[Paper Review] Local contact inhibition leads to universal principles of cell population growth

Gregory J. Kimmel, Jeffrey West+3 more|arXiv (Cornell University)|Aug 23, 2021

Cellular Mechanics and Interactions38 references4 citations

TL;DR

This paper proposes a unifying mechanistic framework explaining universal cancer cell population growth laws through local contact inhibition, where density-dependent birth events driven by available space for division generate exponential, logistic, Gompertz, radial, and fractal growth patterns. The key contribution is the first mechanistic derivation of Gompertzian growth from contact inhibition, validated via agent-based simulations and experimental data fitting.

ABSTRACT

Cancer cell population dynamics often exhibit remarkably replicable, universal laws despite their underlying heterogeneity. Mechanistic explanations of universal cell population growth remain partly unresolved to this day, whereby population feedback between the microscopic and mesoscopic configurations can lead to macroscopic growth laws. We here present a unification under density-dependent birth events via contact inhibition. We consider five classical tumor growth laws: exponential, generalized logistic, Gompertz, radial growth, and fractal growth, which can be seen as manifestations of a single microscopic model. Our theory is substantiated by agent based simulations and can explain growth curve differences in experimental data from in vitro cancer cell population growth. Thus, our framework offers a possible explanation for the large number of mean-field laws that can adequately capture seemingly unrelated cancer or microbial growth dynamics.

Motivation & Objective

• To resolve the long-standing disconnect between descriptive growth laws and their biological mechanisms in cancer cell populations.
• To unify classical tumor growth models—exponential, generalized logistic, Gompertz, radial, and fractal—under a single microscopic mechanism.
• To demonstrate that contact inhibition, defined by local neighborhood size and density-dependent birth rates, generates macroscopic growth laws.
• To validate the model using agent-based simulations and in vitro experimental data from cancer cell lines.
• To provide a mechanistic explanation for the prevalence of Gompertzian growth in tumor dynamics.

Proposed method

• Modeling cell populations using agent-based simulations where each cell's proliferation depends on the number of accessible neighboring sites (birth neighborhood size ω).
• Defining a density-dependent birth rate λ_i,n based on the local availability of space, with ω_i representing the number of neighboring sites available for division.
• Deriving mean-field approximations of population growth by analyzing the dynamics of ω and λ under varying assumptions of spatial constraints.
• Fitting the model to in vitro cancer cell line data using power-law relationships between average birth neighborhood size ω and net growth rate λ, achieving an adjusted R² of 0.7.
• Introducing time-dependent dynamics for dead cell removal via an exponential decay process to model phagocytic clearance of necrotic cells.
• Extending the model to include spatially varying ω or λ through paracrine signaling, allowing for local regulation of proliferation capacity.

Experimental results

Research questions

• RQ1 Can a single microscopic mechanism—local contact inhibition—generate multiple classical macroscopic tumor growth laws?
• RQ2 How does the size of the local interaction region (ω) influence the emergence of different growth dynamics?
• RQ3 What is the mechanistic origin of Gompertzian growth in tumor populations, and can it be derived from spatial constraints?
• RQ4 Why do different cancer cell lines exhibit varying relationships between birth neighborhood size ω and net growth rate λ?
• RQ5 How do transitions from exponential to fractal or radial growth emerge from local spatial constraints?

Key findings

• The model successfully reproduces five classical growth laws—exponential, generalized logistic, Gompertz, radial, and fractal—under varying assumptions of contact inhibition and neighborhood size.
• A power-law relationship between average birth neighborhood size ω and net growth rate λ was identified, with an adjusted R² of 0.7 in fitting experimental data.
• The Gompertz model emerges as a limiting case when ω → 0 and r → r₀/ω, with rω = r₀ in the limit, providing the first mechanistic derivation of Gompertzian growth from contact inhibition.
• Fractal or radial growth dynamics arise naturally when ω is small relative to the system size, with the fractal dimension approaching d−1 as tumor size increases.
• The transition from exponential to non-exponential growth occurs when the tumor's surface area becomes limiting, with radial growth emerging when ω < L, the system domain length.
• Cell shape and adhesion may influence ω, with larger ω suggesting irregular shapes, and necrotic core formation can delay site availability through prolonged dead cell persistence.