CardamomOT: a mechanistic optimal transport-based framework for gene regulatory network inference, trajectory reconstruction and generative modeling

A key challenge in inferring gene regulatory networks (GRNs) governing cellular processes such as differentiation and reprogramming from experimental data lies in the impossibility of directly measuring protein dynamics at the single-cell level, which prevents establishing causal relationships between regulator activity and target responses. In earlier work, we introduced CARDAMOM, an algorithm that uses temporal snapshots of scRNA-seq data to calibrate a GRN-driven mechanistic model of gene expression. However, this method had several limitations: it could only rely on the relative ordering of time points rather than their exact labels, imposed restrictive quasi-stationary assumptions on protein dynamics, and depended on multiple hyperparameters. Here, we present CardamomOT, a new method based on the same mechanistic model that jointly reconstructs the GRN and unobserved protein trajectories from the data within a mechanistic optimal transport framework. By incorporating exact time labels and priors on protein kinetic rates from the literature, and substantially reducing the number of required hyperparameters, our approach addresses these limitations and substantially improves the accuracy and robustness of GRN calibration. We validate our framework on both in silico and experimental datasets, demonstrating computational scalability and consistently improved performance over state-of-the-art methods in both GRN and trajectory reconstruction. In particular, CardamomOT accurately recovers velocity fields driving cellular trajectories and unobserved protein levels, alongside reliable GRN structures. We also show that these improvements make the calibrated mechanistic model suitable to be used as a generative model to predict cellular responses to unseen perturbations. To our knowledge, this is among the first methods to explicitly integrate mechanistic GRN inference, trajectory reconstruction, and simulation of realistic datasets into a unified framework for scRNA-seq time series analysis.