Mathematical model of the Lux luminescence system in the terrestrial bacterium Photorhabdus luminescens.

A mathematical model of the Lux luminescence system, governed by the operon luxCDABE in the terrestrial bacterium Photorhabdus luminescens, was constructed using a set of coupled ordinary differential equations. This model will have value in the interpretation of Lux data when used as a reporter in time-course gene expression experiments. The system was tested on time series and stationary data from published papers and the model is in good agreement with the published data. Metabolic control analysis demonstrates that control of the system lies mainly with the aldehyde recycling pathway (LuxE and LuxC). The rate at which light is produced in the steady state model shows a low sensitivity to changes in kinetic parameter values to those measured in other species of luminescent bacteria, demonstrating the robustness of the Lux system

Stochastic Modelling Approach to the Incubation Time of Prionic Diseases

Transmissible spongiform encephalopathies like the bovine spongiform encephalopathy (BSE) and the Creutzfeldt-Jakob disease (CJD) in humans are neurodegenerative diseases for which prions are the attributed pathogenic agents. A widely accepted theory assumes that prion replication is due to a direct interaction between the pathologic (PrPsc) form and the host encoded (PrPc) conformation, in a kind of an autocatalytic process. Here we show that the overall features of the incubation time of prion diseases are readily obtained if the prion reaction is described by a simple mean-field model. An analytical expression for the incubation time distribution then follows by associating the rate constant to a stochastic variable log normally distributed. The incubation time distribution is then also shown to be log normal and fits the observed BSE data very well. The basic ideas of the theoretical model are then incorporated in a cellular automata model. The computer simulation results yield the correct BSE incubation time distribution at low densities of the host encoded protein

A Bayesian approach to analyzing phenotype microarray data enables estimation of microbial growth parameters

Biolog phenotype microarrays enable simultaneous, high throughput analysis of cell cultures in different environments. The output is high-density time-course data showing redox curves (approximating growth) for each experimental condition. The software provided with the Omnilog incubator/reader summarizes each time-course as a single datum, so most of the information is not used. However, the time courses can be extremely varied and often contain detailed qualitative (shape of curve) and quantitative (values of parameters) information. We present a novel, Bayesian approach to estimating parameters from Phenotype Microarray data, fitting growth models using Markov Chain Monte Carlo methods to enable high throughput estimation of important information, including length of lag phase, maximal ``growth'' rate and maximum output. We find that the Baranyi model for microbial growth is useful for fitting Biolog data. Moreover, we introduce a new growth model that allows for diauxic growth with a lag phase, which is particularly useful where Phenotype Microarrays have been applied to cells grown in complex mixtures of substrates, for example in industrial or biotechnological applications, such as worts in brewing. Our approach provides more useful information from Biolog data than existing, competing methods, and allows for valuable comparisons between data series and across different models

Strong negative self regulation of Prokaryotic transcription factors increases the intrinsic noise of protein expression

Background Many prokaryotic transcription factors repress their own transcription. It is often asserted that such regulation enables a cell to homeostatically maintain protein abundance. We explore the role of negative self regulation of transcription in regulating the variability of protein abundance using a variety of stochastic modeling techniques. Results We undertake a novel analysis of a classic model for negative self regulation. We demonstrate that, with standard approximations, protein variance relative to its mean should be independent of repressor strength in a physiological range. Consequently, in that range, the coefficient of variation would increase with repressor strength. However, stochastic computer simulations demonstrate that there is a greater increase in noise associated with strong repressors than predicted by theory. The discrepancies between the mathematical analysis and computer simulations arise because with strong repressors the approximation that leads to Michaelis-Menten-like hyperbolic repression terms ceases to be valid. Because we observe that strong negative feedback increases variability and so is unlikely to be a mechanism for noise control, we suggest instead that negative feedback is evolutionarily favoured because it allows the cell to minimize mRNA usage. To test this, we used in silico evolution to demonstrate that while negative feedback can achieve only a modest improvement in protein noise reduction compared with the unregulated system, it can achieve good improvement in protein response times and very substantial improvement in reducing mRNA levels. Conclusions Strong negative self regulation of transcription may not always be a mechanism for homeostatic control of protein abundance, but instead might be evolutionarily favoured as a mechanism to limit the use of mRNA. The use of hyperbolic terms derived from quasi-steady-state approximation should also be avoided in the analysis of stochastic models with strong repressors

