Quantifying gene network connectivity in silico: scalability and accuracy of a modular approach

Large, complex data sets that are generated from microarray experiments, create a need for systematic analysis techniques to unravel the underlying connectivity of gene regulatory networks. A modular approach, previously proposed by Kholodenko and co-workers, helps to scale down the network complexity into more computationally manageable entities called modules. A functional module includes a gene's mRNA, promoter and resulting products, thus encompassing a large set of interacting states. The essential elements of this approach are described in detail for a three-gene model network and later extended to a ten-gene model network, demonstrating scalability. The network architecture is identified by analysing in silico steady-state changes in the activities of only the module outputs, communicating intermediates, that result from specific perturbations applied to the network modules one at a time. These steady-state changes form the system response matrix, which is used to compute the network connectivity or network interaction map. By employing a known biochemical network, the accuracy of the modular approach and its sensitivity to key assumptions are evaluated.     

Self-selected modular recurrent neural networks with postural and inertial subnetworks applied to complex movements

 It has been shown that dynamic recurrent neural networks are successful in identifying the complex mapping relationship between full-wave-rectified electromyographic (EMG) signals and limb trajectories during complex movements. These connectionist models include two types of adaptive parameters: the interconnection weights between the units and the time constants associated to each neuron-like unit; they are governed by continuous-time equations. Due to their internal structure, these models are particularly appropriate to solve dynamical tasks (with time-varying input and output signals). We show in this paper that the introduction of a modular organization dedicated to different aspects of the dynamical mapping including privileged communication channels can refine the architecture of these recurrent networks. We first divide the initial individual network into two communicating subnetworks. These two modules receive the same EMG signals as input but are involved in different identification tasks related to position and acceleration. We then show that the introduction of an artificial distance in the model (using a Gaussian modulation factor of weights) induces a reduced modular architecture based on a self-elimination of null synaptic weights. Moreover, this self-selected reduced model based on two subnetworks performs the identification task better than the original single network while using fewer free parameters (better learning curve and better identification quality). We also show that this modular network exhibits several features that can be considered as biologically plausible after the learning process: self-selection of a specific inhibitory communicating path between both subnetworks after the learning process, appearance of tonic and phasic neurons, and coherent distribution of the values of the time constants within each subnetwork. Received: 17 September 2001 / Accepted in revised form: 15 January 2002     

Increasing modularity when downscaling networks from species to individuals

Downscaling networks from species to individuals is a useful approach to incorporate inter‐individual variation and to investigate whether topology of species‐based networks results from processes acting at the scale of individuals, such as foraging behaviour. Here, we analyzed pollen‐transport networks at two scales, i.e. pollinator species–plant species (sp–sp) and pollinator individuals–plant species (i–sp), and assessed whether modularity – a prevalent pattern in most pollination networks – is consistent across both scales. To test this we use three different algorithms developed for the calculation of modularity (unipartite, bipartite and weighted bipartite modularity) and compare the results obtained. Downscaling networks revealed a higher modular structure in i–sp networks than in sp–sp networks, regardless of the modular metric used. Using a null model approach, we show that modularity at the individual scale is originated by the existence of a high heterogeneity and specialization in the partition of pollen resources among conspecific individuals, a pattern which obviously cannot be observed at the species level. Modules in i–sp networks consisted of individuals sometimes neither taxonomically nor functionally related, but sharing common pollen resources at different moments of the flowering season. Interestingly, conspecific individuals may belong to different modules. Both plant and insect phenologies were important drivers of the modularity detected in individual‐based networks, even determining the topological roles of nodes in the networks. A temporal turnover of modules was identified, i.e. modules of individuals assembled and disassembled over time as species modify their foraging choices throughout the flowering season adjusting to ecological conditions. Downscaling from species to individual‐based networks is a promising approach to study the interplay among structural patterns and processes at different, but interdependent organizational levels.     

Directional and quantitative phosphorylation networks.

Directionality in protein signalling networks is due to modulated protein-protein interactions and is fundamental for proper signal progression and response to external and internal cues. This property is in part enabled by linear motifs embedding post-translational modification sites. These serve as recognition sites, guiding phosphorylation by kinases and subsequent binding of modular domains (e.g. SH2 and BRCT). Characterization of such modification-modulated interactions on a proteome-wide scale requires extensive computational and experimental analysis. Here, we review the latest advances in methods for unravelling phosphorylation-mediated cellular interaction networks. In particular, we will discuss how the combination of new quantitative mass-spectrometric technologies and computational algorithms together are enhancing mapping of these largely uncharted dynamic networks. By combining quantitative measurements of phosphorylation events with computational approaches, we argue that systems level models will help to decipher complex diseases through the ability to predict cellular systems trajectories.     

