General Information

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Project Description

The folding of RNA closely parallels the folding of proteins. However, RNA exhibits a greater flexibility than proteins. This increased flexibility also distinguishes RNA from DNA, and is due to the additional oxygen present on each sugar. RNA also differs from DNA in that it typically occurs as a single-stranded structure. However, its bases do have some tendency to pair, a tendency which results in the formation of structures such as hairpin loops and internal loops.

Ribosomes are made up of ribosomal RNA and proteins. Although they differ somewhat among organisms, they exhibit a high degree of similarity. As a result of the size and complexity of ribosomes, it can be helpful to study the structure of a certain smaller part of the ribosome. In particular, it cna be informative to study the 3D structure of motifs found in many ribosomes. We will study the writhing number, a geometric property, of a certain motif found in the large subunit of many ribosomes. Writhing number is related to a topological property, linking number, and to another geometric property, twist, and it describes the non-planarity of a space curve. The importance of understanding the 3D structure of RNA is underlined by the fact that a single sequence of RNA can play multiple roles by taking on different tertiary structures.

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Weekly Log

Week 1:

This week, I was introduced to the members of Professor Olson's group, and to the projects each of them is working on. In general, their group studies biopolymer structures. They have written programs that allow the visualization and analysis of the 1D, 2D, and 3D structures of nucleic acids [1][2], and they are working to understand the primary, secondary, and tertiary structures of nucleic acids. They aim to understand the relationships between these levels of organization, and in particular the relationship between genome sequence and tertiary 3D structures of DNA.

The project I will be working on concerns the structure of RNA. More specifically, I will be studying structures found in the ribosomal RNA that makes up ribosomes. I will be studying a geometric property called the writhing number of a certain motif found in ribosomes. I spent the week reading about the research area of Professor Olson's group, about RNA and ribosomes, and about writhing number [3] and other topological and geometric properties of molecules.

Week 2:

This week, I was introduced to PyMOL, a program used to visualize molecules. We can upload a Protein Data Bank file to this program, and generate an interactive image of the molecule. We are interested primarily in a small part of a ribosome, and we can use PyMOL to select this part and visualize it. I worked on finding an efficient way to modify a file from the PDB to include only the part of interest.

I also continued reading about writhing number [4]. Most research concerning the writhing number of nucleic acids focuses on closed, double-stranded DNA, which it studies as a ribbon. The smooth ribbon model involves selecting an appropriate axis (a smooth closed space curve) and an appropriate material frame. The discrete ribbon model involves selecting an appropriate sequence of vertices and a material frame associated with each edge. In order to compute writhe, only the axis is needed. Therefore, I need to select an appropriate sequence of vertices to model the atoms in an RNA molecule. For pieces of the structure which lie along the backbone, this is fairly straightforward. When studying DNA, the phosphorous atoms are often chosen as the locations of the vertices. However, the RNA structure we are studying also involves paired bases which we consider to be adjacent. In this case, the choice of vertex position is less clear. Although we have not yet decided which atoms to use as vertices, I was able to begin writing a program that computes the writhe from a sequences of vertices.

Week 3:

This week, I used PyMOL to create images of the motif in several ribosomes taken from the PDB. Studying these images allowed me to see the ways in which these motifs are similar across ribosomes, but also the ways in which they differ. Once I verify that my program for computing writhe is working correctly, I'll be able to begin computing the writhe of these motifs. For each one, I plan to compute the writhe of discrete curves formed by several different choices of vertices. I also plan to compare writhe across ribosomes from different organisms. Is this motif, and in particular its geometry, one of the common attributes in ribosomes, or is it one of the ways in which ribosomes differ? In addition, the PDB includes, for certain organisms, multiple entries for ribosomes. For example, it includes ribosomes at different stages of protein synthesis or ribosomes bound to different antibiotics. I plan to compare the writhe of the motif from these different "versions" of ribosomes in order to try to understand the funciton of the motif.

Week 4:

This week, I focused on finishing my program to compute writhe. I verified that it gave an output of zero for curves lying in a plane, and I verified that the output was unchanged when I rotated or translated a curve. I also began to consider which choice of vertices might be most appropriate. I read about the standard reference frame fit to each base by 3DNA [5], which involved learning about the least-squares fitting procedure. I worked on finding a way to obtain the coordinates of the origins of each base's reference frame.

