Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains
<p>One of the main challenges in developmental biology is elucidating the mechanisms underlying the formation and maintenance of complex spatial and temporal structures. This thesis aims to explore two different and yet complementary approaches to address this challenge.</p> <p>Fir...
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| Format: | Thesis |
| Language: | English |
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2012
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| _version_ | 1826315406530314240 |
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| author | Woolley, T Thomas Woolley |
| author2 | Maini, P |
| author_facet | Maini, P Woolley, T Thomas Woolley |
| author_sort | Woolley, T |
| collection | OXFORD |
| description | <p>One of the main challenges in developmental biology is elucidating the mechanisms underlying the formation and maintenance of complex spatial and temporal structures. This thesis aims to explore two different and yet complementary approaches to address this challenge.</p> <p>Firstly, we investigate a number of specific developmental systems in order to suggest mechanisms underlying their observed biological behaviour. Critically, we show that, without modifications, standard mathematical formulations are unable to capture certain details. In particular, it is demonstrated that accurate descriptions of domain growth need to be included in order to construct mathematical models that compare favourably with experimental systems. In conjunction with understanding biological development better, we also analytically investigate the existence of spot patterns in a paradigm patterning model, resulting in the use of numerical methods to compare theory with simulation.</p> <p>The second approach used to investigate spatial-temporal complexity is more theoretical; we aim to characterise the effects of stochastic perturbations and growth on pattern generation. To achieve this we derive a stochastic description of biochemical reactions, diffusion and domain growth that is consistent with the deterministic description in the thermodynamic limit. This is then used to determine conditions under which robust patterns form.</p> <p>By exploring developmental complexity through these two different approaches of creating broad analytical methods and investigating specific biological models, we not only gain a deeper insight into the creation of complexity in specific cases but also a wider appreciation of how noise can affect such systems.</p> |
| first_indexed | 2024-03-06T18:03:26Z |
| format | Thesis |
| id | oxford-uuid:009a0956-ad51-49ea-b3ac-1accf6fb017a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:25:07Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:009a0956-ad51-49ea-b3ac-1accf6fb017a2024-12-01T08:41:10ZSpatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domainsThesishttp://purl.org/coar/resource_type/c_db06uuid:009a0956-ad51-49ea-b3ac-1accf6fb017aOrdinary differential equationsProbability theory and stochastic processesMathematicsPartial differential equationsBiology and other natural sciences (mathematics)Mathematical biologyEnglish2012Woolley, TThomas WoolleyMaini, PGaffney, EBaker, R<p>One of the main challenges in developmental biology is elucidating the mechanisms underlying the formation and maintenance of complex spatial and temporal structures. This thesis aims to explore two different and yet complementary approaches to address this challenge.</p> <p>Firstly, we investigate a number of specific developmental systems in order to suggest mechanisms underlying their observed biological behaviour. Critically, we show that, without modifications, standard mathematical formulations are unable to capture certain details. In particular, it is demonstrated that accurate descriptions of domain growth need to be included in order to construct mathematical models that compare favourably with experimental systems. In conjunction with understanding biological development better, we also analytically investigate the existence of spot patterns in a paradigm patterning model, resulting in the use of numerical methods to compare theory with simulation.</p> <p>The second approach used to investigate spatial-temporal complexity is more theoretical; we aim to characterise the effects of stochastic perturbations and growth on pattern generation. To achieve this we derive a stochastic description of biochemical reactions, diffusion and domain growth that is consistent with the deterministic description in the thermodynamic limit. This is then used to determine conditions under which robust patterns form.</p> <p>By exploring developmental complexity through these two different approaches of creating broad analytical methods and investigating specific biological models, we not only gain a deeper insight into the creation of complexity in specific cases but also a wider appreciation of how noise can affect such systems.</p> |
| spellingShingle | Ordinary differential equations Probability theory and stochastic processes Mathematics Partial differential equations Biology and other natural sciences (mathematics) Mathematical biology Woolley, T Thomas Woolley Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains |
| title | Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains |
| title_full | Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains |
| title_fullStr | Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains |
| title_full_unstemmed | Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains |
| title_short | Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains |
| title_sort | spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains |
| topic | Ordinary differential equations Probability theory and stochastic processes Mathematics Partial differential equations Biology and other natural sciences (mathematics) Mathematical biology |
| work_keys_str_mv | AT woolleyt spatiotemporalbehaviourofstochasticandcontinuummodelsforbiologicalsignallingonstationaryandgrowingdomains AT thomaswoolley spatiotemporalbehaviourofstochasticandcontinuummodelsforbiologicalsignallingonstationaryandgrowingdomains |