JP5484946B2 - Fast graph match search apparatus and method for evaluating similarity between molecules - Google Patents

Description

  The present invention uses a fast graph match search algorithm to find an atomic correspondence between two molecules, virtually superimpose two molecules based on the correspondence, and obtain and evaluate a similarity between the two molecules. The present invention relates to a search apparatus and method.

  In molecular design of medicines and agricultural chemicals, it is frequently performed to superimpose molecular structures related to two molecules in a virtual space. FIG. 13 is a diagram schematically showing superposition of two such molecules (Cholic acid [CHD] and Corticosteron [COR]) in a virtual space. However, it is a very difficult problem to search and determine the optimal superposition for two molecules.

For example, regarding the problem of superposition of molecule A and molecule B, when one molecule A is set to “CMP”, the case of obtaining the target molecule B to be superposed that can be searched by superposition based on it is examined. . Here, “searchable” means that it is assumed that the search can be solved by performing the entire exploration for about 50 years with working hours of 8 hours and 2 days a week. For example, in the case of calculation by hand, when the molecule B is Cystein, it is possible to calculate about 1.3 × 10 ⁷ superpositions to obtain the optimum superposition (FIG. 14A). ). Similarly, in the case of using a desktop computer, when the molecule B is Diaminoprimate, it is possible to calculate about 1.5 × 10 ¹⁵ superpositions to obtain an optimum superposition (FIG. 14B). ). Similarly, even in the case of using an ultra high speed computer, when the molecule B is AMP, it is possible to calculate 8.3 × 10 ²¹ superpositions to obtain the optimum superposition (FIG. 14). (C)). As described above, it is not necessarily a practical method because it takes an enormous amount of time to search for an optimal superposition of the molecule A and the molecule B by full search.

  Therefore, it is required to perform an heuristically high speed while allowing some mistakes in a graph match that obtains an atomic correspondence between two molecules and realizes an optimal superposition of two molecules based on the correspondence.

  In addition, as the prior art documents relating to the compound search algorithm, there are the following six cases.

Japanese Patent No. 4001657 Patent No. 3928000 International Application 01/097094 International Application No. 02/41184 International Application 2007/004643

J. Computer-Aided Molecular Design, 13: 499-512, 1999 Estimation of active confirmations of drugs by a new molecular superposing procedure

  The present invention relates to a molecular match search device that expresses an atomic correspondence between two molecules and superimposes two molecules based on the correspondence with respect to a molecular graph expressing atoms as nodes and chemical bonds as edges. It aims to provide a method.

The present invention has been made to achieve the above object. The fast graph match search apparatus for evaluating similarity between molecules according to claim 1 of the present invention,
Coordinate data relating to each of the atoms (Ai, Aj,...) Constituting the first molecule A and coordinate data relating to each of the atoms (Bk, B1,...) Constituting the second molecule B. Each atom (Ai, Aj,...) And second of the first molecule A in the virtual memory space constructed in the calculation unit and the storage unit according to the computer program input from the storage unit and loaded into the calculation unit. Are associated with each atom (Bk, B1,...) (M (Ai) = Bk) and superposed (i, j, k, l are all natural numbers), The first molecule A, which outputs to the output unit data relating to the optimal interatomic correspondence between one molecule A and the second molecule B and the similarity between the first molecule A and the second molecule B; In the fast graph match search device for evaluating the similarity with the second molecule B,
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, as seen from each atom of the pair of atoms Ai and Bk, First calculation means for obtaining a first similarity index S1 (Ai, Bk) indicating how similar the surrounding environment is;
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, as seen from each atom of the pair of atoms Ai and Bk, A calculation means for obtaining a second similarity index S2 (Ai, Bk) that is calculated by integrating the first similarity index S1 (Aj, B1) for all pairs of surrounding atoms Aj, B1 having the same bond distance. If the surrounding atoms Aj and B1 that are at the same bond distance from each atom of the pair of atoms Ai and Bk are the same element, the first similarity index S1 (Aj, B1) is further multiplied by a coefficient. A second calculating means for calculating a second similarity index S2 (Ai, Bk),
For all pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, the first pair of atoms Ai and Bk is used as the starting point. A third similarity having a value corresponding to the graph match score M (A, B) calculated at that time by creating an overall correspondence by sequentially associating the atoms of the molecule A and the atoms of the second molecule B Computation means for obtaining the index S3 (Ai, Bk), and at the time of creating the correspondence, next select an atom that directly binds to an already associated atom, and select a pair having a high second similarity index S2 Third calculation means for obtaining a third similarity index S3 (Ai, Bk), on the condition that priority is given to
Starting from the pair of starting atoms (Ai, Bk) when the maximum S3 (Ai, Bk) is calculated by the third calculating means, the largest S3 (Aj , B1), the fourth calculation means for obtaining the graph match score M (A, B) in the overall correspondence when the correspondence is continued until there is no pair of atoms that can be handled,
If the graph match score M (A, B) in the fourth calculation means is greater than the threshold value, the correspondence between atoms and the graph match score M calculated by the fourth calculation means for the first molecule A and the second molecule B And fifth output means for outputting (A, B).

