Luke Heaton – Energetic constraints on fungal growth.
Fungi are ubiquitous and ecologically critical organisms, as most natural sources of organic carbon can be broken down and consumed by some member of the fungal kingdom. Fungal growth, reproduction and substrate digestion all require the expenditure of energy, and many fungi recycle parts of the mycelium for nutrients. By accounting for the ways that fungi obtain and consume energy, we show that different rates of growth, recycling and investment in digestion will enable different rates of investment in reproduction. For a given resource environment and time-scale of reproduction our model identifies optimal patterns of resource allocation, and its predictions for maximal growth rates and bioconversion efficiencies are consistent with empirical findings. The model also accounts for the observation that fungi growing on substrates with a high concentration of low molecular weight compounds will not benefit from recycling. In contrast, and consonant with data, recycling offers considerable benefits to fungi growing on recalcitrant substrates, where the individual hyphae are not crowded, and the time taken to consume resource is significantly longer than the fungus’ doubling time.
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Justine Datani – Analytical solutions of separable Master Equations for gene expression
Gene expression is a highly stochastic process. Master Equations (MEs) are discrete probabilistic descriptions, which are often necessary to describe gene transcription due to the low numbers of biomolecules involved and the complexity of the upstream processes. Recent experimental advances have made it possible not only to obtain snapshots of cell populations over time, but also to follow single-cell time histories of gene transcription. However, the analysis of both kinds of data using MEs are hindered: very few analytical solutions exist for models of population snapshot data, and it is not clear how to use MEs for the analysis of single-cell time course data.
As a first step to alleviate these problems, we present the full time-dependent analytical solution for a class of MEs relevant to gene expression, from both the time course and population snapshot viewpoints. The parameters can be arbitrary deterministic or stochastic functions of time.
The time course solution can take full advantage of recorded time-histories relevant in single-cell experiments and in the dynamics of synchronous cell populations. It effectively allows us to study intrinsic noise by accounting explicitly for the specific extrinsic noise that took place over the time history. Using this solution we then derive the population snapshot solution in a novel way, showing that it always takes a very specific form. I will finish with some examples to illustrate the power of this result.