An Investigation of Minimum Data Requirement for Successful Structure Determination of Pf2048.1 with REDCRAFT
Casey A. Cole, Daniela Ishimaru, Mirko Hennig, Homayoun Valafar
AAbstract – Traditional approaches to elucidation of proteinstructures by NMR spectroscopy rely on distance restraintsalso know as nuclear Overhauser effects (NOEs). The use ofNOEs as the primary source of structure determination byNMR spectroscopy is time consuming and expensive.Residual Dipolar Couplings (RDCs) have become analternate approach for structure calculation by NMRspectroscopy. In this work we report our results for structurecalculation of the novel protein PF2048.1 from RDC dataand establish the minimum data requirement for successfulstructure calculation using the software packageREDCRAFT. Our investigations start with utilizing four setsof synthetic RDC data in two alignment media and proceedby reducing the RDC data to the final limit of {CN, NH}and {NH} from two alignment media respectively. Ourresults indicate that structure elucidation of this protein ispossible with as little as {CN, NH} and {NH} to within0.533Å of the target structure.
Keywords : Protein Folding, Residual Dipolar Coupling(RDC), Residual Dipolar Coupling based Residue Assemblyand Filter Tool (REDCRAFT), Secondary Structure.
1 Introduction
Proteins are a class of organic macromolecules thatperform many important biochemical functions in biologicalcells. Protein functions run the entire gamut from structuralsupport and transport of biomaterial, to performingimportant enzymatic activities within a living organism.Unlike the genetic material (DNA/RNA) within Eukaryoticcells, cytosolic proteins are not protected with an additionalbilayer membrane of the nucleus. Therefore, design anddelivery of protein-based intervention of diseases is morepragmatic in the near future than genetic treatment ofdiseases. Furthermore, principles of modern biology stressthe importance of protein structure and its function.Therefore, knowledge of protein structures becomes paramount in understanding the mechanism of their function(or dysfunction) and subsequently, intelligent andappropriate drug design. An understanding of protein structure at atomicresolution serves as the first and critical step inunderstanding the molecular basis of nearly all diseases.While structure determination of proteins is becoming moreroutine, the cost of structure determination remains theprohibitive factor. Thanks to improvements by the StructuralGenomics Initiative[1], [2] and Protein StructureInitiative[3], the cost of experimental structuredetermination of proteins has been reduced fromapproximately $1,000,000 per protein to $100,000.Although this is a significant reduction in cost, it is still animpediment in achieving personalized medicine wherenearly 100,000 protein structures will need to be determinedfor each person. This approximate cost of $10 per personclearly represents a significant economical barrier. In recent years, the use of Residual DipolarCoupling (RDC) data acquired from Nuclear MagneticResonance (NMR) spectroscopy has become a potentialavenue for a significant reduction in the cost of structuredetermination of proteins. Recent work[4]–[7] hasdemonstrated the challenges in structure calculation ofproteins from RDC data alone, and some potential solutionshave been introduced[5], [6], [8]. One such approach namedREDCRAFT[4], [9], [10] has been demonstrated to besuccessful in structure calculation of proteins from areduced set of RDC data. The main objective in thisresearch is to perform a feasibility study for structurecalculation of a novel protein from RDC data. Ourfeasibility study will establish the minimum required datafor unambiguous structure calculation that is optimized for agiven protein. A better understanding of minimum datarequirement will help to alleviate the cost of structuredetermination by avoiding acquisition of unneeded data. Toaccomplish this objective we use a suggested structure ofPF2048.1 as an approximate template for its native An Investigation of Minimum Data Requirement forSuccessful Structure Determination of Pf2048.1 withREDCRAFT
Casey A. Cole , Daniela Ishimaru , Mirko Hennig , and Homayoun Valafar Department of Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, USA Department of Biochemistry and Molecular Biology, Medical University of South Carolina, Charleston, SC 29425 USA Nutrition Research Institute, University of North Carolina at Chapel Hill, Kannapolis, NC 27514, USA * Corresponding Author Email: [email protected] Phone: 1 803 777 2404 Fax: 1 803 777 3767Mailing Address: Swearingen Engineering Center, Department of Computer Science and Engineering, University of SouthCarolina, Columbia, SC 29208, USAtructure. Albeit it is clear that the suggested structure is notthe native structure, we have mounting evidence that thenative structure is less than 4Å away. We argue that ourfindings from a suggested structure is relevant to the actualstructure due to their close structural resemblance.
