Travis Pence
Mathematics and Computer Science undergraduate at the University of South Carolina looking to obtain a PhD in CS. I worked with Dr. Olson and Dr. Young modeling the thermal fluctuations of DNA minicircles at the DIMACS REU at Rutgers University for the summer of 2022. Research supported by NSF grant CCF-1852215.
Project Description
Simulating DNA broadens our understanding of how structure impacts the molecule's behavior. Models of DNA exist which consider all atoms and associated forces, but become computationally intensive for large-scale simulations. The step-parameter model allows for renderings of longer DNA sequences and is packaged into the software emDNA, which currently finds the minimal energy state for an input sequence. My research expands upon emDNA, adding the emDNA-move tool. This tool fluctuates linear or circular sequences of DNA over time and aims to depict the random movement of DNA considering only intrinsic forces. emDNA-move's customization includes specifying how many frames should be rendered and the degree of random movement. This work also presents figures comparing the deformability of each unique tetramer and the coupling of step parameters.
Research Log
Week One
DIMACS began on Wednesday, June 1st with orientation. I was introduced to my mentor Dr. Olson and learned the specifics of my project. I spent the rest of the week becoming more familiar with the background material by reading a paper and watching a conference presentation on DNA minicircles. On Friday, I was introduced to Dr. Young, a recent PhD graduate from Rutgers, and the rest of Dr. Olson's research group. I talked with Dr. Young on replicating the DNA configurations in their 2022 paper to become familiar with the software emDNA.
Week Two
On Monday, I gave a 4 minute talk introducing my project to my peers in the DIMACS program and their mentors. Continuing the plan from last week, I was able to replicate the DNA configurations in the 2022 paper by Friday. I read more background on the math beind the step parameter model and tried to plan how I would implement the math in my research. I also poked around in the emDNA code to attempted to understand the structure of the emDNA software, although as the code was not well documented I had some trouble.
Week Three
This week, I worked on plotting the energy contours for each pairing of the six step parameter deformations where the contours correspond to integer multiples of the principle axis length. I was taked with graphing the eigenvectors, the path of least resistence, for each plot. This involved finding the eigendecomposition and moving along the eigenvectors at certain intervals. However, I am encountering a problem with some of the graphs as the eigenvectors should follow the major and minor axes, but some do not. This only seems to affect the the combination of step parameter units distance and degree.
Week Four
My week started by fixing my previous problem of some eigenvectors not following the major or minor axis. When rotated ellipses are displayed on a graph that is not 1:1 scaling, they become distorted and the previous equations for the major and minor axis are no longer correct. To correct this, I derived a scaling factor to correct the slope of the eigenvectors for these certain graphs. I then moved to generating simulations of dimers moving along eigenvectors in PyMOL. The calculations are done in Mathematica while the conversion from x3DNAparams to PDB is done on Linux using x3DNA. I then preformed these same simulations using tetramers.
Week Five
This week, I converted the code which calculated the movements along the eigenvectors to C++ using the Eigen library. I automated the simulating process where now only a bash script needs to be run. When developing the emDNA tool which will fluctaute DNA configurations, I will need to build off of the emDNA software. Once I obtained the force field and intrinsic step parameter data, I expanded upon my energy contour work to include the step parameter data on corresponding plots. I am now working on generating energy contour plots for all pairs of step deformations for all unique tetramers.
Week Six
To start this week, I created energy contour figures which display the 15 step parameter combinations for all 136 unique tetramers. I then began to look at the emDNA software and understand the structure of the code. I mainly did this by tracing where functions were used by employing the grep command in Linux. Extra time was spent looking at the emDNA-topology tool as I am developing the emDNA-move tool which will have a similar file structure. I was also tasked with generating heat maps for the area of the energy contours by combination of step parameter to compare deformability.
Week Seven
Using Mathematica, I finished writing code to create a heat map given an input of two step parameters and then generated the 15 heat maps for all combinations of step parameters. I continued going through the emDNA code and began to acquire a solid understanding fo the software. Then, I started developing emDNA-move by first creating the parser. This took a considerable amount of time as I have never worked with the TCLAP library, although I was able to follow the parsers for emDNA-topology tool and emDNA.
Week Eight
Most of this week was spent developing emDNA-move. I first created the function to move a tetramer along one of its six eigenvectors by a multiple, chosen from a Gaussian distribution, of that eigenvector's principle axis length. I then looped over each teramer in succesion and updated each tetramers step parameter values. This method of fluctuating DNA holds the first base pair in place, which works when simulating linear DNA. However, when fluctuating circular DNA this will cause the ending base pair to become unattached to the first. A potential fix to this problem is preforming a step of minimization between each step of fluctuation. I also presented my research to my peers and instructors on Friday.
Week Nine
This week, I started by creating figures to compare the coupling of step parameters. Using mathematica, I generated heat maps of the slope of the eigenvector corresponding to the largest eigenvalue for all combinations of step parameters. Most of my week was spent writing my final paper.