Abstract

We expand the standard fluorescence recovery after photobleaching (FRAP) model introduced by Axelrod et al. in 1976. Our goal is to capture some of the following common artifacts observed in the fluorescence measurements obtained with a confocal laser scanning microscope in biofilms: 1) linear drift, 2) exponential decrease (due to bleaching during the measurements), 3) stochastic Gaussian noise, and 4) uncertainty in the exact time point of the onset of fluorescence recovery. To fit the resulting stochastic model to data from FRAP measurements and to estimate all unknown model parameters, we apply a suitably adapted Metropolis-Hastings algorithm. In this way, a more accurate estimation of the diffusion coefficient of the fluorophore is achieved. The method was tested on data obtained from FRAP measurements on a cultivated biofilm.

Highlights

  • Diffusion and mass transport in biofilms have been studied for decades yet have still not been understood completely

  • How does diffusion inside of the biofilm work? How are nutrients transported from one part of the biofilm to another, if any? How are products excreted? One way to look inside a biofilm is by usage of the confocal laser scanning microscope (CLSM) and the fluorescence recovery after photobleaching (FRAP) technique

  • Metropolis-Hastings analyses have been performed on two different models, i.e., on a FRAP model 1) with error model and 2) without error model; i.e., in this case, we fixed the parameters a1, b0, b1, s2, and s0 to their initial values given in Table 1

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Summary

Introduction

Diffusion and mass transport in biofilms have been studied for decades yet have still not been understood completely. They are presumed to play an important role in the resistance against antimicrobial agents and the secretion thereof [1]. There are different ways of mass transport into and inside a biofilm. How does diffusion inside of the biofilm work? One way to look inside a biofilm is by usage of the confocal laser scanning microscope (CLSM) and the fluorescence recovery after photobleaching (FRAP) technique. Because most of the substrates and products from microbial biofilms (e.g., glucose and lactic acid) do not have any viably detectable fluorescence, other sub-

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