A new study published in Applied Intelligence by Jiaming Liu and Qi Tan of South China Normal University and Pei Yang of South China University of Technology tackles exactly this challenge. The team proposes a framework called Condition-Controlled Optimal Transport, or CCOT, which models the transformation between unperturbed and perturbed cellular distributions as a mathematical transport problem. Rather than trying to pair individual cells across conditions, which is impossible with the available data, the method learns a mapping between entire probability distributions of gene expression states. The work, published as volume 56, article 470 of the journal, was supported by the National Natural Science Foundation of China and the Guangdong Basic and Applied Basic Research Foundation.

Optimal transport is a branch of mathematics with roots stretching back to Gaspard Monge in the eighteenth century, concerned with finding the most efficient way to move mass from one distribution to another. In recent years it has found fertile ground in machine learning, and in single-cell biology specifically, where researchers have used it to align datasets across conditions, modalities, and time points. The intuition is appealing: if a drug pushes a population of cells from one transcriptional state distribution to another, the most plausible transformation between those distributions can be framed as an optimal transport map. Learning that map from data then allows one to generate predictions of how a new population of cells will respond.

The central innovation of CCOT lies in its condition-controlled mechanism, which the authors describe as bridging conditional and unconditional models within the optimal transport framework. The idea echoes classifier-free guidance, a technique popularized in the image generation community, where a model is trained to operate both with and without conditioning information and the two modes are interpolated at inference time. In CCOT, the conditioning signal is the drug perturbation itself. By learning transport maps that can function with or without the drug condition, the framework gains a knob that controls how strongly the perturbation shapes the predicted cellular response, allowing the model to balance faithful in-distribution prediction against robust generalization.

Under the hood, CCOT leverages partially input convex neural networks to parameterize the transport maps. Input convex neural networks, introduced in the machine learning literature in 2017, are architectures whose outputs are convex functions of their inputs, a property that makes them natural candidates for computing optimal transport maps via the dual formulation of the transport problem. Prior work, including the supervised training of conditional Monge maps and neural optimal transport approaches for single-cell perturbation responses, established this connection. CCOT extends it by making the condition control explicit and by aligning the learned transport with biological priors, one of three key innovations the authors list alongside the condition-controlled mechanism and cross-drug generalization.

Cross-drug generalization is arguably the property with the greatest practical stakes. Drug discovery pipelines routinely need to prioritize candidate compounds, and experiments are expensive; a model that can only describe drugs it has already seen is of limited use. CCOT is designed to generalize to novel therapeutic compounds, predicting responses out-of-distribution rather than merely interpolating within the training data. This is a notoriously difficult setting, because a new molecule may act through mechanisms only partially represented in the training set, and models can easily fail by defaulting to memorized responses or by producing biologically implausible expression profiles.

The evaluation was carried out on SciPlex3, a benchmark dataset drawn from the massively multiplex chemical transcriptomics work published in Science in 2020, which profiles gene expression at single-cell resolution across many cell types, drugs, and doses. The authors report that CCOT significantly outperforms state-of-the-art methods in capturing complex and nonlinear cellular responses, with its advantage most evident in capturing higher-order statistical properties and gene-specific responses for differentially expressed genes. Because no ground-truth paired control and perturbed cells exist, the evaluation relies on distributional metrics, including maximum mean discrepancy, energy distance, perturbation signatures, the coefficient of determination, and the Fréchet Inception Distance, each probing a different aspect of how closely the predicted distribution matches the observed one.

The appendix results add useful nuance. Across the full 977-gene space, not just the top 50 differentially expressed genes, CCOT retains its advantage on the distribution-level metrics, improving out-of-distribution maximum mean discrepancy by 66 percent over the next best model, while a competing method, ChemCPA, holds a marginal and statistically insignificant lead on some moment-based metrics. Ablation studies underscore the architecture’s dependencies: removing the drug encoder proves catastrophic, driving the coefficient of determination to a dismal negative value, while removing the condition-control mechanism or the cell type alignment degrades every metric. The authors also document a sensitivity analysis of the inner iteration count, finding stable performance for values of five or greater but a performance collapse at fifteen due to the known instability of adversarial min-max optimization, and they settled on ten inner iterations to match baseline configurations exactly.

Training dynamics receive careful treatment as well. Because the dual potential losses in the min-max optimization are adversarial and oscillate rather than decrease monotonically, the team monitors maximum mean discrepancy on the in-distribution test set as the true indicator of distributional alignment, evaluating every fifty batches and selecting the checkpoint with the minimum value as an implicit early stopping mechanism. Over a fixed budget of 100,000 outer iterations, matching the defaults of the CELLOT and CondOT baselines for a strictly controlled comparison, the losses converge from large negative values toward zero with narrowing oscillations, and the best checkpoint was selected at iteration 98,400 within a stable plateau rather than during an unconverged descent.

The broader significance of this work sits at the intersection of generative machine learning and pharmacology. If models like CCOT can reliably predict how cells respond to compounds they have never seen, the implications range from cheaper pre-screening of drug candidates to mechanistic insight into how perturbations propagate through cellular signaling networks. The authors position the framework as a tool for advancing drug discovery and understanding cellular mechanisms, and they have made the complete source code, including training scripts, preprocessing steps, and evaluation code, publicly available on GitHub, with the datasets themselves drawn from publicly accessible repositories. As with any computational prediction, validation against new laboratory experiments remains the ultimate test, but the study offers a principled mathematical route through one of single-cell biology’s most persistent obstacles: predicting the future state of a cell that must be destroyed in order to be measured.

Subject of Research: Machine learning-based prediction of single-cell drug perturbation responses using optimal transport

Article Title: Condition-Controlled optimal transport for cellular perturbation response prediction

Article References: Liu, J., Tan, Q., & Yang, P. (2026). Condition-Controlled optimal transport for cellular perturbation response prediction. Applied Intelligence, 56(15), Article 470. https://doi.org/10.1007/s10489-026-07521-6

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07521-6

Keywords: single-cell sequencing, optimal transport, perturbation response prediction, drug discovery, input convex neural networks, classifier-free guidance, SciPlex3, gene expression, machine learning, computational biology, out-of-distribution generalization, ChemCPA