Devaurs et al. Native State of Complement Protein C3d Analyzed via Hydrogen Exchange and Conformational Sampling Didier Devaurs 1 , Malvina Papanastasiou 2 , Dinler A Antunes 1 , Jayvee R Abella 1 , Mark Moll 1 , Daniel Ricklin 2 , John D Lambris 2 and Lydia E Kavraki 1* Abstract Background: Hydrogen/deuterium exchange detected by mass spectrometry (HDX-MS) is an experimental technique that provides valuable information about a protein’s structure and dynamics. Data produced by HDX-MS experiments is often interpreted using a crystal structure of the protein. However, it has been suggested that more accurate interpretations can be derived from conformational ensembles produced by molecular dynamics simulations than from crystal structures. This assumes that the experimental data can be first computationally replicated from such conformation(s), using a prediction model to derive HDX-MS data from a protein’s structure. Results: In this paper, we analyze the complement protein C3d through HDX-MS data, and we evaluate several methodologies to interpret this data, using an existing HDX-MS prediction model. Although crystal structures of C3d are available, little is known about the variability of its native state. To bridge this gap, since HDX-MS data is known to reflect a protein’s inherent flexibility, we perform an HDX-MS experiment on C3d. To interpret and refine the obtained HDX-MS data, we then need to find a conformation (or a conformational ensemble) of C3d that allows computationally replicating this data. First, we confirm that a crystal structure may not be a good choice for that. Second, we suggest that, even though they are indeed a better choice, conformational ensembles produced by molecular dynamics simulations might not always allow replicating experimental data. Third, we show that coarse-grained conformational sampling of C3d can produce a conformation from which C3d’s HDX-MS data can be computationally replicated and refined from the peptide to the residue level. Conclusions: In the case of the model protein C3d, the similarity between the conformation generated by coarse-grained conformational sampling and available crystal structures establishes that C3d’s native state presents little conformational variability. Yet the ability to obtain a structural model of C3d in solution that provides a good correspondence to experimental HDX-MS data and allows refining this data may prove highly valuable. This could impact many HDX-based applications, from structural analyses to ligand-interaction studies. Keywords: complement protein C3d; protein structure; protein conformational sampling; molecular dynamics; hydrogen/deuterium exchange; mass spectrometry; X-ray crystallography 1 Background Hydrogen/deuterium exchange detected by mass spec- trometry (HDX-MS) is an extremely valuable tech- nique for analyzing various aspects of proteins [1]. It has been used to study protein structure and confor- mational changes, as well as protein folding and in- teractions [2]. The hydrogen/deuterium exchange un- dergone by a protein is influenced by its structure. * Correspondence: [email protected]1 Department of Computer Science, Rice University, 6100 Main Street, Houston, TX 77005, USA Full list of author information is available at the end of the article Although HDX-MS cannot produce a precise three- dimensional model of a protein, it can provide useful structural information [3]. Additionally, since HDX- MS experiments involve monitoring proteins in solu- tion over time, they can generate insights on protein dynamics [4]. HDX-MS also has the advantage of not suffering from the same restrictions as other structural biology techniques: it requires only small quantities of protein sample, and it is not limited by protein size [5]. As such, HDX-MS has proven infinitely valuable to study systems as challenging as, for example, mem- brane proteins [6].
Transcript
Devaurs et al.
Native State of Complement Protein C3dAnalyzed via Hydrogen Exchange andConformational SamplingDidier Devaurs1, Malvina Papanastasiou2, Dinler A Antunes1, Jayvee R Abella1, Mark Moll1,Daniel Ricklin2, John D Lambris2 and Lydia E Kavraki1*
Abstract
Background: Hydrogen/deuterium exchange detected by mass spectrometry (HDX-MS) is an experimentaltechnique that provides valuable information about a protein’s structure and dynamics. Data produced byHDX-MS experiments is often interpreted using a crystal structure of the protein. However, it has beensuggested that more accurate interpretations can be derived from conformational ensembles produced bymolecular dynamics simulations than from crystal structures. This assumes that the experimental data can befirst computationally replicated from such conformation(s), using a prediction model to derive HDX-MS datafrom a protein’s structure.
Results: In this paper, we analyze the complement protein C3d through HDX-MS data, and we evaluateseveral methodologies to interpret this data, using an existing HDX-MS prediction model. Although crystalstructures of C3d are available, little is known about the variability of its native state. To bridge this gap, sinceHDX-MS data is known to reflect a protein’s inherent flexibility, we perform an HDX-MS experiment on C3d.To interpret and refine the obtained HDX-MS data, we then need to find a conformation (or a conformationalensemble) of C3d that allows computationally replicating this data. First, we confirm that a crystal structuremay not be a good choice for that. Second, we suggest that, even though they are indeed a better choice,conformational ensembles produced by molecular dynamics simulations might not always allow replicatingexperimental data. Third, we show that coarse-grained conformational sampling of C3d can produce aconformation from which C3d’s HDX-MS data can be computationally replicated and refined from the peptideto the residue level.
Conclusions: In the case of the model protein C3d, the similarity between the conformation generated bycoarse-grained conformational sampling and available crystal structures establishes that C3d’s native statepresents little conformational variability. Yet the ability to obtain a structural model of C3d in solution thatprovides a good correspondence to experimental HDX-MS data and allows refining this data may prove highlyvaluable. This could impact many HDX-based applications, from structural analyses to ligand-interactionstudies.
Keywords: complement protein C3d; protein structure; protein conformational sampling; molecular dynamics;hydrogen/deuterium exchange; mass spectrometry; X-ray crystallography
1 BackgroundHydrogen/deuterium exchange detected by mass spec-trometry (HDX-MS) is an extremely valuable tech-nique for analyzing various aspects of proteins [1]. Ithas been used to study protein structure and confor-mational changes, as well as protein folding and in-teractions [2]. The hydrogen/deuterium exchange un-dergone by a protein is influenced by its structure.
*Correspondence: [email protected] Department of Computer Science, Rice University, 6100 Main Street,
Houston, TX 77005, USA
Full list of author information is available at the end of the article
Although HDX-MS cannot produce a precise three-dimensional model of a protein, it can provide usefulstructural information [3]. Additionally, since HDX-MS experiments involve monitoring proteins in solu-tion over time, they can generate insights on proteindynamics [4]. HDX-MS also has the advantage of notsuffering from the same restrictions as other structuralbiology techniques: it requires only small quantities ofprotein sample, and it is not limited by protein size [5].As such, HDX-MS has proven infinitely valuable tostudy systems as challenging as, for example, mem-brane proteins [6].
