SAXSMoW 3.0: New advances in the determination of the molecular weight of proteins in dilute solutions from SAXS intensity data on a relative scale

Abstract

SAXSMoW (SAXS Molecular Weight) is an online platform widely used over the past few years for determination of molecular weights of proteins in dilute solutions. The scattering intensity retrieved from small‐angle X‐ray scattering (SAXS) raw data is the sole input to SAXSMoW for determination of molecular weights of proteins in liquid. The current updated SAXSMoW version 3.0 determines the linear dependence of the true protein volume on their apparent protein volume, based on SAXS curves calculated for 67,000 protein structures selected from the Protein Data Bank. SAXSMoW 3.0 was tested against 43 experimental SAXS scattering curves from proteins with known molecular weights. Our results demonstrate that most of the molecular weights determined for the nonglycosylated and also for the glycosylated proteins are in good agreement with their expected molecular weights. Additionally, the average discrepancies between the calculated molecular weights and their nominal values for glycosylated proteins are similar to those for nonglycosylated ones.

1. INTRODUCTION

Small‐angle X‐ray scattering (SAXS) technique is being widely used to retrieve low‐resolution structural information on biomacromolecules in solution. ¹ , ² , ³ , ⁴ After the pioneering works by A. Guinier, ⁵ the SAXS technique found its applications in investigations of polymers, liquid crystals, proteins in solution, and other materials. ⁶ Modern synchrotron‐based X‐ray sources, powerful computers, and specialized software along with new area detectors significantly improved the quality of the results derived from SAXS experiments. ¹ , ² , ⁷ Isotropic systems composed of a diluted set of randomly oriented identical nanoparticles immersed in liquids (e.g., proteins diluted in buffers) are particularly favorable for SAXS data analysis. ⁸ As a matter of fact, in this case the associated SAXS curves are free from frequently complex effects due to anisotropy, size polydispersity, and spatial correlation. ⁷ , ⁹ , ¹⁰ , ¹¹

Using classical setups, SAXS technique allows for the determination of low‐resolution structural parameters of biological systems, such as macromolecules in solution, with sizes ranging from 1 nm up to 50 nm. ¹ , ⁷ The relevant parameters usually determined for macromolecules from SAXS data are the radius of gyration, $R_g$, three‐dimensional low‐resolution envelope, molecular weight, $M_r$, and oligomeric state. ¹ , ² , ³ , ⁴ Knowledge of the molecular weight is particularly helpful for determination of the oligomeric state of proteins in solution.

Several methods for determination of the molecular weight of proteins in solution are reported in the literature. Korasick and Tanner ¹² classified them as: (a) empirical methods, (b) methods based on the determination of the SAXS intensity at $q=0$, $I\left(0\right)$, and (c) methods based on SAXS invariants. One of the empirical methods named as $V_p/1.6$ and another one, based on power‐laws, are generally applicable to large proteins $\left(M_r>100\mathrm{kDa}\right)$, with expect uncertainties in the predicted molecular weight of approximately 25%. ¹² Regarding the $I\left(0\right)$ ‐based methods, SAXS data must be referenced to known protein standards ¹³ or be collected at absolute scale. ⁸ , ¹⁴ The drawback of these methods is the requirement of accurate assessment of protein concentration.

Methods for determinations of molecular weights based on SAXS‐derived invariants ¹⁵ , ¹⁶ and/or volume of correlation ¹⁷ can be applied to SAXS curves measured on a relative scale, thus not requiring neither a reference of SAXS data to standard curves, nor a precise knowledge of protein concentration. Bayesian method is another useful approach that takes into account the results derived from different procedures using statistical approaches. ¹⁸ Being quite straightforward, methods for determination of molecular weights based on SAXS data measured on a relative scale are frequently preferred by SAXS users.

