Citation
Alessandro Abate, Maria Prandini, John Lygeros, S. Shankar Sastry. "Probabilistic Safety and Optimal Control for Survival Analysis of Bacillus Subtilis". Proceedings of the 2nd Conference on Foundations of Systems Biology in Engineering, 527-532, September, 2007.

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.

Electronic downloads

• http://hybrid.stanford.edu/~aabate/pubs.htm

Citation formats

• HTML

  Alessandro Abate, Maria Prandini, John Lygeros, S. Shankar
  Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/441.html">Probabilistic
  Safety and Optimal Control for Survival Analysis of Bacillus
  Subtilis</a>, Proceedings of the 2nd Conference on
  Foundations of Systems Biology in Engineering, 527-532,
  September, 2007.

• Plain text

  Alessandro Abate, Maria Prandini, John Lygeros, S. Shankar
  Sastry. "Probabilistic Safety and Optimal Control for
  Survival Analysis of Bacillus Subtilis". Proceedings of the
  2nd Conference on Foundations of Systems Biology in
  Engineering, 527-532, September, 2007.

• BibTeX

  @inproceedings{AbatePrandiniLygerosSastry07_ProbabilisticSafetyOptimalControlForSurvivalAnalysis,
      author = {Alessandro Abate and Maria Prandini and John
                Lygeros and S. Shankar Sastry},
      title = {Probabilistic Safety and Optimal Control for
                Survival Analysis of Bacillus Subtilis},
      booktitle = {Proceedings of the 2nd Conference on Foundations
                of Systems Biology in Engineering},
      pages = {527-532},
      month = {September},
      year = {2007},
      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.},
      URL = {http://chess.eecs.berkeley.edu/pubs/441.html}
  }
  

Posted by Alessandro Abate on 16 Jun 2008.
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