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HDX-MS has greatly impacted the study of plasmaproteins that undergo dynamic structural transitionsto exert their functional spectrum, such as membersof the complement cascade and other innate immunepathways [7]. Indeed, this technology has been suc-cessfully used to investigate the maturation of the cy-tokine interleukin-1β [8], and to define the binding in-terface between pattern recognition receptors of theficolin family and immunoglobulins [9]. In the comple-ment system, HDX-MS has proven particularly valu-able to examine the various conformational changes ofthe central component C3. C3 is the point of conver-gence for all complement activation routes, the drivingforce of complement response amplification, and a ma-jor source of immune effectors. Over the years, HDX-MS studies have helped elucidate the mechanisms thatdefine the perpetual solution activation of C3 via hy-drolysis [10], and the major conformational transitionof C3 to the potent opsonin C3b upon activation byconvertases [11]. HDX-MS has also helped character-ize the structural effects of point mutations in patientswith a form of functional C3 deficiency [12], and ofa bacterial immune evasion protein that allostericallyinhibits C3b activity [13]. HDX-MS was among thefew structural methods that could be applied to theselarge plasma proteins, which typically exceed 150 kDa;it has provided important insight that was not readilyavailable from X-ray crystallography.
Despite the usefulness of HDX-MS experiments, ithas sometimes proven challenging to interpret the datathey produce, namely deuterium-uptake kinetic curvesfor various peptides extracted from a protein (see Sec-tion 4.1.1). Such a kinetic curve is often reduced toa single number: the peptide’s average protection fac-tor [5], which quantifies the extent to which this partof the protein is protected from exchange (which is, inturn, thought to be influenced by the protein’s struc-ture). Typically, these average protection factors arevisualized on a protein heat map [3] built using astructural model reported in the Protein Data Bank(PDB). However, it has been argued that the corre-spondence between experimental HDX-MS data andsuch structural models is often not satisfactory, espe-cially for models resulting from X-ray crystallographystudies [14]. The reason is that, contrary to crystalstructures, HDX-MS data reflects the inherent vari-ability of a protein’s native state, which emanates fromthe protein’s equilibrium fluctuations. Therefore, itwas suggested that experimental HDX-MS data couldbe better interpreted using a conformational ensem-ble produced by a molecular dynamics (MD) simu-lation [15]. This technique has been used to validateexperimental HDX-MS data and refine it from the pep-tide to the residue level [14].
In this work, we analyze the native state of thecomplement protein C3d through HDX-MS, using theaforementioned methodology and similar ones. A frag-ment of the central complement component C3, theopsonin C3d has recently gained attention as im-mune effector, biomarker, drug targeting structure,and potential therapeutic target itself. Upon comple-ment activation by various triggers, C3 gets cleavedby convertases; the resulting C3b fragment may be-come covalently deposited on the target surface [16].There, C3b can form additional convertases and am-plify opsonization. On many surfaces, and in partic-ular healthy host cells, this process is carefully con-trolled: a set of complement regulators mediates thedegradation of C3b (175 kDa) to iC3b (173 kDa),C3dg (40 kDa) and/or C3d (35 kDa). These late-stage opsonins do not participate in convertase for-mation but still exert important biological functions.Whereas C3d has long been known to help induceadaptive immune responses by binding to CD21 onB cells [17], newer studies have identified C3d as lig-and for the integrin receptor CD11b/CD18 [18], andhave indicated its role in the phagocytic uptake of op-sonized particles [19]. Owing to the fact that C3d isthe final opsonin stage and remains covalently boundto cells that experienced complement attack, it hasevolved into an important surface biomarker in thediagnosis of complement-mediated clinical conditions,such as antibody-mediated rejection during transplan-tation [20]. Furthermore, its newly discovered rolesin innate and adaptive immune effector functions putC3d into the spotlight as potential therapeutic tar-get. C3d-binding entities based on antibodies or smallmolecules are therefore being developed and investi-gated [21, 22]. Though important as an individual op-sonin, C3d also corresponds to the thioester-containingdomain (TED) in C3, C3b and iC3b. This domain ful-fills important functions during the activation of C3and serves as binding site for natural ligands and im-mune evasion proteins alike [13,23,24]. Therefore, gain-ing additional structural information about this im-portant opsonin and immune mediator, expanding onearly crystal structures of C3d [25], is highly impor-tant. At the same time, its comparatively small sizewithin the family of C3 opsonins facilitates the estab-lishment of experimental and computational analysesfor the purpose of this study.
In this paper, we report on an HDX-MS experimentwe have performed to gather data about C3d’s nativestate (see Section 2.1). To interpret this experimen-tal HDX-MS data in relation to C3d’s structure, weneeded to find a conformation (or a conformational en-semble) of C3d from which this data could be first com-putationally replicated. For that, we had to choose an
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HDX prediction model (i.e., a theoretical model defin-ing how to derive HDX data from a protein’s structure)among those available in the literature. We selected atheoretical model built on a phenomenological approx-imation of the protection factors of a protein’s residues(see Section 4.1.2) [15, 26]. Using this model, we com-pare various strategies to obtain a conformation (or aconformational ensemble) of C3d from which its exper-imental HDX-MS data can be computationally repli-cated (see Sections 2.2 to 2.5).• First, we point out that computationally deriv-
ing HDX-MS data from C3d’s crystal structuredoes not produce good estimates of its experimen-tal HDX-MS data. This confirms that, as notedin [14], using only a crystal structure may be lim-iting when interpreting HDX-MS data in certainapplications.• Second, we show that better estimates of C3d’s ex-
perimental HDX-MS data are obtained when com-putationally deriving HDX-MS data from con-formations or conformational ensembles producedby MD simulations. However, as we observe onlysmall improvements and a clear lack of consis-tency, we argue that using MD conformationsmight not always be an accurate way to inter-pret HDX-MS data either. We also explain whyincreasing the temperature in an MD simulationto broaden conformational sampling does not im-prove results.• Third, we suggest that using coarse-grained con-
formational sampling might be a better strategyto obtain conformations that allow computation-ally replicating experimental HDX-MS data. Byexploring C3d’s native state with such a method,we obtain a conformation, referred to as the“HDX conformation”, yielding the best estimatesof C3d’s experimental HDX-MS data.
Finally, we analyze the HDX conformation of C3d, andwe elaborate on what it reveals about C3d’s nativestate (see Section 2.6). We also use this HDX con-formation to refine C3d’s experimental HDX-MS datafrom the peptide level to the residue level, and we dis-cuss the usefulness of this data (see Section 2.7).
