Computational approaches for modelling intrinsic noise and delays in genetic regulatory networks

This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a molecular biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003; Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004; Horikawa et al., 2006).

基因电路研究综述

基因网络相关的研究是生物信息学的重要研究领域．基因电路方法是目前基因网络研究的一种重要方法，本文从以下角度介绍基因电路研究的进展情况及相关研究成果；构成基因电路的基本模块；基因电路的设计与实现；人工基因电路的应用．

Synchronization of Heteroclinic Circuits Through Learning in Chains of Neural Motifs

The synchronization of oscillatory activity in networks of neural networks is usually implemented through coupling the state variables describing neuronal dynamics. In this study we discuss another but complementary mechanism based on a learning process with memory. A driver network motif, acting as a teacher, exhibits winner-less competition (WLC) dynamics, while a driven motif, a learner, tunes its internal couplings according to the oscillations observed in the teacher. We show that under appropriate training the learner motif can dynamically copy the coupling pattern of the teacher and thus synchronize oscillations with the teacher. Then, we demonstrate that the replication of the WLC dynamics occurs for intermediate memory lengths only. In a unidirectional chain of N motifs coupled through teacher-learner paradigm the time interval required for pattern replication grows linearly with the chain size, hence the learning process does not blow up and at the end we observe phase synchronized oscillations along the chain. We also show that in a learning chain closed into a ring the network motifs come to a consensus, i.e. to a state with the same connectivity pattern corresponding to the mean initial pattern averaged over all network motifs.

Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

Interaction Signatures Stabilizing the NAD(P)-Binding Rossmann Fold: A Structure Network Approach

The fidelity of the folding pathways being encoded in the amino acid sequence is met with challenge in instances where proteins with no sequence homology, performing different functions and no apparent evolutionary linkage, adopt a similar fold. The problem stated otherwise is that a limited fold space is available to a repertoire of diverse sequences. The key question is what factors lead to the formation of a fold from diverse sequences. Here, with the NAD(P)-binding Rossmann fold domains as a case study and using the concepts of network theory, we have unveiled the consensus structural features that drive the formation of this fold. We have proposed a graph theoretic formalism to capture the structural details in terms of the conserved atomic interactions in global milieu, and hence extract the essential topological features from diverse sequences. A unified mathematical representation of the different structures together with a judicious concoction of several network parameters enabled us to probe into the structural features driving the adoption of the NAD(P)-binding Rossmann fold. The atomic interactions at key positions seem to be better conserved in proteins, as compared to the residues participating in these interactions. We propose a ``spatial motif'' and several ``fold specific hot spots'' that form the signature structural blueprints of the NAD(P)-binding Rossmann fold domain. Excellent agreement of our data with previous experimental and theoretical studies validates the robustness and validity of the approach. Additionally, comparison of our results with statistical coupling analysis (SCA) provides further support. The methodology proposed here is general and can be applied to similar problems of interest.

A Gaussian network model study suggests that structural fluctuations are higher for inactive states than active states of protein kinases

We performed Gaussian network model based normal mode analysis of 3-dimensional structures of multiple active and inactive forms of protein kinases. In 14 different kinases, a more number of residues (1095) show higher structural fluctuations in inactive states than those in active states (525), suggesting that, in general, mobility of inactive states is higher than active states. This statistically significant difference is consistent with higher crystallographic B-factors and conformational energies for inactive than active states, suggesting lower stability of inactive forms. Only a small number of inactive conformations with the DFG motif in the ``in'' state were found to have fluctuation magnitudes comparable to the active conformation. Therefore our study reports for the first time, intrinsic higher structural fluctuation for almost all inactive conformations compared to the active forms. Regions with higher fluctuations in the inactive states are often localized to the aC-helix, aG-helix and activation loop which are involved in the regulation and/or in structural transitions between active and inactive states. Further analysis of 476 kinase structures involved in interactions with another domain/protein showed that many of the regions with higher inactive-state fluctuation correspond to contact interfaces. We also performed extensive GNM analysis of (i) insulin receptor kinase bound to another protein and (ii) holo and apo forms of active and inactive conformations followed by multi-factor analysis of variance. We conclude that binding of small molecules or other domains/proteins reduce the extent of fluctuation irrespective of active or inactive forms. Finally, we show that the perceived fluctuations serve as a useful input to predict the functional state of a kinase.

