta-hairpin prion protein H1 peptide) exhibit a funnel-like almost barrierless free energy profile, leading to nonexponential folding kinetics matching rather well the available experimental data. Moreover, using the free energy profile provided by Muñoz et al. [Muñoz et al. Nature 1997, 390: 196-199], this model was also applied to reproduce the two-state folding kinetics of the C-terminal beta-hairpin of protein GB1, yielding an exponential folding kinetics with a time constant (approximately 5 micros) in excellent agreement with the experimentally observed one (approximately 6 micros). Finally, the folding kinetics obtained by solving the diffusion equation, considering either a one-dimensional or a two-dimensional free energy surface, are also compared in order to understand the relevance of the possible kinetic coupling between conformational degrees of freedom in the folding process.

Diffusion↗

PubMed2005

Airflow dispersion in unsaturated soil.

Dispersion data is abundant for water flow in the saturated zone but is lacking for airflow in unsaturated soil. However, for remediation processes such as soil vapour extraction, characterization of airflow dispersion is necessary for improved modelling and prediction capabilities. Accordingly, gas-phase tracer experiments were conducted in five soils ranging from uniform sand to clay at air-dried and wetted conditions. The disturbed soils were placed in one-dimensional stainless steel columns, with sulfur hexafluoride used as the inert tracer. The tested interstitial velocities were typical of those present in the vicinity of a soil vapour extraction well, while wetting varied according to the water-holding capacity of the soils. Results gave dispersivities that varied between 0.42 and 2.6 cm, which are typical of values in the literature. In air-dried soils, dispersion was found to increase with the pore size variability of the soil. For wetted soils, particle shape was an important factor at low water contents, while at high water contents, the proportion of macroporous space filled with water was important. The relative importance of diffusion decreased with increasing interstitial velocity and water content and was, in general, found to be minor compared to mechanical mixing across all conditions studied.

Diffusion↗