Project Title:
A Glazier-Graner-Hogeweg (GGH) Model of the Four-Cell Stage Caenorhabditis elegans Embryo

Project Description (short):
In this project, we will study the dynamics of cell shapes, cell positioning and cell-cell interactions in the four-cell embryo of the nematode C. elegans. Students will have the opportunity to use microscopy, image processing software and mathematical modeling software to create a computer model of the mechanical forces affecting this stage of embryogenesis. (Longer description here.)

Skills needed:

Biology:

Completion of Cell Biology and Genetics. Willingness and excitement to use microscopes and work with computers on image processing and analysis.

Mathematics:

Completion of Calculus III, with experience in Linear Algebra a definite plus. Other areas of expertise that would be helpful for this project include experience using technical software, computer programming expertise, and/or some knowledge of physics or biology.

Start Date:
January 2009

End Date:
December 2009

Mentors:
Prof. Tim Walson (Biology) tdwalston@truman.edu
Prof. Scott Thatcher (Mathematics), thatcher@truman.edu

Current Students:

• Clayton Davis (Mathematics)
• Elise Walck (Biology)
• Kurt Warnhoff (Biology)
• Allie Wehrman (Computer Science)

Accomplishments:

• Walck, Elise and Davis, Clayton. "A Cellular Potts Model of Caenorhabditis elegans Embryonic Development in the Four-Cell Stage." Poster at the 2007 Joint meeting of the Society for Mathematical Biology and the Japanese Society for Mathematical Biology. San Jose, California. July 31 - August 3, 2007. (First place award in the undergraduate poster contest.)
• Davis, C., Participant at Developing Multi-cell Developmental and Biomedical Simulations with CompuCell3D workshop, Indiana University Biocomplexity Institute, 2007.
• Wehrman, Alexandra. 'A Semi-Automated Procedure for Segmenting Early Embryogenesis in Caenorhabditis elegans' Poster at annual meeting of the Society for Mathematical Biology. Fields Institute, University of Toronto, Canada. July 2008.
• Walck, E., Davis, C., Thatcher, S., and Walston, T. A Glazier-Granier-Hogeweg (GGH) Model for Caenorhabditis elegans embryonic development. Poster presentation. C. elegans Development and Evolution Meeting, 2008.
• Walck, E., Davis, C., Thatcher, S., and Walston, T. A Glazier-Granier-Hogeweg (GGH) Model for Caenorhabditis elegans embryonic development at the four-cell stage. Oral seminar presentation. Truman State University Student Research Conference, 2008.
• Chelle King Porter accepted to Fast-Track masters program in Biology; will continue work in Walston lab
• Alexandra Wehrman, Kurt Warnhoff, Scott Thatcher, Tim Walston. "Segmenting Early Embryogenesis in C. elegans" Capitol Appreciation Day, Jefferson City, MO, February 2009.
• Alexandra Wehrman, Kurt Warnhoff, Scott Thatcher, Tim Walston. 'A Semi-Automated Procedure for Segmenting Early Embryogenesis in Caenorhabditis elegans' Donald Danforth Center for Plant Sciences. July 2008.

About Prof. Walston:
Dr. Walston earned his B.A. in Biology at Taylor University, a small liberal arts college in rural Indiana. He then moved to Wisconsin and got his M.S. in Cellular and Molecular Biology at UW-LaCrosse and his Ph.D. in Genetics at UW-Madison. He is currently in his third year as an assistant professor of biology at Truman. His research interests include exploring the genes that regulate cell polarity and cell migration. He uses the genetic model system, Caenorhabditis elegans for his investigations. Dr. Walston enjoys bicycling and fishing when he gets some free time.

About Prof. Thatcher:
Dr. Scott Thatcher has taught at Truman since the fall of 2000. He received a Ph.D. in Mathematics from Northwestern University in 2000 and a B.A. in Physics and Mathematics from Carleton College in 1993. Academic interests include geometry, topology, computational modeling, mathematical biology, and (most recently) Glazier-Graner-Hogeweg modeling of C. elegans embryogenesis. Other interests include open source software, typography, and (most recently) his new son Thomas.

Project Description (long):

The nematode C. elegans serves as a great model system for understanding cell-cell interactions during embryogenesis. This is primarily because the embryo is made of only 959 cells and every embryo has an invariant cell lineage (Sulston et al., 1983). Every blastomere has a name based on the founder cell that it is from and the subsequent mitotic division orientations that led to that cell. The second mitotic division creates the 4-cell embryo, which consists of two daughters of the AB founder cell (ABa and ABp), EMS and P2 (Figure 1). In the next cell division, EMS will divide to form two founder cells, E and MS. Progeny from the E blastomere will undergo gastrulation and will eventually form all of the cells of the gut (or endoderm). The cells in the MS lineage will form most of the mesodermal tissue in the embryo.

