JP4963082B2 - Complex structure prediction apparatus, method, and program - Google Patents

Description

  The present invention predicts a complex structure when a plurality of three-dimensional structures such as proteins are docked by calculating a docking score representing an interaction energy according to the relative arrangement of the plurality of three-dimensional structures. Relates to the device.

  In recent years, bioinformatics for processing a huge amount of biological information with a computer has been rapidly progressing. In this type of field, predicting the structure of a complex (docking structure) formed by a plurality of structures is important for the study of the properties of the object. The structure that forms the complex typically includes a protein. It is also considered important to predict the complex structure for DNA, saccharides and the like. Furthermore, not only in the field of biotechnology but also in other fields such as carbon nanotubes, the prediction of the composite structure is considered useful. Here, a conventional technique for predicting a complex structure will be described by mainly taking up proteins.

  It is known that many proteins that form a complex maintain almost the same shape as a single protein. In complex structure prediction, three-dimensional structure data (atomic coordinate data) of two proteins are input. Then, while changing the relative arrangement of the two three-dimensional structure data little by little, the compatibility of both structures in each relative arrangement is calculated, and a candidate for the complex structure is obtained from the calculation result of the compatibility. In the suitability calculation, a score representing the magnitude of interaction energy between the two structures is preferably calculated. Such a fitness score is hereinafter referred to as a docking score.

  As a conventional technique for predicting a composite structure, a shape complementarity search by fast Fourier transform (FFT) has been proposed. In this prediction technique, roughly, (1) each of the two structural data is converted into grid data, and (2) the suitability when the two grid data are superimposed is calculated. Hereinafter, the grid data and the compatibility calculation process using the grid data will be described using a simple diagram.

  FIG. 1 shows an example of grid data. Grid data is generated by discretizing the original structure data. The structural data is given by coordinate data representing the three-dimensional position of atoms that make up the protein. On the other hand, grid data is data given to each of a plurality of grids arranged in a cubic lattice. Converting from coordinate data to grid data is called gridding.

  In the example of FIG. 1, one protein is a receptor (receptor) as a target object, and the other protein is a ligand as a query object. In this example, the grid data of the receptor is energy field data at each grid position created by the receptor. Further, the grid data of the ligand is data on the amount of particles in each grid. In the figure, “1” is attached to the grid on the object surface, “9i” is attached to the grid inside the object, and “0” is attached to the grid outside the object.

Next, the suitability calculation using the two grid data of FIG. 1 will be described. In the fitness calculation, a fitness score when two grid data are superimposed is calculated. As described above, the fitness score is referred to as a docking score here. The docking score represents the magnitude of interaction energy between two objects. The docking score S is represented by the following formula (1).

  In formula (1), R is the energy field of the receptor, and L is the particle amount of the ligand. (L, m, n) is the arrangement of the receptors. (I, j, k) is the displacement amount of the position of the ligand. The docking score S is an interaction energy when the receptor is fixed and the ligand is moved in the x, y, and z directions by (i, j, k) and superimposed.

  As shown in FIG. 2, in the complex structure prediction, the docking score at each position is calculated while relatively moving two grid data in parallel. This process is performed at high speed by FFT. In the example of FIG. 2, the receptor is fixed and the ligand is moved. Then, on the right side of FIG. 2, an arrangement in which the docking score S is highest is conceptually shown.

  Moreover, as shown in FIG. 3, the two structures are rotated relatively. In the example shown, the ligand is rotated. Although FIG. 3 shows a state in which the ligand is rotated by 90 degrees, it is a matter of course that the ligand is actually rotated more finely. The rotation is realized by explicitly rotating the object based on the coordinate data. While rotating the coordinate data, grid data is created at each angle, and a search by the parallel movement of FIG. 2 is performed using the grid data.

  With the parallel movement of FIG. 2 and the rotation of FIG. 3, the docking score is calculated for each relative arrangement while finely changing the relative arrangement of the two structures. Then, for example, a predetermined number of complex structures with higher docking scores are obtained and output as prediction results.

  1 to 3, the grid data is represented in two dimensions. Actually, however, the grid data is three-dimensional data, and translation and rotation are also performed in the three-dimensional direction. .

Next, a calculation example using the conventional prediction technique will be further described. As a conventional calculation example, ZDOCK disclosed in Non-Patent Document 1 is known. In this prior art, an approximate value of energy due to electrostatic interaction when two grid data are shifted and overlapped is calculated by the following equation (2).

  In equation (2), E (l, m, n) is the electrostatic field of the target object and q (l, m, n) is the charge of the query object. S (i, j, k) is the electrostatic interaction energy when the query object is shifted (i, j, k) with respect to the target object.

  In ZDOCK, the sum of the electrostatic interaction score and the shape complementarity score is used as a fitness score, that is, a docking score. Specifically, the sum of S (i, j, k) in equation (2) and S (i, j, k) in equation (1) is used as the docking score. Using this score, the complex structure is searched. In the search process, the parallel movement and the rotational movement are performed as described above, and the score at each position is obtained. That is, in the search by parallel movement, convolution calculation is performed by FFT, and the docking score S is calculated at all (i, j, k) within the movement range. In the search by rotational movement, one object is explicitly rotated.

  FIG. 4 is a block diagram showing a configuration for calculating a score according to equation (2). Here, since the target object is stopped and the query object is moved, the former is expressed as Static and the latter is expressed as Mobile. In the score calculation, the FFT processing is performed on each of the target object and the query object, both the converted data are multiplied, and then the inverse Fourier transform (IFFT) is performed to obtain the score. As shown in the figure, the query object (Mobile) is rotated, and the process surrounded by the dotted line (Fourier transform of the query object and subsequent multiplication and inverse Fourier transform) is repeated each time it rotates. Search by translation is performed.

  The composite structure prediction is basically performed according to the above principle. However, in a low-dimensional complex number and real number multiplication process, only a very simple model can be expressed, and it is not easy to obtain high prediction accuracy.

  Therefore, it is required to perform higher-dimensional processing. As a prediction technique that meets such requirements, a method using a pair potential has been proposed. In this prediction technique, as described below, a pair potential matrix is introduced, vectors and matrices are processed, and a docking score is calculated.

