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Comparison of 2D Similarity and 3D Superposition. Application to Searching a
Conformational Drug Database
Martin Thimm,*,† Andrean Goede,‡ Stefan Hougardy,† and Robert Preissner‡ Institut fu¨r Informatik, Humboldt-Universita¨t zu Berlin, 10099 Berlin, Germany, and Institut fu¨r Biochemie, Charite´, Monbijoustrasse 2, 10117 Berlin, Germany In a database of about 2000 approved drugs, represented by 105 structural conformers, we have performed2D comparisons (Tanimoto coefficients) and 3D superpositions. For one class of drugs the correlation betweenstructural resemblance and similar action was analyzed in detail. In general Tanimoto coefficients and 3Dscores give similar results, but we find that 2D similarity measures neglect important structural/funtionalfeatures. Examples for both over- and underestimation of similarity by 2D metrics are discussed. The requiredadditional effort for 3D superpositions is assessed by implementation of a fast algorithm with a processingtime below 0.01 s and a more sophisticated approach (0.5 s per superposition). According to the improvementof similarity detection compared to 2D screening and the pleasant rapidity on a desktop PC, full-atom 3Dsuperposition will be an upcoming method of choice for library prioritization or similarity screeningapproaches.
based procedures explore configuration data from crystal-lographic databases;18 others emphasize the distinct features The accessibility of large compound databases has changed of bound ligand conformations especially for the muscarinic from exclusive inhouse databases of large pharmaceutical acetyl-choline receptor.19 Simulated annealing for difference companies to inexpensive publicly available sources.1 At this minimization20 or clustering procedures21 for better coverage time about two million different compounds can be purchasedfrom different vendors.2 In this context established methods of the low-energy conformational space22 are applied.
such as 2D similarity searching are increasingly applied to The selection of the right features for the prediction of identify active compounds for experimental assays. It was bioactivity requires compound class specific techniques to generally accepted that similar compounds having Tanimoto obtain reasonable performance.23 It was shown that the coefficients larger than 0.85 will exhibit similar biological inclusion of 3D information via 3D field descriptors generates activity.3 This assumption could be reaffirmed at a lower level of 80% similar activity.4 In different assays the fraction Typical 3D QSAR studies in this field are restricted to a of active 0.85 similars declined to 60%-40%.5 In a recent limited set of compounds matching the pharmacophore analysis considering more than a hundred different assays model.25,26 To complement this technique shape-based ap- the estimation of the chance that a compound that is > 0.85 proaches are implemented27 and successfully applied to Tanimoto similar to an active is itself active was further similar problems as considered in the analysis of this paper.28 reduced to 30%.6 The resulting risk of missing attractivecompounds gives rise to a number of analyses comparing The similarity is in the eye of the beholder, as Kubinyi different molecular descriptors and similarity metrics for illustrated.29,30 The scoring of the 3D similarity remains different purposes.7,8 But nevertheless even the accuracy of difficult because the balance between geometrical and the prediction of one of six drug classes remains at 66%.9 physicochemical31 terms may influence the results toward Descriptors representing 3D information10,11 and pharma- scaffold hoppers32 or R-group similarities.33 For this analysis cophore based approaches12,13 are opportunities to overcome we selected the drug class of the neuroleptics because these the weaknesses of 2D descriptors. However a lot of experi- compounds are known to have a number of potential side ence and intuition has to be invested to achieve reasonable effects such as extrapyrimidal adverse events. The therapeutic results.14 The superposition of 3D structures is a time- action of neuroleptics is mediated by their interaction with consuming task. For an extensive review on methods for transmitter receptors in particular with the subtypes of the structural alignment see ref 15 and the references therein.
dopamine-receptor. Here we focus on side effects that can Structural flexibility has to be taken into account. The latter be explained by the affinity to further receptors: histamine-, problem can be approached either during comparison16 or serotonin-, adrenergic, and muscarinic receptor.34 This can prior to comparison.17 Different approaches for the generation roughly be estimated by the similarity with compounds from of conformers exhibit strengths and weaknesses. Knowledge indication classes directly addressing these receptors suchas antipsychotics, psychoanaleptics, or antihistamines. The * Corresponding author e-mail: thimm@informatik.hu-berlin.de.
† drug classification scheme according to the WHO recom- mendation35 was utilized to this end.
