The generalized work functional (GWF) method of Wu, Li, and Ma (2022) identified, for the C7eq-to-C7ax isomerization of alanine dipeptide, the first rigorous one-dimensional reaction coordinate (1D-RC) — a single linear combination of internal coordinates that fully determines the committor, the probability that a configuration proceeds to product. The source work left open whether the method and the structure-to-function roadmap it supports — stated by its authors as tentative — generalize beyond this smallest test case: larger proteins, other functional dynamics (ligand binding, allostery), enhanced sampling built on the RC, and experimental confirmation that the RC determines biological activity. Later work by the same group resolved several strands: exact reaction coordinates for HIV-1 protease flap opening (six RCs, 198 residues, PNAS 2022) and, via true reaction coordinates (tRCs) computed from energy relaxation of a single structure, 10^5- to 10^15-fold accelerated conformational changes and ligand dissociation in PDZ2 and HIV-1 protease, together with a proposed mechanism of PDZ allostery (Nature Communications 2025). A precise core remains open: no experimental test has confirmed that GWF-identified reaction coordinates determine biological activity (the PDZ allostery mechanism remains an untested computational hypothesis); generality across functional-dynamics classes (enzymatic catalysis, protein-protein interaction, folding) and application of the method outside the developers' group are unestablished; and the stated theoretical questions — whether linearity of true RCs is general, and whether the GWF is the fundamental mechanical operator controlling protein dynamics — remain unanswered.

Background

A reaction coordinate (RC) is a small set of collective coordinates of a molecule that governs a transition between two long-lived states, such as a protein's inactive and active conformations. The rigorous, widely accepted criterion for a 'true' RC is the committor: for any configuration, the RC must fully determine the committor, the probability that a trajectory launched from that configuration with randomized momenta reaches the product state rather than the reactant. Since the late 1990s, and since Ma and Dinner's 2005 neural-network identification of RCs for alanine dipeptide isomerization (a small peptide, N-acetyl-alanine-N'-methylamide, that is the standard testbed for RC methods), finding exact RCs in complex molecules has been a central open problem in molecular biophysics, because candidate coordinates must be searched among an impractically large space and committor evaluation requires rare-event sampling. Wu, Li, and Ma (JCTC 2022; bioRxiv preprint 10.1101/2022.01.08.475519) introduced the generalized work functional (GWF) — a mechanical operator that quantifies how potential energy flows through each internal coordinate (dihedral angles, i.e. rotations about bonds, and improper dihedrals, the out-of-plane angular coordinates that measure distortion from planarity) along a transition. Its leading singular vectors identify the coordinates that carry the dominant energy flow, and they showed that for the C7eq-to-C7ax isomerization of alanine dipeptide in vacuum (C7eq and C7ax being the peptide's two standard metastable conformers), the leading singular vector is a rigorous one-dimensional RC that determines the committor with accuracy far exceeding prior methods. They proposed a tentative 'roadmap' in which such RCs — collective motions spanning many residues — are the physical mechanism by which protein structure determines function; the preprint's Discussions section names the development of enhanced-sampling algorithms (methods such as metadynamics and umbrella sampling that apply bias potentials along chosen collective variables to bridge the gap between simulation timescales, ~microseconds, and functional timescales, milliseconds to seconds) built on such RCs as a future direction, while the roadmap's structure-to-function link itself remains tentative and untested. The authors' own subsequent work then reshaped the problem: PNAS 2022 showed HIV-1 protease flap opening (the gating motion of the two glycine-rich flaps of this 198-residue drug-target enzyme) is intrinsically multi-dimensional, with six exact RCs each a linear combination of ~240 backbone dihedrals, so 'one-dimensional' is a property of alanine dipeptide's transition rather than a general guarantee; Nature Communications 2025 showed true RCs can be computed from energy-relaxation simulations of a single protein structure (simulations that watch a structure prepared away from equilibrium release its stored energy) — removing the previous need for pre-existing unbiased reactive trajectories — and that biasing them accelerates conformational changes and ligand dissociation in the PDZ2 domain (a protein interaction module whose allostery — modulation of ligand affinity by effectors binding at a distal site — has been an unsolved puzzle for over two decades; see Gianni and Jemth, 'Allostery Frustrates the Experimentalist') and in HIV-1 protease by 10^5- to 10^15-fold, with the accelerated trajectories following natural transition pathways. Independent groups have pursued parallel, non-GWF routes to RCs (e.g., deep learning of the committor, reviewed by Mori et al. 2026) and independent models of PDZ allostery (contact-cluster modeling by Dorbath et al.), but no work outside the developers' group has applied or tested the GWF framework.

