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

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

Analysis of host response to bacterial infection using error model based gene expression microarray experiments

A key step in the analysis of microarray data is the selection of genes that are differentially expressed. Ideally, such experiments should be properly replicated in order to infer both technical and biological variability, and the data should be subjected to rigorous hypothesis tests to identify the differentially expressed genes. However, in microarray experiments involving the analysis of very large numbers of biological samples, replication is not always practical. Therefore, there is a need for a method to select differentially expressed genes in a rational way from insufficiently replicated data. In this paper, we describe a simple method that uses bootstrapping to generate an error model from a replicated pilot study that can be used to identify differentially expressed genes in subsequent large-scale studies on the same platform, but in which there may be no replicated arrays. The method builds a stratified error model that includes array-to-array variability, feature-to-feature variability and the dependence of error on signal intensity. We apply this model to the characterization of the host response in a model of bacterial infection of human intestinal epithelial cells. We demonstrate the effectiveness of error model based microarray experiments and propose this as a general strategy for a microarray-based screening of large collections of biological samples

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

Human dissemination of genes and microorganisms in Earth's Critical Zone

Earth's Critical Zone sustains terrestrial life and consists of the thin planetary surface layer between unaltered rock and the atmospheric boundary. Within this zone, flows of energy and materials are mediated by physical processes and by the actions of diverse organisms. Human activities significantly influence these physical and biological processes, affecting the atmosphere, shallow lithosphere, hydrosphere, and biosphere. The role of organisms includes an additional class of biogeochemical cycling, this being the flow and transformation of genetic information. This is particularly the case for the microorganisms that govern carbon and nitrogen cycling. These biological processes are mediated by the expression of functional genes and their translation into enzymes that catalyze geochemical reactions. Understanding human effects on microbial activity, fitness and distribution is an important component of Critical Zone science, but is highly challenging to investigate across the enormous physical scales of impact ranging from individual organisms to the planet. One arena where this might be tractable is by studying the dynamics and dissemination of genes for antibiotic resistance and the organisms that carry such genes. Here we explore the transport and transformation of microbial genes and cells through Earth's Critical Zone. We do so by examining the origins and rise of antibiotic resistance genes, their subsequent dissemination, and the ongoing colonization of diverse ecosystems by resistant organisms

Hybrid assembly of an agricultural slurry virome reveals a diverse and stable community with the potential to alter the metabolism and virulence of veterinary pathogens

Background: Viruses are the most abundant biological entities on Earth, known to be crucial components of microbial ecosystems. However, there is little information on the viral community within agricultural waste. There are currently ~ 2.7 million dairy cattle in the UK producing 7–8% of their own bodyweight in manure daily, and 28 million tonnes annually. To avoid pollution of UK freshwaters, manure must be stored and spread in accordance with guidelines set by DEFRA. Manures are used as fertiliser, and widely spread over crop fields, yet little is known about their microbial composition. We analysed the virome of agricultural slurry over a 5-month period using short and long-read sequencing. Results: Hybrid sequencing uncovered more high-quality viral genomes than long or short-reads alone; yielding 7682 vOTUs, 174 of which were complete viral genomes. The slurry virome was highly diverse and dominated by lytic bacteriophage, the majority of which represent novel genera (~ 98%). Despite constant influx and efflux of slurry, the composition and diversity of the slurry virome was extremely stable over time, with 55% of vOTUs detected in all samples over a 5-month period. Functional annotation revealed a diverse and abundant range of auxiliary metabolic genes and novel features present in the community, including the agriculturally relevant virulence factor VapE, which was widely distributed across different phage genera that were predicted to infect several hosts. Furthermore, we identified an abundance of phage-encoded diversity-generating retroelements, which were previously thought to be rare on lytic viral genomes. Additionally, we identified a group of crAssphages, including lineages that were previously thought only to be found in the human gut. Conclusions: The cattle slurry virome is complex, diverse and dominated by novel genera, many of which are not recovered using long or short-reads alone. Phages were found to encode a wide range of AMGs that are not constrained to particular groups or predicted hosts, including virulence determinants and putative ARGs. The application of agricultural slurry to land may therefore be a driver of bacterial virulence and antimicrobial resistance in the environment. [MediaObject not available: see fulltext.

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

Transcriptome analyses of the Giardia lamblia life cycle

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Molecular and Biochemical Parasitology 174 (2010): 62-65, doi:10.1016/j.molbiopara.2010.05.010.We quantified mRNA abundance from 10 stages in the Giardia lamblia life cycle in vitro using Serial Analysis of Gene Expression (SAGE). 163 abundant transcripts were expressed constitutively. 71 transcripts were upregulated specifically during excystation and 42 during encystation. Nonetheless, the transcriptomes of cysts and trophozoites showed major differences. SAGE detected co-expressed clusters of 284 transcripts differentially expressed in cysts and excyzoites and 287 transcripts in vegetative trophozoites and encysting cells. All clusters included known genes and pathways as well as proteins unique to Giardia or diplomonads. SAGE analysis of the Giardia life cycle identified a number of kinases, phosphatases, and DNA replication proteins involved in excystation and encystation, which could be important for examining the roles of cell signaling in giardial differentiation. Overall, these data pave the way for directed gene discovery and a better understanding of the biology of Giardia lamblia.BJD, DSR, and FDG were supported by NIH grants AI42488, GM61896, DK35108, and AI051687. DP and SGS were supported by grants from the Swedish Natural Science Research Council, the Swedish Medical Research Council, and the Karolinska Institutet. AGM, SRB, SPP, and MJC were supported by NIH grant AI51089 and by the Marine Biological Laboratory’s Program in Global Infectious Diseases, funded by the Ellison Medical Foundation

Antimicrobial resistance in dairy slurry tanks: A critical point for measurement and control

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