Recent technology breakthrough in spatial molecular profiling has enabled the comprehensive molecular characterizations of single cells while preserving spatial information. It provides new opportunities to delineate how cells from different origins form tissues with distinctive structures and functions. One immediate question in analysis of spatial molecular profiling data is how to identify spatially variable genes. Most of the current methods build upon the geostatistical model with a Gaussian process that relies on selecting ad hoc kernels to account for spatial expression patterns. To overcome this potential challenge and capture more types of spatial patterns, we introduce a Bayesian approach to identify spatially variable genes via Ising model. The key idea is to use the energy interaction parameter of the Ising model to characterize spatial expression patterns. We use auxiliary variable Markov chain Monte Carlo algorithms to sample from the posterior distribution with an intractable normalizing constant in the Ising model. Simulation results show that our energy-based modeling approach led to higher accuracy in detecting spatially variable genes than those kernel-based methods. Applying our method to two real spatial transcriptomics datasets, we discovered novel spatial patterns that shed light on the biological mechanisms. The proposed method presents a new perspective for analyzing spatial transcriptomics data.
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