- Research
- Open Access
An efficient algorithmic approach for mass spectrometry-based disulfide connectivity determination using multi-ion analysis
- William Murad^{1},
- Rahul Singh^{1}Email author and
- Ten-Yang Yen^{2}
https://doi.org/10.1186/1471-2105-12-S1-S12
© Murad et al; licensee BioMed Central Ltd. 2011
- Published: 15 February 2011
Abstract
Background
Determining the disulfide (S-S) bond pattern in a protein is often crucial for understanding its structure and function. In recent research, mass spectrometry (MS) based analysis has been applied to this problem following protein digestion under both partial reduction and non-reduction conditions. However, this paradigm still awaits solutions to certain algorithmic problems fundamental amongst which is the efficient matching of an exponentially growing set of putative S-S bonded structural alternatives to the large amounts of experimental spectrometric data. Current methods circumvent this challenge primarily through simplifications, such as by assuming only the occurrence of certain ion-types (b-ions and y-ions) that predominate in the more popular dissociation methods, such as collision-induced dissociation (CID). Unfortunately, this can adversely impact the quality of results.
Method
We present an algorithmic approach to this problem that can, with high computational efficiency, analyze multiple ions types (a, b, b^{ o }, b^{ * }, c, x, y, y^{ o }, y^{ * }, and z) and deal with complex bonding topologies, such as inter/intra bonding involving more than two peptides. The proposed approach combines an approximation algorithm-based search formulation with data driven parameter estimation. This formulation considers only those regions of the search space where the correct solution resides with a high likelihood. Putative disulfide bonds thus obtained are finally combined in a globally consistent pattern to yield the overall disulfide bonding topology of the molecule. Additionally, each bond is associated with a confidence score, which aids in interpretation and assimilation of the results.
Results
The method was tested on nine different eukaryotic Glycosyltransferases possessing disulfide bonding topologies of varying complexity. Its performance was found to be characterized by high efficiency (in terms of time and the fraction of search space considered), sensitivity, specificity, and accuracy. The method was also compared with other techniques at the state-of-the-art. It was found to perform as well or better than the competing techniques. An implementation is available at: http://tintin.sfsu.edu/~whemurad/disulfidebond.
Conclusions
This research addresses some of the significant challenges in MS-based disulfide bond determination. To the best of our knowledge, this is the first algorithmic work that can consider multiple ion types in this problem setting while simultaneously ensuring polynomial time complexity and high accuracy of results.
Keywords
- Disulfide Bond
- Polynomial Time Complexity
- Maximum Weight Match
- Initial Match
- Match Threshold
Background
The contributions of this paper in context of the aforementioned challenges include: (1) Development of a highly efficient strategy for multi-ion disulfide bond analysis by considering a, b, b^{ o }, b^{ * }, c, x, y, y^{ o }, y^{ * }, and z ion types. To the best of our knowledge, this is the first algorithmic work that has considered all these ion-types in S-S bond determination. (2) A fully polynomial-time algorithm that selectively generates only those regions of the search space where the correct solutions reside with a high likelihood. (3) A multiple-regression-based data driven method to calculate the critical parameters modulating the search, so as to ensure that the correct bonding topologies are not missed due to the truncation of the search space. At the same time, the parameter selection ensures that the search is focused on the most promising regions of the search-space, and (4) A local-to-global strategy that builds a globally consistent bonding pattern based on MS data at the level of individual bonds.
The proposed approach also implements the probability-based scoring model proposed in [8] for each specific disulfide bond based on the number of MS/MS matches and their respective abundance. These scores reflect the significance of the specific disulfide bond and can form the basis of analysis, such as that conducted in [9], to estimate the accuracy of peptide assignment to tandem mass spectra.