2 Results and DiscussionThe three-dimensional structure of C3d was resolvedby X-ray crystallography almost two decades ago [25].In our work, we use a similar description of C3d’sstructure produced by a more recent X-ray crystallog-raphy study of C3d in complex with the extracellularfibrinogen-binding protein (Efb) [23]; it can be foundin the PDB under ID 2GOX. In this crystal structure,C3d contains 297 residues, where residue 1 correspondsto residue 991 of the full complement protein C3.
C3d can be described as a single-domain α-proteincontaining twelve α-helices and five 310-helices. Werefer to these helices using the notations introducedin [25]. Overall, the helices of C3d are organized intoan α-α barrel: an inner barrel of helices enclosed withinan outer barrel of helices. Most consecutive helices al-ternate between the inner barrel and the outer bar-rel; the remaining helices are not located on the sidebut at the ends of the barrel. The inner barrel is com-posed of six parallel α-helices: α1 (Glu22 to Thr41), α3
(Thr86 to Leu102), α5 (Lys149 to Ala164), α8 (Ser196to Met209), α10 (Gln236 to Leu253), and α12 (Ser278to Asp295). The outer barrel contains six parallel he-lices running anti-parallel to those of the inner bar-rel; they comprise one 310-helix, T1 (Ala7 to Leu13),and five α-helices: α2 (Leu49 to Arg70), α4 (Ser107to Lys121), α7 (Ser174 to Asn189), α9 (Pro215 toThr223), and α11 (Phe256 to Gln269). The remaininghelices are rather short; they include one α-helix, α6
(Asp166 to Gln171), and four 310-helices: T2 (Gln43 toPhe47), T3 (Gln137 to Ile140), T4 (Gly142 to Arg144),and T5 (Tyr190 to Asn192).
The ends of the barrel differ significantly: one is aconvex surface containing the thioster region involvedin cell-surface attachment; the other is a concave sur-face containing a large acidic pocket [25]. It has beenobserved that Efb binds to C3d on one side of thisacidic pocket [23,24]. Various ligands of C3d are knownto bind in the same region, while complement recep-tor 2 (CR2) binds over the whole acidic pocket [22].Finally, note that C3d also features a disulfide bridgebetween Cys111 and Cys168.
2.1 HDX-MS Experiment on C3d
As part of this work, following the methodology pre-sented in Section 4.2.1, we performed an HDX-MS ex-periment on C3d, alone in solution. Therefore, the dataproduced by this experiment is expected to charac-terize C3d’s native state. This HDX-MS experimentproduced deuterium-uptake curves for 86 peptides ex-tracted from C3d (see Table 1). Only six amino acids ofC3d are not included in any peptide: Phe156, Glu187–Tyr190 and Leu248. Therefore, the HDX-MS experi-ment achieved a coverage of 98% of the protein. Theredundancy of the data, through the presence of over-lapping peptides is also good: 87% of amino acids areincluded in more than one peptide, 62% in more thantwo peptides, and 41% in more than three.
Traditionally, this data would be interpreted by (i)converting the deuterium-uptake curves into averageprotection factors of peptides, and (ii) visualizing theseaverage protection factors as a heat map using a crys-tal structure (if available). The first drawback of this
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Table 1 HDX-MS data experimentally-obtained for C3d. Results are reported as fraction of deuterium uptake over time for eachpeptide: since the maximum number of deuterium atoms that can be incorporated by a peptide is known, one can compute theratio of effective deuterium uptake over maximal deuterium uptake. The fraction of deuterium uptake is given at seven time pointsfor the 86 peptides extracted from C3d. The first two and last three peptides are not used in the attempts to computationallyreproduce this data.
time points (sec) time points (sec)10 30 100 300 1000 3000 10000 10 30 100 300 1000 3000 10000
approach is the loss of information it causes (from a ki-netic curve to a single number). Second, it can be diffi-cult to deal with overlapping peptides whose data maynot be consistent. Finally, as suggested in [14], thereexist more meaningful ways to analyze experimentally-observed HDX-MS data, such as refining this datafrom the peptide to the residue level. However, thisrequires using a protein conformation or a conforma-tional ensemble from which the experimental HDX-MSdata can be first computationally replicated. This alsonecessitates an HDX prediction model that allows de-riving HDX-MS data from protein structure, such asthe one presented in Section 4.1.2.
In the context of our work, to refine and interpretC3d’s experimental HDX-MS data, we first have toreproduce the deuterium-uptake data reported in Ta-ble 1. For that, we need to find a conformation (or aconformational ensemble) from which this data can beaccurately derived. Note that, as the N-terminus andC-terminus are known to undergo significant levels ofback-exchange, our confidence in the HDX-MS datagathered for the corresponding peptides is rather low.Therefore, the first two and last three peptides (itali-cized in Table 1) are not considered in the attempt toreproduce C3d’s HDX-MS data, which leaves us with81 peptides to perform this analysis.
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0
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Differences between experimentally-observed and structurally-derived deuterium-uptake curves of peptides
PDB conformation (average difference: 1.23)
Minimized conformation (average difference: 1.06)
Peptides
Figure 1 Deriving HDX-MS data from two conformations of C3d. Histograms of differences (for the 81 peptides extracted fromC3d) obtained when assessing the goodness-of-fit between the experimental HDX-MS data obtained for C3d and the HDX-MS dataderived from the PDB conformation of C3d, or from a minimized version of this conformation.
2.2 HDX-MS Data Derived from the Crystal Structureof C3d
We started by trying to reproduce C3d’s experimen-tal HDX-MS data, using its crystal structure, the HDXprediction model described in Section 4.1.2, and themethodology presented in Section 4.2.2. Although itwas suggested that using a crystal structure to repro-duce HDX-MS data may not be the most accurate wayof doing so [14], our objective was to obtain a baselineagainst which other strategies could be compared. Wesubsequently refer to the crystal structure of C3d re-ported in the PDB (under ID 2GOX) as its “PDBconformation.”
Our results show that the HDX-MS data which iscomputationally derived from the PDB conformationof C3d does not fit well the experimentally-observeddata (see Figure 1). The average difference betweenthe structurally-derived and experimentally-observedHDX-MS data across all peptides is 1.23 (see Sec-tion 4.2.2). Discrepancies are especially significant onthe right-hand side of the chart, which correspondsto peptides of C3d comprising the region betweenresidues Met191 and Ala242. This region includes he-lices T5, α8 and α9, the beginning of helix α10, as wellas the loops between them. It is located on the sideof the α-α barrel and does not cover areas of C3dwith known major biological activity. Therefore, thediscrepancies observed in this region cannot be linked,a priori, to any biologically-relevant conformationalchange in C3d.
