Gene trajectory inference for single-cell data by optimal transport metrics.

Single-cell RNA sequencing has been widely used to investigate cell state transitions and gene dynamics of biological processes. Current strategies to infer the sequential dynamics of genes in a process typically rely on constructing cell pseudotime through cell trajectory inference. However, the presence of concurrent gene processes in the same group of cells and technical noise can obscure the true progression of the processes studied. To address this challenge, we present GeneTrajectory, an approach that identifies trajectories of genes rather than trajectories of cells. Specifically, optimal transport distances are calculated between gene distributions across the cell-cell graph to extract gene programs and define their gene pseudotemporal order. Here we demonstrate that GeneTrajectory accurately extracts progressive gene dynamics in myeloid lineage maturation. Moreover, we show that GeneTrajectory deconvolves key gene programs underlying mouse skin hair follicle dermal condensate differentiation that could not be resolved by cell trajectory approaches. GeneTrajectory facilitates the discovery of gene programs that control the changes and activities of biological processes.

Spatiotemporally heterogeneous coordination of cholinergic and neocortical activity.

Variation in an animal's behavioral state is linked to fluctuations in brain activity and cognitive ability. In the neocortex, state-dependent circuit dynamics may reflect neuromodulatory influences such as that of acetylcholine (ACh). Although early literature suggested that ACh exerts broad, homogeneous control over cortical function, recent evidence indicates potential anatomical and functional segregation of cholinergic signaling. In addition, it is unclear whether states as defined by different behavioral markers reflect heterogeneous cholinergic and cortical network activity. Here, we perform simultaneous, dual-color mesoscopic imaging of both ACh and calcium across the neocortex of awake mice to investigate their relationships with behavioral variables. We find that higher arousal, categorized by different motor behaviors, is associated with spatiotemporally dynamic patterns of cholinergic modulation and enhanced large-scale network correlations. Overall, our findings demonstrate that ACh provides a highly dynamic and spatially heterogeneous signal that links fluctuations in behavior to functional reorganization of cortical networks.

Decomposing a deterministic path to mesenchymal niche formation by two intersecting morphogen gradients.

Organ formation requires integrating signals to coordinate proliferation, specify cell fates, and shape tissue. Tracing these events and signals remains a challenge, as intermediate states across many critical transitions are unresolvable over real time and space. Here, we designed a unique computational approach to decompose a non-linear differentiation process into key components to resolve the signals and cell behaviors that drive a rapid transition, using the hair follicle dermal condensate as a model. Combining scRNA sequencing with genetic perturbation, we reveal that proliferative Dkk1+ progenitors transiently amplify to become quiescent dermal condensate cells by the mere spatiotemporal patterning of Wnt/ß-catenin and SHH signaling gradients. Together, they deterministically coordinate a rapid transition from proliferation to quiescence, cell fate specification, and morphogenesis. Moreover, genetically repatterning these gradients reproduces these events autonomously in "slow motion" across more intermediates that resolve the process. This analysis unravels two morphogen gradients that intersect to coordinate events of organogenesis.

Biwhitening Reveals the Rank of a Count Matrix.

Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the spectral properties of large noise matrices. However, utilizing such tools is not straightforward when the data matrix consists of count random variables, e.g., Poisson, in which case the noise can be heteroskedastic with an unknown variance in each entry. In this work, we focus on a Poisson random matrix with independent entries and propose a simple procedure, termed biwhitening, for estimating the rank of the underlying signal matrix (i.e., the Poisson parameter matrix) without any prior knowledge. Our approach is based on the key observation that one can scale the rows and columns of the data matrix simultaneously so that the spectrum of the corresponding noise agrees with the standard Marchenko-Pastur (MP) law, justifying the use of the MP upper edge as a threshold for rank selection. Importantly, the required scaling factors can be estimated directly from the observations by solving a matrix scaling problem via the Sinkhorn-Knopp algorithm. Aside from the Poisson, our approach is extended to families of distributions that satisfy a quadratic relation between the mean and the variance, such as the generalized Poisson, binomial, negative binomial, gamma, and many others. This quadratic relation can also account for missing entries in the data. We conduct numerical experiments that corroborate our theoretical findings, and showcase the advantage of our approach for rank estimation in challenging regimes. Furthermore, we demonstrate the favorable performance of our approach on several real datasets of single-cell RNA sequencing (scRNA-seq), High-Throughput Chromosome Conformation Capture (Hi-C), and document topic modeling.

Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise.

A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix by the Gaussian kernel with pairwise distances, and to follow with a certain normalization (e.g. the row-stochastic normalization or its symmetric variant). We demonstrate that the doubly-stochastic normalization of the Gaussian kernel with zero main diagonal (i.e., no self loops) is robust to heteroskedastic noise. That is, the doubly-stochastic normalization is advantageous in that it automatically accounts for observations with different noise variances. Specifically, we prove that in a suitable high-dimensional setting where heteroskedastic noise does not concentrate too much in any particular direction in space, the resulting (doubly-stochastic) noisy affinity matrix converges to its clean counterpart with rate m -1/2, where m is the ambient dimension. We demonstrate this result numerically, and show that in contrast, the popular row-stochastic and symmetric normalizations behave unfavorably under heteroskedastic noise. Furthermore, we provide examples of simulated and experimental single-cell RNA sequence data with intrinsic heteroskedasticity, where the advantage of the doubly-stochastic normalization for exploratory analysis is evident.

KLT picker: Particle picking using data-driven optimal templates.

Particle picking is currently a critical step in the cryo-EM single particle reconstruction pipeline. Despite extensive work on this problem, for many data sets it is still challenging, especially for low SNR micrographs. We present the KLT (Karhunen Loeve Transform) picker, which is fully automatic and requires as an input only the approximated particle size. In particular, it does not require any manual picking. Our method is designed especially to handle low SNR micrographs. It is based on learning a set of optimal templates through the use of multi-variate statistical analysis via the Karhunen Loeve Transform. We evaluate the KLT picker on publicly available data sets and present high-quality results with minimal manual effort.

Steerable Principal Components for Space-Frequency Localized Images.

As modern scientific image datasets typically consist of a large number of images of high resolution, devising methods for their accurate and efficient processing is a central research task. In this paper, we consider the problem of obtaining the steerable principal components of a dataset, a procedure termed "steerable PCA" (steerable principal component analysis). The output of the procedure is the set of orthonormal basis functions which best approximate the images in the dataset and all of their planar rotations. To derive such basis functions, we first expand the images in an appropriate basis, for which the steerable PCA reduces to the eigen-decomposition of a block-diagonal matrix. If we assume that the images are well localized in space and frequency, then such an appropriate basis is the prolate spheroidal wave functions (PSWFs). We derive a fast method for computing the PSWFs expansion coefficients from the images' equally spaced samples, via a specialized quadrature integration scheme, and show that the number of required quadrature nodes is similar to the number of pixels in each image. We then establish that our PSWF-based steerable PCA is both faster and more accurate then existing methods, and more importantly, provides us with rigorous error bounds on the entire procedure.