Mordred: a molecular descriptor calculator — TEI-tagged view

Hirotomo MoriwakipersName, Yu-Shi TianpersName, Norihito KawashitapersName, Tatsuya TakagipersName (2018date). “Mordred: a molecular descriptor calculator.” Journal of Cheminformaticstitle·j.

Object of study — Mordredterm's descriptorterm coverage, software architecture, correctness controls, algorithms, interfaces, and performance

Research question — how to provide a fast, maintainable, permissively licensed molecular-descriptor calculatorterm with broad coverage and reliable results

Contribution — an open-source cross-platform descriptorterm calculatorterm with automatic preprocessing, reference tests, parallel execution, and more than 1,800 descriptorsterm

Full text — tagged

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Mordredterm: a molecular descriptorterm·def calculatorterm Abstract Molecular descriptorsterm are widely employed to present molecular characteristicsterm in cheminformaticsterm. Various molecular-descriptor-calculation software programs have been developed. However, users of those programs must contend with several issues, including software bugs, insufficient update frequencies, and software licensing constraints. To address these issues, we propose Mordredterm, a developed descriptor-calculation software applicationterm that can calculate more than 1800 two- and three-dimensional descriptorsterm. It is freely available via GitHub. Mordredterm can be easily installed and used in the command line interface, as a web applicationterm, or as a high-flexibility Python package on all major platforms (Windows, Linux, and macOS). Performance benchmark results show that Mordredterm is at least twice as fast as the well-known PaDEL-Descriptorterm and it can calculate descriptorsterm for large molecules, which cannot be accomplished by other software. Owing to its good performance, convenience, number of descriptorsterm, and a lax licensing constraint, Mordredterm is a promising choice of molecular descriptor calculation softwareterm that can be utilized for cheminformaticsterm studies, such as those on quantitative structure–property relationshipsterm.

The online version of this article (10.1186/s13321-018-0258-y) contains supplementary material, which is available to authorized users.

Background A molecular descriptorterm·def is defined as the “final result of a logical and mathematical procedureterm, which transforms chemical information encoded within a symbolic representation of a moleculeterm into a useful numberterm or the result of some standardized experiment” [ 1 ]. Many types of molecular descriptorsterm have been developed, such as the number of carbon atoms; molecular weight; predictive values of LogP (XLogP [ 2 ], ALogP [ 3 ], etc.); properties calculated from two-dimensional (2D) structures (e.g., Eccentric Connectivity Index [ 4 ]) and three-dimensional (3D) structures (e.g., charged partial surface area (CPSA) [ 5 ]); and properties based on quantum mechanics (orbital energies of highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), etc.). Quantitative structure–property relationshipterm (QSPR) models frequently use molecular descriptorsterm. They are studied to predict the activity, toxicity, and other properties resulting from the chemical structures of compounds.

The steps in a general procedure of QSPR model constructionterm·def using molecular descriptorsterm are outlined below. Split the dataset into training and test datasetsterm for evaluating the predicted performance of the model. Calculate numerous molecular descriptorsterm of each compound in the datasets. Construct a reliable model of the training dataset to predict the target activity or property from these calculated descriptorsterm using classification or regression methodsterm (e.g., multiple regression analysis, partial least squares regression, support vector machine (SVM), and random forest). Evaluate the performance of the constructed model by predicting the target activities of the compounds in the test dataset that are not used for model construction.

