The Generic Sensory Automaton (GENSA) for modeling affinity-based dynamics and interactions in biology

Mathematics and computer science play a pivotal role in modern biology. Dynamical models based on differential equations are particularly adapted to describe dynamic behaviors of many biological processes. However, traditional dynamical system theory face limitations to capture nonlinear behaviors of biological systems such as the immune system. Also, dynamical system theory does not always make it possible to model stochastic rare events that biological systems face and process.
To overcome such limitations, we introduce the GENSA (GENeric Sensory Automaton), a new mathematical framework aimed at modeling biological systems, like the immune system, as computational and reactive systems. Unlike conventional approaches that rely on object-based descriptions and differential equations, the GENSA emphasizes the sensory properties of the immune system, framing it as an automaton capable of detecting and responding to environmental changes, so as to maintain or evolve toward homeostasis. As such, the GENSA can function either as a discretized model of differential equations or as an agent, offering a robust alternative to traditional dynamical systems.
The capacity of the GENSA to detect events in its environment and modify its state in response to environmental cues is formalized through mathematical notions of specificity and sensitivity. Two fundamental instances of the GENSA are provided: the Neyman-Pearson GENSA (NP-GENSA) and the Random Distortion Testing GENSA (RDT-GENSA). These two GENSAs embed distinct decision types and satisfy functional redundancy and we say that they are de-generate.