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. 2023 Jun 20;63(13):4079–4087. doi: 10.1021/acs.jcim.3c00113

Comparative Performance of Computer Simulation Models of Intrinsically Disordered Proteins at Different Levels of Coarse-Graining

Eric Fagerberg †, Marie Skepö †,‡,*
PMCID: PMC10336962  PMID: 37339604

Abstract

graphic file with name ci3c00113_0007.jpg

Coarse-graining is commonly used to decrease the computational cost of simulations. However, coarse-grained models are also considered to have lower transferability, with lower accuracy for systems outside the original scope of parametrization. Here, we benchmark a bead-necklace model and a modified Martini 2 model, both coarse-grained models, for a set of intrinsically disordered proteins, with the different models having different degrees of coarse-graining. The SOP-IDP model has earlier been used for this set of proteins; thus, those results are included in this study to compare how models with different levels of coarse-graining compare. The sometimes naive expectation of the least coarse-grained model performing best does not hold true for the experimental pool of proteins used here. Instead, it showed the least good agreement, indicating that one should not necessarily trust the otherwise intuitive notion of a more advanced model inherently being better in model choice.

1. Introduction

In order to decrease the computational cost of molecular simulations, coarse-graining (CG) can be an option, enabling simulations of both larger systems and slower processes. The idea is to average out finer details while keeping the degrees of freedom having the greatest impact on conformation and, thereby, obtaining a much simpler model.1 The potential energy function considers only an effective interaction between pseudoatoms, also denoted as beads, as in beads-on-a-string, or CG sites. A smoother free energy surface is attained, allowing for larger integration steps, which is why CG models may decrease the computational load by several orders of magnitude.2,3 Both the level of CG, i.e., the mapping of atoms or chemical fragments to pseudoatoms, and the effective energy potential vary widely depending on what properties are of interest or the main system of study. This could be mechanical properties,4 physical response to stimuli,5 protein folding,6−10 phase behavior of proteins,11 partitioning free energies,12 protein–protein interactions,13−15 structural properties,16 or aggregation,17−19 though models may find use or later be extended beyond the initial target properties. However, the simplifications introduced may also have drawbacks of lower transferability, having decreased accuracy for systems dissimilar to the parametrization source systems of the model.20 The choice of the model must be considered carefully.

Intrinsically disordered proteins (IDPs) lack a single specified structure, instead existing as an ensemble of wide-ranging conformers in solution.21−23 Despite this, they are biologically relevant, having roles in, for example, cell signaling, transcription, and regulation.24−27 In addition, they are abundant — estimates indicate 32% of residues in eukaryotic proteins to be disordered.28

Their flexibility, having an energy landscape of many, often shallow, minima rather than a single deep minimum,29−31 requires longer simulations in the absence of enhanced sampling techniques in order to properly explore all conformers of relevance. From that perspective, CG modeling is an excellent and advantageous fit for studying IDPs.

Recently, Baul et al.32 presented a two-bead per amino acid CG model named SOP-IDP, which was found to have, after parametrization, excellent agreement with small-angle X-ray scattering (SAXS) data for a curated set of IDPs. The same model was later used to find distinctions between Aβ40 and Aβ42 conformational ensembles.33 The SOP-IDP model was in part based on earlier two-bead models focused on folding,,34 but also in part based on a model by Cragnell et al.,35 more simple in terms of the number of parameters, size of the training set, and having a one-bead per amino acid mapping. Despite its simplicity and limited training set, it has been shown to have some transferability.36 Given the relationship between the models and the results of the SOP-IDP model, we here ask the question: How much more performance is gained by the more advanced, computationally expensive SOP-IDP model? Taking this somewhat provocative question, given that one should expect better performance from a more advanced model, one step further, we investigate how much more a yet more advanced model than the SOP-IDP model offers in terms of performance. The model of choice in this regard was the Martini 2 model,37,38 with the corrections of Stark et al.39 (hereafter referred to as “Martini Stark”). This model offers a four-bead per amino acid, thus being the most high-resolution model in this study.

