The Grey Box Virtual Cell: Unifying Mechanistic and Neural Models through Standardized Benchmarking

Abstract

Efforts to build a predictive, whole-cell representation have historically relied on integrating diverse biochemical measurements into mechanistic frameworks. However, a divide has emerged between these explicit "Glass Box" models and newer data-driven "Black Box" foundation models. In this work, we propose a formal mathematical unification of these paradigms: the "Grey Box" Virtual Cell. We derive a hybrid state-space formulation that couples mechanistic conservation laws with latent neural representations. Furthermore, to address the lack of rigorous validation standards, we introduce the WCM-Hard Benchmark Suite, a set of eight standardized challenges ranging from essentiality screening to combinatorial drug synergy. We provide a reference implementation of a hybrid cell and demonstrate its performance on these benchmarks. Crucially, our ablation studies reveal that purely mechanistic baselines fail to capture dynamic diauxic shifts that the hybrid architecture navigates successfully. This work provides both the theoretical foundation and the practical testing ground for the next generation of whole-cell models.

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