Learning the Edit Costs of Graph Edit Distance Applied to Ligand-Based Virtual Screening

Abstract

Background: Graph edit distance is a methodology used to solve error-tolerant graph matching. This methodology estimates a distance between two graphs by determining the minimum number of modifications required to transform one graph into the other. These modifications, known as edit operations, have an edit cost associated that has to be determined depending on the problem. Objective: This study focuses on the use of optimization techniques in order to learn the edit costs used when comparing graphs by means of the graph edit distance. Method: Graphs represent reduced structural representations of molecules using pharmacophore-type node descriptions to encode the relevant molecular properties. This reduction technique is known as extended reduced graphs. The screening and statistical tools available on the ligand-based virtual screening benchmarking platform and the RDKit were used. Results: In the experiments, the graph edit distance using learned costs performed better or equally good than using predefined costs. This is exemplified with six publicly available datasets: DUD-E, MUV, GLL&GDD, CAPST, NRLiSt BDB, and ULS-UDS. Conclusion: This study shows that the graph edit distance along with learned edit costs is useful to identify bioactivity similarities in a structurally diverse group of molecules. Furthermore, the target-specific edit costs might provide useful structure-activity information for future drug-design efforts.

Ligand-Based Virtual Screening Based on the Graph Edit Distance

“…In general, using several datasets at once makes the learnt parameters less specific for the application at hand, and thus, the classification ratios tend to decrease. In spite of this possible disadvantage, our method returns better classification ratios than the one in [35] in all the datasets.…”

“…Figure 6 shows the percentage of times that each cost configuration obtains the highest classification ratio taking into account all the 127 targets, given the four configurations proposed in [35], one configuration proposed in [33] and our deduced configuration. Our method obtains the best classification ratio the highest number of times.…”

“…In [ 33 ], they map reduced graphs into sets of shortest paths. Finally, in [ 34 , 35 ], they perform the comparison on the graphs using the Graph Edit Distance (GED). GED considers the distance between two graphs as the minimum cost of modifications required to transform one graph into another.…”

“…In an initial paper [ 34 ], the edit costs were imposed and extracted from [ 33 ], given the chemical expertise of the authors and considering the different node and edge types. Later, in [ 35 ], authors presented an algorithm for optimising those edit costs based on minimising the distance between correctly classified molecules and maximising the distance between incorrectly classified molecules. That work was inspired in a similar one carried out by Birchall et al [ 39 ], in which the authors optimise the transformation costs of a String Edit Distance method to compare molecules using reduced graphs.…”

“…The main problem of the algorithm in [ 35 ] was the huge computational cost, which depends on the number of edit costs to be optimised. Thus, for practical reasons, in the experimental section in [ 35 ], they presented four experiments, in which only one edit cost was optimised in each experiment. They imposed the other costs (126 in total) to be the ones defined in [ 33 ].…”