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Parameter Analysis in Models of Yeast Cell Polarization and Stem Cell Lineage

Renardy, Marissa
http://rave.ohiolink.edu/etdc/view?acc_num=osu1522848361551388

Abstract Details

2018, Doctor of Philosophy, Ohio State University, Mathematics.
Understanding the effects of unknown parameters and estimating their values has become a major task in all areas of systems biology. This task is especially challenging in models that are expensive to evaluate or that contain a large number of parameters. This dissertation consists of two major parts, each one addressing the issue of parameter analysis in a different biological context. In the first chapter, we present a methodology for parameter sensitivity analysis and parameter estimation and apply this methodology to a large spatial model for yeast mating polarization. The model consists of 11 partial differential equations with 35 unknown parameters, and we seek to understand the effects of these parameters and estimate their values from experimental data. In models with such a large number of parameters, traditional methods for parameter estimation can become computationally intractable. Our methodology provides a dramatic improvement in computational efficiency from the replacement of model simulation by evaluation of a polynomial surrogate model. This allows us to perform derivative-based parameter sensitivity analysis to reduce the parameter count, followed by rapid Bayesian parameter estimation that would otherwise be prohibitively expensive to perform. We first tested our methodology on a smaller ordinary differential equation (ODE) model of the heterotrimeric G-protein cycle, which shows results consistent with published single-point parameter estimates. Then, applying our methodology to the full spatial model, we are able to reduce the parameter count via sensitivity analysis and obtain probability distributions of the 15 most sensitive parameters. We show that a wide range of parameter values permit polarization in the model. In the second chapter, we consider a compartmental ODE stem cell lineage model for tissue growth. We compare three variants of hierarchical stem cell lineage tissue models with different combinations of negative feedbacks. We perform equilibrium and stability analysis on each variant and perform parameter sensitivity analysis to examine the possible strategies for the cells to achieve certain performance objectives. For example, among the performance objectives are that the system obtain a positive stable steady state with a small proportion of stem to differentiated cells, and that the system is able to recover quickly from injury. Our results suggest that multiple negative feedback loops must be present in the stem cell lineage to keep the fractions of stem cells to differentiated cells in the total population as robust as possible to variations in cell division parameters, and to minimize the time for tissue recovery in a non-oscillatory manner. We also find that the probability of symmetric stem cell division, which has been previously studied in connection with mutation accumulation, affects these performance objectives only when there is no regulatory feedback on stem cell replication.
Ching-Shan Chou (Advisor)
Adriana Dawes (Committee Member)
Dongbin Xiu (Committee Member)
117 p.
Mathematics
mathematical biology; computational biology; parameter estimation; sensitivity analysis; cell polarization; cell lineage

Recommended Citations

Citations

  • Renardy, M. (2018). Parameter Analysis in Models of Yeast Cell Polarization and Stem Cell Lineage [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1522848361551388

    APA Style (7th edition)

  • Renardy, Marissa. Parameter Analysis in Models of Yeast Cell Polarization and Stem Cell Lineage. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1522848361551388.

    MLA Style (8th edition)

  • Renardy, Marissa. "Parameter Analysis in Models of Yeast Cell Polarization and Stem Cell Lineage." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1522848361551388

    Chicago Manual of Style (17th edition)

osu1522848361551388
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This open access ETD is published by The Ohio State University and OhioLINK.