The fact that a PDB conformation does not typ-ically provide good estimates of experimental HDX-MS data is due to the very nature of HDX-MS ex-periments, which monitor proteins in solution, con-trary to X-ray crystallography. Since HDX-MS datareflects the inherent flexibility of a protein, a singleconformation was not expected to provide good esti-mates [26]. Therefore, it was suggested that HDX-MSdata could be accurately reproduced only as an av-erage over an ensemble of conformations representingthe native state of a protein, such as an ensemble ex-tracted from an MD simulation [15].
2.3 HDX-MS Data Derived from MD Simulations ofC3d
Following the methodology described in Section 4.2.3,we performed three MD simulations of C3d (whichwere 100 ns long) to try and obtain better estimatesof its experimental HDX-MS data. The premise of thisexperiment is that an MD simulation can produce aricher representation of a protein’s native state thana crystal structure, by sampling the protein’s equilib-rium fluctuations.
Our results confirm that using a conformational en-semble extracted from an MD simulation allows de-riving HDX-MS data that fits the experimental databetter than when using the PDB conformation. Aggre-gating the histogram of differences obtained for eachMD ensemble (see Figure 2) yields an average differ-ence of about 1.05 (as compared to 1.23 with the PDB
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Differences between experimentally-observed and structurally-derived deuterium-uptake curves of peptides
MD ensemble 1 (average difference: 1.03)
MD ensemble 2 (average difference: 1.07)
MD ensemble 3 (average difference: 1.04)
Peptides
Figure 2 Deriving HDX-MS data from MD simulations of C3d. Histograms of differences (for the 81 peptides extracted from C3d)obtained when assessing the goodness-of-fit between the experimentally-observed HDX-MS data and the HDX-MS data derived fromensembles of conformations extracted from three MD simulations of C3d.
conformation). However, Figure 2 shows that there aresignificant discrepancies between the HDX-MS datasets derived from the three MD ensembles: for nu-merous peptides, the deuterium-uptake curves derivedfrom these ensembles are not consistent. This is due tothe fact that the sampling performed by MD signifi-cantly differs across simulations. Therefore, this raisesquestions about using MD to characterize the variabil-ity of a protein’s native state, as captured through anHDX-MS experiment. Previous studies, such as [14],have usually based their analysis on a single MD sim-ulation. Our experiment shows that results obtainedthis way might not always be reproducible.
Another important fact that raises questions aboutusing MD conformational ensembles to replicate ex-perimental HDX-MS data is that a single conforma-tion might provide better estimates than the wholeensemble. For example, the conformation obtained atthe end of the energy minimization step of MD (seeSection 4.2.3) provides reasonable estimates. Indeed,aggregating the histogram of differences obtained withthis “minimized conformation” (see Figure 1) yields anaverage difference of 1.06, which is similar to the aver-ages obtained with the MD ensembles (1.03, 1.07 and1.04, respectively).
This prompted us to determine which conformationswithin the three MD ensembles would provide the bestestimates of C3d’s experimental HDX-MS data. Forthat, we applied the HDX prediction model to each
conformation in these ensembles, instead of comput-ing averages. In each MD ensemble, we selected theconformation providing the best estimates. These MDconformations produce even better estimates than theminimized conformation of C3d. Aggregating the his-tograms of differences obtained with these MD confor-mations (see Figure 3) yields average differences be-tween 0.88 and 0.92. Despite such consistency in termsof average difference, Figure 3 shows that the HDX-MSdata sets derived from the three MD conformationsare far from being consistent. Indeed, discrepancies be-tween histograms are even worse than when using thefull MD ensembles.
Although we observe a slight improvement in HDXprediction, as compared to what C3d’s crystal struc-ture produced, it is still not good enough to considerthat the experimental HDX-MS data has been repli-cated. Errors in HDX prediction are especially high onthe right-hand side of the chart, which corresponds toregion [Met191–Ala242] of C3d. To investigate whetherthese errors were due to this region being more flexi-ble than other parts of C3d, we examined the B fac-tors reported in the PDB. No correlation was foundbetween B factors and errors in HDX prediction. Wealso performed a normal mode analysis of C3d, usingProDy [27]. No correlation was found between normalmodes and errors in HDX prediction.
The extent of discrepancies between experimentally-observed and structurally-derived HDX-MS data ini-tially prompted us to think that they might have
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Differences between experimentally-observed and structurally-derived deuterium-uptake curves of peptides
MD conformation 1 (average difference: 0.88)
MD conformation 2 (average difference: 0.92)
MD conformation 3 (average difference: 0.89)
Peptides
Figure 3 Deriving HDX-MS data from MD conformations of C3d. Histograms of differences (for the 81 peptides of C3d) obtainedwhen assessing the goodness-of-fit between the experimentally-observed HDX-MS data and the HDX-MS data derived from singleconformations extracted from three MD simulations of C3d.
captured significant conformational differences corre-sponding to distinct states of C3d. This would havebeen surprising, as C3d is not known to be very flex-ible [24]. In fact, we show in what follows that thesediscrepancies do not correspond to structural differ-ences. We believe that the failure to replicate C3d’sexperimental HDX-MS data using MD conformations(or conformational ensembles) is a consequence of MDnot sampling C3d’s native state thoroughly enough.Note that this issue remained, even after extendingone of the MD simulations from 100 ns to 300 ns.
2.4 HDX-MS Data Derived from High-TemperatureMD Simulations of C3d
The computational cost of MD makes it often im-practical to run a simulation for long enough to pro-duce a thorough exploration of a protein’s native state.Various methods have been proposed to improve per-formance, such as temperature-accelerated replica ex-change, umbrella sampling, metadynamics, or acceler-ated MD [28, 29]. As our objective was not to evalu-ate these methods, we decided to try and broaden thescope of MD’s conformational exploration by simplyincreasing the temperature.
We performed four additional MD simulations ofC3d, following our previous methodology (see Sec-tion 4.2.3), except for the temperature of the produc-tion stage. In this experiment, we used four differenttemperatures: 350 K, 400 K, 450 K, and 500 K (in-stead of 300 K, as in the previous experiment). From
each produced trajectory, which was 200 ns long, weextracted a set of 1000 conformations at regular timesteps. We then determined, in each set, which confor-mation provided the best estimates of C3d’s experi-mental HDX-MS data.