Although both open-source and proprietary software have been developed for calculating molecular descriptorsterm—such as PaDEL-Descriptorterm [ 6 ], BlueDesc [ 7 ], ChemoPy [ 8 ], PyDPI [ 9 ], Rcpi [ 10 ], cinfony [ 11 ], and Dragon [ 12 ]—they each have advantages and disadvantages (Table 1 ). The freely available PaDEL-Descriptorterm can calculate 1875 molecular descriptorsterm and fingerprints. It provides several interfaces (e.g., a graphical user interface (GUI), command line interface (CLIterm), Konstanz Information Miner (KNIME) [ 13 ], and Rapid Miner [ 14 ]), and it has been cited by other papers more than 300 times. Moreover, it can calculate descriptorsterm in parallel. Thus, these advantages make it one of the best choices among open-source molecular-descriptor calculatorsterm. However, we determined that it has several defects (Table 2 ), which implies that careful verifications and modifications are required when using it. Table 1 Comparison features of major descriptorterm calculation software Mordredterm PaDEL-Descriptorterm BlueDesc ChemoPy PyDPI Rcpi Cinfony Dragon Number of descriptorsterm 1825 1875 174 1135 615 307 – a 5270 Citation count b – 598 – 48 17 21 38 148 Library Python2/3 – – Python2 Python2 R Python2/3 – Parallel computation ✓ ✓ – – – – – – GUI – ✓ – – – – – ✓ CLIterm ✓ ✓ ✓ – – – – ✓ KNIME – ✓ – – – – – ✓ RapidMiner – ✓ – – – – – – Web Interface ✓ – – – – – – ✓ c Last release 2018/1/20 2014/7/21 2008/10/3 2013/2/1 2015/11/10 2017/11/18 2015/8/1 ? d License BSD-3-Clause e GPL GPL GPL Artistic license BSD-2-clause/GPLv2/GPLv3 Proprietary Source code distribution Github Official site Official site Google code pypi github github – Other advantages Easy to use with libSVM Can also calculate protein descriptorterm Can also calculate protein descriptorterm Include analysis tool Other disadvantages Some bugs are founded No configurable options Require many manually installed dependencies Payware a Depends on backends b Citation counts on Google Scholar (accessed on 2018/01/16) c Provided by e-Dragon, which uses the old version of Dragon d Unknown; however, Dragon is being actively developed e “This software is free for all (e.g. personal, academic, non-profit, non-commercial, government, commercial, etc.) to use.” ( http://yapcwsoft.com/dd/padeldescriptorterm , accessed on 2018/01/16) Table 2 Defects identified in the descriptorterm calculation software Software Details CDK Theoretically, the roto-translation of a molecule should not change any molecular property. However, TPSA and LengthOverBreadth descriptorsterm resulted in different values of molecules before and after roto-translation transformation The value of ChiPathCluster is invalid because the patterns are not adequate (fixed in the latest version of CDK) PaDEL Several molecules (e.g., Cyanidin) resulted in invalid values in many descriptorsterm (e.g., nH (hydrogen count) returned 12) when using the default configuration owing to a bug in the aromaticity detecting procedure and/or 3D conformer generator of PaDEL-Descriptorterm. This caused breakage of an aromatic ring and attachment to an invalid hydrogen Some descriptorsterm use the log sum exponential (LSE) function ( LSE 1 below), which is prone to arithmetic overflow or underflow. The LSE trick ( LSE 2 below) should be used to avoid this issue LSE 1 x 1 , x 2 , … , x n = log ∑ i = 1 n exp x i \[\begin{array}{*{20}c} {{\text{LSE}}_{2} \left( {x_{1} ,x_{2} , \ldots , x_{n} } \right) = x^{ *} + \log \left( {\mathop \sum \limits_{i = 1}^{n} \exp \left( {x_{i} - x^{*} } \right)} \right)} \\ {x^{ *} = \hbox{max} \left( {x_{1} ,x_{2} , \ldots ,x_{n} } \right)} \\ \end{array}\] LSE 2 x 1 , x 2 , … , x n = x ∗ + log ∑ i = 1 n exp x i - x ∗ x ∗ = max x 1 , x 2 , … , x n In the constitutional descriptorterm, discrepancies might be induced in the algorithm implementation owing to incorrect code reuse ChemoPy Cannot calculate exact values of modified Zagreb index 2 Meanwhile, BlueDesc is a simple software program for calculating descriptorsterm. Because BlueDesc can output the results in libSVM input file format, users can easily construct SVM models. However, BlueDesc can calculate only 174 descriptorsterm, and it has no configurable options. ChemoPy, a free software environment that calculates both 2D and 3D descriptorsterm, can calculate 1135 descriptorsterm. ChemoPy is available as a Python package and is convenient for constructing models using Python machine-learning packages. However, it can be difficult to employ it by non-Python users who are not familiar with the construction of the Python interface. (As described later, this disadvantage can be overcome by using several web interfaces that incorporate ChemoPy.) To date, ChemoPy only supports Python 2.

