Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects.

In insect respiration, oxygen from the air diffuses through a branching system of air-filled tubes to the cells of the body and carbon dioxide produced in cellular respiration diffuses out. The tracheal system has a very large surface area, so water loss is a potential threat and the question of how insects regulate oxygen uptake and water loss has been an important issue in insect physiology for the past century. The tracheal system starts at spiracles on the surface of the body that insects can open and close, and three phases are observed experimentally, open or closed for relatively long periods of time and opening and closing rapidly, which is called fluttering. In previous work we have shown that during this flutter phase, no matter how small the percentage of time that the spiracles are open, the insect can absorb almost as much oxygen as if the spiracle were always open, if the insect flutters fast enough. This left open the question of water loss during the flutter phase, which is the question addressed in this paper. We formulate a stochastic diffusion-convection model for the concentration of water vapor in the tracheae. Mathematical analysis of the model yields an explicit formula for water loss as a function of six non-dimensional parameters and we use experimental data from various insects to show that, for parameters in the physiological ranges, water loss during the flutter phase is approximately proportional to the percentage of time open. This means that the insect can solve the oxygen uptake versus water loss problem by choosing to have their spiracles open a small percentage of time during the flutter phase and fluttering rapidly.

Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks.

Stochastic gene expression dynamics can be modelled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner's Poisson representation. Here, we systematically investigate the Poisson representation in complex stochastic gene regulatory networks. We show that when the gene of interest is unregulated, the discrete and continuous descriptions of stochastic gene expression are always related by the Poisson representation, no matter how complex the model is. This generalizes the results obtained in Dattani & Barahona (Dattani & Barahona 2017 J. R. Soc. Interface 14, 20160833 (doi:10.1098/rsif.2016.0833)). In addition, using a simple counter-example, we find that the Poisson representation in general fails to link the two descriptions when the gene is regulated. However, for a general stochastic gene regulatory network, we demonstrate that the discrete and continuous models are approximately related by the Poisson representation in the limit of large protein numbers. These theoretical results are further applied to analytically solve many complex gene expression models whose exact distributions are previously unknown.

Multiscale Tumor Modeling With Drug Pharmacokinetic and Pharmacodynamic Profile Using Stochastic Hybrid System.

Effective cancer treatment strategy requires an understanding of cancer behavior and development across multiple temporal and spatial scales. This has resulted into a growing interest in developing multiscale mathematical models that can simulate cancer growth, development, and response to drug treatments. This study thus investigates multiscale tumor modeling that integrates drug pharmacokinetic and pharmacodynamic (PK/PD) information using stochastic hybrid system modeling framework. Specifically, (1) pathways modeled by differential equations are adopted for gene regulations at the molecular level; (2) cellular automata (CA) model is proposed for the cellular and multicellular scales. Markov chains are used to model the cell behaviors by taking into account the gene expression levels, cell cycle, and the microenvironment. The proposed model enables the prediction of tumor growth under given molecular properties, microenvironment conditions, and drug PK/PD profile. Simulation results demonstrate the effectiveness of the proposed approach and the results agree with observed tumor behaviors.