Extreme-mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole in a galactic core, are expected to be key sources for LISA. Modeling these systems with ...sufficient accuracy for LISA science requires going to second (or postadiabatic) order in gravitational self-force theory. Here we present a practical two-timescale framework for achieving this and generating postadiabatic waveforms. The framework comprises a set of frequency-domain field equations that apply on the fast, orbital timescale, together with a set of ordinary differential equations that determine the evolution on the slow, inspiral timescale. Our analysis is restricted to the special case of quasicircular orbits around a Schwarzschild black hole, but its general structure carries over to the realistic case of generic (inclined and eccentric) orbits in Kerr spacetime. In our restricted context, we also develop a tool that will be useful in all cases: a formulation of the frequency-domain field equations using hyperboloidal slicing, which significantly improves the behavior of the sources near the boundaries. We give special attention to the slow evolution of the central black hole, examining its impact on both the two-timescale evolution and the earlier self-consistent evolution scheme.
Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, ...second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this Letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.
Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are ...consistent with post-Newtonian calculations in the weak field, and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modeling extreme-mass-ratio inspirals and will be useful in modeling intermediate-mass-ratio systems.
Genomic and other high dimensional analyses often require one to summarize multiple related variables by a single representative. This task is also variously referred to as collapsing, combining, ...reducing, or aggregating variables. Examples include summarizing several probe measurements corresponding to a single gene, representing the expression profiles of a co-expression module by a single expression profile, and aggregating cell-type marker information to de-convolute expression data. Several standard statistical summary techniques can be used, but network methods also provide useful alternative methods to find representatives. Currently few collapsing functions are developed and widely applied.
We introduce the R function collapseRows that implements several collapsing methods and evaluate its performance in three applications. First, we study a crucial step of the meta-analysis of microarray data: the merging of independent gene expression data sets, which may have been measured on different platforms. Toward this end, we collapse multiple microarray probes for a single gene and then merge the data by gene identifier. We find that choosing the probe with the highest average expression leads to best between-study consistency. Second, we study methods for summarizing the gene expression profiles of a co-expression module. Several gene co-expression network analysis applications show that the optimal collapsing strategy depends on the analysis goal. Third, we study aggregating the information of cell type marker genes when the aim is to predict the abundance of cell types in a tissue sample based on gene expression data ("expression deconvolution"). We apply different collapsing methods to predict cell type abundances in peripheral human blood and in mixtures of blood cell lines. Interestingly, the most accurate prediction method involves choosing the most highly connected "hub" marker gene. Finally, to facilitate biological interpretation of collapsed gene lists, we introduce the function userListEnrichment, which assesses the enrichment of gene lists for known brain and blood cell type markers, and for other published biological pathways.
The R function collapseRows implements several standard and network-based collapsing methods. In various genomic applications we provide evidence that both types of methods are robust and biologically relevant tools.
Aerobic glycolysis (AG; i.e., nonoxidative metabolism of glucose despite the presence of abundant oxygen) accounts for 10%–12% of glucose used by the adult human brain. AG varies regionally in the ...resting state. Brain AG may support synaptic growth and remodeling; however, data supporting this hypothesis are sparse. Here, we report on investigations on the role of AG in the human brain. Meta-analysis of prior brain glucose and oxygen metabolism studies demonstrates that AG increases during childhood, precisely when synaptic growth rates are highest. In resting adult humans, AG correlates with the persistence of gene expression typical of infancy (transcriptional neoteny). In brain regions with the highest AG, we find increased gene expression related to synapse formation and growth. In contrast, regions high in oxidative glucose metabolism express genes related to mitochondria and synaptic transmission. Our results suggest that brain AG supports developmental processes, particularly those required for synapse formation and growth.
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•Brain aerobic glycolysis regionally relates to synaptic growth gene expression•Oxidative glycolysis instead relates to mitochondria and synaptic transmission•In humans, whole-brain aerobic glycolysis peaks during childhood•Neotenous regions of the adult brain maintain relatively high aerobic glycolysis
The human brain, especially that of children, has a high basal metabolic rate. Aerobic glycolysis (AG; nonoxidative metabolism of glucose despite abundant oxygen) accounts for 10%–12% of brain glucose consumption in adults. Here, Goyal et al. report that, in resting adults, AG correlates with the persistence of gene expression typical of infancy (transcriptional neoteny) and supports developmental processes required for synapse formation and neurite growth.
The human cerebral cortex has tremendous cellular diversity. How different cell types are organized in the human cortex and how cellular organization varies across species remain unclear. In this ...study, we performed spatially resolved single-cell profiling of 4000 genes using multiplexed error-robust fluorescence in situ hybridization (MERFISH), identified more than 100 transcriptionally distinct cell populations, and generated a molecularly defined and spatially resolved cell atlas of the human middle and superior temporal gyrus. We further explored cell-cell interactions arising from soma contact or proximity in a cell type-specific manner. Comparison of the human and mouse cortices showed conservation in the laminar organization of cells and differences in somatic interactions across species. Our data revealed human-specific cell-cell proximity patterns and a markedly increased enrichment for interactions between neurons and non-neuronal cells in the human cortex.
Because mouse models play a crucial role in biomedical research related to the human nervous system, understanding the similarities and differences between mouse and human brain is of fundamental ...importance. Studies comparing transcription in human and mouse have come to varied conclusions, in part because of their relatively small sample sizes or underpowered methodologies. To better characterize gene expression differences between mouse and human, we took a systems-biology approach by using weighted gene coexpression network analysis on more than 1,000 microarrays from brain. We find that global network properties of the brain transcriptome are highly preserved between species. Furthermore, all modules of highly coexpressed genes identified in mouse were identified in human, with those related to conserved cellular functions showing the strongest between-species preservation. Modules corresponding to glial and neuronal cells were sufficiently preserved between mouse and human to permit identification of cross species cell-class marker genes. We also identify several robust human-specific modules, including one strongly correlated with measures of Alzheimer disease progression across multiple data sets, whose hubs are poorly-characterized genes likely involved in Alzheimer disease. We present multiple lines of evidence suggesting links between neurodegenerative disease and glial cell types in human, including human-specific correlation of presenilin-1 with oligodendrocyte markers, and significant enrichment for known neuro-degenerative disease genes in microglial modules. Together, this work identifies convergent and divergent pathways in mouse and human, and provides a systematic framework that will be useful for understanding the applicability of mouse models for human brain disorders.
Transcriptomic profiling of complex tissues by single-nucleus RNA-sequencing (snRNA-seq) affords some advantages over single-cell RNA-sequencing (scRNA-seq). snRNA-seq provides less biased cellular ...coverage, does not appear to suffer cell isolation-based transcriptional artifacts, and can be applied to archived frozen specimens. We used well-matched snRNA-seq and scRNA-seq datasets from mouse visual cortex to compare cell type detection. Although more transcripts are detected in individual whole cells (~11,000 genes) than nuclei (~7,000 genes), we demonstrate that closely related neuronal cell types can be similarly discriminated with both methods if intronic sequences are included in snRNA-seq analysis. We estimate that the nuclear proportion of total cellular mRNA varies from 20% to over 50% for large and small pyramidal neurons, respectively. Together, these results illustrate the high information content of nuclear RNA for characterization of cellular diversity in brain tissues.
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of ...large scales, discussed in Pound Phys. Rev. D 92, 104047 (2015). Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.
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