Topology based control of biological genetic networks

The traditional control scheme has been to input a signal into a plant, where the signal is derived from either an open-loop or a closed-loop. This control strategy requires that the plant be able to accept inputs or can be modified to do so. However, this situation is not always true in biological genetic networks; in these systems, there is often no input or obvious modification to allow inputs.We believe that they require a new paradigm for control. Biotechnology techniques are such that it is easier to make topological changes to a genetic network than it is to either change the states of the pathway or add more elements to the pathway. Thus, for such genetic networks it is important to develop a theory of control based on making large-scale changes (e.g. genetic mutations) to the topology of the network; we provide steps towards such a theory. We highlight some useful results from monotone and hybrid systems theory, and show how these results can be used for such a topological control scheme. We consider the cancer-related p53 pathway as an example; we analyze this system using control theory and devise a controller.

[1]  M. Savageau.  Michaelis-Menten mechanism reconsidered: implications of fractal kinetics. , 1995, Journal of theoretical biology.

[2]  Timothy S. Ham,et al.  Production of the antimalarial drug precursor artemisinic acid in engineered yeast , 2006, Nature.

[3]  John Lygeros,et al.  Controllers for reachability specifications for hybrid systems , 1999, Autom..

[4]  Feng Xu,et al.  A new kinetic model for heterogeneous (or spatially confined) enzymatic catalysis : Contributions from the fractal and jamming (overcrowding) effects , 2007 .

[5]  L. Glass.  Combinatorial and topological methods in nonlinear chemical kinetics , 1975 .

[6]  A. Wartenberg,et al.  Introduction to biotechnology. , 1989 .

[7]  Bernard R. Glick,et al.  Molecular biotechnology : principles and applications ofrecombinant DNA , 2010 .

[8]  L. Vassilev,et al.  In Vivo Activation of the p53 Pathway by Small-Molecule Antagonists of MDM2 , 2004, Science.

[9]  H. Kunze,et al.  A graph theoretical approach to monotonicity with respect to initial conditions II , 1999 .

[10]  David Angeli,et al.  Multi-stability in monotone input/output systems , 2003, Syst. Control. Lett..

[11]  C. Rao,et al.  Control motifs for intracellular regulatory networks. , 2001, Annual review of biomedical engineering.

[12]  J. Lygeros,et al.  A game theoretic approach to controller design for hybrid systems , 2000, Proceedings of the IEEE.

[13]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[14]  A. Levine,et al.  The p53 pathway: positive and negative feedback loops , 2005, Oncogene.

[15]  T. Léveillard,et al.  The MDM2 C-terminal Region Binds to TAFII250 and Is Required for MDM2 Regulation of the Cyclin A Promoter* , 1997, The Journal of Biological Chemistry.

[16]  Bruce H. Krogh,et al.  Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations , 1999, HSCC.

[17]  Bohdan Wasylyk,et al.  p53-independent functions of MDM2. , 2003, Molecular cancer research : MCR.

[18]  Claire J. Tomlin,et al.  Reachability Algorithm for Biological Piecewise-Affine Hybrid Systems , 2007, HSCC.

[19]  James J. Collins,et al.  A Tunable Genetic Switch Based on RNAi and Repressor Proteins for Regulating Gene Expression in Mammalian Cells , 2007, Cell.

[20]  C. Tomlin,et al.  Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. , 2004, Systems biology.

[21]  M. Savageau.  Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways. , 1998, Bio Systems.

[22]  F. McCormick,et al.  Opposing Effects of Ras on p53 Transcriptional Activation of mdm2 and Induction of p19ARF , 2000, Cell.

[23]  M. Takagi,et al.  Regulation of p53 Translation and Induction after DNA Damage by Ribosomal Protein L26 and Nucleolin , 2005, Cell.

[24]  Eduardo D. Sontag,et al.  Monotone and near-monotone biochemical networks , 2007, Systems and Synthetic Biology.

[25]  El Houssine Snoussi.  Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach , 1989 .

[26]  M. Hirsch.  Stability and convergence in strongly monotone dynamical systems. , 1988 .

[27]  J. Gouzé,et al.  A class of piecewise linear differential equations arising in biological models , 2002 .

[28]  H. D. Jong,et al.  Qualitative simulation of genetic regulatory networks using piecewise-linear models , 2004, Bulletin of mathematical biology.

[29]  Vijay Kumar,et al.  Computational Techniques for Analysis of Genetic Network Dynamics , 2005, Int. J. Robotics Res..

[30]  Margaret Ashcroft,et al.  Regulation of p53 stability , 1999, Oncogene.