Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Tripogon loliiformis elicits a rapid physiological and structural response to dehydration for desiccation tolerance

Resurrection plants can withstand extreme dehydration to an air-dry state and then recover upon receiving water. Tripogon loliiformis (F.Muell.) C.E.Hubb. is a largely uncharacterised native Australian desiccation-tolerant grass that resurrects from the desiccated state within 72 h. Using a combination of structural and physiological techniques the structural and physiological features that enable T. loliiformis to tolerate desiccation were investigated. These features include: - (i) a myriad of structural changes such as leaf folding, cell wall folding and vacuole fragmentation that mitigate desiccation stress; - (ii) potential role of sclerenchymatous tissue within leaf folding and radiation protection; - (iii) retention of ~70% chlorophyll in the desiccated state; - (iv) early response of photosynthesis to dehydration by 50% reduction and ceasing completely at 80 and 70% relative water content, respectively; - (v) a sharp increase in electrolyte leakage during dehydration, and; - (vi) confirmation of membrane integrity throughout desiccation and rehydration. Taken together, these results demonstrate that T. loliiformis implements a range of structural and physiological mechanisms that minimise mechanical, oxidative and irradiation stress. These results provide powerful insights into tolerance mechanisms for potential utilisation in the enhancement of stress-tolerance in crop plants.