Figure 1. A 4-cell C. elegans embryo. The 4-cell embryo consists of two daughters from the AB cell, ABa and ABp, and two daughters from the P1 cell, P2 and EMS. Shortly after the birth of EMS, it extends an anterior protrusion ventral to ABa (arrow).

This project will examine the shape of the cells in the four-cell embryo, with particular focus on the EMS blastomere. While the other blastomeres maintain a round or polygonal shape, the anterior side of the EMS blastomere extends and then retracts a protrusion underneath its anterior neighbor ABa (Figure 1). We are developing a computer model that explores the forces acting upon the blastomeres and the subsequent contribution to cell shape. Kajita et al. have previously described a computer model that establishes the proper orientation of C.elegans blastomeres using a spring and damper triangulated network (Kajita et al., 2003). However, their model fails to account for adhesion between cells. This results in gaps between the cells in the model embryo that are not present in actual embryos. Additionally, in their model, EMS adopts a round or trapezoidal shape that lacks the anterior protrusion.

We are designing a Glazier-Graner-Hogeweg (GGH) model based on the CompuCell3D environment. GGH modeling uses a fixed three-dimensional lattice and assigns cellular identities to each voxel in the lattice (Chaturvedi et al., 2005; Cickovski et al., 2005; Izaguirre et al., 2004). The model then calculates the energy within the system and tests random changes until it has adopted a lowest energy conformation. Current CompuCell models explore morphogenesis and cell sorting of tissues and organs with individual cells represented by only a few voxels (Mombach et al., 1995). In contrast, our model of only four cells assigns many voxels to each cell, allowing us to examine sub-cellular forces and interactions with high resolution. While computationally intensive in comparison to the Kajita model, the simplicity of the GGH model will allow for greater flexibility in modeling the forces involved in the four-cell embryo.

Once the initial wild-type model has been developed, the consequences of loss of certain cell-cell interactions will be able to be explored. For example, removal of the function of three genes responsible for adhesion between cells in the early embryo prevents the formation of the protrusion in EMS, resulting in a trapezoidal shape (TW, unpublished data). By changing parameters in the model, we would anticipate being able to explain possible phenotypes obtained through mutagenesis or directed removal of gene function. In addition, we hope to use the model to explore the differences between C. elegans and other nematodes from the Rhabditid class that have similar embryonic geometries.

In conclusion, this project will explore the dynamic shapes and positions of the blastomeres in the 4-cell C. elegans embryo. The study will focus on the forces between the cells that cause stereotypic four-cell arrangement of the C. elegans embryo. This will be accomplished with the development of a GGH model of the C. elegans embryo.

References:

• Chaturvedi, R., Huang, C., Kazmierczak, B., Schneider, T., Izaguirre, J., Glimm, T., Hentschel, H., Glazier, J., Newman, S., Alber, M. 2005. On multiscale approaches to three-dimensional modeling of morphogenesis. Journal of the Royal Society Interface 2, 237-253.
• Cickovski, T., Huang, C., Chaturvedi, R., Glimm, T., Hentschel, H., Alber, M., Glazier, J., Newman, S., Izaguirre, J. (2005) A framework for three-dimensional simulation of morphogenesis. IEEE/ACM Transactions on Computational Biology and Bioinformatics 2, 273-288.
• Goldstein, B., Takeshita, H., Mizumoto, K., Sawa, H. 2006. Wnt signals can function as positional cues in establishing cell polarity. Developmental Cell 10, 391-396.
• Izaguirre, J., Chaturvedi, R., Huang, C., Cickovski, T., Coffland, J., Thomas, G., Forgacs, G., Alber, M., Hentschel, H., Newman, S., Glazier, J. 2004. CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics 20, 1129-1137.
• Kajita, A., Yamamura, M., Kohara, Y. 2003. Computer simulation of the cellular arrangement using physical model in early cleavage of the nematode Caenorhabditis elegans. Bioinformatics 19, 704-716.
• Mombach, J., Glazier, J., Raphael, R., Zajac, M. (1995) Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations. Physical Review Letter 75, 2244-2247.
• Sulston, J. E., Schierenberg, E., White, J. G., Thomson, J. N. 1983. The embryonic cell lineage of the nematode Caenorhabditis elegans. Developmental Biology 100, 64-119.
• Walston, T. and Hardin, J. 2006. Wnt signaling directs asymmetric cell divisions in C. elegans embryos. Seminars in Developmental Biology 17, 204-213.