Robustness: mechanisms and consequences

Abstract

Biological systems are robust to perturbation by mutations and environmental fluctuations. New data are shedding light on the biochemical and network-level mechanisms responsible for robustness. Robustness to mutation might have evolved as an adaptation to reduce the effect of mutations, as a congruent byproduct of adaptive robustness to environmental variation, or as an intrinsic property of biological systems selected for their primary functions. Whatever its mechanism or origin, robustness to mutation results in the accumulation of phenotypically cryptic genetic variation. Partial robustness can lead to pre-adaptation, and thereby might contribute to evolvability. The identification and characterization of phenotypic capacitors - which act as switches of the degree of robustness - are critical to understanding the mechanisms and consequences of robustness.

Figure 1

Robustness properties of a simple negative autoregulatory feedback loop. (a) A transcriptional repressor protein (orange) inhibits its own production by binding the cis-regulatory region (gray) of the gene that produces it (orange rectangle with promoter indicated by hollow arrow). The repressor counteracts the activity of an activator protein (blue), which binds to the same region and is present at constant concentration A. The repressor concentration, R, is determined by the regulatory circuit, which includes the negative feedback with repression constant r and degradation of the protein at rate d. In this simple example, we assume no post-transcriptional regulation and instantaneous transcription and translation. Each bound molecule of the repressor acts independently to counteract the activator. (b) A modification of the circuit in (a) is shown, in which repressor molecules act cooperatively. Without cooperativity the rate of change of R is a linear function of R (c). With cooperativity the rate of change of R is a non-linear function of R with a sigmoidal repression term, r f(R) (d). In the two cases there is the same stable equilibrium value of R, R_eq, at which the concentration of the repressor does not change. That is, both cases are robust to fluctuations in R. R_eq is a decreasing function of r. Without cooperativity, changes in r correspond to relatively large changes in R_eq (e). If we consider r to be genetically determined, e.g. by amino acids that determine the affinity of the repressor for its cognate DNA site, then this circuit is not robust to genetic variation. With increasing cooperativity, represented by increasing values of the Hill coefficient m, changes in r correspond to smaller changes in R_eq (f). This circuit is then more robust to genetic variation.

Figure 2

Robustness properties of graded and sigmoidal relationships between the concentration of a factor and its effect. (a) With a graded response, the effect of a factor, R, is not robust to perturbations in its concentration; perturbations of the same magnitude have effects of the same magnitude, across the range of concentrations of R (as shown in orange and blue). (b) With a sigmoidal, switch-like response, the effect is highly robust in some regions (blue), but has catastrophic loss of robustness in others (orange).