This latter choice requires some motivation, as there are a few competitors. Primarily, there are more recent corrections made by Benayad et al.,40 which uses the same tuning strategy as Stark et al. of setting up a hyperparameter to scale interaction parameters. However, they find a different optimal value, in conflict with Stark et al. The latter tunes parameter for protein–protein interactions, as found by osmotic second virial coefficient experimental data, while the former tunes for liquid–liquid phase separation (LLPS) properties, e.g., droplet formation, excess transfer energy of a protein from/to solution and a droplet. Here, we take a cue from a study by Dannenhoffer-Lafage and Best,41 who found in the parametrization of a CG model a conflict between tuning for single-chain properties and LLPS properties and make an a priori hypothesis that there may be a similar situation here, choosing the parameters of Stark et al. as we are investigating single-chain properties.

Additionally, the newer version of Martini (version 3) should be considered. However, previous testing of a beta version of this model yielded less good results for an IDP.42 LLPS properties have, however, been semiquantitatively predicted,43 which would indicate that, if the “LLPS versus single chain properties conflict” is a general problem, this latest iteration of Martini is on the side of computing LLPS properties. Indeed, a recent paper published while this work was in progress showed Martini 3 to underestimate IDP dimensions for several IDPs.44

The performance measure employed here is the radius of gyration (Rg), experimentally available through SAXS data, as found in the curated data set by Baul et al. This observable can be computed for all models considered. Still, it should be stressed that the performance of other properties may be different and, in some cases, cannot be reasonably considered for highly CG models.

2. Models and Methods

2.1. The Bead-Necklace Model

The bead-necklace model of Cragnell et al.,35 which traces its roots from studies of complexation between polyelectrolytes and macroions45 and surface adsorption of IDPs,46,47 considers each amino acid residue and the end terminals as a hard sphere with a radius of 2 Å. The hard spheres are linked with a harmonic potential, with the equilibrium distance set to 4.1 Å and a force constant of 0.4 N/m. The amino acid residues are differentiated by their charge, which is set to a fixed value of either +1, 0, or −1. To set these charges, a short titration simulation was run in the software Faunus,48,49 which uses the intrinsic pKa values of Nozaki and Tanford.50 Electrostatics were treated through an extended Debye–Hückel potential where the volume of the particles was taken into account, and van der Waals interactions were considered through a soft short-range attractive potential, set to be the same for all amino acids, giving an attractive potential of 0.6 kT at the closest contact. Explicit counterions, one for each protein charge, were modeled as hard spheres of 2 Å radius and a +1 or −1 charge.

Simulations employing the bead-necklace model were performed using the software MOLSIM,51 in the canonical ensemble, thus, a constant number of particles, temperature, and volume, through the Monte Carlo Metropolis algorithm.52 A cubic simulation box was used, with a side length large enough to contain each protein’s contour length in the box. Periodic boundary conditions were applied in all directions, and the minimum image convention was employed to truncate long-ranged Coulomb interactions. Four trial moves were used: single-bead translation, pivot rotation, translation of the whole chain, and the slithering move.53 The probability of a single-bead trial move was 17 times more likely than the other moves, according to previous research that established this as a good ratio.35,36 For the starting structure, beads were randomly distributed in the box. For the initial equilibration of the system, 200,000 cycles of Monte Carlo simulation were used, followed by 1,000,000 cycles for the production run.

