37 research outputs found
Transcriptional delay stabilizes bistable gene networks
Transcriptional delay can significantly impact the dynamics of gene networks.
Here we examine how such delay affects bistable systems. We investigate several
stochastic models of bistable gene networks and find that increasing delay
dramatically increases the mean residence times near stable states. To explain
this, we introduce a non-Markovian, analytically tractable reduced model. The
model shows that stabilization is the consequence of an increased number of
failed transitions between stable states. Each of the bistable systems that we
simulate behaves in this manner
Effects of cell cycle noise on excitable gene circuits
We assess the impact of cell cycle noise on gene circuit dynamics. For
bistable genetic switches and excitable circuits, we find that transitions
between metastable states most likely occur just after cell division and that
this concentration effect intensifies in the presence of transcriptional delay.
We explain this concentration effect with a 3-states stochastic model. For
genetic oscillators, we quantify the temporal correlations between daughter
cells induced by cell division. Temporal correlations must be captured properly
in order to accurately quantify noise sources within gene networks.Comment: 15 pages, 8 figure
Effects of Cell Cycle Noise on Excitable Gene Circuits
We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a three-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks
Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations
Delay is an important and ubiquitous aspect of many biochemical processes.
For example, delay plays a central role in the dynamics of genetic regulatory
networks as it stems from the sequential assembly of first mRNA and then
protein. Genetic regulatory networks are therefore frequently modeled as
stochastic birth-death processes with delay. Here we examine the relationship
between delay birth-death processes and their appropriate approximating delay
chemical Langevin equations. We prove that the distance between these two
descriptions, as measured by expectations of functionals of the processes,
converges to zero with increasing system size. Further, we prove that the delay
birth-death process converges to the thermodynamic limit as system size tends
to infinity. Our results hold for both fixed delay and distributed delay.
Simulations demonstrate that the delay chemical Langevin approximation is
accurate even at moderate system sizes. It captures dynamical features such as
the spatial and temporal distributions of transition pathways in metastable
systems, oscillatory behavior in negative feedback circuits, and
cross-correlations between nodes in a network. Overall, these results provide a
foundation for using delay stochastic differential equations to approximate the
dynamics of birth-death processes with delay