Communicating oscillatory networks: frequency domain analysis.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: Constructing predictive dynamic models of interacting signalling networks remains one of the great challenges facing systems biology. While detailed dynamical data exists about individual pathways, the task of combining such data without further lengthy experimentation is highly nontrivial. The communicating links between pathways, implicitly assumed to be unimportant and thus excluded, are precisely what become important in the larger system and must be reinstated. To maintain the delicate phase relationships between signals, signalling networks demand accurate dynamical parameters, but parameters optimised in isolation and under varying conditions are unlikely to remain optimal when combined. The computational burden of estimating parameters increases exponentially with increasing system size, so it is crucial to find precise and efficient ways of measuring the behaviour of systems, in order to re-use existing work. RESULTS: Motivated by the above, we present a new frequency domain-based systematic analysis technique that attempts to address the challenge of network assembly by defining a rigorous means to quantify the behaviour of stochastic systems. As our focus we construct a novel coupled oscillatory model of p53, NF-kB and the mammalian cell cycle, based on recent experimentally verified mathematical models. Informed by online databases of protein networks and interactions, we distilled their key elements into simplified models containing the most significant parts. Having coupled these systems, we constructed stochastic models for use in our frequency domain analysis. We used our new technique to investigate the crosstalk between the components of our model and measure the efficacy of certain network-based heuristic measures. CONCLUSIONS: We find that the interactions between the networks we study are highly complex and not intuitive: (i) points of maximum perturbation do not necessarily correspond to points of maximum proximity to influence; (ii) increased coupling strength does not necessarily increase perturbation; (iii) different perturbations do not necessarily sum and (iv) overall, susceptibility to perturbation is amplitude and frequency dependent and cannot easily be predicted by heuristic measures.Our methodology is particularly relevant for oscillatory systems, though not limited to these, and is most revealing when applied to the results of stochastic simulation. The technique is able to characterise precisely the distance in behaviour between different models, different systems and different parts within the same system. It can also measure the difference between different simulation algorithms used on the same system and can be used to inform the choice of dynamic parameters. By measuring crosstalk between subsystems it can also indicate mechanisms by which such systems may be controlled in experiments and therapeutics. We have thus found our technique of frequency domain analysis to be a valuable benchmark systems-biological tool.Peer Reviewe

Computational modelling and analysis of the molecular network regulating sporulation initiation in Bacillus subtilis

BACKGROUND: Bacterial spores are important contaminants in food, and the spore forming bacteria are often implicated in food safety and food quality considerations. Spore formation is a complex developmental process involving the expression of more than 500 genes over the course of 6 to 8 hrs. The process culminates in the formation of resting cells capable of resisting environmental extremes and remaining dormant for long periods of time, germinating when conditions promote further vegetative growth. Experimental observations of sporulation and germination are problematic and time consuming so that reliable models are an invaluable asset in terms of prediction and risk assessment. In this report we develop a model which assists in the interpretation of sporulation dynamics. RESULTS: This paper defines and analyses a mathematical model for the network regulating Bacillus subtilis sporulation initiation, from sensing of sporulation signals down to the activation of the early genes under control of the master regulator Spo0A. Our model summarises and extends other published modelling studies, by allowing the user to execute sporulation initiation in a scenario where Isopropyl β-D-1-thiogalactopyranoside (IPTG) is used as an artificial sporulation initiator as well as in modelling the induction of sporulation in wild-type cells. The analysis of the model results and the comparison with experimental data indicate that the model is good at predicting inducible responses to sporulation signals. However, the model is unable to reproduce experimentally observed accumulation of phosphorelay sporulation proteins in wild type B. subtilis. This model also highlights that the phosphorelay sub-component, which relays the signals detected by the sensor kinases to the master regulator Spo0A, is crucial in determining the response dynamics of the system. CONCLUSION: We show that there is a complex connectivity between the phosphorelay features and the master regulatory Spo0A. Additional we discovered that the experimentally observed regulation of the phosphotransferase Spo0B for wild-type B. subtilis may be playing an important role in the network which suggests that modelling of sporulation initiation may require additional experimental support. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12918-014-0119-x) contains supplementary material, which is available to authorized users

Elucidation of functional consequences of signalling pathway interactions

<p>Abstract</p> <p>Background</p> <p>A great deal of data has accumulated on signalling pathways. These large datasets are thought to contain much implicit information on their molecular structure, interaction and activity information, which provides a picture of intricate molecular networks believed to underlie biological functions. While tremendous advances have been made in trying to understand these systems, how information is transmitted within them is still poorly understood. This ever growing amount of data demands we adopt powerful computational techniques that will play a pivotal role in the conversion of mined data to knowledge, and in elucidating the topological and functional properties of protein - protein interactions.</p> <p>Results</p> <p>A computational framework is presented which allows for the description of embedded networks, and identification of common shared components thought to assist in the transmission of information within the systems studied. By employing the graph theories of network biology - such as degree distribution, clustering coefficient, vertex betweenness and shortest path measures - topological features of protein-protein interactions for published datasets of the p53, nuclear factor kappa B (NF-κB) and G1/S phase of the cell cycle systems were ascertained. Highly ranked nodes which in some cases were identified as connecting proteins most likely responsible for propagation of transduction signals across the networks were determined. The functional consequences of these nodes in the context of their network environment were also determined. These findings highlight the usefulness of the framework in identifying possible combination or links as targets for therapeutic responses; and put forward the idea of using retrieved knowledge on the shared components in constructing better organised and structured models of signalling networks.</p> <p>Conclusion</p> <p>It is hoped that through the data mined reconstructed signal transduction networks, well developed models of the published data can be built which in the end would guide the prediction of new targets based on the pathway's environment for further analysis. Source code is available upon request.</p