2.2. The Martini 2 Model with Modifications of Stark et al

Starting structures of the IDPs were obtained through the Robetta protein structure prediction service using the RoseTTAFold algorithm,54 with the exception of Histatin 5 (Hst5), which used a starting structure obtained from the final configuration of an atomistic molecular dynamics simulation previously published.55 The starting structures were converted to the Martini 2 resolution using the martinize.py38 script (version 2.4), with all residues set to have a secondary structure as a random coil. GROMACS version 2019.2,56−59 including associated tools, was used to further set up and perform the simulations. Initially, the box sizes were set to be the largest distances between the atoms in the initial structure, including a specified distance for the smaller proteins, of 20 Å, but increased to, initially, 40 Å for the larger proteins. More specifically, the Gromacs command gmx editconf was used, with input -d first set to 1.0; notice that Gromacs uses nm as the default length unit, which increases the box size so that the box edge is the specified distance away from any part of the protein in all directions. As initial results were gathered, box sizes were increased accordingly. The starting systems were energy minimized in a “dry” state, without solvent molecules, then solvated by GROMACS tool solvate. Solvent molecules were replaced by a number of ions (Na+, Cl–) via the GROMACS tool genion to achieve the specific salt content of each system. The system was thereafter energy minimized and equilibrated for 5 ns in the canonical ensemble, with the temperature held constant through the velocity-rescale algorithm60 using a temperature coupling parameter, referred to as tau-t in Gromacs, of 1 ps, grouping proteins, water, and ions separately,61 thus one coupling for each of these groups of particles. Another 5 ns equilibration in the isothermal–isobaric ensemble, e.g., constant pressure, constant temperature, and a constant number of particles, followed, using a Parrinello-Raman barostat,62 with a coupling constant of 12. Settings followed the recommendations of de Jong et al.63 The leapfrog algorithm64 with a 20 fs time step was used to integrate the equations of motion, a Verlet cutoff scheme, periodic boundary conditions in all directions, and a reaction field with a relative dielectric constant of 15 for electrostatics. Three replicates for each system were simulated. The simulation length for each system is detailed in SI, with a minimum of 5000 ns.

2.3. Scaling Law for IDPs

As the most minimal model possible, a scaling law for IDPs developed by Cragnell et al.36 is considered. The scaling law predicts Rg according to

2.3. 1

where N is the number of amino acids in a protein. This scaling law considers no regard for the amino acid’s identity. In general, scaling laws with exponents roughly equal to 0.6 approximate self-avoiding random coil and exponents equal to 0.5 approximate random coils.65

2.4. The Data Set of IDPs

The original data set compiled by Baul et al. has been used as a basis. However, a few changes were necessary, as some of the cited studies did not provide full information on experimental conditions. For instance, in the case of Prothymosin α, where a study by Uversky et al.66 was originally cited, the amount of salt used in the experiment was not detailed, and information was not available. In the case of α-synuclein, the cited study did not state the salt concentration used. We, therefore, considered the study of Ahmed et al.67 instead, in which a lower Rg was found, which would compare more favorably with the result of the SOP-IDP model. The proteins KEIF68 and (Histatin 5)269 were also considered for the bead-necklace model and the Martini Stark model.

2.5. Evaluation Metrics

To compute errors for each system and model, a signed percentage deviation is used, defined here as

2.5. 2

where Rg,exp is the radius of gyration found in the experiment, and Rg,sim is the radius of gyration found from a given simulation model. To compare the models across all systems, a modified Pearson χ2 value was used

2.5. 3

where Ei is the experimental Rg for system i, and Si is the simulation predicted Rg for system i. To further analyze the models in the form of biases, the fraction of charged residues, FCR = f+ + f–, with f+ being the fraction of positively charged residues and f– being the fraction of negatively charged residues, the net charge per residue, NCPR = | f+ – f–|, hydrophobicity as per the Kyte-Doolittle scale,70 the proline content, and disorder score as per the PrDOS algorithm71 were considered. FCR, NCPR, and the hydrophobicity score were estimated via the CIDER Web server.72

3. Results and Discussion

3.1. Predictions of the Radius of Gyration of Model IDPs

The full comparison of predicted Rg using the models considered in this study with the experimental data is presented in Table 1.

Table 1. List of IDPs in Data Set of Baul et al., Along with Experimental Rg and Results from the Scaling Lawa.

