Formulating a Mathematical Model for Living Systems

Prigogine’s 1978 concept of dissipative structures, drawing parallels with living systems, forms the basis for exploring life’s unique traits. However, these identified similarities prove insufficient in capturing the entirety of life. To address this gap, our proposed modeling approach emphasizes the distinctive ability of living organisms to observe other systems—an attribute intricately tied to quantum mechanics’ "measurement" processes, as highlighted by Howard Pattee. This article introduces a comprehensive mathematical model centered on quantum dynamical dissipative systems, portraying living systems as entities defined by their observational capacities within this framework. The exploration extends to the core dynamics of these systems and the intricacies of biological cells, including the impact of membrane potentials on protein states. Within this theoretical structure, the model is expanded to multicellular living systems, revealing how cells observe quantum dynamical systems through protein state changes influenced by membrane potentials. The conclusion acknowledges the current theoretical status of the model, underscoring the crucial need for experimental validation, particularly regarding the superposition state of membrane proteins under the influence of an electric field.