  FIG. 5 shows an example of a pair potential matrix. This pair potential matrix is disclosed in Non-Patent Document 2. In the pair potential matrix, elements that can constitute the structure are classified into a plurality of types. In this example, it is assumed that the atoms forming the protein are classified into 18 types. Any pair of interaction energies made from these 18 types is placed in the form of a matrix as shown. In the example in the figure, the interaction energy (potential value) is represented by the amount of energy change when a water molecule around one type of atom is removed and replaced with another atom. For example, the energy change when the water molecules around the type 1 atom are replaced with the type 2 atom becomes the potential value of the type 1 and type 2 pair.

  When using a pair potential matrix, the distance between elements is also taken into account. Here, as shown in the figure, it is assumed that when atomic pairs are at a distance equal to or shorter than a predetermined cut-off distance (for example, 6 angstroms), these atomic pairs have interaction energy of a pair potential fish line. Therefore, for example, when the type 2 atom and the type 3 atom are at a distance equal to or smaller than the cutoff distance, it is determined from the pair potential matrix that the interaction energy is −0.850. In addition, the change of the interaction energy according to the distance of an atom pair may be further considered.

In addition, in another example of the pair potential, in this example, the value of the potential is expressed by the following secondary form score. In this case, each atom is classified into, for example, 20 to 200 types. The pair potential is represented by, for example, the sum of the Lennard-Jones potential and the Coulomb potential. If an atom of type i and an atom of type j exist at a distance d, the potential value is expressed by the following equation (3).

In Expression (3), the first and second terms correspond to the Lennard-Jones potential, and the third term corresponds to the Coulomb potential. Here, “1 / d ¹² ” in the first matrix of the first term is the i-th element of the same matrix. Also, “1” in the third matrix of the first term is the jth element of the same matrix. Similarly, “1 / d ⁶ ” in the first matrix of the second term is the i-th element of the same matrix, and “1” in the third matrix is the j-th element of the same matrix.

Next, score calculation on the grid using the pair potential will be described. Here, as in the example of FIGS. 1 to 3, the score when the receptor and the ligand are docked is calculated. The grid data of the receptor is represented by the following vector. This equation (4) represents the grid formation of the receptor.

The grid data of the ligand is expressed by the following vector. This equation (5) represents grid formation of the ligand.

In this case, partial energy when the receptor grid (i, j, k) and the ligand grid (l, m, n) are superposed is expressed by the following equation (6). Here, the matrix A is a pair potential matrix.

A value obtained by adding the contributions of all grids is a docking score S of the receptor and the ligand as shown in the following formula (7).

  In Expression (7), the docking score S is a score when the receptor is arranged at (1, m, n) and the ligand is arranged by being shifted (i, j, k) from the receptor.

  Next, Dima et al. Suitably used for the above score calculation. Will be described (Non-Patent Document 3). In this method, the docking score formula is modified as follows.

First, paying attention to the fact that the pair potential matrix A is a target matrix, the pair potential matrix A is decomposed as shown in the following equation (8). Here, eigenvalue decomposition is performed.

U is an orthogonal matrix (eigenvector), and D is a diagonal matrix (eigenvalue). Further, by compressing the dimension of the eigenvalue in the diagonal matrix D, the pair potential matrix A is approximated as shown in Equation (9). Specifically, eigenvalues after the (r + 1) th magnitude are set to zero.

  On the matrix, the eigenvalues from the first row and the first column to the r-th row and the r-th column remain, and other portions (including eigenvalues after the (r + 1) th row and the (r + 1) th column) may be zero. The value of r is the number of eigenvalues of the diagonal matrix left in the approximation process, and can be called the approximate eigenvalue number or approximate dimension number.

Approximated pair potential matrices are divided into the left matrix UDr and right matrix U ^T. Left matrix UDr is multiplied receptor gridding vector R, also gridding vector R ligand is applied to the right matrix U ^T (Equation (10)). The former is first grid data R ′ and the latter is second grid data L ′.

When the first grid data R ′ (receptor side) and the second grid data L ′ (ligand side) are used, the docking score is expressed as the following equation (11).

  Here, the docking score is originally represented by the product of the receptor gridded vector data, the pair potential matrix, and the ligand gridded vector data. Dima et al. In this method, the pair potential matrix in the docking score formula is subjected to eigenvalue decomposition and approximation, and divided into a left matrix and a right matrix. Further, when the product of the receptor and the left matrix is replaced with the first grid data R ′, and the product of the right matrix and the ligand is replaced with the second grid data L ′, the above equation is obtained. In this way, the docking score is represented by the product of the first grid data R ′ and the second grid data L ′. In this modified expression, the elements after the (r + 1) -th dimension of the first grid data R ′ are 0 by the approximation process, and therefore the docking score is obtained by the sum of r number of real convolutions. r is the number of approximate eigenvalues or approximate dimensions as described in connection with equation (9), and specifically, the eigenvalues that are left when approximating a diagonal matrix obtained by eigenvalue decomposition of a pair potential matrix. It corresponds to the number of.

  FIG. 6 shows a diagram of Dima et al. The structure for calculation of the docking score by the method of is shown. Here, similarly to the above-described example, the first grid data R ′ on the receptor side is fixed, and the second grid data L ′ on the ligand side is moved. Therefore, in the figure, the former is represented as Static and the latter is represented as Mobile. In the score calculation, r forward FFTs and 1 backward FFT are performed. More specifically, the FFT is performed on the static and the FFT result is stored. Also, FFT is performed r times on the Mobile. Each FFT result for the Mobile is multiplied with the Static FFT result. The r multiplication results obtained in this way are summed, and a reverse FFT is performed to obtain a docking score.

  In the score calculation of FIG. 6, a storage area and a memory area as a work area are required. The minimum required memory is considered as follows. Let N be the size in the one-dimensional direction in the three-dimensional FFT. N is the number of grids. That is, the score calculation unit 33 searches for a docking structure in an N × N × N grid space. In this case, an area of r × N × N × N is required to store the FFT result of the static portion. Further, an N × N × N area is required as an FFT work area. Further, an area of N × N × N is required as the sum storage area. When these are added together, an area of (r + 2) × N × N × N is required.

