CN113035268A - Protein structure optimization method based on multi-objective decomposition optimization strategy - Google Patents

Protein structure optimization method based on multi-objective decomposition optimization strategy Download PDF

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CN113035268A
CN113035268A CN202110380246.6A CN202110380246A CN113035268A CN 113035268 A CN113035268 A CN 113035268A CN 202110380246 A CN202110380246 A CN 202110380246A CN 113035268 A CN113035268 A CN 113035268A
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周成鹏
沈红斌
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Abstract

A protein structure optimization method based on a multi-objective decomposition optimization strategy comprises the steps of firstly generating different conformations of a structure to be optimized through random disturbance to serve as target particles, namely, each particle corresponds to one conformation, allocating a unique weight vector to each particle, then updating the position and the speed of each particle according to the unique weight vector of each particle by utilizing a particle swarm algorithm, screening out non-dominant particles to be placed into a solution set during each updating, obtaining the non-dominant particle set which is a final solution set after the maximum iteration number is reached, and finally sequencing the structure in the final solution set by utilizing a marginal utility method and taking the conformation with the minimum marginal utility value as the optimized protein structure. The invention adopts multiple energy functions to relieve the deviation caused by a single energy function, utilizes the particle swarm algorithm to search in the protein structure space, and adopts the decomposition strategy to decompose the multi-target problem into a series of single-target subproblems, thereby avoiding the oscillation problem caused by unclear optimization direction of particles in the searching process and ensuring that the optimization effect is more stable.

Description

Protein structure optimization method based on multi-objective decomposition optimization strategy
Technical Field
The invention relates to a technology in the field of protein biology and pattern recognition, in particular to a protein structure optimization method based on a multi-objective decomposition optimization strategy.
Background
The structure and function of proteins are closely related, and the high-precision structure is important for understanding the functions of proteins. Optimization of protein structure is a key step to obtain more accurate protein structure. The existing technology generally combines an energy function and an optimization algorithm, takes information of an initial structure as a constraint, and iteratively searches in a protein conformation space to find a conformation with the lowest energy function value. The effectiveness of this technique depends on the accuracy of the energy function used, but because of the diversity of protein structures, the existing single energy function cannot accurately describe the states of all proteins, so when a search is performed by using a single energy function, the result is often biased, and the optimization fails. And the process of selecting a plurality of energy functions as multiple targets to guide the search can effectively alleviate potential deviation brought by a single energy function. However, most of these multi-objective methods use a dominant relationship to solve a non-dominant solution set, so that the direction of search cannot be directly controlled, and there is no suitable mechanism to maintain the diversity of the final solution set. The loss of diversity means the loss of the advantage of multi-objective optimization, and meanwhile, due to the lack of a clear optimization objective, the optimization process often has oscillation phenomenon, so that the convergence is weakened, and the protein structure is degraded.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a protein structure optimization method based on a multi-objective decomposition optimization strategy, which adopts multiple energy functions to relieve the deviation caused by a single energy function and utilizes a particle swarm algorithm to search in a protein structure space. When the multi-objective optimization problem is processed, a decomposition strategy is adopted to decompose the multi-objective problem into a series of single-objective subproblems, and the series of single-objective subproblems are connected with each particle in the particle swarm optimization, so that each particle has an exact optimization direction, the oscillation problem of the particle caused by unclear optimization direction in the searching process is avoided, the convergence of the algorithm is enhanced, the diversity of the finally obtained structure is ensured, and the optimization effect is more stable.
The invention is realized by the following technical scheme:
the invention relates to a protein structure optimization method based on a multi-objective decomposition optimization strategy, which comprises the steps of firstly generating different conformations of a structure to be optimized through random disturbance as target particles, namely, each particle corresponds to one conformation, allocating a unique weight vector to each particle, then updating the position and the speed of each particle according to the unique weight vector of each particle by utilizing a particle swarm algorithm, screening out non-dominant particles to be put into a solution set during each updating, obtaining the non-dominant particle set as a final solution set after the maximum iteration times are reached, and finally sequencing the structures in the final solution set by utilizing a marginal utility method and taking the conformation with the minimum marginal utility value as an optimized protein structure.
The method specifically comprises the following steps:
s1: given a protein structure of amino acid sequence length L, a defined number N of conformational populations { x ] are generated by random perturbation1，...xNI.e. a population of particles, each corresponding to a conformation, and vectorizing the particles.