Methods
Abbreviations and their definitions
Abbreviation | Definition |
---|---|
DMS | Set of mass values corresponding to all possible disulfide-bonded peptide structures that can be obtained from a digested protein. |
PMS | Set of mass values of ions that undergo dissociation to produce product ions (set of precursor ions). |
IM | Correspondence obtained when the difference between the detected mass of a targeted ion from the PMS and the calculated mass of a possible disulfide-bonded peptide structure from the DMS is less than a match threshold T_{ IM }. |
T _{ IM } | Initial Match threshold. Threshold used to define a mass window centered on a PMS value within which a correspondence between a DMS value and a PMS value may be found. |
ε | DMS trimming parameter used to trim the DMS set. To trim the DMS set by ε means to remove as many elements from DMS as possible without losing meaningful mass values. |
TrimSet | Set of trimmed mass values from the DMS set. |
PM | Peptide Mass: cysteine-containing peptide mass value. |
TempSet | Temporary mass set containing possible disulfide bonded peptide structures. |
FMS | Set of mass values of every disulfide-bonded fragment structure that can be obtained from fragment ions, which can be of types a, b, b^{ o }, b^{ * }, c, x, y, y^{ o }, y^{ * }and z. |
TMS | Set of mass values of the product ions obtained after the MS/MS step (MS/MS spectra). |
VM | Correspondence obtained when the difference between a precursor ion fragment mass from TMS and a disulfide-bonded fragment structure mass from FMS falls below a validation match threshold T_{ VM }. |
T _{ VM } | Validation Match threshold. Threshold used to define a mass window centered at a TMS value in which a correspondence between a FMS value and a TMS value may be found. |
δ | FMS trimming parameter used to trim the FMS set. To trim the DMS set by δ means to remove as many elements from FMS as possible without losing meaningful fragment ions mass values. |
FragSet | Set containing the mass values of fragment ions generated by the method GENFRAGS(.) in the APROX-FMS routine. |
Unfortunately, the sizes of both FMS and DMS grow exponentially. For a disulfide-bonded peptide structure consisting of k peptides, considering that there are f different fragment ion types possible, up to f^{ k } types of fragment arrangements may occur in the FMS. If the i th fragment ion consists of p_{ i } amino acid residues, then the complexity to compute the entire FMS for a disulfide-bonded peptide structure is using a brute-force approach. The DMS also grows exponentially. To understand this, let P = {p_{ 1 }, p_{ 2 }, …, p_{ k }} be the list of cysteine-containing peptides in a polypeptide chain. Further, let C = {c_{ 1 }, c_{ 2 }, …, c_{ i }} be the list of the number of cysteines per cysteine-containing peptide p_{ i }. If is the total number of cysteines in a protein, the number of possible disulfide connectivity patterns (DMS size) is [1, 14]: .
The subset-sum formulation: towards polynomial-time matching
Given the growth characteristics of the DMS and the FMS, an exhaustive search-and-match strategy is clearly infeasible in the general case. This is especially true if multiple ion types are considered. Indexing [11, 12] and filtering [15] are two possible approaches that have been considered for ameliorating this problem. In this paper we explore an alternative strategy that is based on the key insight that the entire search space (DMS or FMS) does not need to be generated to determine the matches. That is, we only want to generate the few disulfide bonded peptides whose mass is close to the (given) experimental spectra rather than generate all possible peptide combinations and subsequently testing and discarding most of these. This insight allows us to re-cast the DMS and FMS generation as instances of the subset-sum problem [16]. Recall, that given the pair (S, t), where S is a set of positive integers and t ∈ Z^{+}, the subset-sum problem asks whether there exists a subset of S that adds up to t. While the subset-sum problem is itself NP-Complete, it can be solved using approximation strategies to obtain near-optimal solutions, in polynomial-time [16].
Polynomial time DMS mass list construction
Running APROX-DMS on the ST8SiaIV C^{ 142 }-C^{ 292 }bond
Property | Value |
---|---|
CCP | {716, 728, 749, 863, 864, 891, 976, 1096, 1105, 1161, 1204, 1274, 1359, 1367, 1418, 1480, 1593, 1733, 1754, 1846, 1863, 1864, 1976, 2179, 2292, 2351, 2617, 2737, 2822} |
PMS _{ val } | {2050.5} (Precursor ion mass) |
ε | 0.02530 |
T _{ IM } | 1.0 |
DMS | {728, 749, 863, 891, 976, 1105, 1161, 1204, 1274, 1367, 1418, 1480, 1593, 1639, 1702, 1754, 1846, 1908, 1994, 2050} – (value in bold is a valid IM) |
TrimSet | {716, 864, 1096, 1359, 1476, 1733, 1863, 1864, 1865, 1867, 1976, 2022} |
IM | {2050.0} (KTCAVVGNSGIL – CDEIHLY) – SS-bond: C^{ 142 }-C^{ 292 } |
The complexity of both routines MERGE and TRIM is O(|DMS|+|TempSet|) and O(|DMS|), respectively. Further, for any fixed ε > 0, our algorithm is a (1 + ε)-approximation scheme. That is, for any fixed ε > 0, the algorithm runs in polynomial time. The proof of the polynomial time complexity of APPROX-DMS can be obtained by direct analogy to the proof of the polynomial time complexity of the subset sum approximation algorithm from [16] and is outlined in Appendix A.