Furthermore, PyDPI can calculate small molecule descriptorsterm as well as protein descriptorsterm. However, it has advantages and limitations that are similar to those of ChemoPy. In addition, Rcpi (the protein and small molecule descriptorterm calculation package for R [ 15 ]) is the only R package to calculate small molecular descriptorsterm and protein descriptorsterm. It can calculate only 307 small molecular descriptorsterm. Cinfony is another Python package. It is a Python wrapper of numerous other libraries (e.g., Open Babel [ 16 ], RDKitterm [ 17 ], Chemistry Development Kit (CDK) [ 18 ], Indigo [ 19 ], JChem [ 20 ], and OPSIN [ 21 ]). Thus, it requires many manually installed dependencies, which is a complicated processterm·var. Moreover, a new version has not been released since December 2012 [ 22 ]. Dragon is another widely used application software that is used to calculate molecular descriptorsterm. It can calculate numerous descriptorsterm, and it has several interfaces, such as a GUI, CLIterm, web (e-Dragon [ 23 ], which is based on an older free version of Dragon), and KNIME. However, it is proprietary shareware; its source code is not open, and it is not easy to publish constructed quantitative structure–activity relationship (QSAR) models, such as Ecological Structure Activity Relationships (ECOSAR) [ 24 ], on account of licensing issues. Furthermore, some descriptorterm calculation programs do not have a user-friendly interface and/or it is difficult to set up the environment. Thus, several web-based descriptorterm calculation interfaces have been developed, such as ChemDes [ 25 ] and BioTriangle [ 26 ]. ChemDes can calculate all descriptorsterm that can be calculated by ChemoPy, CDK, RDKitterm, Open Babel, BlueDesc, and PaDEL. Moreover, BioTriangle can manipulate not only small molecules, but also nucleic acid and protein. Because users do not need to install any software except a web browser, which can be accessed from any device, web user interfaces (UIs) are convenient.

In this paper, we propose Mordredterm, a newly developed molecular-descriptor calculation software program. The software can calculate more than 1800 descriptorsterm at high speed, and it can be used from the CLIterm and web UI, as well as with Python 2 and 3 libraries. Mordredterm was released under the three-clause Berkeley Software Distribution (BSD) licenseterm, which allows both commercial and non-commercial use.

Implementation Motivation and Mordredterm concepts Mordredterm was designed to be a software program that is easy to install and use, supports abundant molecular descriptorsterm, has a high calculation speed, and includes automated teststerm. Molecular-descriptor calculation programs usually have many dependent software programs that must be manually installed. All direct dependent libraries in Mordredterm, except for RDKitterm and NumPyterm [ 27 ], are coded in pure Python (enum34, networkx, six, tqdm) to simplify the installation. RDKitterm and NumPyterm are widely used Python libraries and can be easily installed via the pre-compiled libraries distributed by the Anaconda cloud [ 28 ]. Therefore, users can install Mordredterm using a single command (see Code 1 below). Because Mordredterm can be employed as a web service or from a CLIterm, and with Python 2 and 3 libraries, users ranging from beginners to experts can employ it.

Preprocessing of moleculesterm affects the descriptor valuesterm·var in most molecular-descriptor calculatorsterm. However, for each descriptorterm, Mordredterm automatically preprocesses molecules (adds or removes hydrogen atoms, performs Kekulization, and detects molecular aromaticity). For example, a topological index descriptorterm was reported by Balaban et al. [ 29 ]. along with a numerical example. To reproduce the values, the input molecule should not have explicit hydrogen atomsterm. Therefore, explicit hydrogen atomsterm are automatically removed in Mordredterm. This procedure ensures correctness of preprocessingterm, which is usually not checked in other software.