Published on Web 00/00/0000 PAGE EST: 6.9 Table 1. Antipsychotics Used for the Data Base Search: Name,
• the correlation between 2D and 3D similarity, • the fitness of Tanimoto coefficients for the drug class • whether a simple geometric score will be useful as 3D • whether 3D superposition will be useful to detect similar Drug Classification. Recently, the recommendations of
the WHO Expert Committee responsible for updating theWHO Model List of Essential Medicines were published.35For the first time, a list of all items on the Model List sortedaccording to their 5-level Anatomical Therapeutic Chemical(ATC) classification codes was given. As the therapeuticsubgroup is determined by the second level and the chemicalcomponent describes the lower level(s) of classification it isuseful for this type of analysis, correlating structural similar-ity with similar therapeutic action.
The pharmacological action of neuroleptics is mediated by their interaction with transmitter receptors in particularwith the subtypes of the dopamine-receptor. Therefore(particular) neuroleptics are known to have a number of sideeffects and are dubbed “dirty drugs”.36 Here we focus oneffects that can be explained by the affinity to furtherreceptors: histamine-receptor (H1), serotonin-receptors (5-HT2A/B,5-HT3), adrenergic receptor (alpha 1), and musca-rinic acetyl-choline receptor (M).34 This can roughly beestimated by the similarity with compounds from indicationclasses directly addressing these receptors: N05A (antipsy-chotics), N06 (psychoanaleptics), D04/R06 (antihistamines, • paths of different lengths (2 to 7) between atoms of the same type and same order of the bonds, e.g. CdCN, CCd Data. All comparisons are performed on a database of
N for a path of length 2, or OdCCdN for a path of length 2086 3D-structures of drugs extracted from our inhouse database. This complies with the number of approved drugs Because of the limited length of the fingerprint it is not included in the ChemIDplus database,37 which contains a total possible to assign a special bit for only one pattern. Instead of 177 000 chemical structures. To improve the conditions of this each pattern is assigned a small number of positions for the 3D-comparisons 85 800 conformers were computed (say 4 or 5) along the fingerprint which are set to 1. Therefore with Catalyst38 according to the algorithm of Smellie.39 The the fingerprints of two molecules can be the same while the Anatomical Therapeutic Chemical (ATC) Classification molecules are different. Additionally, the positions corre- System is used for the classification of drugs. It is controlled sponding to a special pattern account for the occurrence of by the WHO Collaborating Centre for Drug Statistics the pattern. Multiple appearances of the same pattern give Methodology40 and was first published in 1976. The database the same fingerprint. Therefore featureless molecules (such covers 218 ATC-major classes (like N05A). 185 ATC-major as C20H22 or C30H32) give the same fingerprint. Neverthe- classes are represented by at least 3 structures, this meets less the fingerprints indicate whether a compound can be a 98% of all such classes containing at least 3 different actual substructure of another molecule. The Tanimoto coefficient low molecular weight compoundsswithout e.g. combina- between two fingerprints is the proportion of the bits in tions, bandages, or proteins. Table 1 shows the 13 members common and the bits in at least one fingerprint of the ATC-class N05A (antipsychotics) that were used forthe database search.
2D-Comparison. The 2D-comparison of the molecules
was carried out using the Tanimoto coefficients41 computed where BC is the number of bits which are 1 in both by the corresponding procedure of Accord from Accelrys.38 fingerprints, whereas B1 and B2 are the number of bits which For this reason the fingerprints of the structures are calculated are 1 in the first or the second fingerprint, respectively.
using the Daylight algorithm42 and compared by the Tan- 3D Score. The 3D-superposition-algorithms investigated
imoto similarity measure for bit strings. Fingerprints are here are designed to find spatial similarity between mol- Boolean arrays of a given length. To evaluate the fingerprint ecules. We follow the paradigm that a necessary condition each pattern of the molecule is generated. Such patterns are for functional similarity is similar geometry. For this reason the scoring function is built to measure spatial similarity only.
