Publications

Segmentation of the Drosophila embryo is initiated by localized maternal signals. In this context, anteriorly localized Bicoid activates the gap genes in the anterior half of the embryo while posteriorly localized Nanos represses the translation of maternal hunchback mRNA to pattern the posterior half. The non-segmented termini are patterned by the localized activation of mitogen-activated protein kinase. Yet, the spatial extent of the terminal patterning system in regulating gap genes beyond poles remains unknown. We investigated the patterning potential of the terminal system using mutagenized embryos that lack both the anterior and the posterior maternal signaling systems. Using a combination of quantitative imaging and mathematical modeling, we analyzed the spatial patterns of gap genes in the early Drosophila embryo. We found that this mutant embryo develops symmetric cuticle patterns along the anteroposterior axis with two segments on each side. Notably, the terminal system can affect the expression of Krüppel in the torso region. Our mathematical model recapitulates the experimental data and reveals the potential bistability in the terminal patterning system. Collectively, our study suggests that the terminal system can act as a long-range inductive signal and establish multiple gene expression boundaries along the anteroposterior axis of the developing embryo.

The previously reported Q is a thermoresponsive coiled-coil protein capable of higher-order supramolecular assembly into fibers and hydrogels with upper critical solution temperature (UCST) behavior. Here, we introduce a new coiled-coil protein that is redesigned to disfavor lateral growth of its fibers and thus achieve a higher crosslinking density within the formed hydrogel. We also introduce a favorable hydrophobic mutation to the pore of the coiled-coil domain for increased thermostability of the protein. We note that an increase in storage modulus of the hydrogel and crosslinking density is coupled with a decrease in fiber diameter. We further fully characterize our α-helical coiled-coil (Q2) hydrogel for its structure, nano-assembly, and rheology relative to our previous single domain protein, Q, over the time of its gelation demonstrating the nature of our hydrogel self-assembly system. In this vein, we also characterize the ability of Q2 to encapsulate the small hydrophobic small molecule, curcumin, and its impact on the mechanical properties of Q2. The design parameters here not only show the importance of electrostatic potential in self-assembly but also provide a step towards predictable design of electrostatic protein interactions.

We survey the phase diagram of high-pressure molecular hydrogen with path integral molecular dynamics using a machine-learned interatomic potential trained with Quantum Monte Carlo forces and energies. Besides the HCP and C2/c-24 phases, we find two new stable phases both with molecular centers in the Fmmm-4 structure, separated by a molecular orientation transition with temperature. The high temperature isotropic Fmmm-4 phase has a reentrant melting line with a maximum at higher temperature (1450K at 150GPa) than previously estimated and crosses the liquid-liquid transition line around 1200K and 200GPa.

The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this can be accomplished by treating the boundary alone as an unknown curve. Alternatively, one can treat the entire object as unknown and use a more general volumetric representation, without making use of the known sound speed. Both lead to strongly nonlinear and nonconvex optimization problems for which recursive linearization provides a useful framework for numerical analysis. After extending our shape optimization approach developed earlier for impenetrable bodies, we carry out a systematic study of both methods and compare their performance on a variety of examples. Our findings indicate that the volumetric approach is more robust, even though the number of degrees of freedom is significantly larger. We conclude with a discussion of this phenomenon and potential directions for further research.

A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach extends to the oscillatory equations of mathematical physics, including the Helmholtz and Maxwell equations, but we will address these in a companion paper, since the nature of the problem is somewhat different and includes the consideration of quasiperiodic boundary conditions and resonances. Unlike lattice sum-based methods, the scheme is insensitive to the unit cell's aspect ratio and is easily coupled to adaptive fast multipole methods (FMMs). Our analysis relies on classical “plane-wave” representations of the fundamental solution, and yields an explicit low-rank representation of the field due to all image sources beyond the first layer of neighboring unit cells. When the aspect ratio of the unit cell is large, our scheme can be coupled with the nonuniform fast Fourier transform (NUFFT) to accelerate the evaluation of the induced field. Its performance is illustrated with several numerical examples.

First principle theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, specially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regime. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near L

LaRh

To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension, gives access to a synthetic 2D Chern number. It is, however, still unclear how the synthetic 2D Chern number is related to the Chern number that is defined from a parametric variable that evolves with time. Here we show that in periodically driven systems in the adiabatic limit, the synthetic 2D Chern number is a multiple of the Chern number defined from the parametric variable. The synthetic 2D Chern number can thus be engineered via how the parametric variable evolves in its own space. We justify our claims by investigating Thouless pumping in two 1D tight-binding models, a three-site chain model and a two-1D-sliding-chains model. The present findings could be extended to higher dimensions and other periodically driven configurations.

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous 1/f-noise at strong disorder.

We report on the strong field ionization of H2 by a corotating two-color laser field. We measure the electron momentum distribution in coincidence with the kinetic energy release (KER) of dissociating hydrogen molecules. In addition to a characteristic half-moon structure, we observe a low-energy structure in the electron momentum distribution at a KER of about 3.5 eV. We speculate that the outgoing electron interacts with the molecular ion, despite the absence of classical recollisions under these conditions. Time-dependent density functional theory simulations support our conclusions.