Flexible and Robust Patterning by Centralized Gene Networks

• Autorzy: Vakulenko S. , Radulescu O.
• Języki publikacji: EN

Abstrakty

EN

We investigate the possibility of programming arbitrarily complex space-time patterns, and transitions between such patterns, by gene networks. We consider networks with two types of nodes. The v-nodes, called centers, are hyperconnected and interact one to another via u-nodes, called satellites. This centralized architecture realizes a bow-tie scheme and possesses interesting properties. Namely, this organization creates feedback loops that are capable to generate any prescribed patterning dynamics, chaotic or periodic, or stabilize a number of prescribed equilibrium states. We show that activation or silencing of a node can sharply switch the network dynamics, even if the activated or silenced node is weakly connected. Centralized networks can keep their flexibility, and still be protected against environmental noises. Finding an optimized network that is both robust and flexible is a computationally hard problem in general, but it becomes feasible when the number of satellites is large. In theoretical biology, this class of models can be used to implement the Driesch-Wolpert program, allowing to go from morphogen gradients to multicellular organisms.

Słowa kluczowe

EN

Gene networks; Pattern formation; Positional information; Driesch-Wolpert theory; bifurcation; viability; computability

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 118, nr 4
• Strony: 345--369
• Opis fizyczny: Bibliogr.56 poz.

Twórcy

autor

Vakulenko S.

autor

Radulescu O.

• DIMNP - UMR 5235 CNRS/UM1/UM2, Universite de Montpellier 2, Montpellier, France,