Parameters estimation
APPROX-DMS depends on two important parameters, namely, the match threshold T_{ IM } and the trimming parameter ε. The match threshold is responsible for defining a “matching window”. This is necessary due to practical considerations such as the sensitivity of the instrument (i.e. 0.01Da, 0.1Da, and 1.0Da) and experimental noise, due to which an exact match is a rarity. We conducted an empirical study by using different values of T_{ IM } for all our datasets. Based on the results, the T_{ IM } value of ±1.0Da was found to minimize missing matches as well as the occurrence of false positives. Considering the smallest precursor ion mass involved, in these studies, the above value of T_{ IM } guaranteed a matching accuracy of 99.86%.
Polynomial time FMS construction
Determining the globally consistent bond topology
In Eq. (4), the numerator corresponds to the sum of each validation match for a disulfide bond multiplied by the matched MS/MS fragment normalized intensity value (I_{ N }). Here, VM_{ i } is a binary value which is set to 1 if a confirmatory match was found for fragment i. The denominator similarly contains the sum of each experimental MS/MS fragment ion from TMS multiplied by I_{ N }. Here, TMS_{ i } is a binary variable which indicates the presence of a fragment i in the MS/MS spectrum.
Next, the globally consistent bond topology is found by solving the maximum weight matching problem for the graph G. A matching M in the graph G is a set of pair-wise non-adjacent edges; that is, two edges do not share a common vertex. A maximum weight matching is defined as a matching M that contains the largest possible sum of the weights (match scores) of each possible edge (disulfide bond). We use the Gabow algorithm [17], as implemented in [18] for computing the maximum weight match.
Results
The proposed method was validated utilizing experimental data obtained using a capillary liquid chromatography system coupled with a Thermo-Fisher LCQ ion trap mass spectrometer LC/ESI-MS/MS system. Details of the experimental protocols can be found in [19, 20]. We used data from nine eukaryotic glycosyltransferases. These molecules and their Swiss-Prot ID were: ST8Sia IV [Q92187], Beta-lactoglobulin [P02754], FucT VII [Q11130], C2GnT-I [Q09324], Lysozyme [P00698], FT III [P21217], β1-4GalT [P08037], Aldolase [P00883], and Aspa [Q9R1T5].
We conducted five sets of experiments to investigate the proposed method and its efficacy. These experiments included: (1) Analysis of method’s efficiency, showing how the method successfully reduced the DMS and FMS search spaces. (2) Analysis of the effect of incorporating multiple ion types, demonstrating the importance of considering non-b/y ions in the determination of disulfide bonds. (3) Comparative analysis of the proposed method with established predictive techniques. (4) Comparative analysis of the method with MassMatrix, an established MS-based approach which can be used for determining S-S bonds. In both experiment 3 and experiment 4, the aforementioned set of glycosyltransferases and their known S-S bond topology provided us with the ground truth. (5) Analysis of the method in terms of established performance measures: Accuracy (Q_{ 2 }), Sensitivity (Q_{ c }), Specificity (Q_{ nc }), and Matthew’s correlation coefficient (c).
Analysis of efficiency of the search
DMS and FMS mass space sizes comparison
Protein | Disulfide Bond | Full Search (exponential) | Proposed Search (polynomial) | DMS decrease | FMS decrease | ||
---|---|---|---|---|---|---|---|
DMS size | FMS size | DMS size | FMS size | ||||
Beta-LG | C^{82}C^{176} | 2152 | 2169 | 1870 | 78 | 13.1% | 96.4% |
ST8Sia IV | C^{142}C^{292} | 1246 | 1792 | 1038 | 106 | 16.7% | 94.1% |
C^{156}C^{356} | 1246 | 2640 | 1038 | 255 | 16.7% | 90.3% | |
FucT VII | C^{318}C^{321} | 581 | 115 | 528 | 34 | 9.1% | 70.4% |
C^{68}C^{76} | 879 | 103 | 681 | 41 | 22.5% | 60.2% | |
C^{211}C^{214} | 879 | 1819 | 681 | 107 | 22.5% | 94.1% | |
B1,4-GalT | C^{134}C^{176} | 2149 | 1189 | 1127 | 77 | 47.6% | 93.5% |
C^{247}C^{266} | 2149 | 5480 | 1127 | 426 | 47.6% | 92.2% | |
Average DMS and FMS decrease | 21.8% | 86.4% |
Effects of incorporating multiple ion types: a case study
In this experiment, we investigated the effect of incorporating multiple ion types (a, b, b^{ o }, b^{ * }, c, x, y, y^{ o }, y^{ * }, and z) in determining the S-S bonds as opposed to considering only b/y-ions. We found that multiple instances of combinations between b/y ions and other ions types occurred by analyzing the confirmatory matches for the different disulfide bonds. These combinations are available as supplemental information (see Additional File 2).