Mordredterm calculates more than 1800 default molecular descriptorsterm, including all those implemented by RDKitterm (seven modules) and original implementations (42 modules) (Table 3 ). To note, PaDEL-Descriptorterm can calculate the largest number of descriptorsterm among other related open-source software programs by providing 1875 molecular descriptorsterm. The number of default descriptorsterm calculated by Mordredterm is comparable, which suggests that Mordredterm can be used as alternative descriptorterm calculation software in QSAR studies. Table 2 lists the defects identified in other descriptorterm calculation applications. These defects were fixed in the development of Mordredterm. Moreover, users can employ optional descriptorsterm by passing parameters or generating product termsterm of descriptorsterm. For example, n-membered ring descriptorsterm calculate the number of n-membered rings; n = 3 to n = 12 can be calculated by default. If the number of a larger ring, e.g., 14- to 16-membered ring macrolides, is required, the calculation can be easily achieved by passing the parameter of an n value that is larger than 12 without modifying the source code. These unique functions significantly increase the descriptorterm calculation abilities and distinguish Mordredterm from other previously developed software. Table 3 List of Mordredterm descriptorsterm Descriptorterm name Number of descriptorsterm (preset) 2D ABCIndex 2 AcidBase 2 AdjacencyMatrix 13 Aromatic 2 AtomCount 16 Autocorrelation 606 BCUT a 24 BalabanJ a 1 BaryszMatrix a 104 BertzCT 1 BondCount 9 CarbonTypes 10 Chi 56 Constitutional 16 DetourMatrix 14 DistanceMatrix 13 EState 316 EccentricConnectivityIndex 1 ExtendedTopochemicalAtom 45 FragmentComplexity 1 Framework 1 HydrogenBond a 2 InformationContent 42 KappaShapeIndex 3 Lipinski 2 McGowanVolume 1 MoeType a 53 MolecularDistanceEdge 19 MolecularId 12 PathCount 21 Polarizability 2 RingCount 138 RotatableBond a 2 SLogP a 2 TopoPSA a 2 TopologicalCharge 21 TopologicalIndex 4 VdwVolumeABC 1 VertexAdjacencyInformation 1 WalkCount 21 Weight 2 WienerIndex 2 ZagrebIndex 4 3D CPSA 43 GeometricalIndex 4 GravitationalIndex 4 MoRSE 160 MomentOfInertia 3 a RDKitterm wrapper To implement molecular descriptorsterm that can efficiently perform very large calculations, certain calculation algorithms were improved. Accordingly, Mordredterm can calculate all descriptorsterm of molecules as large as a maitotoxinterm (molecular weight of 3422; it is the largest non-polymer compound in nature) in an acceptable calculation timeterm (approximately 1.2 s on an Intel ® Core™ i7-5930 K CPU, DDR4-2133 (quad channel) 64 GB memory machine.). On the contrary, most other software packages have difficulty in calculating complicated descriptorsterm for large molecules; e.g., PaDEL-Descriptorterm falls into a missing valueterm·var from a “time out” in such cases. For further information on these improvements, the Mordredterm documentation can be referenced.

Most descriptorterm calculation software programs do not include automated teststerm to check descriptor valuesterm·var in a distribution package. In Mordredterm, all descriptorsterm are automatically tested to verify whether Mordredterm can calculate precise results using the reference valuesterm of the molecular descriptorsterm. The reference valuesterm were collected from published studies, consensual findings of multiple descriptor-calculation programs, and results of manual checks according to the calculation algorithms published. The variations among descriptor valuesterm·var calculated by Mordredterm and other software programs are confirmed in Additional files 1 and 2 . All tests are performed at each commit on the GitHub repository as well as when a new version is released. In addition, users can locally execute tests to check the installation success and calculate valid results on user platforms.

