Abstract
Cooperative interactions are widespread in biochemical networks, providing the nonlinear response that underlies behavior such as ultrasensitivity and robust switching. We introduce a temporal correlation function—the conditional activity—to study the behavior of these phenomena. Applying it to the bistable genetic switch in bacteriophage lambda, we find that cooperative binding between binding sites on the prophage DNA lead to non-Markovian behavior, as quantified by the conditional activity. Previously, the conditional activity has been used to predict allosteric pathways in proteins; here, we show that it identifies the rare unbinding events which underlie induction from lysogeny to lysis.
Highlights
Cells use biochemical networks to sense, process information, and respond to their environments
We designed the conditional activity to be a quantitative measure of the deviation from Markovian dynamics
Because non-Markovian dynamics are a general feature of systems exhibiting cooperativity, the conditional activity can be used to study the interactions and flow of information in such systems
Summary
Cells use biochemical networks to sense, process information, and respond to their environments. Many cellular behaviors have been found to be controlled by genetic switches, in which the expression levels of a set of genes form a stable memory of a transient stimulus, allowing the cell to make a decision and remember it These networks range from a simple bistable switch to complicated networks involving dozens of genes and many stable states of the switch (fixed points). In Arabidopsis thaliana, a fifteen-gene network was identified whose fixed points correspond to the ten flower cell types (Espinosa-Soto et al, 2004) This is typical of many gene regulatory networks, where the phenotype corresponds not to expression of any single gene, but rather to the collective state of the system. This map elucidates the often non-intuitive connection between genotype and phenotype in these networks, and may be used to design experimental interventions which most effectively modify or disrupt this collective behavior, and most directly affect phenotype
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