SAXS methods for determination of protein molecular weight usually consider that the protein density is independent of protein nature, and spatially and time constant within the molecular volume. Under these conditions, proteins with electron density ${\rho }_p$ _, embedded in a homogeneous liquid matrix with electron density ${\rho }_m$, can be well described by a two‐electron density model with sharp interfaces. Specifically, SAXSMoW procedure assumes that the protein mass density is equal to 1.37 g/cm³. However, eucaryotic proteins or heterologous proteins expressed in the eucaryotic expression systems can undergo post‐translational modifications, such as glycosylation, which might affect their average densities. The glucan content might impact the scattered SAXS intensity because of the additional excluded volume caused by the glycosylations at the surface of the protein molecules. ¹⁹

SAXSMoW version 2.0 is an open‐access program widely used by the SAXS community for determination of the molecular weights of proteins in dilute solutions from SAXS curves measured on a relative scale. In the present work, we describe several improvements of SAXSMoW 2.0 that led to a new updated version of the program, SAXSMoW 3.0.

2. DESCRIPTION OF SAXSMoW METHOD

The calculation of the protein molecular weight by using SAXSMoW ¹⁵ requires the input of only a single 1D‐SAXS curve determined on a relative scale, produced by a monodisperse protein sample in a dilute solution. This procedure is based on the calculation of truncated values of the Porod invariant, $Q^{\prime }$, associated with the integration of Kratky functions ($I\left(q\right).q^2$) from $q=0$ up to $q=q_{\max }$. In other words, the truncated Porod invariant $Q^{\prime }\left(q_{\max }\right)$, is defined as,

$$Q^{\prime }\left(q_{\max }\right)={\int }_0^{q_{\max }}I\left(q\right).q^2\mathit{dq}$$ (1)

Notice that the true Porod invariant, $Q$, is defined as $Q={\int }_0^{\infty }I\left(q\right).q^2\mathit{dq}$. The reason for the use of truncated Porod invariants—instead of the Porod invariant itself ‐ is that the experimental SAXS curves at high $q$ are usually very noisy and the necessary extrapolation of the $I\left(q\right).q^2$ function up to $q=\infty$ can be very imprecise. SAXSMoW version 2.0 ¹⁶ allowed to select one of two different integration limits, the first being given by $q_{\max }=8/R_g$, and the second one being the $q_{\max }$ value that satisfies the relationship $\mathit{log}\frac{I\left(0\right)}{I\left(q_{\max }\right)}=2.25$. The user could select one of these values for $q_{\max }$ depending on the statistical quality of their SAXS results at high $q$ ‐value.

The volume of identical proteins in dilute solution, $V_p$, is determined from SAXS curves on a relative scale by applying the known equation $V_p=2{\pi }^{2}I\left(0\right)/Q$ ⁹. Thus, by using a truncated integral, $Q^{\prime }\left(q_{\max }\right)$, instead of the true protein volume, one determines an apparent volume $V_p^{\prime }\left(q_{\max }\right)$ given by

$$V_p\prime \left(q_{\max }\right)=\frac{2{\pi }^{2}I\left(0\right)}{Q\prime \left(q_{\max }\right)}$$ (2)

Notice that the apparent volume $V_p\prime \left(q_{\max }\right)$ is higher than the particle volume $V_p$ for all finite $q_{\max }$ values. After having determined the apparent volume of the protein by applying Equation (2), the next step is to calculate the true molecular volume. The SAXSMoW program relies on the existence of a linear relationship between the true protein volume $V_p$ and the apparent volume $V_p\prime$ derived from SAXS data by applying Equation (2).

The relationship between true protein volumes $V_p$ and apparent volumes $V_p\prime$ for different $q_{\max }$ values was implemented in SAXSMoW 1.0 and 2.0 versions based on 1,148 structurally characterized proteins ² deposited to the Protein Data Bank (PDB). ²⁰ Thus, the volumes $V_p$ of protein monomers could be considered as a priori known parameters. Furthermore, the apparent protein volumes $V_p\prime$ were determined by successively calculating (a) the SAXS intensity curves corresponding to the proteins selected from the PDB by applying the Crysol program, ²¹ (b) the truncated Porod invariants $Q^{\prime }\left(q_{\max }\right)$ for different $q_{\max }$ values by using Equation (1), and, finally, (c) the apparent volume $V_p^{\prime }\left(q_{\max }\right)$ by Equation (2). Since the plots of the $V_p\left(V_p^{\prime }\right)$ functions for different $q_{\max }$ values exhibit, in all cases, linear dependences, the protein volumes were determined by applying the equation $V_p=A\left(q_{\max }\right)+B\left(q_{\max }\right).V_p\prime \left(q_{\max }\right)$. The calculations of the coefficients $A$ and $B$ were performed for six different $q_{\max }$ values. Finally, the molecular weights of proteins were calculated by assuming a mass density equal to 1.37 g/cm³.