  According to the present invention, when a molecule graph in which atoms are represented as nodes and chemical bonds are represented as edges, the atoms between the two molecules are made to correspond and two molecules are superposed on each other based on the correspondence. Can be sought.

It is a figure which shows the example of a structure of the computer system which implement | achieves the high-speed algorithm of the molecular structure by the graph matching which concerns on embodiment of this invention. It is a flowchart of the program for superimposition and the display of the molecular structure by the fast graph match search algorithm which concerns on embodiment of this invention. A diagram schematically showing atoms (nodes) and bonds (edges) of molecules A and B (FIG. 3 (1)), and molecules calculated based on molecules A and B shown in FIG. 3 (1) It is an example (FIG. 3 (2)) of a graph match score. 3 is a flowchart of a fast graph match search algorithm for obtaining an atomic correspondence {m (Ai)} between a molecule A and a molecule B and a graph match score M (A, B) in step S10 shown in FIG. It is a figure which shows a part of molecule | numerator A and a part of molecule | numerator B, Comprising: It is a figure for demonstrating calculation of parameter | index S1 regarding the atom Ai and the atom Bk. It is a figure which shows a part of molecule | numerator A and a part of molecule | numerator B, Comprising: It is a figure for demonstrating calculation of parameter | index S2 regarding the atom Ai and the atom Bk. It is a figure which shows a part of molecule | numerator A and a part of molecule | numerator B, Comprising: It is a figure for demonstrating calculation of parameter | index S3 regarding the atom Ai and the atom Bk. It is a figure which shows a part of molecule | numerator A and a part of molecule | numerator B, Comprising: It is a figure for demonstrating calculation of the graph match score M0 in step S1008 of FIG. It is a figure which shows a part of molecule | numerator A and a part of molecule | numerator B, Comprising: It is a figure for demonstrating the fine adjustment in step S1012 of FIG. It is a figure which shows typically adjusting the twist angle and displaying the molecule | numerator A and the molecule | numerator B more superimposed. A diagram (Fig. 11 (a)) in which atomic coordinates are output by superimposing a set of {m (Ai)} corresponding to a query atom {Ai}, and a diagram in which atomic coordinates corresponding to a common skeleton are output from the query structure. (FIG. 11B). For a problem with a total number of combinations of 10 ¹² or less, the maximum score is obtained by full search, and the calculation time for the total search combination number when compared with the solution by the fast graph match search algorithm according to the embodiment of the present invention is calculated. A graph (Fig. 12 (1)), a graph of the correct answer rate for the total number of exploration combinations (Fig. 12 (2)), and a graph of the relationship between the correct score difference and the cumulative correct rate (Fig. 12 (3)). It is a figure which shows typically superimposing two molecules (Cholic acid [CHD] and Corticosteron [COR]) in virtual space. FIG. 5 is a diagram showing an example of a molecule B to be superposed that can be searched by superposition based on the case where one molecule A is “CMP” regarding the problem of superposition of molecule A and molecule B. .

  DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments according to the present invention will be described below with reference to the drawings.

  The high-speed algorithm for molecular structure based on graph matching according to the present embodiment is performed using a computer, and a program described in an appropriate program language such as C language is executed on the computer (described later). This is realized by expanding coordinate data relating to atoms constituting various molecules in a virtual memory space constructed on a computer.

  FIG. 1 is a diagram showing an example of the configuration of a computer system 2 that implements a high-speed molecular structure algorithm based on graph matching according to the present embodiment. The computer system 2 includes an output unit 12 such as a display, an input unit such as a keyboard 16 and a mouse 18, and a central processing unit 14 including a calculation unit, a storage unit, a communication control unit, and the like. The central processing unit 14 is configured to be connected to the external server 8 and the external database 10 via an external network such as the Internet 4 and transmit / receive data to / from the external server 8 and the external database 10.

  Data relating to atomic coordinates for various molecules used in the present embodiment is data in a PDB (protein data bank; protein structure data bank) format, and is usually provided from an external commercial or public database 10 or the like. The For example, data relating to atomic coordinates for various molecules in the PDB format is downloaded from an external commercial and public database 10 via the external network 4 and stored in a storage unit attached to the computer system 2. These data are read from the storage unit and used when executing the processing according to the flowchart shown in FIG.

1. FIG. 2 is a flowchart of molecular structure superimposition and processing performed by the high-speed graph match search algorithm according to the present embodiment. With reference to FIG. 2, the superposition process of the molecular structure according to the present embodiment will be described. First, the atomic coordinates in the PDB format for one of the superimposed molecules (referred to as molecule A) are read (step S02). Based on the read atomic coordinates in the PDB format, the bond distance, bond order, and rotatable bond of molecule A are set (step S04). The setting of the molecular bond distance, bond order, and rotatable bond will be described later.

  In parallel with step S02 and step S04, the atomic coordinates in the PDB format for the other molecule of superposition (molecule B) are read (step S06). There may be a plurality of molecules B. Next, the bond distance, bond order, and rotatable bond are set for one of the molecules B (step S08).

