Gene circuit with a single negative feedback. (a) Circuit
architecture
with repressor-only control of activator transcription and activator-only
control of repressor transcription. (b, c) System design space with
the effective rate constant for inactivation of the activator, β2, represented on the horizontal axis and that for the repressor,
β4, on the vertical axis. (b) Enumeration of the
qualitatively distinct phenotypes identified by color, where the color
bar represents the case number for each of the qualitatively distinct
phenotypes. (c) The phenotypic trait represented as a heat map on
the z axis of the system design space is the number
of eigenvalues with positive real part. The color bar in this case
represents the value of the phenotypic trait: blue for zero eigenvalues
with positive real part (monostability), red for one eigenvalue with
positive real part (bistability), and yellow for two complex eigenvalues
with positive real part (unstable focus). (d) Temporal behavior of
the full GMA system at the nominal operating point (●) within
the region having the potential for sustained oscillation.