Publications

Cerebellar granule cells, which constitute half the brain's neurons, supply Purkinje cells with contextual information necessary for motor learning, but how they encode this information is unknown. Here we show, using two-photon microscopy to track neural activity over multiple days of cerebellum-dependent eyeblink conditioning in mice, that granule cell populations acquire a dense representation of the anticipatory eyelid movement. Initially, granule cells responded to neutral visual and somatosensory stimuli as well as periorbital airpuffs used for training. As learning progressed, two-thirds of monitored granule cells acquired a conditional response whose timing matched or preceded the learned eyelid movements. Granule cell activity covaried trial by trial to form a redundant code. Many granule cells were also active during movements of nearby body structures. Thus, a predictive signal about the upcoming movement is widely available at the input stage of the cerebellar cortex, as required by forward models of cerebellar control.

Differential binding of transcription factors (TFs) at cis-regulatory loci drives the differentiation and function of diverse cellular lineages. Understanding the regulatory interactions that underlie cell fate decisions requires characterizing TF binding sites (TFBS) across multiple cell types and conditions. Techniques, e.g. ChIP-Seq can reveal genome-wide patterns of TF binding, but typically requires laborious and costly experiments for each TF-cell-type (TFCT) condition of interest. Chromosomal accessibility assays can connect accessible chromatin in one cell type to many TFs through sequence motif mapping. Such methods, however, rarely take into account that the genomic context preferred by each factor differs from TF to TF, and from cell type to cell type. To address the differences in TF behaviors, we developed Mocap, a method that integrates chromatin accessibility, motif scores, TF footprints, CpG/GC content, evolutionary conservation and other factors in an ensemble of TFCT-specific classifiers. We show that integration of genomic features, such as CpG islands improves TFBS prediction in some TFCT. Further, we describe a method for mapping new TFCT, for which no ChIP-seq data exists, onto our ensemble of classifiers and show that our cross-sample TFBS prediction method outperforms several previously described methods.

We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile "Extensor" particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rod-like particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau-deGennes Q-tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule/motor-protein systems. We apply the quasi-equilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a non-standard Q-tensor theory. We demonstrate through simulation that this "BQ-tensor" theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the BQ-tensor model to study the dynamics of Extensor suspensions in circular and bi-concave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment find novel dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In bi-concave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O(n) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples

We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations, the approach presented here is new and leads to a rigorous analysis of Wood's anomalies. These arise when illuminating a grating at specific combinations of the angle of incidence and the frequency of the wave, for which the lattice sums diverge. They were discovered by Wood in 1902 as singularities in the spectral response. The primary tools in our approach are the Euler-Maclaurin formula and a steepest descent argument. The resulting algorithm has super-algebraic convergence and requires only milliseconds of CPU time.

We describe a modular approach to identify and inhibit protein–protein interactions (PPIs) that are mediated by protein secondary and tertiary structures with rationally designed peptidomimetics. Our analysis begins with entries of high-resolution complexes in the Protein Data Bank and utilizes conformational sampling, scoring, and design capabilities of advanced biomolecular modeling software to develop peptidomimetics.

Macronovae (kilonovae) that arise in binary neutron star mergers are powered by radioactive beta decay of hundreds of r-process nuclides. We derive, using Fermi's theory of beta decay, an analytic estimate of the nuclear heating rate. We show that the heating rate evolves as a power law ranging between t−6/5 and t−4/3. The overall magnitude of the heating rate is determined by the mean values of nuclear quantities, e.g. the nuclear matrix elements of beta decay. These values are specified by using nuclear experimental data. We discuss the role of higher order beta transitions and the robustness of the power law. The robust and simple form of the heating rate suggests that observations of the late-time bolometric light curve ∝ t−4/3 would be direct evidence of a r-process driven macronova. Such observations could also enable us to estimate the total amount of r-process nuclei produced in the merger.

Macronovae (kilonovae) that arise in binary neutron star mergers are powered by radioactive beta decay of hundreds of r-process nuclides. We derive, using Fermi's theory of beta decay, an analytic estimate of the nuclear heating rate. We show that the heating rate evolves as a power law ranging between t−6/5 to t−4/3. The overall magnitude of the heating rate is determined by the mean values of nuclear quantities, e.g., the nuclear matrix elements of beta decay. These values are specified by using nuclear experimental data. We discuss the role of higher order beta transitions and the robustness of the power law. The robust and simple form of the heating rate suggests that observations of the late-time bolometric light curve ∝t−43 would be a direct evidence of a r-process driven macronova. Such observations could also enable us to estimate the total amount of r-process nuclei produced in the merger.

We quantify the error in the results of mixed baryon--dark-matter hydrodynamic simulations, stemming from outdated approximations for the generation of initial conditions. The error at redshift 0 in contemporary large simulations, is of the order of few to ten percent in the power spectra of baryons and dark matter, and their combined total-matter power spectrum. After describing how to properly assign initial displacements and peculiar velocities to multiple species, we review several approximations: (1) {using the total-matter power spectrum to compute displacements and peculiar velocities of both fluids}, (2) scaling the linear redshift-zero power spectrum back to the initial power spectrum using the Newtonian growth factor ignoring homogeneous radiation, (3) using longitudinal-gauge velocities with synchronous-gauge densities, and (4) ignoring the phase-difference in the Fourier modes for the offset baryon grid, relative to the dark-matter grid. Three of these approximations do not take into account that dark matter and baryons experience a scale-dependent growth after photon decoupling, which results in directions of velocity which are not the same as their direction of displacement. We compare the outcome of hydrodynamic simulations with these four approximations to our reference simulation, all setup with the same random seed and simulated using Gadget-III.

The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning to com- putational physics. Here, we present a high-order accurate pseudo-spectral approach, applicable to closed surfaces of genus one in three dimensional space, with a view toward applications in plasma physics and fluid dynamics.