# Estimating the division rate from indirect measurements of single cells

## TL;DR

This paper investigates how to estimate the division rate of bacteria based on indirect measurements of size, providing a theoretical reconstruction formula and demonstrating its effectiveness through numerical simulations and experimental data.

## Contribution

It introduces a method to estimate division rates from size data within the adder model, including a reconstruction formula and numerical validation.

## Key findings

- Reconstruction of division rate is feasible despite ill-posedness.
- Numerical methods yield satisfactory results on simulated data.
- Application to experimental data confirms practical utility.

## Abstract

Is it possible to estimate the dependence of a growing and dividing population on a given trait in the case where this trait is not directly accessible by experimental measurements, but making use of measurements of another variable? This article adresses this general question for a very recent and popular model describing bacterial growth, the so-called incremental or adder model. In this model, the division rate depends on the increment of size between birth and division, whereas the most accessible trait is the size itself. We prove that estimating the division 10 rate from size measurements is possible, we state a reconstruction formula in a deterministic and then in a statistical setting, and solve numerically the problem on simulated and experimental data. Though this represents a severely ill-posed inverse problem, our numerical results prove to be satisfactory.