Constraint Semantics for Multi-level Organization

Abstract

Biological organisation is inherently multi-level: molecular processes, membrane dynamics, cellular geometry and tissue context reciprocally constrain one another, often through boundary-mediated feedback. A recurring theme in theoretical biology is that such organisation is not well captured by models that assume a fixed repertoire of variables and a pre-given state space: what counts as a relevant state description can depend on organisational context and history. The principle of biological relativity further sharpens the same challenge from a different angle, emphasising that no level is causally privileged and that cross-level feedback can close into circular causality. These lines of work motivates for a structural multi-level semantics for modeling the biological pathways. We introduce a constraint-based semantic framework that distinguishes an evolving organisational scaffold--the admissible multi-level patterns and interfaces--from the pathways that traverse and coordinate them. This separation yields mathematical, loop-level diagnostics for boundary-driven circular causality: it identifies when organisational trajectories induce persistent reparameterisations of local state descriptions, and it classifies cyclic regimes into reversible loops, stable history-dependent loops, and unique (rare) organisational reconfigurations. The framework is accompanied by a systematic crosswalk to mainstream causal, dynamical and computational approaches, clarifying what is gained when interfaces and local-global consistency are treated as semantic, rather than purely parametric, structure. We demonstrate the approach on a canonical excitable-cell exemplar by modelling a single Hodgkin spike as a cross-level interface loop coupling membrane, molecular and cellular constraints. Without re-deriving Hodgkin-Huxley kinetics, the resulting diagnostics provide an explicit semantics for boundary-mediated feedback and spike-induced history dependence, including when cyclic activity imprints persistent changes in effective excitability. Together, the case study and comparisons position constraint semantics as a practical mathematical layer for multi-level biological organisation: compatible with existing mechanistic models, yet designed to expose circular causal closure and organisation-dependent state descriptions that standard formalisms typically leave implicit. AMS subject classifications92C30, 92C46, 92B05, 55U10, 55R10