Exploring focal adhesion data: dynamic parameter extraction from FRAP and FLAP experiments using Chemical Master Equation

Luciana Renata de Oliveira^1*Matheus Gimenez Fernandes¹José Patane¹Jean-Marc Schwartz²Jose Krieger¹Christoph Ballestrem^2,3Ayumi Aurea Miyakawa^4*

• ¹Laboratório de Genética e Cardiologia Molecular, Instituto do Coração (InCor), Faculdade de Medicina da Universidade de São Paulo, São Paulo, Rio Grande do Sul, Brazil
• ²Faculty of Biology, Medicine and Health, The University of Manchester, Manchester, England, United Kingdom
• ³Division of Cell Matrix Biology and Regenerative Medicine, School of Biological Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester, England, United Kingdom
• ⁴Heart Institute, Clinical Hospital, Faculty of Medicine, University of São Paulo, São Paulo, Brazil

The dynamic behavior of proteins within cellular structures can be studied using fluorescence recovery after photobleaching (FRAP) and fluorescence localization after photobleaching (FLAP) experiments. These techniques provide insights into molecular mobility by estimating parameters such as turnover rates (k T ) and diffusion coefficients (D). However, traditional deterministic models often rely on simplifying assumptions that may not fully capture the stochastic nature of molecular interactions. In this study, we developed a novel stochastic model based on the analytical solution of the chemical master equation to extract dynamic parameters from FRAP and FLAP experiments in the focal adhesion (FA) network. Our approach extends beyond standard FRAP/FLAP analysis by inferring additional parameters, such as protein-specific entry (k In ) and exit (k Out ) rates, allowing a deeper understanding of protein turnover and interactions. To validate our model, we analyzed previously published experimental data from NIH3T3 fibroblasts expressing GFPtagged FA proteins, including tensin 1, talin, vinculin, α-actinin, ILK, α-parvin, kindlin-2, paxillin, p130Cas, VASP, FAK, and zyxin. These proteins participate in mechanotransduction, cytoskeletal organization, and adhesion regulation, exhibiting distinct dynamic behaviors within FA structures.Furthermore, we constructed an interaction network to quantify how vinculin and actin influence talin dynamics, leveraging our model to uncover their regulatory roles in FA turnover. Using an analytical solution of the chemical master equation, our framework provides a generalizable approach for studying protein dynamics in any system where FRAP and FLAP data are available.