Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Evolutionarily stable and fragile modules of yeast biochemical network

Gene and protein interaction networks have evolved to precisely specify cell fates and functions. Here, we analyse whether the architecture of these networks affects evolvability. We find evidence to suggest that in yeast these networks are mainly acyclic, and that evolutionary changes in these parts do not affect their global dynamic properties. In contrast, feedback loops strongly influence dynamic behaviour and are often evolutionarily conserved. Feedback loops are often found to reside in a clustered manner by means of coupling and nesting with each other in the molecular interaction network of yeast. In these clusters some feedback mechanisms are biologically vital for the operation of the module and some provide auxiliary functional assistance. We find that the biologically vital feedback mechanisms are highly conserved in both transcription regulation and protein interaction network of yeast. In particular, long feedback loops and oscillating modules in protein interaction networks are found to be biologically vital and hence highly conserved. These data suggest that biochemical networks evolve differentially depending on their structure with acyclic parts being permissive to evolution while cyclic parts tend to be conserved

Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks

The gene regulatory network (GRN) is the central decision‐making module of the cell. We have developed a theory called Buffered Qualitative Stability (BQS) based on the hypothesis that GRNs are organised so that they remain robust in the face of unpredictable environmental and evolutionary changes. BQS makes strong and diverse predictions about the network features that allow stable responses under arbitrary perturbations, including the random addition of new connections. We show that the GRNs of E. coli, M. tuberculosis, P. aeruginosa, yeast, mouse, and human all verify the predictions of BQS. BQS explains many of the small- and large‐scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response. BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation. DOI: http://dx.doi.org/10.7554/eLife.02863.00

Modelling Gene Regulatory Networks

This thesis presents the results of mathematical modeling of both individual genes and small networks of genes. The regulation of gene activity is essential for the proper functioning of cells, which employ a variety of molecular mechanisms to control gene expression. Despite this, there is considerable variation in the precise number and timing of protein molecules that are produced. This is because gene expression is fundamentally a noisy process, subject to a number of sources of randomness, including uctuations in metabolite levels, the environment and ampli ed by the very low number of molecules involved. I have developed a probabilistic model of the burst size distribution (the number of proteins produced by the binding of one promoter) of a single gene. Recent experimental data provides excellent agreement with the model, but also reveals limitations of currently available data in determining the origin of variations in expression. A second strand of my work has addressed the dynamics of networks of genes. A network motif is a sub-graph that occurs more often in the network than would be expected by chance. The recurrent presence of certain motifs has been linked to systematic di erences in the functional properties of networks. I have developed models of the possible dynamical behaviour, in particular for the bi-fan motif, a small sub-network with four genes. This motif has been identi ed as the most prevalent in the regulatory networks of both the bacterium Escherichia coli and Saccharaomyces cerevisiae. The results of this work show that the microscopic details of the interactions are of paramount importance, with few inherent constraints on the network dynamics from consideration of network structure alone. This result is relevant to all attempts to model gene networks without su ciently detailed knowledge of the mechanisms of interaction

A combination of transcriptional and microRNA regulation improves the stability of the relative concentrations of target genes

It is well known that, under suitable conditions, microRNAs are able to fine tune the relative concentration of their targets to any desired value. We show that this function is particularly effective when one of the targets is a Transcription Factor (TF) which regulates the other targets. This combination defines a new class of feed-forward loops (FFLs) in which the microRNA plays the role of master regulator. Using both deterministic and stochastic equations we show that these FFLs are indeed able not only to fine-tune the TF/target ratio to any desired value as a function of the miRNA concentration but also, thanks to the peculiar topology of the circuit, to ensures the stability of this ratio against stochastic fluctuations. These two effects are due to the interplay between the direct transcriptional regulation and the indirect TF/Target interaction due to competition of TF and target for miRNA binding (the so called "sponge effect"). We then perform a genome wide search of these FFLs in the human regulatory network and show that they are characterizedby a very peculiar enrichment pattern. In particular they are strongly enriched in all the situations in which the TF and its target have to be precisely kept at the same concentration notwithstanding the environmental noise. As an example we discuss the FFL involving E2F1 as Transcription Factor, RB1 as target and miR-17 family as master regulator. These FFLs ensure a tight control of the E2F/RB ratio which in turns ensures the stability of the transition from the G0/G1 to the S phase in quiescent cells.Comment: 23 pages, 10 figure

Designing synthetic networks in silico : A generalised evolutionary algorithm approach

Background: Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes). Results: The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction. Conclusions: In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses

Mathematical and computational modelling of post-transcriptional gene relation by micro-RNA

Mathematical models and computational simulations have proved valuable in many areas of cell biology, including gene regulatory networks. When properly calibrated against experimental data, kinetic models can be used to describe how the concentrations of key species evolve over time. A reliable model allows ‘what if’ scenarios to be investigated quantitatively in silico, and also provides a means to compare competing hypotheses about the underlying biological mechanisms at work. Moreover, models at different scales of resolution can be merged into a bigger picture ‘systems’ level description. In the case where gene regulation is post-transcriptionally affected by microRNAs, biological understanding and experimental techniques have only recently matured to the extent that we can postulate and test kinetic models. In this chapter, we summarize some recent work that takes the first steps towards realistic modelling, focusing on the contributions of the authors. Using a deterministic ordinary differential equation framework, we derive models from first principles and test them for consistency with recent experimental data, including microarray and mass spectrometry measurements. We first consider typical mis-expression experiments, where the microRNA level is instantaneously boosted or depleted and thereafter remains at a fixed level. We then move on to a more general setting where the microRNA is simply treated as another species in the reaction network, with microRNA-mRNA binding forming the basis for the post-transcriptional repression. We include some speculative comments about the potential for kinetic modelling to contribute to the more widespread sequence and network based approaches in the qualitative investigation of microRNA based gene regulation. We also consider what new combinations of experimental data will be needed in order to make sense of the increased systems-level complexity introduced by microRNAs

MicroRNA-mediated regulatory circuits: outlook and perspectives

MicroRNAs have been found to be necessary for regulating genes implicated in almost all signaling pathways, and consequently their dysfunction influences many diseases, including cancer. Understanding of the complexity of the microRNA-mediated regulatory network has grown in terms of size, connectivity and dynamics with the development of computational and, more recently, experimental high-throughput approaches for microRNA target identification. Newly developed studies on recurrent microRNA-mediated circuits in regulatory networks, also known as network motifs, have substantially contributed to addressing this complexity, and therefore to helping understand the ways by which microRNAs achieve their regulatory role. This review provides a summarizing view of the state-of-the-art, and perspectives of research efforts on microRNA-mediated regulatory motifs. In this review, we discuss the topological properties characterizing different types of circuits, and the regulatory features theoretically enabled by such properties, with a special emphasis on examples of circuits typifying their biological significance in experimentally validated contexts. Finally, we will consider possible future developments, in particular regarding microRNA-mediated circuits involving long non-coding RNAs and epigenetic regulators

Emerging properties of animal gene regulatory networks

Gene regulatory networks (GRNs) provide system level explanations of developmental and physiological functions in the terms of the genomic regulatory code. Depending on their developmental functions, GRNs differ in their degree of hierarchy, and also in the types of modular sub-circuit of which they are composed, although there is a commonly employed sub-circuit repertoire. Mathematical modelling of some types of GRN sub-circuit has deepened biological understanding of the functions they mediate. The structural organization of various kinds of GRN reflects their roles in the life process, and causally illuminates both developmental and evolutionary process