2 Background and Method
RDCs can be acquired via NMR spectroscopy. Thetheoretical basis of RDC interaction had been establishedand experimentally observed in 1963 [11]. However, it hasonly become a more prevalent source of data for structuredetermination of biological macromolecules in recent yearsdue to availability of alignment media. Upon thereintroduction of order to an isotropically tumblingmolecule, RDCs can be easily acquired. The RDCinteraction between two atoms in space can be formulated asshown in Eq. (1). D ij = D max ⟨ (θ ij ( t ))− ⟩ (1) D max =−μ γ i γ j h ( π r ) (2)In this equation, D ij denotes the residual dipolarcoupling in units of Hz between nuclei i and j. The θ ij represents the time-dependent angle of the internuclearvector between nuclei i and j with respect to the externalmagnetic field, and the angle brackets signify timeaveraging. In Eq. (2), D max represents a scalar multiplierdependent on the two interacting nuclei. In this equation, γ i and γ j are nuclear gyromagnetic ratios, r is the internucleardistance (assumed fixed for directly bonded atoms), h is themodified Planck's constant and μ represents thepermeability of free space. While generating a protein structure from a givenset of residual dipolar couplings is nontrivial, it isstraightforward to determine how well a given structure fitsa set of RDCs. Through algebraic manipulation of Eq. (1)RDC interaction can be represented as shown in Eq. (3), D ij = v ij ∗ S ∗ v ijT (3)where S represents the Saupe order tensor matrix [11] and v ij denotes the normalized interacting vector between the twointeracting nuclei i and j . REDCRAFT takes advantage ofthis principle by quantifying the fitness of a protein to a given set of RDCs (in units of Hz) and calculating a root-mean-squared deviation as shown in Eq. (4). In thisequation D ij and D' ij denote the computed andexperimentally acquired RDCs respectively, N , representsthe total number of RDCs for the entire protein, and M represents the total number of alignment media in whichRDC data have been acquired. In this case a smaller fitnessvalue indicates a better structure. Fitness = √ ∑ j = M ∑ i = N ( D ij − D ' ij ) M ∗ N (4)The REDCRAFT algorithm and its success inprotein structure elucidation has been previously describedand documented in detail [4], [9], [10], [12], [13]. Here wepresent a brief overview. REDCRAFT calculates structuresfrom RDCs using two separate stages. In the first stage( Stage-I ), a list of all possible discretized torsion angles iscreated for each pair of adjoining peptide planes. This list isthen filtered based on allowable regions within theRamachandran space [14]. The list of torsion angles thatremain are then ranked based on fitness to the RDC data.These lists of potential angle configurations are used toreduce the search space for the second stage.
Stage-II begins by constructing the first twopeptide planes of the protein. Every possible combinationof angles from
Stage-I between peptide planes i and i+1 areevaluated for fitness with respect to the collected data, andthe best n candidate structures are selected, where n denotesthe search depth. The list of dihedral angles correspondingto the top n structures are then combined with everypossible set of dihedral angles connecting the next peptideplane to the current fragment. Each of these candidatestructures is evaluated for fitness and the best n are againselected and carried forward for additional rounds ofelongation. All combination of dihedral angles worse thanthe best n are eliminated, thus removing an exponentialnumber of candidate structures from the search space. Thiselongation process is repeated iteratively, incrementallyadding peptide planes until the entire protein is constructed.The number of RDCs required to correctly fold anovel protein with a bundle of four nearly parallel heliceswith REDCRAFT has not been previously examined in asystematic manner. Here we investigate the effect ofreducing the available RDCs on the quality of the resultingcomputational structure. Collecting fewer RDCs per peptideplane can substantially reduce data collection times. Inparticular, N- H RDCs are easily collected because theyavoid expensive C labeling. Furthermore, N- H RDCvalues are typically large in magnitude, reducing the effectof measurement error. C α - H α RDCs are large in magnitudebut require C labeling, complicating sample preparation.RDCs for additional vectors can be collected, but with adecreasing utility and at a greater expense.
