Stochastic gene expression as a many-body problem

by: Masaki Sasai, Peter G Wolynes

PNAS, Vol. 100, No. 5. (4 March 2003), pp. 2374-2379.

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Abstract

Gene expression has a stochastic component because of the single-molecule nature of the gene and the small number of copies of individual DNA-binding proteins in the cell. We show how the statistics of such systems can be mapped onto quantum many-body problems. The dynamics of a single gene switch resembles the spin-boson model of a two-site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way, the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed weakly frustrated stochastic networks than for randomly connected networks. 10.1073/pnas.2627987100

@article{citeulike:1314109, abstract = {Gene expression has a stochastic component because of the single-molecule nature of the gene and the small number of copies of individual DNA-binding proteins in the cell. We show how the statistics of such systems can be mapped onto quantum many-body problems. The dynamics of a single gene switch resembles the spin-boson model of a two-site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way, the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed weakly frustrated stochastic networks than for randomly connected networks. 10.1073/pnas.2627987100}, author = {Sasai, Masaki and Wolynes, Peter G. }, citeulike-article-id = {1314109}, doi = {10.1073/pnas.2627987100}, journal = {PNAS}, keywords = {biophys, field-theory, gene\_expression}, month = {March}, number = {5}, pages = {2374--2379}, posted-at = {2008-05-02 15:06:42}, priority = {2}, title = {Stochastic gene expression as a many-body problem}, url = {http://dx.doi.org/10.1073/pnas.2627987100}, volume = {100}, year = {2003} }

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TY - JOUR ID - citeulike:1314109 L3 - citeulike-article-id:1314109 TI - Stochastic gene expression as a many-body problem JF - PNAS VL - 100 IS - 5 SP - 2374 EP - 2379 N2 - Gene expression has a stochastic component because of the single-molecule nature of the gene and the small number of copies of individual DNA-binding proteins in the cell. We show how the statistics of such systems can be mapped onto quantum many-body problems. The dynamics of a single gene switch resembles the spin-boson model of a two-site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way, the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed weakly frustrated stochastic networks than for randomly connected networks. 10.1073/pnas.2627987100 KW - biophys KW - field-theory KW - gene_expression AU - Sasai, Masaki AU - Wolynes, Peter PY - 2003/03/04/ UR - http://dx.doi.org/10.1073/pnas.2627987100 ER -

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