Decomposing the parameter space of biological networks via a numerical discriminant approach
Many systems in biology (as well as other physical and engineering systems) can be described by systems of ordinary differential equation containing large numbers of parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and characterize the steady...
| Main Authors: | , , , |
|---|---|
| Format: | Conference item |
| Language: | English |
| Published: |
Springer Verlag
2020
|
| _version_ | 1797079723450302464 |
|---|---|
| author | Harrington, H Mehta, D Byrne, H Hauenstein, J |
| author_facet | Harrington, H Mehta, D Byrne, H Hauenstein, J |
| author_sort | Harrington, H |
| collection | OXFORD |
| description | Many systems in biology (as well as other physical and engineering systems) can be described by systems of ordinary differential equation containing large numbers of parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and characterize the steady-state solutions as the model parameters vary, a technically challenging problem in a high-dimensional parameter landscape. Rather than simply determining the number and stability of steady-states at distinct points in parameter space, we decompose the parameter space into finitely many regions, the number and structure of the steady-state solutions being consistent within each distinct region. From a computational algebraic viewpoint, the boundary of these regions is contained in the discriminant locus. We develop global and local numerical algorithms for constructing the discriminant locus and classifying the parameter landscape. We showcase our numerical approaches by applying them to molecular and cell-network models. |
| first_indexed | 2024-03-07T00:49:48Z |
| format | Conference item |
| id | oxford-uuid:85fcaaef-cbd5-4ff8-b3ce-14d92f8070d2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:49:48Z |
| publishDate | 2020 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:85fcaaef-cbd5-4ff8-b3ce-14d92f8070d22022-03-26T22:01:13ZDecomposing the parameter space of biological networks via a numerical discriminant approachConference itemhttp://purl.org/coar/resource_type/c_5794uuid:85fcaaef-cbd5-4ff8-b3ce-14d92f8070d2EnglishSymplectic Elements at OxfordSpringer Verlag2020Harrington, HMehta, DByrne, HHauenstein, JMany systems in biology (as well as other physical and engineering systems) can be described by systems of ordinary differential equation containing large numbers of parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and characterize the steady-state solutions as the model parameters vary, a technically challenging problem in a high-dimensional parameter landscape. Rather than simply determining the number and stability of steady-states at distinct points in parameter space, we decompose the parameter space into finitely many regions, the number and structure of the steady-state solutions being consistent within each distinct region. From a computational algebraic viewpoint, the boundary of these regions is contained in the discriminant locus. We develop global and local numerical algorithms for constructing the discriminant locus and classifying the parameter landscape. We showcase our numerical approaches by applying them to molecular and cell-network models. |
| spellingShingle | Harrington, H Mehta, D Byrne, H Hauenstein, J Decomposing the parameter space of biological networks via a numerical discriminant approach |
| title | Decomposing the parameter space of biological networks via a numerical discriminant approach |
| title_full | Decomposing the parameter space of biological networks via a numerical discriminant approach |
| title_fullStr | Decomposing the parameter space of biological networks via a numerical discriminant approach |
| title_full_unstemmed | Decomposing the parameter space of biological networks via a numerical discriminant approach |
| title_short | Decomposing the parameter space of biological networks via a numerical discriminant approach |
| title_sort | decomposing the parameter space of biological networks via a numerical discriminant approach |
| work_keys_str_mv | AT harringtonh decomposingtheparameterspaceofbiologicalnetworksviaanumericaldiscriminantapproach AT mehtad decomposingtheparameterspaceofbiologicalnetworksviaanumericaldiscriminantapproach AT byrneh decomposingtheparameterspaceofbiologicalnetworksviaanumericaldiscriminantapproach AT hauensteinj decomposingtheparameterspaceofbiologicalnetworksviaanumericaldiscriminantapproach |