SUMMARY: Imagine if we could simultaneously predict spatial protein expression in tissues from their routine Hematoxylin and Eosin (H&E) stained images, and create tissue images given protein expression profiles thus enabling virtual simulations of how protein expression alterations impact histology in complex diseases like cancer. Such an approach could lead to more informed diagnostic and therapeutic decisions for precision medicine at lower costs and shorter turnaround times, more detailed insights into underlying disease pathology as well as improvement in predictive and generative performance. In this study, we investigate the intricate correlation between protein expressions obtained from Hyperion mass cytometry and histopathological microstructures in conventional H&E stained glioblastoma (GBM) samples, unveiling morphological patterns and cellular-level spatial alterations associated with protein expression changes. To model these complex relationships, we propose a novel generative-predictive framework called Ouroboros for producing H&E images from protein expressions and simultaneously predicting protein expressions from H&E images. Our comprehensive sample-independent validation over 9920 tissue spots from 4 GBM samples encompassing visual image analysis, quantitative analysis, subspace alignment and perturbation experiments shows that the proposed generative-predictive approach offers significant improvements in predicting protein expression from images in comparison to baseline methods as well as accurate generation of virtual GBM sample images. This proof of concept study can contribute to advancing our understanding of histological responses to protein expression perturbations and lays the foundations for further developments in this area. AVAILABILITY AND IMPLEMENTATION: Implementation and associated data for the proposed approach are available at the URL: https://github.com/Srijay/Ouroboros.

MOTIVATION: The negative binomial distribution has been shown to be a good model for counts data from both bulk and single-cell RNA-sequencing (RNA-seq). Gaussian process (GP) regression provides a useful non-parametric approach for modelling temporal or spatial changes in gene expression. However, currently available GP regression methods that implement negative binomial likelihood models do not scale to the increasingly large datasets being produced by single-cell and spatial transcriptomics. RESULTS: The GPcounts package implements GP regression methods for modelling counts data using a negative binomial likelihood function. Computational efficiency is achieved through the use of variational Bayesian inference. The GP function models changes in the mean of the negative binomial likelihood through a logarithmic link function and the dispersion parameter is fitted by maximum likelihood. We validate the method on simulated time course data, showing better performance to identify changes in over-dispersed counts data than methods based on Gaussian or Poisson likelihoods. To demonstrate temporal inference, we apply GPcounts to single-cell RNA-seq datasets after pseudotime and branching inference. To demonstrate spatial inference, we apply GPcounts to data from the mouse olfactory bulb to identify spatially variable genes and compare to two published GP methods. We also provide the option of modelling additional dropout using a zero-inflated negative binomial. Our results show that GPcounts can be used to model temporal and spatial counts data in cases where simpler Gaussian and Poisson likelihoods are unrealistic. AVAILABILITY AND IMPLEMENTATION: GPcounts is implemented using the GPflow library in Python and is available at https://github.com/ManchesterBioinference/GPcounts along with the data, code and notebooks required to reproduce the results presented here. The version used for this paper is archived at https://doi.org/10.5281/zenodo.5027066. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.