Here, N (the number of grids) is practically 50 to 350, for example. If N = 350, the memory area corresponding to N × N × N is approximately 200 MB. In this case, at least a memory area of about (r + 2) × N × N × N = (r + 2) × 200 MB is required.
Chen R, Li and L, WengZ, "ZDOCK: An Initial-stage Protein-Docking Algorithm", Proteins: Structure, Function, and Bioinformatics, 52: 80-87 (2003) Chao Zhang, GeorgeVasmatzis, James L. Cornette and Charles DeLisi, "Determination of AtomicDesolvation Energies From the Structures of Crystallized Proteins", J. Mol. Biol. (1997) 267, pp707-726 Dima Kozakov, RyanBrenke, Stephen R. Comeau, and Sandor Vajda, "PIPER: An FFT-Based ProteinDocking Program with Pairwise Potentials", PROTEINS: Structure, Function, and Bioinformatics, 65: 392-406 (2006)

  However, in the complex structure prediction technique using the conventional pair potential matrix, Dima et al. Although the pair potential matrix approximation processing is performed as seen in the above method, the calculation amount is still large. And, in order to prevent the calculation amount from becoming enormous, the size of the pair potential matrix that can be used is limited, which is a factor that lowers the score accuracy and lowers the prediction accuracy. It becomes a factor to narrow the scope of application.

  The application range of the prediction technique will be further described. For example, consider the case where a sugar complex structure is predicted as a substance other than protein. In this case, since there are many types of elements that make sugar, the pair potential matrix becomes large, and the amount of calculation becomes enormous. Therefore, it is not easy at present to predict the sugar complex structure using the pair potential matrix. Actually, it is only in the case of proteins that the complex structure can be predicted using the pair potential matrix, and the current situation is that the pair potential matrix is not used to predict the complex structure of substances other than proteins. I can say that. Therefore, in order to make it possible to predict the complex structure of substances other than proteins, it is desirable to be able to use a pair potential matrix having a larger number of types. For this reason, it is desirable to reduce the amount of calculation.

  Further, the conventional technique has a drawback that a large amount of memory is required for score calculation. As described with reference to FIG. 6, the required memory size is represented by (r + 2) × N × N × N, and increases in proportion to r. r is the number of approximate eigenvalues or approximate dimensions described above, that is, corresponds to the number of eigenvalues remaining in approximation of a diagonal matrix obtained by decomposing a pair potential matrix. When r is increased, the score accuracy (prediction accuracy) increases, but the memory size becomes enormous. Conversely, if r is reduced, the memory size is suppressed, but the score accuracy is reduced. In the conventional calculation example, since the score calculation is executed in a memory saving environment in which the memory size is limited, r is set small even at the expense of accuracy. For example, when applying the 18-dimensional pair potential matrix described above, r is set to 2 or 4, and the 18-dimensional matrix is approximated to a 2-dimensional or 4-dimensional matrix. It is desirable to solve such a problem and increase r (number of approximate eigenvalues or approximate number of dimensions) without increasing the memory size to obtain high accuracy.

  The present invention has been made under the above-mentioned background, and one object of the present invention is to predict a complex structure that can calculate a docking score with a small amount of calculation and can use a pair potential having more types. To provide technology. Another object of the present invention is to make it possible to calculate a docking score with higher accuracy with a smaller memory size.

  The complex structure prediction apparatus of the present invention predicts a complex structure when a plurality of three-dimensional structures are docked by calculating a docking score representing an interaction energy according to the relative arrangement of the plurality of three-dimensional structures. A device that classifies a plurality of types of structure input units that input the first input structure and the second input structure, which are the plurality of three-dimensional structures to be docked, and elements that can form the three-dimensional structure. A pair potential matrix storage unit for storing a pair potential matrix in which interaction energy of an arbitrary pair made from the type is arranged, and compressing the pair potential matrix based on the first input structure and the second input structure, Any pair of interaction energies made of any element appearing in the first input structure and any element appearing in the second input structure The first input structure and the second input structure are obtained by using a pair potential matrix deforming unit that generates a compressed pair potential matrix in which-is arranged, the first input structure, the second input structure, and the compressed pair potential matrix. From the grid processing unit that converts and generates first structural grid data and second structural grid data for score calculation including a collection of data in units of grids, and from the first structural grid data and the second structural grid data And a score calculation unit for calculating a docking score of the first input structure and the second input structure.

  As described above, according to the present invention, the pair potential matrix is compressed, and the docking score is calculated using the compressed pair potential matrix. Therefore, the calculation amount in the docking score calculation process can be reduced. Since the amount of calculation can be reduced, it is possible to process pair potentials with more types.

  Further, the pair potential matrix transformation unit further performs singular value decomposition for decomposing the compressed pair potential matrix into a first orthogonal matrix, a diagonal matrix, and a second orthogonal matrix, and outputs a plurality of eigenvalues of the diagonal matrix. An approximation process may be performed in which the eigenvalue of the approximate eigenvalue number is left by setting the part to 0.

  In addition, the grid processing unit uses the diagonal matrix approximated to the first orthogonal matrix and the second orthogonal matrix as the compressed pair potential matrix, and uses the first input structure and the first orthogonal matrix. The first structure grid data may be generated from a matrix and the approximated diagonal matrix, and the second structure grid data may be generated from the second input structure and the second orthogonal matrix.

  In addition, the score calculation unit, for the combination of the first structural grid data and the second structural grid data, the number of times corresponding to the approximate eigenvalue number that is the number of eigenvalues left in the approximate process, FFT processing, Multiplication processing may be performed and the sum of the processing results may be obtained.

  The score calculation unit includes a first memory area for performing FFT processing on a combination of the first structural grid data and the second structural grid data, and a second memory for obtaining a sum of the processing results. The area may be used to calculate the score.

  The score calculation unit may calculate a docking score in each relative arrangement when the first structural grid data and the second structural grid data are relatively moved.

  Moreover, the composite structure prediction apparatus may include a structure rotating unit that rotates at least one of the first input structure and the second input structure before being gridded.

  In addition, the complex structure prediction apparatus may include a candidate selection unit that compares the docking scores in the respective relative arrangements calculated by the score calculation unit and selects the complex structure candidates.

  Another aspect of the present invention is a complex in which a complex structure when a plurality of three-dimensional structures are docked is predicted by calculating a docking score representing an interaction energy according to the relative arrangement of the plurality of three-dimensional structures. A structure prediction method, wherein a first input structure and a second input structure that are the plurality of three-dimensional structures to be docked are input, elements that can form the three-dimensional structure are classified into a plurality of types, and the plurality of types A pair potential matrix in which interaction energy of an arbitrary pair formed from the array is read out from a pair potential matrix storage unit, the pair potential matrix is compressed based on the first input structure and the second input structure, and the first potential matrix is compressed. An interaction energy of an arbitrary pair formed by an arbitrary element appearing in the input structure and an arbitrary element appearing in the second input structure is arranged. The compressed pair potential matrix is generated, and the first input structure and the second input structure are converted using the first input structure, the second input structure, and the compressed pair potential matrix, and data of each grid is converted. First structure grid data and second structure grid data for calculating a score consisting of a group are generated, and the first input structure and the second input structure are generated from the first structure grid data and the second structure grid data. Calculate the docking score.

  According to another aspect of the present invention, a computer executes a process of calculating a docking score representing an interaction energy according to a relative arrangement of the plurality of three-dimensional structures with respect to a complex structure when the plurality of three-dimensional structures are docked. A composite structure prediction program that acquires a first input structure and a second input structure that are the plurality of three-dimensional structures to be docked, classifies elements that can form a three-dimensional structure into a plurality of types, and A pair potential matrix in which an interaction energy of an arbitrary pair made from the type is arranged is read from a pair potential matrix storage unit, the pair potential matrix is compressed based on the first input structure and the second input structure, An arbitrary pair of arbitrary elements that appear in the first input structure and arbitrary pairs that appear in any element that appears in the second input structure A compressed pair potential matrix in which energy is arranged, and the first input structure and the second input structure are transformed using the first input structure, the second input structure, and the compressed pair potential matrix, and a grid Generating a first structure grid data and a second structure grid data for calculating a score, each of which is a collection of data, and from the first structure grid data and the second structure grid data, the first input structure and the second structure grid data; The computer is caused to execute a process for calculating a docking score of a two-input structure.

  In the present invention, the pair potential matrix is compressed based on the first input structure and the second input structure as described above, and the docking score is calculated using the compressed pair potential matrix. Therefore, the docking score is calculated with a small amount of calculation. Yes, and it is possible to handle pair potentials with more types.

  Hereinafter, a complex structure prediction apparatus according to an embodiment of the present invention will be described with reference to the drawings. In the following, description of matters common to those described as background art will be omitted as appropriate.

  First, the principle of structure prediction by the composite structure prediction apparatus of the present invention will be described. In the present invention, the first input structure and the second input structure are docked. Here, as an example, protein docking is taken up as in the background art, and the first input structure is a receptor and the second input structure is a ligand.

  Prior art Dima et al. In this method, the pair potential matrix was eigenvalue decomposed, grid data was generated from it, and the docking score was calculated by convolution integration.

  In contrast, in the present invention, the pair potential matrix is first compressed as follows. The compression process is performed based on data of two objects to be docked, that is, based on input receptor and ligand data.

  FIG. 7 illustrates the compression process using a simple example. The pair potential matrix A before compression is a 5 × 5 matrix. It is assumed that only type 1, 4 and 5 atoms appear in the receptor and only type 1 and 3 atoms appear in the ligand. In this case, the pair potential matrix A is compressed into a matrix A 'of any combination of types 1, 4, 5 and types 1, 3. In the figure, dotted lines are drawn in rows corresponding to receptor types 1, 4, and 5 and dotted lines are drawn in columns corresponding to ligand types 1 and 3. In the compression process, the value of the intersection of the dotted lines is drawn. Left behind. As a result, as shown in the figure, the matrix becomes 3 × 2, and the dimension of the matrix becomes small.

  In the above, the pair potential matrix before compression includes all combinations of potential values created by all atom types that may constitute the protein. On the other hand, in the compression process, the pair potential matrix is transformed into a matrix composed of an arbitrary pair of potentials made of arbitrary atoms that actually constitute the receptor and arbitrary atoms that actually constitute the ligand. That is, the pair potential matrix is compressed so as to have a matrix having only pair potential values that can be created by atoms that actually appear in the receptor and ligand to be predicted.

  In other words, the compression process is a process of deleting the non-appearance type, that is, the potential of the combination that cannot appear in the receptor and ligand to be docked is deleted. By such compression processing, the potential of the pair unnecessary for the score calculation because it does not exist in the protein to be predicted is deleted, and the dimension of the pair potential matrix can be reduced.

  The reduced pair potential matrix obtained by the above compression process is referred to as a compressed pair potential matrix A ′. The compressed pair potential matrix A 'is processed as follows.

In the prior art, eigenvalue decomposition is performed using the feature that the pair potential matrix is a square or symmetric matrix. However, the compressed pair potential matrix A ′ is a non-square, asymmetric matrix and cannot be eigenvalue decomposed. Therefore, in the present invention, the compressed pair potential matrix A ′ is subjected to singular value decomposition as shown in the following equation (12).

U and V are orthogonal matrices (left and right eigenvectors), and D is a diagonal matrix (eigenvalues). U and V correspond to the first orthogonal matrix and the second orthogonal matrix of the present invention. The compressed pair potential matrix A ′ is approximated as in the prior art. That is, the eigenvalues after the (r + 1) th magnitude in the diagonal matrix D are set to 0, and the dimension with the smaller eigenvalues in the diagonal matrix D is compressed (formula (13)).

  On the actual matrix, the eigenvalues from the first row and the first column to the rth row and the rth column remain, and the other parts (including eigenvalues after the (r + 1) th row and the (r + 1) th column) become 0. Good. r is the number of eigenvalues left in the approximation process. Here, for r, the same terms as in the description of the prior art are used, that is, r is called an approximate eigenvalue number or an approximate dimension number (r may be called an approximate number, an approximate eigenvalue remaining number, etc.). Good).

Approximated compressed pair potential matrix A 'is divided into left matrix UDr and right matrix V ^T. The receptor gridding vector R is multiplied by the left matrix UDr to obtain first grid data R ′. Also, the right matrix V ^T is multiplied by the ligand grid vector R to obtain second grid data L ′ (formula (14)).

The first grid data R ′ and the second grid data L ′ correspond to the first structure grid data and the second structure grid data of the present invention, respectively. When the first grid data R ′ (receptor side) and the second grid data L ′ (ligand side) are used, the docking score is expressed as the following equation (15).

  Here, the docking score is originally represented by the product of the receptor gridded vector data, the pair potential matrix, and the ligand gridded vector data (see Expression (7)). The pair potential matrix is compressed and approximated and divided into a left matrix and a right matrix. Further, when the product of the receptor and the left matrix is replaced with the first grid data R ′, and the product of the right matrix and the ligand is replaced with the second grid data L ′, the above equation is obtained. In this way, the docking score is represented by the product of the first grid data and the second grid data. In this modified expression, the elements after the (r + 1) -th dimension of the first grid data R ′ are 0 by the approximation process, and therefore the docking score is obtained by the sum of r number of real convolutions. As described in relation to the equation (13), r is the number of approximate eigenvalues or approximate dimensions, and the eigenvalue remaining when approximating the diagonal matrix obtained by “singular value decomposition” of the pair potential matrix. It corresponds to the number of.

  The principle of composite structure prediction according to the present invention has been described above. In the present invention, since the pair potential matrix is compressed, the amount of calculation can be reduced. Since the amount of calculation is small, it is possible to process a larger pair potential matrix with more types. This is advantageous in improving the prediction accuracy by increasing the score accuracy.

  In addition, the fact that a larger pair potential matrix having more types as described above can be used means that a variety of large pair potential matrices can be used. This is also advantageous for expanding the application range of the prediction technique using the pair potential matrix, and it is considered that the complex structure of substances other than proteins can also be predicted. Substances other than proteins are, for example, sugar and DNA. Moreover, the substance of the field | area different from biotechnology, such as a carbon nanotube, may be sufficient. When predicting a complex structure of a substance other than a protein, if there are many types of elements such as atoms constituting the substance, the pair potential matrix becomes large, which increases the amount of calculation. However, when the present invention is applied, since the pair potential matrix is compressed, an increase in the amount of calculation can be suppressed.

  Actually, there is no application example of the pair potential matrix to a substance other than protein for the full solution search using the fast Fourier transform as described in the present embodiment. The reason for this is considered that the pair potential matrix becomes large as described above. On the other hand, according to the present invention, it can be expected that the versatility of complex structure prediction is increased, the scope of application is expanded, and it can be applied to substances other than proteins.

  Next, a specific configuration of the complex structure prediction apparatus according to the present embodiment will be described. FIG. 8 shows the configuration of a computer that realizes the composite structure prediction apparatus from the hardware aspect. In FIG. 8, the computer 1 is a personal computer, for example, but may be a larger computer. The program execution unit 3 includes a processor such as a CPU, and the program storage unit 5 and the processing data storage unit 7 include a memory. The computer also includes an external storage device 11 such as a hard disk, and further includes an input device 13, an output device 15, a recording medium mounting unit 17, a communication unit 19, and the like.

  The program storage unit 5 stores a program for realizing the complex structure prediction apparatus and method according to the present embodiment. In particular, the program storage unit 5 inputs three-dimensional structure data to be docked, and compresses the pair potential matrix. Deformation is performed, three-dimensional structure data is rotated, grid data is generated, docking score calculation is performed by FFT, complex structure candidates are selected, and a program for outputting a prediction result is stored. The complex structure prediction apparatus and method according to the present embodiment are realized by executing such a complex structure prediction program mainly in the program execution unit 3 of the computer 1. The contents of these programs are described in the description of the complex structure prediction apparatus below.

  The processing data storage unit 7 stores data to be processed and data after processing. The processing data storage unit 7 stores, for example, input structure data to be docked, a pair potential matrix, and a processing result docking score. In addition, the memory functions as a work area for processing by the program execution unit 3, and is used as an FFT work area, a data storage area, and the like.

  Data input / output to / from the computer 1 is typically performed via the input device 13 and the output device 15. In addition, data input / output may be performed between the recording medium and the recording medium via the recording medium mounting unit 17. Data input / output may be performed via the communication unit 19. That is, these configurations may function as an input unit and an output unit.

  When the communication unit 19 is used, the computer 1 may be connected to a WEB server, and data may be input / output via a network. Further, the computer 1 may have the function of a WEB server. Then, structure data to be docked via WEB may be input, and a prediction result may be returned by output to WEB.

  FIG. 9 shows the complex structure prediction apparatus of the present embodiment in the form of a functional block diagram. As illustrated, the complex structure prediction apparatus 21 includes a structure input unit 23, a pair potential matrix storage unit 25, a pair potential matrix transformation unit 27, a structure rotation unit 29, a grid processing unit 31, a score calculation unit 33, and a candidate selection unit. 35 and a prediction result output unit 37.

  The structure input unit 23 inputs data of the first input structure and the second input structure to be docked. In the example of the present embodiment, the first input structure is a receptor and the second input structure is a ligand. The input structure data is coordinate data and consists of position coordinates of each atom constituting the protein. As described above, the input device 13, the recording medium mounting unit 17, the communication unit 19, and the like of FIG. 1 can function as the structure input unit 23.

  The pair potential matrix storage unit 25 stores a pair potential matrix as illustrated in FIG. As the pair potential matrix storage unit 25, the memory and the external storage device of FIG.

  The pair potential matrix transformation unit 27 includes a compression unit 41, a singular value decomposition unit 43, an approximation unit 45, a left matrix generation unit 47, and a right matrix generation unit 49 as illustrated. As described with reference to FIG. 7, the compression unit 41 transforms the pair potential matrix A into a matrix composed of an arbitrary pair of potentials formed by an arbitrary atom appearing in the receptor and an arbitrary atom appearing in the ligand. Thus, a compressed pair potential matrix A ′ is generated. More specifically, the compression unit 41 detects all types of atoms that appear in the receptor and all types of atoms that appear in the ligand. Then, a potential value corresponding to an arbitrary combination of types detected from both structures is extracted from the pair potential matrix. The extracted potential values are arranged to generate a compressed pair potential matrix as shown in FIG. As a result, the pair potential matrix is compressed into a low-dimensional matrix having only pair potential values that can be created by atoms actually appearing in the receptor and ligand to be predicted.

The singular value decomposition unit 43 performs singular value decomposition processing on the compressed pair potential matrix A ′, and decomposes it into an orthogonal matrix U, a diagonal matrix D, and an orthogonal matrix V. The approximating unit 45 approximates the compressed pair potential matrix A ′ by compressing the diagonal matrix D obtained by singular value decomposition. At this time, in the approximation process, as described above, r (number of approximate eigenvalues or approximate dimension) eigenvalues are left, but the value of r may be input and specified from the input device 11 or the like. Further, the left matrix generation unit 47 and the right matrix generation unit 49 divide the matrix after decomposition and approximation, and generate the left matrix UDr and the right matrix V ^T described above.

  The structure rotating unit 29 rotates the ligand that is the second input structure. The ligand is rotated little by little in accordance with preset angle data. Each time the ligand is rotated, the grid of the ligand and score calculation described below are performed, thereby realizing a search for rotational movement.

The grid processing unit 31 converts the receptor and the ligand using the receptor (first input structure), the ligand (second input structure), and the compressed pair potential matrix A ′, so that the first grid data R ′ and the second grid are converted. Data L ′ is generated. Compressing the pair potential matrix A 'as the product of the left matrix UDr and right matrix V ^T is obtained from the pair potential matrix deformation portion 27 is used (the left matrix and the right matrix, compression pair potential matrix A is approximated' is ).

  The grid processing unit 31 includes a first grid generation unit 51 and a second grid generation unit 53. The 1st grid production | generation part 51 performs the grid formation regarding the receptor which is a 1st input structure. The receptor is entered in the form of coordinate data. The first grid generator 51 grids the receptor and converts it into the form of vector data R, and further multiplies the receptor vector data R by the left matrix UDr to obtain first grid data R ′.

The 2nd grid production | generation part 53 performs the grid formation regarding the ligand which is a 2nd input structure. This grid formation is performed on the ligand that has undergone the rotation process in the structure rotation unit 29. The second grid generation unit 53 converts the ligand into a grid and converts it into the form of vector data L, and further multiplies the right matrix V ^T by the ligand vector data L to obtain second grid data L ′.

  The score calculation unit 33 calculates a docking score from the first grid data R ′ and the second grid data L ′.

  FIG. 10 shows the configuration of the score calculation unit 33. In the score calculation, the first grid data R ′ on the receptor side is fixed and the second grid data L ′ on the ligand side is moved, as in the example of the prior art. Therefore, in the figure, the former is represented as Static and the latter is represented as Mobile.

  The score calculation unit 33 includes an FFT unit 61, a multiplication processing unit 63, an addition processing unit 65, and an inverse FFT unit 67. Conventionally, FFT processing is individually performed on Static and Mobile, but in this embodiment, FFT processing is performed by the FFT unit 61 for the combination of Static and Mobile. Then, Static and Mobile after FFT are multiplied by the multiplication processing unit 63. These processes are performed r times. r is the number of approximate eigenvalues or the number of approximate dimensions (the number of eigenvalues left in the approximation process of the diagonal matrix obtained by singular value decomposition of the compressed pair potential matrix A ′). Then, the sum of the r calculation results is obtained by the addition processing unit 65, and further, an inverse FFT process is performed by the inverse FFT unit 67 to obtain a docking score.

  FIG. 11 shows the memory size required for the processing of the score calculation unit 33 described in FIG. The score calculation unit 33 generally uses two memory areas. The three areas on the left side of FIG. 11 are the same memory area, which is the first memory area 71. One of the right ends is the second memory area 73. The first memory area 71 is an area for inputting both Static (first grid data R ′) and Mobile (second grid data L ′), and is an FFT work area. The second memory area 73 is a sum storage area.

  Each memory area has a size of N × N × N. N is the size in the one-dimensional direction in the three-dimensional FFT, and is represented by the number of grids. That is, the score calculation unit 33 searches for a docking structure in an N × N × N grid space.

  In the prior art, FFT processing is separately performed for Static and Mobile. In the present embodiment, as shown in FIG. 10, FFT processing is performed for the combination of Static and Mobile. Done. Therefore, as shown in FIG. 11, a combination of Static and Mobile is input to the first memory area 71.

  As shown in the figure, the input Static and Mobile are subjected to FFT processing in the first direction (x direction) and further subjected to FFT processing in the second direction (y direction). Further, FFT processing and multiplication processing in the third direction (z direction) are performed, and the processing result is stored in the second memory area 73.

  In this way, in the present embodiment, score calculation is realized by the two memory areas 71 and 73. As the input size, 2 × (N / 2) × (N / 2) × (N / 2) is required as shown at the left end of FIG. As the FFT work area, an N × N × N area is required. Further, an area of N × N × N is required as the sum storage area. As shown in the figure, the input area (2 × (N / 2) × (N / 2) × (N / 2)) is included in the FFT work area (N × N × N). The size is 2 × N × N × N.

  N is practically 50 to 350. If N = 350, the memory area corresponding to N × N × N is approximately 200 MB. Therefore, it can be said that the memory size required by the score calculation unit 31 is approximately 400 MB or less.

  As a feature of the above configuration, the memory size necessary for the score calculation is r (number of approximate eigenvalues or approximate dimensions: the number of eigenvalues remaining in the approximation process of the diagonal matrix obtained by singular value decomposition of the compressed pair potential matrix. (In the prior art, the required memory size has increased in proportion to r). Therefore, even if r is increased, the memory size does not become enormous. From this, r can be enlarged, the score accuracy can be improved, and the prediction accuracy can be improved. High accuracy can be obtained even in a memory-saving environment.

  Returning to FIG. 9, the candidate selection unit 35 selects a complex structure candidate using the receptor as the first input structure and the docking score of the ligand as the second input structure. In the complex structure prediction apparatus 21 of the present embodiment, the ligand is rotated. Then, when the ligand is at each angle, the score calculation unit 33 calculates a docking score in each arrangement when the receptor and the ligand are translated. Therefore, the score calculation unit 33 calculates the docking score S in each relative arrangement when the receptor and the ligand are translated and rotated little by little. A large number of docking scores S obtained in this manner are compared, and a predetermined number of relative arrangements are determined as candidates for the complex structure from the one with the higher docking score S.

  For example, assume that the amount of parallel movement in one direction is 80 grids, and the direction is rotated by 6 degrees in two directions. In this case, a docking score S of 80 × 80 × 80 × 60 × 60 is obtained. Then, about 1000 relative arrangements from the larger docking score S are obtained as data representing the candidate complex structure.

  The prediction result output unit 37 is configured to output a prediction result of the complex structure. As the prediction result, candidate data of the above complex structure is output together with the docking score S of each candidate. As described above, the output device 15, the recording medium mounting unit 17, the communication unit 19, and the like of FIG. 1 can function as the prediction result output unit 37.

  The configuration of each part of the complex structure prediction apparatus 21 according to the present embodiment has been described above. Next, the operation of the complex structure prediction apparatus 21 will be described with reference to FIG. In FIG. 12, the data name is shown with a rectangular frame, and the process name is shown with an oval frame.

  As shown in FIG. 12, when the first input structure (receptor) and the second input structure (ligand) are input from the structure input unit 23, the pair potential matrix is read from the pair potential matrix storage unit 25.

Then, the pair potential matrix is compressed by the pair potential matrix transformation unit 27 using the first input structure and the second input structure (S1). Here, as described above, the pair potential matrix is compressed so as to be a matrix in which potentials of only pairs of atoms appearing in the first input structure and the second input structure are arranged (that is, the non-appearance type is deleted). ) Further, the singular value decomposition of the compressed pair potential matrix A ′ and the approximation of the diagonal matrix D are performed. The compressed pair potential matrix A 'is divided, the left matrix UDr and right matrix V ^T is obtained.

  Further, the ligand that is the second input structure is rotated by the structure rotating unit 29 according to preset angle data, and a rotating structure is obtained (S3).

The receptor having the first input structure is gridded by the first grid generation unit 51, and the first grid data R ′ is obtained using the left matrix UDr (S5). Further, the ligand that is the second input structure that has been rotated is gridded by the second grid generation unit 53, and the second grid data L ′ is obtained using the right matrix V ^T (S7).

  Then, the score calculation unit 33 performs a convolution calculation on the first grid data R ′ and the second grid data L ′, and a docking score S is obtained (S9). Further, as a filtering process, a candidate for the complex structure is selected by the candidate selection unit 35 (S11), and the selected candidate is output from the prediction result output unit 37 as output data together with the corresponding score.

  FIG. 13 is an example of output data, and shows a calculation example by the complex structure prediction apparatus 21 of the present embodiment. In this example, the size of the grid subjected to 3D-FFT (the number of grids in one direction) is 80. The grid interval (grid size) is 1.2 angstroms. The center positions of the ligand and the receptor are the center coordinates of a sphere that includes each object. As output data, the relative arrangement of the ligand and the receptor is arranged as a complex structure candidate in descending order of the docking score S. The relative arrangement is represented by the rotation angle of the ligand and the amount of movement of the ligand with the center position as the origin. The docking score S in each relative arrangement is also output as shown.

  The preferred embodiments of the present invention have been described above. According to the present embodiment, as described above, the pair potential matrix is compressed, and the docking score is calculated using the compressed pair potential matrix. Therefore, the calculation amount in the docking score calculation process can be reduced. Since the amount of calculation can be reduced, it is possible to process a large pair potential with more types. As a result, the score accuracy can be improved, and the range of the prediction target can be expanded to predict the complex structure of substances other than proteins.

  Being able to process a large pair potential matrix as described above is advantageous for improving the accuracy of the prediction by increasing the score accuracy, and furthermore, as already described, the application of the prediction technology using the pair potential is applied. It is also advantageous to expand the range. And application to substances other than protein is expected. Substances other than proteins are sugars and DNA, for example, as already mentioned. Moreover, the substance of field | areas other than biotechnology may be sufficient. When a complex structure of a substance other than protein is predicted, if there are many types of elements such as atoms constituting the substance, the pair potential matrix becomes large, and the amount of calculation becomes large in the conventional technique. However, when the present invention is applied, since the pair potential matrix is compressed, an increase in the amount of calculation can be suppressed and a large pair potential matrix can be processed.

  According to the present invention, the compressed pair potential matrix is decomposed into a first orthogonal matrix, a diagonal matrix, and a second orthogonal matrix by a singular value decomposition process, and a part of a plurality of eigenvalues of the diagonal matrix is set to zero. An approximation process is performed in which eigenvalues of the number of approximate eigenvalues are left. Thus, by performing singular value decomposition, the compressed pair potential matrix can be suitably used for docking score calculation, and the calculation amount can be reduced by approximation processing.

  Further, according to the present invention, the diagonal matrix approximated to the first orthogonal matrix and the second orthogonal matrix are used as the compressed pair potential matrix. First structural grid data is generated from the first input structure, the first orthogonal matrix and the approximated diagonal matrix, and second structural grid data is generated from the second input structure and the second orthogonal matrix. By using such grid data, score calculation can be suitably performed.

  Further, according to the present invention, the score calculation unit performs FFT processing for the number of approximate eigenvalues, which is the number of eigenvalues left in the approximation process, for the combination of the first structural grid data and the second structural grid data. And the multiplication process is performed, and the sum of the processing results is obtained. If the score calculation unit is configured in this way, as described with reference to FIG. 13, the memory size necessary for the score calculation is not proportional to the number of approximate eigenvalues (the eigenvalues remaining when the diagonal matrix is approximated). Therefore, the memory size can be reduced. In addition, more eigenvalues can be left in the approximation, and score accuracy can be improved. Thus, the docking score can be calculated with higher accuracy with a smaller memory size.

  According to the present invention, the score calculation unit obtains the sum of the first memory area for performing FFT processing on the combination of the first structural grid data and the second structural grid data, and the processing result. The second memory area is used to calculate the score. As a result, as described above, the memory size can be reduced, and the accuracy can be improved by leaving more eigenvalues in the approximation.

  Moreover, according to this invention, the docking score in each relative arrangement | positioning when the 1st structure grid data and the 2nd structure grid data are moved relatively is calculated. Thereby, the complex structure can be predicted by performing a search by parallel movement.

  Further, according to the present invention, at least one of the first input structure and the second input structure is rotated before being gridded. In the present example, the ligand is rotated. As a result, a complex structure can be predicted by performing a search based on rotational movement.

  Further, according to the present invention, the docking score in the relative arrangement of each of the first input structure and the second input structure is compared, and a complex structure candidate is selected. Thereby, the candidate of a complex structure is calculated | required as a prediction result of a complex structure.

  The preferred embodiments of the present invention have been described above. However, the present invention is not limited to the above-described embodiments, and it goes without saying that those skilled in the art can modify the above-described embodiments within the scope of the present invention.

  As described above, the complex structure prediction apparatus according to the present invention can predict the structure of a complex such as a protein, and is useful in fields such as biotechnology and bioinformatics.