  Subsequently, a high-speed graph match search algorithm is performed to obtain the correspondence {m (Ai)} from the atom (Ai) of the molecule A to the molecule B (Bk) and the graph match score M (A, B) at that time ( i and k are both natural numbers) (step S10). Here, the graph match score M (A, B) is an index indicating the degree of optimization in a graph match that obtains an atomic correspondence between two molecules and realizes an optimal superposition of two molecules based on the correspondence. is there. Details of the graph match score M (A, B), the correspondence {m (Ai)}, and the fast graph match search algorithm will be described later.

  It is confirmed whether or not the graph match score M (A, B) is larger than the threshold (step S12). That it is larger than the threshold means that the correspondence (m (Ai)) for superimposition that realizes the graph match score M (A, B) is sufficiently appropriate (Yes in step S12). At this time, the twist angle of the molecule B with respect to the molecule A is adjusted (step S14), and the atomic alignment and superposition of the molecules A and B are output (step S16). The adjustment of the twist angle, and the output of atomic alignment and structure superposition will also be described later.

  Further, it is determined whether there is a next molecule B (step S18). If there is the next molecule B (Yes in step S18), the processing after the setting of the bond distance, bond order, and rotatable bond (step S08) for the next molecule B is repeated.

  If the molecule B disappears (No at Step S18), the basic skeleton (or common skeleton) is output to the output unit 12 (Step S20), and the process is terminated.

2. Setting of Bonding Distance, Bonding Order, and Rotatable Bonding “Setting of bond distance, bond order, and rotatable bond” performed in steps S04 and S08 in FIG. 2 will be described.

(2.1) Bond distance In the molecular structure indicated by the data related to the PDB format, bonds between atoms may not be defined. Therefore, in this embodiment, when the interatomic distance between atom i and atom j is shorter than 2.00 mm in one molecule, the chemical bond is set on the data assuming that a chemical bond exists (i and j are Both are natural numbers). This “interatomic distance” is calculated based on atomic coordinates read from the PDB. Furthermore, when two atoms are taken up in one molecule, the number of chemical bonds connecting these two atoms is defined as “bond distance”. If there are multiple paths connecting these two atoms, take the smallest one. By extending the bonds one by one, the bond distance is set between all atoms in one molecule.

(2.2) Bond Order In the molecular structure indicated by the data related to the PDB format, the bond order between atoms is not defined and generally does not contain a hydrogen atom. Therefore, the bond order is determined based on the interatomic distance according to the rules shown in Table 1 below.

(2.3) Rotatable bond For all of the directly coupled atom pairs (atom i and atom j), the definition process of “(2.1) Bond distance” above is the one where there is no bond between the pair of atoms. Run as. As a result, when the bond distance is not set between the atom pair (atom i and atom j) and the bond between atom i and atom j is a single bond, between the atom i and atom j pair Is set to be “rotatable connection”.

3. Molecular Graph Match Score Definition The molecular graph match score M (A, B) is defined in the high-speed molecular structure algorithm based on graph matching according to the present embodiment. Note that {M (A, B)} indicates a molecular graph match score between the molecule A and the molecule B. FIG. 3A is a diagram schematically showing atoms (nodes) and bonds (edges) of the molecules A and B. FIG.
Hereinafter, the definitions ((Definition 1), (Definition 2), (Definition 3) and (Definition 4)) of the molecular graph match score M (A, B) used in the present embodiment will be described.

(Definition 1); “Ai” indicates the i-th atom of the molecule A. “Ai-Aj” indicates a connection between Ai and Aj.

(Definition 2); The fact that the atom i (Ai) of the molecule A corresponds to the atom k (Bk) of the molecule B is expressed as “m (Ai) = Bk”. That is, m (Ai) = Bk indicates the atom k of the molecule B to which the atom i of the molecule A corresponds.

数１の各項は、以下の通り定義される。なおＥ（Ａｉ，Ａｊ）は、実行ｍｏｄｅにより異なる値を持つ。この実行ｍｏｄｅは、図１に示す入力部等を介して事後的に外部から設定され得るものである。

(Definition 3)
The molecular graph match score M (A, B) is defined by the following formula (Equation 1).

Each term of Equation 1 is defined as follows. Note that E (Ai, Aj) has a different value depending on the execution mode. This execution mode can be set later from the outside via the input unit shown in FIG.

  FIG. 3B is an example of a molecular graph match score calculated based on the molecule A and the molecule B shown in FIG. If the patterns are the same, the elements are the same, and the edges are all single bonds. Therefore, the values shown in FIG. 3B (particularly M (A, B) = 14) are obtained regardless of the execution mode. .

4). High-Speed Graph Match Search Algorithm FIG. 4 is a high-speed graph for obtaining the atomic correspondence {m (Ai)} and the graph match score M (A, B) between the molecule A and the molecule B in step S10 shown in FIG. It is a flowchart of a match search algorithm. Hereinafter, the fast graph match search algorithm will be described in detail with reference to this flowchart.

[Step S1002]; First, for all combinations (Ai, Bk) of the atoms constituting the molecule A and the atoms constituting the molecule B, “S1 (Ai, Bk) defined in the following Equation 2 and Table 3 ) ”.