In the current version of SAXSMoW program, SAXSMoW 3.0, the SAXS intensity functions $I\left(q\right)$ were also determined by using CRYSOL program ²¹ (ATSAS suite package) ²² but in this case the calculations were conducted for a much higher number (67,000) of nonglycosylated proteins selected from the PDB. ²⁰ The SAXS intensity for $q=0$, $I\left(0\right)$, and the truncated integrals $Q^{\prime }\left(q_{\max }\right)$ (Equation 1) were determined for 40 different $q_{\max }$ values, and finally the corresponding apparent volumes, $V_p^{\prime }$, were computed by Equation (2). The volumes V _p ·V _p of the proteins selected from the PDB are plotted in Figure 1 as functions of their calculated apparent volume $V_p^{\prime }$. The $V_p$ versus $V_p^{\prime }$ functions determined for all protein data sets, shown in Figure 1, indicate overall linear dependences for every selected $q_{\max }$ value, as already observed in the previous versions of SAXSMoW. ¹⁶ The linear and angular coefficients corresponding of equation $V_p=A+B·V_p^{\prime }$ that best fitted to the total set of $V_p\left(V_p^{\prime }\right)$ points corresponding to 67,000 proteins were determined for a number of different $q_{\max }$ values, ranging from 0.1 to 0.5 Å⁻¹ with $∆q$ of 0.01 Å⁻¹. Thus, the coefficients $A\left(q_{\max }\right)$ and $B\left(q_{\max }\right)$ are calculated in SAXSMoW 3.0 for 40 different $q_{\max }$ values.

FIGURE 1.

Molecular volume $V_p$ of 67,000 nonglycosylated proteins selected from the PDB as a function of their apparent volume $V_p^{\prime }(q_{\max }$) derived from SAXS data. The results corresponding to only three different $q_{\max }$ values are plotted for clarity. The dashed line corresponds to the case for which $V_p=V_p^{\prime }(q_{\max }$ =∞). The protein files were selected from the PDB by using the criteria of a resolution better than 2.0 Å and sequence identity ≤90%

It is worth noting that the points in Figure 1 associated to the 67,000 selected proteins are dispersed around and close to the best fitted straight lines with an average absolute discrepancy around 10%. ¹⁶ Therefore, since the determination of molecular weights relies on the validity of the linear equation $V_p=A+B·V_p^{\prime }$, one can a priori expect that the average discrepancies between molecular weights determined by the SAXSMoW program and the actual molecular weights will also be around 10%.

3. VALIDATION OF SAXSMoW 3.0

The molecular weights of nonglycosylated proteins associated with a set of 31 experimental SAXS curves, predominantly selected from the SASBDB data repository ²³ were determined using SAXSMoW 3.0 program. The SAXS intensities at $q=0$, $I\left(0\right)$, for all proteins selected from the SASBDB data repository were determined by extrapolating the linear part of the Guinier plot to $q=0$. Moreover, after selecting adequate $q_{\max }$ values, the truncated Porod invariants, $Q^{\prime }\left(q_{\max }\right)$, were automatically obtained for each of the curves by applying the procedure proposed by Piiadov et al. ¹⁶ Finally, the apparent protein volume $V_p\prime$ was determined by applying Equation (2), the protein volume by using the linear function $V_p=A+B.V_p^{\prime }$, and the molecular weight by assuming a protein mass density equal to 1.37 g/cm³.

The molecular weights $M_r$ and oligomeric state number n determined from SAXS data for 31 nonglycosylated proteins by using SAXSMoW 3.0 are reported in Table 1. The average absolute discrepancy of the molecular weights of proteins with respect to their expected molecular weight defined as $<D_g>=<\left[\left|M_r-n.M_n\right|/\left(n.M_n\right)\right]>*100\%—\text{where}$ $M_n$ is the molecular weight of the monomer determined based on protein sequence—is equal to 12.4%.

TABLE 1.