Bibliografia

• [1] M. Aldana, Boolean dynamics of networks with scale-free topology, Physica D 185, 45 - 66, 2003.
• [2] M. Aldana, and P. Cluzel, A natural class of robust networks, Proc. Natl. Acad. Sci. U.S.A. 100, 8710 - 8714, 2003.
• [3] R. Albert and A.L. Barabási, Rev. Modern Physics 74, 47-97, 2002.
• [4] D.V. Anosov (ed), Dynamical Systems 9: Dynamical Systems with Hyperbolic Behaviour, Encyclopedia of Mathematical Sciences Vol. 66. Translated from Russian., Springer V., Berlin, Heidelberg, New-York, 1995.
• [5] J.P. Aubin, A. Bayen, N. Bonneuil and P. Saint-Pierre, Viability, Control and Games: Regulation of complex evolutionary systems under uncertainty and viability constraints, Springer-Verlag. 2005
• [6] A.B. Babin and M.I. Vishik, Regular attractors of semigroups and evolution equations, J. Math. Pure Appl. 62, 441 - 491, 1983.
• [7] A. Barron, Universal Approximation Bounds for superpositions of a sigmoidal functions, IEEE Trans. On Inf. theory 39, 930-945. 1993
• [8] E. Berezikov, Evolution of microRNA diversity and regulation in animals, Nature Reviews Genetics 12, 846-860, 2011.
• [9] S.N. Chow and K. Lu, Invariant manifolds for flows in Banach spaces, J. Differential equations 74, 285-317, 1988.
• [10] P. Constantin, C. Foias, B. Nicolaenko and R. Temam, Integrable manifolds and inertial manifolds for dissipative differential equations, Springer, New-York, 1989.
• [11] M. Csete and J. Doyle, Bow ties, metabolism and disease, Trends Biotechnol 22, 446-450, 2004.
• [12] E.N. Dancer and P. Poláˇcik, Realization of vector fields and dynamics of spatially homogeneous parabolic equations, Memoirs of Amer. Math. Society 140, no. 668, 1999.
• [13] M. Delbrück, Discussion: Unitées biologiques douées de continuité génétique, Actes du colloque international du CNRS, pp. 33-3, Editions du CNRS, Paris, 1949.
• [14] K. Funahashi and Y. Nakamura, Approximation of dynamical systems by continuous time recurrent neural networks, Neural Networks 6, 801-806, 1993.
• [15] D. Henry, Geometric Theory of Semiliniar Parabolic Equations, Springer, New York, 1981.
• [16] J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. of Natl. Acad. USA 79, 2554-2558, 1982.
• [17] S.A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theor. Biol. 22, 437-67, 1969.
• [18] P. Koiran and C. Moore, Closed-form analytic maps in one and two dimensions can simulate universal Turing machines, Theoretical Computer Science 210, 217-223, 1999.
• [19] A. Lesne, Complex networks: from graph theory to biology, Letters in Math. Phys. 78, 235-262, 2006.
• [20] X. Li, J.J. Cassidy, C.A. Reinke, S. Fischboeck, and R.W. Carthew, A MicroRNA Imparts Robustness against Environmental Fluctuation during Development, Cell 137, 273-282, 2009.
• [21] M.Z. Ludwig, Manu, P. Kittler, K.P. White, and M. Kreitman, Consequences of Eukaryotic Enhancer Architecture for Gene Expression Dynamics, Development, and Fitness, PLoS Genetics 7, e1002364, 2011.
• [22] H. Ma, A. Sorokin, A. Mazein, A. Selkov, E. Selkov, O. Demin, and I. Goryanin, The Edinburgh human metabolic network reconstruction and its functional analysis, Molecular Systems Biology 3, 135, 2007.
• [23] R. Mane, Reduction of semilinear parabolic equations to finite dimensional C1 - flow, Geometry and Topology, Lecture Notes in Mathematics, No. 597, Springer -Verlag, New -York, 361-378, 1977.
• [24] M. Marion, Approximate inertial manifolds for reaction-diffusion equations in high space dimension, J. Dyn. Diff. Equations 1, 245-267, 1989.
• [25] N.J. Martinez, M.C. Ow, M.I. Barrasa, M. Hammell, R. Sequerra, L. Doucette-Stamm, F.P. Roth, V.R. Ambros, and A.J.M. Walhout, A C. elegans genome-scale microRNA network contains composite feedback motifs with high flux capacity, Genes Dev. 22, 2535-2549, 2008.
• [26] H. Meinhardt, Models of biological pattern formation, Academic Press, London, 1982.
• [27] M. Mezard and R. Zecchina, Random k-satisfiability problem: From an analytic solution to an efficient algorithm, Phys. Rev. E 66, 056126, 2002.
• [28] E. Mjolness, D.H. Sharp and J. Reinitz, A connectionist model of development, J. Theor. Biol. 152, 429-453, 1991.
• [29] J.D. Murray, Mathematical Biology, Springer, New York, 1993.
• [30] M.H.A. Newman, Alan Mathison Turing. 1912-1954, Biogr.Mems Fell.R.Soc. 1, 253-263, 1955.
• [31] R. Newhouse, D. Ruelle and F. Takens, Occurence of strange axiom A attractors from quasi periodic flows, Comm.Math. Phys. 64, 35-40, 1971.
• [32] K.M. Page, P.K. Maini and N.A.M. Monk, Complex pattern formation in reaction-diffusion systems with spatially varying parameters, Physica D 202, 95-115, 2005.
• [33] M.E. Peter, Targeting of mRNAs by multiple miRNAs: the next step, Oncogene 29, 2161-2164, 2010.
• [34] P. Poláˇcik, Complicated dynamics in Scalar Semilinear Parabolic Equations, In Higher Space Dimensions, Journ. of Diff. Eq. 89, 244 - 271, 1991.
• [35] M.I. Rabinovich and H.D.I. Abarbanel, The role of chaos in neural systems, Neuroscience 87 (N1), 5-14, 1998.
• [36] J. Reinitz and D. H. Sharp, Mechanism of formation of eve stripes, Mechanisms of Development 49, 133-158, 1995.
• [37] D. Ruelle, Elements of differentiable dynamics and bifurcation theory, Acad. Press, Boston, 1989.
• [38] D. Ruelle and F. Takens, On the nature of turbulence, Comm. Math. Phys 20, 167 -192, 1971.
• [39] K.P. Rybakowski, Realization of arbitrary vector fields on center manifolds of parabolic Dirichlet BVP's, J. Differential Equations 114, 199-221, 1994.
• [40] M. Scott, F.J. Poulin and H. Tang, Approximating intrinsic noise in continuous multispecies models, Proc. Roy. Soc. A 467, 718-737, 2011.
• [41] R. Shalgi, D. Lieber, M. Oren, Y. Pilpel, Global and Local Architecture of the Mammalian microRNATranscription Factor Regulatory Network, Plos Comp. Bio. 3, 1291-1304, 2007.
• [42] H.T. Siegelmann and E.D. Sontag, Turing computability with neural networks, Appl. Math. Lett. 4, 6, 1991.
• [43] H.T. Siegelmann and E.D. Sontag, On the computational power of neural nets, J. Comp. Syst. Sci. 50, 132-150, 1995.
• [44] S. Smale, Mathematics of Time, Springer, New - York. 1980.
• [45] M. Talagrand, Spin glasses, a Challenge for Mathematicians. Springer-Verlag. 2003.
• [46] K.C. Tu and B.L. Bassler, Multiple small RNAs act additively to integrate sensory information and control quorum sensing in Vibrio harveyi, Genes Dev. 21, 221-233, 2007.
• [47] C. Teuscher and E. Sanchez, A revival of Turings forgotten connectionist ideas: exploring unorganized machines, Springer-Verlag, London, 2001.
• [48] R. Thomas, Laws for the dynamics of regulatory networks, Int J Dev Biol. 42, 479485, 1998.
• [49] A.M. Turing, The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. B 237, 37-72, 1952.
• [50] A.M. Turing, Intelligent Machinery, in B. Melzer and D. Michie, editors, Machine Intelligence, volume 5 of National Physical Laboratory Report, 3-23, Edinburgh University Press, Edinburgh, 1969.
• [51] S.A. Vakulenko, A system of coupled oscillators can have arbitrary prescribed attractors, J. Phys. A. Math. Gen. 27, 2335-2349, 1994.
• [52] S.A. Vakulenko and P.V. Gordon, Neural networks with prescribed large time behaviour, J. Phys. A. Math. Gen 31, 9555-9570, 1998.
• [53] S.A. Vakulenko, Dissipative systems generating any structurally stable chaos, Advances in Diff. Equations 5, 1139-1178, 2000.
• [54] L. Wolpert, Positional information and pattern formation, in C.H. Waddington, editor, Towards a theoretical biology 3.Drafts. Aldine Publishing Company, Chicago, 1970.
• [55] L. Wolpert, R. Beddington, T. Jessell, P. Lawrence, E. Meyerowitz and J. Smith, Principles of Development. Oxford University Press, Oxford, 2002.
• [56] S. Wu, S. Huang, J. Ding, Y. Zhao, L. Liang, T. Liu, R. Zhan and X. He, Multiple microRNAs modulate p21Cip1/Waf1 expression by directly targeting its 3' untranslated region. Oncogene 29, 2302-2308, 2010.