Inferring Metabolic States from Single Cell Transcriptomic Data via Geometric Deep Learning

Abstract

The ability to measure gene expression at single-cell resolution has elevated our understanding of how biological features emerge from complex and interdependent networks at molecular, cellular, and tissue scales. As technologies have evolved that complement scRNAseq measurements with things like single-cell proteomic, epigenomic, and genomic information, it becomes increasingly apparent how much biology exists as a product of multimodal regulation. Biological processes such as transcription, translation, and post-translational or epigenetic modification impose both energetic and specific molecular demands on a cell and are therefore implicitly constrained by the metabolic state of the cell. While metabolomics is crucial for defining a holistic model of any biological process, the chemical heterogeneity of the metabolome makes it particularly difficult to measure, and technologies capable of doing this at single-cell resolution are far behind other multiomics modalities. To address these challenges, we present GEFMAP (Gene Expression-based Flux Mapping and Metabolic Pathway Prediction), a method based on geometric deep learning for predicting flux through reactions in a global metabolic network using transcriptomics data, which we ultimately apply to scRNAseq. GEFMAP leverages the natural graph structure of metabolic networks to learn both a biological objective for each cell and estimate a mass-balanced relative flux rate for each reaction in each cell using novel deep learning models.

H. R. Steach and S. Viswanath—Co-lead author.

M. Perlmutter and S. Krishnaswamy—Co-senior author.

A Supplemental Information

1.1 A.1 Supplemental Methods

Source code, GEM files, datasets, and other resources are openly available at our Github repository (https://github.com/KrishnaswamyLab/metabolic_GNN).

Transcriptomic Data. Bulk RNA sequencing data was obtained from the Precision RNA-seq Expression Compendium for Independent Signal Exploration (PRECISE) [27] that was collected from 15 studies conducted in the same laboratory using a standardized protocol and includes information on experimental conditions and measured growth rates. The original data contains over 250 samples and approximately 150 experimental conditions, which we augmented to over 3000 samples by adding Gaussian noise to gene expression values.

Single cell RNA sequencing data from human embryoid body cells was obtained from [22]; filtering and normalization was done identically to the original publication.

Objective Function Prediction Network. The graph neural network used to infer the objective c takes in torch geometric graph objects as input and utilizes the RMSProp optimizer. For all experiments, a learning rate $lr = 0.0001$ trained on 3 epochs with a batch size of 80 as training parameters with a (60-20-20) train-test-validation split. For E. coli data the parameter $\beta$ in the loss function was set to 0.1, and for human EB data was set to 0.25.

Objective Function Solver Networks. All four flux prediction/estimation models utilize the Adam optimizer with a learning rate $lr = 0.01$ trained on 100 epochs. A train/test split of 80-20 is applied to the dataset. In order to compute the training losses, we use the mean squared error between the predicted and ground truth values. The performance metrics are computed by taking the mean and standard deviation of the Pearson Correlation Coefficient (PCC) between the predicted and ground truth values over 5 runs of each model.