Molecular weights ($M_r$) and oligomeric state numbers ($n$) of nonglycosylated proteins determined by applying SAXSMoW 3.0 to a set of 31 SAXS data, most of them extracted from the SASBDB repository ²³

SASBDB ID	Protein	$q_{\max }$ (Å−1)	$M_n$ (kDa)	$M_r$ (kDa) (discrepancy)	$n$
SASDJD2	Human respiratory syncytial virus A (RSV) phosphoprotein oligomerization domain	0.386 (M1)	4.5	21.5 (+19.7%)	4
SASDAQ2	Ubiquitin	0.058 (M1)	9	5.7 (−36.2%)	1
SASDAG2	Lysozyme	0.014 (M1)	14	10.2 (−26.9%)	1
SASDAB2	Cytochrome c	0.017 (M1)	12	9.1 (−24.0%)	1
SASDAK2	Myoglobin	0.025 (M1)	17	11.6 (−31.7%)	1
SASDAN2	RNase	0.028 (M1)	16	12.3 (−23.1%)	1
SASDA82	Apoferritin	0.230 (M2)	20	567.7 (+18.3)	24
SASDAR3	PsrP functional binding region	0.358 (M1)	22.12	22.0 (−0.3%)	1
SASDBY9	Immunoglobulin domains 3,4 of Nucleoporin Pom152	0.279 (M1)	25.6	24.0 (−6.2%)	1
SASDAA8	Chymotrypsinogen	0.022 (M1)	26	25.7 (−1.3%)	1
SASDBP4	Membrane lipoprotein FrpD	0.262 (M2)	26.76	25.8 (−3.6%)	1
SASDBY3	Aureochrome	0.197 (M2)	28.65	86.1 (+24.5%)	2
SASDCF3	Nucleolysin	0.292 (M1)	30	30.1 (+1.1%)	1
SASDB76	Deglycosylated myelin‐associated glycoprotein	0.238 (M2)	35	44.1 (+25.9%)	1
SASDLQ2	l‐lactate dehydrogenase	0.231 (M1)	35.31	131.6 (−6.81%)	4
SASDFS8	Alcohol dehydrogenase 1	0.008 (M1)	36.75	142.7 (−2.9%)	4
SASDBZ2	Class I fructose‐1,6‐bisphosphate aldolase	0.181 (M1)	38.1	328.8 (−13.4%)	10
SASDA68	Aldolase	0.008 (M1)	39.3	157.2 (+0.1%)	4
SASDAL2	Ovalbumin	0.028 (M1)	43	44.1 (+2.4%)	1
SASDAK6	Glucose Isomerase	0.236 (M1)	43.23	177.8 (+2.8%)	4
SASDAA4	GbpA	0.256 (M2)	54	52.9 (+3.3%)	1
SASDGY4	Beta‐amylase	0.190 (M1)	57	223.9 (−1.8%)	4
SASDGY4	Beta‐amylase	0.019 (M1)	57.25	223.9 (−2.2%)	4
SASDBQ5	Cyclohexanone monooxygenase	0.185 (M2)	60.70	70.6 (+16.4%)	1
SASDBB5	Cyclohexanone monooxygenase	0.306 (M1)	60.75	66.8 (+10%)	1
SASDFQ8	Bovine serum albumin	0.290 (M1)	66	69.5 (+5.2%)	1
SASDFR8	Bovine serum albumin	0.203 (M1)	66	141.0 (+6%)	2
SASDCT7	PYR16	0.209 (M2)	71.65	77.8 (+8.7%)	1
SASDAF6	Kgp gingipain	0.198 (M2)	73.86	80.4 (+8.9%)	1
SASDCR3	PutA	0.132 (M2)	119.18	234.4 (+1.7%)	2
SASDAK4	CRM1 RanGTP	0.222 (M1)	148	163.6 (+10.6%)	1
SASDJP3	Alpha‐2‐macroglobulin	0.221 (M2)	161	708.6 (+10.0)	4

Note: $M_n,$ expected nominal molecular weight of the monomer determined; M1 and M2, upper limits of integration of the $I\left(q\right).q^2$ function given by $q_{\max }=8/R_g$ and derived from $\mathit{log}\frac{I\left(0\right)}{I\left(q_{\max }\right)}=2.25$, respectively.

