[Show abstract][Hide abstract] ABSTRACT: The chemotaxis pathway of the bacterium Rhodobacter sphaeroides shares many similarities with that of Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have correctly predicted that the E. coli output behaviour is unchanged under scaling of its ligand input signal; this property is known as fold-change detection (FCD). In the light of recent experimental results suggesting that R. sphaeroides may also show FCD, we present theoretical assumptions on the R. sphaeroides chemosensory dynamics that can be shown to yield FCD behaviour. Furthermore, it is shown that these assumptions make FCD a property of this system that is robust to structural and parametric variations in the chemotaxis pathway, in agreement with experimental results. We construct and examine models of the full chemotaxis pathway that satisfy these assumptions and reproduce experimental time-series data from earlier studies. We then propose experiments in which models satisfying our theoretical assumptions predict robust FCD behaviour where earlier models do not. In this way, we illustrate how transient dynamic phenotypes such as FCD can be used for the purposes of discriminating between models that reproduce the same experimental time-series data.
Journal of The Royal Society Interface 01/2013; 10(80):20120935. · 4.91 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper considers the problem of synchronizing the outputs of nodes in a network of N coupled dynamical systems in the presence of uncertainty. A computational approach is used to design coupling dynamics that ensure synchrony when nodes are subject to model uncertainty and that minimize nodal deviation from synchrony in the presence of input noise. The main result of this paper recasts the problem of designing the coupling a robust stability problem with a structured uncertainty element. A coupling satisfying the criteria of this robust stability problem can then be designed through an application of the small-gain theorem and μ-synthesis techniques.
Proceedings of the American Control Conference 06/2012;
[Show abstract][Hide abstract] ABSTRACT: The chemotaxis pathway of the bacterium Rhodobacter sphaeroides has many
similarities to the well-studied pathway in Escherichia coli. It
exhibits robust adaptation and has several homologues of the latter's
chemotaxis proteins. Recent theoretical results have been able to
correctly predict that the chemotactic response of Escherichia coli
exhibits the same output behavior in response to scaled ligand inputs, a
dynamic property known as fold-change detection (FCD), or input-scale
invariance. In this paper, we present theoretical assumptions on the R.
sphaeroides chemotaxis sensing dynamics that can be analytically shown
to yield FCD behavior in a specific ligand concentration range. Based on
these assumptions, we construct two models of the full chemotaxis
pathway that are able to reproduce experimental time-series data from
earlier studies. To test the validity of our assumptions, we propose a
series of experiments in which our models predict robust FCD behavior
where earlier models do not. In this way, we illustrate how a dynamic
phenotype such as FCD can be used for the purposes of discriminating
between two models that reproduce the same experimental time-series
[Show abstract][Hide abstract] ABSTRACT: This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators.
IEEE Transactions on Automatic Control 01/2012; 57:478-483. · 2.72 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance.
[Show abstract][Hide abstract] ABSTRACT: This paper investigates the chemotaxis behavior of the bacterium R. sphaeroides. We review the results of a recent study comparing different possible mathematical models of this bacterium's chemotaxis decision mechanisms. It was found that only one of the aforesaid models could explain the experimental chemotactic response data. From a control theoretic perspective, we show that, compared to the other models posed, this model exhibits better and more robust chemotactic performance. This decision mechanism parallels a feedback architecture that has been used extensively to improve performance in engineered systems. We suggest that this mechanism may play a role in maintaining the chemotactic performance of this and potentially other bacteria.
[Show abstract][Hide abstract] ABSTRACT: This paper is concerned with global asymptotic output synchronization in networks of identical feedback systems. Using an operator theoretic approach based on an incremental small gain theorem, the method reformulates the synchronization problem as one of achieving incremental stability using a coupling operator that plays the role of an incrementally stabilizing feedback. In this way, conditions on static or dynamic coupling operators that achieve output synchronization of nodes of arbitrary structure are derived. These conditions lead to a methodology for the construction of coupling architectures that ensure output synchronization of a wide range of systems. The result is illustrated for a network of biochemical oscillators.
Proceedings of the 49th IEEE Conference on Decision and Control, CDC 2010, December 15-17, 2010, Atlanta, Georgia, USA; 01/2010
[Show abstract][Hide abstract] ABSTRACT: Developing methods for understanding the connectivity of signalling pathways is a major challenge in biological research. For this purpose, mathematical models are routinely developed based on experimental observations, which also allow the prediction of the system behaviour under different experimental conditions. Often, however, the same experimental data can be represented by several competing network models.
In this paper, we developed a novel mathematical model/experiment design cycle to help determine the probable network connectivity by iteratively invalidating models corresponding to competing signalling pathways. To do this, we systematically design experiments in silico that discriminate best between models of the competing signalling pathways. The method determines the inputs and parameter perturbations that will differentiate best between model outputs, corresponding to what can be measured/observed experimentally. We applied our method to the unknown connectivities in the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. We first developed several models of R. sphaeroides chemotaxis corresponding to different signalling networks, all of which are biologically plausible. Parameters in these models were fitted so that they all represented wild type data equally well. The models were then compared to current mutant data and some were invalidated. To discriminate between the remaining models we used ideas from control systems theory to determine efficiently in silico an input profile that would result in the biggest difference in model outputs. However, when we applied this input to the models, we found it to be insufficient for discrimination in silico. Thus, to achieve better discrimination, we determined the best change in initial conditions (total protein concentrations) as well as the best change in the input profile. The designed experiments were then performed on live cells and the resulting data used to invalidate all but one of the remaining candidate models.
We successfully applied our method to chemotaxis in R. sphaeroides and the results from the experiments designed using this methodology allowed us to invalidate all but one of the proposed network models. The methodology we present is general and can be applied to a range of other biological networks.
BMC Systems Biology 10/2009; 3:105. · 2.98 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states, the algorithm employs an LMI approach to compute both upper and lower bounds on reachable regions. Rather than performing computations in the state-space, this method uses impact maps to find the reachable sets on the switching surfaces of the system. This tool can then be used to deduce safety and performance results about the system.
[Show abstract][Hide abstract] ABSTRACT: This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, December 9-11, 2008, Cancún, México; 01/2008
[Show abstract][Hide abstract] ABSTRACT: This paper is concerned with the global analysis of asymptotic synchronization of outputs in networks of identical oscillators. The oscillator models are assumed to possess a cyclic feedback structure. Such networks of oscillators abound in biochemistry, and are exemplified by circadian rhythm and cardiac cell networks. The main result exploits an incremental output feedback passivity property of cyclic feedback systems to prove global asymptotic output synchronization in a network composed of identical cyclic feedback systems. This result is illustrated on a network of Goodwin oscillators.
American Control Conference, 2007. ACC '07; 08/2007