Fractional $$({\varvec{s}},{\varvec{p}})$$-Robin–Venttsel’ problems on extension domains

We study a nonlocal Robin–Venttsel’-type problem for the regional fractional p-Laplacian in an extension domain $$\Omega $$ Ω with boundary a d-set. We prove existence and uniqueness of a strong solution via a semigroup approach. Markovianity and ultracontractivity properties are proved. We then consider the elliptic problem. We prove existence, uniqueness and global boundedness of the weak solution.

Duality of capacities and Sobolev extendability in the plane

We reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involved in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give an alternative proof of the necessary condition for a Jordan planar domain to be $$W^{1,\,q}$$ W 1 , q -extension domain when $$2<q<\infty$$ 2 < q < ∞ .

Molecular Mechanism of Secreted Amyloid-β Precursor Protein in Binding and Modulating GABABR1a

A recent phenomenal study discovered that the extension domain of secreted amyloid-β precursor protein (sAPP) can bind to the intrinsically disordered sushi 1 domain of the γ-aminobutyric acid type B...

Reconstructed evolutionary history of the yeast septins Cdc11 and Shs1

Septins are GTP-binding proteins conserved across metazoans. They can polymerize into extended filaments and, hence, are considered a component of the cytoskeleton. The number of individual septins varies across the tree of life—yeast (Saccharomyces cerevisiae) has seven distinct subunits, a nematode (Caenorhabditis elegans) has two, and humans have 13. However, the overall geometric unit (an apolar hetero-octameric protomer and filaments assembled there from) has been conserved. To understand septin evolutionary variation, we focused on a related pair of yeast subunits (Cdc11 and Shs1) that appear to have arisen from gene duplication within the fungal clade. Either Cdc11 or Shs1 occupies the terminal position within a hetero-octamer, yet Cdc11 is essential for septin function and cell viability, whereas Shs1 is not. To discern the molecular basis of this divergence, we utilized ancestral gene reconstruction to predict, synthesize, and experimentally examine the most recent common ancestor (“Anc.11-S”) of Cdc11 and Shs1. Anc.11-S was able to occupy the terminal position within an octamer, just like the modern subunits. Although Anc.11-S supplied many of the known functions of Cdc11, it was unable to replace the distinct function(s) of Shs1. To further evaluate the history of Shs1, additional intermediates along a proposed trajectory from Anc.11-S to yeast Shs1 were generated and tested. We demonstrate that multiple events contributed to the current properties of Shs1: (1) loss of Shs1–Shs1 self-association early after duplication, (2) co-evolution of heterotypic Cdc11–Shs1 interaction between neighboring hetero-octamers, and (3) eventual repurposing and acquisition of novel function(s) for its C-terminal extension domain. Thus, a pair of duplicated proteins, despite constraints imposed by assembly into a highly conserved multi-subunit structure, could evolve new functionality via a complex evolutionary pathway.

Slowly folding surface extension in the prototypic avian hepatitis B virus capsid governs stability

Hepatitis B virus (HBV) is an important but difficult to study human pathogen. Most basics of the hepadnaviral life-cycle were unraveled using duck HBV (DHBV) as a model although DHBV has a capsid protein (CP) comprising ~260 rather than ~180 amino acids. Here we present high-resolution structures of several DHBV capsid-like particles (CLPs) determined by electron cryo-microscopy. As for HBV, DHBV CLPs consist of a dimeric α-helical frame-work with protruding spikes at the dimer interface. A fundamental new feature is a ~ 45 amino acid proline-rich extension in each monomer replacing the tip of the spikes in HBV CP. In vitro, folding of the extension takes months, implying a catalyzed process in vivo. DHBc variants lacking a folding-proficient extension produced regular CLPs in bacteria but failed to form stable nucleocapsids in hepatoma cells. We propose that the extension domain acts as a conformational switch with differential response options during viral infection.

Newly acquired N-terminal extension targets threonyl-tRNA synthetase-like protein into the multiple tRNA synthetase complex

A typical feature of eukaryotic aminoacyl-tRNA synthetases (aaRSs) is the evolutionary gain of domains at either the N- or C-terminus, which frequently mediating protein–protein interaction. TARSL2 (mouse Tarsl2), encoding a threonyl-tRNA synthetase-like protein (ThrRS-L), is a recently identified aaRS-duplicated gene in higher eukaryotes, with canonical functions in vitro, which exhibits a different N-terminal extension (N-extension) from TARS (encoding ThrRS). We found the first half of the N-extension of human ThrRS-L (hThrRS-L) is homologous to that of human arginyl-tRNA synthetase. Using the N-extension as a probe in a yeast two-hybrid screening, AIMP1/p43 was identified as an interactor with hThrRS-L. We showed that ThrRS-L is a novel component of the mammalian multiple tRNA synthetase complex (MSC), and is reliant on two leucine zippers in the N-extension for MSC-incorporation in humans, and mouse cell lines and muscle tissue. The N-extension was sufficient to target a foreign protein into the MSC. The results from a Tarsl2-deleted cell line showed that it does not mediate MSC integrity. The effect of phosphorylation at various sites of hThrRS-L on its MSC-targeting is also explored. In summary, we revealed that ThrRS-L is a bona fide component of the MSC, which is mediated by a newly evolved N-extension domain.