  S1 (Ai, Bk) is an index indicating how similar the surrounding environment (whether there are atoms of the same type at the same bond distance) in the pair of atoms Ai and Bk.

  For example, in a part of the molecule A and a part of the molecule B shown in FIG. 5, the atom Aj at a bond distance of 2 from the atom Ai and the atom Bl at a bond distance of 2 from the atom Bk corresponding to the atom Ai Is the same element, the value of s1 (Aj, Bl) is “1”. Whether the atom of the molecule A and the atom of the molecule B, which are at the same bond distance around the pair of the atom Ai and the atom Bk, is the same for all {j, l} pairs, “1” or “0” Set to integrate. The above-mentioned S1 (Ai, Bk) becomes larger as there are many cases where the same element is present at the same bond distance as viewed from the corresponding atoms Ai, Bk.

[Step S1004]; Next, “S2 (Ai, Bk)” defined in the following Equation 3 and Table 4 is obtained for all sets of {i, k}.

  S2 (Ai, Bk) is the above-mentioned surrounding environment for all pairs of surrounding atoms Aj, B1 that are at equal bond distances from each atom of the pair of corresponding atoms Ai, Bk. This is an index for accumulating S1 (Aj, B1), which is an index indicating how much they are similar. Multiply (Aj, Bl) by a coefficient (12 in the above table). Therefore, for each atom of the corresponding pair of atoms Ai and Bk, if the surrounding environment is similar and the surrounding environment is similar, it is an index that increases.

  For example, S2 (Ai, Bk) is examined in a part of the molecule A including the atom Ai and a part of the molecule B including the atom Bk shown in FIG. For every pair of an atom Aj at a certain bond distance from the atom Ai (2 in FIG. 6) and an atom B1 at an equal bond distance from the atom Bk, s2 (Aj, B1), that is, S1 (Aj, B1) Or S1 (Aj, Bl) × 12 is integrated. In particular, if Aj and Bl are the same element, S1 (Aj, Bl) is multiplied by a predetermined number (here, 12 times) and integrated to obtain S2. It is assumed that the bond distance from atom Ai and atom Bk varies from 1 to the maximum value (that is, bond distance from atom Ai or atom Bk to the farthest atom). As described above, S1 (Aj, B1) is an index indicating how similar the surrounding environment (Am, Bn, etc. in FIG. 6) is in the pair of atoms Aj, B1.

  In the above S2 (Ai, Bk), S1 (Aj, B1) of the atom pair (Aj, B1) at the same bond distance position is integrated with respect to the corresponding two atoms Ai, Bk. If B1) is the same element, S1 (Aj, B1) is multiplied by a predetermined number (12 times) and integrated. Ai, Bk) increases. The coefficient “12” may be another numerical value.

[Step S1006]; Next, “S3 (Ai, Ak)” defined in the following Equation 4 and Table 5 is obtained for all {i, k} pairs.

  S3 (Ai, Bk) starts from a pair of atoms Ai and Bk, and successively creates an overall correspondence by associating the atoms of molecule A and atoms of molecule B, and the graph match score M (A , B). Here, when creating a correspondence, it is a condition that priority is given to the next selection of an atom that directly binds to an already associated atom, and the selection of a pair having a high index S2.

  For example, S3 (Ai, Bk) is examined in a part of the molecule A including the atom Ai and a part of the molecule B including the atom Bk shown in FIG. The starting point is a pair of atoms Ai and Bk. The atoms Aj, Ap, and Ar are directly bonded to the atom Ai. The atoms Bk, Bq, and Bs are directly bonded to the atom Bk. Of the (3 × 3 = 9) pairs of atoms that can be formed from {Aj, Ap, Ar} and {Bl, Bq, Bs}, S2 of the pair (Aj, Bl) is the largest. Then, the atom Aj and the atom Bl are associated with each other.

  Next, atoms Ap, Ar, At, and Av are directly bonded to Ai-Aj that has been associated in molecule A. The atoms Bq, Bs, Bu, and Bw are directly bonded to Bk-Bl that has been associated in the molecule B. Among the (4 × 4 = 16) pairs of atoms that can be formed from {Ap, Ar, At, Av} and {Bq, Bs, Bu, Bw}, S2 of the pair (Ap, Bq) Is the maximum, the atom Ap and the atom Bq are associated with each other. Thereby, in the molecule A, the association of the atoms Ai, Aj, and Ap is completed, and in the molecule B, the association of the atoms Bk, B1, and Bq is completed.

  Such association is sequentially repeated until there are no corresponding atom pairs. When the association is completed, a graph match score M under the association is obtained. Such association and graph match score M calculation are performed for all {i, k} pairs.

  In the above S3 (Ai, Bk), for each combination of all {Ai, Bk}, S2 (for the corresponding pair of atoms Ai, Bk) is gradually increased from the periphery of the starting point {Ai, Bk} of the pair of atoms. If the surrounding environment is similar, and if the surrounding environment is similar to that of the surrounding environment, the atom of the molecule A and the atom of the molecule B are associated with each other, focusing on the size of the index) A match score will be calculated.