Increasing the temperature to 350 K did not produceanything different from the previous MD simulations.Therefore, we report only the results achieved by thethree other MD simulations (see Figure 4). From theseresults, it appears that increasing the temperature isnot beneficial: the average differences obtained withthe MD simulations at 400 K, 450 K and 500 K are0.92, 0.99 and 1.11 respectively. An interesting out-come of this experiment is that the histograms of dif-ferences are significantly different from those of previ-ous MD simulations (compare Figures 3 and 4). Thisshows that increasing temperature had the intendedeffect of broadening the sampling of C3d’s conforma-tional space. This is confirmed by data on the radiusof gyration, Rg, of various conformations of C3d: forthe PDB conformation, Rg = 18 A; the largest radiusobserved in regular MD simulations is Rg = 18.7 A;the largest radius observed in high-temperature MDsimulations is Rg = 19 A at 400 K, Rg = 19.6 A at450 K, and Rg = 22.2 A at 500 K.
To sum up, increasing the temperature in MD canbroaden the sampling of a protein’s conformationalspace. However, in this case, it did not yield a con-formation from which good estimates of C3d’s experi-mental HDX-MS data could be derived. One reason is
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Differences between experimentally-observed and structurally-derived deuterium-uptake curves of peptides
MD conformation 400K (avg diff: 0.92)
MD conformation 450K (avg diff: 0.99)
MD conformation 500K (avg diff: 1.11)
Peptides
Figure 4 Deriving HDX-MS data from high-temperature MD simulations of C3d. Histograms of differences obtained when assessingthe goodness-of-fit between the experimentally-observed HDX-MS data and the HDX-MS data derived from single conformationsextracted from MD simulations of C3d at 400 K, 450 K and 500 K respectively.
that, when temperature is too high, the protein startsunfolding and conformations are generated outside thenative state. We recognize that increasing tempera-ture is not the most efficient way to improve MD’sperformance, and that more sophisticated variants ofMD [28, 29] could be successful in producing a goodHDX predictor for C3d. However, in this study, wechose to follow a different approach because we be-lieve that coarse-grained conformational sampling canbe a valuable alternative to all-atom simulations, suchas classical (molecular mechanics) MD.
2.5 HDX-MS Data Derived from Coarse-GrainedConformational Sampling of C3d
We argue, here, that using “coarse-grained” conforma-tional sampling can help broaden the exploration ofC3d’s conformational space in a beneficial way. Notethat we use the term “coarse-grained” in its most gen-eral sense. In this context, numerous coarse-grainedcomputational tools can be considered: MD-like meth-ods using coarse-grained force fields [30], Monte-Carlo-based simulations [31, 32], methods using elastic net-work models [33], or robotics-inspired conformationalsampling methods [34–37], among others. Here, we usea computational tool called SIMS [38], which combinesa robotics-inspired conformational sampling methodwith the Rosetta modeling software [39] (see Sec-tion 4.2.4).
We refer to the conformation produced by this exper-iment (cf. Section 4.2.4) as the “HDX conformation” of
C3d. Indeed, this conformation provides very good es-timates of C3d’s experimental HDX-MS data (see Fig-ure 5). The average difference between experimentally-observed and structurally-derived deuterium-uptakecurves across all peptides is only 0.6. Therefore, wecan consider that deriving HDX-MS data from thisconformation allows replicating C3d’s experimentally-observed HDX-MS data. This is the first step towardinterpreting and refining this experimental data.
2.6 Examination of the HDX Conformation of C3dThe HDX conformation of C3d, which allows repli-cating its experimental HDX-MS data, is very similarto the PDB conformation (see Figure 6). All the he-lices forming the α-α barrel are conserved in the HDXconformation, although some are slightly different: α1
is extended from [Glu22–Thr41] to [Gly21–Thr41],α5 is shortened from [Lys149–Ala164] to [Asp150–Ala164], α7 is shortened from [Ser174–Asn189] to[Leu175–Asn189], α10 is shortened from [Gln236–Leu253] to [Tyr238–Leu253], α12 is shortened from[Ser278–Asp295] to [Thr279–Asp295], and T1 is short-ened from [Ala7–Leu13] to [Ala7–Lys11]. The disul-fide bridge between Cys111 and Cys168 is also con-served. On the other hand, two small helices have dis-appeared (T4 and T5), and α6 has been shortened from[Asp166–Gln171] to [Asp166–Glu169]. Another differ-ence is that the α-α barrel of the HDX conformation(Rg = 19 A) is slightly wider than the α-α barrel of
Devaurs et al. Page 9 of 15
0
1
2
3
Differences between experimentally-observed and structurally-derived deuterium-uptake curves of peptides
PDB conformation (average difference: 1.2)
HDX conformation (average difference: 0.6)
Peptides
Figure 5 Deriving HDX-MS data from coarse-grained conformational sampling of C3d. Histograms of differences obtained whenassessing the goodness-of-fit between the experimentally-observed HDX-MS data of C3d and the HDX-MS data derived from itsPDB conformation or its HDX conformation (i.e., the conformation produced by coarse-grained conformational sampling).
the PDB conformation (Rg = 18 A). However, we donot consider these to be significant differences.
The HDX conformation is also similar to other crys-tal structures obtained for C3d itself [18, 25, 40, 41] orfor other molecules that contain C3d as their TED(see Section 1), such as C3 [42]. This confirms thatthis C3d state is rather stable, in the sense that itdisplays little conformational variability. Indeed, com-paratively to other areas of C3, and particularly itsa-chain, the C3d/TED domain has typically been con-sidered stable. The strong similarity between the HDXconformation of C3d and its crystal structures demon-strates that they all are reasonably good representa-tions of the three-dimensional structure of C3d in so-lution. Therefore, these conformations may be suitableto interpret experimental data, such as results of lig-and interaction analyses, which may benefit functionalstudies and drug development efforts.
Despite the similarity between the HDX conforma-tion of C3d and its crystal structures, small differencesexist, mostly in terms of width of the α-α barrel. Wewish to stress that the HDX conformation should onlybe regarded as an averaged representation of C3d’sflexibility, as captured in its experimental HDX-MSdata. In other words, we do not consider this con-formation to be a better representation of C3d’s na-tive state than its crystal structures. Indeed, the HDXconformation does not appear to be energetically sta-ble. First, after performing an energy minimization of
the HDX conformation, we obtained a conformationwhose energy is higher than the minimized version ofthe PDB conformation. Second, after running an MDsimulation starting from the HDX conformation, weobserved that, except at the very beginning, all gen-erated conformations were more similar to the PDBconformation than to the HDX conformation, in termsof width of the α-α barrel.
