On the Mathematics of the Law of Mass Action

In 1864,Waage and Guldberg formulated the "law of mass action." Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In our view, sufficient understanding has been acquired to warrant a formal mathematical consolidation. A major goal of this consolidation is to solidify the mathematical foundations of mass action chemistry -- to provide precise definitions, elucidate what can now be proved, and indicate what is only conjectured. In addition, we believe that the law of mass action is of intrinsic mathematical interest and should be made available in a form that might transcend its application to chemistry alone. We present the law of mass action in the context of a dynamical theory of sets of binomials over the complex numbers.Comment: 40 pages, no figure

Analysis of cell proliferation and tissue remodelling uncovers a KLF4 activity score associated with poor prognosis in colorectal cancer

Human cancers can be classified based on gene signatures quantifying the degree of cell proliferation and tissue remodelling (PR). However, the specific factors that drive the increased tissue remodelling in tumours are not fully understood. Here we address this question using colorectal cancer as a case study. We reanalysed a reported cohort of colorectal cancer patients. The patients were stratified based on gene signatures of cell proliferation and tissue remodelling. Putative transcription factors activity was inferred using gene expression profiles and annotations of transcription factor targets as input. We demonstrate that the PR classification performs better than the currently adopted consensus molecular subtyping (CMS). Although CMS classification differentiates patients with a mesenchymal signature, it cannot distinguish the remaining patients based on survival. We demonstrate that the missing factor is cell proliferation, which is indicative of good prognosis. We also uncover a KLF4 transcription factor activity score associated with the tissue remodelling gene signature. We further show that the KLF4 activity score is significantly higher in colorectal tumours with predicted infiltration of cells from the myeloid lineage. The KLF4 activity score is associated with tissue remodelling, myeloid cell infiltration and poor prognosis in colorectal cancer

Efficient Syntax-Driven Lumping of Differential Equations

We present an algorithm to compute exact aggregations of a class of systems of ordinary differential equations (ODEs). Our approach consists in an extension of Paige and Tarjan’s seminal solution to the coarsest refinement problem by encoding an ODE system into a suitable discrete-state representation. In particular, we consider a simple extension of the syntax of elementary chemical reaction networks because (i) it can express ODEs with derivatives given by polynomials of degree at most two, which are relevant in many applications in natural sciences and engineering; and (ii) we can build on two recently introduced bisimulations, which yield two complementary notions of ODE lumping. Our algorithm computes the largest bisimulations in O(r⋅s⋅logs)O(r⋅s⋅log⁡s) time, where r is the number of monomials and s is the number of variables in the ODEs. Numerical experiments on real-world models from biochemistry, electrical engineering, and structural mechanics show that our prototype is able to handle ODEs with millions of variables and monomials, providing significant model reductions

Genome-wide methylation analysis identifies genes silenced in non-seminoma cell lines

Silencing of genes by DNA methylation is a common phenomenon in many types of cancer. However, the genome wide effect of DNA methylation on gene expression has been analysed in relatively few cancers. Germ cell tumours (GCTs) are a complex group of malignancies. They are unique in developing from a pluripotent progenitor cell. Previous analyses have suggested that non-seminomas exhibit much higher levels of DNA methylation than seminomas. The genomic targets that are methylated, the extent to which this results in gene silencing and the identity of the silenced genes most likely to play a role in the tumours’ biology have not yet been established. In this study, genome-wide methylation and expression analysis of GCT cell lines was combined with gene expression data from primary tumours to address this question. Genome methylation was analysed using the Illumina infinium HumanMethylome450 bead chip system and gene expression was analysed using Affymetrix GeneChip Human Genome U133 Plus 2.0 arrays. Regulation by methylation was confirmed by demethylation using 5-aza-2-deoxycytidine and reverse transcription–quantitative PCR. Large differences in the level of methylation of the CpG islands of individual genes between tumour cell lines correlated well with differential gene expression. Treatment of non-seminoma cells with 5-aza-2-deoxycytidine verified that methylation of all genes tested played a role in their silencing in yolk sac tumour cells and many of these genes were also differentially expressed in primary tumours. Genes silenced by methylation in the various GCT cell lines were identified. Several pluripotency-associated genes were identified as a major functional group of silenced genes

Induction and regulation of matrix metalloproteinase-12in human airway smooth muscle cells

BACKGROUND: The elastolytic enzyme matrix metalloproteinase (MMP)-12 has been implicated in the development of airway inflammation and remodeling. We investigated whether human airway smooth muscle cells could express and secrete MMP-12, thereby participating in the pathogenesis of airway inflammatory diseases. METHODS: Laser capture microdissection was used to collect smooth muscle cells from human bronchial biopsy sections. MMP-12 mRNA expression was analysed by quantitative real-time RT-PCR. MMP-12 protein expression and secretion from cultured primary airway smooth muscle cells was further analysed by Western blot. MMP-12 protein localization in bronchial tissue sections was detected by immunohistochemistry. MMP-12 activity was determined by zymography. The TransAM AP-1 family kit was used to measure c-Jun activation and nuclear binding. Analysis of variance was used to determine statistical significance. RESULTS: We provide evidence that MMP-12 mRNA and protein are expressed by in-situ human airway smooth muscle cells obtained from bronchial biopsies of normal volunteers, and of patients with asthma, COPD and chronic cough. The pro-inflammatory cytokine, interleukin (IL)-1β, induced a >100-fold increase in MMP-12 gene expression and a >10-fold enhancement in MMP-12 activity of primary airway smooth muscle cell cultures. Selective inhibitors of extracellular signal-regulated kinase, c-Jun N-terminal kinase and phosphatidylinositol 3-kinase reduced the activity of IL-1β on MMP-12, indicating a role for these kinases in IL-1β-induced induction and release of MMP-12. IL-1β-induced MMP-12 activity and gene expression was down-regulated by the corticosteroid dexamethasone but up-regulated by the inflammatory cytokine tumour necrosis factor (TNF)-α through enhancing activator protein-1 activation by IL-1β. Transforming growth factor-β had no significant effect on MMP-12 induction. CONCLUSION: Our findings indicate that human airway smooth muscle cells express and secrete MMP-12 that is up-regulated by IL-1β and TNF-α. Bronchial smooth muscle cells may be an important source of elastolytic activity, thereby participating in remodeling in airway diseases such as COPD and chronic asthma

