A network dynamics approach to chemical reaction networks

A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in chemical reaction network theory, and which directly relates to the thermodynamics of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This directly leads to the characterization of the set of equilibria and their stability. Both the form of the dynamics and the deduced dynamical behavior are very similar to consensus dynamics. The assumption of complex-balancedness is revisited from the point of view of Kirchhoff's Matrix Tree theorem, providing a new perspective. Finally, using the classical idea of extending the graph of chemical complexes by an extra 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action outflows is given.Comment: 18 page

Consensus and meta-analysis regulatory networks for combining multiple microarray gene expression datasets

Microarray data is a key source of experimental data for modelling gene regulatory interactions from expression levels. With the rapid increase of publicly available microarray data comes the opportunity to produce regulatory network models based on multiple datasets. Such models are potentially more robust with greater confidence, and place less reliance on a single dataset. However, combining datasets directly can be difficult as experiments are often conducted on different microarray platforms, and in different laboratories leading to inherent biases in the data that are not always removed through pre-processing such as normalisation. In this paper we compare two frameworks for combining microarray datasets to model regulatory networks: pre- and post-learning aggregation. In pre-learning approaches, such as using simple scale-normalisation prior to the concatenation of datasets, a model is learnt from a combined dataset, whilst in post-learning aggregation individual models are learnt from each dataset and the models are combined. We present two novel approaches for post-learning aggregation, each based on aggregating high-level features of Bayesian network models that have been generated from different microarray expression datasets. Meta-analysis Bayesian networks are based on combining statistical confidences attached to network edges whilst Consensus Bayesian networks identify consistent network features across all datasets. We apply both approaches to multiple datasets from synthetic and real (Escherichia coli and yeast) networks and demonstrate that both methods can improve on networks learnt from a single dataset or an aggregated dataset formed using a standard scale-normalisation

Consensus analysis of multiagent networks via aggregated and pinning approaches

This is the post-print version of of the Article - Copyright @ 2011 IEEEIn this paper, the consensus problem of multiagent nonlinear directed networks (MNDNs) is discussed in the case that a MNDN does not have a spanning tree to reach the consensus of all nodes. By using the Lie algebra theory, a linear node-and-node pinning method is proposed to achieve a consensus of a MNDN for all nonlinear functions satisfying a given set of conditions. Based on some optimal algorithms, large-size networks are aggregated to small-size ones. Then, by applying the principle minor theory to the small-size networks, a sufficient condition is given to reduce the number of controlled nodes. Finally, simulation results are given to illustrate the effectiveness of the developed criteria.This work was jointly supported by CityU under a research grant (7002355) and GRF funding (CityU 101109)

Distributed Consensus of Linear Multi-Agent Systems with Adaptive Dynamic Protocols

This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics. Two distributed adaptive dynamic consensus protocols are proposed, based on the relative output information of neighboring agents. One protocol assigns an adaptive coupling weight to each edge in the communication graph while the other uses an adaptive coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for any undirected connected communication graphs without using any global information. A sufficient condition for the existence of these adaptive protocols is that each agent is stabilizable and detectable. The cases with leader-follower and switching communication graphs are also studied.Comment: 17 pages, 5 figue