• bonds (single, double,.) between atoms of special types By this it is possible to find superpositions which we would COMPARISON OF 2D SIMILARITY AND 3D SUPERPOSITION not have found by simultaneously trying to incorporate One good news is that the second subproblem is known physicochemical features. So it may happen that few of the to be solvable in polynomial time.43 A way to solve the geometrically found hits turn out to be biologically irrelevant, superposition problem is to enumerate all possible assigments but we considerably lower the risk of losing most interesting and to compute the rigid motion for each of them. But here and relevant hits that come from different chemical structures.
the bad news is that the number of possible assignments Similarity of molecules is measured by superposition. In grows highly exponential in the number of atoms. With this general the superposition problem may be decomposed into naive approach only instances with very few atoms (less than two subproblems: First, we have to find an assignment (or matching) of the atoms of one molecule to the atoms of the With the help of a branch-and-bound approach, a widely other molecule, that tells us which atom on one side has to used technique in optimization, we are able the reduce the be superimposed with which atom on the other side (or not number of assignments to be tested dramatically. Doing this superimposed at all). Second, a rigid motion is computed to we are able to solve the superposition problem up to optimally perform this action. There are two competing optimality quite fast (10 atoms: few seconds, 16 atoms: 1-2 1. The more atoms are actually superimposed the better Since drug-like molecules are often larger and since the above-mentioned running times are still far too slow we have 2. The distances of the matched atoms should be as small to find ways to overcome these difficulties. We can no longer as possible. A way to balance these two goals is the following hope to solve the problem exactly, i.e., the solution of the scoring function: Consider two molecules A and B with m algorithm described next will not be guaranteed to be the and n atoms, respectively (m e n). Given an assignment M best possible, but we will get it very quickly without losing that maps the atoms aM of A, i ) 1,., k, k much quality. In what follows we describe the two algorithms atoms bM, j ) 1,., k. The resulting superposition has the Fast 3D-Superposition. The algorithm presented here can
roughly be sketchted by the following steps: score(A, B, M) ) k e(-rmsd(M)) 2. orientation according to principal moments of inertia The first term, k/m, measures the proportion of actually The first orientation (in step 2) is of course independent superimposed atoms of the smaller molecule, the second of transformations of the coordinate system and quite stable term, the root-mean-square distance of these atoms for small alterations of the atomic positions. The normaliza-tion of the atomic sets is unique except for possible rotations (original arrangement and rotations of 180° around the x-, y-, or z-axis). This means that the degree of freedom is strongly reduced and the assignment of pairs of atoms isrelatively straightforward for identical and slightly modified quantifies the distance of matched atoms.
atomic sets because only four possible normalizations have By this definition we try to find a superposition with many to be checked to identify related atoms: imagine determining atoms superimposed with small distance. The first term the correct orientation of a credit card (magnetic strip: top increases with the number of superimposed atoms, but in surface, right; top surface, left; bottom surface right; bottom the majority of cases this will make the second term decrease surface, left). In a first step the centers of mass of the two since more assigned atoms will result in higher rmsd.
atomic sets are determined. All the coordinates of the atoms Observe that the value of the scoring function is always included are transformed to superimpose the centers of mass.
between 0 and 1, where larger values mean higher similarity.
To determine the least and largest (orthogonal) expansion, The scoring function is not restricted to molecules of the the plane and the straight line of minimal quadratic distance same size. It is also possible to compare molecules of quite to all atoms have to be computed. The normal line of the different size, since the first term of our scoring function plane gives the least expansion and the straight line of allows us to find smaller molecules inside larger ones.
minimal quadratic distance points at the largest expansion.
3D Comparison. Since no polynomial time algorithm is
Using these directions one atomic set is rotated such that known to solve the superposition problem as described above the major directions coincide. There are four possible to optimality, we have to use heuristic methods to get good normalizations for an atomic set that coincide with the solutions in reasonable time. We have implemented two exception of 180° rotations around the x-, y-, or z-axes. In a different approaches, a fast one and a more sophisticated further step all four normalizations are used to determine the pairs of atoms between the two atomic sets. This In general the superposition problem may be decomposed normalization procedure is stable even if additional atoms into two subproblems: First, find the assignment for the two are included in one of the sets. Therefore, the normalization atom sets, i.e., which atom in one molecule should be of the atomic set can be used to identify pairs of correspond- superimposed with which atom in the other molecule.
