CN111402964A - Molecular conformation search method based on mixed firework algorithm - Google Patents
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Abstract
The invention provides a molecular conformation search method based on a mixed firework algorithm, which is characterized by comprising the following steps of: comprises the following steps: s1, setting a docking area of the receptor molecule, and representing the docking area by a docking box, wherein the docking box is used for storing ligand conformation; s2, initializing a plurality of initial fireworks, wherein each fireworks represents a ligand conformation; expressing the ligand conformation as a solution vector, and setting a receptor-ligand binding affinity scoring function as a fitness function; s3, constructing a solution space by the solution vector, wherein the solution space comprises a plurality of layers; s4, constructing operators of the firework algorithm; s5, a mixed firework algorithm is constructed by combining the firework algorithm and the local search algorithm, and the mixed firework algorithm is used for searching for the approximately optimal ligand conformation in the butt joint box. The invention reduces the average time consumption of the butt joint on the test compound in the molecular butt joint, and improves the speed of the molecular butt joint; meanwhile, an approximate optimal value of the fitness function can be found, and the precision of molecular docking is improved.
Description
Technical Field
The invention relates to the field of computer-aided drug design, mainly relates to molecular docking, and particularly relates to a conformation search method.
Background
Molecular docking is an important technology in the field of computer-aided drug research, and is widely applied to multiple links of new drug research and development, such as early virtual screening in a drug discovery stage, discovery of drug action targets, research of drug potential action mechanisms, prediction of drug metabolism sites and the like. The molecular docking operation is to place the molecules with known three-dimensional structures on the active sites of the target molecules one by one, predict the binding mode and affinity of the two, and select out the ligand with the best affinity of the receptor close to the natural conformation through a scoring function.
The search for conformation in molecular docking is an extremely complicated problem, and molecular conformation is a different structure of a molecule in which the connection mode of each atom is not changed but the position of each atom with respect to the central atom is changed. From the calculation, the molecular docking is an optimization task, the molecular conformation search algorithm has great influence on the search speed and the hit rate of the system, and the currently adopted algorithm has the problems of low prediction precision and long time for molecular docking.
Disclosure of Invention
In order to achieve the purpose, the invention adopts the following technical scheme: a molecular conformation search method based on a mixed firework algorithm comprises the following steps:
s1, setting a docking area of the receptor molecule, and representing the docking area by a docking box, wherein the docking box is used for storing ligand conformation;
s2, initializing a plurality of initial fireworks, wherein each initial fireworks represents a ligand conformation; expressing the ligand conformation as a solution vector, and setting a receptor-ligand binding affinity scoring function as a fitness function;
s3, constructing a solution space by the solution vectors, wherein the solution space comprises a plurality of layers which respectively represent different explosion ranges of the fireworks;
s4, constructing operators of the firework algorithm;
s5, a mixed firework algorithm is constructed by combining the firework algorithm and the local search algorithm, and the mixed firework algorithm is used for searching for the approximately optimal ligand conformation in the butt joint box.
Compared with the prior art, the invention has the following beneficial effects: the method takes the firework algorithm as a global optimizer to quickly locate promising regions in a solution space, and the local search algorithm is integrated into the firework algorithm to perform local fine search, so that the local search capability is enhanced, the average time of butt joint on a test compound in molecular butt joint is reduced, and the molecular butt joint speed is increased; meanwhile, the approximate solution can be positioned to a local minimum value by a local search algorithm, so that an approximate optimal value of the fitness function is found, and the precision of molecular docking is improved.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a logic block diagram of program execution in embodiment 1.
FIG. 3 is a graph of the binding affinity results of example 1.
FIG. 4 is a graph showing the RMSD results of example 1.
Detailed Description
The technical solution of the present invention is further explained with reference to the drawings and the embodiments.
As shown in fig. 1, the invention provides a molecular conformation search method based on a mixed firework algorithm, which comprises the following steps:
s1, setting a docking area of the receptor molecule, and representing the docking area by a docking box, wherein the docking box is used for storing ligand conformation;
s2, initializing a plurality of initial fireworks, wherein each initial fireworks represents a ligand conformation; expressing the ligand conformation as a solution vector, and setting a receptor-ligand binding affinity scoring function as a fitness function;
s3, constructing a solution space by the solution vectors, wherein the solution space comprises a plurality of layers which respectively represent different explosion ranges of the fireworks;
s4, constructing operators of the firework algorithm;
s5, a mixed firework algorithm is constructed by combining the firework algorithm and the local search algorithm, and the mixed firework algorithm is used for searching for the approximately optimal ligand conformation in the butt joint box.