We also observed that consideration of multiple ion-types led to significant increase in the match scores of the true disulfide bonds, whereas only a modest increase was noticed for false positives. This allowed us to increase the threshold we use on the match score V_{ s } to identify high-quality matches from 30 to 80 (a 166% increase). The positive effect of this increment on the specificity of the method can be illustrated by considering the protein Aldolase. In this molecule, consideration of only b/y ions led to a false positive S-S bond identification between cysteines C^{135}-C^{202} (V_{ s }=30.8, with (original) threshold 30) However, when the multiple ions-types were considered with the (increased) threshold on the match score, no S-S bond was found between C^{135}-C^{202} (V_{ s }= 53.2, (incremented) threshold 80).
Comparative studies with predictive techniques
Comparison with predictive methods
Protein | Known Pattern | Proposed Algorithm | DiANNA 1.1 | DISULFIND | PreCys |
---|---|---|---|---|---|
ST8Sia IV | C^{142}C^{292}, C^{156}C^{356}, | C ^{ 142 } C ^{ 292 } , C ^{ 156 } C ^{ 356 } | C^{11}C^{156}, C^{142}C^{292}, C^{169}C^{356} | None | C^{142}C^{356}, C^{156}C^{292} |
Beta-LG | C^{82}C^{176}, C^{122}C^{135} | C ^{ 82 } C ^{ 176 } | C^{12}C^{137}, C^{82}C^{176}, C^{126}C^{135} | None | None |
FucT VII | C^{68}C^{76}, C^{211}C^{214}, C^{318}C^{321} | C ^{ 68 } C ^{ 76 } , C ^{ 211 } C ^{ 214 } , C ^{ 318 } C ^{ 321 } | C^{68}C^{321}, C^{76}C^{211}, C^{214}C^{318} | C^{76}C^{318} | C^{68}C^{76}, C^{211}C^{214}, C^{318}C^{321} |
B1,4-GalT | C^{134}C^{176}, C^{247}C^{266} | C ^{ 134 } C ^{ 176 } , C ^{ 247 } C ^{ 266 } | C^{23}C^{176}, C^{30}C^{144}, C^{266}C^{341} | None | C^{134}C^{247}, C^{176}C^{266} |
C2GnT-I | C^{59}C^{413}, C^{100}C^{172}, C^{151}C^{199}, C^{372}C^{381} | C ^{ 59 } C ^{ 413 } , C ^{ 151 } C ^{ 199 } , C ^{ 372 } C ^{ 381 } | C^{13}C^{172}, C^{59}C^{217}, C^{151}C^{234}, C^{199}C^{372}, C^{381}C^{413} | Not supported | C^{59}C^{381}, C^{100}C^{372}, C^{151}C^{172}, C^{199}C^{413} |
Lysozyme | C^{24}C^{145}, C^{48}C^{133} | C ^{ 24 } C ^{ 145 } , C ^{ 48 } C ^{ 133 } , | C^{24}C^{145}, C^{48}C^{133}, C^{82}C^{98}, C^{94}C^{112} | C^{24}C^{145}, C^{48}C^{133}, C^{82}C^{98}, C^{94}C^{112} | C^{82}C^{145} |
FT III | C^{81}C^{338}, C^{91}C^{341} | C ^{ 81 } C ^{ 338 } | C^{16}C^{91}, C^{81}C^{143}, C^{129}C^{338} | None | C^{81}C^{91} |
Aldolase | None | None | C^{73}C^{339}, C^{135}C^{290}, C^{115}C^{240}, C^{178}C^{202} | None | None |
Aspa | None | None | C^{4}C^{275}, C^{60}C^{217}, C^{66}C^{151}, C^{123}C^{145} | None | None |
Comparative studies with MassMatrix
Comparison with MassMatrix
Protein | Known Pattern | Proposed Method | MassMatrix |
---|---|---|---|
ST8Sia IV | C^{142}C^{292}, C^{156}C^{356} | C^{ 142 }C^{ 292 } [V_{ s }:131;pp:109;pp2:41], C^{ 156 }C^{ 356 } [V_{ s }:100;pp:97;pp2:6] | C^{142}C^{292} [V^{ * }_{ s }:54;pp:15;pp2:13], C^{156}C^{356} [V^{ * }_{ s }:77;pp:23;pp2:15] |
Beta-LG | C^{82}C^{176}, C^{122}C^{135} | C^{ 82 }C^{ 176 } [V_{ s }:100;pp:49;pp2:16] | C^{82}C^{176} [V^{ * }_{ s }:68;pp:14;pp2:14] |
FucT VII | C^{68}C^{76}, C^{211}C^{214}, C^{318}C^{321} | C^{ 68 }C^{ 76 } [V_{ s }:105;pp:41;pp2:98], C^{ 211 }C^{ 214 } [V_{ s }:100;pp:13;pp2:20], C^{ 318 }C^{ 321 } [V_{ s }:100;pp:31;pp2:70] | C^{68}C^{76} [V^{ * }_{ s }:12;pp:9;pp2:3], C^{211}C^{214} [V^{ * }_{ s }:78;pp:16;pp2:11], C^{318}C^{321} [V^{ * }_{ s }:46;pp:28;pp2:16] |
