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The spectral Markov method
SpecMark (spectral Markov) is a method for calculating the joint probability distribution over species in a regulatory network. This software is free for scientific use. Please contact us if you plan to use this software for commercial purposes. Do not further distribute without prior permission of the authors. Please forward links to related publications so we can learn about your research.
Cascades
The application of SpecMark to cascades is described in "A stochastic spectral analysis of transcriptional regulatory cascades" (with supplementary material here). The preprint is freely available here. Corresponding sourcecode is implemented in MATLAB and can be downloaded here. Screenshots are below. If used in your scientific work, please cite as:
Aleksandra M. Walczak, Andrew Mugler, and Chris H. Wiggins,
"A stochastic spectral analysis of transcriptional regulatory cascades,"
Proc. Natl. Acad. Sci. USA, 106(16):6529-6534, 2009.
See also related work on the application of the spectral method to models of gene expression with bursts and regulation: A. Mugler, A. M. Walczak, and C. H. Wiggins, Phys. Rev. E, 80:041921, 2009. The preprint is freely available here.
Dynamics
The application of the spectral method to
intrinsically noisy oscillatory driving is
described in the freely available preprint
"Telling time
with an intrinsically noisy clock".
Corresponding sourcecode,
including a full demonstratrion and scripts to produce
all results and figures in the manuscript,
is implemented in MATLAB and
will be available here once the manuscript is accepted for publication.
Screenshots are below.
Screenshots:
)
Cascades: marginal probability distributions for species in a cascade.
)
Cascades: joint probability distribution for two adjacent species in a cascade.
)
Dynamics: distributions of oscillation-driven parent and regulated child
at key phases.
)
Dynamics: time-averaged child distribution and input-output information
(inset) vs frequency.
A.M.W. was supported by the PCTS Fellowship and Columbia's Professional Schools Diversity Short-Term Visiting Fellowship.
C.H.W. was supported by
NIH 5PN2EY016586-03 and NIH 1U54CA121852-01A1;
C.H.W. and A.M. were supported by NSF ECS-0332479;
A.M. was supported by NSF DGE-0742450.