How motifs condition critical thresholds for tipping cascades in complex networks: Linking Micro- to Macro-scales

In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erd\"os-R\'enyi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease of the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of very high motif occurrence for each of the four investigated motifs suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erd\"os-R\'enyi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole

Dynamics of Tipping Cascades on Complex Networks

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy or engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change of the system. Many systems with tipping points can be modeled as networks of coupled multistable subsystems, e.g. coupled patches of vegetation, connected lakes, interacting climate tipping elements or multiscale infrastructure systems. In such networks, tipping events in one subsystem are able to induce tipping cascades via domino effects. Here, we investigate the effects of network topology on the occurrence of such cascades. Numerical cascade simulations with a conceptual dynamical model for tipping points are conducted on Erd\H{o}s-R\'enyi, Watts-Strogatz and Barab\'asi-Albert networks. Additionally, we generate more realistic networks using data from moisture-recycling simulations of the Amazon rainforest and compare the results to those obtained for the model networks. We furthermore use a directed configuration model and a stochastic block model which preserve certain topological properties of the Amazon network to understand which of these properties are responsible for its increased vulnerability. We find that clustering and spatial organization increase the vulnerability of networks and can lead to tipping of the whole network. These results could be useful to evaluate which systems are vulnerable or robust due to their network topology and might help to design or manage systems accordingly.Comment: 22 pages, 12 figure

Pathological consequences of VCP mutations on human striated muscle

*These authors have contributed equally to this work. Mutations in the valosin-containing protein (VCP, p97) gene on chromosome 9p13-p12 cause a late-onset form of autosomal dominant inclusion body myopathy associated with Paget disease of the bone and frontotemporal dementia (IBMPFD). We report on the pathological consequences of three heterozygous VCP (R93C, R155H, R155C) mutations on human striated muscle. IBMPFD skeletal muscle pathology is characterized by degenerative changes and filamentous VCP-and ubiquitin-positive cytoplasmic and nuclear protein aggregates. Furthermore, this is the first report demonstrating that mutant VCP leads to a novel form of dilatative cardiomyopathy with inclusion bodies. In contrast to post-mitotic striated muscle cells and neurons of IBMPFD patients, evidence of protein aggregate pathology was not detected in primary IBMPFD myoblasts or in transient and stable transfected cells using wild-type-VCP and R93C-, R155H-, R155C-VCP mutants. Glutathione S-transferase pull-down experiments showed that all three VCP mutations do not affect the binding to Ufd1, Npl4 and ataxin-3. Structural analysis demonstrated that R93 and R155 are both surface-accessible residues located in the centre of cavities that may enable ligand-binding. Mutations at R93 and R155 are predicted to induce changes in the tertiary structure of the VCP protein. The search for putative ligands to the R93 and R155 cavities resulted in the identification of cyclic sugar compounds with high binding scores. The latter findings provide a novel link to VCP carbohydrate interactions in the complex pathology of IBMPFD. Keywords: VCP; p97; myopathy; cardiomyopathy; IBMPFD Abbreviations: GST = glutathione S-transferase; IBMPFD = inclusion body myopathy associated with Paget disease of the bone and frontotemporal dementia; PBS = phosphate-buffered saline; SDS = sodium dodecyl sulphate; VCP = valosin-containing protei