Konstantin Mischaikow

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  Dynamic Signatures Generated by Regulatory Networks
  Konstantin Mischaikow

  Consider a regulatory network presented as a directed graph with annotated edges that indicate if the first node is up-regulating or down-regulating the second node. What kind of dynamics can this network generate? While this may seem to be an inadequately posed question it arises fairly often in biological contexts. Our motivation for addressing it arises from gene regulatory networks where we assume that the nodes represent genes and act as switches. However, we do not assume that we know the appropriate parameter values let alone the nonlinear reactions that govern the switches. Nevertheless, as I will describe in this talk, for moderate sized networks we can give a mathematically justifiable, computationally tractable,  description of the global dynamics for a large class of ode models and a wide range of parameter values.

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  Measuring Molecules using Persistent Homology
  Konstantin Mischaikow
  No abstract has been provided.
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  Database for Dynamic Signatures of Gene Regulatory Networks: Theory
  Konstantin Mischaikow
  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 focus on the theoretical justification for the approach that we are taking.