Since the experimental HDX-MS data reflects the in-herent variability of a protein’s native state, a confor-mational ensemble describing this state would providea better HDX prediction than a single conformation.We still believe this to be true, but only if the ensem-ble is a good representation of this state. Our resultsshow that this could not be achieved for C3d by simplyusing MD. On the other hand, coarse-grained confor-mational sampling provided us with a conformationyielding good HDX predictions. Predictions could beeven better if this method was used to generate con-formational ensembles, but evaluating these ensembleswould be too computationally-expensive. In practice,it is reasonable enough to use a single conformation forHDX prediction, instead of a conformational ensemble.The only caveat is that this conformation should notbe regarded as a better representation of a protein’snative state than a conformational ensemble. It shouldonly be considered as a mean to interpret and refineexperimental HDX-MS data.
Devaurs et al. Page 10 of 15
PDB conformation
HDX conformation
Figure 6 PDB and HDX conformations of C3d. Bothconformations are depicted using the ribbon model.
2.7 Refinement of C3d’s HDX-MS Experimental DataA clear benefit of using the HDX prediction model wechose and a protein conformation to replicate exper-imental HDX-MS data is that it allows refining thisdata from the peptide level to the residue level. In-deed, in this HDX prediction model, the HDX-MSdata is first derived from the protein’s structure atthe residue level, and then aggregated at the pep-tide level (see Section 4.1.2). Therefore, this methodprovides residue-level HDX-MS information at no ex-perimental or computational cost. Another techniquewas proposed to obtain residue-level information, butit requires collecting experimental HDX-MS data withhigh levels of redundancy, in terms of overlapping pep-tides [43]. On the other hand, the method we use canbe applied to any experimental dataset, irrespective ofthe level of redundancy.
Using the HDX prediction model and the HDX con-formation of C3d, we refined the peptide-level HDX-MS data reported in Table 1 into a list of protectionfactors for C3d’s residues. These protection factors arevisualized on the HDX conformation of C3d as a heatmap (see Figure 7). This is a clear improvement overthe classical methodology producing such heat maps atthe peptide level [3]. Some observations derived fromFigure 7 were expected: for example, helices generallybenefit from higher protection factors than loop re-gions. On the other hand, local packing density inducesan unexpected result: the highest protection factors
17
0
ln P
proline
Figure 7 Heat-map visualization of the protection factors ofC3d’s residues. Protection factors are derived from, anddepicted on, the HDX conformation of C3d. Prolines arecolored in green. Other residues are colored using a spectrumcorresponding to the range of protection values.
are observed within two loop regions (Ala75, Phe76and Ser85).
Obtaining residue-level HDX-MS data is consideredhighly valuable for most HDX-based applications, in-cluding ligand interaction studies. If an HDX-MS ex-periment is performed on a complex involving C3d andone of its ligands, refining the experimentally-observeddata at the residue level and comparing it to the dataobtained for C3d alone can help characterize the inter-action interface or even locate key residues maintainingthe complex. Moreover, comparing residue-level HDX-MS data obtained for complexes involving distinct lig-ands can help explain potential differences in bindingaffinity and engineer more potent binders during ratio-nal drug design. This may be particularly importantto alleviate the possible absence of suitable co-crystalstructures, or to increase the throughput in screeningand hit validation.
3 ConclusionsIn this paper, we have analyzed the native state ofthe complement protein C3d. Although several crys-tal structures of C3d are available [23, 25], little isknown about its inherent variability in solution. Togather data that could help bridge this gap, we per-formed an HDX-MS experiment on C3d. As a result,we obtained deuterium-uptake curves for 86 peptidesextracted from C3d. To interpret this experimental
Devaurs et al. Page 11 of 15
data in relation to C3d’s structure, it is imperativeto have a conformation (or a conformational ensem-ble) of C3d from which this data can be replicated.As a crystal structure might not be the most accuratepredictor for experimental HDX-MS data [14], we usedvarious conformational sampling techniques to gener-ate alternative conformations of C3d.
Although using a conformational ensemble producedby an MD simulation was thought to be an appropri-ate way to reproduce experimentally-obtained HDX-MS data [14], our study shows that this might not al-ways be true. First, we observe that a single conforma-tion of such ensemble can be a better HDX predictorthan the whole ensemble. Second, at least in the caseof C3d, there seems to be a lack of consistency betweenthe HDX predictions obtained with different MD sim-ulations. Third, using MD conformations yields HDXpredictions that are only slightly better than whenusing C3d’s crystal structure. All this indicates thatMD might not produce a representation of a protein’snative state that can capture its inherent variabilityin the same way as HDX-MS data does. This is par-ticularly surprising for C3d because, comparatively toother regions of C3, the C3d/TED has typically beenconsidered very stable.
As an alternative to MD simulations, we suggestusing coarse-grained conformational sampling to ob-tain good HDX predictors. At least for the model pro-tein C3d, such sampling could generate a conformationfrom which the best estimates of C3d’s experimentalHDX-MS data could be derived. As a result, this HDXconformation can be used to interpret the experimen-tal data and refine it from the peptide to the residuelevel. Although not necessarily a better representationof C3d’s native state than crystal structures or MD-derived conformational ensembles, the HDX conforma-tion can be regarded as an average representation ofthe variability of C3d’s native state that is captured inits experimental HDX-MS data. Therefore, this confor-mation contains valuable information that may guidestructural studies or help identifying hitherto unrecog-nized areas of structural dynamics.
The similarity between the HDX conformation wehave obtained for C3d and its crystal structures con-firms the stability of its native state: it seems to displaylittle conformational variability. Therefore, in prac-tice, C3d’s crystal structures can be regarded as good-enough representations of its three-dimensional struc-ture in solution. Combining this structure with theresidue-level HDX-MS data we have obtained for C3dcould prove extremely valuable for ligand interactionstudies, with potential implications for rational drugdesign.
As part of our future work, we plan to investigatewhether the results reported in this paper can be
generalized to yield a comprehensive HDX predictionand refinement methodology. More specifically, we willexamine whether coarse-grained conformational sam-pling is generally better than MD at producing confor-mations that are good HDX predictors. We will evalu-ate our methodology on several proteins. We envisionseveral applications for an accurate HDX predictionmethod. First, it would allow evaluating the consis-tency between crystallographic and HDX-MS data, incases where it is not certain whether both datasetscorrespond to the same protein state. Second, if aprotein’s native state is described in the PDB, andif only HDX-MS data is available for another (non-native) protein state, it would be possible to obtain astructural model of this non-native state. Finally, thepossibility to refine HDX-MS data from the peptide tothe residue level will benefit all the applications of theHDX-MS technique itself [2].
4 MethodsIn the Methodological Background, we outline gen-eral concepts underpinning the HDX-MS experimen-tal technique, and we introduce the HDX predictionmodel chosen for this study. Then, in the Experimen-tal Methods, we present the specific details of our ex-perimental and computational methodology.
