Control Theory Tools for Eludicating the Phosphotransfer Network in Rhodobacter Sphaeroides: A Feasibility Study

Lead Research Organisation: University of Oxford
Department Name: Engineering Science

Abstract

Recent advances in molecular biology allow us to explore relationships between microscopic processes. Such studies are useful for determining the structure of underlying biochemical reaction networks so that the mechanisms through which biological systems achieve robust functionality can be identified. Nonetheless, in many instances these studies still lack the resolution sufficient for distinguishing between many plausible interconnections, such as direct and indirect links between molecular components. At this point, mathematical modelling should be used to effectively guide the design of novel experiments and help delineate further biochemical network architectures. A synergy should exist between experiment design and model development, so that not only can realistic models be developed from experimental data, but also new experiments can be designed from models enabling an increased understanding of the system under study. For this to be undertaken and provide a realistic framework for future developments we need to be able to distinguish between the accuracy of different approaches, and for this we need to start with a system that is experimentally well characterised, but with a number of outstanding questions. In this speculative feasibility study in Systems Biology, we propose a 3-stage 'cyclic' procedure that will involve both a control theoretical and an experimental programme in order to understand the phosphotransfer network of R. sphaeroides, using the well-researched phosphotransfer network structure of E. coli as a starting point. This procedure will consist of: (1) Development of various biochemical reaction network models that can explain experimental data. First, two techniques that are proposed will be assessed on the E. coli phosphotransfer network using available experimental data and then both existing and new data will be used for constructing possible phosphotransfer networks for our model organism, R. sphaeroides. One technique is based on control theory and optimization and the other is a hybrid approach which combines statistical modelling and first principles modelling specific to biochemical reactions; (2) Designing the 'best' new experiment with the aim of differentiating between possible R. sphaeroides phosphotransfer network models using control theory tools. These carefully designed experiments will be implemented in the experimental programme; (3) Invalidating some of these models, and proposing new ones for further study - two control theory techniques will be developed for this purpose. This programme will allow comparison of the effectiveness of the two different approaches for parts (1) and (3). If successful, this procedure will lay the groundwork for the development of novel approaches to experimental design across a wide range of biological network problems at a level not attempted previously.

Publications

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Anderson J (2009) On validation and invalidation of biological models. in BMC bioinformatics

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August E (2009) A new computational tool for establishing model parameter identifiability. in Journal of computational biology : a journal of computational molecular cell biology

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August E (2009) Efficient, sparse biological network determination in BMC Systems Biology

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Hamadeh A (2011) Feedback control architecture and the bacterial chemotaxis network. in PLoS computational biology

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Papachristodoulou A (2009) Analysis of Polynomial Systems With Time Delays via the Sum of Squares Decomposition in IEEE Transactions on Automatic Control

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Papachristodoulou A (2009) Robust Stability Analysis of Nonlinear Hybrid Systems in IEEE Transactions on Automatic Control

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Roberts MA (2010) Adaptation and control circuits in bacterial chemotaxis. in Biochemical Society transactions

 
Description We have met all the targets outlined in the original proposal. We developed a modelling strategy in order to understand the structure of signal transduction networks, iterating between network determination, experiment design and model invalidation. The idea behind this approach is that many mathematical models can explain experimental data for a biological system, but at most one is correct. In order to differentiate between models, one needs to invalidate incorrect models, using appropriate experimental evidence. The aim of this project was to develop a methodological framework to design experiments that would allow invalidation. The methodology that we developed was tested using the phosphotransfer network responsible for chemotaxis in a model organism, Rhodobacter sphaeroides.



As part of this project, we developed three control engineering inspired systems biology tools: (1) a network determination technique that uses Linear Programming for efficient, sparse network determination. This technique was applied to different types of networks (transcriptional, metabolic and chemical) using real experimental data - for more details see "Efficient, sparse biological network determination" by E. August and A. Papachristodoulou, BMC Systems Biology 2009, 3:25. (2) Experiment design algorithms for discrimination, based on initial condition design, dynamic input design and design of structural modifications. (3) Model invalidation tools in discrete and continuous time, that use experimental data to show that models are invalid - for more details see "On Validation and Invalidation of Biological Models" by J. Anderson and A. Papachristodoulou, BMC Bioinformatics 2009, 10:132. Blending the above three layers, we developed an iterative method that involves network determination, experiment design and model invalidation and applied it successfully to the forward signalling part of the chemotaxis pathway of our model organism, Rhodobacter sphaeroides. We proposed 4 competing models of the possible signalling mechanism and then designed experiments to invalidate three of them - for more details see "A model invalidation-based approach for elucidating biological signalling pathways, applied to the chemotaxis pathway in R. sphaeroides" by M. A. J. Roberts, E. August, A. Hamadeh, P. K. Maini, P. E. McSharry, J. P. Armitage and A. Papachristodoulou, BMC Systems Biology 2009, 3:105. We also repeated our methodology and applied it on the feedback mechanism. Additional research was performed on the identifiability of parameters in biochemical networks from input-output data - for more details see "A new computational tool for establishing model parameter identifiability" by E. August and A. Papachristodoulou, Journal of Computational Biology. June 2009, 16(6): 875-885, and some preliminary work has been done on the analysis of biochemical reaction networks resulting from this model development cycle.
Exploitation Route The project offers a new approach for understanding the structure of biochemical networks and could have use in Industry. In addition to the 4 peer reviewed papers, the work was disseminated at several conferences (IEEE Conference on Decision and Control 2008, International Conference on Systems Biology 2008 and 2009, BioSysBio 2008 and Bacterial Locomotion and Signal Transduction 2009) as well as several workshops (Wellcome Trust workshop on Engineering Principles in Biology, Weismann Institute on Systems Biology of Cancer, and at two workshops of the Institute of Mathematics and its Applications at the University of Minneapolis: "Organization of Biological Networks" and "Design Principles in Biological Systems") and University seminars (Imperial College, University of Manchester, University of Liege, California Institute of Technology).
Sectors Digital/Communication/Information Technologies (including Software),Healthcare,Manufacturing/ including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology

URL http://sysos.eng.ox.ac.uk/control/sysos/index.php/Chemotaxis_in_Rhodobacter_sphaeroides:_A_Feasibility_Study
 
Description The algorithms that were developed as part of this project are having impact on the identifiability, parameter estimation, model invalidation and model discrimination by experiment design for systems biology projects. Moreover, the experimental results, in combination with the modelling approach have inspired new experiments and new testable hypotheses. Contribution Method: The research has inspired a new approach at experiment design.
Sector Digital/Communication/Information Technologies (including Software),Healthcare,Manufacturing/ including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology
Impact Types Cultural