Characterizing excitability and its applications to immunity

Abstract: The functions of many biological systems — including spiking neurons and activating macrophages — depend on excitable dynamics: a small perturbation triggers a rapid, nonlinear ramp followed by a return to equilibrium. While this behavior is common biologically, excitability lacks a precise mathematical definition, and the generic properties of these systems remain unclear. Prior work in theoretical neuroscience has explored in detail specific models that produce excitable behavior. This work describes the emergence of excitable dynamics near different types of bifurcations, and shows that distinct mathematical structures describe different types of neurons and their computational properties. Importantly, the same perturbation can have opposite effects depending on the mathematical origin of the excitability and the timing of the perturbation relative to the state of the system. Thus predicting and controlling the behavior of these systems depends on understanding the underlying dynamical structure, which demands enumeration of the types of excitable systems and their mathematical properties. We will take a two-pronged approach to define and classify excitable systems. First, we will extend transition path theory (TPT) to excitable systems and use it to define excitability precisely. Second, we will combine TPT with machine learning to map dynamical behavior over a broad class of models to enumerate the types of excitability.

Both normal and pathological immune responses ‘flare’ — immune signaling molecules (cytokines) and immune cell populations amplify transiently before returning to baseline. This behavior suggests that systemic immune responses may be excitable. Observational data and modeling of multiple sclerosis and the existence of genetic disorders that cause spontaneous recurrent hyperinflammatory flares support this hypothesis. As in neuroscience, minimal dynamical models of these excitations could be powerful tools to understand the information processing capabilities of the immune system and develop strategies to intervene in systemic immune responses. However, we generally lack tractable experimental systems in which to make the controlled perturbations and quantitative observations necessary to test these hypotheses. To enable investigation of the excitable properties of systemic immune responses, we will study a ‘cytokine storm’ response triggered by a systemic pulse of the pathogen-associated molecular pattern lipopolysaccharide (LPS) in larval zebrafish. We will use this system to test properties such as the existence of an excitation threshold, and use our new classification of excitable systems to develop models capturing key nonlinear features of the response. Ultimately, we aim to understand which perturbations, at what stage of the response, would be necessary to return a systemic immune response to a homeostatic fixed point, allowing for the design of dynamical interventions.