Library design Mordredterm consists of two main classes: “Descriptorterm” and “Calculatorterm” (Fig. 1 ). The algorithms of molecular descriptorsterm are implemented in the subclass of the Descriptor classterm. Because there are interdependencies between the molecular-descriptor calculations, one subclass can depend on other subclasses for better efficiency in Mordredterm. Many descriptor-calculation algorithms provide multiple results, which complicates the treatment of descriptor valuesterm·var. However, each Descriptorterm instance provided for users returns a single value in Mordredterm, which makes it simple and convenient to use (Code 2). When necessary, users can employ uncommon-range descriptorsterm by passing parameters, as shown in Code 3. Although all Mordredterm descriptorsterm can be calculated by constructing descriptorterm instances, as shown in Code 2, this approach is not very convenient. Hence, each Descriptor classterm has a preset configuration, and users can obtain a set of descriptorsterm by using this preset method (Code 4). They can be used in an instance of the Calculator classterm (Additional file 3 ). Fig. 1 Overview of Mordredterm library. Mordredterm consists of two main classes: descriptorterm and calculatorterm. Users can register descriptorsterm on a Calculatorterm instance. A Calculatorterm instance can calculate descriptorsterm in parallel The Calculator classterm manages the dependencies of Descriptorsterm, caches the results, handles errors, and enables parallel computingterm. Users can register the Descriptorterm instance (register itself), Descriptor classterm (preset of Descriptorterm), module (presets of all descriptorsterm in the module), or a list of these in a Calculatorterm instance. To calculate descriptorsterm of a single molecule, an instance of Calculatorterm can be used as a function. To calculate descriptorsterm of multiple molecules, the map method in Calculatorterm can be used. The map method can calculate descriptorsterm in the CPU parallel using the multiprocessing module in the standard Python library (Code 5).

These kinds of applications have missing valuesterm·var, even if there are no bugs in them. For example, a part of the autocorrelation descriptorterm cannot be calculated for small molecules. However, unintended missing valuesterm·var might cause errors or result in incorrect values. Therefore, it is important to reduce the missing valuesterm·var caused by software bugs or calculation timeouts. In Mordredterm, when the result is a missing valueterm·var, an instance of the subclass MissingValueBaseterm is returned. It contains an Exceptionterm that notifies users about the issue that triggered the exceptionterm (Code 6).

As an option, if the expression of “MissingValue” is not necessary, these missing valuesterm·var can be filled with “NaNterm” or deleted by the fill_missing or drop_missing method of the Result class. Moreover, users can obtain results as a dictionary using the asdict method of the Result class (Code 7).

The product termterm is often used to consider the interaction between features in a linear model. Mordredterm can easily calculate the product termterm using the “descriptor arithmeticterm” feature. Instances of descriptorsterm can be calculated by employing a unary/binary operator with other descriptorsterm (Code 8).

The full executable code example of Code 2–8 can be found in Additional file 4 .