We have also applied SAXSMoW 3.0 to calculate molecular weights of glycosylated proteins selected from the SASBDB repository. ²³ In addition to the SAXS curves for different proteins selected from the SASBDB database, several experimental SAXS data sets collected at the Brazilian synchrotron light source (LNLS) by our group were also included in the analysis. The resulting molecular weight of 11 glycosylated proteins are reported in Table 2, revealing that most of the percentual discrepancies of the experimental molecular weights with respect to their nominal values are below 10%. In fact, for the selected set of proteins, the average absolute discrepancy in their molecular weights is <D _g > = 6.5%, which is even smaller than that determined for nonglycosylated proteins. Despite of having been applied only to a rather limited number of SAXS intensity sets, the results reported in Table 2 suggest that of SAXSMoW 3.0 can also be used for the determination of the molecular weight of glycosylated proteins.

TABLE 2.

Molecular weights ($M_r$) and oligomeric state numbers ($n$) of glycosylated proteins determined by SAXSMoW 3.0 for a set of 11 SAXS data, most of them extracted from the SASBDB repository. ²³

SASBDB ID	Protein	$q_{\max }$ (Å−1)	$M_n$ (kDa)	$M_r$ (kDa) (discrepancy)	$n$
SASDDG2	Immunoglobulin	0.294 (M1)	24.94	57.1 (+14.4%)	2
SASDDH2	Immunoglobulin	0.282 (M1)	25.66	53.6 (+4.4%)	2
LPMO9H 24	Lytic polysaccharide monooxygenase	0.256 (M1)	33.23	33.7 (+1.5%)	1
SASDB46	Glycosylated myelin‐associated glycoprotein	0.480	35	39.9 (+13.9)	1
17b IgG Fc 6.0 24	Immunoglobulin	0.287 (M1)	53.6	55.4 (+3.3%)	1
SASDB55	Glycosylated myelin‐associated glycoprotein	0.116 (M1)	54	109.9 (+1.8%)	2
SASDB26	Glycosylated myelin‐associated glycoprotein	0.490 (M2)	54	61.9 (+14.7%)	1
MtAAOx 25	Aryl‐alcohol oxidase	0.22 (M1)	68.3	80.1 (+17.2%)	1
SASDJK3	Alpha‐2‐macroglobulin	0.411 (M2)	161	708.3 (+10.8%)	4
SASDJL3	Alpha‐2‐macroglobulin	0.241 (M2)	161	719.2 (+11.7%)	4
SASDJL3	Alpha‐2‐macroglobulin	0.221 (M2)	174	740.4 (+6.4%)	4

Note: $q_{\max }$, M1, M2, and $M_n$, were defined in the caption of Table 1.

For some proteins their absolute discrepancies between the experimentally determined molecular weights and their expected values are rather high (D _g  > 10%, Figure 2). This could be due to different reasons, namely (a) the shape of the protein is very anisotropic, (b) the statistical quality of SAXS data is quite low, (c) the protein solution is not actually in dilute state, and/or (d) the solution contains a mixture of different proteins. Therefore, before starting any determination of molecular weights of proteins using SAXSMoW, these conditions should be examined and carefully evaluated.

FIGURE 2.

Discrepancies of the molecular weights of protein oligomers determined by applying SAXSMoW 3.0 ($M_r$) with respect to their known molecular weights, for a number of experimental SAXS curves, most of them selected from the SASBDB repository. ²³ Black symbols correspond to 32 nonglycosylated proteins and red symbols to 11 glycosylated proteins

It is worth noticing that excellent results in the determination of molecular weights of glycosylated proteins by using SAXSMoW 2.0 were previously reported by Guttmann and collaborators. ¹⁹

4. BENCHMARKS AND PARTICULAR EXAMPLES

Although the determination of low‐resolution structures of macromolecules in solution by SAXS has become more and more straightforward, a link between experimental results and their biological interpretation remains challenging. It is noteworthy that the correct interpretation of SAXS experimental results requires an adequate assumption for the quaternary state of the protein in solution. Therefore, we have evaluated some of the cases when SAXSMoW 3.0 could be of help for the determination of the oligomeric state of globular proteins ranging from monomer to large oligomers, with rather high accuracy. The structural parameters obtained from our analyses are summarized in Tables 1 and 2.

