Stochastic Modeling

Stochastic discrete modeling is an alternative approach to the mathematical formalizations of stochastic differential equations and the Gillespie algorithm simulations. One aspect of my research has focused on the development of a stochastic framework for discrete models that we called Stochastic Discrete Dynamical Systems (SDDS), see details in [1]. This framework introduces stochasticity in the transitions that are described by propensity probabilities for activations and degradations. This approach allows the use of tools from computational algebra as well as techniques from Markov decision processes theory for model analysis and for optimal control methods. This framework also provides a setup for cell population simulations. We have used SDDS to investigate the ability of feedforward loop motifs involving miRNAs to stabilizes network dynamics, see [2]. Also, parameter estimation techniques for the propensity parameters of SDDS can be found in [3]. Optimal control methods using SDDS can be found in [4].

References

  1. Modeling Stochasticity and Variability in Gene Regulatory Networks. David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Seda Arat, Reinhard Laubenbacher. EURASIP Journal on Bioinformatics and Systems Biology,2012:5, 2012.http://bsb.eurasipjournals.com/content/2012/1/5.

  2. Stabilizing Gene Regulatory Networks Through Feedforward Loops. Claus Kadelka, David Murrugarra, Reinhard Laubenbacher. Chaos, 23, 025107, 2013. Paper.

  3. Estimating Propensity Parameters using Google PageRank and Genetic Algorithms. David Murrugarra, Jacob Miller, and Alex Mueller. Frontiers in Neuroscience, 10:513, 2016. Full text.

  4. A Near-Optimal Control Method for Stochastic Boolean Networks. Boris Aguilar, Pan Fang, Reinhard Laubenbacher, and David Murrugarra. Letters in Biomathematics, 7(1), 67-80, 2020. Full text.