Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics

The novel ECF56 SigG1-RsfG system modulates morphological differentiation and metal-ion homeostasis in Streptomyces tsukubaensis

Extracytoplasmic function (ECF) sigma factors are key transcriptional regulators that prokaryotes have evolved to respond to environmental challenges. Streptomyces tsukubaensis harbours 42 ECFs to reprogram stress-responsive gene expression. Among them, SigG1 features a minimal conserved ECF s2–s4 architecture and an additional C-terminal extension that encodes a SnoaL_2 domain, which is characteristic for ECF s factors of group ECF56. Although proteins with such domain organisation are widely found among Actinobacteria, the functional role of ECFs with a fused SnoaL_2 domain remains unknown. Our results show that in addition to predicted self-regulatory intramolecular amino acid interactions between the SnoaL_2 domain and the ECF core, SigG1 activity is controlled by the cognate anti-sigma protein RsfG, encoded by a co-transcribed sigG1-neighbouring gene. Characterisation of ¿sigG1 and ¿rsfG strains combined with RNA-seq and ChIP-seq experiments, suggests the involvement of SigG1 in the morphological differentiation programme of S. tsukubaensis. SigG1 regulates the expression of alanine dehydrogenase, ald and the WhiB-like regulator, wblC required for differentiation, in addition to iron and copper trafficking systems. Overall, our work establishes a model in which the activity of a s factor of group ECF56, regulates morphogenesis and metal-ions homeostasis during development to ensure the timely progression of multicellular differentiation.This work was partially funded by National Funds through FCT-Fundação para a Ciência e a Tecnologia, I.P., under the project ERA-IB-2/0001/2015. It was further supported by FEDER - Fundo Europeu de Desen-volvimento Regional funds through the COMPETE 2020 - Operational Programme for Competitiveness and Internationalisation (POCI), Portugal 2020; and by Portuguese funds through FCT Fundação para a Ciência e a Tecnologia, I.P/Ministério da Ciência, Tecnologia e Ensino Superior POCI-01-0145-FEDER-007274 and NORTE-01-0145-FEDER-000012. BBSRC supported this work through the Institute Strategic Programme grant BB/J004561/1 to the John Innes Centre. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. R.O. was supported by the FCT fellowship SFRH/ BD/107862/2015 and by the EMBO fellowship ASTF438-2015, M.V.M. was supported by the FCT fellowship SFRH/BPD/95683/2013 and the FCT contract DL57/2016/CP1355/CT0023 and D.C.P. and G.F. were supported through the IMPRS-Mic and the ERASynBio project ECFexpress (BMBF grant 031L0010B). The authors are grateful to Kim Findlay at the Bioimaging platform of the John Innes Centre (JIC, UK) for performing the SEM imaging of S. tsukubaensis samples, Mervyn Bibb (JIC, UK) for the pIJ12333 plasmid , Mark Buttner (JIC, UK) for his comments and discussion regarding the work and Paula Tamagnini (i3S, PT) for comments on the manuscript. The authors acknowledge the support of the i3S Scientific Platforms Cell Culture and Genotyping, Biochemical and Biophysical Technologies and Proteomics

Fast variables determine the epidemic threshold in the pairwise model with an improved closure

Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks exhibiting degree heterogeneity, directed and/or weighted links and clustering. However, extra features of the disease dynamics or of the network lead to an increase in system size and analytical tractability becomes problematic. Various `closures' can be used to keep the system tractable. Focusing on SIR epidemics on regular but clustered networks, we show that even for the most complex closure we can determine the epidemic threshold as an asymptotic expansion in terms of the clustering coefficient.We do this by exploiting the presence of a system of fast variables, specified by the correlation structure of the epidemic, whose steady state determines the epidemic threshold. While we do not find the steady state analytically, we create an elegant asymptotic expansion of it. We validate this new threshold by comparing it to the numerical solution of the full system and find excellent agreement over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. The technique carries over to pairwise models with other closures [1] and we note that the epidemic threshold will be model dependent. This emphasises the importance of model choice when dealing with realistic outbreaks

Mean-field models for non-Markovian epidemics on networks

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission themessage passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length

Temporal networks of face-to-face human interactions

The ever increasing adoption of mobile technologies and ubiquitous services allows to sense human behavior at unprecedented levels of details and scale. Wearable sensors are opening up a new window on human mobility and proximity at the finest resolution of face-to-face proximity. As a consequence, empirical data describing social and behavioral networks are acquiring a longitudinal dimension that brings forth new challenges for analysis and modeling. Here we review recent work on the representation and analysis of temporal networks of face-to-face human proximity, based on large-scale datasets collected in the context of the SocioPatterns collaboration. We show that the raw behavioral data can be studied at various levels of coarse-graining, which turn out to be complementary to one another, with each level exposing different features of the underlying system. We briefly review a generative model of temporal contact networks that reproduces some statistical observables. Then, we shift our focus from surface statistical features to dynamical processes on empirical temporal networks. We discuss how simple dynamical processes can be used as probes to expose important features of the interaction patterns, such as burstiness and causal constraints. We show that simulating dynamical processes on empirical temporal networks can unveil differences between datasets that would otherwise look statistically similar. Moreover, we argue that, due to the temporal heterogeneity of human dynamics, in order to investigate the temporal properties of spreading processes it may be necessary to abandon the notion of wall-clock time in favour of an intrinsic notion of time for each individual node, defined in terms of its activity level. We conclude highlighting several open research questions raised by the nature of the data at hand.Comment: Chapter of the book "Temporal Networks", Springer, 2013. Series: Understanding Complex Systems. Holme, Petter; Saram\"aki, Jari (Eds.