Development of Morphogen Gradient: The Role of Dimension and Discreteness

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuum descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region

Theoretical Analysis of Dynamic Processes for Interacting Molecular Motors

Biological transport is supported by collective dynamics of enzymatic molecules that are called motor proteins or molecular motors. Experiments suggest that motor proteins interact locally via short-range potentials. We investigate the fundamental role of these interactions by analyzing a new class of totally asymmetric exclusion processes where interactions are accounted for in a thermodynamically consistent fashion. Theoretical analysis that combines various mean-field cal- culations and computer simulations suggests that dynamic properties of molecular motors strongly depend on interactions, and correlations are stronger for interacting motor proteins. Surprisingly, it is found that there is an optimal strength of interactions (weak repulsion) that leads to a maxi- mal particle flux. It is also argued that molecular motors transport is more sensitive to attractive interactions. Applications of these results for kinesin motor proteins are discussed

Gravitational Uncertainty and Black Hole Remnants

Possible existence of black holes remnants provides a suitable candidates for dark matter. In this paper we study the possibility of existence for such remnants. We consider quantum gravitational induced corrections of black hole's entropy and temperature to investigate the possibility of such relics. Observational scheme for detection of these remnants and their cosmological constraints are discussed.Comment: 17 pages, 6 figure

On the Order of the Schur Multiplier of a Pair of Finite p-Groups

In 1998, G. Ellis defined the Schur multiplier of a pair $(G,N)$ of groups and mentioned that this notion is a useful tool for studying pairs of groups. In this paper, we characterize the structure of a pair of finite $p$-groups $(G,N)$ in terms of the order of the Schur multiplier of $(G,N)$ under some conditions.Comment: 11 pages, to appear in Journal of Advanced Research in Pure Mathematic

Does Resource Commercialization Induce Local Conservation? A Cautionary Tale From Southwestern Morocco

Ecotourism, bioprospecting and non-timber product marketing have been promoted recently as market-based instruments for environment protection, but without sound understanding of the resulting net conservation effects. We present evidence on the local conservation effects of recent argan oil commercialization in Morocco, which seems a promising case study in conservation through resource commercialization. Our empirical analysis shows, however, that resource commercialization is not creating strong net conservation incentives because assumptions implicit in the prevailing logic prove incorrect in this case. Generally, the experience of southwestern Morocco provides a cautionary tale about the assumed efficacy of conservation strategies founded on resource commercialization.Resource /Energy Economics and Policy,