A cellular automaton model of osteogenic differentiation reveals identifiability limits of endpoint assays

Standard differentiation assays sample cell states only at discrete time points, while the underlying progression unfolds continuously and heterogeneously across cells. As a result, different combinations of proliferation, commitment, and maturation dynamics can converge to similar endpoint measurements. This many-to-one mapping between latent trajectories and observable readouts constitutes a partially observed inverse problem that limits mechanistic interpretation. Although this ambiguity is inherent to many experimental systems, it is rarely examined using models that connect cell-state dynamics to assay-level quantities. We present OsteoMin, a coarse-grained cellular automaton that links stochastic transitions between pre-osteoblast and osteoblast states to experimentally measurable readouts of alkaline phosphatase activity, collagen deposition, and mineralization. Model parameters were constrained using literature-reported kinetics and evaluated against dexamethasone and menaquinone-4 perturbations. The frame-work reproduces qualitative assay trends and enables systematic analysis of how cell-state progression, matrix maturation, and external perturbations shape differentiation outcomes. Using this framework, we quantify the identifiability limits of endpoint assays and test whether standard measurements can distinguish underlying differentiation mechanisms. Distinct perturbation families often produce similar endpoint responses (macro-F1 {approx} 0.42), indicating limited discriminative power. Incorporating temporal trajectories improves separability (macro-F1 {approx} 0.78), demonstrating that most identifiable information resides in marker dynamics rather than terminal measurements. Sobol analysis shows early markers depend on proliferation timing, whereas late mineralization is governed by nonlinear matrix maturation and parameter interactions. Together, these results show that endpoint assays constrain overall progression but do not uniquely identify underlying mechanisms. OsteoMin provides a framework linking differentiation dynamics to assay observables and a basis for assessing identifiability in endpoint-driven systems.