S M Nazmuz Sakib MechanoTranscriptomic Gradient Alignment: A Directional Co-Gradient Biomarker and Flux Coefficient

Abstract

Background: We introduce the S M Nazmuz Sakib MechanoTranscriptomic Gradient Alignment (MTGA) framework for solid tumors, formalizing a directional coupling between tissue stiffness gradients and malignant cell-state gradients.

Methods: The core statistic, the Sakib Alignment Index κS, averages the local cosine of the angle between ∇E stiffness) and ∇S (cell-state score) with scale-aware weighting; the companion Sakib Flux Coefficient μS estimates a signed mechanosensitivity slope relating ∇S to ∇E. We describe multi-scale estimation, spatially autocorrelated nulls, registration/stability diagnostics, and edge-versus-core enrichment.

Results: Using synthetic data and analysis-ready plotting primitives, we provide ten ready-to-compile illustrations.

Conclusion: Contextualized against durotaxis and spatial transcriptomics, and recent mechanotranscriptomic analytics, the framework appears conceptually novel: prior work studied stiffness heterogeneity and gene-expression gradients, but not a single directional alignment index nor a signed flux fit across tumor sections. We outline how to apply MTGA on AFM/MRE/SHG or force-inference layers co-registered to Visium-like grids, with spatially-constrained nulls via Moran spectral randomization.