Identifying temporal and spatial patterns of variation from multimodal data using MEFISTO

• Method: MEFISTO (Multi-omics Factor Analysis Informed by Spatial and Temporal Omics) is an extension of MOFA that uses Gaussian Process (GP) priors on latent factors to model spatial or temporal dependencies between samples.
• Key Capabilities: It performs spatio-temporally informed dimensionality reduction, allowing factors to change smoothly over time/space. It also enables robust interpolation of data for unobserved locations or time points.
• Application: MEFISTO successfully analyzed data from spatial transcriptomics, longitudinal microbiome studies, and single-cell multi-omics atlases to align and extract common developmental or temporal patterns.

PubMed: 35027765 DOI: 10.1038/s41592-021-01343-9 Overview generated by: Gemini 2.5 Flash, 27/11/2025

Background and Objective

Factor analysis, as implemented in tools like MOFA (Multi-Omics Factor Analysis), is widely used for dimensionality reduction and multi-omics integration. However, these models traditionally assume that samples are independent of one another. This assumption fails in modern high-resolution biological studies that profile molecular data with temporal (time-series) or spatial dependencies (e.g., spatial transcriptomics, longitudinal cohorts, developmental atlases).

This paper introduces MEFISTO (Multi-omics Factor Analysis Informed by Spatial and Temporal Omics), an extension of the MOFA framework, designed to: 1. Perform factor analysis while explicitly accounting for spatial or temporal dependencies between samples. 2. Perform spatio-temporally informed dimensionality reduction and imputation on high-dimensional multi-omics data. 3. Separate smooth (e.g., developmental trajectory) from non-smooth (e.g., technical noise) patterns of variation.

Methods: The MEFISTO Framework

Core Algorithm and Innovation

MEFISTO maintains the core latent factor model of MOFA, where data from different omics layers is modeled as a linear combination of shared latent factors. The key innovation is how it models these latent factors:

• Spatio-Temporal Prior: MEFISTO incorporates a Gaussian Process (GP) prior on the factor values. This GP prior allows the factors to be smooth functions of the observed spatial or temporal coordinates (i.e., time points, spatial locations).
• Modeling Dependencies: By using the GP prior, MEFISTO learns latent factors that are constrained to change gradually over space or time, which aligns with biological reality (e.g., developmental progression, cellular diffusion). Factors not relevant to the spatial/temporal axes are modeled with a non-smooth prior.
• Joint Integration: Like MOFA, MEFISTO can integrate data from multiple omics modalities measured on the same samples and simultaneously identify shared and modality-specific sources of variation.

Applications

MEFISTO was validated across diverse datasets with structured dependencies: 1. Spatial Transcriptomics: Applied to mouse organ data to reconstruct the spatial organization of gene expression. 2. Longitudinal Microbiome Study: Used to capture smooth temporal changes in the gut microbiome. 3. Single-Cell Multi-Omics: Applied to a mouse gastrulation atlas to align complex single-cell transcriptomic and epigenetic data along a developmental pseudotime axis.

Key Results and Capabilities

Informed Dimensionality Reduction

In all applications, MEFISTO successfully found latent factors that were biologically relevant and showed a smooth progression across the given time points or spatial coordinates.

Interpolation and Imputation

The GP prior allows MEFISTO to perform robust interpolation—predicting factor values and corresponding omics data for unobserved time points or spatial locations. This is crucial for filling gaps in time-series experiments.

Data Alignment

MEFISTO’s ability to identify underlying common factors makes it excellent for aligning multiple related datasets. For instance, it can align single-cell data from different samples or studies onto a common developmental trajectory, identifying the shared underlying factors of biological variation.

Conclusions and Significance

MEFISTO is a versatile and essential tool for the analysis of modern biological data that contains temporal or spatial structure. By incorporating Gaussian Process priors into the factor analysis framework, it overcomes the independence assumption of classical methods.

MEFISTO’s capabilities in spatio-temporally informed dimensionality reduction, interpolation, and multi-dataset alignment make it a powerful method for extracting meaningful, smooth biological patterns from complex single-cell and multi-omics atlases.