The particle vectorization representation refers to: using an internal coordinate system, bond lengths and angles between conformational atoms are fixed, and only three torsion angles for each amino acid are chosen as references, and any one protein structure can be represented as xi＝[φ1，ψ1，ω1，...，φL，ψL]And a vector of length 3L-3.
S2: three energy values of each particle are calculated, and a weight vector with the same number as the number of the particles is generated. The weight vector and the decomposition strategy are combined and then assigned to each particle. Then initializing the speed of the particles, and constructing an initial solution set, wherein the initial solution set specifically comprises the following steps:
s21: the three energy functions used include Rosetta energy function, CHARM < energy function, RWplus energy function.
S22: weight vector λiThe method of using simple-lattice design for generation ofThe body is as follows:
Figure BDA0003012655440000021
wherein: n, N is the particle size, M is the number of energy functions, where M is 3, H is the separation distance, and satisfies
Figure BDA0003012655440000022
S23: the decomposition strategy adopts a PBI method, which specifically comprises the following steps: minimizegpbi(x|λ，z*)＝d1+θd2，
Figure BDA0003012655440000023
k∈
{Rosetta，RWplus，CHARMM}，F(x)＝(fRosetta(x)，fRWplus(x)，fCHARMM(x) θ is a penalty coefficient.
S24, initializing the personal optimal position of each particle to be the particle, defining the neighborhood of each particle to be T particles which are most similar to the weight vector of each particle, and initializing the global optimal position to be the particle with the minimum PBI value in the neighborhood.
S3: updating the current position and speed by utilizing a particle swarm algorithm, wherein the particle swarm updating specifically comprises the following steps: updating each particle update step
Figure BDA0003012655440000024
Updating the current position of each particle
Figure BDA0003012655440000025
Wherein:
Figure BDA0003012655440000026
is the update step length of the ith particle in the t iteration, w is the inertia coefficient, c1，c2As a cognition coefficient, r1，r2Is [0, 1 ]]A random number in between, and a random number,
Figure BDA0003012655440000027
for the individual optimal position of the ith particle in t iterations,
Figure BDA0003012655440000028
and (5) globally optimizing the structure of the ith particle in the process of t iterations.
S4: after each iteration, recalculating the three energy values of each particle, screening out non-dominated solutions and putting the non-dominated solutions into a solution set, wherein each particle updates the individual optimum and the global optimum according to the weight vector of the particle, and the method specifically comprises the following steps:
s41: respectively calculating three energy function values of respective particles
S42: determining non-dominant particles in the current particle swarm, comparing the particles with solutions in the solution set respectively, putting the particles into the solution set when the particles are not dominated by any solution in the solution set, and deleting the particles from the solution set when the solutions in the solution set are dominated by the current particles.
S43: and each particle calculates the fitness at the moment according to the weight vector of the particle and the current three energy values, and when the fitness is smaller than the optimal fitness of the individual, the optimal individual is updated to be the current position, otherwise, the optimal individual position is kept.
S44: and for the particles in each particle neighborhood, calculating the PBI values obtained by three energies of all the particles in the neighborhood and the weight vector of the current particle, selecting the particle with the minimum PBI value to compare with the global optimum of the current particle, updating the global optimum position of the current particle when the particle with the minimum PBI value is smaller than the global optimum of the current particle, and otherwise, keeping the global optimum position of the current particle unchanged.
S3 and S4 are performed until the maximum number of iterations is reached.
S5: sequencing the structures in the final solution set and outputting the sequenced structures as an optimal structure, specifically comprising:
s51: constructing a marginal utility function: u shapex，w＝w1fRosetta(x)+w2fCHARMM(x)+w3fRWplus(x) Wherein: x is the position of the particle, fRosetta(x)，fCHARMM(x)，fRWplus(x) For three energy function values, wiIs a rightA coefficient of gravity of and satisfies w1+w2+w3＝1，wi≥0；
S52: to wiRandom sampling is carried out for S times, and the value of each time is
Figure BDA0003012655440000031
Then, the values are averaged to obtain the final marginal utility value
Figure BDA0003012655440000032
S53: and sequencing each particle after obtaining the marginal utility value, and outputting the conformation with the minimum marginal utility value as the optimized protein structure.
