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REVIEW 2 major objections 1 minor 103 references

Coarse-grained protein models require internal friction between beads to accurately reproduce their dynamics in water.

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2026-06-26 02:29 UTC pith:CJYAXBB3

load-bearing objection The paper shows internal friction helps match velocity correlations in this CG protein model, but the fitting to just RDF and autocorrelations limits how far the necessity claim travels. the 2 major comments →

arxiv 2606.27133 v1 pith:CJYAXBB3 submitted 2026-06-25 cond-mat.soft cond-mat.stat-mechphysics.bio-ph

Unraveling Internal Friction in a Coarse-Grained Protein Model

Carlos Monago , J. A. de la Torre , Rafael Delgado-Buscalioni , Pep Espa\~nol This is my paper
classification cond-mat.soft cond-mat.stat-mechphysics.bio-ph
keywords coarse-grainingprotein dynamicsinternal frictionMori-Zwanzig formalismhydrodynamic interactionsmolecular dynamics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that coarse-grained models of globular proteins in water must include internal friction between beads, which arises from the atomic motions removed during coarse-graining. Elastic forces and solvent hydrodynamic friction alone do not suffice to match the time-dependent behavior observed in all-atom simulations. The authors compare the coarse-grained trajectories directly to molecular dynamics references and introduce a self-averaging optimization that evolves model parameters until the radial distribution function and bead velocity correlations agree with the atomistic data.

Core claim

In order to accurately reproduce the dynamics of a globular protein in water using a coarse-grained model, not only a precise determination of elastic couplings and the Stokesian self-friction of each bead is required. Critically, the inclusion of internal friction between beads is also necessary for a faithful representation of protein dynamics. Parameters are optimized by a self-averaging method that integrates the coarse-grained dynamics with an evolution equation until the radial distribution function and the time correlation of bead velocities match the corresponding all-atom values.

What carries the argument

The internal friction term in the dissipative bead-bead interactions, arising from unresolved internal degrees of freedom via the Mori-Zwanzig projection.

Load-bearing premise

Matching only the radial distribution function and the time correlation of bead velocities is sufficient to guarantee that the coarse-grained model with added internal friction faithfully captures the full protein dynamics.

What would settle it

A side-by-side comparison in which a coarse-grained model that includes the fitted internal friction is tested against all-atom results on an observable not used in the fitting procedure, such as the long-time mean-squared displacement of the protein center of mass or its rotational correlation time.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Coarse-grained trajectories without internal friction will produce incorrect relaxation rates and diffusion behavior even when structure is matched.
  • The self-averaging optimization supplies a consistent route to determine the full set of dissipative parameters including internal friction.
  • Protein simulations on timescales inaccessible to all-atom methods become reliable once internal friction is incorporated.
  • Standard hydrodynamic-only treatments of bead interactions systematically omit a source of dissipation that affects all time correlations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar internal friction contributions are likely required when coarse-graining other macromolecules whose internal motions are integrated out.
  • The method could be tested on non-equilibrium driving, where internal friction would alter the rate of energy dissipation in steered simulations.
  • If the claim holds, existing hydrodynamic coarse-grained force fields will need reparameterization before they can predict folding pathways or ligand binding kinetics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The manuscript develops a coarse-grained (CG) protein model via the Mori-Zwanzig formalism and claims that, in addition to elastic couplings and Stokesian self-friction, internal friction between beads is critically necessary to reproduce the dynamics of a globular protein in water. This necessity is demonstrated by comparing all-atom MD reference data with CG simulations whose parameters (including internal-friction coefficients) are optimized through a self-averaging procedure so that the radial distribution function and bead-velocity time correlations match the MD values.

Significance. If the necessity claim can be shown to hold for observables beyond the two fitted quantities, the work would provide a concrete route to incorporate missing dissipative effects from unresolved degrees of freedom into CG biomolecular models, moving beyond purely hydrodynamic dissipation.

major comments (2)
  1. [Abstract] Abstract: the claim that internal friction is 'critically necessary for a faithful representation of protein dynamics' is supported only by improved matching of the two quantities (RDF and velocity autocorrelation) to which the internal-friction coefficients are explicitly fitted; because agreement on these observables is achieved by construction, an independent test on at least one unfitted dynamical signature (e.g., center-of-mass diffusion or conformational relaxation spectrum) is required to substantiate the necessity assertion.
  2. [Methods (self-averaging procedure)] Self-averaging optimization procedure: the evolution equation for the CG parameters (elastic constants, self-friction, and internal-friction matrix) is driven to reproduce MD-derived RDF and velocity correlations; this leaves unconstrained longer-time transport and cross-correlations, so the manuscript must show that the internal-friction term improves predictions for these additional properties rather than merely compensating for the limited constraint set.
minor comments (1)
  1. The precise functional form of the internal-friction term (e.g., whether it is a pairwise distance-dependent matrix or a constant) and its relation to the Mori-Zwanzig memory kernel should be stated with an explicit equation to allow reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We agree that the necessity of internal friction requires demonstration on observables beyond the fitted RDF and velocity correlations, and we will revise the manuscript to include such independent tests.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that internal friction is 'critically necessary for a faithful representation of protein dynamics' is supported only by improved matching of the two quantities (RDF and velocity autocorrelation) to which the internal-friction coefficients are explicitly fitted; because agreement on these observables is achieved by construction, an independent test on at least one unfitted dynamical signature (e.g., center-of-mass diffusion or conformational relaxation spectrum) is required to substantiate the necessity assertion.

    Authors: We acknowledge that the current support for the necessity claim rests on the two quantities used in the self-averaging optimization. In the revised manuscript we will add direct comparisons, for models with and without the internal-friction matrix, of the center-of-mass diffusion coefficient and the conformational relaxation spectrum against the all-atom MD reference. These unfitted observables will serve as an independent validation. revision: yes

  2. Referee: [Methods (self-averaging procedure)] Self-averaging optimization procedure: the evolution equation for the CG parameters (elastic constants, self-friction, and internal-friction matrix) is driven to reproduce MD-derived RDF and velocity correlations; this leaves unconstrained longer-time transport and cross-correlations, so the manuscript must show that the internal-friction term improves predictions for these additional properties rather than merely compensating for the limited constraint set.

    Authors: We agree that the optimization is performed on a limited set of statistics. The revised version will therefore report the performance of the optimized models (with versus without internal friction) on longer-time transport coefficients and cross-correlations that are not part of the fitting target, thereby testing whether the internal-friction term captures additional dissipative physics. revision: yes

Circularity Check

1 steps flagged

Self-averaging optimization ensures targeted matches by construction

specific steps
  1. fitted input called prediction [Abstract]
    "We propose to optimize the parameters of the CG model through a self-averaging method that integrates the CG dynamics with an evolution equation for the CG parameters. This approach ensures that selected quantities, such as the radial distribution function and the time correlation of bead velocities, match the corresponding MD values."

    Parameters including the internal-friction term are evolved until the chosen MD-derived observables (RDF, velocity autocorrelations) are reproduced. Reported agreement and necessity of internal friction for 'faithful representation' are therefore achieved by construction of the optimization rather than serving as an independent test.

full rationale

The paper optimizes CG parameters (elastic couplings, self-friction, internal friction) via a self-averaging evolution equation so that RDF and bead-velocity time correlations exactly match MD values. The central claim that internal friction is 'critically necessary' for faithful dynamics therefore reduces to the fitting targets rather than an independent derivation or prediction of untargeted observables. This matches the fitted_input_called_prediction pattern with no load-bearing self-citation or self-definition of the model equations themselves.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 1 invented entities

The central claim rests on the Mori-Zwanzig derivation plus several fitted friction and coupling parameters whose values are determined by matching to all-atom data; internal friction is introduced as an additional dissipative term without independent evidence outside the fit.

free parameters (3)
  • internal friction coefficients between beads
    Optimized via self-averaging to reproduce MD velocity correlations.
  • elastic coupling constants
    Determined to match structural statistics from MD.
  • Stokesian self-friction per bead
    Set as part of the precise determination required for dynamics matching.
axioms (1)
  • domain assumption Mori-Zwanzig formalism provides the correct stochastic dynamics for the coarse-grained beads including both reversible and irreversible interactions
    Invoked at the outset to justify the form of the CG equations of motion.
invented entities (1)
  • internal friction between CG beads no independent evidence
    purpose: To capture dissipative effects arising from the eliminated internal degrees of freedom within each bead
    Introduced to resolve the discrepancy with all-atom MD; no independent falsifiable prediction is stated.

pith-pipeline@v0.9.1-grok · 5777 in / 1658 out tokens · 47138 ms · 2026-06-26T02:29:14.088370+00:00 · methodology

0 comments
read the original abstract

Understanding the dynamic behavior of complex biomolecules requires simplified models that not only make computations feasible but also reveal fundamental mechanisms. Coarse-graining (CG) achieves this by grouping atoms into beads, whose stochastic dynamics can be derived using the Mori-Zwanzig formalism, capturing both reversible and irreversible interactions. In liquid, the dissipative bead-bead interactions have so far been restricted to hydrodynamic couplings. However, friction does not only arises from the solvent but notably, from the internal degrees of freedom missing in the CG beads. This leads to an additional ''internal friction'' whose relevance is studied in this contribution. By comparing with all-atom molecular dynamics (MD), we neatly show that in order to accurately reproduce the dynamics of a globular protein in water using a coarse-grained (CG) model, not only a precise determination of elastic couplings and the Stokesian self-friction of each bead is required. Critically, the inclusion of internal friction between beads is also necessary for a faithful representation of protein dynamics. We propose to optimize the parameters of the CG model through a self-averaging method that integrates the CG dynamics with an evolution equation for the CG parameters. This approach ensures that selected quantities, such as the radial distribution function and the time correlation of bead velocities, match the corresponding MD values.

Figures

Figures reproduced from arXiv: 2606.27133 by Carlos Monago, J. A. de la Torre, Pep Espa\~nol, Rafael Delgado-Buscalioni.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) The Bovine Pancreatic Trypsin Inhibitor pro [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Radial distribution function (RDF) of the beads for [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Average VACF over all beads for the microscopic [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Protein center-of-mass velocity time correlation [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

discussion (0)

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