From Syntax to Semantics: Geometric Stability as the Missing Axis of Perturbation Biology

TL;DR

Drawing on Waddington's epigenetic landscape, geometric stability is proposed as a missing axis of evaluation: the directional coherence of cellular responses to perturbation that distinguishes interventions that guide cells coherently toward stable states from those that scatter them across the state manifold.

Abstract

The capacity to precisely edit genomes has outpaced our ability to predict the consequences. A cell can be genetically perfect and therapeutically useless: edited exactly as intended, yet unstable, drifting toward unintended fates, or selected for properties that compromise safety. This paradox reflects a deeper gap in how we evaluate biological intervention. Current frameworks excel at measuring what was done to a cell but remain blind to what the cell has become. We argue that this blindness stems from treating cells as collections of independent variables rather than as dynamical systems occupying positions on high-dimensional state manifolds. Drawing on Waddington's epigenetic landscape, we propose geometric stability as a missing axis of evaluation: the directional coherence of cellular responses to perturbation. This metric distinguishes interventions that guide cells coherently toward stable states from those that scatter them across the state manifold. Validation across diverse perturbation datasets reveals that geometric stability captures regulatory architecture invisible to conventional metrics, discriminating pleiotropic master regulators from lineage-specific factors without prior biological annotation. As precision medicine increasingly relies on cellular reprogramming, the question shifts from ``did the intervention occur?'' to ``is the resulting state stable?'' Geometric stability provides a framework for answering.

Figures (2)

• Figure 1: The Geometric Tax: linear metrics obscure biological stability.a. Standard dimensionality reduction projects high-dimensional cell states onto a flat plane (Linear Illusion, inset), where two populations (blue, red) appear to overlap, suggesting similar phenotypes. Mapping these populations onto the underlying biological manifold (Manifold Reality) reveals distinct stability properties invisible to linear projections. The blue population occupies a deep valley (high barrier), representing a robust cell state resistant to perturbation. The red population sits on a shallow ridge (low barrier), representing an unstable state prone to drift. This stability difference constitutes the Geometric Tax of engineering cells into non-native configurations. b. Geometric stability quantified through perturbation coherence. High-stability perturbations (left, e.g., KLF1) produce shift vectors that align coherently, indicating cells move together along a shared trajectory toward the mean direction (solid arrow). Low-stability perturbations (right, e.g., CEBPA) scatter cells in divergent directions despite similar magnitude shifts, with the mean direction (dashed arc) representing dispersed cellular responses. The Shesha stability score (Sp) captures this distinction as the mean cosine similarity between individual shift vectors and the population mean. Together, panels a and b demonstrate how manifold curvature, invisible to linear projections, determines whether perturbations produce stable or fragile cellular states.
• Figure 2: Geometric stability validated across CRISPR datasets and linked to cellular stress.a. Magnitude-stability relationship in Norman et al. CRISPRa dataset norman2019exploring ($n=236$ perturbations). Shesha stability score correlates strongly with effect magnitude (Spearman $\rho=0.953$, $p<10^{-100}$). Color indicates local perturbation density. Dashed line shows linear fit. b. Independent validation in the Replogle et al. genome-scale CRISPRi screen Replogle2022 (K562 cells). Point color indicates discordance (deviation from expected stability given magnitude); point size indicates cell count per perturbation. Labeled genes illustrate biological interpretation: BLVRB (biliverdin reductase, metabolic) shows high stability relative to magnitude, consistent with pathway-specific effects. CEBPB (C/EBP family transcription factor) and CENPW (centromere protein) show low stability relative to magnitude, consistent with pleiotropic or cell-division-wide effects. BUB3 (spindle checkpoint) demonstrates that low stability is not merely a proxy for cell cycle arrest. Grey shading indicates 95% confidence interval. c. Functional consequence of geometric instability. Stability negatively correlates with DDIT3 expression (Spearman $\rho=-0.28$, $p=0.041$), a canonical marker of cellular stress Oyadomari2003. Perturbations producing incoherent cellular responses (low stability) induce elevated stress signatures. Point shading encodes stability (darker = higher). Linear fit shown with 95% confidence interval. Notably, no perturbations occupy the high-stability/high-stress quadrant, suggesting that geometric coherence is a prerequisite for cellular homeostasis.