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Pathway modules in the Canalizing Dynamics of the Drosophila Segment Polarity Network
The paradigmatic example of a complex system is the web of biochemical interactions that make up life. We still know very little about the organization of life as a dynamical, interacting network of genes, proteins and biochemical reactions. How do biochemical networks—containing many regulatory, signaling, and metabolic processes—achieve reliability and robustness? Cells function reliably despite noisy dynamic environments, which is all the more impressive given that control strategies implemented by intra and inter-cellular processes cannot rely on a centralized, global view of the relevant networks. Are the resulting complex dynamics made up of relatively autonomous modules? If so, what is their functional role and how can they be identified? How robust is the collective computation performed by intra-cellular networks to mutations, delays and stochastic noise? To address these questions, we are focused on developing both novel methodologies and informatics tools to study control and collective computation in automata networks used to model gene regulation and biochemical signaling.
Modeling of biochemical signaling, regulation, modularity, robutsness and emergent computation in the dynamics of complex networks. Our methodology identifies canalizing control patterns in discrete automata models of biochemical networks. Currently working with models of genetic regulation in yeast , flowering of Arabidopsis thaliana; body segmentation in Drosophila, intracellular signal transduction in fibroblasts, biochemical pathways in granular leukemic lymphocytes, an integrated genome-scale transcriptional and metabolic network for E-Coli, and others. Our approach allows us to model biochemical signaling, regulation, modularity [Kolchinsky and Rocha, 2011], robutsness and emergent computation in the dynamics of complex networks modeled as automata networks.
Two-symbol Schemata Redescription of the Transition Look-Up tables of Automata
Schema Redescription in Cellular Automata
Schema redescription with two symbols is a method to eliminate redundancy in the transition tables of Boolean automata. One symbol is used to capture redundancy of individual input variables, and another to capture permutability in sets of input variables: fully characterizing the canalization present in Boolean functions. Two-symbol schemata explain aspects of the behavior of automata networks that the characterization of their emergent patterns does not capture. We have used our method to show that despite having very different collective behavior, CA rules can be very similar at the local interaction level [Marques-Pita and Rocha, 2011]—leading us to question the tendency in complexity research to pay much more attention to emergent patterns than to local interactions. We have also used schema redescription to obtain more amenable search spaces of CA rules for the Density Classification Task—obtaining some of the best known rules for this task. [Marques-Pita and Rocha, 2008, Marques-Pita, Mitchell, and Rocha, 2008].
Emergent Computation in the AND Rule
Origin of Representations in Evolving Cellular Automata
We have been interested on the problem of how information, symbols, representations and the like can arise from a purely dynamical system of many components. This is a topic of particular interest in Cognitive Science, where the notions of representation and symbol often divide the field into opposing camps. Often, in the area of Embodied Cognition the idea of self-organization in dynamical systems leads many researchers to reject representational or semiotic elements in their models of cognition. This attitude seems not only excessive, but indeed absurd as it ignores the informational processes so important for biological organisms. Therefore, we have been working both on a re-formulation of the concept of representation for embodied cognition, as well as on simulations of dynamical systems (using Celular Automata) where one can study the origin of representations.
The Evolving Cellular Automata experiments of Crutchfield, Mitchell et al, in the late 1990′s were very exciting, as the ability of evolved cellular automata to solve non-trivial computation tasks seemed to provide clues about the origin of representations and information from dynamical systems [Mitchell, 1998] [Rocha ,1998b]. We conducted additional experiments which extended the density classification task with more difficult logical tasks [Rocha ,2000; Rocha, 2004]. Later, we proposed a re-formulation of the concept of representation in cognitive science and artificial life which is based on this work, but argues that the type of emergent computations observed in these experiments do not produce representations quite as rich as those as observed in biology and cognition [Rocha and Hordijk ,2005]. These experiments allow us to think about how to evolve symbols from artificial matter in computational environments. The figure above, depicts a space-time diagram and particle model of a CA rule evolved to solve the AND task . Some additional Figures and experiment details of CA rules for logical tasks in our experiments are also available.
