Aplicação da técnica da transformada integral generalizada e do método de Monte Carlo via cadeia de Markov na dinâmica de transporte de massa e cinética em biossensores SPR

Abstract

The study of biomolecular interactions is essential for biology and pharmacology, with Surface Plasmon Resonance (SPR) biosensors serving as gold-standard tools due to their real-time, label-free detection capabilities. However, the precise and accurate analysis of kinetic constants from raw data is often hindered by mass transport limitations (MTL) and the intrinsic complexity of surface reactions. To address this challenge, this thesis proposes an innovative hybrid approach for mathematical modeling and parameter estimation in SPR biosensors, combining numerical-analytical methods and stochastic inference. To solve the direct problem, mathematical models based on convectiondiffusion partial differential equations coupled with surface reactions were formulated. The thesis expands upon traditional approaches by analyzing three interaction mechanisms: the 1:1 Langmuir binding model, the sequential two-site binding model (for bivalent analytes), and the competitive binding model (two analytes competing for a single site). These systems were solved using the Generalized Integral Transform Technique (GITT). The method's performance was verified through comparison with the Method of Lines (MoL) and literature data, revealing that GITT ensures automatic error control, high accuracy, and remarkable computational efficiency compared to purely numerical approaches. For the inverse problem, the research applied Bayesian statistical inference via the Markov Chain Monte Carlo (MCMC) method, employing the Metropolis-Hastings algorithm. This method was used to estimate the kinetic parameters of association and dissociation. Initial code verification was performed using simulated data corrupted by Gaussian noise, where the Markov chains converged to the exact values. Subsequently, the model was validated with real experimental data of the interaction between the SARS-CoV-2 spike protein (RBD) (wild-type and chimeric) and the human ACE2 enzyme. The methodology estimated the kinetic parameters in good agreement with the literature, demonstrating that the chimeric variant has a higher binding affinity. In conclusion, the framework integrating GITT and MCMC fills an important gap in SPR analysis. It enables the accurate evaluation of complex molecular interactions under transport limitations and provides full posterior distributions and rigorous uncertainty quantification, resulting in highly reliable diagnoses and kinetic interpretations