4.1. Mixed state systems

Bovine serum albumin (BSA) is one of the most studied protein with approximately globular shape and, thus, an interesting target for analysis of the molecular weight in solution. For concentrations used in typical SAXS experiments BSA exists in solution as a mixture of dimers and monomers (id entry: SASDDN3 ²⁶ ). The pair distribution function $P\left(r\right)$ determined for BSA from the overall SAXS dataset exhibits a quasi‐symmetric profile for all analyzed oligomeric states. However, the radius of gyration $R_g$ calculated by SAXSMoW from SAXS curves obtained for a monomeric sample (SAXSDFQ8) and for a dimeric sample (SASDFR8) were 27 and 39 Å with a $D_{\max }$ equal to 82 and 127 Å, respectively, while for SAXS curve from a mixture of BSA monomers and dimers (SASDDN3) intermediate values $R_g$ = 30 Å and $D_{\max }$ = 110 Å were obtained.

The molecular weights for monomeric BSA (SAXSDFQ8) and for dimeric BSA (SASDFR8) computed by SAXSMoW 3.0 and reported in Table S1 are 69.5 and 141.0 kDa, respectively. Thus, the molecular weights obtained by SAXSMoW 3.0 are quite close to the expected molecular weight $M_e=n·M_n$ _, with a percentual discrepancy of 5.2% for monomers and 6% for dimers. For the third SAXS curve also associated to BSA (SASDDN3) the molecular weight derived by SAXSMoW 3.0 is $M_r$ = 80.5 kDa, which corresponds to an intermediate molecular weight between those of monomers and dimers, being quite far from both of them. This result indicates that in some cases, SAXSMoW 3.0 can be a useful tool for identification and characterization of mixtures of proteins in different oligomeric states.

4.2. Glycosylated proteins

The glycosylation moieties of proteins are characterized by variability of the glycosidic linkages and considerable heterogeneity. Additionally, glycosylations can be quite extended and branched. A priori, the glycan content might have an impact on the SAXS curves acquired from glycosylated proteins in solution by increasing their apparent volumes $V_p\prime$. Therefore, glycosylation is expected to affect the determination of structural parameters derived from SAXS curves.

In order to evaluate the impact of glycosylation on the protein molecular weights determined by SAXSMoW 3.0, we have analyzed the results reported in Table S1, corresponding to aryl‐alcohol oxidase from Thermothelomyces thermophilus (MtAAOx) and lytic polysaccharide monooxygenase (MtLPMO9H) from the same fungi, as two examples.

The fungal aryl‐alcohol oxidase MtAAOx is a heavily N‐glycosylated globular enzyme. ²⁵ The nonglycosylated form of MtAAOx has a radius of gyration $R_g$ = 27.2 Å and $M_r$ = 69.3 kDa, with a slight positive discrepancy from the expected value (68.3 kDa). However, based on SAXS data, for the glycosylated form of this enzyme these parameters are $R_g$ = 29.3 Å and $M_r$ = 80.1 kDa, with discrepancies of 17.5% from the expected value (68.3 kDa) based on its amino acid sequence.

A similar result was obtained for the lytic polysaccharide monooxygenase MtLPMO9H. ²⁴ This protein is a two‐domain enzyme with a flexible and highly glycosylated linker peptide. The expected molecular weight based on the amino acid sequence is 33.2 kDa, whereas the molecular weight determined by SAXSMoW 3.0 is 47 kDa, with a rather high (24%) discrepancy. ²⁴

As already mentioned, both proteins considered here, namely aryl‐alcohol oxidase and lytic polysaccharide monooxygenase, are particularly highly glycosylated. On the other hand, the results from SAXSMoW 3.0 led in both cases to molecular weights higher than their expected values (on ~17.5% and 24.0%, respectively). Taking into consideration that the determination of the expected molecular weight derived from the amino acid sequence does not include glycosylations, the true molecular weights of very highly glycosylated proteins can be quite a bit higher than the theoretical values derived from the protein sequences. This may explain the observed rather high discrepancies between the molecular weights determined by SAXSMoW 3.0 from their expected values reported in Table S1.