The novel protein PF2048.1 is a 9.16 kDa, 71residue monomeric protein with less than 17% sequenceidentity to any structurally characterized protein in PDB (asof April, 2015) serves as the primary target of ourinvestigations. PF2048.1 was expressed in
E. coli as an N-terminal His -GB1 fusion that can be efficiently cleaved byTEV protease introducing a single (non-native) Gly residueat position –1. Nearly complete assignments for backboneand sidechain protons, carbons and nitrogens were obtainedusing standard methods. The resulting 1045 NOE restraintstogether with TALOS backbone torsion restraints wereemployed to determine an experimental target structure.Using this reference structure and the structural alignmentsoftware 3D-Blast [15] we were able to investigate thestructural uniqueness of PF2048.1. Of the resulting proteins1AEP, a 161 residue apolipoprotein, was identified as thetop entry with the highest 3D-Blast score (score of 54.4).We then utilized msTALI [16] to align 1AEP and PF2048.1based on structural similarity. The final alignment identified26 residues to be structurally conserved to within 2.9Åbetween the two proteins, corresponding to about 36% (26conserved / 71 total residues = 0.36) structural similarity.Figure 1 shows the resulting alignment between the twostructures. The two's overall structural deviation wascalculated to be 5.265Å. Due to its novelty in both sequence and structurePF2048.1 is an ideal candidate to study the effectiveness ofcomputing protein structure from solely residual dipolarcouplings. In addition, the unique arrangement of the helicalsecondary structural elements of this protein will provide arealistic exploration of the challenges that REDCRAFT will be faced during structure calculation purely from RDCs. Using REDCAT [17], [18] and the referencestructure residual dipolar couplings were simulated in twoalignment media using the order tensors in Table 1. Error of ± -4 -4 -4 -6x10 -4 -4
40 50 -60Table 2. Columns 2 and 3 display minimum and maximum RDC values for each vector set using the order tensors in Table 1 in two alignment media (M1 and M2). The last column summarizes the range of uniformly distributed noisethat was added to each dataset. RDC Minimum Maximum Added noiseM1 N-C -2.029 1.287 ±0.1HzN-H -18.904 11.815 ±1HzC-H -3.557 5.692 ±0.3HzC α -H α -23.32 37.312 ±1.97HzM2 N-C -1.544 2.574 ±0.1HzN-H -14.178 23.63 ±1HzC-H -7.115 4.269 ±0.3HzC α -H α -46.64 27.984 ±1.97Hz Our evaluation will proceed by incrementalreduction in the data quantity; maintaining the RDC datathat are easiest to acquire from NMR spectroscopy. To thatend, we will proceed by first eliminating C α - H α RDC datafrom both alignment media since its acquisition increasesthe cost of protein production significantly. The secondphase of our investigation will focus on reducing the RDCdata sets from 3 RDCs per alignment medium, to 3 frommedium 1 and 1 from medium 2, followed by 2 frommedium 1 and 1 from medium 2.
Figure 1. NOE structure of PF2048.1 (green) aligned to 1AEP (blue) using PyMOL. According to PyMOL the two exhibited structural dissimilarity of 5.265Å. he software REDCRAFT will be utilized for ourstructure calculation without refinement in any otherauxiliary program such as Xplor-NIH[19] or CNS[20]. Weanticipated that consistent with principles of InformationTheory, more extensive search parameters of REDCRAFTwill need to be enabled as a function of reduced datasets tocompensate for the absence of information. The software package PyMOL[21] was utilized inorder to calculate the bb-rmsd (backbone root mean squareddeviation) between the REDCRAFT structure and the targetstructure (the NOE structure from which the RDC data weregenerated). The measure of bb-rmsd is prevalently used toestablish the structure similarity between two proteins andvalues under 3.5Å can signify presence of structuralresemblance, while values under 2Å can be interpreted asstrong structural resemblance. Our objective is to calculatestructures of PF2048.1 using REDCRAFT that exhibitstructural similarity to the target protein under 2Å.The other measure we will use to evaluatestructures is the RDC fitness score calculated byREDCRAFT (discussed in detail in section 2.2). This fitnessscore provides information about how well the RDCs fit thefinal structure. A score is considered to be of high quality ifits score falls at or below the error level of the data (in ourcase <1Hz). The lower the score the better the structure.
3 Results and Discussion
To evaluate the ability of REDCRAFT to predict the correct structure of PF2048.1, five test cases were established. In each of the cases the amount of data was varied to simulate five different possible data sets. The data sets are summarized in Table 3.