  [Step S1008]; Next, starting from the correspondence of the starting atom (Ai, Bk) when the maximum S3 (Ai, Bk) is calculated in Step S1006, The correspondence with the one having the maximum S3 (Aj, Bl) is continued until there is no pair of atoms that can be handled, and the graph match score M0 (A, B) in the whole correspondence is obtained. At this time, the atom of the molecule A may not be directly bonded in the corresponding pair of atoms and the corresponding pair of the next atom, and similarly, the atom of the molecule B is not directly bonded. Also good.

For example, for the part of the molecule A including the atom Ai and the part of the molecule B including the atom Bk shown in FIG. 8, the association of the atom pairs performed in step S1008 is examined. First, a pair of atoms (a × b) that can be formed from all the atoms constituting the molecule A (for example, a) and all the atoms constituting the molecule B (for example, b). Of these, in the pair of atoms Ai and Bk, S3 (obtained in step S1006) is greater than any other pair, that is, the maximum. Then, first, a pair of atoms Ai and Bk is associated.
Next, (a-1) atoms constituting the molecule A excluding Ai and (b-1) atoms constituting the molecule B excluding Bk are formed as (a -1) Among the pairs of (b-1), it is assumed that S3 is larger than any other pair in the pair of atoms Aj and Bl. Then, a pair of atoms Aj and Bl is associated therewith. At this time, Aj is not necessarily directly coupled to Ai, and Bl is not necessarily directly coupled to Bj (the same applies hereinafter).

Next, atoms that can be formed from (a-2) atoms constituting molecule A excluding Ai and Aj and (b-2) atoms constituting molecule B excluding Bk and Bl Of the (a-2) × (b-2) pairs of each other, in the pair of atoms Aj2 and B12, S3 is greater than any other pair. Then, a pair of atoms Aj2 and B12 is associated therewith.
Next, from (a-3) atoms constituting molecule A excluding Ai, Aj, and Aj2, and (b-3) atoms constituting molecule B excluding Bk, Bl, and Bl2. Suppose that among the (a-3) × (b-3) pairs of atoms that can be formed, S3 is larger than any other pair in the pair of atoms Aj3 and B13. Then, a pair of atoms Aj3 and B13 is associated therewith.
Next, (a-4) atoms constituting molecule A excluding Ai, Aj, Aj2, and Aj3, and (b-4) atoms constituting molecule B excluding Bk, Bl, Bl2, and Bl3. Among the (a-4) × (b-4) pairs of atoms that can be formed with each other atom, the pair of atoms Aj4 and B14 is assumed to have S3 larger than any other pair. Then, a pair of atoms Aj4 and B14 is associated therewith.

  Such association is sequentially repeated until there are no corresponding atom pairs. When the association is completed, a graph match score M0 under the association is obtained.

  In step S1008, based on a large number of (eg, a × b) S3 obtained in step S1006, that is, M (A, B), an association that can be a final candidate, and a graph match under the association A score M0 is calculated.

  [Step S1010]; It is confirmed whether or not the calculated M0 (A, B) is the maximum value that can be assumed. Specifically, it is confirmed whether M0 (A, B) is equal to M (A, A) or M (B, B). As shown in FIG. 3B, since M (A, A) (or M (B, B)) is considered to be the maximum value, this step S1010 needs to calculate the graph match score any more. It is done to see if there is no.

  If they are equal (step S1010 / Yes), the atom correspondence {m (Ai)} and the graph match score M0 (A, B) are output in step S1016, and the process ends. If they are not equal (step S1010 · No), the process proceeds to step S1012.

  [Step S1012]; In step S1012, the fine adjustment of the association that can be the final candidate is performed.

  In {Bk, B1} of molecule B corresponding to one bonded {Ai, Aj} pair in molecule A, one is replaced with the other atom Bn, and the correspondence of atoms in molecule A is changed only for the replaced atom. The graph match score M1 (A, B) is obtained by changing. The case where the atom Bn does not have a corresponding atom in the molecule A may be used.

  For example, in the part of the molecule A including atoms Ai, Aj, and Am and the part of the molecule B including atoms Bk, B1, and Bn shown in FIG. An example of the change will be described. It is assumed that Ai and Bk, Aj and Bl, and Am and Bn are associated with each other, and Ai and Aj are combined. Here, B1, which is one of {Bk, B1}, and Bn are exchanged, Aj and Bn are associated, and Am and B1 are associated at the same time. That is, m (Aj) = Bl is m (Aj) = Bn, and m (Am) = Bn is m (Am) = Bl. Other atom mappings are not moved. The graph match score M1 (A, B) is obtained based on the association that is only partially changed.

  The association may be changed such that the atom Bk in the example of FIG. 9 is replaced with Bp (not shown).

  [Step S1014]; It is confirmed whether or not the calculated M1 (A, B) is larger than M0 (A, B). That is, in step S1012, the fluctuation of the graph match score M1 (A, B) calculated from the atom adjustment with fine adjustment is confirmed. If the calculated M1 (A, B) is larger than M0 (A, B) (Yes in step S1014), the value of M1 (A, B) is overwritten on M0 (A, B) (step S1015), and S1012 The graph match score M1 (A, B) calculated from the atom correspondence further fine-tuned in is obtained.

