StochDetBioModel · Stochastic and deterministic modelling of biological and biochemical phenomena with applications to circadian rhythms and pattern formation

Stochastic and deterministic modelling of biological and biochemical phenomena with applications to circadian rhythms and pattern formation

During the project we derived and applied efficient analytical and computational methods for reaction-diffusion systems with stochastic effects in biology and biochemistry. These methods have been applied to particular systems of circadian rhythms and skin pattern formation. The research results have been published in international journals or their publication is in progress. Besides the scientific outputs, an important contribution of the project was the research training of the Fellow, Dr Tomas Vejchodsky, in mathematical biology under the guidance of the Scientist in charge, Prof Philip K. Maini. In addition, the Fellow acquired new complementary skills such as presentation skills, communication skills, career planning, project proposal preparation, etc. The unique experience from the University of Oxford, one of the world’s top universities, will be very beneficial in his future career, as well as the network of new collaborators he has gained from his time here. Furthermore, the project included outreach activities in the form of a summer school and a popularization article. At the Wolfson Centre for Mathematical Biology (WCMB) of the University of Oxford, the Fellow received extensive training through research. The new expertise he gained includes stochastic modelling of biochemical processes, stochastic processes, stochastic differential equations, dynamical systems, gene regulatory networks, tensor methods for high-dimensional problems, Turing instability and spatial pattern formation, and modelling of circadian rhythms. The number of research results exceeded the plan, because the Fellow made full use of the collaborative opportunities offered by the WCMB. Besides two planned publications as direct outputs of the project, the Fellow co-authored several more research papers. These papers conform with the original plan of the project and present results on numerical aspects of reaction-diffusion problems, describe a new method for model reduction of biochemical systems, apply this method to a model system for circadian rhythms, analyse the stochastic effects in the modelling of reaction networks, present the potential of tensor-structured numerical approaches for the solution of high-dimensional stochastic biochemical systems, and study the effects of unilateral sources on the Turing instability with the potential to model mutant colouration in mammals (e.g. the king cheetah). As a product of the project the Fellow published or offered for publication six research papers in total, see Section 2.A of this report. The research results have also been presented at scientific conferences. The Fellow participated at eight conferences during the course of the project. He attended the Preconditioning (June 2013, Oxford) and OCCAM (July 2013, Oxford) conferences. He presented talks "Guaranteed and robust error bounds for singularly perturbed problems in arbitrary dimension" at MAFELAP (June 2013, Brunel University), "Deterministic and stochastic models of circadian rhythms" at Equadiff (August 2013, Prague), "Two-sided bounds of eigenvalues with applications to trace inequalities" at AM2013 (May 2013, Prague), "Deterministic and stochastic modelling of biochemical processes: An introduction and open problems" at AIME@CZ (March 2014, Prague), and "Challenges for numerical methods in biochemistry: Can we solve 20-dimensional PDE?" at PANM 17, (June 2014, Dolni Maxov). The talks at AIME@CZ and PANM 17 were invited. Finally, he organized, together with Shuohao Liao, a minisymposium entitled "Numerical methods for high-dimensional problems in biology" within the conference ECMTB 2014 (June 2014, Gothenburg), where he also presented the poster "Delayed quasi-steady state assumptions for system reduction". The Fellow used the opportunity of the collaborative environment of the WCMB and acquired new collaborators. Besides working with the scientist in charge of the project (Philip K. Maini), he cooperated both with researchers from the University of Oxford (Andrew Duncan, Radek Erban, Shuohao Liao, Tomislav Plesa, etc.) and people from other universities, for example, Mark Ainsworth (Brown University, USA), Mark Sturrock (The Ohio State University, USA), and Hehu Xie (Chinese Academy of Sciences, Beijing). The cooperation with all these researchers yielded joint papers that have been published or their publication is in progress. Thanks to the link with Gabriel Barrenechea, who gave a talk at the Mathematical Institute of the University of Oxford, the Fellow has been invited to the University of Strathclyde, Glasgow, to present his research at the Mathematics and Statistics seminar. The Fellow has also been active in student supervision and teaching. He served as the TA for the course of Radek Erban "Stochastic Modelling of Biological Processes". He co-supervised the doctoral students Shuohao Liao and Tomislav Plesa. Furthermore, he co-supervised master theses of Tomislav Plesa, Fernando Gallego Bordallo, and Juanjuan Sun. Within the project the Fellow planned his future independent career. He wrote two project proposals. First, he took part in the competition of the Neuron fund for the Neuron Grant. While ultimately unsuccessful, his project passed to the second round together with three other projects. Second, he submitted a proposal for a research grant to the Czech Science Foundation. Results of this competition are not known, yet. The Fellow also worked on gaining new complementary skills. He attended a New Researchers Meeting and he has participated in three courses of the series "Building A Successful Career In The Sciences" as well as in the "Presentation skills" course. All these courses were organized by the University of Oxford. To conclude, the project ran smoothly and according to plan. It was fruitful in terms of research results, collaboration, professional training, complementary skills, and outreach activities. As such it seems to be very beneficial for the future career of the Fellow.

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