In step S1, the center position and the side length of the docking box are set, the center of the docking box is set as the geometric center of all the atoms in the receptor binding pocket, and the side length of the docking box is determined by the maximum distance between any two atoms in the receptor binding pocket.
In step S2, the molecular conformation search process is represented using the following optimization problem model:
min F(X)
s.t.g(X)≤0
a constraint function g (x) constrains the ligand conformation in the docking box for the protein, and for all solutions not in the docking box, treats them as invalid solutions; the objective function f (x) corresponds to the receptor-ligand binding affinity scoring function, i.e. the fitness function. The solution to the optimization problem is represented as
i is 1,2, … … N, wherein,
represents the central position of the conformation of the ligand,
is the rotation angle of the ligand conformation, i.e. the orientation information of the ligand conformation,
has a value range of [ -pi, pi [ -pi [ ]]；
Respectively representing each twistable bond angle in the ligand conformation, and the value range is [ -pi, pi]Wherein 1,2, …, b denotes the number of b twistable bonds in the ligand.
In step S3, a solution space is constructed by the solution vector, the solution space comprises three layers which respectively represent three explosion ranges of the fireworks, wherein the first layer refers to the range of the central position change of the ligand conformation under the condition that the orientation of the ligand conformation and the twistable bond angle are fixed; the second level refers to the range of orientation rotation of the ligand conformation under the condition that the central position of the ligand conformation and the twistable bond angle are fixed; the third level refers to the range of twistable bond rotations of the ligand conformation under conditions of fixed central position and orientation of the ligand conformation.
Step S4 includes:
(1) constructing explosion operators
The explosion operator comprises the firework explosion range and the number of sparks generated by the firework explosion.
The firework explosion range calculation method comprises the following steps: the fireworks are sorted according to the fitness function value from small to large and then divided into three equal parts, preferably, the fireworks in the first equal part are the fireworks with smaller fitness function values, namely the fireworks with the fitness function values belonging to a first preset range and the fireworks with high quality are exploded at the third level, the twistable key angles of the fireworks are randomly changed, and the small-range explosion phenomenon of the fireworks is simulated; the fireworks in the second equal part contain the fireworks with fitness function values belonging to a second preset range, the fireworks are exploded in the second level, and the orientation of the fireworks can be randomly changed to simulate the explosion phenomenon; the fireworks of the third equal portion contain the fireworks that the fitness function value belongs to third preset range, explode in first level, change its central point at random, simulation fireworks explosion phenomenon on a large scale. After the fireworks explosion, explosion sparks are generated, each of which represents a ligand conformation.
The calculation formula of the number of sparks generated by fireworks explosion is as follows:
Si＝M-ri
wherein S isiIndicating fireworks XiThe number of sparks resulting from the explosion, M being the number of sparks per firework which are most exploded, riIndicating fireworks XiThe sequence number of the fitness function value of (1);
(2) constructing mutation operators
L individuals are randomly selected from the current fireworks and the explosion sparks, a plurality of dimensions are randomly selected from each individual, namely solution vectors, values on the dimensions are multiplied by a variable which is subject to Gaussian distribution to obtain the variant spark individuals, and each variant spark represents a ligand conformation.
The ith spark
The k variable of
The variation was performed according to the following formula:
wherein Gaussian (1,1) represents a Gaussian distribution random number with the mean and the variance both being 1, and if the variant spark is an infeasible solution, a variant spark is randomly generated in a solution space.
(3) Firework selection strategy
The selection strategy is that the fireworks with the minimum fitness value in the candidate set are deterministically selected to the next generation as the fireworks, and the remaining N-1 fireworks are selected by a roulette method, wherein N is an integer which is greater than or equal to 2.
In the above formula, RMSDabThe root mean square error of N atom positions between structures a and b is calculated as the difference between two small molecules a and b with similar three-dimensional structures. Wherein the position of the atom i in the structure a is
The position of the atom i in the structure b is
The above formulaMiddle, RMSDaThe RMSD of all the firework individuals except a in the current firework individual a to the candidate set K is the sum of the RMSDs of the firework individuals a and K, and the difference of the firework individuals a is represented. If the difference is larger, the number of firework individuals similar to the individual is smaller, and the probability that the individual is selected is larger.