Chain N Rg, Exp Scaling law SOP-IDP Bead-necklace Martini Stark Comment
Hst5 24 13.8 ± 0.04 13.9 13.6 13.8 14.4  
ACTR 71 26.3 ± UNK 26.3 24.0 25 24.3 Exp. T = 278 K
Nucleoporin 81 27 ± 4 28.5 25.9 26.8 29.7 Exp. T = 296 K
SH4-UD 85 29 ± 0.4 29.3 27.8 26.6 26.5 Exp. T = 277 K
Sic1 90 32.1 ± 0.8 30.3 28.4 30.7 33.4 Bead necklace from Cragnell et al.35
p53 93 28.7 ± UNK 30.9 29.5 31.5 27.4 Exp. T = 293 K
Proth. α 111 37.9 ± 0.9 34.3 39.1 72.3 (44.6) 37.2 Exp. T = 296 K, 0 (150) mM NaCl
ERM TADn 122 38.1 ± 0.7 36.3 31.4 33.0 30.9 Exp. T = 293 K
hNHE1 131 37.5 ± UNK 37.8 32.5 34.1 31.3 Exp. T = 278 K
Alp. Syn. 140 40.0 (35.5 ± 0.5) 39.3 35.4 36.0 28.8 T = 293, 200 mM NaCl
An16 185 50 ± 5 46.3 43.2 43.2 49.5  
Osteopontin 273 55 ± 1.7 58.3 47.2 55.6 60.5  
K19 99 35 ± 1 32.0 29.6 30.1 28.7 Exp. T = 288 K
K18 130 38 ± 3 37.6 34.8 35.8 32.5 Exp. T = 288 K
K17 143 36 ± 2 39.8 37.4 38.9 35.4 Exp. T = 288 K
K10 167 40 ± 1 43.6 39 39.9 36.3 Exp. T = 288 K
K27 171 37 ± 2 44.2 40.6 42 39.3 Exp. T = 288 K
K16 174 39 ± 3 44.7 41.8 43.8 40.0 Exp. T = 288 K
K25 185 41 ± 2 46.3 39.7 39.1 34.2 Exp. T = 288 K
K32 202 41.5 ± 3 48.8 44.7 46.4 40.1 Exp. T = 288 K
K23 254 49 ± 2 54.7 47.3 47.6 48.9 Exp. T = 288 K
K44 283 52 ± 2 59.6 51 52.2 50.8 Exp. T = 288 K
hTau23 352 53 ± 3 67.7 57.1 59.9 52.3 Exp. T = 288 K
hTau40 441 65 ± 3 77.4 62.9 64.1 40.8 Exp. T = 288 K, 140 mM NaCl
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a

Included are also simulations using the SOP-IDP model of Baul et al.,32 the bead-necklace model of Cragnell et al.,35 and the Martini Stark model with the modifications of Stark et al.39 All Rg given in Å. The number after ± indicates an error. UNK denotes the error to be unknown, i.e., not reported in the original literature.

For easier comparison across different IDPs, the percentage value is also calculated; see Table 2.

Table 2. Signed Percentage Deviation of Each Model from the Experiment in Terms of Rga.

Chain N %, Scaling law %, SOP-IDP %, Bead-necklace %, Martini Stark
Hst5 24 +1 –1 0 +5
ACTR 71 0 –9 –5 –7
Nucleoporin 81 +5 –4 –1 +10
SH4-UD 85 +1 –4 –8 –9
Sic1 90 –6 –12 –4 +4
p53 93 +8 +3 +10 –5
Proth. α 111 –10 +3 +18 –2
ERM TADn 122 –5 –18 –13 –20
hNHE1 131 +1 –13 –9 –17
Alp. Syn. 140 +11 0 +1 –19
An16 185 –7 –14 –14 –1
Osteopontin 273 +6 –14 +1 +10
K19 99 –8 –15 –14 –18
K18 130 –1 –8 –6 –14
K17 143 +11 +4 +8 –1
K10 167 +9 –3 0 –9
K27 171 +20 +10 +14 +6
K16 174 +15 +7 +12 +3
K25 185 +13 –3 –5 –17
K32 202 +18 +8 +12 –3
K23 254 +14 –3 –3 0
K44 283 +15 –2 0 –2
hTau23 352 +28 +8 +13 –1
hTau40 441 +19 –3 –1 –37
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a

Rounded to the closest integer.

