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WIREs Syst Biol Med
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Systems biology of robustness and homeostatic mechanisms

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All organisms are subject to large amounts of genetic and environmental variation and have evolved mechanisms that allow them to function well in spite of these challenges. This property is generally referred to as robustness. We start with the premise that phenotypes arise from dynamical systems and are therefore system properties. Phenotypes occur at all levels of the biological organizational hierarchy, from gene products, to biochemical pathways, to cells, tissues, organs, appendages, and whole bodies. Phenotypes at all these levels are subject to environmental and genetic challenges against which their form and function need to be protected. The mechanisms that can produce robustness are diverse and several different kinds often operate simultaneously. We focus, in particular, on homeostatic mechanisms that dynamically maintain form and function against varying environmental and genetic factors. Understanding how homeostatic mechanisms operate, how they reach their set point, and the nature of the set point pose difficult challenges. In developmental systems, homeostatic mechanisms make the progression of morphogenesis relatively insensitive to genetic and environmental variation so that the outcomes vary little, even in the presence of severe mutational and environmental stress. Accordingly, developmental systems give the appearance of being goal‐oriented, but how the target phenotype is encoded is not known. We discuss why and how individual variation poses challenges for mathematical modeling of biological systems, and conclude with an explanation of how system population models are a useful method for incorporating individual variation into deterministic ordinary differential equation (ODE) models.

This article is categorized under:

  • Models of Systems Properties and Processes > Mechanistic Models
  • Physiology > Mammalian Physiology in Health and Disease
  • Physiology > Organismal Responses to Environment
  • Biological Mechanisms > Regulatory Biology
Coefficients of variation of 200 metabolites from 60 individuals (B.sed on data from Saito et al., ). Values range from 0.02 to 1, with a mean of 0.41. If a population has a CV of 0.41 and a mean of μ, this means that 32% of a population will have values either>1.41×μ and < 0.59×μ
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Scatterplots relating variation among several metabolites and fluxes in two subpopulations with high (red) and low (black) plasma homocysteine. Homocysteine (Hcy) is a highly reactive and toxic amino acid, produced in the methionine cycle, normally kept at very low concentrations. An elevated level of Hcy in the blood is a risk factor for cardiovascular disease. In each case the variables are clearly correlated, but the correlations are very different for the two subpopulations. The many nonlinearities and allosteric interactions in OCM cause the large differences in the associations among variables in subpopulations, which differ in slopes and elevations
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Stability of extracellular serotonin to polymorphisms in serotonin metabolism genes. The extracellular serotonin concentration as a function of variation in tryptophan hydroxylase (TPH) and the serotonin reuptake transporter (SERT), scaled relative to the wild‐type values. The wild type is indicated by the large circle. The effects on enzyme activity of polymorphisms in genes for TPH and SERT are indicated by small circles. Polymorphisms shown for TPH are C2745A and R441H, which reduce activity to 65% and 40% of normal, respectively. Those for SERT are the short repeat allele (s) in the regulatory region of the gene and the I425V snp, which reduce activity to 33% of normal and increase activity to about 150% if normal, respectively
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Environmental destabilization of homeostasis. Stability of the DNMT reaction rate to polymorphisms in the MS and MTHFR genes, scaled relative to the wild‐type values. The wild types are indicated by the large circles. The small circles show the locations of genetic polymorphisms, taken from Table . (a) Stability under normal concentration of vitamin B12. (b) A vitamin B12 deficiency causes a “tilt” in the phenotypic landscape, and mutations that were cryptic with respect to phenotypic variation, now produce different, abnormal, DNMT phenotypes
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Multiple stabilization of the DNMT reaction. In addition to product inhibition (Figure (d)), the DNMT reaction is also stabilized by allosteric regulation of CBS and MTHFR by SAM (shown in Figure ). In the absence of these two regulators the DNMT reaction rate is nonlinearly proportional to methionine input, which supplies methyl groups. When both CBS and MTHFR are regulated the DNMT reaction rate is quite insensitive to methionine input. The reason is that these two regulations enable more methyl group input from the folate cycle. Regulation of MTHFR alone provides much more stability than regulation of CBS alone. This implies that the regulation of CBS evolved first, because had regulation of MTHFR been established first there would be little fitness benefit of adding regulation of CBS. The improvement of DNMT is strongest at low methionine input, suggesting that the regulations may be an adaptation to prolonged periods of protein deficiency. Based on (Reprinted with permission from Nijhout, Reed, Anderson, et al. ())
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Stability of the TS and AICART reactions to polymorphisms in MS, MTHFR and TS genes. The rates of the reactions as pairwise functions of variation in the activities of MTHFR, MS and TS, scaled relative to the wild‐type values. The wild types are indicated by the large circles. The small circles show the locations of genetic polymorphisms, taken from Table . The left column shows the phenotypic landscapes with all allosteric regulatory interactions in place. The right column shows the same phenotypic surfaces after removing the allosteric regulation of MTHFR by SAM (see Figure ). In each case, removing the allosteric regulation causes the phenotypic surface to be “tilted,” so that polymorphisms that produced nearly identical phenotypes (z axis), and were “cryptic” with respect to phenotypic variation, now produce different, abnormal, phenotypic values
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Sensitivity and homeostasis in OCM. Gray bars below (d) show the temporal pattern of amino acid input into blood compartment of the model shown in Figure , to match known fluctuations of amino acids with meals. This amino acid influx produces fluctuations in both fluxes and metabolite concentrations. (a) The reaction of SHMT interconverts serine and glycine varies greatly, and can even change direction. (b) Metabolite concentrations and fluxes can change more than twofold in the course of a few hours. (c) The rates of the TS, AICART and DNMT reactions, and the concentration of glutathione, are quite stable and are little affected by variation in the other enzymes and metabolites in the system. Indeed, these four factors are stabile because of fluctuations in other parts of the system that counteract the effects of variation in amino acid influx, and act as homeostatic regulators. (d) Removal of one of these regulators (product inhibition by SAH), destabilizes the DNMT reaction, which now becomes much more sensitive to amino acid fluctuations. Based on (Reprinted with permission from Nijhout et al., ())
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Patterning network in an early Drosophila embryo. The mRNA for the bicoid and caudal transcription factors are laid down as the egg is made and, after fertilization, stimulate expression of the so‐called gap genes, which also mutually stimulate and inhibit each other's expression. Caudal is initially homogeneously distributed but is inhibited by bicoid. Hunchback is unusual in that at low concentrations it stimulates krüppel, but at high concentrations inhibits its expression. The gap genes form a banding pattern on the embryo that in turn controls a progressively more refined expression of subsequent genes that control formation of the segments
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System properties of phosphorylation cascades. The mitogen activated kinase (MAPK) cascade is stimulated by a variety of growth factors and controls gene expression that leads to cell proliferation and growth. Double phosphorylations at each stage in the three‐step cascade (MAPKKK ‐ > MAPKK ‐ > MAPK) lead to a progressively sharper sigmoidal dose–response relationships
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System properties of biochemical reaction chains. The relationship between flux through a sequential reaction chain and the activity of any one enzyme in the chain becomes progressively more nonlinear with increasing chain length. (a) Effect of variation in one enzyme on the flux through enzymatic chains of length n (scaled to 1). (b) Emergence of dominance from a nonlinear mechanism. A gene with two alleles (A and a) with different “activities” are shown, with alleles acting additively, so that the heterozygote (Aa) is half‐way between the two homozygotes (AA and aa). The effect of the three genotypes (x‐axis) on the phenotype (y‐axis) is not additive, but the phenotype of the heterozygote is much closer to that of one of the homozygotes (AA). Thus the a allele is additive (co‐dominant) at the genotypic level but dominant at the phenotypic level. This emergence of dominance arises in any system in which the relationship between genes and traits is nonlinear. Based on (Gilchrist and Nijhout (2001); Kacser and Burns (1981))
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Reaction diagram for one‐carbon metabolism (OCM). OCM consists of the folate cycle, the methionine cycle, and the glutathione synthesis pathway. Its function is to capture methyl groups from amino acids (methionine, serine, and glycine) that are used by a variety of methyl transferase reactions in the biosynthesis of more complex molecules. Enzymes are indicated by their acronyms in blue ellipses. Metabolites are in boxes. Black arrows indicate traditional enzymatic reactions. Red arrows indicate allosteric regulatory reactions by which metabolites alter the activities of enzymes. This metabolic network is made up of several interlocking cycles. Enzymes—AICART: aminoimidazole carboxamide ribonucleotide transferase; BHMT: betaine‐homocysteine methyltransferase; CBS: cystathionine β‐synthase; DHFR: dihydrofolate reductase; DNMT: DNA methyltransferase; FTD: 10‐formyl tetrahydrofolate dehydrogenase; FTS: 10‐formyl tetrahydrofolate synthase; GNMT: glycine N‐methyltransferase; MAT‐I: methionine adenosyl transferase I; MAT‐III: methionine adenosyl transferase III; MS: methionine synthase; MTCH: 5,10‐methenyl tetrahydrofolate cyclohydrolase; MTD: 5,10‐methylenetetrahydrofolate dehydrogenase; MTHFR: 5,10‐methylenetetrahydrofolate reductase; NE: non‐enzymatic conversion; PGT: phosphoribosyl glycinamide transformalase; SAAH: S‐adenosyl homocysteine hydrolase; SHMT: serine hydroxy methyltransferase; TS: thymidylate synthase. Metabolites—10f‐THF: 10‐formyl tetrahydrofolate; 5mTHF: 5‐methyl tetrahydrofolate; CH=THF: 5‐10‐methenyl tetrahydrofolate; CH2‐THF: 5‐10‐methylenetetrahydrofolate; DHF: dihydrofolate; Hcy: homocysteine; Met: methionine; SAH: S‐adenosyl homocysteine; SAM: S‐adenosyl methionine; THF: tetrahydrofolate. (Modified from, and absed on Nijhout et al. (2006); Nijhout, Reed, Budu, and Ulrich (2004); Reed et al. (2008); Reed, Gamble, Hall, and Nijhout (2015))
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Feedback mechanisms that can produce homeostasis. (a) Chair‐shaped curve characteristic of a homeostatic mechanism, with a more or less broad homeostatic plateau in which variation in an input (I in the diagrams below) has little or no effect on the output (Z in the diagrams below) of a system, flanked by regions where very low or very high levels of input produce a proportional response. Three motifs are shown that can exhibit this property, depending on parameter values and reaction kinetics. (b) A typical product feedback inhibition mechanism in which the product of a reaction inhibits an enzyme earlier in the biosynthetic chain. (c) Feedforward activation of a downstream reaction can stabilize an intermediate metabolite. (d) Mutual inhibition among parallel reactions can stabilize Z to variation in I. Here metabolite Z inhibits the synthesis of X, and X inhibits the breakdown of Z. (Modified from Reed, Best, Golubitsky, Stewart, and Nijhout ())
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Biological Mechanisms > Regulatory Biology
Models of Systems Properties and Processes > Mechanistic Models
Physiology > Organismal Responses to Environment
Physiology > Mammalian Physiology in Health and Disease

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