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A small subset of natural proteins within biomolecular systems stands out due to unique structural features, most notably the presence of topological knots in their native conformations. These knots introduce particularly complex folding mechanisms and complicate the selection of appropriate reaction coordinates, as knot formation can proceed through multiple pathways involving several transition states. Some proteins with such topological characteristics are well documented and serve as excellent models for studying folding mechanisms. This project focuses on the folding behavior of leptin, a biologically significant protein involved in appetite regulation and energy metabolism. Leptin exhibits a distinctive architecture known as Pierce-Lasso Topology (PLT), characterized by a punctured loop that plays a critical role in its folding process. Using structure-based models and the Energy Landscape Visualization Method (ELViM), the study aims to assess how variations in the N-terminal segment of leptin influence the distribution of slipknot and plug folding pathways. The primary objective is to identify an N-terminal length that balances these competing pathways, thereby informing predictions of structurally relevant mutations. The methodology involves computational simulations with coarse-grained models, thermodynamic analysis with the Weighted Histogram Analysis Method (WHAM), and structural visualization through tools such as VMD and UCSF Chimera. Ultimately, this research contributes to a deeper understanding of the fundamental principles governing protein topology and advances the rational design of proteins with tailored structural properties.
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