One of the hallmarks of the cerebral cortex is the extreme diversity of interneurons. The two largest subtypes of cortical interneurons, parvalbumin- and somatostatin-positive cells, are morphologically and functionally distinct in adulthood but arise from common lineages within the medial ganglionic eminence.This makes them an attractive model for studying the generation of cell diversity. Here we examine how developmental changes in transcription and chromatin structure enable these cells to acquire distinct identities in the mouse cortex. Generic interneuron features are first detected upon cell cycle exit through the opening of chromatin at distal elements. By constructing cell-type-specific gene regulatory networks, we observed that parvalbumin- and somatostatin-positive cells initiate distinct programs upon settling within the cortex. We used these networks to model the differential transcriptional requirement of a shared regulator, Mef2c, and confirmed the accuracy of our predictions through experimental loss-of-function experiments. We therefore reveal how a common molecular program diverges to enable these neuronal subtypes to acquire highly specialized properties by adulthood. Our methods provide a framework for examining the emergence of cellular diversity, as well as for quantifying and predicting the effect of candidate genes on cell-type-specific development.
Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids) or when the solution is needed in the bulk, nearly-singular integrals must be evaluated at many targets. We show that precomputing a linear map from surface density to an effective source representation renders this task highly efficient, in the common case where each object is "simple", ie, its smooth boundary needs only moderately many nodes. We present a kernel-independent method needing only an upsampled smooth surface quadrature, and one dense factorization, for each distinct shape. No (near-)singular quadrature rules are needed. The resulting effective sources are drop-in compatible with fast algorithms, with no local corrections nor bookkeeping. Our extensive numerical tests include 2D FMM-based Helmholtz and Stokes BVPs with up to 1000 objects (281000 unknowns), and a 3D Laplace BVP with 10 ellipsoids separated by 1/30 of a diameter. We include a rigorous analysis for analytic data in 2D and 3D.
The cytoskeleton -- a collection of polymeric filaments, molecular motors, and crosslinkers -- is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here we present aLENS, a novel computational framework to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments -- molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate different mixtures of tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating self-emergent phenomena such as bundle formation and buckling, and elucidating how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of active matter aggregates.
A fast, high-order numerical method for the simulation of single-excitation states in quantum optics
We consider the numerical solution of a nonlocal partial differential equation which models the process of collective spontaneous emission in a two-level atomic system containing a single photon. We reformulate the problem as an integro-differential equation for the atomic degrees of freedom, and describe an efficient solver for the case of a Gaussian atomic density. The problem of history dependence arising from the integral formulation is addressed using sum-of-exponentials history compression. We demonstrate the solver on two systems of physical interest: in the first, an initially-excited atom decays into a photon by spontaneous emission, and in the second, a photon pulse is used to an excite an atom, which then decays.
Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries
A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as $1/|r|^\alpha$ with $\alpha$ close to $1$, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.
We present `latentcor`, an R package for correlation estimation from data with mixed variable types. Mixed variables types, including continuous, binary, ordinal, zero-inflated, or truncated data are routinely collected in many areas of science. Accurate estimation of correlations among such variables is often the first critical step in statistical analysis workflows. Pearson correlation as the default choice is not well suited for mixed data types as the underlying normality assumption is violated. The concept of semi-parametric latent Gaussian copula models, on the other hand, provides a unifying way to estimate correlations between mixed data types. The R package `latentcor` comprises a comprehensive list of these models, enabling the estimation of correlations between any of continuous/binary/ternary/zero-inflated (truncated) variable types. The underlying implementation takes advantage of a fast multi-linear interpolation scheme with an efficient choice of interpolation grid points, thus giving the package a small memory footprint without compromising estimation accuracy. This makes latent correlation estimation readily available for modern high-throughput data analysis.
