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.

Glycosyltransferases of the Cellulose Synthase Like D (CSLD) subfamily have been reported to be involved in tip growth and stem development in Arabidopsis. The csld2 and csld3 mutants are root hair defective and the csld5 mutant has reduced stem growth. In this study, we produced double and triple knockout mutants of CSLD2, CSLD3, and CSLD5. Unlike the single mutants and the csld2/csld3 double mutant, the csld2/csld5, csld3/csld5, and csld2/ csld3/csld5 mutants were dwarfed and showed severely reduced viability. This demonstrates that the cooperative activities of CSLD2, CSLD3, and CSLD5 are required for normal Arabidopsis development, and that they are involved in important processes besides the specialized role in tip growth. The mutant phenotypes indicate that CSLD2 and CSLD3 have overlapping functions with CSLD5 in early plant development, whereas the CSLD2 and CSLD3 proteins are non-redundant. To determine the biochemical function of CSLD proteins, we used transient expression in tobacco leaves. Microsomes containing heterologously expressed CSLD5 transferred mannose from GDP-mannose onto endogenous acceptors. The same activity was detected when CSLD2 and CSLD3 were co-expressed but not when they were expressed separately. With monosaccharides as exogenous acceptors, microsomal preparations from CSLD5-expressing plants mediated the transfer of mannose from GDP-mannose onto mannose. These results were supported by immunodetection studies that showed reduced levels of a mannan epitope in the cell walls of stem interfascicular fibers and xylem vessels of the csld2/csld3/csld5 mutant.

Based on the dynamical structure theory for complex networks recently developed by one of us and on the physical-chemical models for gene regulation, developed by Shea and Ackers in the 1980's, we formulate a direct and concise mathematical framework for the genetic switch controlling phage lambda life cycles, which naturally includes the stochastic effect. The dynamical structure theory states that the dynamics of a complex network is determined by its four elementary components: The dissipation (analogous to degradation), the stochastic force, the driving force determined by a potential, and the transverse force. The potential may be interpreted as a landscape for the phage development in terms of attractive basins, saddle points, peaks and valleys. The dissipation gives rise to the adaptivity of the phage in the landscape defined by the potential: The phage always has the tendency to approach the bottom of the nearby attractive basin. The transverse force tends to keep the network on the equal-potential contour of the landscape. The stochastic fluctuation gives the phage the ability to search around the potential landscape by passing through saddle points. With molecular parameters in our model fixed primarily by the experimental data on wild-type phage and supplemented by data on one mutant, our calculated results on mutants agree quantitatively with the available experimental observations on other mutants for protein number, lysogenization frequency, and a lysis frequency in lysogen culture. The calculation reproduces the observed robustness of the phage lambda genetic switch. This is the first mathematical description that successfully represents such a wide variety of major experimental phenomena. Specifically, we find: (1) The explanation for both the stability and the efficiency of phage lambda genetic switch is the exponential dependence of saddle point crossing rate on potential barrier height, a result of the stochastic motion in a landscape; and (2) The positive feedback of cI repressor gene transcription, enhanced by the CI dimer cooperative binding, is the key to the robustness of the phage lambda genetic switch against mutations and fluctuations in kinetic parameter values.