Abstract
BackgroundA number of publications have recently examined the occurrence and properties of the feed-forward motif in a variety of networks, including those that are of interest in genome biology, such as gene networks. The present work looks in some detail at the dynamics of the bi-fan motif, using systems of ordinary differential equations to model the populations of transcription factors, mRNA and protein, with the aim of extending our understanding of what appear to be important building blocks of gene network structure.ResultsWe develop an ordinary differential equation model of the bi-fan motif and analyse variants of the motif corresponding to its behaviour under various conditions. In particular, we examine the effects of different steady and pulsed inputs to five variants of the bifan motif, based on evidence in the literature of bifan motifs found in Saccharomyces cerevisiae (commonly known as baker's yeast). Using this model, we characterize the dynamical behaviour of the bi-fan motif for a wide range of biologically plausible parameters and configurations. We find that there is no characteristic behaviour for the motif, and with the correct choice of parameters and of internal structure, very different, indeed even opposite behaviours may be obtained.ConclusionEven with this relatively simple model, the bi-fan motif can exhibit a wide range of dynamical responses. This suggests that it is difficult to gain significant insights into biological function simply by considering the connection architecture of a gene network, or its decomposition into simple structural motifs. It is necessary to supplement such structural information by kinetic parameters, or dynamic time series experimental data, both of which are currently difficult to obtain.
Highlights
A number of publications have recently examined the occurrence and properties of the feed-forward motif in a variety of networks, including those that are of interest in genome biology, such as gene networks
A network motif in the sense introduced by Alon and coworkers is a pattern or small sub-graph that occurs more often in the true network than in an ensemble of networks generated by randomly rewiring the edges in the true network, where the number of nodes and the degree of each node is kept fixed
This nomenclature is due to the arrangement in C in which both inputs act as promoters, in comparison to A and D which are both fully incoherent, whilst B may be considered to be partially incoherent, as one of the second tier proteins has incoherent inputs, whilst the other has coherent inputs (the model used in this case is given in equation (1), in which we consider co-operative binding
Summary
A number of publications have recently examined the occurrence and properties of the feed-forward motif in a variety of networks, including those that are of interest in genome biology, such as gene networks. The concept of a network motif, introduced by Alon and coworkers [1], has rapidly become one of the central topics of interest in the analysis of complex networks. These networks promise to provide a framework for the understanding of biological processes involving many components such as intra- or inter-cellular networks of interacting genes or proteins. The analysis of such frameworks is one of the key techniques in the rapidly emerging field of systems biology, which makes extensive use of protein interaction, metabolic and gene regulatory networks. The work of Prill et al [3] has looked at how one aspect of motifs, their stability, influences biological network organisation and the abundance of different motifs in the network
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