Understanding the biophysical processes underlying biological and biotechnological processes is a prerequisite for therapeutic treatments and technological innovation. With the exponential growth of computational processing speed, experimental findings in these fields have been complemented by dynamic simulations of developmental signaling and genetic interactions. Models provide means to evaluate "emergent" properties of systems sometimes inaccessible by reductionist approaches, making them test beds for biological inference and technological refinement.
The complexity and interconnectedness of biological processes pose special challenges to modelers; biological models typically possess a large number of unknown parameters relative to their counterparts in other physical sciences. Estimating these parameter values requires iterative testing of parameter values to find values that produce low error between model and data. This is a task whose length grows exponentially with the number of unknown parameters. Many biological systems require spatial representation (i.e., they are not well-mixed systems and change over space and time). Adding spatial dimensions complicates parameter estimation by increasing computational time for each model evaluation. Defining error for model-data comparison is also complicated on spatial domains. Different metrics compare different features of data and simulation, and the desired features are dependent on the underlying research question.
This dissertation documents the modeling, parameter estimation, and simulation of two spatiotemporal modeling studies. Each study addresses an unanswered research question in the respective experimental system. The former is a 3D model of a nanoscale amperometric glucose biosensor; the model was used to optimize the sensor's design for improved sensitivity to glucose. The latter is a 3D model of the developmental gap gene system that helps establish the bodyplan of Drosophila melanogaster; I wished to determine if the embryo's geometry alone was capable of accounting for observed spatial distributions of gap gene products and to infer feasible genetic regulatory networks (GRNs) via parameter estimation of the GRN interaction terms. Simulation of the biosensor successfully predicted an optimal electrode density on the biosensor surface, allowing us to fabricate improved biosensors. Simulation of the gap gene system on 1D and 3D embryonic demonstrated that geometric effects were insufficient to produce observed distributions when simulated with previously reported GRNs. Noting the effects of the error definition on the outcome of parameter estimation, I conclude with a characterization of assorted error definitions (objective functions), describe data characteristics to which they are sensitive, and end with a suggested procedure for objective function selection. Choice of objective function is important in parameter estimation of spatiotemporal system models in varied biological and biotechnological disciplines.
|Advisor:||Gribskov, Michael, Rundell, Ann|
|Commitee:||Fleet, James, Gribskov, Michael, Rundell, Ann, Umulis, David|
|School Location:||United States -- Indiana|
|Source:||DAI-B 76/08(E), Dissertation Abstracts International|
|Subjects:||Neurosciences, Applied Mathematics, Developmental biology|
|Keywords:||Drosophila, Gap genes, Mathematical modeling, Morphogenesis, Objective functions, Optimization|
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