Improving the algorithm Several descriptorsterm are algorithmically improved in Mordredterm. A summary of the improvements is shown in Table 4 . For example, the DetourMatrix descriptorterm [ 30 ] requires the solving of the longest path problemterm between all nodes, which is an NP-hard problem. Thus, it is difficult to solve this problem efficiently. An algorithm [ 31 ] was already reported to solve this problem. However, it is not adequately efficient. The longest path problemterm cannot be solved using the divide and conquer method. However, it can be solved using the articulation pointterm. The articulation pointterm refers to the vertex, which disconnects the graph when it is removed. Chemicals generally form a sparse graph that has many articulation pointsterm. Hence, we use this property to solve DetourMatrix. First, all articulation pointsterm are found (this can be efficiently solved) and the chemical structures are split into subgraphs. Then, the longest path is searched using the depth-first searchterm for all subgraphs (usually this can be solved because subgraphs are smaller than the original graph). Finally, the longest paths of subgraphs are merged. Other elements are filled by adding the longest paths of each subgraph. Table 4 Summary of descriptorterm improvement Descriptorterm Summary Chi Depth-first searchterm is used instead of SMARTS pattern matching DetourMatrix Molecular graph is divided into a small graph by articulation pointsterm Framework Specialize to Framework descriptorterm MolecularId Cache parts of the calculation to avoid its redundancy For example, to calculate the longest path from atom 1 to atom 5 shown in Fig. 2 , the longest path of atom 1 to atom 4 (subgraph 1; magenta) and atom 4 to atom 5 (subgraph 2; cyan) are added. This algorithm provides a possible approach for calculating DetourMatrix for most non-polymer compounds (Fig. 1 ). For example, DetourMatrix of a maitotoxinterm can be calculated in approximately 1.2 s on an Intel ® Core™ i7-5930 K CPU, DDR4-2133 (quad channel) 64 GB memory machine. Fig. 2 DetourMatrix algorithm. The chemical structures are split into subgraphs by all articulation pointsterm. Then, the detour matrix of each subgraph is calculated. Finally, the detour matrices of subgraphs are merged and other elements are filled The Chi descriptorterm is calculated by matching all Smiles Arbitrary Target Specification (SMARTS) patterns in CDK. This approach is time consuming and cannot be used to calculate the higher-order Chi descriptorterm. The depth-first searchterm is used in Mordredterm to overcome these issues.

The Framework descriptorterm is calculated using the function to match the molecular framework in CDK. However, during this processterm·var, this function also performs extra calculations to solve more general cases, such as enumerating the atoms in a molecular framework. Those calculations are not necessary for the derivation of the Framework descriptorterm and they are removed in Mordredterm.

The MolecularId descriptorterm calls the internal pure function with the same arguments many times in CDK. The returned values of these function calls are cached to avoid same calculationsterm in Mordredterm.

Create user interface The CLIterm is additionally implemented for non-Python users (Code 9). Accordingly, the entire set or subset of molecular descriptorsterm can be calculated in CPU parallel computingterm. The results are provided in CSV format.

Mordredterm is also available as a web applicationterm (Fig. 3 ). The web interface is available when the Mordredterm web module is executed (to this end, the Mordredterm web package is required; the method to install this package is explained in the GitHub repository). The web interface enables beginners to easily calculate descriptorsterm and study QSAR. In addition, Mordredterm can be installed on a server by an administrator. In this case, users can calculate descriptorsterm using resources of the server simply by accessing the web page. Fig. 3 Web interface. a Top page of the web interface to upload a structure file, b preview page to check the conformation of compounds, c result page to confirm the descriptive statistics value of calculated descriptorsterm and download the results The web interface can work with a multi-core processor. Submitted tasks are fairly processed. A demonstration server is available at http://mordredterm.phs.osaka-u.ac.jp . This demonstration page works well on most widely used web browsers with current versions, such as Safari version 10+, Google Chrome version 61+, Internet Explorer version 11+, Microsoft Edge version 40+, and Firefox version 55+. However, certain browsers on some devices with legacy graphics drivers may not support this page, in which case another browser should be considered.

The usage of this demonstration page is quite simple. Briefly, a SMILE or SDF file containing single or multiple structures can be uploaded from the front page. Hydrogens can be automatically added when needed. “Generate 3D conformer” and “Desalt” buttons provide two preprocessing options. When the submission succeeds, the structures are displayed at the center of the screen. When multiple structures are uploaded, the structure can be shifted without refreshing the page by clicking the arrow buttons. If 3D conformers are provided or created, conformers can be scaled by using the middle button of the mouse, and they can be rotated by the left button of the mouse. The uploaded molecules can be downloaded in both SMILES and SDF formats by clicking the download button, which is on the right of the displayed file name. Atom names can be confirmed by hovering over the mouse.

