Synopsis Gene regulatory networks, cellular biochemistry, tissue function, and whole body physiology are imbued with myriad overlapping and interacting homeostatic mechanisms that ensure that many phenotypes are robust to genetic and environmental variation. Animals also often have plastic responses to environmental variables, which means that many different phenotypes can correspond to a single genotype. Since natural selection acts on phenotypes, this raises the question of how selection can act on the genome if genotypes are decoupled from phenotypes by robustness and plasticity mechanisms. The answer can be found in the systems biology of the homeostatic mechanisms themselves. First, all such mechanisms operate over a limited range and outside that range the controlled variable changes rapidly allowing natural selection to act. Second, mutations and environmental stressors can disrupt homeostatic mechanisms, exposing cryptic genetic variation and allowing natural selection to act. We illustrate these ideas by examining the systems biology of four specific examples. We show how it is possible to analyze and visualize the roles of specific genes and specific polymorphisms in robustness in the context of large and realistic nonlinear systems. We also describe a new method, system population models, that allows one to connect causal dynamics to the variable outcomes that one sees in biological populations with large variation.

BackgroundThere are large differences between men and women of child-bearing age in the expression level of 5 key enzymes in one-carbon metabolism almost certainly caused by the sex hormones. These male-female differences in one-carbon metabolism are greatly accentuated during pregnancy. Thus, understanding the origin and consequences of sex differences in one-carbon metabolism is important for precision medicine.ResultsWe have created a mathematical model of hepatic one-carbon metabolism based on the underlying physiology and biochemistry. We use the model to investigate the consequences of sex differences in gene expression. We give a mechanistic understanding of observed concentration differences in one-carbon metabolism and explain why women have lower S-andenosylmethionine, lower homocysteine, and higher choline and betaine. We give a new explanation of the well known phenomenon that folate supplementation lowers homocysteine and we show how to use the model to investigate the effects of vitamin deficiencies, gene polymorphisms, and nutrient input changes.ConclusionsOur model of hepatic one-carbon metabolism is a useful platform for investigating the mechanistic reasons that underlie known associations between metabolites. In particular, we explain how gene expression differences lead to metabolic differences between males and females.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-018-0621-7) contains supplementary material, which is available to authorized users.

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Background Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding involves genomics, neurochemistry, electrophysiology, and behavior. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders. This paper presents a new deterministic model of serotonin metabolism and a new systems population model that takes into account the large variation in enzyme and transporter expression levels, tryptophan input, and autoreceptor function. Results We discuss the steady state of the model and the steady state distribution of extracellular serotonin under different hypotheses on the autoreceptors and we show the effect of tryptophan input on the steady state and the effect of meals. We use the deterministic model to interpret experimental data on the responses in the hippocampus of male and female mice, and to illustrate the short-time dynamics of the autoreceptors. We show there are likely two reuptake mechanisms for serotonin and that the autoreceptors have long-lasting influence and compare our results to measurements of serotonin dynamics in the substantia nigra pars reticulata. We also show how histamine affects serotonin dynamics. We examine experimental data that show very variable response curves in populations of mice and ask how much variation in parameters in the model is necessary to produce the observed variation in the data. Finally, we show how the systems population model can potentially be used to investigate specific biological and clinical questions. Conclusions We have shown that our new models can be used to investigate the effects of tryptophan input and meals and the behavior of experimental response curves in different brain nuclei. The systems population model incorporates individual variation and can be used to investigate clinical questions and the variation in drug efficacy. The codes for both the deterministic model and the systems population model are available from the authors and can be used by other researchers to investigate the serotonergic system.

There are two stages generally recognized in the viral capsid assembly: nucleation and elongation. This paper focuses on the nucleation stage and develops mathematical models for HIV-1 viral capsid nucleation based on six-species dynamical systems. The Particle Swarm Optimization (PSO) algorithm is used for parameter fitting to estimate the association and dissociation rates from biological experiment data. Numerical simulations of capsid protein (CA) multimer concentrations demonstrate a good agreement with experimental data. Sensitivity and elasticity analysis of CA multimer concentrations with respect to the association and dissociation rates further reveals the importance of CA trimer-of- dimers in the nucleation stage of viral capsid self- assembly.