Graduation Year


Date of Submission


Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts



Reader 1

Professor Helen Wong

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2022 Aryaman Gulati


Proteins play several critical roles in our body. They are required for the structure, function, and regulation of the body’s organs and tissues. Every cell contains them. These cells function properly & efficiently because of proteins that power them. Knot Theory, meanwhile, may seem far removed from the realities of our day-to-day lives. You may be wondering how this highly abstract and theoretical branch of mathematics is relevant to you in any way, not least with regards to the cells and organs that enable life. Let’s stop for a second to consider. How do these life-enabling proteins and a highly abstract field of mathematics come together? What do knots tell us about proteins? And why should we care? This paper extends Flapan et al. 's topological model to describe protein folding1, which is motivated by the computer simulation of Bolinger et al2. Flapan et al. introduce a topological folding model that describes pathways for the formation of all currently known protein knot types and predicts knot types that might be identified in the future. Flapan et al.’s current topological model is constrained to a maximum of two twists in each of the loops, a and b, in the knots. This thesis extends Flapan et al. 's model by considering how the model describes pathways for currently-known proteins and predicts novel knot types, when the loops, a & b, have a maximum of three twists.

This thesis is restricted to the Claremont Colleges current faculty, students, and staff.