CN103116712B - Based on the protein HP model solution method of variable angle distance QEA algorithm - Google Patents
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Abstract
The present invention proposes the protein HP model solution method based on variable angle distance QEA algorithm, described method is by applying in protein secondary structure prediction by the quantum evolutionary algorithm based on variable angle distance, in quantum evolutionary algorithm frame foundation, introduce variable angle distance evolution strategy; HP configuration expression adopt flexible and efficient direction separate form; The diversity of separating to increase direction introduces a kind of direction traction mechanism, thus makes the present invention can find protein minimum energy configuration expeditiously; Described method adopts direction to separate the coordinate solution substituted in the past, is conducive to invalid closed loop HP configuration and detects and repair, thus raising method execution speed.The inventive method employs direction and separates technology or the strategies such as form, rollback method, direction traction policy, variable angle distance, makes efficiency of the present invention is more better than additive method.
Description
Technical field
The invention belongs to technical field of biological information, relate to the protein HP model solution method based on variable angle distance QEA algorithm.
Background technology
Protein folding, i.e. Protein Structure Prediction Problem are one of key problems of field of bioinformatics.Protein folding is how Study on Protein natural structure is formed, and how the polypeptied chain namely with certain amino acid sequence progressively forms space structure specific to protein.At present many " conformational disease " or claim " folding sick " all to cause molecule to assemble even precipitation to cause by protein folding is abnormal, such as: senile dementia (protein conformation change), cystic fibrosis (protein can not fold), familial hypercholesterolemia (protein Misfolding), family's amyloid disease (protein precipitation) etc.Therefore deeply understand protein folding mechanism and become urgent all the more.Along with going deep into of protein folding research, the biological function that protein has depends on the space folding structure of protein to a great extent, and the space structure therefore understanding protein is significant in field of biology.Means by experiment, can measure the formation of protein chain, but the space structure of protein will be observed very difficult.Research shows, according to amino acid sequence and the energy model of protein, utilizes theoretical calculation method to predict it is feasible scheme to protein structure.At present, the program has become an important tool in protein engineering.
Because the complicacy of authentic protein folding problem is too high, theoretical circles propose some simplified models.Wherein, research is the HP lattice model that Dill etc. proposes the most widely.This model is divided into two classes 20 seed amino acids: hydrophobic type amino acid (H) and hydrophilic amino acid (P).Each amino acid monomer can regard a bead as, and H is designated as black ball, and P is Archon.Like this, an amino acid sequence can be regarded as a chain be made up of black and white ball, and the centre of sphere distance of adjacent two balls is 1.HP lattice model is put amino acid chain zero lap in two dimension or three-dimensional unit grids, require that each ball must be put on a lattice point, and two balls adjacent on chain position after being put into lattice point plane or space is still adjacent.The energy function of HP model is:
Wherein, n is chain length.If i, j be all black ball and their centre of sphere distance is 1 time, σ
ij=-1; Other situation, σ
ij=0.
Although HP lattice model is a simplified model, still more difficult to solving of this model protein folding problem.This problem is proved to be np complete problem, and it is infeasible for therefore utilizing deterministic algorithm to carry out solving.In recent ten years, some scholars attempt using some evolution algorithm to solve HP model, find the configuration of minimum energy, as: genetic algorithm (GA), difference algorithm (DE), particle cluster algorithm (PSO) etc.These algorithms, are evolved to it by iterative manner as solution mainly with a certain specific scale HP lattice point coordinate, thus attempt to obtain optimum coordinates solution (i.e. minimum energy configuration), but these algorithms all exist certain defect.Wherein, genetic algorithm, along with popularization, cannot obtain optimum solution (as being the example of 50,60,64,85 for amino acid number, can not find the configuration of minimum energy), and speed of convergence is slow; Though difference algorithm is better than genetic algorithm performance, can find minimum energy configuration for disclosed example, speed of convergence also has much room for improvement; Though particle cluster algorithm has fine raising in speed of convergence, but there is the defect being easily absorbed in local optimum.
Summary of the invention
Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, for the defect of additive method, protein HP model solution method based on variable angle distance QEA algorithm is proposed, described method is by adopting the lattice point direction of HP configuration as solution, simplify the expression of HP configuration, the detection efficiency of invalid configuration overlap can be improved simultaneously; And then utilize the quantum evolutionary algorithm based on variable angle distance to carry out the optimizing of travel direction solution, and incoming direction traction technique improves the diversity that direction is separated during evolution, thus guaranteeing that separate diversity also improves speed of convergence simultaneously, final realization finds minimum energy protein configuration with minimum time cost.
