WormGUIDES is an open-source dynamic embryonic system designed to facilitate global understanding of cellular decisions in the developing nervous system of the nematode C. elegans. WormGUIDES was designed to allow investigation and exploration of the observational results of the C. elegans life cycle from laboratory experiments. In the process of a mechanistic C. elegans model development, some functionalities of WormGUIDES needed to be enhanced to support model validation and verification. In this study, a new way to visualize 3-dimentional vectors within WormGUIDES was investigated and presented. Then, the practical values of this method were demonstrated by visualizing two biologically significant directions (i.e., division orientation and cell polarity) of individual embryonic cells in C. elegans. Lastly, a mathematic approach was designed to illustrate the differences between these two sets of vectors and provide easy indications of the location of these individual cells that have large data discrepancies within the C. elegans embryonic system.
In the past several years, a consortium of biologists, computer scientists, and microscopists from the Memorial Sloan Kettering Cancer Center, Yale University, the University of Connecticut, and the National Institute of Health have worked together to create a novel systems-level resource that will facilitate examination of cellular decisions in the developing nervous system of the nematode C. elegans. This resource, used for global understanding in dynamic embryonic systems, is WormGUIDES [
The source code for the desktop version of WormGUIDES is located on GitHub for free download [
Currently, there are two important functions embedded within WormGUIDES. One of these functions is designed to contain and display the C. elegans lineage tree information from previous experiments [
Additionally, WormGUIDES contains several utilities to support user search and query. The WormGUIDES interface is illustrated in
As shown in
WormGUIDES provides the intuitive creation and sharing of interactive visualizations. Users can create custom color schemes to highlight features of interest. Multiple color layers can be combined to create an interactive 4D illustration of key events or features. This view of the embryo can then be shared with others encoded in a URL text string. This functionality can be used to visualize arbitrary single cell data superimposed on the model by computing a mapping from data into RGB. A color space and outputting a URL which assigns each cell in the embryo a unique data-driven color.
In the agent-based modeling for C. elegans embryogenesis, several important biological concepts (such as the previously mentioned examples of division orientation and cell polarity) are represented in the format of vectors. Therefore, a good visualization of 3D vectors with RGB values is necessary. To convert the vector directions into RGB values, we must first setup a defined range for each vector to map onto the RGB value. Since the magnitude of the vector is not necessary to find the division orientation, we can normalize the XYZ components of vectors. By normalizing the vectors, we set the max value for the XYZ vectors at 1 and the min at −1, therefore allowing the RGB values, from 0 to 255, to be easily mapped onto the vector values. We visualize these 3D vectors in WormGUIDES using a simple algorithm. By associating the X, Y, and Z directions with R, G, and B values, respectively, we can create a colored system of cells in WormGUIDES that defines in which direction the mother cell will split into its daughters.
An important example of a vector to visualize is cell division orientation, defined as the direction in which a parent cell splits into two daughter cells. Cell division orientation is important for morphogenesis, cell fate, and tissue homeostasis. In this section, we use our color schemes to visualize the division of orientation, measured from tracked cell positions. In C. elegans embryogenesis, the division orientation is closely related to another concept, cell polarity, which is defined as “the asymmetric organization of several cellular components, including its plasma membrane, cytoskeleton or organelles” [
A MatLab program is created to calculate the division orientations from observational datasets, derived directly from the microscopic images from Dr. Bao’s lab. Each dataset contains the cell list at a specific timestamp during the observation. The interval of observation is around 60 seconds. The pseudo code of division orientation calculation is illustrated in
cell locations. Then, we align the XYZ axes with the individual body axis of cell separately: X axis for the Anterior-posterior (AP) direction, the Y axis for the Ventral-dorsal (DV) direction, and the Z axis for the Left-right (LR) direction. The pseudo code of division orientation calculation is illustrated in
Following the procedure described in Section 2.4, the collection of visualization results is shown in
In our study, we define cell polarity as the main factor for determining division orientation. As we previously mentioned in Section 3, it is difficult to model the cell polarity directly from observation. However, in Section 3.1 we observed that the division orientation of AB related cells at each generation have similar directions at the early development phase. As a result, we may assume cell polarity for each cell in the AB sub-lineage tree in a generation is the same. The cell polarity of all the cells of same generation within AB sub-lineage tree is thereby calculated by averaging the division orientations for the generation of cells. Then, adding the X, Y, and Z components of the vectors to get the main vector, normalizing this main vector, and splitting it back into components should allow the cell polarity to be easily mapped onto its respective RGB values.
As illustrated in
To find the differences between the observed division orientation and calculated
Cell Polarity, a DotProduct function was developed in MatLab to quantify the discrepancy of these two set of vectors. Each vector is associated with individual cell that can be used to link the vectors between these two datasets. Since only the direction, not the quantity, of the vector is of interest, all the vectors are normalized first before the dot production operation. The results are easy to understand: the closer the value of dot product is to 1, the closer the two individual vectors match. For the demonstration purpose, the top 10 cells with the large differences between these two vectors are listed in
As shown in
WormGUIDES is an open-source dynamic embryonic system developed by collaborations between Memorial Sloan Kettering Cancer Center, Yale, University of Connecticut Medical Center and the National Institute of Health. WormGUIDES can support the examination of cellular divisions in the developing nervous system of the nematode C. elegans. To facilitate mechanistic embryonic system model development, we need a visualization tool to identify the locations & ranges of 3D vector data and the discrepancy between 3D vectors datasets. In this paper, we have presented a new way to visualize 3D vectors within WormGUIDES. We have laid out the implementation details and demonstrated the functionality by visualizing both the division orientation and the calculated cell polarity of individual embryonic cells in AB sub-lineage of C. elegans. Different