Parent-Of-Origin Effects in Autism Identified through Genome-Wide Linkage Analysis of 16,000 SNPs

Autism is a common heritable neurodevelopmental disorder with complex etiology. Several genome-wide linkage and association scans have been carried out to identify regions harboring genes related to autism or autism spectrum disorders, with mixed results. Given the overlap in autism features with genetic abnormalities known to be associated with imprinting, one possible reason for lack of consistency would be the influence of parent-of-origin effects that may mask the ability to detect linkage and association.We have performed a genome-wide linkage scan that accounts for potential parent-of-origin effects using 16,311 SNPs among families from the Autism Genetic Resource Exchange (AGRE) and the National Institute of Mental Health (NIMH) autism repository. We report parametric (GH, Genehunter) and allele-sharing linkage (Aspex) results using a broad spectrum disorder case definition. Paternal-origin genome-wide statistically significant linkage was observed on chromosomes 4 (LOD(GH) = 3.79, empirical p<0.005 and LOD(Aspex) = 2.96, p = 0.008), 15 (LOD(GH) = 3.09, empirical p<0.005 and LOD(Aspex) = 3.62, empirical p = 0.003) and 20 (LOD(GH) = 3.36, empirical p<0.005 and LOD(Aspex) = 3.38, empirical p = 0.006).These regions may harbor imprinted sites associated with the development of autism and offer fruitful domains for molecular investigation into the role of epigenetic mechanisms in autism

Circadian Preference Modulates the Neural Substrate of Conflict Processing across the Day

Human morning and evening chronotypes differ in their preferred timing for sleep and wakefulness, as well as in optimal daytime periods to cope with cognitive challenges. Recent evidence suggests that these preferences are not a simple by-product of socio-professional timing constraints, but can be driven by inter-individual differences in the expression of circadian and homeostatic sleep-wake promoting signals. Chronotypes thus constitute a unique tool to access the interplay between those processes under normally entrained day-night conditions, and to investigate how they impinge onto higher cognitive control processes. Using functional magnetic resonance imaging (fMRI), we assessed the influence of chronotype and time-of-day on conflict processing-related cerebral activity throughout a normal waking day. Sixteen morning and 15 evening types were recorded at two individually adapted time points (1.5 versus 10.5 hours spent awake) while performing the Stroop paradigm. Results show that interference-related hemodynamic responses are maintained or even increased in evening types from the subjective morning to the subjective evening in a set of brain areas playing a pivotal role in successful inhibitory functioning, whereas they decreased in morning types under the same conditions. Furthermore, during the evening hours, activity in a posterior hypothalamic region putatively involved in sleep-wake regulation correlated in a chronotype-specific manner with slow wave activity at the beginning of the night, an index of accumulated homeostatic sleep pressure. These results shed light into the cerebral mechanisms underlying inter-individual differences of higher-order cognitive state maintenance under normally entrained day-night conditions

Family-Centered Preventive Intervention for Military Families: Implications for Implementation Science

In this paper, we report on the development and dissemination of a preventive intervention, Families OverComing Under Stress (FOCUS), an eight-session family-centered intervention for families facing the impact of wartime deployments. Specific attention is given to the challenges of rapidly deploying a prevention program across diverse sites, as well as to key elements of implementation success. FOCUS, developed by a UCLA-Harvard team, was disseminated through a large-scale demonstration project funded by the United States Bureau of Navy Medicine and Surgery (BUMED) beginning in 2008 at 7 installations and expanding to 14 installations by 2010. Data are presented to describe the range of services offered, as well as initial intervention outcomes. It proved possible to develop the intervention rapidly and to deploy it consistently and effectively

Local is not always better: the impact of climate information on values, behavior and policy support

In the current research, we experimentally examined the effect of providing local or global information about the impacts of climate change on individuals’ perceived importance of climate change and on their willingness to take action to address it, including policy support. We examined these relationships in the context of individuals’ general value orientations. Our findings, from 99 US residents, suggest that different kinds of climate information (local, global, or none) interact with values vis-à-vis our dependent variables. Specifically, while self-transcendent values predict perceived importance and pro-environmental behavior across all three information conditions, the effect on policy support is less clear. Furthermore, we detected a “reactance effect” where individuals with self-enhancing values who read local information thought that climate change was less important and were less willing to engage in pro-environmental behavior and support policy than self-enhancing individuals in the other information conditions. These results suggest that policy makers and public communicators may want to be cognizant of their audience’s general value orientation. Local information may not only be ineffective but may also prove counterproductive with individuals whose value orientations are more self-enhancing than self-transcendent

Monotone and near-monotone biochemical networks

Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion