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arxiv: 2604.10704 · v1 · submitted 2026-04-12 · ❄️ cond-mat.soft · physics.bio-ph

A Soft Penetrable Sphere Colloid Model for the Description of Charge and Excluded Volume Interactions in Antibody Solutions

Peter Schurtenberger , Marco Polimeni , Sophia Marzouk , Robin Curtis , Emanuela Zaccarelli , Anna Stradner This is my paper

Pith reviewed 2026-05-10 15:46 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.bio-ph
keywords soft penetrable sphere modelantibody solutionsprotein-protein interactionscolloid modellight scatteringmonoclonal antibodiesexcluded volume interactionscharge interactions
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The pith

A soft penetrable sphere model describes antibody interactions using only structural net charges and dimensions.

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

The paper introduces a soft penetrable sphere colloid model that incorporates the Y-shaped geometry of antibodies and their associated charge and ion distributions through analogies to soft colloids and star polyelectrolytes. Traditional hard-sphere colloid models require effective net charges not obtainable from molecular structure and overestimate excluded-volume effects at high concentrations, restricting them to descriptive use. The new model aims to enable quantitative, predictive calculations of solution properties such as osmotic compressibility and apparent hydrodynamic radius as functions of concentration and ionic strength. It achieves agreement with static and dynamic light scattering data on two monoclonal antibodies as well as with center-of-mass structure factors from amino-acid-level simulations, all without additional fitted parameters beyond the known net charge and overall size.

Core claim

The soft penetrable sphere model quantitatively reproduces experimental data from static and dynamic light scattering at low and high ionic strength for two well-characterized monoclonal antibodies using the net charges and the overall mAb dimensions directly obtained from their molecular structure, while also matching the center-of-mass static structure factor from computer simulations based on a weakly coarse-grained amino-acid-level description.

What carries the argument

The soft penetrable sphere model based on analogies to soft colloids and star polyelectrolytes, which incorporates the Y-shaped antibody geometry and the corresponding charge and ion distribution to treat both electrostatic and excluded-volume interactions.

Load-bearing premise

That analogies to soft colloids and star polyelectrolytes sufficiently capture the Y-shaped antibody geometry and its corresponding charge and ion distribution so that no additional effective parameters are required beyond the structural net charge and overall dimensions.

What would settle it

Light-scattering measurements or structure-factor data for a third monoclonal antibody, calculated solely from its known net charge and dimensions, that deviate substantially from the model's predictions for osmotic compressibility or hydrodynamic radius.

Figures

Figures reproduced from arXiv: 2604.10704 by Anna Stradner, Emanuela Zaccarelli, Marco Polimeni, Peter Schurtenberger, Robin Curtis, Sophia Marzouk.

Figure 1
Figure 1. Figure 1: Differently coarse-grained representations of the Y-shaped antibody, consisting of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Potential of mean force (PMF) as a function of the center-center distance [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: S(0) vs. c for different models using excluded volume interactions only. Shown are the theoretical results for hard spheres based on the approximation by Carnahan and Starling (eqn. 12) and σhs = 10 nm as the blue line, and for the SPS model using the hybridized￾mean spherical approximation (HMSA) closure relation and the PMF from the generic model parameters given in table 1. Also shown are the results fr… view at source ↗
Figure 4
Figure 4. Figure 4: Center of mass structure factor S cm(q) for excluded volume interactions. Shown are data from the SPS model (black solid line), the hard sphere colloid model (dashed blue line), and the simulations using the aa-coarse grained model (open black symbols) for three different concentrations. A: 50 mg/ml, 7 mM ionic strength structure; B: 100 mg/ml, 7 mM ionic strength structure; C: 150 mg/ml, 7 mM ionic streng… view at source ↗
Figure 5
Figure 5. Figure 5: Potential of mean force (PMF) as a function of the center-center distance [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Potential of mean force (PMF) as a function of the center-center distance [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Center of mass structure factor S cm(q) as a function of the magnitude of the scattering vector q for several concentrations and two ionic strengths. Shown are data directly obtained from simulations using the aa-coarse-grained model (black symbols) and calculations using liquid state theory (eqn. 14) with the PMF obtained from the SPS model (red solid line) and the classical colloid model (blue dashed lin… view at source ↗
Figure 8
Figure 8. Figure 8: A comparison of the measured S(0) vs. c obtained for mAb-1 at two ionic strengths (7 mM and 57 mM) with different models. Shown are the experimental data (7 mM: solid black circles; 57 mM: solid black squares, data taken from ref. 19), and the theoretical results for the SPS model using the HMSA closure relation (blue solid line) and the colloid model with Zef f determined for each concentration using eqn.… view at source ↗
Figure 9
Figure 9. Figure 9: A comparison of the measured normalized hydrodynamic radius [PITH_FULL_IMAGE:figures/full_fig_p029_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Measured effective structure factor S(q) vs. q obtained for mAb-1 at two ionic strengths (7 mM and 57 mM) compared with calculated structure factors S(q) for the colloid and SPS models. Shown are the experimental data (A: 7 mM ionic strength, 20 mg/ml (open blue circles), 50 mg/ml (open red squares); B: 57 mM ionic strength, 20 mg/ml (solid blue triangles); C: 7 mM ionic strength, 150 mg/ml (solid blue ci… view at source ↗
Figure 11
Figure 11. Figure 11: Decoupling approximation applied to the center-of-mass structure factor [PITH_FULL_IMAGE:figures/full_fig_p033_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Initial concentration dependence of S(0) (left) and Rh,app Rh,0 (right) for mAb-1 in 7 mM (black circles) and 57 mM (black squares) ionic strength compared with predictions for the linear virial regime calculated for the SPS model (black lines). Experimental data taken from ref.20 . Rh,app Rh,0 is well reproduced by the SPS model for both ionic strengths investigated, but [PITH_FULL_IMAGE:figures/full_fi… view at source ↗
Figure 13
Figure 13. Figure 13: Initial concentration dependence of S(0) (top) and ionic strength dependence of kD (bottom) for mAb-2. Shown are experimental data for S(0) at 10 mM (black circles), 50 mM (blue squares), and 110 mM (red diamonds) ionic strength compared with predictions for the linear virial regime calculated for the SPS model (solid lines). The bottom graph shows the experimental data for kD as a function of the ionic s… view at source ↗
read the original abstract

Colloid models have frequently been used to successfully describe the influence of protein-protein interactions on antibody solution properties, but they suffer from inherent problems due to the anisotropic shape of the particles. The net charge required to describe electrostatic interactions is an effective quantity that cannot directly be obtained from the known molecular structure of an antibody, and the solution structure caused by excluded volume interactions is strongly overestimated at high concentrations due to the assumption of hard sphere interactions. As a result, these models have descriptive rather than predictive power. Here we present an improved, soft penetrable sphere model based on analogies to soft colloids and star polyelectrolytes that take into account the Y-shaped antibody form and the corresponding charge and ion distribution. The model not only correctly describes the concentration and ionic strength dependence of thermodynamic and collective dynamics quantities such as the osmotic compressibility and the apparent hydrodynamic radius, but also reproduces the center-of-mass static structure factor obtained in computer simulations using a weakly coarse-grained model, in which the antibody is described at an amino acid level. We demonstrate that this soft penetrable sphere model quantitatively reproduces experimental data from static and dynamic light scattering at low and high ionic strength for two well-characterized monoclonal antibodies (mAbs) using the net charges and the overall mAb dimensions directly obtained from their molecular structure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a soft penetrable sphere colloid model for monoclonal antibody solutions, based on analogies to soft colloids and star polyelectrolytes to incorporate the Y-shaped geometry and associated charge/ion distributions. It claims that net charges (from residue counting at given pH) and overall dimensions (from PDB structures) are the sole inputs, with no additional effective parameters required. The model is asserted to quantitatively reproduce experimental static and dynamic light scattering data on osmotic compressibility and apparent hydrodynamic radius for two mAbs across concentrations and ionic strengths, as well as center-of-mass static structure factors from independent amino-acid-level coarse-grained simulations.

Significance. If the central claim of structure-derived, parameter-free inputs holds, the work would advance colloidal modeling of anisotropic proteins by addressing overestimation of excluded volume in hard-sphere models and the effective-charge issue in prior approaches. The dual validation against light scattering experiments and simulations, plus explicit use of molecular structure for charges and size, represents a strength that could aid predictive formulation of high-concentration antibody solutions. This bridges soft-matter analogies to biomolecular applications in a falsifiable manner.

major comments (2)
  1. [§2] §2 (model definition): The softness length scale and penetrability exponent in the interaction potential are introduced via analogy to star polyelectrolytes rather than derived by explicit integration or averaging over the three Fab/Fc domains in the PDB coordinates. This mapping is load-bearing for the abstract claim that 'net charges and the overall mAb dimensions directly obtained from their molecular structure' are the only inputs; any non-computed choice risks an implicit effective parameter.
  2. [Results section] Results section (comparison to light scattering): The quantitative match to SLS/DLS data at low and high ionic strength is presented, but the manuscript must explicitly document the pKa values and residue-counting procedure used to obtain net charge from sequence, and confirm that softness parameters were not adjusted to fit these same data sets (or the simulation structure factors).
minor comments (2)
  1. [Figures] Figure captions: Include explicit labels for each ionic strength and concentration series to improve readability of the osmotic compressibility and hydrodynamic radius plots.
  2. [Methods] The description of the weakly coarse-grained simulation model lacks a reference or brief methods summary sufficient for independent reproduction of the center-of-mass structure factor extraction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of our model definition and validation that we will address to improve clarity and transparency. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [§2] §2 (model definition): The softness length scale and penetrability exponent in the interaction potential are introduced via analogy to star polyelectrolytes rather than derived by explicit integration or averaging over the three Fab/Fc domains in the PDB coordinates. This mapping is load-bearing for the abstract claim that 'net charges and the overall mAb dimensions directly obtained from their molecular structure' are the only inputs; any non-computed choice risks an implicit effective parameter.

    Authors: We agree that the softness parameters are not directly computed from the PDB coordinates but are instead motivated by analogies to star polyelectrolytes, as stated in the manuscript. These parameters determine the shape of the interaction potential but are not fitted or adjusted to match the light scattering data or simulation results presented; they are fixed based on literature values for similar soft systems and applied consistently. The system-specific inputs remain the net charge (from sequence) and overall dimensions (from PDB). To strengthen the manuscript, we will revise Section 2 to provide more detail on the choice of these parameters and update the abstract to clarify that the potential form is based on soft colloid analogies while the key inputs are structure-derived. This addresses the concern without introducing effective parameters tuned to the current study. revision: partial

  2. Referee: [Results section] Results section (comparison to light scattering): The quantitative match to SLS/DLS data at low and high ionic strength is presented, but the manuscript must explicitly document the pKa values and residue-counting procedure used to obtain net charge from sequence, and confirm that softness parameters were not adjusted to fit these same data sets (or the simulation structure factors).

    Authors: We will incorporate these suggestions in the revised manuscript. We will add a subsection or paragraph detailing the pKa values employed (standard values from literature for each amino acid type) and the exact procedure for counting charged residues at the specified pH to compute the net charge. Furthermore, we will explicitly state in the results section that the softness length scale and penetrability exponent were not adjusted to fit the experimental SLS/DLS data or the simulation-derived structure factors; they were predetermined from the star polyelectrolyte analogy and held constant for all comparisons. This will enhance the reproducibility and address the referee's valid point on transparency. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model inputs from structure and analogies are independent of fitted outputs

full rationale

The paper defines the soft penetrable sphere model via physical analogies to soft colloids and star polyelectrolytes, taking net charge and overall dimensions as direct inputs from molecular structure (PDB/residue counting). It then shows quantitative agreement with independent experimental light-scattering data and coarse-grained simulation structure factors. No quoted step reduces a claimed prediction to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames an empirical pattern as a derivation. The central claim therefore remains externally falsifiable against the cited data sets rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the validity of mapping antibody geometry to a soft penetrable sphere via star-polyelectrolyte analogies; no explicit free parameters are declared in the abstract, but the softness length scale is implicitly introduced by the analogy.

axioms (1)
  • domain assumption Antibody charge and ion distribution can be approximated by that of a star polyelectrolyte with equivalent arm number and length.
    Invoked to justify the soft penetrable sphere form.
invented entities (1)
  • soft penetrable sphere no independent evidence
    purpose: To represent the Y-shaped antibody with distributed charge and allow particle overlap at high concentration.
    New modeling entity introduced to overcome hard-sphere limitations.

pith-pipeline@v0.9.0 · 5556 in / 1349 out tokens · 31077 ms · 2026-05-10T15:46:07.311347+00:00 · methodology

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