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

Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.National Institutes of Health (U.S.) (Grant P50-GM068762)National Institutes of Health (U.S.) (Grant R24-DK090963)United States. Army Research Office (Grant W911NF-09-0001)German Research Foundation (Grant GSC 111

Glutamate mediated metabolic neutralization mitigates propionate toxicity in intracellular Mycobacterium tuberculosis

Metabolic networks in biological systems are interconnected, such that malfunctioning parts can be corrected by other parts within the network, a process termed adaptive metabolism. Unlike Bacillus Calmette-Guérin (BCG), Mycobacterium tuberculosis (Mtb) better manages its intracellular lifestyle by executing adaptive metabolism. Here, we used metabolomics and identified glutamate synthase (GltB/D) that converts glutamine to glutamate (Q → E) as a metabolic effort used to neutralize cytoplasmic pH that is acidified while consuming host propionate carbon through the methylcitrate cycle (MCC). Methylisocitrate lyase, the last step of the MCC, is intrinsically downregulated in BCG, leading to obstruction of carbon flux toward central carbon metabolism, accumulation of MCC intermediates, and interference with GltB/D mediated neutralizing activity against propionate toxicity. Indeed, vitamin B12 mediated bypass MCC and additional supplement of glutamate led to selectively correct the phenotypic attenuation in BCG and restore the adaptive capacity of BCG to the similar level of Mtb phenotype. Collectively, a defective crosstalk between MCC and Q → E contributes to attenuation of intracellular BCG. Furthermore, GltB/D inhibition enhances the level of propionate toxicity in Mtb. Thus, these findings revealed a new adaptive metabolism and propose GltB/D as a synergistic target to improve the antimicrobial outcomes of MCC inhibition in Mtb

Recruitment Constraints in Singapore's Fluted Giant Clam (Tridacna squamosa) Populations - A Dispersal Model Approach

10.1371/journal.pone.0058819PLoS ONE83

Enzyme sequestration as a tuning point in controlling response dynamics of signalling networks

Signalling networks result from combinatorial interactions among many enzymes and scaffolding proteins. These complex systems generate response dynamics that are often essential for correct decision-making in cells. Uncovering biochemical design principles that underpin such response dynamics is a prerequisite to understand evolved signalling networks and to design synthetic ones. Here, we use in silico evolution to explore the possible biochemical design space for signalling networks displaying ultrasensitive and adaptive response dynamics. By running evolutionary simulations mimicking different biochemical scenarios, we find that enzyme sequestration emerges as a key mechanism for enabling such dynamics. Inspired by these findings, and to test the role of sequestration, we design a generic, minimalist model of a signalling cycle, featuring two enzymes and a single scaffolding protein. We show that this simple system is capable of displaying both ultrasensitive and adaptive response dynamics. Furthermore, we find that tuning the concentration or kinetics of the sequestering protein can shift system dynamics between these two response types. These empirical results suggest that enzyme sequestration through scaffolding proteins is exploited by evolution to generate diverse response dynamics in signalling networks and could provide an engineering point in synthetic biology applications

Genome-Wide Diet-Gene Interaction Analyses for Risk of Colorectal Cancer

Dietary factors, including meat, fruits, vegetables and fiber, are associated with colorectal cancer; however, there is limited information as to whether these dietary factors interact with genetic variants to modify risk of colorectal cancer. We tested interactions between these dietary factors and approximately 2.7 million genetic variants for colorectal cancer risk among 9,287 cases and 9,117 controls from ten studies. We used logistic regression to investigate multiplicative gene-diet interactions, as well as our recently developed Cocktail method that involves a screening step based on marginal associations and gene-diet correlations and a testing step for multiplicative interactions, while correcting for multiple testing using weighted hypothesis testing. Per quartile increment in the intake of red and processed meat were associated with statistically significant increased risks of colorectal cancer and vegetable, fruit and fiber intake with lower risks. From the case-control analysis, we detected a significant interaction between rs4143094 (10p14/near GATA3) and processed meat consumption (OR = 1.17; p = 8.7E-09), which was consistently observed across studies (p heterogeneity = 0.78). The risk of colorectal cancer associated with processed meat was increased among individuals with the rs4143094-TG and -TT genotypes (OR = 1.20 and OR = 1.39, respectively) and null among those with the GG genotype (OR = 1.03). Our results identify a novel gene-diet interaction with processed meat for colorectal cancer, highlighting that diet may modify the effect of genetic variants on disease risk, which may have important implications for prevention. © 2014