  [Step S1016]; If the calculated M1 (A, B) is not greater than M0 (A, B) (No at Step S1014), output the atom correspondence and the graph match score M0 (A, B) and end To do.

5. Structure superimposition of molecule The structure superposition display based on the atomic correspondence obtained by the flowcharts shown in FIGS. 4 and 2 will be described. In superimposing the molecular structures of the molecule A and the molecule B, the atom {m (Ai)} corresponding to the atom {Ai} of the molecule A is appropriately superimposed and displayed. Kabsch's method (McLachlan, AD. Gene duplications in the structural evolution of chymotrypsin.Journal of Molecular Biology, 128, 49-79, 1979.Kabsch, W. A solution for the best rotation to relate two sets of vectors. Acta Crystallographica, 32A, 922-923, 1976.) may be used.

At this time, the corresponding twist angles between the two molecules are aligned by the following method.
(1) Atoms {Ai, Aj, Ak, Al} of molecules A bonded by graph matching are similarly bonded to atoms {m (Ai), m (Aj), m (Ak), m (Al )} And the bonds Aj-Ak and m (Aj) -m (Ak) are both rotatable bonds, the twist angle {m (Ai), m (Aj), m of the molecule B Let (Ak), m (Al)} be equivalent to the corresponding twist angle {Ai, Aj, Ak, Al} of molecule A.

  FIG. 6 schematically represents the state of (1) above. In determining whether or not it is “rotatable coupling”, data set in steps S04 and S08 in FIG. 2 and “(2.3) rotatable coupling” is used.

6). Example of superposition of molecular structure by high-speed graph match search algorithm and its processing.
The program for realizing the superposition of the molecular structure by the high-speed graph match search algorithm shown in FIG. 2 and the flowchart for its processing is implemented, the query (molecule A) is G39 (Tough Mill), and the search target database is the entire PDB. Calculations were performed as ligands (9445 species). A desktop computer with an operating frequency of 2.4 GHz was used. The calculation time was 8 minutes 56 seconds.

In Table 6 below, {m (Ai)} corresponding to the query atom {Ai} by the above calculation is displayed side by side. The leftmost column shows examples of a query (molecule A) and a search target molecule (molecule B). The number of atoms is shown in the second column from the left end. In the third column from the left end, the graph match score between molecule A (G39 (Tough Mill)) and molecule B is shown. The fourth column from the left shows the graph match score with self (self molecule). The right part shows atomic alignment. When the atomic species arranged in each column (vertical) match, it corresponds to a common skeleton. Here, if the atomic species arranged in each column (vertical) match 90% or more, “**” is shown in the bottom row, and if 50% or more matches, “++” is shown in the bottom row.

  FIG. 11 is a diagram (FIG. 11A) in which atomic coordinates are output by superimposing a set of {m (Ai)} corresponding to an atom {Ai} of the query atomic query, and a common skeleton from the query structure. It is the figure (FIG.11 (b)) which output the atomic coordinate which corresponds.

7). Algorithm Performance Evaluation Performance evaluation of the fast graph match search algorithm according to the present embodiment was performed.

(7.1 Algorithm performance evaluation (1))
In this embodiment, an approximate solution is given to an NP difficult problem with an unknown polynomial time algorithm. For a problem with a total number of combinations of 10 ¹² or less, a maximum score (= correct answer) was obtained by all searches, and compared with a solution by the fast graph match search algorithm according to the present embodiment. FIG. 12A is a graph of the calculation time for the total number of search combinations. From the bottom, the calculation time according to the present embodiment, the calculation time according to the total search, and the calculation according to the total search with respect to the calculation time according to the present embodiment. Shows the time ratio. The algorithm according to this embodiment can be calculated in 10 ⁻⁴ to 10 ⁻³ seconds in the graph search range. In the case of full exploration, it takes 10 ^-4 to 10 ⁶ seconds.

  FIG. 12 (2) is a graph showing the correct answer rate with respect to the total number of search combinations. In the exploration range of the graph, correct answers were found at an average rate of 97%. Further, FIG. 12 (3) is a graph showing the relationship between the correct score difference and the cumulative correct rate. Even in the case of an incorrect answer, the score difference from the correct answer was a maximum of two points. From the graphs and numerical values shown in FIGS. 12 (1) to 12 (3), the fast graph match search algorithm according to this embodiment is considered to have high performance.

(7.2 Algorithm performance evaluation (2))
Perform heuristic graph matching using Bron's clique search algorithm (Bron C. & Kerbosch J. Algorithm 457: Finding all cliques of an undirected graph. Communications of the Association for Computing Machinery, 16, 575-577, 1973) Simcomp method (Hattori, M., Okuno, Y., Goto, S. & Kanehisa, M. Development of a chemical structure comparison method for integrated analysis of chemical and genomic information in the metabolic pathways.Journal of American Chemical Society, 125, 11853-11865, 2003).

