article published yes Fabrizio Olmeda author 69dbf5fb-8a76-11ed-866b-fb486d8b5689 Steffen Rulands author EdHa department IST-BRIDGE: International postdoctoral program project Enzyme-substrate kinetics form the basis of many biomolecular processes. The interplay between substrate binding and substrate geometry can give rise to long-range interactions between enzyme binding events. Here we study a general model of enzyme-substrate kinetics with restricted long-range interactions described by an exponent −𝛾. We employ a coherent-state path integral and renormalization group approach to calculate the first moment and two-point correlation function of the enzyme-binding profile. We show that starting from an empty substrate the average occupancy follows a power law with an exponent 1/(1−𝛾) over time. The correlation function decays algebraically with two distinct spatial regimes characterized by exponents −𝛾 on short distances and −(2/3)⁢(2−𝛾) on long distances. The crossover between both regimes scales inversely with the average substrate occupancy. Our work allows associating experimental measurements of bound enzyme locations with their binding kinetics and the spatial conformation of the substrate. https://research-explorer.ista.ac.at/download/17892/18053/2024_PhysReviewE_Olmeda.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ American Physical Society2024 eng 2470-0045 2470-0053 39294986 00129967010000410.1103/PhysRevE.110.024404 1102 Olmeda, Fabrizio, and Steffen Rulands. “Field Theory of Enzyme-Substrate Systems with Restricted Long-Range Interactions.” <i>Physical Review E</i>, vol. 110, no. 2, 024404, American Physical Society, 2024, doi:<a href="https://doi.org/10.1103/PhysRevE.110.024404">10.1103/PhysRevE.110.024404</a>. F. Olmeda, S. Rulands, Physical Review E 110 (2024). Olmeda F, Rulands S. Field theory of enzyme-substrate systems with restricted long-range interactions. <i>Physical Review E</i>. 2024;110(2). doi:<a href="https://doi.org/10.1103/PhysRevE.110.024404">10.1103/PhysRevE.110.024404</a> Olmeda, Fabrizio, and Steffen Rulands. “Field Theory of Enzyme-Substrate Systems with Restricted Long-Range Interactions.” <i>Physical Review E</i>. American Physical Society, 2024. <a href="https://doi.org/10.1103/PhysRevE.110.024404">https://doi.org/10.1103/PhysRevE.110.024404</a>. F. Olmeda and S. Rulands, “Field theory of enzyme-substrate systems with restricted long-range interactions,” <i>Physical Review E</i>, vol. 110, no. 2. American Physical Society, 2024. Olmeda, F., &#38; Rulands, S. (2024). Field theory of enzyme-substrate systems with restricted long-range interactions. <i>Physical Review E</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevE.110.024404">https://doi.org/10.1103/PhysRevE.110.024404</a> Olmeda F, Rulands S. 2024. Field theory of enzyme-substrate systems with restricted long-range interactions. Physical Review E. 110(2), 024404. 178922024-09-08T22:01:12Z2025-09-08T09:17:18Z