(4cg) Analysis and Optimization of Cellular Networks: a Systems Approach

The success of human genome project has ushered a new era that emphasizes on a systemic or integrated approach known as systems biology, to ascertain the cellular behavior arising from complex cellular networks [1]. Systems biology lies at the interface of biology and systems theory including control systems engineering. Other than the familiar use of the word ?systems? as a designation for physical systems, the term here also refers to the study of physical systems through: modeling, formulation of mathematical descriptions, analysis, and design [2]. Control systems approaches have been instrumental in this discipline, for example in the elucidation of chemotaxis adaptive mechanism [3], in the identification of control motifs in regulatory networks [4], and in the unraveling of design principles in circadian rhythm architecture [5]. In addition, several concepts from control engineering, in particular robustness, have diffused into systems biology to define many characteristics of cellular behavior. Robustness describes the ability of a system to maintain the desired performance/behavior under intrinsic and extraneous uncertainties [6]. In biological systems, these uncertainties can arise from inherent stochastic nature of gene expression (intrinsic) [7] or variations in the extracellular species concentration (extraneous). In fact, there appears to be an intimate link between the complexity and robustness in cellular functions [8].

Unraveling Design Principles using Sensitivity Analysis: Stochastic and Oscillatory Biological Systems

The size and complexity of cellular networks prevent the deduction of cellular behavior based solely on intuition. Systems analysis can help to unravel this complexity. One such method is sensitivity analysis [9], in which linear sensitivities quantify how much the system behavior changes as the parameters are varied. In cellular networks, high sensitivities point to the weakest links in the system which cellular behavior strongly depends on. By mapping these critical pathways back to the genotype, one can point to the set of genes and interactions that control the cellular behavior. Sensitivity analysis traditionally applies to continuous systems, i.e, differential equations, as these are the most common representation of engineered systems. However, the characteristics of cellular processes, such as nonlinear behavior (e.g., oscillations) and low concentration (nanomolar) of molecules, limit the application of classical sensitivity analysis and thus require the development of new methodologies for analysis.

One focus in my research is the development of non-traditional sensitivity analysis to investigate common systems in biology, in particular discrete stochastic and oscillatory systems. Sensitivity analysis has been formulated for discrete stochastic systems which prevail in cellular level modeling [10]. In these systems, the chemical reactions occur as discrete events due to the low copy number of species involved, which accurately describe many cellular processes such as binding and unbinding of a transcription factor on a promoter [7]. Application of traditional sensitivity analysis to continuum representations of these systems can give incorrect results, in particular for systems with multiple steady states such as a bistable gene switch [10].

Another common dynamics of cellular networks is an oscillatory behavior of a limit cycle, for example in circadian rhythms, neuronal activities, and cell cycles. Here, past sensitivity analysis has mainly focused on the period and amplitude of the oscillations, with applications to models of circadian rhythm [5, 11, 12]. There exists very little work on the sensitivity analysis of the phase of oscillations, which describes the entrainment property of an oscillatory system such as circadian rhythm, to external forcing functions. The enabling concept for the phase analysis is the isochorns, collection of points that evolve to the same position in the limit cycle, which allows quantification of phase shifts between different limit cycles. Different measures of phase sensitivity analysis can be developed from this approach including the phase response curve (PRC) and the peak-to-peak sensitivity.

Optimizing Cellular Networks in Synthetic Biology: Stochastic Gene Switch

Advances in the recombinant DNA technology allow scientists to construct synthetic gene networks with specific functions such as a repressilator [13] and a gene switch [14]. These techniques set the foundation for building plug-and-play gene modules with predictable performance, which will make up a list of standardized parts [15]. From these parts, one can construct a functional module that can perform a specific task. The design effort in synthetic biology will become decoupled from the fabrication, analogous to the manufacture of integrated chip. Existing methodologies for designing the gene modules take on different approaches, such as combinatorial synthesis [16], design-then-mutate [17], and in silico evolution [18]. None of these approaches however considers the stochastic nature of cellular processes explicitly. As aforementioned, the inherent stochastic noise can induce distinguishing behavior that is not observable in continuum models [19].

Another focus in my research is in the development of methodology for the gene network optimization, using a bistable gene switch as an illustrative example. The optimization is formulated as a constrained nonlinear programming, where the stochastic effects are explicitly taken into account in the constraints. The goal is to produce plug-and-play gene modules that can robustly perform under the stochastic nature of cellular processes. The comparison between the proposed method and other design technique such as bifurcation analysis, highlighted the importance of stochastic effects in the design of a gene network.

References:

[1] H.Kitano. Science, 295:1662-1664, 2002.

[2] C.-T. Chen. Linear System Theory and Design. Oxford University Press, New York, NY, 1999.

[3] T.-M. Yi, Y. Huang, M. I. Simon, and J. Doyle. Proc. Natl. Acad. Sci. USA, 97:4649-4653, 2000.

[4] C. Rao and A. P. Arkin. Annu. Rev. Biomed. Eng., 3:391-419, 2001.

[5] J. Stelling, E. D. Gilles, and F. J. Doyle III. Proc. Natl. Acad. Sci. USA, 101:13210-13215, 2004.

[6] J. Stelling, U. Sauer, Z. Szallasi, F. J. Doyle III, and J. Doyle. Cell, 118:675-685, 2004.

[7] H. H. McAdams and A. Arkin. Trends Genet., 15:65-69, 1999.

[8] D. A. Lauffenburger. Proc. Natl. Acad. Sci. USA, 97:5031-5033, 2000.

[9] A. Varma, M. Morbidelli, and H. Wu. Parametric Sensitivity in Chemical Systems, Oxford University Press, New York, NY, 1999.

[10] R. Gunawan, Y. Cao, L. Petzold, and F. J. Doyle III. Biophys. J., 88:2530-2540, 2005.

[11] J.-C. Leloup and A. Goldbeter. J. Theor. Biol., 230:541-562, 2004.

[12] D. E. Zak, J. Stelling, and F. J. Doyle III. Comp. Chem. Eng., 29:663-673, 2005.

[13] M. B. Elowitz and S. Leibler. Nature, 403:335-338, 2000.

[14] T. S. Gardner, C. R. Cantor, and J. J. Collins. Nature, 403:339-342, 2000.

[15] BioBricks. Registry of Standard Biological Parts. http://parts.mit.edu.

[16] C. C. Guet, M. B. Elowitz, W. Hsing, and S. Leibler. Science, 296:1466-1470, 2002.

[17] Y. Yokobayashi, R. Weiss, and F. H. Arnold. Proc. Natl. Acad. Sci. USA, 99:16587-16591, 2002.

[18] P. Francois and V. Hakim. Proc. Natl. Acad. Sci. USA, 101:580-585, 2004.

[19] M. Samoilov, S. Plyasunov, and A. P. Arkin. Proc. Natl. Acad. Sci. USA, 102:2310-2315, 2005.