PhD Student Ali Heydari and Dr. Sindi collaborate with Dr. Maxime Theillard to use level-set methods for studying reaction/diffusion of prion aggregates in actively dividing cells.

Blood coagulation is a complex biochemical process in which dozens of plasma proteins take part in a nearly 100 enzymatic reactions involving positive feedback (where a blood clot is initiated) and negative feedback (where the growth of the blood clot is stopped). Both overclotting and uncerclotting are associated with diseases and, as such, understanding the regulation of this system is important. However, comparisons between mathematical models of coagulation and coagulation experiments and assays were vague and qualitative. Moreover, mathematical models were only consistent with these experimental assays for a relatively narrow range of experimental conditions. In order for more informative comparisons between models and experiments it was clear that interdisciplinary collaboration and the use of statistical approaches, including sensitivity analysis and uncertainty quantification were necessary. 

As part of this work we have a number of on-going projects, 

• We are working on methods to enable precise quantitative comparisons between in vitro coagulation assays and mathematical models. We hypothesized a reason for the quantitative disagreement was that mathematical models were not modeling the full experimental assays. In particular, mathematical models did not include the chromogenic substrates, synthetic peptides designed to measure the activity in a patient’s blood sample in an experimental assay. We decided to build a model from the ground up that was designed to depict the precise experimental assay and observed that two significant outcomes: (i) it is possible to have a quantitatively accurate comparison between models and coagulation assays, (ii) chromogenic substrates alter the underlying reactions they are designed to measure by inhibiting the coagulation processes themselves. 

• We are working to understand modifiers of bleeding disorders. The bleeding disorder hemophilia A is characterized by an inability to form effective clots and is clinically classified by a deficiency in the coagulation factor VIII. Treatment of hemophilia A is costly, and the bleeding disorder varies considerably among individuals. Intriguingly, a small fraction of hemophilia A patients exhibit much better clotting that is predicted by their measured factor VIII levels. This suggests the presence of a yet-unknown-factor influencing the bleeding phenotype of a hemophila A patient. A traditional clinical approach would be to collect patient samples to uncover the link; however, the rarity of this phenotype in an already rare bleeding disorder, along with considerable variability between individuals, would make it impossible to collect enough samples to be statistically significant. Our team took a data-driven approach by using a previously published mathematical model (Leiderman/Fogelson) and conducted a global sensitivity analysis by varying the levels of all plasma proteins (as well as many other parameters) to identify possible candidates. We found, for our model, the combination of an exceptionally high level in the clotting factor II and low level in the clotting factor V lead to improved clotting when factor VIII was at hemophilia A levels. Remarkably this non-intuitive model prediction was subsequently experimentally validated on hemophilia A samples. 

This research lies at the intersection of deep learning, computer vision, and bioinformatics. The goal of our work is to develop computational methods for better downstream analysis of complex biological systems and datasets (such as single-cell RNA Sequencing and Spatial Transcriptomics). To achieve this, we have used a deep generative model to generate realistic synthetic single-cell data. Creating realistic in-silico data will help enable robust analysis of single-cell data and foster greater reproducibility in research no such data. The next aspect of this research focuses on developing large-scale deep learning models and transfer learning models for enhancing learning from small datasets.  Our goal is to design an "all-in-one" network that can be quickly fine-tuned on small datasets to accurately perform domain-specific tasks, such as clustering, cell-type identification, and data generation. This pre-trained core enables researchers to transfer the vast existing knowledge to their downstream analyses, allowing efficient and accurate predictions for datasets that are orders of magnitude smaller than the training data. 

Many genetic disorders – including cancer – are caused by structural modifications of an individual’s genome. Structural variation (SV) in genomes consists of rearrangements ranging anywhere from a few nucleotides in length to millions of nucleotides in length. Originally, SVs such as inversions, insertions and deletions were thought to be rare, but today SVs have been be linked to some heritable diseases and implicated in a number of cancers. With continually decreasing costs of DNA sequencing and the availability of high-quality reference genonmes for a variety of species, the common paradigm for SV discovery has been to sequence reads from an individual genome and map these reads to the reference genome. Regions in the individual genome corresponding to an SV will be revealed by discordant configurations of mapped fragments. Unfortunately, deciphering the resulting data is complicated by both errors in the data and computational complexities arising from millions (and even billions) of observed data points.

Because of the high-volume of data and the error-prone and noisy sequencing data, sophisticated mathematical approaches are required to successfully predict SVs. What distinguishes my work from others is use of statistical modeling to consider the configuration of a set of reads suggesting a potential SV.

We have several projects in this area including:

• Developing likelihood based models for determining not just the presence of a SV, but the likelihood that it is a true SV from an erroneous configuration of reads.

• Leveraging multiple individuals to boost the signal of true SVs by combining