The invention relates to a system for realizing the method, which comprises the following steps: the system comprises an initialization module, a multi-objective decomposition strategy optimization module and a candidate solution screening module. Wherein: the initialization module receives a protein structure to be optimized, generates a protein conformation population by using a random disturbance mode, distributes a weight vector to each protein conformation, initializes parameters, and inputs the conformation population into the multi-objective decomposition strategy optimization module. The multi-objective decomposition strategy optimization module adopts a particle swarm algorithm combined with a decomposition strategy to optimize each conformation in a specific direction, and after the maximum iteration times are reached, the protein conformation solution set is input into the candidate solution screening module. And the candidate solution screening module calculates the marginal utility value of each protein conformation, and outputs the conformation with the minimum marginal utility value as the optimized protein structure.
Technical effects
The invention integrally solves the defects of poor diversity and unstable optimization effect of the protein conformation solution set obtained by the prior art.
Compared with the prior art, the method adopts a decomposition strategy, so that each particle corresponds to a determined subproblem, and has an exact updating direction in the iterative optimization process, thereby avoiding the oscillation phenomenon, accelerating the convergence process and ensuring that the obtained solution has stronger convergence. Because each particle corresponds to a solution in an optimization direction, the diversity of understanding is ensured, the probability of successful optimization is increased, and the stability of an optimization result is higher.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The present embodiment takes the protein structure R1029 provided by the International protein Structure prediction Competition CASP14 as an example to illustrate a specific implementation manner.
As shown in FIG. 1, the present embodiment relates to a protein structure optimization method based on a multi-objective decomposition optimization strategy, which comprises the following steps:
s1: the initial protein structure R1029 amino acid sequence length 125 was randomly perturbed to generate a defined number N-66 of conformational populations { x }1，...x66I.e. a particle group, vectorizing the particles, and only selecting three torsion angles of each amino acid as a reference, so that any one protein structure can be represented as xi＝[φ1，ψ1，ω1，...，φ66，ψ66]The length is 3 × 66-3 ═ 195 dimensional vector.
S2: three energy values for each particle are calculated while generating weight vectors for 66 in three-dimensional space. The weight vector and the decomposition strategy are combined and then assigned to each particle. Then initializing the speed of the particles, and constructing an initial solution set, wherein the initial solution set specifically comprises the following steps:
s21: the energy functions used include Rosetta energy function, CHARMM energy function, RWplus energy function.
S22: weight vector λiThe generation of the method uses a simple-lattice design method, which comprises the following steps:
Figure BDA0003012655440000041
wherein: 66, where 3 is the number of energy functions and H10 is the separation distance of the coordinate axes, and are formed
Figure BDA0003012655440000042
A weight vector, which is assigned to 66 constellations respectivelyIn the particle.
S23: the decomposition strategy employs a PBI method with a penalty factor θ set to 20.
S24, initializing the personal optimal position of each particle to be the particle, simultaneously defining the neighborhood of each particle as 8 particles which are most similar to the weight vector of each particle, and then initializing the global optimal position to be the particle with the minimum PBI value in the neighborhood.
S3: updating the current position and speed by utilizing a particle swarm algorithm, wherein the particle swarm updating specifically comprises the following steps: updating each particle update step
Figure BDA0003012655440000043
Updating the current position of each particle
Figure BDA0003012655440000044
Wherein:
Figure BDA0003012655440000045
for the update step of the ith particle in the t iteration, w is the inertia coefficient and is set to 1.2, c1，c2Are set to 2, r for cognition coefficient1，r2Is [0, 1 ]]A random number in between, and a random number,
Figure BDA0003012655440000046
for the individual optimal position of the ith particle in t iterations,
Figure BDA0003012655440000047
and (5) globally optimizing the structure of the ith particle in the process of t iterations.
S4: after each iteration, recalculating the three energy values of each particle, judging the non-dominated relationship among the particles, screening out non-dominated solutions and putting the non-dominated solutions into a solution set, and updating the individual optimum and the global optimum of each particle according to the PBI value defined by the respective weight vector, which specifically comprises the following steps:
s41: and respectively calculating three energy function values of the respective particles, namely a Rosetta energy function, a CHARMM energy function and a RWPlus energy function.
S42: determining non-dominant particles in the current particle swarm, comparing the particles with solutions in the solution set respectively, putting the particles into the solution set when the particles are not dominated by any solution in the solution set, and deleting the particles from the solution set when the solutions in the solution set are dominated by the current particles.