ing atoms. Two atoms form a pair if they are mutually the Second, find the rigid motion that gives the optimal nearest atoms, and their distance is lower than a given cutoff superposition of the atom sets, given the assignment. Our value. Different cutoff values were tested showing that a two approaches mainly differ in the effort made to solve the cutoff of 2.5 Å performed best for sets of densely packed atoms. For all four normalizations the number of atom pairs is chosen, and the root-mean-square distance (rmsd) is • step 2 Enumerate all possible assignments of these s
calculated for the related atomic pairs. The normalizations atoms to their nearest neighbors (including the possibility are weighted on the basis of these values. The best that an atom is assigned to have no matching partner), carry normalization (largest number of pairs) is used in a further out the appropriate rigid motion, and pick the one with the step to improve the alignment. For the given set of pairs the best score value (on this partial instance of already fixed optimal superposition is estimated, followed by a new search of related pairs until the assignment of the atoms does not • step 3 Fix the assignment on these s atoms and perform
the implied rigid motion to all atoms. Go to step 1 while Sophisticated 3D-Superposition. The second algorithm
there are atoms that are not yet fixed.
We conclude this section with some implementation 1. Reduce the given instance to a smaller artificial instance details. Since the solution of Phase 1, the artificial pseudo- that is in a certain sense similar to the original one.
molecule, may look quite different for different numbers r, 2. Solve this artificial instance optimally with the above- we perform this step for several different values of r. The mentioned branch-and-bound technique.
optimal solution of Phase 2 may not be exactly what we 3. Lift the solution of the smaller, artificial instance to a want, since we observed in numerous tests of the exact solution for the original problem. Next we describe the three algorithm that there are instances that have quite a number of solutions with very similar score values but very different Phase 1: Reduction to a smaller artificial instance
assignments. To overcome this we store not only the best The running time of the exact algorithm mainly depends solution but the best n of them (seen during the branch-and- on the number of atoms of the two molecules; so the aim of bound process). Phase 3 also depends on the predefined this phase is to construct, starting with the original molecules, number s, so again as in Phase 1 we perform this phase for new, artificial pseudomolecules with fewer pseudoatoms, that several different values of s. As one would expect, the quality are still spatially similar to the original molecules. This is of the solution increases with the size of the r- and s-intervals done iteratively in the following way, sometimes called and with n, but so does the running time. (Running time grows nearly proportional with n and the number of different • Start with the original molecule, call every atom a s-values and superproportional in the number of different r-values, since larger r-values get more and more expensive.) • While the number of pseudoatoms is larger than a Our standard parameters for drug-like molecules are r∈{3, 4, 5}, s∈{3, 4}, n ) 40. We determined them as a - look for those two pseudoatoms with the smallest result of numerous tests trying to find an optimal tradeoff distance and merge them to a new pseudoatom. The coordinates of this new pseudoatom are given by the Although we cannot prove the optimality for our algo- weighted center of gravity of the two merged ones, which rithms, we wanted to see how far away we are in the relevant cases. As a test we computed 3D-scores for quite a number So in every such step the number of pseudoatoms is of instances which were known to have large 3D-scores decreased by one. As a remark we should say that we take (>0.70) up to optimality with the branch-and-bound algo- into account how many original atoms are represented by a rithm mentioned above. (As a remark we should say that pseudoatom by attaching weights to it. The idea is that the this is possible in these casesswith still very large running new instance constructed in this way still carries the spatial timesssince branch-and-bound algorithms tend to find very information of the original molecule to a certain extent.
good resultssif they existsquite “fast”.) The results showed Phase 2: Exact solution of artificial instance
that in all cases the sophisticated approach was within five Now we solve our artifical instance with the exact algorithm. The solution of this step is the starting point ofPhase 3.
Phase 3: Lift of intermediate solution to the original
instance
To compare the two 3D-superposition algorithms with the The rigid motion which led to the solution in Phase 2 may 2D-approach we selected 13 antipsychotics (ATC code also be applied to the original instance. The idea of our N05A) and computed both Tanimoto coefficients and 3D- approach is now that, since the smaller artificial instance is scores (fast and sophisticated) for each of them with all drugs spatially similar to the original one, the position of the in the database (with more than 14 non-hydrogen atoms).
