Theoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination
<p>This thesis is concerned with methodologies for the accurate quantitative modelling of molecular biological systems. The first part is devoted to the chemical Langevin equation (CLE), a stochastic differential equation driven by a multidimensional Wiener process. The CLE is an approximation...
| প্রধান লেখক: | |
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| অন্যান্য লেখক: | |
| বিন্যাস: | গবেষণাপত্র |
| ভাষা: | English |
| প্রকাশিত: |
2010
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| বিষয়গুলি: |
| _version_ | 1826298404256350208 |
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| author | Mélykúti, B |
| author2 | Etheridge, A |
| author_facet | Etheridge, A Mélykúti, B |
| author_sort | Mélykúti, B |
| collection | OXFORD |
| description | <p>This thesis is concerned with methodologies for the accurate quantitative modelling of molecular biological systems. The first part is devoted to the chemical Langevin equation (CLE), a stochastic differential equation driven by a multidimensional Wiener process. The CLE is an approximation to the standard discrete Markov jump process model of chemical reaction kinetics. It is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. We observe that the CLE is not a single equation, but a family of equations with shared finite-dimensional distributions. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m_1 pairs of reversible reactions and m_2 irreversible reactions, there is another, simple formulation of the CLE with only m_1+m_2 Wiener processes, whereas the standard approach uses 2m_1+m_2. Considerable computational savings are achieved with this latter formulation. A flaw of the CLE model is identified: trajectories may leave the nonnegative orthant with positive probability.</p><p>The second part addresses the challenge when alternative, structurally different ordinary differential equation models of similar complexity fit the available experimental data equally well. We review optimal experiment design methods for choosing the initial state and structural changes on the biological system to maximally discriminate between the outputs of rival models in terms of L_2-distance. We determine the optimal stimulus (input) profile for externally excitable systems. The numerical implementation relies on sum of squares decompositions and is demonstrated on two rival models of signal processing in starving Dictyostelium amoebae. Such experiments accelerate the perfection of our understanding of biochemical mechanisms.</p> |
| first_indexed | 2024-03-07T04:46:19Z |
| format | Thesis |
| id | oxford-uuid:d368c04c-b611-41b2-8866-cde16b283b0d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:46:19Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:d368c04c-b611-41b2-8866-cde16b283b0d2022-03-27T08:11:00ZTheoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discriminationThesishttp://purl.org/coar/resource_type/c_db06uuid:d368c04c-b611-41b2-8866-cde16b283b0dBiology and other natural sciences (mathematics)Probability theory and stochastic processesControl engineeringOrdinary differential equationsNumerical analysisChemical kineticsDynamical systems and ergodic theory (mathematics)EnglishOxford University Research Archive - Valet2010Mélykúti, BEtheridge, APapachristodoulou, A<p>This thesis is concerned with methodologies for the accurate quantitative modelling of molecular biological systems. The first part is devoted to the chemical Langevin equation (CLE), a stochastic differential equation driven by a multidimensional Wiener process. The CLE is an approximation to the standard discrete Markov jump process model of chemical reaction kinetics. It is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. We observe that the CLE is not a single equation, but a family of equations with shared finite-dimensional distributions. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m_1 pairs of reversible reactions and m_2 irreversible reactions, there is another, simple formulation of the CLE with only m_1+m_2 Wiener processes, whereas the standard approach uses 2m_1+m_2. Considerable computational savings are achieved with this latter formulation. A flaw of the CLE model is identified: trajectories may leave the nonnegative orthant with positive probability.</p><p>The second part addresses the challenge when alternative, structurally different ordinary differential equation models of similar complexity fit the available experimental data equally well. We review optimal experiment design methods for choosing the initial state and structural changes on the biological system to maximally discriminate between the outputs of rival models in terms of L_2-distance. We determine the optimal stimulus (input) profile for externally excitable systems. The numerical implementation relies on sum of squares decompositions and is demonstrated on two rival models of signal processing in starving Dictyostelium amoebae. Such experiments accelerate the perfection of our understanding of biochemical mechanisms.</p> |
| spellingShingle | Biology and other natural sciences (mathematics) Probability theory and stochastic processes Control engineering Ordinary differential equations Numerical analysis Chemical kinetics Dynamical systems and ergodic theory (mathematics) Mélykúti, B Theoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination |
| title | Theoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination |
| title_full | Theoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination |
| title_fullStr | Theoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination |
| title_full_unstemmed | Theoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination |
| title_short | Theoretical advances in the modelling and interrogation of biochemical reaction systems: alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination |
| title_sort | theoretical advances in the modelling and interrogation of biochemical reaction systems alternative formulations of the chemical langevin equation and optimal experiment design for model discrimination |
| topic | Biology and other natural sciences (mathematics) Probability theory and stochastic processes Control engineering Ordinary differential equations Numerical analysis Chemical kinetics Dynamical systems and ergodic theory (mathematics) |
| work_keys_str_mv | AT melykutib theoreticaladvancesinthemodellingandinterrogationofbiochemicalreactionsystemsalternativeformulationsofthechemicallangevinequationandoptimalexperimentdesignformodeldiscrimination |