Computational biology related. A small python module providing useful analytical functions for a (popular) stochastic gene expression model.
We consider a variant of the two-state transcription bursting model (see Shahrezaei et al., 2008 and many others...) in which translation and protein degradation reaction are assumed to be deterministic (see Paszek et al., 2007).
This assumption is suited when the average protein level is large, which is the case for most proteins in mammalian cells.
Analytical results on the corresponding steady-state distribution were derived for example in (Paszek et al., 2007). During my thesis, I also derived an expression for the associated auto-correlation function of protein level (given in Bertaux et al., 2014).
Giving the 6 "biochemical" parameters
(kon, koff, ksm, rm, ksp, rp)
is equivalent to give the 6 quantities
(Ton, Toff, EM, HLm, EP, HLp)
which are respectively the mean duration the gene stays ON, the mean
duration the gene stays OFF, the mean mRNA level (of the steady-state
distribution), the mRNA half-life, the mean protein level (of the
steady-state distribution) and the protein half-life.
(kon=1/Toff, koff=1/Ton) are also equivalent to
(EG=Ton/(Ton+Toff), rg=kon+koff) where
EG is the average fraction of the time the gene is
rg is rate constant associated with both ON and OFF switching.
Because the translation and protein degradation are deterministic,
just sets the scale for protein levels, but their fluctuation properties
are independent of
Finding parameters from protein level fluctuation properties
Because we were interested in finding parameterizations from protein
level fluctuations properties, we finally found that if it exists, a
single parameterization is compatible with a given protein level noise
CV) and mixing time (half auto-correlation time) when the three
rp are fixed.
See the function
Examples of use