Calculating biological behaviors of epigenetic states in the phage ? life cycle

Abstract

The biology and behavior of bacteriophage lambda regulation have been the focus of classical investigations of molecular control of gene expression. Both qualitative and quantitative aspects of this behavior have been systematically characterized experimentally. Complete understanding of the robustness and stability of the genetic circuitry for the lysis-lysogeny switch remains an unsolved puzzle. It is an excellent test case for our understanding of biological behavior of an integrated network based on its physical, chemical, DNA, protein, and functional properties. We have used a new approach to non-linear dynamics to formulate a new mathematical model, performed a theoretical study on the phage lambda life cycle, and solved the crucial part of this puzzle. We find a good quantitative agreement between the theoretical calculation and published experimental observations in the protein number levels, the lysis frequency in the lysogen culture, and the lysogenization frequency for mutants of O(R). We also predict the desired robustness for the lambda genetic switch. We believe that this is the first successful example in the quantitative calculation of robustness and stability of the phage lambda regulatory network, one of the simplest and most well-studied regulatory systems.

Quantitative kinetic analysis of the bacteriophage λ genetic network

“…Our study, revealing the CII and Q dynamic controls, could serve as a benchmark to test models and computer simulations of the genetic network such as those proposed recently (14)(15)(16)(17). A more complete understanding of the operation of the genetic network will require further detailed study of individual steps, the identification and characterization of other modules, known or unknown, by using the current methods as well as genetics, theoretical modeling, and mathematical analyses.…”

“…For instance, the complex negative control of lytic functions during the lysogenic response has been generally ignored, and the relative importance of different key regulators in determining the decision is poorly understood, in particular for different values of moi. Theoretical studies have provided detailed predictions of the execution of lytic and lysogenic pathways (14)(15)(16)(17). These predictions have not been adequately tested in an experiment.…”

Stochastic Phenotype Transition of a Single Cell in an Intermediate Region of Gene State Switching

“…This implies the time scale (iii) is usually much faster than (i). Most of the previous works have focused on two other scenarios: when (ii) is even much slower than (i), in which bimodal distribution of the protein copy number can occur even without positive feedback [9]; Or when (ii) is much faster than (iii), in which the gene states are in a rapid pre-equilibrium and often the diffusion approximation of CME is also applied [10,12]. Not enough attention has been paid to a third intermediate scenario in which the gene-state switching is much faster than γ but actually is slower than the protein synthesis, thus the copy-number fluctuations of protein.…”

“…On the other hand, as in many of the previous works [12], it is often assumed that the gene-state switching is extremely rapid. In this case, the full CME in Fig.…”

“…Furthermore, the variance of local fluctuations around each stable steady state x * (phenotypic state) can be approximated by 1/ d 2 Φi(x) dx 2 | x=x * [10,20]. One can clearly see from It is indispensable to emphasize that although the diffusion approximation of CME that was always applied [12,15] can also give rise to a landscape function, in the worst-case scenario, it might even reverse the relative stability of the coexisting phenotypic states and give incorrect saddle-crossing rates [10,24].…”