Phase Retrieval with Holography and Untrained Priors: Tackling the Challenges of Low-Photon Nanoscale Imaging
Phase retrieval is the inverse problem of recovering a signal from magnitude-only Fourier measurements, and underlies numerous imaging modalities, such as Coherent Diffraction Imaging (CDI). A variant of this setup, known as holography, includes a reference object that is placed adjacent to the specimen of interest before measurements are collected. The resulting inverse problem, known as holographic phase retrieval, is well-known to have improved problem conditioning relative to the original. This innovation, i.e. Holographic CDI, becomes crucial at the nanoscale, where imaging specimens such as viruses, proteins, and crystals require low-photon measurements. This data is highly corrupted by Poisson shot noise, and often lacks low-frequency content as well. In this work, we introduce a dataset-free deep learning framework for holographic phase retrieval adapted to these challenges. The key ingredients of our approach are the explicit and flexible incorporation of the physical forward model into an automatic differentiation procedure, the Poisson log-likelihood objective function, and an optional untrained deep image prior. We perform extensive evaluation under realistic conditions. Compared to competing classical methods, our method recovers signal from higher noise levels and is more resilient to suboptimal reference design, as well as to large missing regions of low frequencies in the observations. To the best of our knowledge, this is the first work to consider a dataset-free machine learning approach for holographic phase retrieval.
Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows
In cellular vortical flows, namely arrays of counterrotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semirigid filaments long enough to broadly sample the vortical field. Using simulation, we find a surprising variety of long-time transport behavior—random walks, ballistic transport, and trapping—depending upon the filament’s relative length and effective flexibility. Moreover, we find that filaments execute Lévy walks whose diffusion exponents generally decrease with increasing filament length, until transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid filaments, whose dynamics is finite dimensional, show a surprising variety of transport states and chaos. Fast filament dispersal is related to an underlying geometry of “conveyor belts.” Evidence for these various transport states is found in experiments using arrays of counterrotating rollers, immersed in a fluid and transporting a flexible ribbon.
Application of ensemble pharmacophore-based virtual screening to the discovery of novel antimitotic tubulin inhibitors
Tubulin is a well-validated target for herbicides, fungicides, anti-parasitic, and anti-tumor drugs. Many of the non-cancer tubulin drugs bind to its colchicine site but no colchicine-site anticancer drug is available. The colchicine site is composed of three interconnected sub-pockets that fit their ligands and modify others’ preference, making the design of molecular hybrids (that bind to more than one sub-pocket) a difficult task. Taking advantage of the more than eighty published X-ray structures of tubulin in complex with ligands bound to the colchicine site, we generated an ensemble of pharmacophore representations that flexibly sample the interactional space between the ligands and target. We searched the ZINC database for scaffolds able to fit several of the subpockets, such as tetrazoles, sulfonamides and diarylmethanes, selected roughly 8000 compounds with favorable predicted properties. A Flexi-pharma virtual screening, based on ensemble pharmacophore, was performed by two different methodologies. Combining the scaffolds that best fit the ensemble pharmacophore-representation, we designed a new family of ligands, resulting in a novel tubulin modulator. We synthesized tetrazole 5 and tested it as a tubulin inhibitor in vitro. In good agreement with the design principles, it demonstrated micromolar activity against in vitro tubulin polymerization and nanomolar anti-proliferative effect against human epithelioid carcinoma HeLa cells through microtubule disruption, as shown by immunofluorescence confocal microscopy. The integrative methodology succedes in the design of new scaffolds for flexible proteins with structural coupling between pockets, thus expanding the way in which computational methods can be used as significant tools in the drug design process.
Motile cilia are slender, hair-like cellular appendages that spontaneously oscillate under the action of internal molecular motors and are typically found in dense arrays. These active filaments coordinate their beating to generate metachronal waves that drive long-range fluid transport and locomotion. Until now, our understanding of their collective behavior largely comes from the study of minimal models that coarse-grain the relevant biophysics and the hydrodynamics of slender structures. Here we build on a detailed biophysical model to elucidate the emergence of metachronal waves on millimeter scales from nanometer scale motor activity inside individual cilia. Our study of a 1D lattice of cilia in the presence of hydrodynamic and steric interactions reveals how metachronal waves are formed and maintained. We find that in homogeneous beds of cilia these interactions lead to multiple attracting states, all of which are characterized by an integer charge that is conserved. This even allows us to design initial conditions that lead to predictable emergent states. Finally, and very importantly, we show that in nonuniform ciliary tissues, boundaries and inhomogeneities provide a robust route to metachronal waves.