S43: and each particle calculates the PBI value at the moment according to the weight vector of the particle and the current three energy values, and when the PBI value is less than the optimal fitness of the individual, the individual optimal is updated to be the current position, otherwise, the optimal position of the individual is kept.
S44: and for the particles in each particle neighborhood, calculating the PBI values obtained by three energies of all the particles in the neighborhood and the weight vector of the current particle, selecting the particle with the minimum PBI value to compare with the global optimum of the current particle, updating the global optimum position of the current particle when the particle with the minimum PBI value is smaller than the global optimum of the current particle, and otherwise, keeping the global optimum position of the current particle unchanged.
S3, S4 are repeated until the maximum number of iterations is met, where the maximum number of iterations is 3000.
S5: sequencing the structures in the final solution set and outputting the sequenced structures as an optimal structure, specifically comprising:
s51: constructing a marginal utility function: u shapex，w＝w1fRosetta(x)+w2fCHARMM(x)+w3fRWplus(x) Wherein: x is the position of the particle, fRosetta(x)，fCHARMM(x)，fRWplus(x) For three energy function values, wiIs a weight coefficient and satisfies w1+w2+w3＝1，wi≥0；
S52: to wiRandom sampling is carried out for 20000 times, and the value of each time is
Figure BDA0003012655440000051
Then, the values are averaged to obtain the final marginal utility value
Figure BDA0003012655440000052
S53: and sequencing each particle after obtaining the marginal utility value, and outputting the conformation with the minimum marginal utility value as the optimized protein structure.
The evaluation index adopted by the method is GDT-TS (Global distance testtotal score)
Through specific practical experiments, the obtained experimental data are as follows:
Figure BDA0003012655440000053
the other comparison methods are the leading methods in the field, and the data of the methods are all from the official website of the protein structure prediction competition CASP 14. It can be seen that the method improves the protein structure by 2.4 points under the GDT-TS index, which is higher than other methods.
Compared with the prior art, the method has the advantages that each particle corresponds to a specific sub-problem due to the adoption of a decomposition strategy, so that an exact updating direction is provided in the iterative optimization process, the oscillation phenomenon is avoided, the convergence process is accelerated, and the obtained solution has stronger convergence. And each particle corresponds to a solution in an optimization direction, so that the diversity of understanding is ensured, the possibility of optimization is increased, and the optimization result is more stable.
The foregoing embodiments may be modified in many different ways by those skilled in the art without departing from the spirit and scope of the invention, which is defined by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (6)

1. A protein structure optimization method based on a multi-objective decomposition optimization strategy is characterized in that firstly, different conformations of a structure to be optimized are generated through random disturbance and serve as target particles, namely each particle corresponds to one conformation, a unique weight vector is distributed to each particle, then the position and the speed of each particle are updated according to the unique weight vector of each particle by utilizing a particle swarm algorithm, non-dominant particles are screened out and put into a solution set every time the update is carried out, the non-dominant particle set obtained after the maximum iteration times are reached is a final solution set, and finally, a marginal utility method is used for sequencing the structure in the final solution set and the conformation with the minimum marginal utility value serves as the optimized protein structure.