Furthermore, in addition to the method based on the amino acid sequence, the molecular weights of the abovementioned proteins were also determined by using other experimental techniques. For aryl‐alcohol oxidase the experimentally determined molecular weight was 79.5 kDa, very close to the result yielded by SAXSMoW 3.0 (80.1 kDa). ²⁵ For lytic polysaccharide monooxygenase, the molecular weight determined by the experimental techniques was 47.0 kDa, with a discrepancy of 7% as compared to the result obtained by SAXSMoW 3.0 (50.5 kDa). ²⁴ Taken together, these results indicate that the molecular weights of the proteins in solution calculated by SAXSMoW 3.0 are quite comparable to the true molecular weights of MtAAOx and MtLPMO9H determined by independent experimental methods, even though both enzymes have a high content of glycan decorations.

5. CONCLUDING REMARKS

In the new version of SAXSMoW program (SAXSMoW 3.0) described here, the number of proteins selected for the calculation of the function relating their molecular volume $V_p$ and their apparent volume $V_p^{\prime }$ was greatly increased, from 1,148 for SAXSMoW 2.0 up to 67,000 for SAXSMoW 3.0. The results confirmed the linear dependences of $V_p$ on $V_p^{\prime }$ for all selected $q_{\max }$ values.

Furthermore, the number of $A\left(q_{\max }\right)$ and $B\left(q_{\max }\right)$ coefficients of the linear function relating the true protein volume $V_p$ and their apparent volume $V_p^{\prime }$ was increased from 6 in the previous SAXSMoW versions to 40 in SAXSMoW 3.0 program. This allows for more robust determination molecular weights.

Finally, the results of the validation of SAXSMoW 3.0 for several particular examples of SAXS data demonstrate that this program can be a useful tool for identification of mixtures of proteins in different oligomeric states and can be successfully applied not only to nonglycosylated, but also to glycosylated proteins, in line with the results reported in the literature. ¹⁹

The open beta‐version of SAXSMoW package is available at http://saxs.ifsc.usp.br/.

CONFLICT OF INTEREST

The authors declare no potential conflict of interest.

AUTHOR CONTRIBUTIONS

Mario de Oliveira Neto: Conceptualization (lead); data curation (lead); formal analysis (lead); funding acquisition (supporting); investigation (supporting); methodology (lead); resources (supporting); supervision (lead); validation (lead); visualization (lead); writing – original draft (lead); writing – review and editing (lead). Adriano F. Fernandes: Formal analysis (supporting); investigation (supporting); software (supporting); validation (supporting); visualization (lead); writing – original draft (supporting). Vassili Piiadov: Conceptualization (lead); formal analysis (lead); investigation (lead); methodology (supporting); software (lead); validation (lead); visualization (supporting). Aldo F. Craievich: Conceptualization (lead); methodology (lead); resources (supporting); supervision (supporting); validation (supporting); writing – original draft (lead); writing – review and editing (lead). Evandro A. de Araujo: Conceptualization (supporting); data curation (lead); formal analysis (lead); investigation (lead); validation (lead); visualization (lead); writing – original draft (lead); writing ‐ review and editing (lead). Igor Polikarpov: Conceptualization (lead); funding acquisition (lead); investigation (lead); methodology (lead); resources (lead); supervision (lead); writing – original draft (lead); writing – review and editing (lead).

Supporting information

Table S1 Outputs from SAXSMoW 3.0 referring to several SAXS curves corresponding to selected SAXS data, most of them extracted from the SAXSDBD repository. Upper part: Effects of a mixture of protein monomers and dimers. Lower part: Effects of high glycosylation. 𝑅𝑔: radius of gyration, 𝑀𝑛: molecular weight of the proteins in monomeric state computed. 𝑀𝑟 and 𝑛: molecular weights and oligomeric state number, respectively, determined by SAXSMoW 3.0.

de Oliveira Neto M, de Freitas Fernandes A, Piiadov V, Craievich AF, de Araújo EA, Polikarpov I. SAXSMoW 3.0: New advances in the determination of the molecular weight of proteins in dilute solutions from SAXS intensity data on a relative scale. Protein Science. 2022;31:251–258. 10.1002/pro.4227