A round-robin graph match was performed for the same 50 molecular groups selected at random, and all comparisons were performed in 1225 cases (all), and 136 cases in which any method found a subgraph (which is definitely correct) (partial) For, the score according to the definition of the present embodiment and the execution time (actual time required for the graph match) were compared. The maximum number of trials (Rmax) in the simcomp method was varied from 1.5 × 10 ⁴ (default value) to 10 ⁸ .

As a result (see Table 7 below), the fast graph match search algorithm according to the present embodiment found all 136 partial graphs (partials), whereas the simcomp method failed in 10 cases (7%). . The execution time was fast in this method except for one example, and the average was 48 milliseconds. There was no reversal in the subgraphs that could be found by increasing Rmax, only the execution time of the simcomp method increased. Also, in all comparisons (all), any Rmax except Rmax = 1.5 × 10 ⁴ and the fast graph match search algorithm according to the present embodiment is 96 milliseconds late (however, the score of the found graph match is high). I found a high-scoring graph match at a faster speed. From these numerical values, the fast graph match search algorithm according to the present embodiment is considered to have high performance.

2 ... computer system, 4 ... internet, 8 ... external server, 10 ... external database, 12 ... output unit, 14 ... central processing unit, 16 ... keyboard, 18. ··mouse.

Claims (7)

Coordinate data relating to each of the atoms (Ai, Aj,...) Constituting the first molecule A and coordinate data relating to each of the atoms (Bk, B1,...) Constituting the second molecule B. Each atom (Ai, Aj,...) And second of the first molecule A in the virtual memory space constructed in the calculation unit and the storage unit according to the computer program input from the storage unit and loaded into the calculation unit. Are associated with each atom (Bk, B1,...) (M (Ai) = Bk) and superposed (i, j, k, l are all natural numbers), The first molecule A, which outputs to the output unit data relating to the optimal interatomic correspondence between one molecule A and the second molecule B and the similarity between the first molecule A and the second molecule B; In the fast graph match search device for evaluating the similarity with the second molecule B,
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, as seen from each atom of the pair of atoms Ai and Bk, First calculation means for obtaining a first similarity index S1 (Ai, Bk) indicating how similar the surrounding environment is;
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, as seen from each atom of the pair of atoms Ai and Bk, A calculation means for obtaining a second similarity index S2 (Ai, Bk) that is calculated by integrating the first similarity index S1 (Aj, B1) for all pairs of surrounding atoms Aj, B1 having the same bond distance. If the surrounding atoms Aj and B1 that are at the same bond distance from each atom of the pair of atoms Ai and Bk are the same element, the first similarity index S1 (Aj, B1) is further multiplied by a coefficient. A second calculating means for calculating a second similarity index S2 (Ai, Bk),
For all pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, the first pair of atoms Ai and Bk is used as the starting point. A third similarity having a value corresponding to the graph match score M (A, B) calculated at that time by creating an overall correspondence by sequentially associating the atoms of the molecule A and the atoms of the second molecule B Computation means for obtaining the index S3 (Ai, Bk), and at the time of creating the correspondence, next select an atom that directly binds to an already associated atom, and select a pair having a high second similarity index S2 Third calculation means for obtaining a third similarity index S3 (Ai, Bk), on the condition that priority is given to
Starting from the pair of starting atoms (Ai, Bk) when the maximum S3 (Ai, Bk) is calculated by the third calculating means, the largest S3 (Aj , B1), the fourth calculation means for obtaining the graph match score M (A, B) in the overall correspondence when the correspondence is continued until there is no pair of atoms that can be handled,
If the graph match score M (A, B) in the fourth calculation means is greater than the threshold value, the correspondence between atoms and the graph match score M calculated by the fourth calculation means for the first molecule A and the second molecule B A high-speed graph match search device for evaluating similarity between molecules, including a fifth output means for outputting (A, B). Furthermore,
After calculating the graph match score M (A, B) by the fourth calculating means, {Bk of the second molecule B corresponding to one combined {Ai, Aj} pair in the first molecule A , B1}, one of the atoms is replaced with another atom Bn, and only for the replaced atom, the correspondence of the atoms in the first molecule A is changed to obtain a finely adjusted graph match score M (A, B). Including 6 calculation means,
If the finely adjusted graph match score M (A, B) calculated by the sixth calculation means is larger than the graph match score M (A, B) calculated by the third calculation means The fifth output means performs output by overwriting the finely adjusted graph match score M (A, B) on the graph match score M (A, B). Fast graph match search device. The graph match score M (A, B) is defined by the following formula 1, each term of the following formula 1 is defined by the following table 1, and the value of the execution mode in the following table 1 is externally input via the input means. The high-speed graph match search device according to claim 1, wherein the high-speed graph match search device is set.

The first similarity index “S1 (Ai, Bk)” in the first calculating means is defined by the following Equation 2 and Table 2,
The second similarity index “S2 (Ai, Bk)” in the second calculating means is defined by the following Equation 3 and Table 3,
The third similarity index “S3 (Ai, Bk)” in the third calculation means is defined by the following Equation 4 and Table 4 as claimed in any one of claims 1 to 3: The described high-speed graph match search device.