B1,4-GalT | C^{134}C^{176}, C^{247}C^{266} | C^{ 134 }C^{ 176 } [V_{ s }:100;pp:61;pp2:29], C^{ 247 }C^{ 266 } [V_{ s }:195;pp:88;pp2:177] | C^{134}C^{176} [V^{ * }_{ s }:34;pp:9;pp2:7], C^{247}C^{266} [V^{ * }_{ s }:31;pp:7;pp2:7] |
C2GnT-I | C^{59}C^{413}, C^{100}C^{172}, C^{151}C^{199}, C^{372}C^{381} | C^{ 59 }C^{ 413 } [V_{ s }:158;pp:237;pp2:61], C^{ 151 }C^{ 199 } [ V_{ s }:100;pp:93;pp2:15], C^{ 372 }C^{ 381 } [V_{ s }:100;pp:81;pp2:79] | None |
Lysozyme | C^{24}C^{145}, C^{48}C^{133} | C^{ 24 }C^{ 145 } [V_{ s }:140;pp:65;pp2:88], C^{ 48 }C^{ 133 } [V_{ s }:100;pp:62;pp2:55] | C^{48}C^{133} [V^{ * }_{ s }:135;pp:51;pp2:33] |
FT III | C^{81}C^{338}, C^{91}C^{341} | C^{ 81 }C^{ 338 } [V_{ s }:100;pp:179;pp2:93] | None |
Aldolase | None | None | None |
Aspa | None | None | None |
Quantitative assessment and analysis of the method’s performance
If the set of disulfide bonds are denoted by P and the set of cysteines not forming disulfide bonds by N, then true positive (TP) predictions occur when disulfide bonds that exist are correctly predicted. False negative (FN) predictions occur when bonds that exist are not predicted as such. Similarly, a true negative (TN) prediction correctly identifies cysteine pairs that do not form a bond. Finally, a false positive (FP) prediction, incorrectly assigns a disulfide link to a pair of cysteines, which are not actually bonded. Based on these definitions, we use the following four standard measures to analyze the proposed method.
Sensitivity (Q_{c}) = TP/P (7)
Specificity (Q_{nc}) = TN/N (8)
Accuracy (Q_{2}) = TP + TN/P + N (9)
Sensitivity, specificity, accuracy and Mathew’s correlation coefficient results for all nine proteins analyzed
Protein | Q _{ c } | Q _{ nc } | Q _{ 2 } | c |
---|---|---|---|---|
ST8Sia IV | 1.00 | 1.00 | 1.00 | 1.00 |
Beta-LG | 0.50 | 1.00 | 0.95 | 0.69 |
FucT VII | 1.00 | 1.00 | 1.00 | 1.00 |
C2GnT-I | 0.75 | 1.00 | 0.98 | 0.86 |
Lysozyme | 1.00 | 1.00 | 1.00 | 1.00 |
B1,4-GalT | 1.00 | 1.00 | 1.00 | 1.00 |
FT III | 0.50 | 1.00 | 0.94 | 0.69 |
Aldolase | X | 1.00 | 1.00 | X |
Aspa | X | 1.00 | 1.00 | X |
Conclusions
We have presented an algorithmic framework for determining S-S bond topologies of molecules using MS/MS data. The proposed approach is computationally efficient, data driven, and has high accuracy, sensitivity, and specificity. It is not limited either by the connectivity pattern or by the variability of product ion types generated during the fragmentation of precursor ions. Furthermore, the approach does not require user intervention and can form the basis for high-throughput S-S bond determination.
Declarations
Acknowledgements
WM and RS were supported by funding from NSF grant IIS-0644418 (CAREER). T-YY was supported by NSF grant CHE-0619163 and NIH grant P20MD000544.
This article has been published as part of BMC Bioinformatics Volume 12 Supplement 1, 2011: Selected articles from the Ninth Asia Pacific Bioinformatics Conference (APBC 2011). The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2105/12?issue=S1.
Authors’ Affiliations
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