Category: Science

Summary: Estimating when stronger scaffold-guided substrate handoff turns an enzyme cascade from bulk-leaky turnover into a bridge-localized donor-scaffold-acceptor channeling state.

Scaffold proteins and metabolon-like assemblies can make multistep biochemical pathways more efficient by passing substrates directly between enzymes, but it is not obvious when that organization becomes the dominant dynamical route rather than a modest correction to ordinary bulk turnover. This experiment asks for the threshold where stronger scaffold-guided handoff reorganizes the leading mode into a donor-scaffold-acceptor bridge.

The script builds dense disordered gain operators for enzyme cascades and increases the scaffold-mediated transfer strength while carrying a threshold bracket across larger system sizes. Repeated eigensolves are used to detect when the dominant mode stops looking like broadly leaking turnover and instead localizes on a structured channeling path that links donor, scaffold, and acceptor components.

That makes the result a structural transition map for biochemical channeling, not just a kinetic comparison of fast and slow pathways. The goal is to identify when scaffold assembly qualitatively changes how flux is organized in a large, heterogeneous cascade, a threshold the docstring notes has not been systematically mapped in this dense finite-size form.

Method: Dense non-symmetric eigensolves with iterative deepening and bisection on scaffold-guided handoff strength across N=64 to 2048 disordered enzyme-cascade operators.

What is measured: Critical scaffold-channeling threshold, localization of the dominant mode, bridge-versus-bulk turnover concentration, leading eigenvalue behavior, and bracket width.