From the above values, a “total” score is determined for each model according to a modified Pearson χ2, which was found to be 15.4 for the scaling law, 7.1 for the SOP-IDP model, 7.6 for the bead-necklace model, and 17.8 for the Martini Stark model. The difference found between SOP-IDP and the bead-necklace model should be considered small or nonexistent as a consistent 1% difference would, in this case, translate to a χ2 difference of about 0.2. In contrast, a consistent 2% difference yields a χ2 difference of about 0.8, particularly in the light of experiments also suffering from various levels of experimental uncertainty, detailed in Table 1. Thus, no overall performance increase is found, using the Rg as a performance metric. The Martini Stark model, on the other hand, has much lower performance than expected. Our expectations are based on the a priori assumption that a less coarse-grained model should have greater transferability and the expectation of the corrections of Stark et al. to have improved not just protein–protein interactions but also intrachain interactions. Probably, the corrections have had a positive impact, but seemingly not enough to be competitive with computationally less demanding models.

3.2. Deviations between Simulations and Experiments with Respect to IDP Properties

One should consider whether any model performs better for any subclass of IDPs in the data set, thus if this particular data set may favor some models above others. Therefore, we also consider different metrics that could be a basis of bias, choosing the value of Rg, number of amino acids, FCR, NCPR, hydrophobicity, proline content, and disorder score as computed by the PrDOS algorithm.71 The data are plotted as a function of each of these metrics for each model in Figures 1–6. The specific value for each metric for each individual protein is found in SI Table S1.

Figure 1.

Figure 1

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(Left) Simulated Rg plotted versus experimental Rg for each model. A perfect model would have all values distributed on the dashed black line. Trendlines for each model are also added, with R2 being: 0.96 for the scaling law, 0.95 for the SOP-IDP model, 0.95 for the bead-necklace model, and 0.86 for the Martini Stark model. (Right) The size of each protein in terms of the number of amino acids plotted against the signed percentage error. Trendlines have R2 of 0.67 for the scaling law, 0.19 for the SOP-IDP model, 0.19 for the bead-necklace model, and −0.25 for the Martini Stark model.

Figure 6.

Figure 6

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Signed percentage error of each model versus disorder score. The black dashed line denotes a perfect match; i.e., each prediction has a signed percentage error of zero. Trendlines for each model included, with R2 being 0.01 for the scaling law, 0.16 for the SOP-IDP model, 0.11 for the bead-necklace model, and 0.32 for the Martini Stark model.

Figure 2.

Figure 2

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Signed percentage error of each model versus FCR. The black dashed line denotes a perfect match; i.e., each prediction has a signed percentage error of zero. Trendlines for each model included, with R2 being 0 for the scaling law, 0.19 for the SOP-IDP model, 0.38 for the bead-necklace model, and −0.14 for the Martini Stark model.

Figure 4.

Figure 4

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Signed percentage error of each model versus hydrophobicity. The black dashed line denotes a perfect match; i.e., each prediction has a signed percentage error of zero. Trendlines for each model included, with R2 being 0.22 for the scaling law, −0.08 for the SOP-IDP model, −0.18 for the bead-necklace model, and −0.24 for the Martini Stark model.

3.2.1. Model Deviations as a Function of IDP length

Investigating the error as a function of size (first defining size as the experimentally found Rg), we plot the signed percentage error for each model against the protein size in Figure 1 (left). Seemingly, the SOP-IDP and Martini Stark models tend to underestimate Rg as Rg becomes larger. In contrast, the scaling law has a tendency to overestimate Rg for large Rg. Defining size as the number of amino acids (Figure 1, right), the overall trends from using Rg remain except for the SOP-IDP model. In particular, the trendline R2 for the scaling law is considerably higher than for the other models, indicating that this model’s tendency to overestimate Rg for large proteins is strong. The overprediction could be due to an overly large exponent (a current setting of roughly 0.6 indicates self-avoiding random coil) or a too-large prefactor. By fitting the experimental Rg data to an equation of the same form as eq 1, a fit of

3.2.1. 4

with an R2 of 0.93 was found. The exponent found in eq 1 is closer to 0.5, indicating that the data set resembles random coils better than self-avoiding random walks.

