Inference of Self-Limiting Neutrophil Swarming Dynamics Using Bayesian Physics-Informed Neural Networks

Abstract

Neutrophil swarming is a critical immune response in mammals and fish, in which neutrophils are recruited to inflammatory sites where they coordinate into a swarm that neutralizes pathogens. While excessive swarming can drive prolonged inflammation, a quantitative understanding of swarming dynamics remains limited. We developed a one-dimensional radial reaction–diffusion model of neutrophil swarming with two kinetic parameters, in order to capture the self-limiting swarming dynamics in both murine and human neutrophils in response to different inflammatory stimulus sizes. To ensure that the inverse problem is well-posed, we first performed sensitivity and identifiability analyses. We then developed a physics-informed neural network (PINN) to infer the key parameters governing swarm expansion and self-limitation. To account for uncertainty in noisy experimental measurements, we further extended this framework to a Bayesian PINN (B-PINN), which provides credible intervals for the inferred parameters. Both models were validated against synthetic data generated by numerical simulation and subsequently applied to in vitro experimental data from human and murine neutrophils in response to three bioparticle cluster sizes. The PINN-inferred dynamics show that larger bioparticle clusters are associated with greater cumulative recruitment and larger swarms in both species. The models further reveal species-specific differences in both the amplitude of initial recruitment and the timescale on which it self-limits. Additionally, the B-PINN posterior distributions quantify uncertainty in these species- and cluster size-dependent trends and identify where additional measurements would be most informative. To our knowledge, this is the first application of physics-informed machine learning to model neutrophil swarming dynamics. This framework provides a starting point for systematically comparing recruitment dynamics between human and murine neutrophils and offers guidance for future experimental design. 1 Author Summary Neutrophils are small but among the most numerous immune cells, and among the first to respond to infection or tissue damage. They coordinate into dense clusters called swarms to isolate and destroy pathogens. Remarkably, swarming is self-limiting: recruitment eventually slows rather than continuing without control, helping protect healthy tissue from excessive inflammation. How these dynamics vary with stimulus size and between species remains difficult to quantify. Researchers can now trigger neutrophil swarming on a chip while precisely controlling the target size, but measurements of swarm growth are sparse and noisy. We combined a mathematical model of swarming with machine learning to infer these dynamics from such data. Our approach estimates the initial strength and duration of recruitment, with uncertainty bounds. Applying our approach to neutrophils from humans and mice, we found that larger targets drive stronger recruitment in both species, yet the two differ in the strength and timing of their response. Our analysis also showed that measuring the swarm radius early in swarm formation would be especially valuable for distinguishing these dynamics. This work provides a quantitative framework for designing more informative experiments, comparing swarming across species, and supporting translation of findings from mouse studies to human immune responses.