I also read about research concerning motifs in RNA [6] in order to get a better understanding of the motivation behind studying the geometry of this motif. Some researchers believe that all RNA structures can be thought of as simply a concatenation of a few simple RNA motifs. If this is the case, it is important to understand commonly occurring motifs.

Week 5:

This week, I compared the output of my writhing number program to that of another program. I identified a couple of errors in my code, and in particular I learned that any curve with reflectional or rotoreflectional symmetry has a writhing number of zero. This property will not apply directly to the motif we are studying, as it will not have these types of symmetry. However, this helped me to better understand the geometric meaning of the writhing number.

Once I had verified that the output of my program was consistent with that of the other program, I began computing writhe for different choices of vertices in some of the motifs. I studied the outputs to see if I could identify any possible patterns. However, since I was working with only a few examples and since these structures are so diverse, any patterns I noticed may not show up in a larger set of structures.

Week 6:

This week, I worked on getting the necessary information about the location of a motif from an Excel file containing about 700 ribosomes. I then computed the writhing number of each of these motifs for several choices of vertices. Next week, I may compute the writhing number for other choices of vertices. Also, certain ribosomes don't contain the motif as defined. However, if other ribosomes from the same species do contain the motif, I plan to use the location of the motif in those ribosomes to compute the writhing number for the ribosome without the motif.

Week 7:

This week, I spent some time trying to understand the writhing number data I had obtained. I focused primarily on the data obtained for ribosomes from E. coli, since there are about 170 such ribosomes. For each choice of vertices, I plotted the data on a histogram. This helped me to visualize the distribution of writhing numbers for structures from this species. Towards the end of the week, I created similar histograms for structures from Thermus thermophilus in order to see if there were any clear similarities or differences between the distributions for the two species.

I also presented my final presentation to Professor Olson and the members of her lab. They were able to give me feedback on it before I presented to the other REU students. Additionally, I worked on my final report.

Week 8:

This week, I continued looking at the distributions of writhing numbers, including those for all structures, as well as those for only prokaryotes and for only eukaryotes. In many of these distributions, we are noticing possible bimodality, so I also read about some tests (such as Hartigan's dip test) for unimodality/multimodality.

I also worked on computing writhing numbers for a certain closed structure found within the motif. This could help give insight into more local geometry within the motif. I also completed a first draft of my final report.

Week 9:

This week, I continued computing writhing numbers for various closed structures within the motif. I also continued working on my report. I looked through it with my mentor, made some changes to improve clarity, and incorporated some of the new data.

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References

1. Lu, Xiang‐Jun, and Wilma K. Olson. "3DNA: a software package for the analysis, rebuilding and visualization of three‐dimensional nucleic acid structures." Nucleic acids research 31, no. 17 (2003): 5108-5121.

2. Lu, Xiang-Jun, Harmen J. Bussemaker, and Wilma K. Olson. "DSSR: an integrated software tool for dissecting the spatial structure of RNA." Nucleic acids research 43, no. 21 (2015): e142-e142.

3. Fuller, F. Brock. "The writhing number of a space curve." Proceedings of the National Academy of Sciences 68, no. 4 (1971): 815-819.

4. Clauvelin, Nicolas, Wilma K. Olson, and Irwin Tobias. "Characterization of the geometry and topology of DNA pictured as a discrete collection of atoms." Journal of chemical theory and computation 8, no. 3 (2012): 1092-1107.

5. Olson, Wilma K., Manju Bansal, Stephen K. Burley, Richard E. Dickerson, Mark Gerstein, Stephen C. Harvey, Udo Heinemann et al. "A standard reference frame for the description of nucleic acid base-pair geometry." Journal of molecular biology 313, no. 1 (2001): 229-237.

6. Moore, Peter B. "Structural motifs in RNA." Annual review of biochemistry 68, no. 1 (1999): 287-300.

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Presentations

• First Presentation
• Final Presentation

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Additional Information

My Mentor: Dr. Wilma Olson