A configuration button on the top right provides the selection options for the following descriptorterm calculations. By clicking the “calculate” button, users can obtain the values and summaries of descriptorsterm, as well as the calculation log. To maintain server safety, the maximum molecule number that can be uploaded at one time is limited to 200 in this demonstration server. However, this limitation is not set by default when the user constructs his/her own server.

Results and discussion Performance benchmark To determine the speed of the calculation of molecular descriptorsterm, we performed a benchmark test. All tests were performed on an Intel ® Core™ i7-5930 K CPU, DDR4-2133 (quad channel) 64 GB memory machine. We used entries from the KEGG-drug databaseterm [ 32 ] as the benchmark target. We obtained 3D structures from the LigandBox databaseterm [ 33 ]. Compounds in the dataset were converted from Tripos mol2 format to MDL mol format using Open Babel. Then, the compounds were split with respect to the number of atomsterm·var using RDKitterm to evaluate the time complexity. After these procedures, 7197 compounds remained. The frequency table of the number of atomsterm·var is shown as Table 5 . Table 5 Number of atomsterm·var in the benchmark dataset Number of atomsterm·var Compounds Cumulative percentage (0, 25] 917 12.74 (25, 50] 3412 60.15 (50, 75] 2180 90.44 (75, 100] 366 95.53 (100, 125] 147 97.57 (125, 150] 79 98.67 (150, 175] 37 99.18 (175, 200] 33 99.64 (200, 225] 12 99.81 (225, 250] 7 99.90 (250, 275] 2 99.93 (275, 300] 3 99.97 (300, 325] 1 99.99 (325, 350] 0 99.99 (350, 375] 1 100.00 (·,·] denotes a left-open and right-closed interval We used libPaDEL-Descriptor, which is included in the source code of PaDEL-Descriptorterm, to evaluate the performance of the PaDEL-Descriptorterm because it excludes the extra descriptorterm calculation timeterm, such as the file IO and molecular preprocessing. In addition, it evaluates the exact calculation timeterm. First, each molecular descriptorterm·def was calculated three times to perform a just-in-time compilation. Then, each molecular descriptorterm·def was calculated ten times to evaluate the performance. Garbage collection was performed before each molecular-descriptor calculation. In the Mordredterm benchmark test, calculations were carried out ten times after disabling garbage collection.

The CLI benchmark testterm was performed to estimate real-world and multi-processor performance. We used the same machine. Up to 100 atoms compounds were used from the same dataset to avoid timeouts in PaDEL-Descriptorterm. We performed a benchmark test using one to six (the number of physical cores of an Intel Core i7-5930 K) threadsterm·var (in PaDEL-Descriptorterm) or processesterm·var (in Mordredterm). Each benchmark was repeated ten times.

