Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

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

ISSN exercise & sport nutrition review: research & recommendations

Sports nutrition is a constantly evolving field with hundreds of research papers published annually. For this reason, keeping up to date with the literature is often difficult. This paper is a five year update of the sports nutrition review article published as the lead paper to launch the JISSN in 2004 and presents a well-referenced overview of the current state of the science related to how to optimize training and athletic performance through nutrition. More specifically, this paper provides an overview of: 1.) The definitional category of ergogenic aids and dietary supplements; 2.) How dietary supplements are legally regulated; 3.) How to evaluate the scientific merit of nutritional supplements; 4.) General nutritional strategies to optimize performance and enhance recovery; and, 5.) An overview of our current understanding of the ergogenic value of nutrition and dietary supplementation in regards to weight gain, weight loss, and performance enhancement. Our hope is that ISSN members and individuals interested in sports nutrition find this review useful in their daily practice and consultation with their clients

Growth of single crystals in the (Na1/2Bi1/2)TiO3-(Sr1-xCax)TiO3 system by solid state crystal growth

Ceramics based on (Na1/2B1/2)TiO3 are promising candidates for actuator applications because of large strains generated by an electric field-induced phase transition. For example, the (1-x)(Na1/2Bi1/2)TiO3-xSrTiO(3) system exhibits a morphotropic phase boundary at x = 0.2-0.3, leading to high values of inverse piezoelectric constant d*(33), which can be further improved by the use of single crystals. In our previous work, single crystals of (Na1/2B1/2)TiO3-SrTiO3 and (Na1/2B1/2)TiO3-CaTiO3 were grown by the solid state crystal growth technique. Growth in the (Na1/2B1/2)TiO3-SrTiO3 system was sluggish whereas the (Na1/2B1/2)TiO3-CaTiO3 single crystals grew well. In the present work, 0.8(Na1/2Bi1/2)TiO3-0.2(Sr1-xCax)TiO3 single crystals (with x = 0.0, 0.1, 0.2, 0.3, 0.4) were produced by the solid state crystal growth technique in an attempt to improve crystal growth rate. The dependence of mean matrix grain size, single crystal growth distance, and electrical properties on the Ca concentration was investigated in detail. These investigations indicated that at x = 0.3 the matrix grain growth was suppressed and the driving force for single crystal growth was enhanced. Replacing Sr with Ca increased the shoulder temperature T-s and temperature of maximum relative permittivity T-max, causing a decrease in inverse piezoelectric properties and a change from normal to incipient ferroelectric behavior

Functional modulation and directed assembly of an enzyme through designed non-natural post-translation modification

Post-translational modification (PTM) modulates and supplements protein functionality. In nature this high precision event requires specific motifs and/or associated modification machinery. To overcome the inherent complexity that hinders PTM's wider use, we have utilized a non-native biocompatible Click chemistry approach to site-specifically modify TEM β-lactamase that adds new functionality. In silico modelling was used to design TEM β-lactamase variants with the non-natural amino acid p-azido-L-phenylalanine (azF) placed at functionally strategic positions permitting residue-specific modification with alkyne adducts by exploiting strain-promoted azide–alkyne cycloaddition. Three designs were implemented so that the modification would: (i) inhibit TEM activity (Y105azF); (ii) restore activity compromised by the initial mutation (P174azF); (iii) facilitate assembly on pristine graphene (W165azF). A dibenzylcyclooctyne (DBCO) with amine functionality was enough to modulate enzymatic activity. Modification of TEMW165azF with a DBCO–pyrene adduct had little effect on activity despite the modification site being close to a key catalytic residue but allowed directed assembly of the enzyme on graphene, potentially facilitating the construction of protein-gated carbon transistor systems.DDJ and ARM would like to thank the Advanced Research Computing @ Cardiff facility, especially Thomas Green for help with access and usage of the Raven cluster. DDJ, JEM and ME would like to thank the BBSRC (BB/H003746/1 and BB/ M000249/1), EPSRC (EP/J015318/1) and Cardiff SynBio Initiative/SynBioCite for supporting this work. SR and MFC acknowledge financial support from EPSRC (EP/J000396/1, EP/ K017160/1, EP/K010050/1, EP/G036101/1, EP/M001024/1, EPM002438/1). AMH was supported by a BBSRC studentship, AJZ by a Ministry of Higher Education in Kurdistan Region and Kurdistan Regional Government studentship and ARM by a Cardiff School of Biosciences personal studentship