Table 3. Summary of the RDCs used in each experiment.Set Medium α -H α }2 {C-N, N-H, C-H, C α -H α }2 (4,1) 1 {C-N, N-H, C-H, C α -H α }2 {N-H}3 (3,3) 1 {C-N, N-H, C-H}2 {C-N, N-H, C-H}4 (3,1) 1 {C-N, N-H, C-H}2 {N-H}5 (2,1) 1 {C-N, N-H]2 {N-H}In the sections that follow we will report ourfindings in each of the cases in Table 3 to evaluate thefeasibility of successful protein structure elucidation with the given data set. In this experiment the following RDCscorresponding to the vector set {CN, NH, CH, C α H α } wereutilized in two alignment media. The configuration ofREDCRAFT is summarized in Table 4 below:Table 4. Parameters of REDCRAFT for experiment 1 wherein the Decimation Parameters C.S. denotes ClusterSensitivity and S.T. denotes Score Threshold.SearchDepth DecimationParameters Minimization LennardJones Cutoff200 C.S. S.T. Performedevery residue 50.04 1.0The resulting structure, seen in Figure 2 wasmeasured to have a REDCRAFT fitness score of 0.776 andshowed 1.035Å of structural deviation from our targetstructure. In this experiment two different sets of RDC datawere used in both alignment media. The first set containedfour vectors {CN, NH, CH, C α H α } and the second just onevector set {NH}. The corresponding REDCRAFTparameters for this exercise are summarized in Table 5.Consistent with our expectation, due to the reduction in data Figure 2. Resulting structure (in green) superimposed to the target target structure (in blue). The two exhibited structural difference of1.035Å. uantity, a more thorough search by REDCRAFT wasrequired in order to achieve a comparable result to that ofthe (4,4) exercise. The more thorough search was achievedthrough the adjustment of the C.S. an S.T. terms. Theadjustment of these two terms allow for a more refinedclustering of the search space as a function of reduceddataset N in Eq. (4). Table 5. Parameters of REDCRAFT for experiment 2.SearchDepth DecimationParameters Minimization LennardJones Cutoff200 C.S. S.T. Performedevery 3 rd residue 50.03 0.8The resulting structure (seen in Figure 3) exhibiteda RDC fitness score of 0.741 and a bb-rmsd of 1.594Å withrespect to the target structure. In this experiment two sets of three RDCs {CN,NH, CH} were utilized. Several REDCRAFT configurations(similar to those in experiment 1 and 2) were attempted onthis dataset but it became clear that there was somethinginherently anomalous about constructing a protein withthese two particular sets of RDCs. As a result of thesedifficulties we were forced to incorporate additionalsecondary structural information and perform a more directed folding process. In our case the phi and psi angleswere restricted to oscillate in the range of [-60:-50] and [-50:-40] respectively for the helical residues 3-16, 22-35, 39-52 and 57-70. The addition of secondary structuralconstraints can easily be facilitated through the use ofsecondary structure prediction tools such as Jpred, Jpred3and I-TASSER[22]–[24], or through early interpretation ofthe data available from NMR spectroscopy withoutimposing any additional data acquisition costs. The resulting structure (seen in Figure 4) had aRDC fitness score of 0.382 and a bb-rmsd of 1.002Å withrespect to the target structure.
Figure 4. Resulting structure (in green) aligned to the target structure (in blue). The two showed structural deviation of just 1.001Å.
In this experiment two different sets of RDCs wereused; the first set containing three vectors {CN, NH, CH}and the second containing just one vector {NH}. TheREDCRAFT configuration is summarized in the Table 6below:Table 6. Parameters of REDCRAFT for experiment 4.SearchDepth DecimationParameters Minimization LennardJones Cutoff200 C.S. S.T. Performedevery 3 rd residue 50.03 1.0Surprisingly, this combination of data (although asubset of the 3,3 exercise) was less refractory and did notrequire the incorporation of dihedral restraints or Figure 3. Resulting structure (in green) superimposed to the target structure (in blue). The two showed structural deviation of 1.594Å. odification of search parameters in order to perform amore extensive search of the solution space. The resultingstructure, as seen in Figure 5, exhibits a RDC fitness scoreof 0.741 and bb-rmsd from the target structure of 1.594Å,mirroring the results in 3.2.
