Reaction-diffusion models have been widely successful in explaining a large variety of patterning phenomena in biology ranging from embryonic development to cancer growth and angiogenesis. Firstly proposed by Alan Turing in 1952 and applied to a simple two-component system, reaction-diffusion models describe spontaneous spatial pattern formation, driven purely by interactions of the system components and their diffusion in space. Today, access to unprecedented amounts of quantitative biological data allows us to build and test biochemically accurate reaction-diffusion models of intracellular processes. However, any increase in model complexity increases the number of unknown parameters and thus the computational cost of model analysis. To efficiently characterize the behavior and robustness of models with many unknown parameters is, therefore, a key challenge in systems biology. Here, we propose a novel computational framework for efficient high-dimensional parameter space characterization of reaction-diffusion models. The method leverages the $L_p$-Adaptation algorithm, an adaptive-proposal statistical method for approximate high-dimensional design centering and robustness estimation. Our approach is based on an oracle function, which describes for each point in parameter space whether the corresponding model fulfills given specifications. We propose specific oracles to estimate four parameter-space characteristics: bistability, instability, capability of spontaneous pattern formation, and capability of pattern maintenance. We benchmark the method and demonstrate that it allows exploring the ability of a model to undergo pattern-forming instabilities and to quantify model robustness for model selection in polynomial time with dimensionality. We present an application of the framework to reconstituted membrane domains bearing the small GTPase Rab5 and propose molecular mechanisms that potentially drive pattern formation.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:78487 |
| Date | 16 March 2022 |
| Creators | Solomatina, Anastasia |
| Contributors | Sbalzarini, Ivo F., Goryachev, Andrew, Technische Universität Dresden, Max Planck Institute of Molecular Cell Biology and Genetics |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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