Binding Pattern Reconstructions of FGF-FGFR Budding-Inducing Signaling in Reef-Building Corals

Reef-building corals play an important role in marine ecosystems. However, owing to climate change, ocean acidification, and predation by invasive crown-of-thorns starfish, these corals are declining. As marine animals comprise polyps, reproduction by asexual budding is pivotal in scleractinian coral growth. The fibroblast growth factor (FGF) signaling pathway is essential in coral budding morphogenesis. Here, we sequenced the full-length transcriptomes of four common and frequently dominant reef-building corals and screened out the budding-related FGF and FGFR genes. Thereafter, three-dimensional (3D) models of FGF and FGFR proteins as well as FGF-FGFR binding models were reconstructed. Based on our findings, the FGF8-FGFR3 binding models in Pocillopora damicornis, Montipora capricornis, and Acropora muricata are typical receptor tyrosine kinase-signaling pathways that are similar to the Kringelchen (FGFR) in hydra. However, in P. verrucosa, FGF8 is not the FGFR3 ligand, which is found in other hydrozoan animals, and its FGFR3 must be activated by other tyrosine kinase-type ligands. Overall, this study provides background on the potentially budding propagation signaling pathway activated by the applications of biological agents in reef-building coral culture that could aid in the future restoration of coral reefs.

Engineering spectral properties of non-interacting lattice Hamiltonians

We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

Coarse-grained tight-binding models

Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the blocks, ignoring states having large energy eigenvalues and retaining states with an energy close to the band edge energies. A numerical test using a GaAs/AlAs quantum well shows the computation time can be decreased to less than 5% of the full calculation with errors of less than 1%. We give data for the trade-offs between computing time and loss of accuracy. We also tested calculations of the density of states for a GaAs/AlAs quantum well and find a ten times speedup without much loss in accuracy.

Critical role of DNA unwinding and Cas9 conformational changes in modelling off-target effects

CRISPR-Cas9 off-target effects interfere with the ability to accurately perform genetic edits. To predict off-target effects CRISPR-Cas9 researchers perform high throughput guide RNA mismatch and bulge experiments and then use the data to fit thermodynamic binding models. While impactful from an engineering perspective such models are not based on the experimentally observed target interrogation process and thus incorrectly measure the energetic effects mismatches have on the system. In this work we convert an experimentally deduced qualitive model of target interrogation to a linear ODE model and demonstrate that the mismatch tolerance patterns observed in experiments do not need to be caused by differences in energetic penalties of mismatches but rather are emergent effects of the timing and coordination of target DNA unwinding and Cas9 conformational changes.