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arXiv · 2607.00480

Exponential Sigmoid Equation for Modelling Cell Growth in a Confined Space, Log-Normal Distribution for Modelling Cell Area Distribution of Dense Colonies and Other Methods

Kavinda Jayawardana·Brad Turner
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Abstract

Based on the growth patterns of 166 CHO monoclones observed over a 15 day period, we show that the standard population growth in a confined space equation, i.e. the sigmoid/logistic function, is alone does not capture the complex behaviour of the cell growth in a confined space. Thus, combining the sigmoid function and the exponential of the sigmoid function, we present a more accurate model for modelling cell growth in a confined space. We also present a working algorithm to obtain population growth variables (growth capacity, growth time and growth rate), model the growth patterns of the CHO monoclones, and we include subset of the dataset, along with a sample python script for the reader to replicate the results. Furthermore, we derive a model for cell confluence growth in a confined space, numerically model the confluence and present the reader with a working algorithm. With Kolmogorov-Smirnov analysis conducted on the area of the CHO monoclones, we show that the cell area of the incipient population is normally distributed, the sparse cell population is gamma distributed and the dense colony population is log-normally distributed. Thus, we further derive models for the mean, the standard deviation, the coefficient of variation and the inverse coefficient of variation for the log cell area growth in a confined space, numerically model them and present the reader with working algorithms. Finally, based on the growth patterns of another 48 CHO monoclones observed over a 16 day period, and their titer and viability measurements, we find the correlation coefficients with our calculated growth variables, and titer and viability measurements, and show that our derived growth variables can be used to predict the productivity and the health of a cell. Thus, we conclude our study by demonstrating that the productivity and the health of a cell (also the overall population) are interdependent.

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Kavinda Jayawardana, Brad Turner. 2026-07-01. Exponential Sigmoid Equation for Modelling Cell Growth in a Confined Space, Log-Normal Distribution for Modelling Cell Area Distribution of Dense Colonies and Other Methods. https://arxiv.org/abs/2607.00480

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