2003/01/21 by Masaki Sasai, Peter G. Wolynes
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Bioinformatics and Genomic Networks #Gene Regulatory Network Analysis #cond-mat.dis-nn #cond-mat.stat-mech #physics.bio-ph #q-bio.GN #stochastic dynamics and bifurcation
paper · pdf · doi:10.1073/pnas.2627987100
to appear in Proc. Natl. Acad. Sci. USA
arxiv created 2003/01/21 · openalex publication_date 2003/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.