Dynamics in Boolean Networks

In this thesis several random Boolean networks are simulated. Both completely computer generated network and models for biological networks are simulated. Several different tools are used to gain knowledge about the robustness. These tools are Derrida plots, noise analysis and mean probability for canalizing rules. Some simulations on how entropy works as an indicator on if a network is robust are also included. The noise analysis works by measuring the hamming distance between the state of the network when noise is applied and when no noise is applied. For many of the simulated networks two types of rules are applied: nested canalizing and flat distributed rules. The computer generated networks consists of two types of networks: scale-free and ER-networks. One of the conclusions in this report is that nested canalizing rules are often more robust than flat distributed rules. Another conclusion is that the mean probability for canalizing rules has, for flat distributed rules, a very dominating effect on if the network is robust or not. Yet another conclusion is that the probability distribution for indegrees, for flat distributed rules, has a strong effect on if a network is robust due to the connection between the probability distribution for indegrees and the mean probability for canalizing rules.

[1]  D. West.  Introduction to Graph Theory , 1995 .

[2]  Q. Ouyang,et al.  The yeast cell-cycle network is robustly designed. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Carsten Peterson,et al.  Random Boolean network models and the yeast transcriptional network , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  B. Alberts,et al.  An Introduction to the Molecular Biology of the Cell , 1998 .

[5]  E. Dowell,et al.  Chaotic Vibrations: An Introduction for Applied Scientists and Engineers , 1988 .

[6]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[7]  Carlos Gershenson,et al.  Introduction to Random Boolean Networks , 2004, ArXiv.

[8]  N. Blackstone.  Essential Cell Biology: An Introduction to the Molecular Biology of the Cell.Bruce Alberts , Dennis Bray , Alexander Johnson , Julian Lewis , Martin Raff , Keith Roberts , Peter Walter , 1998 .

[9]  W. Just,et al.  The number and probability of canalizing functions , 2003, math-ph/0312033.

[10]  B. Derrida,et al.  Evolution of overlaps between configurations in random Boolean networks , 1986 .

[11]  Mark Allen Weiss,et al.  Data structures and algorithm analysis , 1991 .

[12]  M. Gustafsson,et al.  Large-scale reverse engineering by the Lasso , 2004, q-bio/0403012.

[13]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[14]  B. Derrida,et al.  Random networks of automata: a simple annealed approximation , 1986 .

[15]  S. Kauffman,et al.  Genetic networks with canalyzing Boolean rules are always stable. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Stuart A. Kauffman.  Understanding genetic regulatory networks , 2003 .

[17]  M. Aldana.  Boolean dynamics of networks with scale-free topology , 2003 .

[18]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[19]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[20]  C. Holbrow,et al.  Nonclassical Physics: Beyond Newton's View , 1998 .

[21]  Edward R. Dougherty,et al.  From Boolean to probabilistic Boolean networks as models of genetic regulatory networks , 2002, Proc. IEEE.

[22]  Nicola J. Rinaldi,et al.  Transcriptional Regulatory Networks in Saccharomyces cerevisiae , 2002, Science.

[23]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[24]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[25]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[26]  I Chih-Lin,et al.  Wireless Communications and Networks , 2004 .