A constructive chemical oscillator model demonstrates the emergence of homeostasis before genetic information through active inference

Homeostasis is a fundamental property of life, intricately regulated by genetic information in extant organisms. However, a central mystery in the origin of life is how primordial life, before the establishment of a genetic system, could have adapted to fluctuating environments and acquired homeostatic capabilities. To address this question, this paper proposes an abstract, proof-of-concept mathematical model to explore how homeostasis could emerge through self-organization from a simple chemical reaction network, without reliance on genetic information or externally defined setpoints. Crucially, the system does not require direct sensory information of either the target value (Topt) or its current state (Tcell); it only evaluates the resulting global performance metric (replication rate). The model utilizes an internal Lotka-Volterra chemical oscillator within a protocell as a “search engine” to periodically vary the system’s phenotype (cell pigmentation). The system then adjusts its internal state by evaluating only the temporal correlation between these internal fluctuations and a single, global performance metric—the cell’s self-replication rate. This simple loop of “exploration by oscillation and optimization by correlation” is realized through a chemically implementable mechanism termed “antagonistic memory molecules.” Numerical simulations demonstrate that the model can autonomously converge to and maintain the optimal temperature for its self-replication, even amid significant fluctuations in the external environment (e.g., solar luminosity and water temperature). These results present the model as a constructive proof-of-concept, demonstrating how a core process of active inference under the free energy principle—minimizing prediction error through action—can emerge from a simple physicochemical system. This research provides a concrete scenario for the acquisition of adaptive capabilities at the origin of life and offers new guiding principles for the design of self-adaptive systems.