  5. The fast graph match search device according to claim 4, wherein the coefficient in Table 3 is 12. Coordinate data relating to each of the atoms (Ai, Aj,...) Constituting the first molecule A and the atoms (Bk, Bl,...) Constituting the second molecule B stored in the storage unit. Each coordinate data (Ai, Aj,...) Of the first molecule A is input in a virtual memory space constructed on the computer according to a given computer program loaded with coordinate data relating to each and loaded into the arithmetic unit. And the corresponding atoms (Bk, B1,...) Of the second molecule B (m (Ai) = Bk) are overlapped (i, j, k, l are all natural numbers) ), An optimal interatomic correspondence between the first molecule A and the second molecule B, and the similarity between the first molecule A and the second molecule B are output to the output unit using the computer. Fast graph match search method for evaluating the similarity between molecule A and second molecule B Oite,
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the first molecule B, as seen from each atom of the pair of atoms Ai and Bk, A first step of obtaining a first similarity index S1 (Ai, Bk) indicating how similar the surrounding environment is;
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, as seen from each atom of the pair of atoms Ai and Bk, A step of obtaining a second similarity index S2 (Ai, Bk) that integrates the first similarity index S1 (Aj, B1) for all pairs of surrounding atoms Aj, B1 having the same bond distance, If the surrounding atoms Aj and B1 that are at the same bond distance from each atom of the pair of Ai and Bk are the same element, the first similarity index S1 (Aj, B1) is further multiplied by a coefficient and integrated. A second step of obtaining a similarity index S2 (Ai, Bk) of 2;
For all pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, the first pair of atoms Ai and Bk is used as the starting point. A third similarity having a value corresponding to the graph match score M (A, B) calculated at that time by creating an overall correspondence by sequentially associating the atoms of the molecule A and the atoms of the second molecule B In the step of obtaining the index S3 (Ai, Bk), at the time of creating the correspondence, the atom that directly binds to the already associated atom is selected next, and the pair having the second second similarity index S2 is selected. A third step for obtaining a third similarity index S3 (Ai, Bk), on the condition that priority is given to
Starting from the pair of starting atoms (Ai, Bk) when calculating the maximum S3 (Ai, Bk) in the third step, the largest S3 (Aj, Bk) among the unsupported pairs of atoms A fourth step of determining a graph match score M (A, B) in the overall correspondence when the correspondence with those having (Bl) is continued until there are no pairs of atoms that can be handled;
If the graph match score M (A, B) in the fourth step is larger than the threshold value, the interatomic correspondence calculated in the fourth step and the graph match score M (A) for the first molecule A and the second molecule B , B) and a fifth step of outputting a high-speed graph match search method for evaluating similarity between molecules. Coordinate data relating to each of the atoms (Ai, Aj,...) Constituting the first molecule A and the atoms (Bk, Bl,...) Constituting the second molecule B stored in the storage unit. Coordinate data relating to each is input, and in the virtual memory space constructed on the computer, each atom (Ai, Aj,...) Of the first molecule A and each atom (Bk) of the second molecule B , Bl,...) (M (Ai) = Bk) to perform superposition (i, j, k, l are all natural numbers), and the first molecule A and the second molecule In a computer program that causes a computer to execute an optimal interatomic correspondence between B and a process of evaluating the similarity between the first molecule A and the second molecule B,
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, as seen from each atom of the pair of atoms Ai and Bk, A first calculation step for obtaining a first similarity index S1 (Ai, Bk) indicating how similar the surrounding environments are;
Regarding all the pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, as seen from each atom of the pair of atoms Ai and Bk, A calculation step for obtaining a second similarity index S2 (Ai, Bk) for integrating the first similarity index S1 (Aj, B1) for all pairs of surrounding atoms Aj, B1 having an equal bond distance, If the surrounding atoms Aj and B1 that are at the same bond distance from each atom of the pair of Ai and Bk are the same element, the first similarity index S1 (Aj, B1) is further multiplied by a coefficient and integrated. A second calculation step for obtaining a second similarity index S2 (Ai, Bk);
For all pairs of atoms Ai and Bk formed by all atoms Ai of the first molecule A and all atoms Bk of the second molecule B, the first pair of atoms Ai and Bk is used as the starting point. A third similarity having a value corresponding to the graph match score M (A, B) calculated at that time by creating an overall correspondence by sequentially associating the atoms of the molecule A and the atoms of the second molecule B This is a calculation step for obtaining the index S3 (Ai, Bk), and at the time of creating the correspondence, the atom that directly binds to the already associated atom is selected next, and the pair that has a high second similarity index S2 is selected. A third calculation step for obtaining a third similarity index S3 (Ai, Bk), on the condition that priority is given to
Starting from the pair of starting atoms (Ai, Bk) when calculating the maximum S3 (Ai, Bk) in the third calculation step, the maximum S3 (Aj , B1), the fourth calculation step for obtaining the graph match score M (A, B) in the overall correspondence when the correspondence is continued until there is no pair of atoms that can be handled,
If the graph match score M (A, B) in the fourth calculation step is larger than the threshold value, the inter-atomic correspondence and the graph match score (A) calculated in the fourth step for the first molecule A and the second molecule B , B) is a computer program that causes a computer to execute a fifth output step.

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