Genetic Networks : Analog Computation and Artificial Design
Genetic regulatory networks have the task of controlling all aspects of life. The concept of a "genetic network" refers to the complex network of interactions between genes and gene products in a cell. Since the 60's genetic regulatory systems have been thought of as "circuits" or "networks" of interacting components, and were described in computer science terms by Stuart Kauffman: The genetic material is the "program" that guides protein production in a cell; protein levels determine the evolution of the network at subsequent times, and thus serve as its "memory". This have been mainly useful metaphor for describing gene networks.
Computability with Gene Networks (GN).
Recent work describes the successful fabrication of synthetic genetic networks. A call to find the computational power of genetic networks was issued by Gardner, Cantor, Collins in their article 2000 nature article appearing in the journal Nature in 2000. They reasoned that, reasoning that "theoretical design of complex and practical gene networks is [now] a realistic and achievable goal."
With A. Ben Hur we considered a model of analog based gene networks, previously proposed by Leon Glass, and proved that they are equivalent computationally to Turing machines. Unlike the neural networks case, these are strongly robust with respect to system's perturbation. While the equations describing the genetic networks are chaotic, we proposed a particular design principle that makes them non-chaotic, robust, and more easily predictable. It is interesting to note that the genetic toggle switch and other networks proposed in fabrications up until today follow this same principle.
With A. Ben Hur we formulated a computational interpretation of the dynamics of a switch-like ODE model of gene networks, and provided that they are equivalent to memory bounded Turing machines. While the equations describing the genetic networks are chaotic in general, we introduced the additional property of adjacency in order to make them non-chaotic and strongly robust. In short, two orthants are said to be adjacent if they differ in exactly one coordinate, and a network with an adjacent truth table will be called adjacent as well. We consider the adjacency more than a trick, but rather as a strategy for fault tolerant programming of gene networks. In fact, the genetic toggle switch constructed by Collins et all in Nature 2000 has this property. We still bear in mind that this holds for synthetic networks, and that nature may have other ways of programming genetic networks, which are not so transparent.
Dynamics of Gene Networks.
With Glass, Edwards, and Aziza, we proposed a new method for understanding the symbolic dynamics of gene networks model and use it as another way to bridge between them and various automata. We then joined with Perkins and Mason to study the Chaotic Dynamics in an Electronic Model of a Genetic Network. Interestingly there are major differences between the mathematical model and their actual hardware implementation.
Genetic Networks for the Design of Robust Artificial Agents: Current work.
Future engineering of complex systems that must remain robust and autonomous without human intervention require methods and materials for intrinsic self-construction and self-repair that make use of environmental feedback. With Rodney Douglass and student Roth (as part of his PhD dissertation at the Institute for Neuroinformatics in Zurich) we demonstrated how a simple multicellular organism with Braitenberg-like behavior can assemble itself by replication from a single artificial cell. This system is roughly analogous to the transcription / translation mechanisms of biological cells, and we showed how the interplay between the gradually increasing complexity of the environment produced by the organization of the successively differentiating cells gives rise to the serial unfolding of the final functional organism that is able to detect and follow a trace of food, while retaining the ability to repair itself after significant damage. With student Harrington we demonstrated a sensor network based on genetic network controllers that have the ability to transfer data with mutli-modalities thus providing an extremely efficient way of passing relevant information. With student Olsen we have been studying how the incorporation of apoptosis increases the robustness of the system to many possible attacks. We continued and studied the reaction of the system to severe possible damage of the genetic regulators and proposed secondary mechanism to equip the system with that would save it from tumor-like constructions which threat to demolish the whole system's healthy functionality.
R. Edwards, H.T. Siegelmann, K. Aziza and L. Glass, "Symbolic dynamics and computation in model gene networks", Chaos 11(1) , 2001
A. Ben-Hur, H.T. Siegelmann, "Computing with Gene Networks," Chaos: An Interdisciplinary Journal of Nonlinear Science, 14(1) pp. 145-151, March 2004 - was chosen as the work to describe in Physics News Update [more informations here]
L. Glass, T. J. Perkins, J. Mason, H. T. Siegelmann and R. Edwards. "Chaotic Dynamics in an Electronic Model of a Genetic Network ," Journal of Statistical Physics, Volume 121 Numbers 5-6: 969-994, 2006
M. Olsen and H. Siegelmann, "Artificial Death for Attaining System Longevity", Proceedings of the 50th Anniversary Summit of Artificial Intelligence Summit, Switzerland, July 2006
Kyle Harrington and Hava Siegelmann, "Adaptive Multi-Modal Sensors", Proceedings of the 50th Anniversary Summit of Artificial Intelligence Summit, Switzerland, July 2006
M. Olsen and H. Siegelmann, "Multi-Agent System that Attains Longevity via Death", Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI), Jan 2007
F. Roth, H.T. Siegelmann and R. J. Douglas, "The Self-Construction and -Repair of a Foraging Organism by Explicitly Specified Development from a Single Cell" Artificial Life, in press