Project Members and Collaborators
Project partially funded by .
- Fundacao para a Ciencia e Tecnologia, Portugal. PTDC/EIA-CCO/114108/2009. Project title: “Collective Computation and Control in Complex Biochemical Systems”
- Fundação Luso-Americana para o Desenvolvimento (Portugal) and National Science Foundation (USA), 2012-2014. Project title: “Network Mining For Gene Regulation And Biochemical Signaling.” (171/11)
Selected Project Publications
- M. Marques-Pita and L.M. Rocha . “Canalization and control in automata networks: body segmentation in Drosophila Melanogaster”. PLoS ONE, 8(3): e55946. doi:10.1371/journal.pone.0055946.
- T. Parmer . Inducing Apoptosis: The Study of a Random Boolean Network Modelling Survival Signalling in T-LGL Leukemia. Undergraduate Thesis for dual degree, BS in cognitive science and BA in biophysics, through the Individualized Major Program at Indiana University.
- A. Kolchinsky, and L.M. Rocha .”Prediction and Modularity in Dynamical Systems“.In: Advances in Artificial Life, Proceedings of the Eleventh European Conference on the Synthesis and Simulation of Living Systems (ECAL 2011). August 8 – 12, 2011, Paris, France,. MIT Press, pp. 423-430.
- M. Mourao . Reverse engineering the mechanisms and dynamical behavior of complex biochemical pathways. PhD Dissertation, Indiana University
- A. Kolchinsky, and L.M. Rocha .”Prediction and modularity in complex dynamical systems” (pdf). In: Proc. of the 8th Int. Conf. on Complex Systems. June 26 – July 1, 2011, Quincy, MA, USA. In Press.
- M. Marques-Pita and L.M. Rocha . “Schema Redescription in Cellular Automata: Revisiting Emergence in Complex Systems“. In: The 2011 IEEE Symposium on Artificial Life, at the IEEE Symposium Series on Computational Intelligence 2011. April 11 – 15, 201, Paris, France,. IEEE Press, pp: 233-240.
- M. Marques-Pita, M. Mitchell, and L.M. Rocha . “The Role of Conceptual Structure in Learning Cellular Automata to Perform Collective Computation“. In: Unconventional Computation: 7th International Conference (UC 2008). Lecture Notes in Computer Science. Springer-Verlag, 5204: 146-163.
- M. Marques-Pita and L.M. Rocha . “Conceptual Structure in Cellular Automata: The Density Classification Task“. In: Artificial Life XI: Eleventh International Conference on the Simulation and Synthesis of Living Systems. S. Bullock, J. Noble, R. A. Watson, and M. A. Bedau (Eds.). MIT Press, pp. 390-397.
- Rocha, Luis M. and W. Hordijk . “Material Representations: From the Genetic Code to the Evolution of Cellular Automata”. Artificial Life. 11 (1-2), pp. 189 – 214
- Almeida e Costa, F. and Rocha, Luis M. . “Embodied and Situated Cognition”. Artificial Life. 11 (1-2), pp. 5 – 11
- Rocha, Luis M. . “Evolving Memory: Logical Tasks for Cellular Automata”. Ninth International Conference on the Simulation and Synthesis of Living Systems (ALIFE9). Boston, Massachusetts, September 12-15th 2004.
- Rocha, Luis M. ." Evolution with Material Symbol Systems." Biosystems. Vol. 60, pp. 95-121.
- Rocha, Luis M. . “Syntactic autonomy, cellular automata, and RNA editing: or why self-organization needs symbols to evolve and how it might evolve them”. In: Closure: Emergent Organizations and Their Dynamics. Chandler J.L.R. and G, Van de Vijver (Eds.) Annals of the New York Academy of Sciences. Vol. 901, pp 207-223.