Phenotypic switching of populations of cells in a stochastic environment

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.Comment: 17 pages, 6 figure

The influence of weight and fat on lamb prices revisited

Previous research has found inconsistencies in the valuation of weight and fat characteristics of lamb carcasses between the saleyard and wholesale markets. In this paper, recent New South Wales saleyard and wholesale price data on different classes of lamb are analysed using hedonic methods to determine the relative influence of weight and fat on prices received. Fat score 2 lambs are heavily discounted relative to fat score 3 lambs, and there are significant seasonal price differentials, but there are no significant premiums or discounts for weight or other fat characteristics. These results hold for both the saleyard and wholesale markets. The implication is that the efficiency of price discovery in the Australian lamb market has improved a little in recent years in the sense that premiums and discounts are now consistent across market levels. However consumers’ stated preferences for large lean lambs are not being reflected in price incentives generated in the live lamb and lamb carcass markets.lamb, marketing, hedonic models, carcass characteristics, Demand and Price Analysis, Livestock Production/Industries, Marketing,

Intrinsic noise in systems with switching environments

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics. Similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread. Existing piecewise-deterministic Markov process (PDMP) approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching. Here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear-noise approximation. Specifically we derive the stationary distributions of a number of model systems, in good agreement with simulations. This improves existing approaches which are limited to the regimes of fast and slow switching.Comment: 15 pages, 11 figure

A stochastic and dynamical view of pluripotency in mouse embryonic stem cells

Pluripotent embryonic stem cells are of paramount importance for biomedical research thanks to their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent state is regulated by complex genetic regulatory network. Latest advances in transcriptomics have made it possible to infer basic topologies of pluripotency governing networks. The inferred network topologies, however, only encode boolean information while remaining silent about the roles of dynamics and molecular noise in gene expression. These features are widely considered essential for functional decision making. Herein we developed a framework for extending the boolean level networks into models accounting for individual genetic switches and promoter architecture which allows mechanistic interrogation of the roles of molecular noise, external signaling, and network topology. We demonstrate the pluripotent state of the network to be a broad attractor which is robust to variations of gene expression. Dynamics of exiting the pluripotent state, on the other hand, is significantly influenced by the molecular noise originating from genetic switching events which makes cells more responsive to extracellular signals. Lastly we show that steady state probability landscape can be significantly remodeled by global gene switching rates alone which can be taken as a proxy for how global epigenetic modifications exert control over stability of pluripotent states.Comment: 11 pages, 7 figure

Do arsenic levels in rice pose a health risk to the UK population?

Consumption of rice and rice products can be a significant exposure pathway to inorganic arsenic (iAs), which is a group 1 carcinogen to humans. The UK follows the current European Commission regulations so that iAs concentrations must be  0.1 mg kg-1 were selected for As speciation using HPLC-ICP-MS. Based on the average concentration of iAs of our samples, we calculated values for the Lifetime Cancer Risk (LCR), Target Hazard Quotient (THQ) and Margin of Exposure (MoE). We found a statistically significant difference between organically and non-organically grown rice. We also found that brown rice contained a significantly higher concentration of iAs compared to white or wild rice. Notably, 28 rice samples exceeded the iAs maximum limit stipulated by the EU (0.1 mg kg-1) with an average iAs concentration of 0.13 mg kg-1; therefore consumption of these rice types could be riskier for infants than adults. Based on the MoE, it was found that infants up to 1 year must be restricted to a maximum of 20 g per day for the 28 rice types to avoid carcinogenic risks. We believe that consumers could be better informed whether the marketed product is fit for infants and young children, via appropriate product labelling containing information about iAs concentration

The role of extracellular DNA in uranium precipitation and biomineralisation.

