On the Calibration of a Size-Structured Population Model from Experimental Data

TL;DR

This paper reviews methods for reconstructing cell division rates from size distribution data and applies them to historical E. coli experimental data to validate the techniques and extract biological insights.

Contribution

It combines a survey of existing reconstruction techniques with their application to real experimental data for validation.

Findings

Reconstructed division rates reveal biologically relevant features.

Techniques remain effective despite old measurement technology.

Provides a validation framework for size-structured population models.

Abstract

The aim of this work is twofold. First, we survey the techniques developed in (Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2008) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the data reported in the classical work of Kubitschek [3] concerning Escherichia coli in vitro experiments measured by means of a Coulter transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah, Fla, USA.) Despite the rather old measurement technology, the reconstructed division rates still display potentially useful biological features.