Propagation of fluctuations in biochemical systems, I: Linear SSC networks
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2007-08-01
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Abstract
We investigate the propagation of random fluctuations through biochemical networks in which the number of molecules of each species is large enough so that the concentrations are well modeled by differential equations. We study the effect of network topology on the emergent properties of the reaction system by characterizing the behavior of variance as fluctuations propagate down chains and studying the effect of side chains and feedback loops. We also investigate the asymptotic behavior of the system as one reaction becomes fast relative to the others. © 2007 Springer Science+Business Media, Inc.
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Anderson, David F, Jonathan C Mattingly, H Frederik Nijhout and Michael C Reed (2007). Propagation of fluctuations in biochemical systems, I: Linear SSC networks. Bulletin of Mathematical Biology, 69(6). pp. 1791–1813. 10.1007/s11538-007-9192-2 Retrieved from https://hdl.handle.net/10161/9281.
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Jonathan Christopher Mattingly
Jonathan Christopher Mattingly grew up in Charlotte, NC, where he attended Irwin Avenue Elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University, where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a professor of mathematics and statistical science.
His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.
Since 2013 he has also been working to understand and quantify gerrymandering and its interaction of a region's geopolitical landscape. This has lead him to testify in a number of court cases including in North Carolina, which led to the NC congressional and both NC legislative maps being deemed unconstitutional and replaced for the 2020 elections.
He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS, the AMS, SIAM and AAAS. He was awarded the Defender of Freedom award by Common Cause for his work on Quantifying Gerrymandering.
H. Frederik Nijhout
Fred Nijhout is broadly interested in developmental physiology and in the interactions between development and evolution. He has several lines of research ongoing in his laboratory that on the surface may look independent from one another, but all share a conceptual interest in understanding how complex traits arise through, and are affected by, the interaction of genetic and environmental factors. 1) The control of polyphenic development in insects. This work attempts to understand how the insect developmental hormones, ecdysone and juvenile hormone, act to control alternative developmental pathways within a single individual. His studies and those of his students have dealt with the control of sequential polyphenism in metamorphosis, of alternate polyphenisms in caste determination of social insects and the many seasonal forms of insects. 2) The regulation of organ and body size in insects. Ongoing research deals with the mechanism by which insects asses their body size and stop growing when they have achieved a characteristic size. Other studies deal with the control of growth and size of imaginal disks. This work is revealing that the control of body and organ size does not reside in any specific cellular or molecular mechanism but that it is a systems property in which cellular, physiological and environmental signals all contribute in inextricable ways to produce the final phenotype. 3) The development and evolution of color patterns in Lepidoptera. Ongoing research attempts to elucidate the evolution of mimicry using genetic and genomic approaches. 4) The development, genetics and evolution of complex traits. Complex traits are those whose variation is affected by many genes and environmental factors and whose inheritance does not follow Mendel’s laws. In practice this involves understanding how genetic and developmental networks operate when there is allelic variation in their genes. This work attempts to reconstruct complex traits through mathematical models of the genetic and developmental processes by which they originate, and uses these models to study the effects of mutation and selection. Currently metabolic networks are being used to develop a deeper understanding of the functional relationships between genetic variation and trait variation, and of the mechanisms by which genetic and environmental variables interact to produce phenotypes. More on web page: http://www.biology.duke.edu/nijhout/
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