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This article is part of the supplement: Selected articles from the 10th International Workshop on Computational Systems Biology (WCSB) 2013: Bioinformatics

Open Access Research

Modeling of 2D diffusion processes based on microscopy data: parameter estimation and practical identifiability analysis

Sabrina Hock12, Jan Hasenauer12 and Fabian J Theis12*

Author Affiliations

1 Institute of Computational Biology, Helmholtz Center Munich, Ingolstädter Landstr. 1, 85764 Neuherberg, Germany

2 Department of Mathematics, Technische Universität München, Boltzmannstr.3, 85747 Garching, Germany

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BMC Bioinformatics 2013, 14(Suppl 10):S7  doi:10.1186/1471-2105-14-S10-S7

Published: 12 August 2013

Abstract

Background

Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters.

Methods

We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes.

Results and conclusion

As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods.