Tomas Gedeon

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  Modeling network dynamics using Boolean formalism: An introduction
  Tomas Gedeon

  A notion of a "network" is central  in modern cell biology. One of the reasons is that there are many experimental methods that can discover gene and regulatory networks in cells and the hope is that the same networks have the same function in different organisms.  If so, then networks would provide a very useful abstraction: the individual chemical species  do not matter, only the structure of their interactions. The conjecture that networks exhibit stereotypical behavior is  false, as dynamics of complex systems will depend on the choice of the model, its parameters, and its initial conditions. Boolean formalism attempts to extract information about dynamic behavior of the networks where each node is either On or Off, and the updates of the states are based on Boolean functions. I will provide basic introduction to discrete Boolean models, review some results and shortcomings and end up with description of switching networks which embed Boolean update functions in a ODE model.

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  Database for Dynamic Signatures of Gene Regulatory Networks: Applications
  Tomas Gedeon
  Experimental data on gene regulation is mostly qualitative, where the only information available about pairwise interactions is the presence of either up-or down- regulation. Quantitative data is often subject to large uncertainty and is mostly in terms of fold differences. Given these realities, it is very difficult to make reliable predictions using mathematical models. The current approach of choosing reasonable parameter values, a few initial conditions and then making predictions based on resulting solutions is severely subsampling both the parameter and phase space. This approach does not produce provable and reliable predictions.
  We present a new approach that uses continuous time Boolean networks as a platform for qualitative studies of gene regulation. In this talk we show how we plan to use this approach in applications ranging from cell cycle dynamics to malaria.
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  Global dynamics of networks under perturbations of network topology
  Tomas Gedeon
  Experimental data on gene regulation is mostly qualitative, where the only information available about pairwise interactions is the presence of either up-or down- regulation. Quantitative data is often subject to large uncertainty and is mostly in terms of fold differences. Given these realities, it is very difficult to make reliable predictions using mathematical models. The current approach of choosing reasonable parameter values, a few initial conditions and then making predictions based on resulting solutions is severely subsampling both the parameter and phase space. This approach does not produce provable and reliable predictions.
  We present a new approach that uses continuous time Boolean networks as a platform for qualitative studies of gene regulation. We compute a Database for Dynamics, which rigorously approximates global dynamics over entire parameter space. The results obtained by this method provably capture the dynamics at a predetermined spatial scale.
  We apply our approach to study neighborhood of a given network in the space of networks. We start with a E2F-Rb network underlying the mammalian cell cycle restriction point and show that majority of the parameters support either the GO, NO-GO, or bistability between these two states. We then sample 100 perturbations of this network and study robustness of this dynamics in the network space.