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Computational biology related. A small python module providing useful analytical functions for a (popular) stochastic gene expression model
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sgeLytics.py

README.md

sgeLytics

Computational biology related. A small python module providing useful analytical functions for a (popular) stochastic gene expression model.

Dependencies

Requires numpy and scipy.

Model description

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.

Reaction Simulation type
GeneON <-> GeneOFF (kon, koff) stochastic
GeneON -> mRNA + GeneON (ksm) stochastic
mRNA -> 0 (rm) stochastic
mRNA -> Prot + mRNA (ksp) deterministic
Prot -> 0 (rp) deterministic

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).

Equivalent parameterizations

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 ON and rg is rate constant associated with both ON and OFF switching.

Because the translation and protein degradation are deterministic, ksp just sets the scale for protein levels, but their fluctuation properties are independent of ksp.

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 timescales rg, rm and rp are fixed.

See the function defineModelFromCVTau_rg_rm_rp.

Examples of use

See example.py.

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