Step S5 includes:
s51, local search is conducted on the current fireworks, whether the local optimum value is accepted or not is determined according to the metropolis criterion, and the local search process is a process of promoting local area excellent individuals;
s52, exploding the current fireworks to generate explosion sparks according to a calculation formula of the fireworks explosion range and a calculation method of the number of the generated sparks;
s53, carrying out local search on the explosion spark, and determining whether to accept the local optimal value according to metropolis criterion;
s54, randomly selecting L individuals from the current fireworks and the explosion sparks to perform mutation according to a mutation operator to obtain the mutation sparks;
s55, selecting N individuals to form the next-generation fireworks according to the next-generation fireworks selection strategy;
s56, if the fitness function value of the firework is converged or the maximum iteration number is reached, the search is ended; otherwise, the process proceeds to step S51.
The local search algorithm comprises at least one of a BFGS algorithm, a DFP algorithm, or an L-BFGS algorithm.
In example 1, 195 receptor-ligand complex docks of the core set in the PDBbind standard test set were used as test subjects, and molecular docking was performed using the search method of the present invention, with 30 runs for each complex dock. Fig. 2 is a block flow diagram of embodiment 1 of the present invention, which is described in detail below with reference to fig. 2.
Preferably, this embodiment is implemented in the framework of molecular docking software Autodock Vina (referred to as Vina for short), and a scoring function of Vina is used as a fitness function. The method comprises the following specific steps:
(1) converting the pdb file of the protein and the mol2 file of the ligand into pdbqt files respectively;
(2) setting the range of the receptor binding pocket, namely setting the central position (center _ x, center _ y, center _ z), length, width and height (size _ x, size _ y, size _ z) of the docking box;
(3) generating initial fireworks: initializing N initial fireworks (each fireworks represents the conformation of a ligand), expressing the conformation of the ligand as a solution vector, and setting a receptor-ligand binding affinity scoring function as a fitness function;
(4) dividing the search range of the ligand conformation solution space into three levels to represent different explosion ranges of the fireworks;
(5) constructing an explosion operator and a mutation operator of a firework algorithm and a next-generation firework selection strategy;
(6) carrying out local search on each current-generation firework by using a BFGS algorithm, wherein the initial firework is the first-generation firework, and determining whether to accept the local optimal value according to a metropolis criterion;
(7) according to a calculation formula of the firework explosion range and a calculation method of the number of sparks generated, the current firework is exploded to generate explosion sparks;
(8) carrying out local search on each explosion spark by using a BFGS algorithm, and determining whether to accept the local optimal value according to a metropolis criterion;
(9) performing firework variation, namely randomly selecting L individuals from modern fireworks and explosion sparks, and randomly selecting a plurality of dimensions for variation according to a variation operator by each individual to generate variation sparks;
(10) selecting N individuals to form the next-generation fireworks according to the next-generation fireworks selection strategy;
(11) is the fitness function value convergent? If yes, turning to the step (13), otherwise, turning to the step (12);
(12) is the maximum number of iterations reached? If yes, turning to the step (13), otherwise, turning to the step (6);
(13) the output approximates the optimal ligand conformation and binding affinity.
The method of the invention is tested on three evaluation indexes by using a test set to a prediction model:
(1) molecular docking run time t (seconds)
(2) Binding affinity BA (kcal/mol)
(3) Root mean square error RMSD
The molecular docking running time t refers to the average time spent in docking on a plurality of test complexes, wherein the time spent in docking a single receptor-ligand complex refers to the time from the beginning of docking to the output of a result, and the index is used for testing the running efficiency of the docking program.
The combination affinity BA is an approximate optimal value of a fitness function finally found by a search algorithm, the smaller the value is, the better the searched result is, and the index is used for testing the accuracy of the search method.
The root mean square error RMSD is a measure of the difference between the ligand conformation predicted by docking software and the native conformation structure, and is defined as follows for two small molecules a and b with similar three-dimensional structures:
RMSDabthe root mean square error of the N atomic positions between the two structures a and b was calculated. Wherein the position of the atom i in the structure a is
The position of the atom i in the structure b is
This index is used to test the accuracy of the search method to predict ligand conformation.
Molecular docking is carried out on 195 compounds of a PDBbind data set by using an original ligand conformation search method in Vina docking software, the average time is 27.05 seconds, and the average time of the molecular docking is only 12.86 seconds after the ligand conformation search method is replaced by the search method, which shows that the search method can greatly shorten the molecular docking time.
