What question did this study set out to answer?

To develop a unified mathematical framework to describe a eukaryotic adherent cell as a coupled dynamical system.

May 12, 2026Open Access

11 Cell Skeleton Phisics & Geometry Mathematical Bio-Computational Engine

Key Points

To develop a unified mathematical framework to describe a eukaryotic adherent cell as a coupled dynamical system.
Decomposed the cell into 11 structural subcomponents characterized by a 6-dimensional geometric state vector.
Utilized a nonlinear ordinary differential equation (ODE) driven by a coupling matrix.
Extended the state to include biochemical fields such as ATP, Ca²⁺, pH, and other cellular parameters.
Defined the full geometric state of the cell in a 66-dimensional space, G_cell ∈ ℝ⁶⁶.

Abstract

Cell Skeleton Phisics & Geometry Mathematical Bio-Computational Engine. A unified mathematical framework describing a eukaryotic adherent cell as a coupled dynamical system. The cell is decomposed into **11 structural subcomponents**, each characterized by a 6-dimensional geometric state vector ` (L, A, V, σ, P, κ) `. The full geometric state `Gcell ∈ ℝ⁶⁶` evolves under a nonlinear ODE driven by a structured coupling matrix `Kcell ∈ ℝ⁶⁶ˣ⁶⁶`, scalar biochemical fields `Φ`, and nonlinear corrections. An extended state `Y ∈ ℝ⁷³` appends ATP, Ca²⁺, pH, cell volume, gene expression, polarity, and active transport flux. Test Results, Tests Scripts, Graphs, Tumor Math Scripts, Data Used From Literature, Digital Program Derived From the Architecture For Data Pipeline Analisis etc. Research Pupose, Open Invite Open Source Project

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