A network perspective on the topological importance of enzymes and their phylogenetic conservation

<p>Abstract</p> <p>Background</p> <p>A metabolic network is the sum of all chemical transformations or reactions in the cell, with the metabolites being interconnected by enzyme-catalyzed reactions. Many enzymes exist in numerous species while others occur only in a few. We ask if there are relationships between the phylogenetic profile of an enzyme, or the number of different bacterial species that contain it, and its topological importance in the metabolic network. Our null hypothesis is that phylogenetic profile is independent of topological importance. To test our null hypothesis we constructed an enzyme network from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database. We calculated three network indices of topological importance: the degree or the number of connections of a network node; closeness centrality, which measures how close a node is to others; and betweenness centrality measuring how frequently a node appears on all shortest paths between two other nodes.</p> <p>Results</p> <p>Enzyme phylogenetic profile correlates best with betweenness centrality and also quite closely with degree, but poorly with closeness centrality. Both betweenness and closeness centralities are non-local measures of topological importance and it is intriguing that they have contrasting power of predicting phylogenetic profile in bacterial species. We speculate that redundancy in an enzyme network may be reflected by betweenness centrality but not by closeness centrality. We also discuss factors influencing the correlation between phylogenetic profile and topological importance.</p> <p>Conclusion</p> <p>Our analysis falsifies the hypothesis that phylogenetic profile of enzymes is independent of enzyme network importance. Our results show that phylogenetic profile correlates better with degree and betweenness centrality, but less so with closeness centrality. Enzymes that occur in many bacterial species tend to be those that have high network importance. We speculate that this phenomenon originates in mechanisms driving network evolution. Closeness centrality reflects phylogenetic profile poorly. This is because metabolic networks often consist of distinct functional modules and some are not in the centre of the network. Enzymes in these peripheral parts of a network might be important for cell survival and should therefore occur in many bacterial species. They are, however, distant from other enzymes in the same network.</p

Drug-Induced Regulation of Target Expression

Drug perturbations of human cells lead to complex responses upon target binding. One of the known mechanisms is a (positive or negative) feedback loop that adjusts the expression level of the respective target protein. To quantify this mechanism systems-wide in an unbiased way, drug-induced differential expression of drug target mRNA was examined in three cell lines using the Connectivity Map. To overcome various biases in this valuable resource, we have developed a computational normalization and scoring procedure that is applicable to gene expression recording upon heterogeneous drug treatments. In 1290 drug-target relations, corresponding to 466 drugs acting on 167 drug targets studied, 8% of the targets are subject to regulation at the mRNA level. We confirmed systematically that in particular G-protein coupled receptors, when serving as known targets, are regulated upon drug treatment. We further newly identified drug-induced differential regulation of Lanosterol 14-alpha demethylase, Endoplasmin, DNA topoisomerase 2-alpha and Calmodulin 1. The feedback regulation in these and other targets is likely to be relevant for the success or failure of the molecular intervention

Confidence from uncertainty - A multi-target drug screening method from robust control theory

<p>Abstract</p> <p>Background</p> <p>Robustness is a recognized feature of biological systems that evolved as a defence to environmental variability. Complex diseases such as diabetes, cancer, bacterial and viral infections, exploit the same mechanisms that allow for robust behaviour in healthy conditions to ensure their own continuance. Single drug therapies, while generally potent regulators of their specific protein/gene targets, often fail to counter the robustness of the disease in question. Multi-drug therapies offer a powerful means to restore disrupted biological networks, by targeting the subsystem of interest while preventing the diseased network from reconciling through available, redundant mechanisms. Modelling techniques are needed to manage the high number of combinatorial possibilities arising in multi-drug therapeutic design, and identify synergistic targets that are robust to system uncertainty.</p> <p>Results</p> <p>We present the application of a method from robust control theory, Structured Singular Value or μ- analysis, to identify highly effective multi-drug therapies by using robustness in the face of uncertainty as a new means of target discrimination. We illustrate the method by means of a case study of a negative feedback network motif subject to parametric uncertainty.</p> <p>Conclusions</p> <p>The paper contributes to the development of effective methods for drug screening in the context of network modelling affected by parametric uncertainty. The results have wide applicability for the analysis of different sources of uncertainty like noise experienced in the data, neglected dynamics, or intrinsic biological variability.</p