4.1 Methodological Background4.1.1 Hydrogen/Deuterium Exchange Detected by
Mass Spectrometry (HDX-MS)
Hydrogen/Deuterium exchange (HDX) is a chemicalphenomenon in which hydrogen atoms of proteins areexchanged with deuterium atoms in the surroundingsolvent [1]. As the mass of deuterium is about twicethe mass of hydrogen, HDX can be monitored by MassSpectrometry (MS): the amount of deuterium incor-porated in a protein, which is referred to as deuteriumuptake, corresponds to an increase in mass. In HDX-MS experiments, only the exchange of amide hydro-gens (i.e., hydrogens attached to backbone nitrogens)is monitored [1]. Therefore, HDX-MS experiments areinterpreted on the basis of a single measurement peramino acid, for all amino acids of a protein, except forproline residues and for the N-terminus because theydo not possess an amide N−H group.
The HDX rates of amino acids can vary up to sev-eral orders of magnitude, depending on pH and tem-perature [44]. The HDX rate of an amino acid in anunstructured peptide is only affected by its neighbors;this “intrinsic” HDX rate, denoted by kint, can be pre-dicted [45, 46]. The HDX rate of an amino acid in aprotein is influenced by additional factors, such as sol-vent accessibility and protein structure; this HDX rate,
Devaurs et al. Page 12 of 15
denoted by kobs, is the one that is observed experi-mentally [4]. The extent to which amide hydrogens ofa protein are protected from being exchanged can bequantified by defining the protection factor of everyamino acid i as Pi = kinti / kobsi .
At the beginning of an HDX-MS experiment, theprotein is equilibrated in H2O at room temperatureunder physiological conditions (pH close to 7). To startthe HDX reaction, the protein is then diluted withexcess D2O. At several time points, the reaction isquenched in a solution sample by bringing the pHdown to 2.5, and the temperature down to 0 ◦C. Pro-teins in the sample are digested using pepsin, whichis active at acidic pH and generates numerous pep-tides typically 6–20 amino acids long. The sample isthen introduced into a chromatography system thatseparates the peptides and sends them into a massspectrometer. The MS analysis identifies the peptidesand quantifies their deuterium uptake. As this anal-ysis is repeated at several time points, an HDX-MSexperiment produces deuterium-uptake kinetic curvesfor various peptides [3]. Additionally, as the maximumnumber of deuterium atoms that can be incorporatedby a peptide is known, results are usually reportedas fraction of deuterium uptake, instead of “absolute”deuterium uptake.
An important aspect of HDX-MS experiments isthat, because sample analysis is performed in H2Osolution, some deuterium atoms incorporated by thepeptides are exchanged back to hydrogens. This phe-nomenon, known as back-exchange, can be detrimentalif deuterium in amide groups start reverting to hydro-gen. This is why digestion and MS analysis have to beperformed rapidly. As back-exchange of amide groupscannot be totally avoided, it has to be accounted forin the analysis of deuterium-uptake curves: if the HDXrate of a peptide is considered as the average rate ofits amino acids, the first two amino acids in the chainhave to be ignored because they systematically un-dergo back-exchange [3, 6].
The levels of HDX undergone by different parts of aprotein are known to be influenced by the protein’sthree-dimensional structure. Several theoretical mod-els have been proposed to define a relationship be-tween a protein’s conformation and HDX data, butnone of them has been widely accepted by the scien-tific community [47]. Among these models, we choseto use the one that performed best in a recent com-parative study [47]. This model relies on the definitionof a phenomenological expression approximating theprotection factors of the protein’s residues [26]. Since
its conception, this model has been applied in severalstudies [14,15,48–50].
The theoretical model is based on the assumptionthat protection from HDX arises from the involve-ment of amide groups in hydrogen bonds and from thepacking density of atoms around amides. More specifi-cally, given a conformation C, the protection factor ofresidue i, Pi(C), can be derived from the phenomeno-logical expression
lnPi(C) = βhNhi (C) + βcN c
i (C) (1)
where Nhi (C) is the number of hydrogen bonds involv-
ing the amide group of residue i, and N ci (C) is the
number of atom contacts (quantifying packing density)involving residue i. Parameters βh and βc have beenestimated by fitting experimentally-determined HDXdata of various proteins: βh = 2 and βc = 0.35 [15].The number of hydrogen bonds, Nh
i (C), is defined asthe number of main-chain oxygens in any residue (ex-cluding residues i − 2, . . . , i + 2) within a cutoff dis-tance of 2.4 A from the amide hydrogen of residue i.The number of atom contacts, N c
i (C), is the numberof heavy atoms (i.e., non-hydrogens) in any residue(excluding residues i − 2, . . . , i + 2) within a cutoffdistance of 6.5 A from the amide hydrogen of residuei. Note that, instead of being derived from a singleconformation, protection factors can be computed asensemble averages over a set of conformations, suchas a conformational ensemble produced by an MD orMonte Carlo simulation [15,26].
Using the protection factors derived from (1), onecan generate deuterium-uptake curves of peptides thatcan be compared to experimentally-obtained HDX-MSdata. For that, we first assume that a residue’s deu-terium uptake follows pseudo-first-order kinetics [3, 6,44]. Since Pi = kinti / kobsi , the fraction of deuteriumincorporated by residue i at time t is thus
where kinti rates are known. Then, the deuterium up-take of peptide j can be considered as an average overthe residues it contains [14]. Note that we systemat-ically exclude from the average the first two aminoacids of the peptide because of back-exchange.
4.2 Experimental Methods4.2.1 HDX-MS ExperimentHuman purified C3d (0.25 mg/mL) was expressedin E. coli, as described in other work [23]. Deu-terium oxide (99.9 atom % D; 151882) was obtainedfrom Aldrich (St. Louis, MO). Tris(2-carboxyethyl)-ohosphine hydrochloride (TCEP-HCl; 20491) and im-mobilized pepsin (20343) were from Thermo Scientific
C3d’s peptides (2 pmol) were analyzed in data-dependent acquisition (DDA) mode. Precursor ionswere acquired in the m/z 300–1500 Da range using atop 3 method and MS/MS scans of the fragment ionswere acquired in them/z 100–1200 Da range. The totalcycle time was 3.8 sec and ions selected for fragmenta-tion were excluded for 20 sec. UPLC parameters wereas described below. Peptide identification took place inProteinLynx Global ServerTM (version 3.0.2, Waters)using 10 ppm peptide tolerance and 0.8 Da fragmenttolerance.
