Abstract
In the context of biology, unlike the well-established Standard Model in physics, many biological processes lack a complete theoretical framework and are often described phenomenologically. A pertinent example is olfaction, the process through which humans and animals distinguish various odors. The conventional biological explanation for olfaction relies on the lock and key model, which, while useful, does not fully account for all observed phenomena. As an alternative or complement to this model, vibration-assisted electron tunnelling has been proposed. Drawing inspiration from the vibration-assisted electron tunnelling model for olfaction, we have developed a theoretical model for electron tunnelling in SARS-CoV-2 virus infection within a non-Markovian framework. We approach this by solving the non-Markovian quantum stochastic Schrödinger equation. In our model, the spike protein and the GPCR receptor are conceptualized as a dimer, utilizing the spin-Boson model to facilitate the description of electron tunnelling. Our analysis shows that electron tunnelling persists even at intermediate and strong coupling limits between the dimer components, presenting a stark contrast to the predictions from Markovian regime models. Notably, Markovian models often yield unphysical negative probabilities, particularly in the strong coupling limit, underscoring significant discrepancies and highlighting the importance of considering non-Markovian dynamics in accurately modeling such quantum processes. This approach enhances our understanding of viral infection mechanisms while also offering deeper insights into the quantum biological process of olfaction.