On the statistical mechanics of prion diseases

We simulate a two-dimensional, lattice based, protein-level statistical mechanical model for prion diseases (e.g., Mad Cow disease) with concommitant prion protein misfolding and aggregation. Our simulations lead us to the hypothesis that the observed broad incubation time distribution in epidemiological data reflect fluctuation dominated growth seeded by a few nanometer scale aggregates, while much narrower incubation time distributions for innoculated lab animals arise from statistical self averaging. We model `species barriers' to prion infection and assess a related treatment protocol.Comment: 5 Pages, 3 eps figures (submitted to Physical Review Letters

In silico evolution of diauxic growth

The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth. Diauxic growth is usually thought of as a an adaptation to maximise biomass production in an environment offering two or more carbon sources. While diauxic growth has been studied widely both experimentally and theoretically, the hypothesis that diauxic growth is a strategy to increase overall growth has remained an unconfirmed conjecture. Here, we present a minimal mathematical model of a bacterial nutrient uptake system and metabolism. We subject this model to artificial evolution to test under which conditions diauxic growth evolves. As a result, we find that, indeed, sequential uptake of nutrients emerges if there is competition for nutrients and the metabolism/uptake system is capacity limited. However, we also find that diauxic growth is a secondary effect of this system and that the speed-up of nutrient uptake is a much larger effect. Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency. Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves. This suggests that the lag-phase is a consequence of stochastic gene expression

Inclusion of neighboring base interdependencies substantially improves genome-wide prokaryotic transcription factor binding site prediction

Prediction of transcription factor binding sites is an important challenge in genome analysis. The advent of next generation genome sequencing technologies makes the development of effective computational approaches particularly imperative. We have developed a novel training-based methodology intended for prokaryotic transcription factor binding site prediction. Our methodology extends existing models by taking into account base interdependencies between neighbouring positions using conditional probabilities and includes genomic background weighting. This has been tested against other existing and novel methodologies including position-specific weight matrices, first-order Hidden Markov Models and joint probability models. We have also tested the use of gapped and ungapped alignments and the inclusion or exclusion of background weighting. We show that our best method enhances binding site prediction for all of the 22 Escherichia coli transcription factors with at least 20 known binding sites, with many showing substantial improvements. We highlight the advantage of using block alignments of binding sites over gapped alignments to capture neighbouring position interdependencies. We also show that combining these methods with ChIP-on-chip data has the potential to further improve binding site prediction. Finally we have developed the ungapped likelihood under positional background platform: a user friendly website that gives access to the prediction method devised in this work

Mathematical modelling for antibiotic resistance control policy: do we know enough?

Background: Antibiotics remain the cornerstone of modern medicine. Yet there exists an inherent dilemma in their use: we are able to prevent harm by administering antibiotic treatment as necessary to both humans and animals, but we must be mindful of limiting the spread of resistance and safeguarding the efficacy of antibiotics for current and future generations. Policies that strike the right balance must be informed by a transparent rationale that relies on a robust evidence base. Main text: One way to generate the evidence base needed to inform policies for managing antibiotic resistance is by using mathematical models. These models can distil the key drivers of the dynamics of resistance transmission from complex infection and evolutionary processes, as well as predict likely responses to policy change in silico. Here, we ask whether we know enough about antibiotic resistance for mathematical modelling to robustly and effectively inform policy. We consider in turn the challenges associated with capturing antibiotic resistance evolution using mathematical models, and with translating mathematical modelling evidence into policy. Conclusions: We suggest that in spite of promising advances, we lack a complete understanding of key principles. From this we advocate for priority areas of future empirical and theoretical research

Lipidomic analysis of plasma samples from women with polycystic ovary syndrome

Abstract Polycystic ovary syndrome (PCOS) is a common disorder affecting between 5 and 18 % of females of reproductive age and can be diagnosed based on a combination of clinical, ultrasound and biochemical features, none of which on its own is diagnostic. A lipidomic approach using liquid chromatography coupled with accurate mass high-resolution mass-spectrometry (LCHRMS) was used to investigate if there were any differences in plasma lipidomic profiles in women with PCOS compared with control women at different stages of menstrual cycle. Plasma samples from 40 women with PCOS and 40 controls aged between 18 and 40 years were analysed in combination with multivariate statistical analyses. Multivariate data analysis (LASSO regression and OPLSDA) of the sample lipidomics datasets showed a weak prediction model for PCOS versus control samples from the follicular and mid-cycle phases of the menstrual cycle, but a stronger model (specificity 85 % and sensitivity 95 %) for PCOS versus the luteal phase menstrual cycle controls. The PCOS vs luteal phase model showed increased levels of plasma triglycerides and sphingomyelins and decreased levels of lysophosphatidylcholines and phosphatidylethanolamines in PCOS women compared with controls. Lipid biomarkers of PCOS were tentatively identified which may be useful in distinguishing PCOS from controls especially when performed during the menstrual cycle luteal phase