It is a figure which shows the example of the grid data used for complex structure prediction. It is a figure which shows the search process by the parallel movement in complex structure prediction. It is a figure which shows the search process by the rotational movement in complex structure prediction. It is a block diagram which shows the structure for the score calculation in a prior art. It is a figure which shows the example of a pair potential matrix. It is a block diagram which shows the structure for calculation of a docking score in a prior art. It is a figure which shows the compression process of a pair potential matrix. It is a figure which shows the structure of the computer which implement | achieves the composite structure prediction apparatus which concerns on embodiment of this invention. It is a block diagram which shows the structure of the composite structure prediction apparatus which concerns on embodiment of this invention. It is a figure which shows the structure of a score calculation part. It is a figure which shows the memory size required for a score calculation process in this Embodiment. It is a figure which shows operation | movement of the composite structure prediction apparatus which concerns on this Embodiment. It is a figure which shows the example of the prediction result of a composite structure.

Explanation of symbols

DESCRIPTION OF SYMBOLS 21 Complex structure prediction apparatus 23 Structure input part 25 Pair potential matrix memory | storage part 27 Pair potential matrix deformation | transformation part 29 Structure rotation part 31 Grid processing part 33 Score calculation part 35 Candidate selection part 37 Prediction result output part

Claims (10)

A complex structure prediction device that predicts a complex structure when a plurality of three-dimensional structures are docked by calculating a docking score representing an interaction energy according to a relative arrangement of the plurality of three-dimensional structures,
A structure input unit for inputting the first input structure and the second input structure, which are the three-dimensional structures to be docked;
A pair potential matrix storage unit that classifies elements that can form a three-dimensional structure into a plurality of types and stores a pair potential matrix in which interaction energy of an arbitrary pair made from the plurality of types is arranged; and
The pair potential matrix is compressed based on the first input structure and the second input structure, and an arbitrary element made up of an arbitrary element appearing in the first input structure and an arbitrary element appearing in the second input structure A pair potential matrix deformation unit for generating a compressed pair potential matrix in which the interaction energy of the pair is arranged;
Using the first input structure, the second input structure, and the compressed pair potential matrix, the first input structure and the second input structure are transformed to obtain a score for calculating a score including a collection of data for each grid. A grid processing unit for generating 1 structure grid data and 2 structure grid data;
A score calculator for calculating a docking score of the first input structure and the second input structure from the first structure grid data and the second structure grid data;
A complex structure prediction apparatus comprising:   The pair potential matrix transformation unit further performs a singular value decomposition that decomposes the compressed pair potential matrix into a first orthogonal matrix, a diagonal matrix, and a second orthogonal matrix, and a part of the plurality of eigenvalues of the diagonal matrix The complex structure prediction apparatus according to claim 1, wherein an approximation process is performed in which eigenvalues of the number of approximate eigenvalues are kept by setting to zero.   The grid processing unit uses the diagonal matrix approximated to the first orthogonal matrix and the second orthogonal matrix as the compressed pair potential matrix, and uses the first input structure, the first orthogonal matrix, and The first structure grid data is generated from the approximated diagonal matrix, and the second structure grid data is generated from the second input structure and the second orthogonal matrix. Complex structure prediction device.   The score calculation unit includes, for the combination of the first structural grid data and the second structural grid data, the number of times corresponding to the approximate eigenvalue number that is the number of eigenvalues left in the approximation process, FFT processing, and multiplication processing The composite structure prediction apparatus according to claim 2, wherein the sum of the processing results is obtained.   The score calculation unit includes a first memory area for performing FFT processing on a combination of the first structural grid data and the second structural grid data, and a second memory area for obtaining a sum of the processing results. The composite structure prediction apparatus according to claim 4, wherein the score is calculated using the synthesizer.   The said score calculation part calculates the docking score in each relative arrangement | positioning when the said 1st structural grid data and the said 2nd structural grid data are moved relatively. The composite structure prediction apparatus according to 1.   The composite structure prediction apparatus according to claim 1, further comprising a structure rotating unit configured to rotate at least one of the first input structure and the second input structure before being gridded.   It has a candidate selection part which compares the docking score in each relative arrangement | positioning calculated by the said score calculation part, and selects the candidate of the said complex structure, The one in any one of Claims 1-7 characterized by the above-mentioned. Complex structure prediction device. A composite structure prediction method for predicting a composite structure when a plurality of three-dimensional structures are docked by calculating a docking score representing an interaction energy according to a relative arrangement of the plurality of three-dimensional structures,
Inputting a first input structure and a second input structure, which are the three-dimensional structures to be docked;
Classifying elements that can form a three-dimensional structure into a plurality of types, reading out a pair potential matrix in which interaction energy of an arbitrary pair made from the plurality of types is arranged, is read from the pair potential matrix storage unit,
The pair potential matrix is compressed based on the first input structure and the second input structure, and an arbitrary element made up of an arbitrary element appearing in the first input structure and an arbitrary element appearing in the second input structure Generate a compressed pair potential matrix that arranges the interaction energy of pairs,
Using the first input structure, the second input structure, and the compressed pair potential matrix, the first input structure and the second input structure are transformed to obtain a score for calculating a score including a collection of data for each grid. 1 structure grid data and 2nd structure grid data are generated,
Calculating docking scores of the first input structure and the second input structure from the first structure grid data and the second structure grid data;
A composite structure prediction method characterized by the above. A complex structure prediction program for causing a computer to execute a process of calculating a docking score representing an interaction energy corresponding to a relative arrangement of a plurality of three-dimensional structures, when a plurality of three-dimensional structures are docked. ,
Obtaining a first input structure and a second input structure which are the plurality of three-dimensional structures to be docked;
Classifying elements that can form a three-dimensional structure into a plurality of types, reading out a pair potential matrix in which interaction energy of an arbitrary pair made from the plurality of types is arranged, is read from the pair potential matrix storage unit,
The pair potential matrix is compressed based on the first input structure and the second input structure, and an arbitrary element made up of an arbitrary element appearing in the first input structure and an arbitrary element appearing in the second input structure Generate a compressed pair potential matrix that arranges the interaction energy of pairs,
Using the first input structure, the second input structure, and the compressed pair potential matrix, the first input structure and the second input structure are transformed to obtain a score for calculating a score including a collection of data for each grid. 1 structure grid data and 2nd structure grid data are generated,
A complex structure prediction program that causes the computer to execute a process of calculating a docking score of the first input structure and the second input structure from the first structure grid data and the second structure grid data.

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