With the growing number of single-cell datasets collected under more complex experimental conditions, there is an opportunity to leverage single-cell variability to reveal deeper insights into how cells respond to perturbations. Many existing approaches rely on discretizing the data into clusters for differential gene expression (DGE), effectively ironing out any information unveiled by the single-cell variability across cell-types. In addition, DGE often assumes a statistical distribution that, if erroneous, can lead to false positive differentially expressed genes. Here, we present Cellograph: a semi-supervised framework that uses graph neural networks to quantify the effects of perturbations at single-cell granularity. Cellograph not only measures how prototypical cells are of each condition but also learns a latent space that is amenable to interpretable data visualization and clustering. The learned gene weight matrix from training reveals pertinent genes driving the differences between conditions. We demonstrate the utility of our approach on publicly-available datasets including cancer drug therapy, stem cell reprogramming, and organoid differentiation. Cellograph outperforms existing methods for quantifying the effects of experimental perturbations and offers a novel framework to analyze single-cell data using deep learning.

Modern datasets often exhibit high dimensionality, yet the data reside in low-dimensional manifolds that can reveal underlying geometric structures critical for data analysis. A prime example of such a dataset is a collection of cell cycle measurements, where the inherently cyclical nature of the process can be represented as a circle or sphere. Motivated by the need to analyze these types of datasets, we propose a nonlinear dimension reduction method, Spherical Rotation Component Analysis (SRCA), that incorporates geometric information to better approximate low-dimensional manifolds. SRCA is a versatile method designed to work in both high-dimensional and small sample size settings. By employing spheres or ellipsoids, SRCA provides a low-rank spherical representation of the data with general theoretic guarantees, effectively retaining the geometric structure of the dataset during dimensionality reduction. A comprehensive simulation study, along with a successful application to human cell cycle data, further highlights the advantages of SRCA compared to state-of-the-art alternatives, demonstrating its superior performance in approximating the manifold while preserving inherent geometric structures.

Individual cells show variability in their signaling dynamics that often correlates with phenotypic responses, indicating that cell-to-cell variability is not merely noise but can have functional consequences. Based on this observation, we reasoned that cell-to-cell variability under the same treatment condition could be explained in part by a single signaling motif that maps different upstream signals into a corresponding set of downstream responses. If this assumption holds, then repeated measurements of upstream and downstream signaling dynamics in a population of cells could provide information about the underlying signaling motif for a given pathway, even when no prior knowledge of that motif exists. To test these two hypotheses, we developed a computer algorithm called MISC (Motif Inference from Single Cells) that infers the underlying signaling motif from paired time-series measurements from individual cells. When applied to measurements of transcription factor and reporter gene expression in the yeast stress response, MISC predicted signaling motifs that were consistent with previous mechanistic models of transcription. The ability to detect the underlying mechanism became less certain when a cell's upstream signal was randomly paired with another cell's downstream response, demonstrating how averaging time-series measurements across a population obscures information about the underlying signaling mechanism. In some cases, motif predictions improved as more cells were added to the analysis. These results provide evidence that mechanistic information about cellular signaling networks can be systematically extracted from the dynamical patterns of single cells.

A defining characteristic of living cells is the ability to respond dynamically to external stimuli while maintaining homeostasis under resting conditions. Capturing both of these features in a single kinetic model is difficult because the model must be able to reproduce both behaviors using the same set of molecular components. Here, we show how combining small, well-defined steady-state networks provides an efficient means of constructing large-scale kinetic models that exhibit realistic resting and dynamic behaviors. By requiring each kinetic module to be homeostatic (at steady state under resting conditions), the method proceeds by (i) computing steady-state solutions to a system of ordinary differential equations for each module, (ii) applying principal component analysis to each set of solutions to capture the steady-state solution space of each module network, and (iii) combining optimal search directions from all modules to form a global steady-state space that is searched for accurate simulation of the time-dependent behavior of the whole system upon perturbation. Importantly, this stepwise approach retains the nonlinear rate expressions that govern each reaction in the system and enforces constraints on the range of allowable concentration states for the full-scale model. These constraints not only reduce the computational cost of fitting experimental time-series data but can also provide insight into limitations on system concentrations and architecture. To demonstrate application of the method, we show how small kinetic perturbations in a modular model of platelet P2Y(1) signaling can cause widespread compensatory effects on cellular resting states.