To perform its function as a tumor suppressor, breast cancer 1 (BRCA1) must dimerize with BRCA1-associated RING domain protein 1 (BARD1). Due to this critical interaction, pathogenic BARD1 variants are also associated with increased breast and ovarian cancer risk. Genetic testing has identified many rare single-nucleotide variants (SNVs) that cause missense amino acid substitutions in BARD1. Currently, 93% (1,692 of 1,819) of BARD1 missense SNVs are classified as a variant of uncertain significance (VUS) in ClinVar. A VUS classification prevents clinicians from using genetic test results to guide patient care. Consequently, there is a strong need to functionally assess BARD1 SNVs to help resolve VUS. We applied a multiplex assay for variant effect called saturation genome editing (SGE) to functionally assess all possible 12,000 SNVs and 2,300 3-base deletions in BARD1. In SGE, we use CRISPR-Cas9 to edit all possible SNVs into a region of BARD1 in haploid HAP1 cells. BARD1 is essential for cell growth, therefore cells edited with loss-of-function variants become depleted from the population. We track which SNVs become depleted from the population by sequencing. We then generate functional scores for each variant by calculating the change in the abundance of a variant in the original SNV library versus its abundance in the cell population after 13 days in culture. Thus far, I have generated reagents for all 14,300 variants and 2,400 have completed the full experimental pipeline. Functional scores for the functionally critical BRCA1 interaction domain show depletion of 94% stop-gain, 48% splice-site, and 21% missense variants relative to 5% synonymous and 6% intronic variants. This ultimately demonstrates SGE’s ability to accurately identify functionally normal and loss-of-function BARD1 variants. Generating functional scores for all possible BARD1 variants will provide the functional evidence needed for reclassifying BARD1 VUS and definitive test results for providers treating patients with BARD1 variants.

Fractal dimension, a measure of geometric complexity, finds application in image analysis, biology and medicine, neuroscience, geology and various other fields, yet existing methods often lack adaptability to finite data sets. Using ideas rooted in geometric measure theory, such as Hausdorff measure and Frostman’s Lemma, this research introduces a novel approach to compute fractal dimensions for finite sets, addressing limitations of traditional methods. Using Python, we developed and tested an algorithm to validate known sets such as the unit interval, square, cube, and fractal objects including the Cantor set and Sierpinski triangle. Comparative analysis was also conducted on established methods, including box-counting and correlation integral algorithms, to demonstrate the algorithm's accuracy in determining fractal dimensions. Pivoting towards data sets, we expect to use the computed fractal dimension of real data as a tool for assessing data and optimizing data compression. Our methods offer an improvement as most existing techniques use statistical methods that are limited to integer dimensions. In addition, recent studies have shown that fractal dimension values can be useful as features in machine learning. We also improve upon the calculation of the local dimension of regions in a data set, allowing for additional insights into complex data sets. This includes identifying regions of high complexity, and we expect to show that this allows for the more effective use of algorithms such as principal component analysis. All of these are increasingly important in our society due to the abundance of high-dimensional datasets in both the physical and social sciences. Overall, the benefits of studying novel ways of calculating the dimension of large data sets include efficient representation of data, improved interpretability, and decreased computational burden, as well as detecting certain features in data such as regions of high complexity.