Figure 5. Resulting structure (in green) superimposed to the target structure (in blue). As in experiment 2, the two exhibited a backbone RMSD of 1.594Å.
The final experiment in establishing the boundariesof data requirement is based on {CN, NH} and {NH}. Dueto further reduction of the datasets we were again forced toincorporate secondary structure constraints along with thefollowing REDCRAFT parameters summarized in Table 7.The ranges for the secondary structure constraints remainedthe same as that of the experiment described in 3.3. Table 7. REDCRAFT parameters for experiment 5 utilizing2,1 RDC sets resulting in a structure 3.03Å from the targetstructure.SearchDepth DecimationParameters Minimization LennardJones Cutoff200 C.S. S.T. Performedevery residue 50.03 0.5The resulting structure in this experiment showedstructural deviation from the target structure of 3.03Å—abb-rmsd that indicates need for further refinement. Carefulinvestigation of the changes in RDC fitness scores revealedthat midway through the last helix (around residue 64) therewas a significant spike in fitness to RDC data (as seen inFigure 6). This prompted a fragmented study of this protein where the structure is determined in two contiguoussegments. Since the spike occurred in the middle of a helix,we chose to terminate the first segment at residue 57 (thebeginning of the affected helix) in an attempt to conservesecondary structure elements as much as possible. Thisapproach yielded two fragments [1:56] and [57:72] havingbb-rmsd's to the target structure of 0.465Å and 0.724Årespectively. Using RDCs to predict the orientation of thetwo fragments (as previously shown in theory [25]) weproperly oriented and connected the two fragments. Theresulting structure (seen in Figure 7) exhibited a RDCfitness score of 0.173 and bb-rmsd of 0.533Å to the targetstructure.
Figure 6. Graph showing the change in RDC fitness (y-axis) throughout the 72 residues (x-axis). A spike can be seen to occur atresidue 64.Figure 7. Resulting structure (green) from experiment 5 superimposed to the target structure (blue). The structural deviationbetween the two was calculated to be 0.533Å.
4 Conclusion
Exploration of the minimum data requirement isuseful in order to establish the expected financial cost of aprotein's structure determination. An exploration mechanismsuch as the one presented here will allow for appropriateallocation of funds as a function of a protein's medical orbiological importance. This is a critical contribution to therepertoire of structure determination approaches especiallyin the context of personalized medicine where funds can beappropriate allocated toward culprit proteins in humandiseases. Our investigation through exploration of the fiveexercises listed in the previous section, has revealed withhigh degree of certainty that structure determination ofPF2048.1 can be accomplished with as little as {CN, NH}and {NH} from two alignment media respectively. Inaddition, we believe that more thorough exploration ofREDCRAFT's search options, combined with addition ofreadily available restraints (such as dihedral restraints) canreduce the needed dataset further. This expectation is rootedon the observance of the results from the {3,3} and {2,1}exercises where dihedral restraints were included as part ofREDCRAFT's analysis. Inclusion of dihedral restraint notonly helped to recover the structure of PF2048.1, but itproduced the most accurate structure (to within 1.001Å ofthe target protein in the case of {3,3}). Of notable interest is the anomalous nature ofstructure determination from the set {3,3} compared to thatof {3,1}. The refractory nature of this dataset is peculiar andin contradiction with the principles of information theory. Inprinciple, inclusion of data should not harm the outcomeunless the included data introduces a level of noise that isnonuniform and more corrupt in nature than the remainderof the data. There is however the possibility of existinginherent degeneracies from the aforementioned set ofvectors that when combined with the heuristics ofREDCRAFT, produce the observed anomalies. Our futurework will investigate these two conjectures. Our future investigation is to determine the solutionstate structure of the protein PF2048.1 from experimentaldata. Our approach will leverage the conclusions of thiswork in order to acquire the least amount of data comparedto the traditional approach of acquiring the most completedataset. We are confident that our new approach will reducethe quantity of acquired data by nearly 90% and thereforeresult in significant reduction in financial and temporal costof protein structure determination by NMR spectroscopy.Although base on the results reported here, structuredetermination should be plausible with {CN, NH} & {NH}datasets, our experimental investigation of this protein willproceed based on acquisition of the {CN, NH, CH} & {NH}as preparation for missing and noisy data.
5 Acknowledgements
This work was supported by NIH Grant Numbers 1R01GM081793 and P20 RR-016461 to Dr. HomayounValafar.
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