Exploring focal adhesion data: dynamic parameter extraction from FRAP and FLAP experiments using chemical master equation

The dynamic behavior of proteins within cellular structures can be studied using fluorescence recovery after photobleaching (FRAP) and fluorescence loss after photobleaching (FLAP) experiments. These techniques provide insights into molecular mobility by estimating parameters such as turnover rates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow> <mml:mrow><mml:mi>T</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow> <mml:mrow><mml:mi>I</mml:mi> <mml:mi>n</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> and exit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow> <mml:mrow><mml:mi>Out</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> rates, allowing a deeper understanding of protein turnover and interactions. To validate our model, we analyzed previously published experimental data from NIH3T3 fibroblasts expressing GFP-tagged FA proteins, including tensin 1, talin, vinculin, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow> </mml:math> -actinin, ILK, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi></mml:mrow> </mml:math> -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. It can be applied to new experimental datasets and reanalyzed from existing data, revealing previously inaccessible molecular interactions and enhancing our understanding of FA dynamics and broader cellular processes.