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

Hock S, Hasenauer J, Theis FJ - BMC Bioinformatics (2013)

Bottom Line: However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters.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.

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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.

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Haptotaxis: Data and schematic description of the process. Haptotaxis: Data and schematic description of the process. (A) Fluorescence staining image taken from [7], which shows the Z-stack projection of non-permeabilized ear dermis stained for CCL21. Left image is the maximum intensity projection and the right image shows same staining as color-coded average projection. Lymphoid vessel boundaries are indicated by the blue dotted line (scale bars: 100µm). (B) Schematic of the dendritic haptotaxis process adapted from [6]. Dendritic cells move along a gradient of immobilized CCL21 towards the lymphatic vessels.
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Figure 1: Haptotaxis: Data and schematic description of the process. Haptotaxis: Data and schematic description of the process. (A) Fluorescence staining image taken from [7], which shows the Z-stack projection of non-permeabilized ear dermis stained for CCL21. Left image is the maximum intensity projection and the right image shows same staining as color-coded average projection. Lymphoid vessel boundaries are indicated by the blue dotted line (scale bars: 100µm). (B) Schematic of the dendritic haptotaxis process adapted from [6]. Dendritic cells move along a gradient of immobilized CCL21 towards the lymphatic vessels.

Mentions: Gradients of signaling molecules can be made visible in-vivo via antibody stainings (see Figure 1 and [5-7]). Combined with microscopy, this yields two-dimensional (2D) images. The color intensity of each pixel provides informations about the concentration (or the number) of signaling molecules. Modern microscopy devices can also generate stacks of images, providing information about the distribution of signaling molecules in three-dimensions (3D) [5,8].


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

Hock S, Hasenauer J, Theis FJ - BMC Bioinformatics (2013)

Haptotaxis: Data and schematic description of the process. Haptotaxis: Data and schematic description of the process. (A) Fluorescence staining image taken from [7], which shows the Z-stack projection of non-permeabilized ear dermis stained for CCL21. Left image is the maximum intensity projection and the right image shows same staining as color-coded average projection. Lymphoid vessel boundaries are indicated by the blue dotted line (scale bars: 100µm). (B) Schematic of the dendritic haptotaxis process adapted from [6]. Dendritic cells move along a gradient of immobilized CCL21 towards the lymphatic vessels.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750519&req=5

Figure 1: Haptotaxis: Data and schematic description of the process. Haptotaxis: Data and schematic description of the process. (A) Fluorescence staining image taken from [7], which shows the Z-stack projection of non-permeabilized ear dermis stained for CCL21. Left image is the maximum intensity projection and the right image shows same staining as color-coded average projection. Lymphoid vessel boundaries are indicated by the blue dotted line (scale bars: 100µm). (B) Schematic of the dendritic haptotaxis process adapted from [6]. Dendritic cells move along a gradient of immobilized CCL21 towards the lymphatic vessels.
Mentions: Gradients of signaling molecules can be made visible in-vivo via antibody stainings (see Figure 1 and [5-7]). Combined with microscopy, this yields two-dimensional (2D) images. The color intensity of each pixel provides informations about the concentration (or the number) of signaling molecules. Modern microscopy devices can also generate stacks of images, providing information about the distribution of signaling molecules in three-dimensions (3D) [5,8].

Bottom Line: However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters.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.

View Article: PubMed Central - HTML - PubMed

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.

Show MeSH