On a more speculative note on the performance of the models as a function of the number of residues in the protein chain, the chain would have the possibility of self-entangling for longer protein chains. Very coarse-grained models, such as the bead-necklace model, should experience less self-entanglement, as less resolved mappings would be less easily entangled. The reverse would tentatively also be true; high-resolution models can self-entangle to a higher degree. Thus, the behavior of the Martini Stark model can be viewed from a polymer theory perspective: with longer chains, there are possibly exaggerated self-entanglement effects. Such an issue would ultimately be related to the possible convergence problem, discussed further below. This effect would speculatively contribute to the observation in Figure 1 (left) of Martini Stark having a slight tendency of predicting too compact structures.

3.2.2. Model Deviations as a Function of IDP Charge Properties

Regarding FCR, the bead-necklace model seems biased and less performing with increasing FCR. This would be somewhat counterintuitive, given that the model was parametrized with Hst5, having the second largest FCR of the entire data set. However, this indication may be fairly influenced by the larger deviation in the prediction of the bead-necklace model with Prothymosin α, having the largest FCR in the data set.

Using net charge per residue (NCPR), the scaling law indicates a weak tendency to overestimate Rg with increasing net charge per residue, though it is a very weak trend (Figure 3).

Figure 3.

Figure 3

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Signed percentage error of each model versus NCPR. The black dashed line denotes a perfect match; i.e., each prediction has a zero signed percentage error. Trendlines for each model included with R2 being 0.29 for the scaling law, 0.15 for the SOP-IDP model, −0.15 for the bead-necklace model, and 0.10 for the Martini Stark model.

3.2.3. Model Deviations as a Function of IDP Hydrophobicity

A trendline showing an increasing negative percentage error with increasing hydrophobicity is indicated for the Martini Stark model, while the reverse is true for the scaling law. Both of these trends are very weak. The bead-necklace model was expected to perform less with increasing hydrophobicity, given that it only differentiates proteins by charged residues. Still, the observed bias for this data set is similar to that of the Martini Stark model.

3.2.4. Model Deviations as a Function of Proline Content

As seen in Figure 5 and the R2 values (given in the figure caption), no strong bias is found regarding proline content. Also, previous research by Cragnell et al.36 found, in particular, the bead-necklace model to be able to predict Rg for IDPs containing proline, though considering a limited data set. Our results confirm these early reports.

Figure 5.

Figure 5

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Signed percentage error of each model versus proline content. The black dashed line denotes a perfect match; i.e., each prediction has a signed percentage error of zero. Trendlines for each model included, with R2 being 0.09 for the scaling law, 0.00 for the SOP-IDP model, −0.09 for the bead-necklace model, and 0.11 for the Martini Stark model.

3.2.5. Model Deviations as a Function of IDP PrDOS Disorder Score

As seen in Figure 6, the Martini Stark model shows less performance with systems with a low PrDOS disorder score; note that the lowest disorder score was 0.47. This was unexpected, as the improvements made by Stark et al. were found using globular proteins such as hen egg white lysozyme, PDB code 1HEL, with a disorder score of 0.18, and bovine chymotrypsinogen, PDB code 2CGA, with a disorder score of 0.13. The opposite trend would have been expected.

As shown by most R2 values, no strong bias is found. Indeed, one could easily confound different variables, even if the correlations were stronger. A larger and more diverse (in terms of sampling different properties) data set could reach different findings.

3.3. Extension with KEIF and (Histatin 5)2

Extending the data set slightly, we also consider how the bead-necklace and Martini Stark models compare with the short peptides KEIF and (Histatin 5)2. The latter, in particular, has been found to be somewhat challenging to simulate even with a fully atomistic model, predicting Rg to be 23.3 Å while SAXS data indicate Rg to be 18.7 Å.69 As well, also the bead-necklace model has previously predicted a too large Rg of 21.0 Å. Here, it is found that the Martini Stark model predicts Rg to be 23.6 Å, in line with the atomistic simulation but deviating compared to the experimental value. The bead-necklace model seems to be the best predictor, albeit still erroneous.

