We develop the mathematics and the models behind cell-replacement therapy for type 1 diabetes: how to manufacture insulin-producing cells at the scale, cost, and consistency that millions of patients require, how to protect them from the immune system, and how to tell whether they will keep working.
Type 1 diabetes is an autoimmune condition. The immune system mistakenly attacks and destroys the beta cells in the pancreas that make insulin. These cells live in clusters called islets and act as a living glucose sensor.
As the beta cells disappear, the body makes little or no insulin. Glucose builds up in the bloodstream while the body's cells cannot access it efficiently for energy. People with Type 1 diabetes replace the missing insulin through injections or a pump. Cell replacement aims to restore the living glucose-sensing system itself.
Our work connects the biology of beta cells with the practical challenges of cell replacement: making the cells, protecting them, and keeping them working.
Replacement cells need to sense glucose and release the right amount of insulin for years, not months.
The cells must be protected from transplant rejection and the autoimmune response that caused type 1 diabetes, ideally without lifelong immunosuppression.
Producing billions of mature, consistent beta cells requires reliable processes, strict quality control, and much more capacity.
Cells need a safe home with enough oxygen, a way to monitor their health, and a practical path to replacement if their function declines.
We combine AI with mathematical models to explore biological questions and identify directions for experimental study. Alongside this work, we develop foundational mathematics in graph theory and combinatorics.
The number of possible combinations quickly becomes too large to test experimentally. Mathematics can help narrow that space. Graph theory can model relationships between genes and cell states. Combinatorics can help explore combinations of edits efficiently. Spectral methods can identify structure that persists across different conditions. Statistics can distinguish reproducible biological effects from experimental noise.
Explore working papers on mathematics and computational biology.
Computational biology
Our revised analysis of CHGA insulin leaders separates binding and processing contributions to predicted antigen presentation, examines agreement between models, and defines a comparison that tests antigen presentation alongside insulin production.
Computational biology / Functional genomics
Across two public human beta-cell CRISPR screens, we show how repeated guide identity and shared controls can create apparent reproducibility without a reliable gene-level phenotype.
Mathematics / Spectral graph theory
We prove the conjectured higher-alphabet spectral bound for Hamming graphs, strengthen it to arbitrary supports in the minimal dimension, and extend the result to unequal coordinate weights.
Mathematics / Extremal combinatorics
We establish a spectral compression principle, construct new obstructions to Hamming-ball optimality, and classify the first two compressed defect layers exactly.