A noble extended stochastic logistic model for cell proliferation with density-dependent parameters

Area of Science:

• Mathematical Biology
• Cell Biology
• Biophysics

Background:

• Cell proliferation is regulated by intrinsic proliferation rate (IPR) and inhibitory molecules.
• Existing models lack flexibility to capture complex density-dependent proliferation mechanisms.

Purpose of the Study:

• To propose an extended logistic growth law incorporating density-dependent IPR and negative feedback.
• To develop a stochastic analog for modeling environmental perturbations and heterogeneity.
• To introduce new measures for cell fitness and maximum sustainable stable cell density (MSSCD).

Main Methods:

• Developed an extended logistic growth law with density-dependent parameters.
• Incorporated environmental resistance and stochastic elements (multiplicative and additive noises).
• Fitted the model to real cell culture datasets and compared it with the standard logistic law.

Main Results:

• The extended model captures density-dependent cell cooperation and negative feedback.
• The model provides conditional MSSCD and a novel cell fitness measure.
• Demonstrated superiority over the logistic law when fitted to experimental data.
• Revealed probabilities of overproliferation, underproliferation, or decay based on parameter sets.

Conclusions:

• The proposed extended logistic growth law offers a more flexible and explanatory framework for cell proliferation.
• The model's parameters provide biological interpretations related to cell interactions and environmental influences.
• The stochastic analog enhances the model's applicability to real-world cell culture scenarios.