For the labeling experiment, 4 µL of purified C3d(0.2 µg/µL in PBS; 10 mM Na2HPO4, 1.8 mMKH2PO4, 2.7 mM KCl and 137 mM NaCl, pH 7.5) wasmixed with 40 µL of deuterated PBS at 24±0.5 ◦C.Samples were quenched at 10, 30, 100, 300, 1000, 3000and 10000 sec using an equal volume (44 µL) of pre-chilled guanidinium hydrochloride-TCEP (3.2 M and0.8 M, respectively) at a final pH 2.4. Samples wereincubated on ice for 2 min prior to LC-MS analy-sis. Non-deuterated samples were prepared similarlyin protiated PBS; fully-deuterated samples were pre-pared by incubating the protein for 48 h at 37±0.5 ◦C.Samples were prepared and analyzed in duplicate usinga Synapt G2S ESI-QToF (Waters) mass spectrometerwith MassLynxTM 4.1 (SCN 916, Waters). Spectrawere acquired in the positive ion mode. Leu-Enk wasco-infused as a lock spray standard. Chromatographicseparation took place on a nano-Acquity UPLC systemwith HDX technology (Waters). Quenched sampleswere injected on an Acquity UPLC R BEH C18 Van-Guard Pre-column (130 A, 1.7 µm, 2.1× 5 mm, WatersP/N 186003975). Peptides were generated upon onlinedigestion (3 min at 300 µL/min using 0.23% v/v formicacid) of C3d using immobilized pepsin. They were sep-arated on an Acquity UPLC R BEH C18 analyticalcolumn (130 A, 1.7 µm, 1 × 100 mm; 186002346, Wa-ters). Chromatographic parameters were: flow rate at40 µL/min; solvents A (0.23% v/v formic acid) andB (0.23% v/v formic acid in acetonitrile). Solvent Bwas ramped from 3% to 10% in 0.2 min, to 38.5%in 19.8 min, to 90% in 2 min, and then kept at 90%for 2 min before re-equilibrating to initial conditions.Data processing took place in DynamX (version 2.0,Waters).
4.2.2 HDX-MS Data Derived from Crystal StructuresUsing the model described in Section 4.1.2, we derivedHDX-MS data from the conformation of C3d reportedin the PDB (i.e., 2GOX). More precisely, we calculated
the fraction of deuterium uptake at all experimentaltime points for the 81 peptides retained for analysis(see Section 2.1). We then compared this data to theexperimentally-obtained data reported in Table 1. Toassess the goodness-of-fit between structurally-derivedand experimentally-observed HDX-MS data, we con-structed a histogram of differences by computing, forevery peptide j, the error
∑t∈T |Dder
j (t) − Dobsj (t)|,
where T is the list of experimental time points, Dderj (t)
is the structurally-derived deuterium uptake at time t,and Dobs
j (t) is the experimentally-observed deuteriumuptake at time t. Note that this histogram can be ag-gregated into an average difference over all peptides.
4.2.3 HDX-MS Data Derived from MD simulationsAll MD simulations were performed with the GRO-MACS v4.6.5 package [51] using the GROMOS96(53a6) force field and the SPC water model. A cubicbox was defined with at least 9 A of liquid layer aroundC3d’s structure (for a total of 15052 water molecules),with periodic boundary conditions. Sodium (Na+) andchloride (Cl−) counter-ions were added to neutralizethe system, with a final concentration of 0.15 mol/L.The algorithms v-rescale (with tau-t = 0.1 ps) andparrinello-rhaman (with tau-p = 2 ps) were used fortemperature and pressure coupling, respectively. Acutoff value of 1.2 nm was used for both the van derWaals and Coulomb interactions, with Fast Particle-Mesh Ewald electrostatics (PME).
The production stage of each MD simulation is pre-ceded by (i) three steps of Energy Minimization (EM)and (ii) eight steps of Equilibration (EQ). The firstEM step is conducted using the steepest-descent al-gorithm and position restraints on C3d’s heavy atoms(5000 kJ−1mol−1nm−1), allowing relaxation of the sol-vent only. The second EM step involves the same al-gorithm, but no restraint. The third EM step usesthe conjugate-gradient algorithm, without restraint,to further relax the protein. The EQ phase startsat a temperature of 310 K, which is maintained for300 ps, applying position restraints on C3d’s heavyatoms (5000 kJ−1mol−1nm−1). This step allows sol-vation layers to form without affecting C3d’s folding.Temperature is then reduced to 280 K, and positionrestraints are gradually reduced. This process is fol-lowed by a progressive temperature increase, up to300 K. Together, these EQ steps constitute the first500 ps of each MD simulation. During the productionstage, the system is not subjected to any restraint, andtemperature remains constant at 300 K.
All MD simulations were run on a single node of ourlocal High-Throughput Computing cluster. Such nodeincludes two octo-core Intel E5-2650v2 Ivy Bridge EPprocessors (2.6 GHz), for a total of 32 threads, sharing
Devaurs et al. Page 14 of 15
32 GB of memory. The performance of an MD sim-ulation of C3d on this architecture is approximately29 ns/day. We initially ran three MD simulations ofC3d and obtained trajectories of 100 ns in length,which is the length of the MD performed in [14]. Then,we extended one of these simulations to 300 ns. Fi-nally, we performed four additional MD simulations of200 ns in length, using increasing temperatures for theproduction stage: 350 K, 400 K, 450 K, and 500 K.From each MD simulation, we extracted a set of 1000conformations at regular time steps along the trajec-tory. Using the HDX prediction model described inSection 4.1.2, we derived HDX-MS data from eachMD conformational ensemble. First, protection factorsof residues were calculated as averages over the con-formational ensembles. Then, within each ensemble,we determined which conformation would provide thebest estimates of C3d’s experimental HDX-MS data.
4.2.4 HDX-MS Data Derived from Coarse-GrainedConformational Sampling
In this work, we used a computational framework de-veloped to explore a protein’s conformational space:Structured Intuitive Move Selector (SIMS) [38]. Thisframework integrates robotics-inspired sampling algo-rithms with the Rosetta modeling software [39]. SIMSfollows a “coarse-grained” approach: the representa-tion of a protein involves only backbone dihedral an-gles; this representation is manipulated in a multi-resolution fashion during sampling. Starting from thePDB conformation of a protein, SIMS can iterativelygenerate an ensemble of low-energy conformations byperturbing previously-generated conformations. Typi-cal perturbations include dihedral angle rotation, loopclosure and others. In this experiment, SIMS was runfor five days on four threads of a 3.6 GHz Intel i7-4790quad-core CPU. Then, from the produced conforma-tional ensemble, we determined which conformationwould provide the best estimates of C3d’s experimen-tal HDX-MS data.
