### Andrew Matteson

Doctoral Candidate

Computational Biology Program

Courant Institute of Mathematical Sciences

New York University

April 23, 2013

Doctoral Dissertation Defense

Computational Methods in Model Merging with Applications to Pharmaceutical Development

Quantitative
biochemical models of cell signaling have been successfully applied to
develop insights into the nature of signaling regulation. These models
have diverse applications to understanding developmental biology, normal
cellular behavior, and disease states. They have been especially
powerful in guiding the development of targeted oncology therapeutics. Construction of biochemical models has several
challenges. One in particular is parameter estimation. Since many
parameters of biological models are not directly measurable, they must
be estimated by some technique. The estimated parameters can exert
large influences on a model's predictions, but uncertainties in the
estimation process tend to give different estimates for the same
parameter when it is estimated using two different sets of data. The incomparability of parameters estimated on
different sets of data is a significant barrier to the creation of
certain kinds of models. In particular, a parameter that appears in two
different signaling pathways must be resolved in order to make a single
model of both pathways. Such models encompassing multiple interacting
pathways would be useful, especially in understanding resistance that
develops to targeted cancer therapeutics; however, estimating parameters
of such multi-pathway models has been extremely challenging. In this work, we introduce and discuss a heuristic
used in conjunction with optimization algorithms to resolve these
challenges. This heuristic is called "model merging." We perform an
example driven exploration of the heuristic for two toy models, one in
which a resolution of parameter estimates is possible and in the case
where it is not. We find advantages in both cases relative to using
optimization alone. We then turn to biological applications. We use
the heuristic to build two models of biological signaling, a cell
signaling model of two interacting receptor signaling pathways, MET and
EGFR, active in renal cancer, and a model of erythropoeitin signaling in
normal and cancerous cells. In both models, parameters for which a
resolution could not be found directly correspond to biological
differences between pathways or cell types. This indicates that the
heuristic is a powerful tool in identifying resolved models.