2 research outputs found
Stochastic Modelling of the Kai-based Circadian Clock
We present two process algebra models of a Kai-protein based circadian clock. Our models are represented in the Bio-PEPA and the continuous pi-calculus process algebras. The circadian clock is not based on transcription and has been shown to persist with a rhythmic signal when removed from a living cell. Our models allow us to speculate as to the mechanisms which allow for the rhythmic signals. We reproduce previous results based on ODE models and then use our models as the basis for stochastic simulation. Keywords: Circadian, ODE, stochastic, temporal logic, Bio-PEPA, Continuous P
Complementary approaches to understanding the plant circadian clock
Circadian clocks are oscillatory genetic networks that help organisms adapt
to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri
is the simplest plant clock discovered so far. Its many advantages as an
experimental system facilitate the testing of computational predictions.
We present a model of the Ostreococcus clock in the stochastic process
algebra Bio-PEPA and exploit its mapping to different analysis techniques, such
as ordinary differential equations, stochastic simulation algorithms and
model-checking. The small number of molecules reported for this system tests
the limits of the continuous approximation underlying differential equations.
We investigate the difference between continuous-deterministic and
discrete-stochastic approaches. Stochastic simulation and model-checking allow
us to formulate new hypotheses on the system behaviour, such as the presence of
self-sustained oscillations in single cells under constant light conditions.
We investigate how to model the timing of dawn and dusk in the context of
model-checking, which we use to compute how the probability distributions of
key biochemical species change over time. These show that the relative
variation in expression level is smallest at the time of peak expression,
making peak time an optimal experimental phase marker. Building on these
analyses, we use approaches from evolutionary systems biology to investigate
how changes in the rate of mRNA degradation impacts the phase of a key protein
likely to affect fitness. We explore how robust this circadian clock is towards
such potential mutational changes in its underlying biochemistry. Our work
shows that multiple approaches lead to a more complete understanding of the
clock