Growth feedback, the inherent coupling
between the synthetic gene
circuit and the host cell growth, could significantly change the circuit
behaviors. Previously, a diverse array of emergent behaviors, such
as growth bistability, enhanced ultrasensitivity, and topology-dependent
memory loss, were reported to be induced by growth feedback. However,
the influence of the growth feedback on the circuit functions remains
underexplored. Here, we reported an unexpected damped oscillatory
behavior of a self-activation gene circuit induced by nutrient-modulating
growth feedback. Specifically, after dilution of the activated self-activation
switch into the fresh medium with moderate nutrients, its gene expression
first decreases as the cell grows and then shows a significant overshoot
before it reaches the steady state, leading to damped oscillation
dynamics. Fitting the data with a coarse-grained model suggests a
nonmonotonic growth-rate regulation on gene production rate. The underlying
mechanism of the oscillation was demonstrated by a molecular mathematical
model, which includes the ribosome allocation toward gene production,
cell growth, and cell maintenance. Interestingly, the model predicted
a counterintuitive dependence of oscillation amplitude on the nutrition
level, where the highest peak was found in the medium with moderate
nutrients, but was not observed in rich nutrients. We experimentally
verified this prediction by tuning the nutrient level in the culture
medium. We did not observe significant oscillatory behavior for the
toggle switch, suggesting that the emergence of damped oscillatory
behavior depends on circuit network topology. Our results demonstrated
a new nonlinear emergent behavior mediated by growth feedback, which
depends on the ribosome allocation between gene circuit and cell growth.
We propose a model of tumor-immune interaction with time delay in immune reaction and noise in tumor cell reproduction. Immune response is modeled as a non-monotonic function of tumor burden, for which the tumor is immunogenic at nascent stage but starts inhibiting immune system as it grows large. Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and uncertainty in the tumor innate proliferation rate are studied by including delay and noise in the appropriate model terms. Stability, persistence and extinction of the tumor are analyzed. We find that delay and noise can both induce the transition from low tumor burden equilibrium to high tumor equilibrium. Moreover, our result suggests that the elimination of cancer depends on the basal level of the immune system rather than on its response speed to tumor growth.
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