Chemotaxis in Rhodobacter sphaeroides: A Feasibility Study


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Recent years have seen the application of mathematical modelling to an increasing number of problems in the biological and medical sciences. A mathematical model can represent an ecosystem, an organ, a cell, or the kinetic reaction between molecules. It can provide useful insights into the dynamics of biological systems and, importantly, guide the scientists who might be overwhelmed by the complexity of their research objects. Many biological processes involve crosstalk and feed-back loops generating complex networks rather than simple linear pathways. Obtaining the topological structure of such networks is important for understanding the mechanism through which robust system functionally is maintained. High throughout experiments now provide a wealth of data that can be used to determine biochemical network structure and to propose mechanistic rate laws with appropriate kinetic parameter values. However, no unique network can account for these data, and the systematic design of new experiments based on current knowledge is essential for further delineating network structure. A synergy between mathematical modelling, control theory and experiment design is therefore fundamental for increasing physiological and biochemical knowledge.

Bacterial chemotaxis is the biasing of movement towards regions of higher concentration of beneficial or lower concentration of toxic chemicals. In bacteria such as Escherichia coli and Rhodobacter sphaeroides, this is achieved when chemical ligands bound to membrane-spanning receptors initiate a signalling cascade of intracellular protein activity leading to the change in activity of the flagellar motor which drives the extracellular flagellum (or flagella), causing the bacterium to move. Chemotaxis in Escherichia coli is one of the best understood pathways in biology and there is a large amount of experimental data on structures, kinetics, in vivo protein concentrations and localisation. This relatively simple pathway has helped to conceptualise the signalling pathway of sensory systems in general. However, with an increasing number of sequenced bacterial genomes it becomes evident that the chemotactical sensory mechanism of many other bacteria is much more complex (Wadhams et al, 2004).

Using recent experimental results, we have devised two working models (blue/dashed or red/solid) of the Rhodobacter sphaeroides chemotaxis signal transduction pathway.

We are developing a theoretical framework in order to design, by judiciously choosing experimental conditions and stimuli, new experiments to differentiate between possible model alternatives. One problem is to find the best initial condition or parameters that maximise the difference between the different models. It can be approached through the notion of observability for a linear system or of a storage function in the case of a nonlinear system. Particularly, for nonlinear systems new and powerful computational tools have been developed to search for this function; one is SOSTOOLS, a recently developed MATLAB toolbox that connects semidefinite programming with the sum of square decomposition. We use these tools also to address the problem of designing the best, possibly time varying, input or pathway deletion that will maximise the differentiability between competing models. In summary, this work intends to optimise the design of experiments that in/validate models and to close the loop between modelling and experiment design to increase our understanding of the connectivity and function of complex biochemical networks, from which the biosciences will benefit greatly. There is a lot to be gained through interdisciplinary research involving scientists from different fields and by borrowing methods from other fields that have a long tradition of working with models of dynamical systems, such as control theory.

This research is supported by EPSRC project E05708X


Engineering Control Theory

See References (Papachristodoulou, 2007: 2714-2719) and (Papachristodoulou, 2007: 2872-2877).


Schematic view of a tethered cell.

We are employing a tethered cell assay, which allows us to measure the response of the bacterium to controlled external stimuli. This allows us to measure the repsonse of the pathway to a variety of stimuli and correlate this with the modelling.

Biochemical kinetic constants used for the model creation are being determined using phosphortransfer assays (Porter et al, 2002).

The proposed interconnectivity is also being tested using in vitro SPR of purified components (Biacore) and in vivo two hybrid experiments.


  • Porter, S.L., and Armitage, J.P. (2002) "Phosphotransfer in Rhodobacter sphaeroides Chemotaxis." J Mol Biol 324: 35-45.
  • Wadhams, G.H., and Armitage, J.P. (2004) "Making sense of it all: bacterial chemotaxis." Nat Rev Mol Cell Biol 5: 1024-1037.
  • Papachristodoulou, A., and El-Samad, H. (2007) "Algorithms for Discriminating Between Biochemical Reaction Network Models: Towards Systematic Experimental Design." Proceedings of the 2007 American Control Conference: 2714-2719
  • Papachristodoulou A., and Recht, B. (2007) "Determining Interconnections in Chemical Reaction Networks." Proceedings of the 2007 American Control Conference: 2872-2877