Problem Statement

The GWF-based true-reaction-coordinate framework has been validated internally on three systems — alanine dipeptide isomerization, HIV-1 protease flap opening, and PDZ2/HIV-1 protease ligand (dis)association — and now makes concrete functional predictions, most notably a mechanism for PDZ domain allostery in which allosteric effectors modulate ligand affinity by interfering with large-scale, fleeting conformational changes (opening of the alpha1-beta1 cleft and the binding groove) that occur during ligand dissociation. The open problem is to establish, or refute, the framework's central claim that true reaction coordinates are the physical link by which protein structure determines biological activity. Three open strands address this claim, and each may be advanced or refuted independently; a full resolution of the central claim is achieved through strand (1), with strands (2) and (3) as independent extensions: (1) Testable confirmation — do GWF-identified RCs determine biological activity? Biological-activity evidence bearing on RC-derived functional predictions would directly advance this strand. A refutation — evidence that function is insensitive to perturbations along the identified RCs while the RCs still determine the committor — would equally answer the question. (2) Generality — does the framework extend across the major classes of protein functional dynamics (enzymatic catalysis, protein-protein interaction, allostery beyond PDZ domains, folding), including whether true RCs remain linear combinations of internal coordinates as system complexity grows, and whether the method's demonstrated accuracy of committor determination persists for these processes? (3) Theoretical grounding — is there a fundamental physical reason the true RCs discovered so far are linear, and is the generalized work functional the fundamental mechanical operator controlling protein dynamics, or one useful operator among several? Validation of any candidate true RC is governed by the committor criterion stated in the Background.

References

  1. Shanshan Wu, Huiyu Li, Ao Ma, 'Uncovering One-Dimensional Reaction Coordinate that Underlies Structure-Function Relationship of Proteins', bioRxiv preprint (2022), DOI: 10.1101/2022.01.08.475519, https://doi.org/10.1101/2022.01.08.475519
  2. Shanshan Wu, Huiyu Li, Ao Ma, 'A Rigorous Method for Identifying a One-Dimensional Reaction Coordinate in Complex Molecules', Journal of Chemical Theory and Computation 18(5), 2836-2844 (2022), DOI: 10.1021/acs.jctc.2c00132, https://doi.org/10.1021/acs.jctc.2c00132
  3. Shanshan Wu, Huiyu Li, Ao Ma, 'Exact reaction coordinates for flap opening in HIV-1 protease', Proceedings of the National Academy of Sciences USA 119(49), e2214906119 (2022), DOI: 10.1073/pnas.2214906119, https://doi.org/10.1073/pnas.2214906119
  4. Shanshan Wu, Ao Ma, 'Mechanism for the rare fluctuation that powers protein conformational change', The Journal of Chemical Physics 156(5), 054119 (2022), DOI: 10.1063/5.0077444, https://doi.org/10.1063/5.0077444
  5. Huiyu Li, Shanshan Wu, Ao Ma, 'Origin of Protein Quake: Energy Waves Conducted by a Precise Mechanical Machine', Journal of Chemical Theory and Computation 18(9), 5692-5702 (2022), DOI: 10.1021/acs.jctc.2c00514, https://doi.org/10.1021/acs.jctc.2c00514
  6. Huiyu Li, Ao Ma, 'Enhanced sampling of protein conformational changes via true reaction coordinates from energy relaxation', Nature Communications 16, 786 (2025), DOI: 10.1038/s41467-025-55983-y, https://doi.org/10.1038/s41467-025-55983-y
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  9. Toshifumi Mori, Kei-ichi Okazaki, Kang Kim, Nobuyuki Matubayasi, 'Deep learning of committor and explainable artificial intelligence analysis for identifying reaction coordinates', Chemical Physics Reviews 7(3), 031303 (2026), DOI: 10.1063/5.0335684, https://doi.org/10.1063/5.0335684
  10. Qiang Cui, 'Identification and understanding of allostery hotspots in proteins: Integration of deep mutational scanning and multi-faceted computational analyses', Journal of Molecular Biology 437(20), 168998 (2025), DOI: 10.1016/j.jmb.2025.168998, https://doi.org/10.1016/j.jmb.2025.168998
  11. Emanuel Dorbath, Fabian Rudolf, Adnan Gulzar, Gerhard Stock, 'Contact Cluster Modeling of Allosteric Communication in PDZ Domains', The Journal of Physical Chemistry B 130(4), 1121-1130 (2026), DOI: 10.1021/acs.jpcb.5c07737, https://doi.org/10.1021/acs.jpcb.5c07737
  12. Stefano Gianni, Per Jemth, 'Allostery Frustrates the Experimentalist', Journal of Molecular Biology 435(4), 167934 (2023), DOI: 10.1016/j.jmb.2022.167934, https://doi.org/10.1016/j.jmb.2022.167934