Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Mathematical analysis of the Escherichia coli chemotaxis signalling pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an {\it Escherichia coli} cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady-state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions, the system may exhibit oscillatory type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins does. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions of the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our manuscript closes by discussing intercell variability of total protein concentration as means of ensuring the overall survival of a population as cells are subjected to different environments

Renin, endothelial no synthase and endothelin gene expression in the 2Kidney-1clip goldblatt model of long-term renovascular hypertension

<p>Abstract</p> <p>Objective</p> <p>Numerous reports have shown the influence of renin, nitric oxide (NO) and the endothelin (ET) systems for regulation of blood pressure and renal function. Furthermore, interactions between these peptides have been reported. Aim of our study was to investigate the relative contribution of these compounds in long-term renovascular hypertension/renal ischemia.</p> <p>Methods</p> <p>Hypertension/left-sided renal ischemia was induced using the 2K1C-Goldblatt rat model. Renal renin, ET-1, ET-3 and endothelial NO synthase (eNOS) gene expression was measured by means of RNAse protection assay at different timepoints up to 10 weeks after induction of renal artery stenosis.</p> <p>Results</p> <p>Plasma renin activity and renal renin gene expression in the left kidney were increased in the clipped animals while eNOS expression was unchanged. Furthermore, an increase in ET-1 expression and a decrease of ET-3 expression was detected in early stenosis.</p> <p>Conclusions</p> <p>While renin is obviously involved in regulation of blood pressure and renal function in unilateral renal artery stenosis, ET-1, ET-3 and endothelium derived NO do not appear to play an important role in renal adaptation processes in long-term renal artery stenosis, although ET-1 and ET-3 might be involved in short-term adaptation processes.</p

Rule-based modeling of biochemical systems with BioNetGen

Totowa, NJ. Please cite this article when referencing BioNetGen in future publications. Rule-based modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate site-specific details about proteinprotein interactions into a model for the dynamics of a signal-transduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of protein-protein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rule-based model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rule-based modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly large-scale models for other biochemical systems. Key Words: Computational systems biology; mathematical modeling; combinatorial complexity; software; formal languages; stochastic simulation; ordinary differential equations; protein-protein interactions; signal transduction; metabolic networks. 1

Small Change: Economics and the British coin-tree

This is the accepted manuscript for the following article: Ceri Houlbrook, “Small Change: Economics and the British coin-tree”, Post Medieval Archaeology, Vol. 49(1), June 2015. The final published version can be found at: http://www.tandfonline.com/doi/full/10.1179/0079423615Z.00000000074 © Society for Post-Medieval Archaeology 2015Throughout the c.2000 year period coins have been circulated in Britain, they have also been ritually employed, most notably as votive deposits. Focusing specifically on the understudied custom of the British coin-tree, whereby coins are ritually embedded into the barks of trees, this paper considers the coin’s role and applicability as a deposit. It aims to demonstrate that our understanding of the coin’s past, present, and future ritual employment is not only aided by a consideration of economics and the coin’s secular function; it would be utterly incomplete without it.Peer reviewedFinal Accepted Versio

Cyr61/CCN1 Displays High-Affinity Binding to the Somatomedin B 1–44 Domain of Vitronectin

OV) family of extracellular-associated (matricellular) proteins that present four distinct functional modules, namely insulin-like growth factor binding protein (IGFBP), von Willebrand factor type C (vWF), thrombospondin type 1 (TSP), and C-terminal growth factor cysteine knot (CT) domain. While heparin sulphate proteoglycans reportedly mediate the interaction of Cyr61 with the matrix and cell surface, the role of other extracellular associated proteins has not been revealed. at high concentrations attenuate Cyr61 binding to immobilized VTNC, while monomeric VTNC was ineffective. Therefore, immobilization of VTNC exposes cryptic epitopes that recognize Cyr61 with high affinity, as reported for a number of antibodies, β-endorphin, and other molecules. domain suggests that VTNC represent a point of anchorage for CCN family members to the matrix. Results are discussed in the context of the role of CCN and VTNC in matrix biology and angiogenesis

Finding Diagnostically Useful Patterns in Quantitative Phenotypic Data.

Trio-based whole-exome sequence (WES) data have established confident genetic diagnoses in ∼40% of previously undiagnosed individuals recruited to the Deciphering Developmental Disorders (DDD) study. Here we aim to use the breadth of phenotypic information recorded in DDD to augment diagnosis and disease variant discovery in probands. Median Euclidean distances (mEuD) were employed as a simple measure of similarity of quantitative phenotypic data within sets of ≥10 individuals with plausibly causative de novo mutations (DNM) in 28 different developmental disorder genes. 13/28 (46.4%) showed significant similarity for growth or developmental milestone metrics, 10/28 (35.7%) showed similarity in HPO term usage, and 12/28 (43%) showed no phenotypic similarity. Pairwise comparisons of individuals with high-impact inherited variants to the 32 individuals with causative DNM in ANKRD11 using only growth z-scores highlighted 5 likely causative inherited variants and two unrecognized DNM resulting in an 18% diagnostic uplift for this gene. Using an independent approach, naive Bayes classification of growth and developmental data produced reasonably discriminative models for the 24 DNM genes with sufficiently complete data. An unsupervised naive Bayes classification of 6,993 probands with WES data and sufficient phenotypic information defined 23 in silico syndromes (ISSs) and was used to test a "phenotype first" approach to the discovery of causative genotypes using WES variants strictly filtered on allele frequency, mutation consequence, and evidence of constraint in humans. This highlighted heterozygous de novo nonsynonymous variants in SPTBN2 as causative in three DDD probands

Targeted Next-Generation Sequencing Analysis of 1,000 Individuals with Intellectual Disability.

To identify genetic causes of intellectual disability (ID), we screened a cohort of 986 individuals with moderate to severe ID for variants in 565 known or candidate ID-associated genes using targeted next-generation sequencing. Likely pathogenic rare variants were found in ∼11% of the cases (113 variants in 107/986 individuals: ∼8% of the individuals had a likely pathogenic loss-of-function [LoF] variant, whereas ∼3% had a known pathogenic missense variant). Variants in SETD5, ATRX, CUL4B, MECP2, and ARID1B were the most common causes of ID. This study assessed the value of sequencing a cohort of probands to provide a molecular diagnosis of ID, without the availability of DNA from both parents for de novo sequence analysis. This modeling is clinically relevant as 28% of all UK families with dependent children are single parent households. In conclusion, to diagnose patients with ID in the absence of parental DNA, we recommend investigation of all LoF variants in known genes that cause ID and assessment of a limited list of proven pathogenic missense variants in these genes. This will provide 11% additional diagnostic yield beyond the 10%-15% yield from array CGH alone.Action Medical Research (SP4640); the Birth Defect Foundation (RG45448); the Cambridge National Institute for Health Research Biomedical Research Centre (RG64219); the NIHR Rare Diseases BioResource (RBAG163); Wellcome Trust award WT091310; The Cell lines and DNA bank of Rett Syndrome, X-linked mental retardation and other genetic diseases (member of the Telethon Network of Genetic Biobanks (project no. GTB12001); the Genetic Origins of Congenital Heart Disease Study (GO-CHD)- funded by British Heart Foundation (BHF)This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1002/humu.2290