KEIF is, on the other hand, predicted by both the bead-necklace model and the Martini Stark model to have Rg of 16.0 Å, smaller than the experimental value of 17.6 Å,68 but in line with previous atomistic simulation (16.4 Å). Thus, all models considered here, even referenced atomistic models, differ very little regarding predicted Rg for KEIF. However, the scaling law prediction, 16.8 Å, is actually the best predictor, which is fairly curious given that the scaling law overall is the worst predictor. Speculatively, the small size of KEIF may play a part in this, as well as (Histatin 5)2. The peptide closest in size to these is Hst5, which was overall well predicted, but Hst5 was also part of the training set for both the scaling law and the bead-necklace model, which is why a more strict evaluation should leave Hst5 out. This leaves the overall conclusion that these smaller peptides are difficult to model.

3.4. The Issue of Convergence

A CG model should generally have a smoother energy landscape than an atomistic model. This would influence the ease at which a simulation reaches convergence.2 With decreasing CG among the bench-marked models here, in principle, the bead-necklace model should have the least issue with convergence, the SOP-IDP model having slightly more convergence time, and the Martini Stark model the most convergence issues, in particular for the very large systems. Indeed, for some systems, plots of Rg versus simulation time indicate replicates being trapped in local minima, see SI, where notable examples are SH4-UD, Prothymosin α, and K44. However, for these examples, the average Rg values across all replicates are fairly similar to experimental values; hence, sampling may still be considered adequate, probably as replicates sample different local minima. The system with the least experimental agreement in the Martini Stark modeling, hTau40, shows two replicates approaching a low value of about 40 Å, with the third also trending toward a lower than expected value. This is particularly unexpected since the RoseTTAFold initial structure aligns well with the experimental Rg. When a smaller simulation box was used, also here two of three replicates trended toward an Rg of about 40 Å (data not shown), indicating the tendency toward this structural region to be strong. Thus, the result is considered to be accurate. Investigating this behavior more closely by considering the contact maps (found in Supporting Information), interactions with several residues in the range 50–100 themselves and with residues around 250 and 370 are underestimated in replicates 2 and 3, which is somewhat counterintuitive. More contracted structures would be expected to have more intrachain interactions, not the opposite. Several differences in local contacts are also observed.

It is noted that the hTau40 system contributes greatly to the χ2 of the Martini Stark model. Exclusion of this system changes the χ2 of all the models to 13.0 for the scaling law, 7.1 for the SOP-IDP model, 7.6 for the bead-necklace model, and 8.8 for the Martini Stark model, showing better performance comparability with the other models. But even with this cherry-picking, the Martini Stark model is least consistent with the experimental data pool of the three simulation models tested here.

3.5. Observations of Systems with Large Prediction/Experiment Discrepancy Using Martini Stark

Among other less well-predicted systems using the Martini Stark model, defined as a percentage deviation greater than 15, it is found that ERM TADn has fairly good convergence (see Supporting Information), with all replicates showing similar behavior, in particular, all intrachain interactions are fairly local, with some longer ranged interactions between residues 80–90. Regarding hNHE1, replicate 1 has a much lower Rg for most of the simulation time until the end, where it achieves similar Rg as the other two replicates. The contact maps indicate that replicate 1 has many long-range interactions while the others do not. Extending the simulation further may increase agreement with experimental data, provided replicates sample similar to the last part of the simulation. However, given that the other replicates still display too low Rg for hNHE1, an increased simulation time would only improve Rg to a limited extent. α-Synuclein has fair convergence, with intrachain interactions being mainly local, with slightly longer-range interactions in residue regions 10–30 and 80–100. K19 has only local intrachain interactions, except in the N-terminal region, up to about residue 15. Lastly, K25 has notable interaction centers around residues 70 and 100 and a weak interaction center at about residue 125.

3.6. Distribution of Counterions

The bead-necklace model includes explicit counterions in the simulations, one counterion for each charge. The radial distribution function (RDF) of the counterion distance to the protein chain is shown in Supporting Information. The results are as expected: proteins with a net positive charge attract negative counterions and repel positive ones and vice versa for proteins with a net negative charge. The degree of this behavior would depend on the distribution of the charges along the protein chain and the radially averaged structure of the protein. All simulations have a minimum of two counterions in the system due to explicit modeling of end terminals, which are charged in the system. Having very few counterions in the simulation box would affect the convergence of the RDF. This is particularly clear in the case of An16 (Figure S63). Convergence of counterion RDF does seemingly not have a large effect on Rg convergence. In particular, An16 has fairly good convergence and slight bias toward smaller Rg in the later part of the simulation.

