Active Subnetworks Research Articles

Thematic review series: Systems Biology Approaches to Metabolic and Cardiovascular Disorders. Multi-organ whole-genome measurements and reverse engineering to uncover gene networks underlying complex traits

Together with computational analysis and modeling, the development of whole-genome measurement technologies holds the potential to fundamentally change research on complex disorders such as coronary artery disease. With these tools, the stage has been set to reveal the full repertoire of biological components (genes, proteins, and metabolites) in complex diseases and their interplay in modules and networks. Here we review how network identification based on reverse engineering, as applied to whole-genome datasets from simpler organisms, is now being adapted to more complex settings such as datasets from human cell lines and organs in relation to physiological and pathological states. Our focus is on the use of a systems biological approach to identify gene networks in coronary atherosclerosis. We also address how gene networks will probably play a key role in the development of early diagnostics and treatments for complex disorders in the coming era of individualized medicine.

Robust emergent activity in dynamical networks

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the microlevel behavior at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find that very different networks evolve to active subnetworks with similar asymptotic characteristics: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. This robustness has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.

Adaptively inferring human transcriptional subnetworks.

Although the human genome has been sequenced, progress in understanding gene regulation in humans has been particularly slow. Many computational approaches developed for lower eukaryotes to identify cis-regulatory elements and their associated target genes often do not generalize to mammals, largely due to the degenerate and interactive nature of such elements. Motivated by the switch-like behavior of transcriptional responses, we present a systematic approach that allows adaptive determination of active transcriptional subnetworks (cis-motif combinations, the direct target genes and physiological processes regulated by the corresponding transcription factors) from microarray data in mammals, with accuracy similar to that achieved in lower eukaryotes. Our analysis uncovered several new subnetworks active in human liver and in cell-cycle regulation, with similar functional characteristics as the known ones. We present biochemical evidence for our predictions, and show that the recently discovered G2/M-specific E2F pathway is wider than previously thought; in particular, E2F directly activates certain mitotic genes involved in hepatocellular carcinomas. Additionally, we demonstrate that this method can predict subnetworks in a condition-specific manner, as well as regulatory crosstalk across multiple tissues. Our approach allows systematic understanding of how phenotypic complexity is regulated at the transcription level in mammals and offers marked advantage in systems where little or no prior knowledge of transcriptional regulation is available.

Frequency Regulation of a Slow Rhythm by a Fast Periodic Input

Many nervous systems contain rhythmically active subnetworks that interact despite oscillating at widely different frequencies. The stomatogastric nervous system of the crab Cancer borealis produces a rapid pyloric rhythm and a considerably slower gastric mill rhythm. We construct and analyze a conductance-based compartmental model to explore the activation of the gastric mill rhythm by the modulatory commissural neuron 1 (MCN1). This model demonstrates that the period of the MCN1-activated gastric mill rhythm, which was thought to be determined entirely by the interaction of neurons in the gastric mill network, can be strongly influenced by inhibitory synaptic input from the pacemaker neuron of the fast pyloric rhythm, the anterior burster (AB) neuron. Surprisingly, the change of the gastric mill period produced by the pyloric input to the gastric mill system can be many times larger than the period of the pyloric rhythm itself. This model illustrates several mechanisms by which a fast oscillatory neuron may control the frequency of a much slower oscillatory network. These findings suggest that it is possible to modify the slow rhythm either by direct modulation or indirectly by modulating the faster rhythm.

SC simulators of passive two-ports

Abstract A method for synthesizing switched capacitor circuits that simulate passive LC ladder networks is proposed. The circuits are developed by cascading lower order SC active subnetworks which serve the purpose of two port simulators. Experimental results from two circuits that are proposed as examples, are also given.

Unified large-signal stability and noise theory for synchronised oscillators

A unified model is developed which is capable of analysing large-signal performance, stability, and noise of synchronised oscillators under rather general conditions. The passive circuitry is arbitrary; the active subnetwork may in principle contain one-port or two-port devices with or without harmonic content. However, only one-port devices operating at a single frequency are treated explicitly. The active device is modelled by its describing function (i.e. its effective admittance) with respect to both carrier and noise signals. The noise analysis directly leads to a new stability criterion, which clearly shows the restrictions and even failure of the hitherto-used criteria. These results are proved by measurements. Finally, the application of the nonlinear theory to the analysis of multiple-device oscillators is illustrated by results.

Time-multiplexed active filters

The inductorless realization of high-order voltage transfer functions is achieved by subdividing a conventional realization into identical memoryless active subnetworks; the realization is then achieved by time multiplexing one of the memoryless active subnetworks such that it effectively replaces the total number of active subnetworks. The result of this time-multiplexing operation is to create a new type of RC-active filter that exhibits many practical advantages, such as lower power dissipation and a considerable saving in circuit complexity. The synthesis technique is illustrated by means of the design of a sixteenth-order low-pass transfer function. Nonideal performance is analyzed.

Electronically tunable time-multiplexed active filters

A simple modification of the time-multiplexed active filter allows the transfer function to be electronically tuned. The method is to allow the switched memoryless active subnetwork to be multiplexed in such a way that a variable time slot is allocated to each stage of the filter. Electronic variation of this time slot achieves a corresponding tuning of the transfer function. In terms of circuitry, a simple modification to the logic drive circuitry is required to make tuning possible.

Synthesis of Transformerless ActiveN-Port Networks

Theorem: An arbitrary symmetric N × N matrix of real rational functions in the complex-frequency variable (a) can be realized as the immittance matrix of an N-port network containing only resistors, capacitors, and N negative-RC impedances, and (b) cannot, in general, be realized as the immittance matrix of an N-port network containing resistors, capacitors, inductors, ideal transformers, and M negative-RC impedances if M < N. The necessary and sufficient conditions for the immittance-matrix realization of transformerless networks of capacitors, self-inductors, resistors, and negative resistors follow as a special case of the theorem. In addition, an earlier result is extended by presenting a procedure for the realization of an arbitrary N × N short-circuit admittance matrix as an unbalanced transformerless active RC network requiring no more than N controlled sources. The passive RC structure has the interesting property that it can always be realized as a (3 N + 1)-terminal network of two-terminal impedances with common reference node and no internal nodes. The active subnetwork can always be realized with N negative-impedance converters.