Non-Monotone Response Modules and Cascades from the EML Operator for Reduced Models of Biological Dynamics

TL;DR

This paper introduces an EML-based structured grammar for reduced nonlinear ODEs to model non-monotone biological responses, capturing overshoot and adaptive transients more efficiently.

Contribution

It presents a novel EML operator framework that simplifies modeling complex biological dynamics with fewer parameters and captures non-monotone responses directly.

Findings

Validated on PKA-R relocalization data with biologically consistent surrogate.

Consistent EML expression trees across multiple perturbation-response traces.

Compressed a 50-state network using EML cascades as a temporal basis.

Abstract

Standard saturating response functions, such as the Hill function, are monotone and therefore cannot represent recruitment-induced overshoot or adaptive transients with a single block. Reproducing such non-monotone responses from saturating primitives requires at least a difference of two blocks with opposing amplitudes, doubling the static-block parameter count. Here, building on a recent mathematical result that a single binary operator, EML, generates all standard elementary functions, we use EML as a structured grammar for reduced nonlinear ODEs. This yields an activation-suppression module that captures overshoot directly. We validate the framework in three settings. First, on PKA-R relocalization data, the EML grammar discovers a reduced surrogate consistent with established mechanistic biology. Second, on Rho-GTPase recruitment data, an exhaustive search over EML expression trees selects the same compositional form across all four perturbation-response traces. Third, a 50-state simulated network is compressed by an EML cascade acting as a fixed temporal basis. Thus we demonstrate the power and potential of EML for reduced models of biological dynamics.