(
A) Two qualitatively different models for Homeodomain transcription factor (HD-TF) action. Model 1: HD-TF acts as a co-factor that only impacts the affinity of CHE-1 for the
che-1 promoter. Specifically, interaction between HD-TF and CHE-1 is cooperative, with the unbinding rate of both HD-TF and CHE-1 lowered from 100 s
–1 to 0.1 s
–1 when both are bound together. Transcription of
che-1 is only initiated when CHE-1 is bound. Model 2: HD-TF induces
che-1 expression independent of CHE-1. Both HD-TF and CHE-1 bind independently, with unbinding rate of 100 s
–1, and
che-1 transcription is initiated when CHE-1 and/or HD-TF is bound. For both models, we compared two variants: one where HD-TF expression is constitutive (Models 1 A, 2 A) and one where HD-TF expression is controlled by CHE-1 binding (Models 1B, 2B). All four models exhibit bistability in their mass action rate equations. For full parameters, see Materials and methods. (
B) Time dynamics of CHE-1 (green) and HD-TF protein level (red), and
che-1 mRNA (blue). All models can reproduce the observed resilience of
che-1 expression under induced CHE-1 depletion (gray interval). For models 1B and 2B, where HD-TF is a target of CHE-1, this required that the half-life of HD-TF is long compared to the interval of induced CHE-1 depletion. (
C) Models 1 A, 1B, and 2B reproduce the persistent
che-1 expression induced by a transient inductive signal. Transient CHE-1 induction was modelled by basal
che-1 expression, that is independent of CHE-1 level, at rate
during the interval indicated in grey. For Model 2 A, constitutive expression of HD-TF induced
che-1 expression already prior to the presence of the inductive signal. (
D) Models 1 A and 1B reproduced the failure to maintain
che-1 expression following a transient external inductive signal (gray interval) in mutants of the ASE motif of the
che-1 promoter, as was observed experimentally (
Leyva-Díaz and Hobert, 2019). In these experiments, mutations of the ASE motif were predicted to abolish binding of CHE-1 to its own promoter and were therefore modelled by setting the CHE-1 binding rate for its own promoter to zero. For Models 2 A and 2B, transient induction of CHE-1 led to expression of HD-TF, which subsequently maintained expression of both HD-TF and CHE-1, contrary to the experimental observations.