Bacterial extra polymeric substances (EPS) have been associated with the extracellular precipitation of uranium. Here we report findings on the biomineralisation of uranium, with extracellular DNA (eDNA) used as a model biomolecule representative of EPS. The complexation and precipitation of eDNA with uranium were investigated as a function of pH, ionic strength and varying concentrations of reactants. The role of phosphate moieties in the biomineralisation mechanism was studied by enzymatically releasing phosphate (ePO4) from eDNA compared to abiotic phosphate (aPO4). The eDNA-uranium precipitates and uranium minerals obtained were characterised by Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FT-IR) spectroscopy, Scanning Electron Microscopy-Energy Dispersive X-Ray analysis (SEM-EDX), X-Ray Powder Diffraction (XRD) and X-Ray Photoelectron Spectroscopy (XPS). ATR-FT-IR showed that at pH 5, the eDNA-uranium precipitation mechanism was predominantly mediated by interactions with phosphate moieties from eDNA. At pH 2, the uranium interactions with eDNA occur mainly through phosphate. The solubility equilibrium was dependent on pH with the formation of precipitate reduced as the pH increased. The XRD data confirmed the formation of a uranium phosphate precipitate when synthesised using ePO4. XPS and SEM-EDX studies showed the incorporation of carbon and nitrogen groups from the enzymatic orthophosphate hydrolysis on the obtained precipitated. These results suggested that the removal of uranium from solution occurs via two mechanisms: complexation by eDNA molecules and precipitation of a uranium phosphate mineral of the type (UO2HPO4)·xH2O by enzymatic orthophosphate hydrolysis. This demonstrated that eDNA from bacterial EPS is a key contributor to uranium biomineralisation

Model reduction methods for classical stochastic systems with fast-switching environments: reduced master equations, stochastic differential equations, and applications

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of infinite time scale separation. In some cases, this leads to master equations with negative transition `rates' or bursting events. We devise a simulation algorithm in discrete time to unravel these master equations into sample paths, and provide an interpretation of bursting events. Focusing on stochastic population dynamics coupled to external environments, we discuss a series of approximation schemes combining expansions in the inverse switching rate of the environment, and a Kramers--Moyal expansion in the inverse size of the population. This places the different approximations in relation to existing work on piecewise-deterministic and piecewise-diffusive Markov processes. We apply the model reduction methods to different examples including systems in biology and a model of crack propagation.Comment: 31 pages, 13 figure

The role of the bacterial cell surface and extracellular macromolecules in U(VI) biosorption and biomineralisation.

Uranium biosorption and biomineralisation are processes exhibited by bacteria that aren’t fully understood at a mechanistic level, making it difficult to consider their use and application in remediation, extraction and reuse. The aim of this study was, therefore, to deconstruct the bacterial cell and characterise the specific roles of cell surface structures and extra polymeric substances, in order to elucidate their contribution to the biosorption and biomineralisation of uranium within live cells. The complexation and precipitation of uranium with extracellular DNA (eDNA) was predominantly mediated by negatively charged phosphate moieties within eDNA. The reaction was dependent on pH, where the formation of a precipitate was reduced as the pH increased. Towards circumneutral pH, acid phosphatase liberated phosphate from eDNA that precipitated uranium as a phosphate-bearing mineral. The biosorption of uranium with bacteria is governed by the interactions with functional groups at the cell surface. The cell wall isolates and lysed cells of B. subtilis 168 exhibited a greater uranium retention capacity in comparison to those from P. putida 33015, live cells and cell membrane isolates from both strains. Carboxyl groups and phosphate groups, from proteins and phosphorylated biopolymers, were responsible uranium biosorption with the cell surface structures. The viability and metabolic activity of live cells of P. putida 33015 and D. radiodurans R1 in the presence of uranium was evaluated. An increase in uranium concentration was directly linked to cell toxicity in both strains. At low concentrations of U(VI) and circumneutral pH, viable cells likely sequestered uranium either through biosorption or through the precipitation of enzymatically generated uranium phosphate minerals that were tethered to the cell surface or within EPS as a tolerance mechanism to cope with uranium toxicity. At higher concentrations of uranium or at low pH where the bacterial growth wasn’t favourable or there was cell death, biosorption to the bacterial biomass present likely occurred