Extensive cross-talk and global regulators identified from an analysis of the integrated transcriptional and signaling network in Escherichia coli

To understand the regulatory dynamics of transcription factors (TFs) and their interplay with other cellular components we have integrated transcriptional, protein-protein and the allosteric or equivalent interactions which mediate the physiological activity of TFs in Escherichia coli. To study this integrated network we computed a set of network measurements followed by principal component analysis (PCA), investigated the correlations between network structure and dynamics, and carried out a procedure for motif detection. In particular, we show that outliers identified in the integrated network based on their network properties correspond to previously characterized global transcriptional regulators. Furthermore, outliers are highly and widely expressed across conditions, thus supporting their global nature in controlling many genes in the cell. Motifs revealed that TFs not only interact physically with each other but also obtain feedback from signals delivered by signaling proteins supporting the extensive cross-talk between different types of networks. Our analysis can lead to the development of a general framework for detecting and understanding global regulatory factors in regulatory networks and reinforces the importance of integrating multiple types of interactions in underpinning the interrelationships between them.

Unprecedented Trapping of Difluorooctamolybdate Anions within an α-Polonium Type Coordination Network

New fluorinated hybrid solids [Mo2F2O5(tr2pr)] (1), [Co3(tr2pr)2(MoO4)2F2]·7H2O (2), and [Co3(H2O)2(tr2pr)3(Mo8O26F2)]·3H2O (3) (tr2pr = 1,3-bis(1,2,4-triazol-4-yl)propane) were prepared from the reaction systems consisting of Co(OAc)2/CoF2 and MoO3/(NH4)6Mo7O24, as CoII and MoVI sources, in water (2) or in aqueous HF (1, 3) employing mild hydrothermal conditions. The tr2pr ligand serves as a conformationally flexible tetradentate donor. In complex 1, the octahedrally coordinated Mo atoms are linked in the discrete corner-sharing {Mo2(μ2-O)F2O4N4} unit in which a pair of tr-heterocycles (tr = 1,2,4-triazole) is arranged in cis-positions opposite to “molybdenyl” oxygen atoms. The anti−anti conformation type of tr2pr facilitates the tight zigzag chain packing motif. The crystal structure of the mixed-anion complex salt 2 consists of trinuclear [Co3(μ3-MoO4)2(μ2-F)2] units self-assembling in CoII-undulating chains (Co···Co 3.0709(15) and 3.3596(7) Å), which are cross-linked by tr2pr in layers. In 3, containing condensed oxyfluoromolybdate species, linear centrosymmetric [Co3(μ2-tr)6]6+ SBUs are organized at distances of 10.72−12.45 Å in an α-Po-like network using bitopic tr-linkers. The octahedral {N6} and {N3O3} environments of the central and peripheral cobalt atoms, respectively, are filled by triazole N atoms, water molecules, and coordinating [Mo8O26F2]6− anions. Acting as a tetradentate O-donor, each difluorooctamolybdate anion anchors four [Co3(μ2-tr)6]6+ units through their peripheral Co-sites, which consequently leads to a novel type of a two-nodal 4,10-c net with the Schläfli symbol {32.43.5}{34.420.516.65}. The 2D and 3D coordination networks of 2 and 3, respectively, are characterized by significant overall antiferromagnetic exchange interactions (J/k) between the CoII spin centers on the order of −8 and −4 K. The [Mo8O26F2]6− anion is investigated in detail by quantum chemical calculations.

Factors influencing the stability of cyclotides: Proteins with a circular backbone and cystine knot motif

Cyclotides are a large family of mini-proteins that have the distinguishing features of a head-to-tail cyclised backbone and a cystine knot formed by six conserved cysteine residues. They are present in plants from the Rubiaceae, Violaceae and Cucurbitaceae families. The unique structural features of the cyclotides make them extremely resistant to chemical, thermal and proteolytic degradation. In this article we review recent Studies from our laboratory that dissect the role of the individual structural elements in defining the stability of cyclotides. The resistance of cyclotides to chemical and proteolytic degradation is in large part due to the cystine knot, whereas the thermal stability is I composite of several features including the cystine knot, the cyclic backbone and the hydrogen bonding network. A range of biological activities of cyclotides is critically dependent oil the presence of the cyclic backbone.