original atoms after this rigid motion is not far from a very To compute the 3D-score of two conformers of molecules good solution. We only have to refine the assignment to these of average size (25 atoms) we need about 0.01 s (fast) and atoms. This is done as follows: The distance of atoms that 0.5 s (sophisticated) (on a 2GHz PC), resulting in a total will be assigned to each other should now be already quite running time of 25 s (fast) and 21 min (sophisticated) to small, so a natural approach is the following: fully compare two molecules, both given by 50 structural • step 0 Declare all atoms to be not fixed.
step 1 Sort those atoms of the first molecule that have
Unfortunately we cannot compare the values of Tanimoto not yet been assigned (fixed) increasingly by their distance coefficients and 3D-scores one-to-one. As mentioned in the to the nearest neighbor in the other molecule, that is still Introduction it is generally accepted that Tanimoto coef- available. Take the first s of them (s is a small predefined ficients larger than 0.85 start to indicate similar activity. To find a corresponding value for the 3D-score we counted the COMPARISON OF 2D SIMILARITY AND 3D SUPERPOSITION Table 2. Number of Hits
Table 3. Number of Hits: Tanimoto vs Soph. 3D
Table 4. Number of Hits: Tanimoto vs Fast 3D
Figure 1. Comparisons with 2D similarity above threshold and
3D similarity below threshold. (a) Superposition of flupentixol(bottom, ATC code: N05AF01) with thiethylperazine (top, ATCcode: R06AD03) Table 5. Number of Hits: Fast 3D vs Soph. 3D
coefficient of 0.89. The similarity is underestimated by the 3D score because the distortions in the tricyclic ring are not properlyrepresented by the conformers. (b) Superposition of tiapride (top, ATC code: N05AL03) and probenecid (bottom, ATC code: M04AB01) with a 3D score of 0.58 and a Tanimoto coefficient of 0.85. The resemblance to probenecid, an antigout drug, is oversti- mated by the Tanimoto coefficient because of the identical chemicalsubgroups (phenyl, sulfonyl).
number of hits with a Tanimoto coefficient larger than 0.85and found that a 3D-score of about 0.75 gives approximately hits, that are clearly relevant from a biological point of view, we can infer that already 3D-score above 0.65 are worth We found 164 hits with a Tanimoto coefficient larger than while to look at. (See Figure 1a) for an example.) 0.85. The 3D-superposition algorithms returned 200 (sophis- The second subset of hits (i.e. 4. column) with large ticated) and 156 (fast) hits with a 3D-score larger than 0.75 Tanimoto coefficents and small 3D-scores largely consists of those hits for which the Tanimoto coefficient highly Since we want to show that the 3D-approach is appropriate overestimates the structural/functional similarity of the to find molecules that have similar activity we first looked molecules. An example can be seen in Figure 1b.
at the ATC codes of the hits with a score value larger than Ad b. For this set of hits the situation changes. The number 0.75 and found that 78, 5% (157 out of 200) (sophisticated) of hits with a large 3D-score that are found by the and 84% (131 out of 156) (fast) of these can be found in sophisticated algorithm are significantly larger than those drug subclasses that are known to have similar activity or found by the fast algorithm, for both the relevant drug classes similar adverse reaction (ATC codes N05A, N06, R06, D04).
and the others (see Tables 3 and 4 for the exact numbers).
The proportion of hits in these classes for Tanimoto Since the 3D-superposition algorithms are not designed coefficients larger than 0.85 is 69% (113 out of 164) (see to incorporate chemical features, there are some hits that are clearly geometrically relevant, but perhaps their prediction To compare the results of the 2D- and 3D-approaches we about similar activity is quite limited. These hits can be found have to look at three different sets of seemingly similar pairs in the second subset (i.e. 4. column).
What we are really aiming for is the first subset (i.e. 3.
a. large Tanimoto coefficient (>0.85), small 3D-score column). Here we find hits that are both geometrically similar and relevant concerning prediction of similar activity and b. small Tanimoto coefficient (<0.85), large 3D-score function. One reason why in these cases Tanimoto coef- ficients do not indicate similarity are slight changes in c. large Tanimoto coefficient (>0.85), large 3D-score chemical structure. Furthermore there are hits with two molecules of somewhat different size. It is known (see ref Ad a. For this set of hits, comparing Tanimoto coefficients 44) that for these instances Tanimoto coefficients are more to both sophisticated and fast 3D-superposition gives a and more inefficient, while our 3D-score is designed to also similar picture (see Tables 3 and 4 for the exact numbers).
