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Probabilistic Safety and Optimal Control for Survival Analysis of Bacillus Subtilis
A. Abate, J. Lygeros, S. Sastry

Citation
A. Abate, J. Lygeros, S. Sastry. "Probabilistic Safety and Optimal Control for Survival Analysis of Bacillus Subtilis". Talk or presentation, December, 2006.

Abstract
The investigation of the stress response network of Bacillus Subtilis ATCC 6633 offers a detailed explanation of how the bacterium reacts to competitive environmental conditions, among the many options, by producing the antibiotic subtilin in order to directly suppress other cells while getting immunized. The mechanisms of this generation are fairly well understood and described by a genetic and protein pathway that involves some non-deterministic interplay between the involved quantities: in particular, the presence of switching modes exhibits the activation/deactivation of certain genes and the production of proteins; these transitions in turn depend non-linearly on the above quantities. According to the general principles of evolution, we may postulate that the way this pathway functions is according to certain criteria and levels of optimality; in this context optimality is intended as a measure of personal fitness or, in the particular instance, of own survival. In particular, one would expect that the switches in the network happen `optimally’ in the above sense. In this work, we look at a recently developed dynamical model for the genetic network describing the production of subtilin and propose modifications for the model to bring it in line with other evidence reported in the literature. We obtain a system that presents partially decoupled high-level dynamics (those dealing with the population size and the nutrient level) and low-level ones (those describing the mechanism of generation of subtilin by the single cell). The high-level model is non-linear and deterministic, while the low-level one is piecewise-affine, hybrid and stochastic. The new model allows one to reinterpret the survival analysis for the single B. subtilis cell and study it as a probabilistic, decentralized safety specification problem over a short time horizon; it is `probabilistic’ because of the certainly stochastic dynamics, as well as according to possible `trembling’ features of the actions; it is `over a short time horizon’ because of the greedy nature of the survival games that are played at this level; it is naturally `decentralized’ because each entity, while optimizing for its own fitness (which depends on global information), does not communicate with the competitors, nor has knowledge of their actions; furthermore, we motivate that the solution of the problem may not be globally optimal. Using recently developed techniques for probabilistic verification in a stochastic hybrid systems setting, we reinterpret the above probabilistic safety problem as a (stochastic) optimal control one, where the controls are (possibly randomized) functions of the state-space that encode the switches in the network. Finally, the solution of this short-time-horizon, stochastic and decentralized optimal control problem yields the structure of the switching behaviors under study. Matching these outcomes with the data in the literature allows concluding that the corresponding mechanisms in the subtilin production network function with a degree of optimality, according to certain survival criteria.

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Citation formats  
  • HTML
    A. Abate, J. Lygeros, S. Sastry. <a
    href="http://chess.eecs.berkeley.edu/pubs/215.html"
    ><i>Probabilistic Safety and Optimal Control for
    Survival Analysis of Bacillus Subtilis</i></a>,
    Talk or presentation,  December, 2006.
  • Plain text
    A. Abate, J. Lygeros, S. Sastry. "Probabilistic Safety
    and Optimal Control for Survival Analysis of Bacillus
    Subtilis". Talk or presentation,  December, 2006.
  • BibTeX
    @presentation{AbateLygerosSastry06_ProbabilisticSafetyOptimalControlForSurvivalAnalysis,
        author = {A. Abate and J. Lygeros and S. Sastry},
        title = {Probabilistic Safety and Optimal Control for
                  Survival Analysis of Bacillus Subtilis},
        month = {December},
        year = {2006},
        abstract = {The investigation of the stress response network
                  of Bacillus Subtilis ATCC 6633 offers a detailed
                  explanation of how the bacterium reacts to
                  competitive environmental conditions, among the
                  many options, by producing the antibiotic subtilin
                  in order to directly suppress other cells while
                  getting immunized. The mechanisms of this
                  generation are fairly well understood and
                  described by a genetic and protein pathway that
                  involves some non-deterministic interplay between
                  the involved quantities: in particular, the
                  presence of switching modes exhibits the
                  activation/deactivation of certain genes and the
                  production of proteins; these transitions in turn
                  depend non-linearly on the above quantities.
                  According to the general principles of evolution,
                  we may postulate that the way this pathway
                  functions is according to certain criteria and
                  levels of optimality; in this context optimality
                  is intended as a measure of personal fitness or,
                  in the particular instance, of own survival. In
                  particular, one would expect that the switches in
                  the network happen `optimallyâ in the above
                  sense. In this work, we look at a recently
                  developed dynamical model for the genetic network
                  describing the production of subtilin and propose
                  modifications for the model to bring it in line
                  with other evidence reported in the literature. We
                  obtain a system that presents partially decoupled
                  high-level dynamics (those dealing with the
                  population size and the nutrient level) and
                  low-level ones (those describing the mechanism of
                  generation of subtilin by the single cell). The
                  high-level model is non-linear and deterministic,
                  while the low-level one is piecewise-affine,
                  hybrid and stochastic. The new model allows one to
                  reinterpret the survival analysis for the single
                  B. subtilis cell and study it as a probabilistic,
                  decentralized safety specification problem over a
                  short time horizon; it is `probabilisticâ
                  because of the certainly stochastic dynamics, as
                  well as according to possible `tremblingâ
                  features of the actions; it is `over a short time
                  horizonâ because of the greedy nature of the
                  survival games that are played at this level; it
                  is naturally `decentralizedâ because each
                  entity, while optimizing for its own fitness
                  (which depends on global information), does not
                  communicate with the competitors, nor has
                  knowledge of their actions; furthermore, we
                  motivate that the solution of the problem may not
                  be globally optimal. Using recently developed
                  techniques for probabilistic verification in a
                  stochastic hybrid systems setting, we reinterpret
                  the above probabilistic safety problem as a
                  (stochastic) optimal control one, where the
                  controls are (possibly randomized) functions of
                  the state-space that encode the switches in the
                  network. Finally, the solution of this
                  short-time-horizon, stochastic and decentralized
                  optimal control problem yields the structure of
                  the switching behaviors under study. Matching
                  these outcomes with the data in the literature
                  allows concluding that the corresponding
                  mechanisms in the subtilin production network
                  function with a degree of optimality, according to
                  certain survival criteria.},
        URL = {http://chess.eecs.berkeley.edu/pubs/215.html}
    }
    

Posted by Alessandro Abate on 24 Apr 2007.
Groups: chess
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