CLAMP: Steady-State ODE Inference of Gene Regulatory Networks from Single-Cell Perturbations

Recovering mechanistic gene regulatory networks from single-cell interventional data is a fundamental challenge of computational biology. While ordinary differential equations (ODEs) offer an interpretable framework, existing single-cell ODE methods primarily target temporal trajectories rather than the steady-state transcriptomic snapshots provided by certain high-throughput CRISPR Perturb-seq protocols. To bridge this gap, we introduce CLAMP, a differentiable framework that reframes sustained genetic perturbation as a coordinate constraint on a Hill-kinetics regulatory network. By clamping perturbed genes to their observed expression and computing implicit gradients through a fixed-point solver, CLAMP jointly fits a single shared regulatory adjacency across all single-gene conditions. This formulation naturally resolves $k$-gene perturbations as $k$ simultaneous clamps, enabling compositional prediction without combinatorial training data. CLAMP is also encoder-agnostic, comparing predicted and observed states through any frozen and differentiable encoder. Evaluated on the Norman 2019 dataset, CLAMP accurately predicts non-additive combinatorial effects and structurally aligns with independent ChIP-seq and lineage signatures. Deploying CLAMP as a mechanistic probe further reveals that current single-cell foundation models struggle to preserve the geometric directions where regulatory signal lives, providing a structural explanation for their performance on perturbation prediction tasks.