Caveat on the Boltzmann distribution function use in biology

TL;DR

This paper critically examines the widespread use of Boltzmann functions in biology, highlighting issues with their flexibility, fitting procedures, and statistical interpretation to ensure proper application in biological data analysis.

Contribution

It analyzes the limitations of Boltzmann functions in biological data fitting and discusses best practices for their statistical use and interpretation.

Findings

Boltzmann functions exhibit plasticity in data fitting.

Fitting procedures can lead to misleading interpretations.

Proper statistical methods are essential for valid conclusions.

Abstract

Sigmoid semilogarithmic functions with shape of Boltzmann equations, have become extremely popular to describe diverse biological situations. Part of the popularity is due to the easy avail- ability of software which fits Boltzmann functions to data, without much knowledge of the fitting procedure or the statistical properties of the parameters derived from the procedure. The purpose of this paper is to explore the plasticity of the Boltzmann function to fit data, some aspects of the optimization procedure to fit the function to data and how to use this plastic function to differentiate the effect of treatment on data and to attest the statistical significance of treatment effect on the data.