Algebraic expressions of conditional expectations in gene regulatory networks

Journal of Mathematical Biology
Vikram Sunkara

Abstract

Gene Regulatory Networks are powerful models for describing the mechanisms and dynamics inside a cell. These networks are generally large in dimension and seldom yield analytical formulations. It was shown that studying the conditional expectations between dimensions (interactions or species) of a network could lead to drastic dimension reduction. These conditional expectations were classically given by solving equations of motions derived from the Chemical Master Equation. In this paper we deviate from this convention and take an Algebraic approach instead. That is, we explore the consequences of conditional expectations being described by a polynomial function. There are two main results in this work. Firstly, if the conditional expectation can be described by a polynomial function, then coefficients of this polynomial function can be reconstructed using the classical moments. And secondly, there are dimensions in Gene Regulatory Networks which inherently have conditional expectations with algebraic forms. We demonstrate through examples, that the theory derived in this work can be used to develop new and effective numerical schemes for forward simulation and parameter inference. The algebraic line of investigation of conditi...Continue Reading

References

Feb 5, 2000·Nature·N Barkai, S Leibler
Feb 5, 2000·Nature·T S GardnerJ J Collins
Apr 25, 2002·Proceedings of the National Academy of Sciences of the United States of America·José M G VilarStanislas Leibler
Oct 17, 2002·Journal of Theoretical Biology·R SrivastavaJ Yin
Apr 11, 2003·Nature·William J BlakeJ J Collins
May 28, 2005·The Journal of Chemical Physics·John Goutsias
Feb 8, 2006·The Journal of Chemical Physics·Brian Munsky, Mustafa Khammash
Sep 6, 2006·Journal of Mathematical Biology·Tobias Jahnke, Wilhelm Huisinga
Sep 18, 2008·Nature Reviews. Molecular Cell Biology·Guy Karlebach, Ron Shamir
Sep 10, 2009·Nature Reviews. Molecular Cell Biology·Ben D MacarthurIhor R Lemischka
Jun 10, 2011·Journal of Mathematical Biology·Pavol BokesMatthew Loose
Jul 27, 2012·The Journal of Chemical Physics·R GrimaT J Newman
Nov 24, 2012·Chemical Engineering Science·P Smadbeck, Y N Kaznessis
Aug 14, 2013·Proceedings of the National Academy of Sciences of the United States of America·Patrick Smadbeck, Yiannis N Kaznessis
May 2, 2014·Proceedings of the National Academy of Sciences of the United States of America·Philipp ThomasRamon Grima
Mar 28, 2017·Journal of Theoretical Biology·Manuel PájaroCarlos Vázquez
Aug 19, 2018·Nature Communications·Zhixing Cao, Ramon Grima

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.