find these hits. (See some examples for both cases in Figure Approximately one-half of this set of hits lies in the above- 2.) For this type of hits the sophisticated approach is clearly mentioned relevant drug classes. A closer inspection for this superior to the fast algorithm. Comparing the numbers in subset (i.e. 3. column) shows that in most of the cases the Table 5 with those in Tables 3 and 4 shows that most of the 3D-score for these hits is larger than 0.65. Looking at these hits for which the two 3D-approaches differ can be found in Figure 2. Comparisons with low Tanimoto coefficients and 3D
Figure 3. Differences between fast and sophisticated superposi-
scores above threshold. (a) Superposition of fluphenazine (bottom, tions. (a) Superposition of perazine (top, ATC code: N05AD10) ATC code: N05AB02) with isothipendyl (top, ATC codes: D04A- with triflupromazine (bottom, ATC code: N05AA05) with a 3D A22, R06AD09) with a 3D score of 0.81 and a Tanimoto coefficient score of 0.77 (sophisticated), 0.50 (fast), and a Tanimoto coefficient of 0.69. The resemblance to isothipendyl, an antihistaminic agent, of 0.84. The resemblance between the two neuroleptics is neglected is neglected by the 2D similarity measure because of missing by the fast superposition algorithm because the centers of gravity chemical groups (trifluoromethyl, piperazin) and quite different sizes do not fit. (b) Superposition of tryptophan (top, ATC code: of the molecules. (b) Superposition of prothipendyl (bottom, ATC N06AX02) and risperidone (bottom, ATC code: N05AX08) with code: N05AX07) and opipramol (top, ATC code: N06AA05) with a 3D score of 0.77 (sophisticated), 0.50 (fast), and a Tanimoto a 3D score of 0.76 and a Tanimoto coefficient of 0.72. The coefficient of 0.44. The similarity to tryptophan, an antidepressant, similarity to opipramol, an antidepressant, is missed by 2D is missed by the fast superposition algorithm because of the very comparison because the middle ring is seven membered in different overall geometry of the molecules.
opipramol (dibenzazepine derivative) and six membered in pro-thipendyl (azaphenothiazine derivative).
cal features that are responsible for the biological activity.
the class discussed here. The main reason for this is that the 2D similarity works poorly when common functional groups fast approach is not able to find hits for two molecules that as in peptides are considered. A similar fragment- or have different overall geometry, in particular small molecules topomer-based steric shape screening was shown to be more that are substructures of larger ones are not found (see Figure selective than 2D similarity,13 especially advantageous “lead- hopping” was observed. A reasonable speed for the in silico Ad c. In this set we find those hits that are quite similar screening of large compound libraries can be achieved by in both chemical structure and size. They are reported as full-atom superposition procedures as presented in this relevant by both approaches. For this type of hits both strategies are most similar. Here again, as in case a, the fast With receptor structures available ligand-docking programs and the sophisticated 3D-algorithm perform comparably.
have been shown to enrich hit lists of in silico screening From our point of view we have therefore seen several approaches,45 but in the case of psycholeptics a number of strong arguments in favor of the 3D-superposition algorithms.
structurally unknown receptors are engaged. Most of the It can be clearly seen that the 3D-approach is able to detect processes involved in ADME are driven by rather unspecific similar activity and similar adverse reaction, even with this interactions between drugs and macromolecules, but drug seemingly simple, purely geometry-based scoring function.
transporters and cytochromes gained increased interest in For large data sets a fast 3D-superposition algorithm early ADME profiling via similarity based structure activity combined with Tanimoto coefficients helps to increase the relation (SIBAR).46 The increased predictive power of the 3D- vs 2D-similarity for side effects demonstrated in this If one aims to really find all, at least geometrically relevant analysis gives rise to the hope that improvements in ADME hitssthis may be important for smaller and more specific and toxicity profiling will be possible.
sets of moleculessit is worthwhile to follow the sophisticated Limitations of the fast 3D superposition approach are 3D-approach (with a somewhat smaller threshold for rel- spherical compounds for which it might fail to find proper evance). We were able to find really relevant hits that cannot assignments. The known size bias and size limitation of 2D be found by simple 2D-methods or by the fast 3D-algorithm.
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