Modularity and the spread of perturbations in complex dynamical systems

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the 'Markov stability' method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., 'relevance networks' or 'functional networks'). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously-coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems

Adoption of an “Open” Envelope Conformation Facilitating CD4 Binding and Structural Remodeling Precedes Coreceptor Switch in R5 SHIV-Infected Macaques

A change in coreceptor preference from CCR5 to CXCR4 towards the end stage disease in some HIV-1 infected individuals has been well documented, but the reasons and mechanisms for this tropism switch remain elusive. It has been suggested that envelope structural constraints in accommodating amino acid changes required for CXCR4 usage is an obstacle to tropism switch, limiting the rate and pathways available for HIV-1 coreceptor switching. The present study was initiated in two R5 SHIVSF162P3N-infected rapid progressor macaques with coreceptor switch to test the hypothesis that an early step in the evolution of tropism switch is the adoption of a less constrained and more “open” envelope conformation for better CD4 usage, allowing greater structural flexibility to accommodate further mutational changes that confer CXCR4 utilization. We show that, prior to the time of coreceptor switch, R5 viruses in both macaques evolved to become increasingly sCD4-sensitive, suggestive of enhanced exposure of the CD4 binding site and an “open” envelope conformation, and this correlated with better gp120 binding to CD4 and with more efficient infection of CD4low cells such as primary macrophages. Moreover, significant changes in neutralization sensitivity to agents and antibodies directed against functional domains of gp120 and gp41 were seen for R5 viruses close to the time of X4 emergence, consistent with global changes in envelope configuration and structural plasticity. These observations in a simian model of R5-to-X4 evolution provide a mechanistic basis for the HIV-1 coreceptor switch