Integration of Fungus-Specific CandA-C1 into a Trimeric CandA Complex Allowed Splitting of the Gene for the Conserved Receptor Exchange Factor of CullinA E3 Ubiquitin Ligases in Aspergilli

ABSTRACT E3 cullin-RING ubiquitin ligase (CRL) complexes recognize specific substrates and are activated by covalent modification with ubiquitin-like Nedd8. Deneddylation inactivates CRLs and allows Cand1/A to bind and exchange substrate recognition subunits. Human as well as most fungi possess a single gene for the receptor exchange factor Cand1, which is split and rearranged in aspergilli into two genes for separate proteins. Aspergillus nidulans CandA-N blocks the neddylation site, and CandA-C inhibits the interaction to the adaptor/substrate receptor subunits similar to the respective N-terminal and C-terminal parts of single Cand1. The pathogen Aspergillus fumigatus and related species express a CandA-C with a 190-amino-acid N-terminal extension domain encoded by an additional exon. This extension corresponds in most aspergilli, including A. nidulans, to a gene directly upstream of candA-C encoding a 20-kDa protein without human counterpart. This protein was named CandA-C1, because it is also required for the cellular deneddylation/neddylation cycle and can form a trimeric nuclear complex with CandA-C and CandA-N. CandA-C and CandA-N are required for asexual and sexual development and control a distinct secondary metabolism. CandA-C1 and the corresponding domain of A. fumigatus control spore germination, vegetative growth, and the repression of additional secondary metabolites. This suggests that the dissection of the conserved Cand1-encoding gene within the genome of aspergilli was possible because it allowed the integration of a fungus-specific protein required for growth into the CandA complex in two different gene set versions, which might provide an advantage in evolution. IMPORTANCE Aspergillus species are important for biotechnological applications, like the production of citric acid or antibacterial agents. Aspergilli can cause food contamination or invasive aspergillosis to immunocompromised humans or animals. Specific treatment is difficult due to limited drug targets and emerging resistances. The CandA complex regulates, as a receptor exchange factor, the activity and substrate variability of the ubiquitin labeling machinery for 26S proteasome-mediated protein degradation. Only Aspergillus species encode at least two proteins that form a CandA complex. This study shows that Aspergillus species had to integrate a third component into the CandA receptor exchange factor complex that is unique to aspergilli and required for vegetative growth, sexual reproduction, and activation of the ubiquitin labeling machinery. These features have interesting implications for the evolution of protein complexes and could make CandA-C1 an interesting candidate for target-specific drug design to control fungal growth without affecting the human ubiquitin-proteasome system.

Measuring the average shape of transition paths during the folding of a single biological molecule

Transition paths represent the parts of a reaction where the energy barrier separating products and reactants is crossed. They are essential to understanding reaction mechanisms, yet many of their properties remain unstudied. Here, we report measurements of the average shape of transition paths, studying the folding of DNA hairpins as a model system for folding reactions. Individual transition paths were detected in the folding trajectories of hairpins with different sequences held under tension in optical tweezers, and path shapes were computed by averaging all transitions in the time domain, 〈t(x)〉, or by averaging transitions of a given duration in the extension domain, 〈x(t|τ)〉τ. Whereas 〈t(x)〉 was close to straight, with only a subtle curvature, 〈x(t|τ)〉τhad more pronounced curvature that fit well to theoretical expectations for the dominant transition path, returning diffusion coefficients similar to values obtained previously from independent methods. Simulations suggested that 〈t(x)〉 provided a less reliable representation of the path shape than 〈x(t|τ)〉τ, because it was far more sensitive to the effects of coupling the molecule to the experimental force probe. Intriguingly, the path shape variance was larger for some hairpins than others, indicating sequence-dependent changes in the diversity of transition paths reflective of differences in the character of the energy barriers, such as the width of the barrier saddle-point or the presence of parallel paths through multiple barriers between the folded and unfolded states. These studies of average path shapes point the way forward for probing the rich information contained in path shape fluctuations.

Secreted amyloid-β precursor protein functions as a GABABR1a ligand to modulate synaptic transmission

Amyloid-β precursor protein (APP) is central to the pathogenesis of Alzheimer’s disease, yet its physiological function remains unresolved. Accumulating evidence suggests that APP has a synaptic function mediated by an unidentified receptor for secreted APP (sAPP). Here we show that the sAPP extension domain directly bound the sushi 1 domain specific to the γ-aminobutyric acid type B receptor subunit 1a (GABABR1a). sAPP-GABABR1a binding suppressed synaptic transmission and enhanced short-term facilitation in mouse hippocampal synapses via inhibition of synaptic vesicle release. A 17–amino acid peptide corresponding to the GABABR1a binding region within APP suppressed in vivo spontaneous neuronal activity in the hippocampus of anesthetized Thy1-GCaMP6s mice. Our findings identify GABABR1a as a synaptic receptor for sAPP and reveal a physiological role for sAPP in regulating GABABR1a function to modulate synaptic transmission.