Quiver Bundles and Wall Crossing for Chains

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C*-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability of the chains implies stability of this new quiver bundle. Our approach uses the Hitchin-Kobayashi correspondence for quiver bundles. Moreover, we use our result to give a new proof of a key lemma on chains (due to \'Alvarez-C\'onsul, Garc\'ia-Prada and Schmitt), which has been important in the study of Higgs bundle moduli; this proof relies on stability and thus avoids the direct use of the chain vortex equations

Additional file 1: Figure S1. of Nanobodies raised against monomeric ɑ-synuclein inhibit fibril formation and destabilize toxic oligomeric species

Additional results. (a) AFM images of starting monomeric solutions of wild-type (wt) ɑS prior to incubation with agitation. (b) Total internal reflection fluorescence microscopy results. Left: representative sum-image in the ThT emission channel (100 frames) and the corresponding reconstruction image in the NR channel (2000 frames). Right: comparison of the total numbers of aggregates and percent of ThT-active aggregates formed in the wt ɑS-only and wt ɑS + nanobody solutions at the same time-point of the aggregation process. (c) Scatter plots and statistical comparison of the distributions of average fibril heights derived from AFM maps (Fig. 1b, c, main text). (d) Quartz crystal microbalance recordings using ɑS (21 μM), nanobody alone (21 μM) or 1:1 mixture of ɑS with nanobody (21 μM : 21 μM) or control peptide (42 μM). (TIF 4648 kb