Complex models for the description of biological structures

Introduction

• Structural biology is of great interest to biologists because macromolecules carry out most of the functions of cells, and because it is only by coiling into specific three-dimensional shapes that they are able to perform these functions.
• Structure determination of large macromolecular assemblies is one of the main challenges in structural genomics. To date, only 1.5% of the structures in the Protein Data Bank (PDB) are of large macromolecular complexes. The reason is that X-ray crystallography, the most prolific and accurate technique for structure determination, has difficulties in the crystallization process of large and unstable assemblies such as membrane proteins and viruses. In the absence of crystals, cryo-electron microscopy (Cryo-EM) is a valuable source of structural information. It is well suited for studying both the structure and dynamics of large macromolecule assemblies. Its main limitation is the relatively low resolution of the data, ranging between 6 to 30 angstrom. This kind of data could be found in the EM Data Bank(EMDB).
• For the PDB database, the problem of fully automatic fast retrieval and classification of the folding data is a challenging task. Recently good classification has already achieved with Group Integration (GI) instead of traditional alignment method, which is highly time consuming. And the most interesting research for cryo-EM data should be synergistically combine them with atomic resolution data/methods for structure determination to overcome the limitations of either method alone.

Goals

• Secondary structure identification of intermediate resolution density map.
• Evaluating the identification ability of various Spherical Harmonic Descriptors (SHD).

Approach

• RENNSH voxelwise classification method.
• RJMCMC model based approach.

Introduction

For the analysis of cellular and subcellular mechanisms, exact knowledge about the cell anatomy is needed. In this subproject, we are therefore developing methods to precisely describe the shapes and shape variations of 3D objects (cells, cell nuclei, nucleoli) in microscopic recordings.

Goals

We are aiming to develop a 3D deformable model framework that is able to decribe shapes and shape variations of different cell types from different organisms (drosophiola S2 cells, arabidopsis thaliana root cells, tobacco protoplasts). The models should be able to handle the noisy and blurred data from different microscopy techniches (from widefield fluorescence microscopy over spinning disk microscopy to confocal laser scanning microscopy)

Approach

We are combining methods to generate robust egde maps with 3D deformable surfaces. The segmentation consists of the following steps:

1. Finding the edges that are relevant for the segmentation task. This is important whenever more than one structure is visible in the recording.
2. Fitting of the model to the data. Prior shape knowledge can be introduced in this step.

In step 1, the introduction of application specific user knowledge is necessary. In many cases, only the expert knows which structure he or she is looking for. This knowledge is learned from one or more training samples. In step 2, we are using parametric and non-parametric deformable surface models. Thus, we can introduce prior shape knowledge that facilitates the segmentation. The parametric segmentation at the same time yields a shape descriptor that can be used for the further description of the structure.

Achievements

The segmentation and modeling of cells and cell nuclei can be performed very robustly and despite the presence of noise and distortions, originating from the recording technique (CLSM and Widefield fluorescence microscopy)

Publications

Introduction

Studying protoplast cell development aims to increase the systems-understanding of molecular processes underlying the control of cell polarity, division, and the reprogramming [reference 1]. This will facilitate identification of key elements and gene networks responsible for totipotency in protoplasts.

Goals

In this context we pursue the goal to develop methods for a robust description of the temporally evolving 2D and 3D cell anatomy of growing and dividing protoplasts that build cell clusters. Moreover robust similarity measures for the description and comparison of complex 3D protein patterns that are invariant to imaging conditions and stainings are developed.

Fig.: Recorded 3D volume including two protoplasts, protein pattern (red), chloroplasts (green), approximated spherical cell model (wire frame), Down right: mercator-projection, patterns in spherical coordinates

References

Publications

Introduction

Arabidopis is an important model organism in molecular plant sciences. To understand various signalling pathways precise measurements of growth rates of responsive organs are essential [2].

Goals

The goal of this work is to automate the measurement of photoreceptor controlled hypocotyl growth rates with computer vision techniques.

Approach

On a 2D image, the hypocotyl and the root can be delineated by two almost parallel curves. This makes the Lateral Coupled Snake (LCS) model [1] a suitable tool for analyzing seedling videos. The LCS model not only gives the contour of a seedling but also defines at every position the longitudinal direction of the seedling stem. When the starting and end points are located, the length of the hypocotyl is ready to be obtained from the model.

Achievements

Positions and shapes of seedlings over time are well located and described by the LCS model. An example of the current result is shown in the following figure, from which one can find that the model acts like a ruler measuring length along a seedling. This work can be extended to root analysis as well.

References

Introduction

In contrast to single cell and cell culture approaches, the goal of this project is the description and modeling of signaling pathways between cells and tissues within their natural environment, e.g. the organism they form, given high resolution 3-D(+t) confocal recordings.

Goals

Using the example of the Arabidopsis Root Apical Meristem, we are going to provide tools for the statistical analysis of cellular key events within a complex organ with sub-cellular resolution. The approach will allow comparative studies within and between different plant populations after genetic manipulations, application of external stress or drug/hormone treatments.

Approach

The analysis and modeling consists of several steps:

• Segmentation of the root into its cells based on tensorial harmonic features extracted from the raw nucleus markers (i.e. DAPI, h2B xFP)
• Detection of anatomic reference structures yielding an organ intrinsic coordinate system (In the case of the Arabidopsis RAM, the Quiescent Centre and the Root Axis)
• Cellular classification by tissue and state

Achievements

We are able to automatically extract the positions of the nuclei and roughly estimate their nucleolus' diameter employing vectorial gray-value based invariants. In a supervised training/classification cycle we are able to distinguish Interphase nuclei from Mitoses and are now aiming at refining the model to describe the distributions of key events in relation to the root anatomy.

Publications

Introduction

Arabidopsis trichomes (leaf hairs) are an interesting example to study cell differentiation [reference 1] and are well suited cell types for the functional analysis of de novo pattern formation. During cell growth, different processes provide for a regular spacing of the trichomes. A close interplay between theoretical modelling and experimental validations has been started to test the relevance of different models for trichome patterning. In this context, there is a need of quantitative data, e.g. trichome positions, to allow the analysis of these processes and their simulation with mathematical models.

Goals

Goal of this project is the automated extraction of quantitative information about trichome patterning on leaves of Arabidopsis thaliana. The extracted quantitative data, e.g. trichome positions, are to support the analysis of these processes and their simulation with mathematical models.

Approach

For this work time series of growing rosette leaves (4D confocal datasets, 3D + time) are used. The approach mainly consists of three parts. The first part is the robust extraction of the leaf surface and midplane from the chlorophyll channel. Local filtering based on gradient directions and gradient magnitude is used to identify surface voxels. In addition voxels belonging to the midplane are identified similarly by using eigenvectors of the Hessian instead. Robustness is increased by applying a scale-space approach and removing unstable responses. The consideration of 4D data in our approach introduces the need for image registration. Symmetry analysis, based on the extracted surface, yields the symmetry plane of the leaf. It is used to robustly detect the pose of the leaf and thus to register a biologically motivated reference coordinate system. This allows for inter-subject registration of the leaves. Trichomes are localized in the GFP channel by first detecting candidates using Hough transform, extracting local 3D invariants, and then validating the candidates using a SVM.

• Extraction of leaf surface
• Registration to a biological reference coordinate system
• Localization of trichomes

Achievements

• Robust extraction of 3D leaf surface for several datasets
• Robust registration to a biological leaf coordinate system for several datasets
• First promising results for the localization of trichomes

References

Publications