FIG. 3 is a graph showing an example of the binding affinity results of the test of example 1, docking runs 30 times, each time recording the minimum of affinity from the first docking to the current docking. FIG. 4 is a graph showing exemplary RMSD results for the tests of example 1, where RMSD is the RMSD value of the ligand versus native crystal conformational structure for each recorded affinity value in FIG. 3. As shown in fig. 3, the binding affinity of the best ligand conformation predicted by the search method of the present invention is smaller in 30 runs, which indicates that the fitness function searched by the search method of the present invention has better accuracy; in fig. 4, the RMSD results of the best ligand conformation predicted by the search method of the present invention are all less than Vina on the same run number results, indicating that the best binding ligand conformation searched by the search method of the present invention is closer to the native conformation and more accurate. The results of fig. 3 and 4 illustrate that the average binding affinity value and RMSD of the best ligand conformation searched by the search method of the present invention is lower, and the accuracy of the docking results is higher.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.
Claims (6)
1. A molecular conformation search method based on a mixed firework algorithm is characterized in that: comprises the following steps:
s1, setting a docking area of a receptor molecule, and representing the docking area by a docking box, wherein the docking box is used for storing ligand conformation;
s2, initializing a plurality of initial fireworks, wherein each initial fireworks represents a ligand conformation; expressing the ligand conformation as a solution vector, and setting a receptor-ligand binding affinity scoring function as a fitness function;
s3, constructing a solution space by the solution vectors, wherein the solution space comprises a plurality of layers which respectively represent different explosion ranges of the fireworks;
s4, constructing operators of the firework algorithm;
and S5, constructing a mixed firework algorithm by combining the firework algorithm and the local search algorithm, and searching the approximately optimal ligand conformation in the butt joint box by using the mixed firework algorithm.
2. The molecular conformation search method based on the mixed firework algorithm as claimed in claim 1, wherein: in the step S3, the solution space includes three levels; the first level refers to the range of variation in the central position of the ligand conformation under conditions of fixed orientation of the ligand conformation and twistable bond angle; the second level refers to the range of orientation rotation of the ligand conformation under the condition that the central position of the ligand conformation and the twistable bond angle are fixed; the third level refers to the range of twistable bond rotations of the ligand conformation under conditions of fixed central position and orientation of the ligand conformation.
3. The molecular conformation search method based on the mixed firework algorithm as claimed in claim 2, wherein: the step S4 includes:
constructing an explosion operator and a mutation operator;
the next generation of firework selection strategy: the next generation of fireworks comprises 1 firework individual with the minimum fitness function value in the candidate set and N-1 firework individual selected according to the roulette method, and the selection probability is calculated according to the difference of the firework individual, wherein the difference is judged by the root mean square error of the atomic position; wherein N is an integer greater than or equal to 2; the candidate set includes current generation fireworks, exploding sparks and variant sparks.
4. The molecular conformation search method based on the mixed firework algorithm as claimed in claim 3, wherein:
the explosion operator comprises a firework explosion range and the number of sparks generated by firework explosion;
the method for calculating the explosion range of the fireworks comprises the following steps: sorting the fireworks according to the fitness function value and dividing the fireworks into three equal parts; the first equal part of fireworks comprises fireworks with fitness function values belonging to a first preset range; the fireworks in the second equal part comprise fireworks with fitness function values belonging to a second preset range; the third equal part of fireworks comprises fireworks with fitness function values belonging to a third preset range;
the calculation formula of the number of sparks generated by the firework explosion is as follows:
Si＝M-ri
wherein S isiIndicating the number of sparks resulting from the explosion of fireworks, M indicating the number of sparks per fireworks which explode at most, riAnd the sequence number of the fitness function values of the fireworks is represented.
5. The molecular conformation search method based on the mixed firework algorithm as claimed in claim 4, wherein: the step S5 includes:
s51, local search is conducted on the current-generation fireworks, and whether the local optimal value is accepted or not is determined according to the metropolis criterion;
s52, exploding the current fireworks according to the calculation method of the fireworks explosion range and the calculation formula of the number of sparks generated by fireworks explosion to generate explosion sparks;
s53, carrying out local search on the explosion spark, and determining whether to accept the local optimal value according to metropolis criterion;
s54, randomly selecting L individuals from the contemporary fireworks and the explosion sparks to perform mutation according to a mutation operator to obtain mutation sparks;
s55, constructing the next-generation fireworks according to the next-generation fireworks selection strategy;
s56, if the fitness function value of the firework is converged or the maximum iteration number is reached, the search is ended; otherwise, the process proceeds to step S51.
6. The molecular conformation search method based on the mixed firework algorithm as claimed in any one of claims 1 to 5, wherein the local search algorithm comprises at least one of a BFGS algorithm, a DFP algorithm or an L-BFGS algorithm.
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