A. Ali Heydari
NIH NRSA Fellow
Ph.D. Candidate 
Applied Mathematics
University of California, Merced

Hi there! My name is Abbas-Ali, and I go by Ali (or A. Ali for official purposes). I am an Applied Math Ph.D. Candidate and an NIH NRSA (F31) fellow mentored by Professor Suzanne Sindi (UC Merced) and Professor Elana Fertig (Johns Hopkins University). The goal of my research is to develop deep learning and mathematical frameworks that help researchers study cancer and prion diseases at finer scales, enabling them to perform more robust downstream analyses. We hope that our novel methodology provides scientists with crucial tools needed to improve the current understanding of many complex diseases, thus significantly advancing the field of mathematical biology and facilitating the development of specialized treatments and healthcare.

I am, by training, a mathematician and a computer scientist interested in machine learning (deep learning, multi-task learning, and transfer learning in particular), computer vision, bioinformatics, and mathematical algorithms for big data and artificial intelligence. As part of my Ph.D. research, we employ multi-scale mathematical models for the study of biological conditions, in particular, prion disease and cancer. According to the National Cancer Institute, cancer is the second cause of death in the United States with approximately 606,520 lives lost annually. One promising avenue in treating cancers is immunotherapy, getting the body's immune system to act against the cancer cells. While immunotherapy has been successful for some patients, many remain non-responsive due, in part, to the individual mutations in their specific cancer type. Recent discoveries on cancer complexity have triggered a shift away from a one-size-fits-all approach toward personalized treatments. Scientists can now measure the gene expression in each cell of a tumor via single-cell RNA-sequencing (scRNAseq), which yields unprecedented resolution.

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Unfortunately, a fundamental problem in cancer gene expression research is the low number of single-cell observations of each cancer subtype, primarily due to a lack of available samples, experimental costs, or ethical reasons. The absence of sufficient data causes a majority of current models and pipelines to lack accuracy and generalizability, resulting in unreliable predictions and therefore impeding the development of personalized treatments. Recently, researchers have focused on using deep generative models to produce realistic single-cell data. However, these mathematical models solely depend on gene expressions and do not consider cells' spatial locations in tissues, which is crucial in understanding t tumor microenvironment's heterogeneity.

Another main issue in single-cell analysis remains the inability to harness sequencing data from different laboratories, even if all experimental setups were the same. Due to the lack of direct comparison between the existing data, researchers need to spend time and resources generating their own data, often in large quantities to allow for meaningful downstream analysis (such as classification and clustering). There is an unmet need for a framework that allows the transfer of existing knowledge to the post-experiment analysis of new sequencing data. Such a model will not only allow for fewer experimental samples, but it can yield more accurate results by leveraging the knowledge learned from existing data. We hypothesize that training a deep neural network with spatially informed synthetic data (in addition to the existing public datasets) will result in a transferable model that can be fine-tuned for domain-specific applications with relatively few samples. My Ph.D. research aims to use deep learning and mathematical modeling to address these problems in cancer immunology.

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Both cancer and prion diseases are epigenetic processes – where the disease is transmitted vertically during cell division and the disease agent is encoded by the host cell itself. The future direction of my research is to understand the genetic basis of fatal diseases, such as cancer, Alzheimer’s, and Creutzfeldt-Jakob, using a combination of mathematical modeling (PDEs, ODEs) and data analysis techniques (machine learning and statistics). In the past few months, I have been working with my advisor, Dr. Suzanne Sindi, and Dr. Maxime Theillard to develop a model of prion protein transmission in a dividing yeast cell. We considered the prion protein concentration as a distribution in a three-dimensional yeast cell and modeled the cell-wall dynamics during division with the level set method. While still early, my work demonstrates features of asymmetric protein segregation known to be important during disease transmission. Compared to my work thus far in yeast cell modeling, cancer cells are far more complicated both in the structure of their cellular properties (rigid cell walls compared to flexible cell membranes) and intracellular dynamics.

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