The total calculation timeterm per molecule is shown in Fig. 4 and the calculation timeterm of each descriptorterm per molecule is shown in Fig. 5 . For the descriptorterm selection in Fig. 5 , the mean calculation timeterm of Mordredterm and/or PaDEL-Descriptorterm was over 0.1 s. DetourMatrix, Framework, and MolecularId descriptorterm calculation using PaDEL-Descriptorterm timed out when calculating descriptions for 5, 40, and 8 compounds. Figure 5 shows that AcidBase, BCUT, BaryszMatrix, Chi, DetourMatrix, Estate, and Framework are dramatically faster than the same calculationsterm in PaDEL-Descriptorterm. The benchmark of Chi, DetourMatrix, Framework, and MolecularId shows the effects of improving the algorithm. On the other hand, a notable algorithm improvement is not achieved in AcidBase, BCUT, BaryszMatrix, or Estate. A performance difference of functions used in these descriptorsterm between CDK and RDKitterm is apparent. PaDEL-Descriptorterm is faster than Mordredterm for many descriptorterm calculations, even though they both use the same algorithm. This is because Java is faster than Python for many cases. However, these descriptorsterm can be calculated in a very short time even if Python is used. Thus, the total calculation timeterm of Mordredterm, shown in Fig. 4 , is much lower than that of PaDEL-Descriptorterm. Some descriptorsterm, such as DetourMatrix, which result in a time-out in PaDEL-Descriptorterm can be calculated using Mordredterm. This improvement not only makes the calculation faster, but it also permits the calculation of descriptorsterm of large molecules that cannot be calculated using other software owing to time complexity. Fig. 4 Calculation timeterm for all descriptorsterm. Comparison of Mordredterm and PaDEL-Descriptorterm in terms of the mean descriptorterm calculation timeterm per molecule arranged by its number of atomsterm·var. The vertical axis shows the mean time of calculating all descriptorsterm of single molecule. The horizontal axis shows class interval of number of atomsterm·var Fig. 5 Calculation timeterm for each descriptorterm. Comparison of Mordredterm and PaDEL-Descriptorterm in terms of the mean descriptorterm calculation timeterm of each kind of descriptorterm over 0.1 s in Mordredterm and/or PaDEL-Descriptorterm. The vertical axis shows the mean time of calculating the descriptorterm of single molecule. The horizontal axis shows the class interval of the number of atomsterm·var The results of the CLI benchmark testterm are shown in Fig. 6 . PaDEL-Descriptorterm can be scaled by up to three threadsterm·var, while Mordredterm can be scaled by up to five threadsterm·var. Moreover, Mordredterm is more than twofold faster than PaDEL-Descriptorterm for all tests, and it is four times faster for the six-thread test. These results demonstrate that Mordredterm is significantly more efficient than PaDEL-Descriptorterm. Fig. 6 Throughput of CLIterm. A comparison of Mordredterm and PaDEL-Descriptorterm on the throughput of the CLIterm using one to six threadsterm·var Comparison with other software Mordredterm is superior to other software programs in several aspects. First, it is open-source software. Moreover, Mordredterm and all software used by it are licensed under the non-copyleft open-source license. This implies that it can be used in proprietary software. In addition, users can easily report a bug, request new features, and send patches on GitHub.

Second, it is easy to use. Mordredterm can be installed using only one command, whereas other Python molecular-descriptor calculation libraries (e.g., cinfony, ChemoPy) have more dependencies that require manual installation. The CLIterm and web interface can also be launched using a single command. Third, it has high flexibility. Mordredterm can calculate uncommon-range descriptorsterm without modifying the source code. Users can create new molecular descriptorsterm, such as the product termterm, by easily using the descriptor arithmeticterm feature. Additionally, the Mordredterm library can be simply accessed by using the presets in the Descriptor classterm. Finally, it is fast. Mordredterm can calculate an entire molecular descriptorterm·def twice as fast as PaDEL-Descriptorterm. Furthermore, the time complexity for some molecular descriptorsterm is reduced in Mordredterm. As a result, it can be used for calculating the descriptorsterm for large molecules that cannot be calculated using other software.

Limitations There are some potential defectsterm in Mordredterm and/or its dependent libraries. We are receptive to feedback, questions, and bug reports via both email and GitHub.

Conclusion In this paper, we proposed one molecular descriptorterm·def calculation software named Mordredterm. This software is easy to install and use, generates abundant molecular descriptorsterm in a high calculation speed. It can be installed using a single command and has a web interface. Mordredterm can calculate more than 1800 descriptorsterm and calculates all descriptorsterm in acceptable time. Our proposed software was released under a 3-clause BSD license on https://github.com/mordred-descriptor .

Additional files Additional file 1. The variations among descriptor valuesterm·var calculated by Mordredterm and other software programs. Additional file 2. A confirmation of the variation among descriptor valuesterm·var calculated by Mordredterm and other software programs (PaDEL-Descriptorterm, chemopy and e-dragon).The results of some descriptorsterm (e.g., 0167) are not available in all software because the descriptorterm of the molecule cannot be algorithmically calculated. Additional file 3. All descriptorterm list. Additional file 4. Code examples.