Robot control and the evolution of modular neurodynamics

Summary A modular approach to neural behavior control of autonomous robots is presented. It is based on the assumption that complex internal dynamics of recurrent neural networks can efficiently solve complex behavior tasks. For the development of appropriate neural control structures an evolutionary algorithm is introduced, which is able to generate neuromodules with specific functional properties, as well as the connectivity structure for a modular synthesis of such modules. This so called ENS ³-algorithm does not use genetic coding. It is primarily designed to develop size and connectivity structure of neuro-controllers. But at the same time it optimizes also parameters of individual networks like synaptic weights and bias terms. For demonstration, evolved networks for the control of miniature Khepera robots are presented. The aim is to develop robust controllers in the sense that neuro-controllers evolved in a simulator show comparably good behavior when loaded to a real robot acting in a physical environment. Discussed examples of such controllers generate obstacle avoidance and phototropic behaviors in non-trivial environments.     

Structure and mechanism of diet specialisation: testing models of individual variation in resource use with sea otters

Studies of consumer-resource interactions suggest that individual diet specialisation is empirically widespread and theoretically important to the organisation and dynamics of populations and communities. We used weighted networks to analyze the resource use by sea otters, testing three alternative models for how individual diet specialisation may arise. As expected, individual specialisation was absent when otter density was low, but increased at high-otter density. A high-density emergence of nested resource-use networks was consistent with the model assuming individuals share preference ranks. However, a density-dependent emergence of a non-nested modular network for 'core' resources was more consistent with the 'competitive refuge' model. Individuals from different diet modules showed predictable variation in rank-order prey preferences and handling times of core resources, further supporting the competitive refuge model. Our findings support a hierarchical organisation of diet specialisation and suggest individual use of core and marginal resources may be driven by different selective pressures.     

Getting to synaptic complexes through systems biology

Large numbers of synaptic components have been identified, but the effect so far on our understanding of synaptic function is limited. Now, network maps and annotated functions of individual components have been used in a systems biology approach to analyzing the function of NMDA receptor complexes at synapses, identifying biologically relevant modular networks within the complex.     

The relative efficiency of modular and non-modular networks of different size

Most biological networks are modular but previous work with small model networks has indicated that modularity does not necessarily lead to increased functional efficiency. Most biological networks are large, however, and here we examine the relative functional efficiency of modular and non-modular neural networks at a range of sizes. We conduct a detailed analysis of efficiency in networks of two size classes: ‘small’ and ‘large’, and a less detailed analysis across a range of network sizes. The former analysis reveals that while the modular network is less efficient than one of the two non-modular networks considered when networks are small, it is usually equally or more efficient than both non-modular networks when networks are large. The latter analysis shows that in networks of small to intermediate size, modular networks are much more efficient that non-modular networks of the same (low) connective density. If connective density must be kept low to reduce energy needs for example, this could promote modularity. We have shown how relative functionality/performance scales with network size, but the precise nature of evolutionary relationship between network size and prevalence of modularity will depend on the costs of connectivity.     

Shapes of astrocyte networks in the juvenile brain

The high level of intercellular communication mediated by gap junctions between astrocytes indicates that, besides individual astrocytic domains, a second level of organization might exist for these glial cells as they form communicating networks. Therefore,the contribution of astrocytes to brain function should also be considered to result from coordinated groups of cells. To evaluate the shape and extent of these networks we have studied the expression of connexin 43, a major gap junction protein in astrocytes, and the intercellular diffusion of gap junction tracers in two structures of the developing brain, the hippocampus and the cerebral cortex. We report that the shape of astrocytic networks depends on their location within neuronal compartments ina defined brain structure. Interestingly, not all astrocytes are coupled, which indicates that connections within these networks are restricted. As gap junctional communication in astrocytes is reported to contribute to several glial functions, differences in the shape of astrocytic networks might have consequences on neuronal activity and survival.     

Scaling down from species to individuals: a flower–visitation network between individual honeybees and thistle plants

Studies of ecological networks usually focus upon interaction patterns among species. However, linkage among species is mediated by their constituting individuals. Thus, every linked species pair in a network encapsulates a new network of interacting individuals. Very few studies outside the sociology of larger animals have investigated networks at the level of the individual. Here, we analyse the structure of a flower–visitation network of individual thistles Cirsium arvense and honeybees Apis mellifera in a small meadow patch in Denmark. We marked and numbered 62 honeybees and 32 thistle stems and monitored all floral visits. The constructed bipartite network of individual plants and bees had a high connectance and low nestedness, but it was not significantly modular. Frequency distributions of number of links per species (i.e. linkage level) had their best fit to a truncated power law, and interactions were asymmetrical. Unipartite networks of either plants or bees had exceedingly short average path length and high clustering. Linkage level of plants increased with their number of flower heads and height of inflorescence (floral display parameters). Overall, the individual network of honeybees and thistles was denser linked than what is known from species pollination networks. Characteristics of both plants (e.g. floral display) and animals (e.g. foraging behaviour) are likely to generate this intra–specific, inter–individual link pattern. Such features of individual–individual networks may scale up and become important drivers of the structure and dynamics of species–species networks.