Poster L26 - Critical phenomenon in immune dynamics: A percolation-type criticality threshold controls immune protein coating of surfaces

Introduction: Complement opsonization, which is one of the most primitive pathways, occurs when complement proteins mark a pathogen for phagocytosis by immune cells. The binding of complement proteins to a pathogens’ surface enhances immune cells’ ability to recognize and engulf the pathogen. However, the immunogenicity mediated by the complement pathway crucially depends on how the complement proteins are presented and several naturally occurring as well as engineered nanoparticles, including exosomes, microvesicles, and viruses, have varying degrees of immunogenicity that directly impact and define the tumor-immune interactions and have direct implication for success of many immunotherapies.

Materials and

Methods: We employ diverse computational models to investigate whether the established biochemical reactions within the complement network can generate emergent properties observed in experimental studies involving nanoparticles. Initially, we adapt an ordinary differential equations (ODE) model to simulate reactions within the alternative pathway of complement activation. Our ODE model accurately preditcs curves representing C3a production and C3b surface adhesion against variations in protein-protein spacing, closely resembling experimental measurements. This ODE model effectively elucidated bulk-scale complement responses to surfaces. To investigate the the behavior at the single-particle level, we developed an agent-based model (ABM), specifically tailored to capture the intricacies of C3-surface interactions at the individual particle scale. Within this ABM framework, C3b proteins are represented as agents capable of spontaneous deposition onto surfaces, generation of new C3b agents through autocatalysis, and diffusion near surfaces to locate binding sites. Moreover, the model accounted for the eventual loss of autocatalytic capabilities in agents over time, simulating the degradation of surface-bound C3 convertases. These processes unfold on a quasi-two-dimensional spherical surface featuring a lattice of complement attachment sites. Consequently, our computational analyses underscore the sufficiency of the complement network’s reaction rates, and concentrations in eliciting a discernible threshold in complement activation as surface properties, such as the distance between C3 attachment points, are varied. Additionally, through systematic scaling analyses of system size, we probed the nature of critical phenomena associated with immune dynamics within the complement system.

Results, Conclusions, and Discussions: Through experimental investigations, we have discerned that the complement system exhibits a threshold-like activation pattern contingent upon a singular geometric parameter: the average separation between potential complement (C3) attachment sites on a designated material surface (see Fig. 1A). Employing a dynamical systems model alongside a spatially resolved ABM, we have delineated that the coating of a given surface by the complement proceeds via a percolation-type threshold (see Fig. 1B and C). In furtherance of understanding the critical phenomena observed within the ODE and AMB, we have demonstrated that our intricate systems model can be simplified to a minimal two-parameter SIR model, commonly employed in the study of infectious diseases, which has been shown to exhibit critical phenomena. This minimalist model captures both the threshold behavior observed in the comprehensive model and the experimental outcomes. We explore how fluctuation measures, such as standard deviations, in the output of the system evolve near the threshold spacing. Our findings indicate a pronounced divergence of these quantities around the threshold, and the flunctuations increase with the physical size of the nanoparticle. Such scaling trends in system size strongly indicate presence of a critical phenomena, rather than alternative models such as nucleation-and-growth. Our findings bear direct relevance to the functional capacities of natural nanoparticles such as exosomes and viruses, alongside engineered nanoparticles utilized in therapeutic drug delivery, in modulating immune responses. Furthermore, a nuanced comprehension of the complement activation threshold across diverse nano-scale systems, encompassing viruses, nanoparticles, and exosomes, stands to illuminate the immunogenicity of both natural and engineered nanoparticles within physiological microenvironments, including the tumor microenvironment. Numerous biological phenomena, spanning neural dynamics, infection propagation, cell membrane organization, tissue morphogenesis, physiological rhythms, and viral replication dynamics, exhibit critical phenomena, although the comprehensive significance of criticality remains a subject of intense debate. Our inquiry delves into the significance of critical phenomena governing the evolution of complement proteins on surfaces. While subject to scholarly discourse, we present evidence showcasing that critical dynamics, owing to their scale-free and reversible attributes, confer unique evolutionary advantages in establishing a robust and efficient system as a primary responder to pathogenic invasions.

Acknowledgements (Optional): We acknowledge support from the National Cancer Institute through the Physical Sciences Oncology Network and support from Penn Engineering.