General Stability Analysis of Synchronized Dynamics in Coupled Systems

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on the master stability function and Gershgorin disc theory, to yield constraints on the coupling strengths to ensure the stability of synchronized dynamics. Systems with specific coupling schemes are used as examples to illustrate our general method.Comment: 8 pages, 1 figur

Will systems biology offer new holistic paradigms to life sciences?

A biological system, like any complex system, blends stochastic and deterministic features, displaying properties of both. In a certain sense, this blend is exactly what we perceive as the “essence of complexity” given we tend to consider as non-complex both an ideal gas (fully stochastic and understandable at the statistical level in the thermodynamic limit of a huge number of particles) and a frictionless pendulum (fully deterministic relative to its motion). In this commentary we make the statement that systems biology will have a relevant impact on nowadays biology if (and only if) will be able to capture the essential character of this blend that in our opinion is the generation of globally ordered collective modes supported by locally stochastic atomisms

Robust regression for periodicity detection in non-uniformly sampled time-course gene expression data

<p>Abstract</p> <p>Background</p> <p>In practice many biological time series measurements, including gene microarrays, are conducted at time points that seem to be interesting in the biologist's opinion and not necessarily at fixed time intervals. In many circumstances we are interested in finding targets that are expressed periodically. To tackle the problems of uneven sampling and unknown type of noise in periodicity detection, we propose to use robust regression.</p> <p>Methods</p> <p>The aim of this paper is to develop a general framework for robust periodicity detection and review and rank different approaches by means of simulations. We also show the results for some real measurement data.</p> <p>Results</p> <p>The simulation results clearly show that when the sampling of time series gets more and more uneven, the methods that assume even sampling become unusable. We find that M-estimation provides a good compromise between robustness and computational efficiency.</p> <p>Conclusion</p> <p>Since uneven sampling occurs often in biological measurements, the robust methods developed in this paper are expected to have many uses. The regression based formulation of the periodicity detection problem easily adapts to non-uniform sampling. Using robust regression helps to reject inconsistently behaving data points.</p> <p>Availability</p> <p>The implementations are currently available for Matlab and will be made available for the users of R as well. More information can be found in the web-supplement <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p

Phenotypic Signatures Arising from Unbalanced Bacterial Growth

Fluctuations in the growth rate of a bacterial culture during unbalanced growth are generally considered undesirable in quantitative studies of bacterial physiology. Under well-controlled experimental conditions, however, these fluctuations are not random but instead reflect the interplay between intra-cellular networks underlying bacterial growth and the growth environment. Therefore, these fluctuations could be considered quantitative phenotypes of the bacteria under a specific growth condition. Here, we present a method to identify “phenotypic signatures” by time-frequency analysis of unbalanced growth curves measured with high temporal resolution. The signatures are then applied to differentiate amongst different bacterial strains or the same strain under different growth conditions, and to identify the essential architecture of the gene network underlying the observed growth dynamics. Our method has implications for both basic understanding of bacterial physiology and for the classification of bacterial strains

Emergent Genome-Wide Control in Wildtype and Genetically Mutated Lipopolysaccarides-Stimulated Macrophages

Large-scale gene expression studies have mainly focused on highly expressed and ‘discriminatory’ genes to decipher key regulatory processes. Biological responses are consequence of the concerted action of gene regulatory network, thus, limiting our attention to genes having the most significant variations is insufficient for a thorough understanding of emergent whole genome response. Here we comprehensively analyzed the temporal oligonucleotide microarray data of lipopolysaccharide (LPS) stimulated macrophages in 4 genotypes; wildtype, Myeloid Differentiation factor 88 (MyD88) knockout (KO), TIR-domain-containing adapter-inducing interferon-β (TRIF) KO and MyD88/TRIF double KO (DKO). Pearson correlations computed on the whole genome expression between different genotypes are extremely high (>0.98), indicating a strong co-regulation of the entire expression network. Further correlation analyses reveal genome-wide response is biphasic, i) acute-stochastic mode consisting of small number of sharply induced immune-related genes and ii) collective mode consisting of majority of weakly induced genes of diverse cellular processes which collectively adjust their expression level. Notably, temporal correlations of a small number of randomly selected genes from collective mode show scalability. Furthermore, in collective mode, the transition from large scatter in expression distributions for single ORFs to smooth linear lines emerges as an organizing principle when grouping of 50 ORFs and above. With this emergent behavior, the role of MyD88, TRIF and novel MyD88, TRIF-independent processes for gene induction can be linearly superposed to decipher quantitative whole genome differential control of transcriptional and mRNA decay machineries. Our work demonstrates genome-wide co-regulated responses subsequent to specific innate immune stimulus which have been largely neglected

Information Routing Driven by Background Chatter in a Signaling Network

Living systems are capable of processing multiple sources of information simultaneously. This is true even at the cellular level, where not only coexisting signals stimulate the cell, but also the presence of fluctuating conditions is significant. When information is received by a cell signaling network via one specific input, the existence of other stimuli can provide a background activity –or chatter– that may affect signal transmission through the network and, therefore, the response of the cell. Here we study the modulation of information processing by chatter in the signaling network of a human cell, specifically, in a Boolean model of the signal transduction network of a fibroblast. We observe that the level of external chatter shapes the response of the system to information carrying signals in a nontrivial manner, modulates the activity levels of the network outputs, and effectively determines the paths of information flow. Our results show that the interactions and node dynamics, far from being random, confer versatility to the signaling network and allow transitions between different information-processing scenarios

An Increase in Mitochondrial DNA Promotes Nuclear DNA Replication in Yeast

Coordination between cellular metabolism and DNA replication determines when cells initiate division. It has been assumed that metabolism only plays a permissive role in cell division. While blocking metabolism arrests cell division, it is not known whether an up-regulation of metabolic reactions accelerates cell cycle transitions. Here, we show that increasing the amount of mitochondrial DNA accelerates overall cell proliferation and promotes nuclear DNA replication, in a nutrient-dependent manner. The Sir2p NAD+-dependent de-acetylase antagonizes this mitochondrial role. We found that cells with increased mitochondrial DNA have reduced Sir2p levels bound at origins of DNA replication in the nucleus, accompanied with increased levels of K9, K14-acetylated histone H3 at those origins. Our results demonstrate an active role of mitochondrial processes in the control of cell division. They also suggest that cellular metabolism may impact on chromatin modifications to regulate the activity of origins of DNA replication

Quantifying the Dynamics of Coupled Networks of Switches and Oscillators

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems