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PreprintCited by 16Protein Structure and DynamicsAdvanced Physical and Chemical Molecular InteractionsFractional Differential Equations Solutions

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Hydrodynamic Radii of Intrinsically Disordered Proteins: Fast Prediction by Minimum Dissipation Approximation and Experimental Validation

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Waszkiewicz, Radost, Michaś, Agnieszka, Białobrzewski, Michał K., Klepka, Barbara P., Cieplak-Rotowska, Maja K., Staszałek, Zuzanna, Cichocki, Bogdan, Lisicki, Maciej, Szymczak, Piotr, Niedzwiecka, Anna·2024·The Journal of Physical Chemistry Letters
DOI 10.1101/2024.02.05.578612PMC PMC11103702

Preprint — published as 10.1021/acs.jpclett.4c00312 · Paper page

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Abstract

The diffusion coefficients of globular and fully unfolded proteins can be predicted with high accuracy solely from their mass or chain length. However, this approach fails for intrinsically disordered proteins (IDPs) containing structural domains. We propose a rapid predictive methodology for estimating the diffusion coefficients of IDPs. The methodology uses accelerated conformational sampling based on self-avoiding random walks and includes hydrodynamic interactions between coarse-grained protein subunits, modeled using the generalized Rotne-Prager-Yamakawa approximation. To estimate the hydrodynamic radius, we rely on the minimum dissipation approximation recently introduced by Cichocki et al . Using a large set of experimentally measured hydrodynamic radii of IDPs over a wide range of chain lengths and domain contributions, we demonstrate that our predictions are more accurate than the Kirkwood approximation and phenomenological approaches. Our technique may prove valuable in predicting the hydrodynamic properties of both fully unstructured and multidomain disordered proteins. TOC Graphic:

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Figure 1 Construction of the coarse-grained globule-linker model (GLM) for an illustratory IDP, H6–SUMO–CNOT1(800–999), containing three ordered domains of different sizes (no. 28 in Table S1). (A) Sequence with highlighted ordered (orange) and disordered (blue) segments, and domain boundaries marked by square brackets. (B) Representative full atom conformation generated by AlphaFold2 (for visualization purposes only;69,70 beads with van der Waals radii; hydrogen atoms omitted for the sake of clarity). Ordered clusters (orange) form dense blobs connected with linkers (blue). (C) Visualization of a representative configuration generated using the GLM method in which beads are displayed with their hydrodynamic radii.
Figure 1 Construction of the coarse-grained globule-linker model (GLM) for an illustratory IDP, H6–SUMO–CNOT1(800–999), containing three ordered domains of different sizes (no. 28 in Table S1). (A) Sequence with highlighted ordered (orange) and disordered (blue) segments, and domain boundaries marked by square brackets. (B) Representative full atom conformation generated by AlphaFold2 (for visualization purposes only;69,70 beads with van der Waals radii; hydrogen atoms omitted for the sake of clarity). Ordered clusters (orange) form dense blobs connected with linkers (blue). (C) Visualization of a representative configuration generated using the GLM method in which beads are displayed with their hydrodynamic radii.CC BY · PubMed Central
Figure 2 Examples of normalized FCS autocorrelation curves with raw fitting residuals for an intrinsically disordered H6–SUMO–GW182SD–mCherry (N = 809; Rh = 66 ± 6 Å) (green) in comparison with apoferritin (N = 4200; Rh = 58 ± 3 Å) (black). The crystal structure of apoferritin (Protein Data Bank entry 2w0o(93)) and the putative conformation of H6–SUMO–GW182SD–mCherry predicted by AlphaFold69 are shown for the purpose of illustration, preserving the relative sizes of the solvent accessible surfaces of atoms.
Figure 2 Examples of normalized FCS autocorrelation curves with raw fitting residuals for an intrinsically disordered H6–SUMO–GW182SD–mCherry (N = 809; Rh = 66 ± 6 Å) (green) in comparison with apoferritin (N = 4200; Rh = 58 ± 3 Å) (black). The crystal structure of apoferritin (Protein Data Bank entry 2w0o(93)) and the putative conformation of H6–SUMO–GW182SD–mCherry predicted by AlphaFold69 are shown for the purpose of illustration, preserving the relative sizes of the solvent accessible surfaces of atoms.CC BY · PubMed Central
Figure 3 (A) Experimental Rh values plotted vs the number of amino acid residues in the protein chain, N, and power law curve fitted to Rh values of folded proteins (FPs) together with the 95% confidence band. (B) Direct comparison of the predicted vs measured Rh values for all of the proteins modeled using the MDA+GLM approach.
Figure 3 (A) Experimental Rh values plotted vs the number of amino acid residues in the protein chain, N, and power law curve fitted to Rh values of folded proteins (FPs) together with the 95% confidence band. (B) Direct comparison of the predicted vs measured Rh values for all of the proteins modeled using the MDA+GLM approach.CC BY · PubMed Central
Figure 4 Comparison of different methods of estimation of Rh. Boxes show interquartile ranges with median confidence bands marked by notches. MDA with GLM ensemble generation (A) performs best on the IDP benchmark set with standard errors of 18.15% and 7.09 Å (compared to 24.80% and 8.46 Å for a simple power law). Methods based on the Kirkwood–Riseman Rh estimation (C and D) typically underestimate hydrodynamic size of the molecule. Power law fits with one free parameter (E) and two free parameters (F) evaluated using leave-one-out cross-validation are compared with the formerly reported power law112 (G) and models based on polyproline II structure propensities without30 (H) and with31 (I) regard to the charge, and a sequence-based model112 (J) that takes into account the total charge of the molecule. Theoretical methods with no knowledge of the presence of domains in the IDP (ND; B and D) significantly overestimate the hydrodynamic size of the molecule. Domain data can be incorporated into our ensemble generation engine leading to more accurate estimates of Rh (A). Note that experimental uncertainty also contributes to the errors presented here and in Table 1.
Figure 4 Comparison of different methods of estimation of Rh. Boxes show interquartile ranges with median confidence bands marked by notches. MDA with GLM ensemble generation (A) performs best on the IDP benchmark set with standard errors of 18.15% and 7.09 Å (compared to 24.80% and 8.46 Å for a simple power law). Methods based on the Kirkwood–Riseman Rh estimation (C and D) typically underestimate hydrodynamic size of the molecule. Power law fits with one free parameter (E) and two free parameters (F) evaluated using leave-one-out cross-validation are compared with the formerly reported power law112 (G) and models based on polyproline II structure propensities without30 (H) and with31 (I) regard to the charge, and a sequence-based model112 (J) that takes into account the total charge of the molecule. Theoretical methods with no knowledge of the presence of domains in the IDP (ND; B and D) significantly overestimate the hydrodynamic size of the molecule. Domain data can be incorporated into our ensemble generation engine leading to more accurate estimates of Rh (A). Note that experimental uncertainty also contributes to the errors presented here and in Table 1.CC BY · PubMed Central

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Metadata

Authors
Waszkiewicz, R., Michaś, A., Białobrzewski, M. K., Klepka, B. P., Cieplak-Rotowska, M. K., Staszałek, Z., Cichocki, B., Lisicki, M., Szymczak, P., & Niedzwiecka, A.
Affiliations
  • University of Warsaw (PL)
  • Institute of Physics (PL)
Corresponding author
Szymczak, Piotr
ORCID
Venue
The Journal of Physical Chemistry Letters
Publisher
openRxiv
Published
2024-02-08
Volume
15
Issue
19
Pages
5024-5033
ISSN
1948-7185 (ISSN-L)
DOI
10.1101/2024.02.05.578612
PMC
PMC11103702
OpenAlex
W4396593132
Cited by
16
References
2
Citations by year
2026: 4 · 2025: 10 · 2024: 2
FWCI
2.18
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • The Journal of Physical Chemistry Letters (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
Funders
  • European Commission (POIG.02.02.00-00-025/09)
  • Narodowe Centrum Nauki (2018/31/D/ST3/02408, 2016/22/E/NZ1/00656)
  • Uniwersytet Warszawski
  • European Regional Development Fund (POIG.02.02.00-00- 025/09)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
  • Physical Sciences › Mathematics › Modeling and Simulation › Fractional Differential Equations Solutions
Keywords
intrinsically disordered proteins, hydrodynamic radius, diffusion coefficient prediction, hydrodynamic interactions, self-avoiding walks, conformational sampling
MeSH terms
Diffusion, Protein Conformation, Hydrodynamics, Intrinsically Disordered Proteins

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