Analysis of feedback loops and robustness in network evolution based on Boolean models

<p>Abstract</p> <p>Background</p> <p>Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.</p> <p>Results</p> <p>In this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions.</p> <p>Conclusion</p> <p>The presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.</p

Investigations into the relationship between feedback loops and functional importance of a signal transduction network based on Boolean network modeling

<p>Abstract</p> <p>Background</p> <p>A number of studies on biological networks have been carried out to unravel the topological characteristics that can explain the functional importance of network nodes. For instance, connectivity, clustering coefficient, and shortest path length were previously proposed for this purpose. However, there is still a pressing need to investigate another topological measure that can better describe the functional importance of network nodes. In this respect, we considered a feedback loop which is ubiquitously found in various biological networks.</p> <p>Results</p> <p>We discovered that the number of feedback loops (NuFBL) is a crucial measure for evaluating the importance of a network node and verified this through a signal transduction network in the hippocampal CA1 neuron of mice as well as through generalized biological network models represented by Boolean networks. In particular, we observed that the proteins with a larger NuFBL are more likely to be essential and to evolve slowly in the hippocampal CA1 neuronal signal transduction network. Then, from extensive simulations based on the Boolean network models, we proved that a network node with the larger NuFBL is likely to be more important as the mutations of the initial state or the update rule of such a node made the network converge to a different attractor. These results led us to infer that such a strong positive correlation between the NuFBL and the importance of a network node might be an intrinsic principle of biological networks in view of network dynamics.</p> <p>Conclusion</p> <p>The presented analysis on topological characteristics of biological networks showed that the number of feedback loops is positively correlated with the functional importance of network nodes. This result also suggests the existence of unknown feedback loops around functionally important nodes in biological networks.</p

Efficient parameter search for qualitative models of regulatory networks using symbolic model checking

Investigating the relation between the structure and behavior of complex biological networks often involves posing the following two questions: Is a hypothesized structure of a regulatory network consistent with the observed behavior? And can a proposed structure generate a desired behavior? Answering these questions presupposes that we are able to test the compatibility of network structure and behavior. We cast these questions into a parameter search problem for qualitative models of regulatory networks, in particular piecewise-affine differential equation models. We develop a method based on symbolic model checking that avoids enumerating all possible parametrizations, and show that this method performs well on real biological problems, using the IRMA synthetic network and benchmark experimental data sets. We test the consistency between the IRMA network structure and the time-series data, and search for parameter modifications that would improve the robustness of the external control of the system behavior

Reliability of Transcriptional Cycles and the Yeast Cell-Cycle Oscillator

A recently published transcriptional oscillator associated with the yeast cell cycle provides clues and raises questions about the mechanisms underlying autonomous cyclic processes in cells. Unlike other biological and synthetic oscillatory networks in the literature, this one does not seem to rely on a constitutive signal or positive auto-regulation, but rather to operate through stable transmission of a pulse on a slow positive feedback loop that determines its period. We construct a continuous-time Boolean model of this network, which permits the modeling of noise through small fluctuations in the timing of events, and show that it can sustain stable oscillations. Analysis of simpler network models shows how a few building blocks can be arranged to provide stability against fluctuations. Our findings suggest that the transcriptional oscillator in yeast belongs to a new class of biological oscillators