2. The method for protein structure optimization based on multi-objective decomposition optimization strategy according to claim 1, which comprises the following steps:
s1: given a protein structure of amino acid sequence length L, a defined number N of conformational populations { x ] are generated by random perturbation1，...xNA particle group, wherein each particle corresponds to one conformation, and vectorizing representation is carried out on the particles;
s2: calculating three energy values of each particle, and generating weight vectors with the same quantity as the number of the particles; combining and then assigning a weight vector and a decomposition strategy to each particle; then initializing the speed of the particles, and constructing an initial solution set, wherein the initial solution set specifically comprises the following steps:
s21: the three energy functions comprise a Rosetta energy function, a CHARMM energy function and a RWPlus energy function;
s22: weight vector λiThe generation of the method uses a simple-lattice design method, which comprises the following steps:
Figure FDA0003012655430000011
wherein: n, N is the particle size, M is the number of energy functions, where M is 3, H is the separation distance, and satisfies
Figure FDA0003012655430000012
S23: the decomposition strategy adopts a PBI method, which specifically comprises the following steps: minimize gpbi(x|λ，z*)＝d1+θd2，subject to x∈Ω，
Figure FDA0003012655430000013
Figure FDA0003012655430000014
F(x)＝(fRosetta(x)，fRWplus(x)，fCHARMM(x) θ is a penalty coefficient;
s24, initializing the personal optimal position of each particle to be self, simultaneously defining the neighborhood of each particle as T particles which are most similar to the weight vector of each particle, and initializing the global optimal position to be the particle with the minimum PBI value in the neighborhood;
s3: updating the current position and speed by utilizing a particle swarm algorithm, wherein the particle swarm updating specifically comprises the following steps: updating each particle update step
Figure FDA0003012655430000015
Updating the current position of each particle
Figure FDA0003012655430000016
Wherein:
Figure FDA0003012655430000017
is the update step length of the ith particle in the t iteration, w is the inertia coefficient, c1，c2As a cognition coefficient, r1，r2Is [0, 1 ]]A random number in between, and a random number,
Figure FDA0003012655430000018
for the individual optimal position of the ith particle in t iterations,
Figure FDA0003012655430000019
the global optimal structure of the ith particle in the process of t iterations is obtained;
s4: after each iteration, recalculating the three energy values of each particle, screening out non-dominated solutions and putting the non-dominated solutions into a solution set, wherein each particle updates the individual optimum and the global optimum according to the weight vector of the particle, and the method specifically comprises the following steps:
s5: and executing S3 and S4 until the maximum iteration number is reached, and sequencing the structures in the final solution set and outputting the structures as optimal structures.
3. The method of claim 2, wherein the particle-vectorized representation is selected from the group consisting of: using an internal coordinate system, bond lengths and angles between conformational atoms are fixed, and only three torsion angles for each amino acid are chosen as references, and any one protein structure can be represented as xi＝[φ1，ψ1，ω1，...，φL，ψL]And a vector of length 3L-3.
4. The method for protein structure optimization based on multi-objective decomposition optimization strategy of claim 1, wherein the step 4 comprises:
s41: respectively calculating three energy function values of respective particles;
s42: determining non-dominant particles in the current particle swarm, comparing the particles with solutions in a solution set respectively, putting the particles into the solution set when the particles are not dominated by any solution in the solution set, and deleting the particles from the solution set when the solutions in the solution set are dominated by the current particles;
s43: each particle calculates the fitness at the moment according to the weight vector of the particle and the current three energy values, if the fitness is smaller than the optimal fitness of the individual, the optimal individual is updated to be the current position, and otherwise, the optimal individual position is kept;
s44: and for the particles in each particle neighborhood, calculating the PBI values obtained by three energies of all the particles in the neighborhood and the weight vector of the current particle, selecting the particle with the minimum PBI value to compare with the global optimum of the current particle, updating the global optimum position of the current particle when the particle with the minimum PBI value is smaller than the global optimum of the current particle, and otherwise, keeping the global optimum position of the current particle unchanged.
5. The method for protein structure optimization based on multi-objective decomposition optimization strategy of claim 1, wherein the step 5 comprises:
s51: constructing a marginal utility function: u shapex，w＝w1fRosetta(x)+w2fCHARMM(x)+w3fRWplus(x) Wherein: x is the position of the particle, fRosetta(x)，fCHARMM(x)，fRWplus(x) For three energy function values, wiIs a weight coefficient and satisfies w1+w2+w3＝1，wi≥0；
S52: to wiRandom sampling is carried out for S times, and the value of each time is
Figure FDA0003012655430000021
Then, the values are averaged to obtain the final marginal utility value
Figure FDA0003012655430000022
S53: and sequencing each particle after obtaining the marginal utility value, and outputting the conformation with the minimum marginal utility value as the optimized protein structure.
6. A system for implementing the protein structure optimization method based on the multi-objective decomposition optimization strategy according to any one of claims 1 to 5, which comprises: the system comprises an initialization module, a multi-objective decomposition strategy optimization module and a candidate solution screening module, wherein: the initialization module receives a protein structure to be optimized, a protein conformation population is generated in a random disturbance mode, meanwhile, a weight vector is distributed to each protein conformation, parameters are initialized, then the conformation population is input to the multi-objective decomposition strategy optimization module, the multi-objective decomposition strategy optimization module adopts a particle swarm algorithm to combine a decomposition strategy to optimize each conformation in a specific direction, after the maximum iteration times are reached, a protein conformation solution set is input to the candidate solution screening module, the candidate solution screening module calculates the marginal utility value of each protein conformation, and the conformation with the minimum marginal utility value is used as the optimized protein structure.
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