3.7. Remarks on the Models

In this study, we only use three models of varying CG level to gain insight into the added performance of more fine-grained models. Additional models would have been useful, as these models might not be the best representative of each CG level. At the same time, it is recognized that the CG level and the number of parameters matter.

To some extent, the SOP-IDP model has an advantage in this data set, as six IDPs (Histatin 5, ACTR, hNHE1, K32, K23, and hTau40) were part of the training set for SOP-IDP. In this context, it is interesting that hNHE1, one of the training set IDPs, is one of the proteins most problematic to simulate with the SOP-IDP model. This could indicate that SOP-IDP parametrization did not overfit the initial training set.

The most advanced model, Martini Stark, was found to have the least good agreement with experimental data. However, this model has a much larger degree of generality since it can also be used to model globular proteins, for which the other models are unfit. Therefore, it may not be surprising that the IDP-specific models outperform the Martini Stark model for an IDP data set.

During the setup of the Martini Stark model, one needs to define the secondary structure for each amino acid. Here, we have let the secondary structure be a coil for the entirety of the IDPs considered. Still, a possibility is to use a prediction tool of secondary structure and set the secondary structure to that predicted. Even if this may seem contrary to the flexibility of IDPs, it can be possible that any segment of an IDP samples a specific secondary structure to such a great extent while still interconverting to other structures. Hence, it is reasonable to set that segment to have a secondary structure throughout the simulation. However, this would be heavily dependent on the accuracy of the method for determining secondary structure, which is why we here avoid such a procedure while noting that it might be possible to achieve higher performance with such a procedure.

4. Conclusions

CG modeling is advantageous because it allows us to simulate complex and dense systems and to achieve an understanding of the underlying physics, the former being next to impossible with atomistic simulations with current computation technology. Here, we present an initial study using a set of 24 IDPs to determine to what extent CG models actually differ with respect to the level of detail.

This initial study concludes that a more fine-grained model may not have more predictive power than a simpler one. No strong biases for either model for a selected number of metrics were found, which would otherwise have motivated the preference of one model for a subclass of IDPs. Future studies should involve a larger pool of IDPs, including increased length of the primary sequence and more diversity in different IDP properties.

Acknowledgments

The computer simulations were enabled by resources provided by LUNARC at Lund University, Sweden. We thank Prof. Dmitri Svergun, Prof. Vladimir Uversky, Prof. Markus Zweckstetter, and Prof. Dave Thirumalai for providing additional information about experimental details. Prof. Dave Thirumalai is also acknowledged for providing information on the SOP-IDP model. We acknowledge the Crafoord Foundation, Sweden, for financial support.

Data Availability Statement

The software package MOLSIM is available at https://github.com/joakimstenhammar/molsim. Gromacs is available at https://manual.gromacs.org. Simulation setup files can be found at https://zenodo.org/record/7523635.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.3c00113.

  • Table of properties for the proteins. Table containing the starting Rg from the RoseTTAFold model and Rg obtained for each replicate for the Martini Stark model, figures of the running average of Rg evolution over time for the Martini Stark simulations, for convergence consideration. Computed contact maps for Martini Stark model and the radial distribution function of counterions versus protein chain for the bead-necklace model. Graphs of average Rg for each macrostep for the bead-necklace simulations for convergence consideration are included. (PDF)

The authors declare no competing financial interest.

Supplementary Material

ci3c00113_si_001.pdf (5.3MB, pdf)

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

ci3c00113_si_001.pdf (5.3MB, pdf)

Data Availability Statement

The software package MOLSIM is available at https://github.com/joakimstenhammar/molsim. Gromacs is available at https://manual.gromacs.org. Simulation setup files can be found at https://zenodo.org/record/7523635.

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