In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:
Based on the protein HP model solution method of variable angle distance QEA algorithm, the concrete steps of described method are as follows:
Steps A, initialization quantum population Q (t), wherein t is evolutionary generation, and initial value is 0;
Step B, measures quantum population Q (t), and generate direction and separate population moveDirect (t), body represents a configuration one by one;
Step C, checks that direction is separated, judges whether configuration occurs closed loop; If there is closed loop, then configuration is invalid, utilizes the reparation of rollback method;
Step D, calculates fitness value to population moveDirect (t);
Step e, preserves the optimum solution bestSoFar in population moveDirect (t);
Step F, judges whether optimum solution bestSoFar is that disclosed minimum value or t reach maximum algebraically, if meet, then termination algorithm; Otherwise, continue next step;
Step G, adopts variable angle distance Quantum rotating gate evolvement method, upgrades Q (t), generate quantum population of new generation;
Step H, evolutionary generation t adds 1;
Step I, measures quantum population Q (t), generates direction of new generation and separates population moveDirect (t);
Step J, checks that direction is separated, and judges whether effectively (namely whether occurring closed loop) this configuration; If invalid, rollback method is utilized to repair;
Step K, calculates fitness value to population moveDirect (t);
Step L, the optimum solution assignment in selection bestSoFar and moveDirect (t) is to bestSoFar;
Step M, judges whether satisfied traction condition, if meet, then draws population moveDirect (t), and calculates fitness value, by the optimum solution assignment in bestSoFar and moveDirect (t) to bestSoFar; Go to step F.
In described steps A, initialization quantum population, make measure quantum bit be 0 or 1 probability be 1/2.
In described step B, measure the quantum bit in quantum population, generate binary bits, if be 00, corresponding direction value is 1, represents direction upwards; If be 01, corresponding direction value is i, represents direction to the right; If be 10, corresponding direction value is-1, represents that direction is downward; If be 11, corresponding direction value is-i, represents direction left; And then produce direction solution population.Wherein direction value 1 ,-1, i ,-i be all plural numbers, i is imaginary unit.
In described step C, described configuration occurs that closed loop refers to: separate according to direction and calculate any one section of direction value sum, if 0, then illustrate that closed loop appears in this configuration, this configuration is invalid.
In described step C, the reparation of described rollback method refers to: make conflict point select other direction, if conflicted with still having, then selects other directions above; If all directions are attempted all, still cannot repair, then return back to previous point, reparation be carried out to this point and attempts, until form an effective configuration.
In described step D, calculate fitness value refer to by direction solution to search on this configuration chain be not connected but spatially adjacent black ball to (H to) number, this numerical value is multiplied by-1, is the energy of this configuration.
In described step e, namely optimum solution is the individuality of minimum energy.
In described step G, variable angle distance strategy refers to and adopts angular distance to adjust the anglec of rotation, before rotation, first direction will be separated the form that population changes into binary bits, and recycling variable angle distance carries out quantum rotation evolution; Described anglec of rotation θ
jcalculate according to following formula:
The arbitrary constant of normal distribution between [2,10] that in formula, k chooses; J is quantum bit sequence number, and j is natural number;
represent a jth quantum bit in quantum chromosomes
and ground state | 0> and | the angular distance between 1>;
calculated by following formula:
In formula, α
jand β
jfor
probability amplitude; x
jfor
measured value 0 or 1; b
jfor a jth bit value 0 or 1 of current optimum scale-of-two solution b; ∧ is for shipping calculation.
In described step M, described traction condition refers to that optimum individual 10 generation did not change or every 30 generations; If meet this traction condition, then all configurations are drawn.
Traction object is that linear fraction on configuration is become folding chain, increase chain is not connected but adjacent H to (black ball to) number.Be conducive to a certain extent jumping out local optimum.
The invention has the beneficial effects as follows: the present invention proposes the protein HP model solution method based on variable angle distance QEA algorithm, described method is by applying in protein secondary structure prediction by the quantum evolutionary algorithm based on variable angle distance, in quantum evolutionary algorithm frame foundation, introduce variable angle distance evolution strategy; HP configuration expression adopt flexible and efficient direction separate form; In order to increase the diversity incoming direction traction mechanism of separating in direction, thus make the present invention can find protein minimum energy configuration expeditiously; Described method adopts direction to separate the coordinate solution substituted in the past, is conducive to invalid closed loop HP configuration and detects and repair, thus raising method execution speed.The inventive method employs technology or the strategies such as direction solution, rollback method, direction traction, variable angle distance, makes efficiency of the present invention is more better than additive method.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of the protein HP model solution method that the present invention is based on variable angle distance QEA algorithm.
Fig. 2 is the process flow diagram whether inspection protein HP configuration is invalid.
Fig. 3 is the process flow diagram of calculated direction solution fitness value.
Fig. 4 is variable angle distance evolution process flow diagram.
Fig. 5 is the results contrast of the inventive method and difference algorithm, particle cluster algorithm.
Embodiment
Below in conjunction with accompanying drawing, the protein HP model solution method based on variable angle distance QEA algorithm that the present invention proposes is described in detail:
As shown in Figure 1, the present invention is based on the protein HP model solution method of variable angle distance QEA algorithm, it is as follows that it performs step
The first step is initialization quantum population Q (t), and be provided with 2N quantum bit (N represented amino acid number), each quantum bit is:
(namely | 0> and | 1> equiprobability occur); Arrange population scale is 30 simultaneously.
Second step, measures quantum population Q (t), generates direction and separates population moveDirect (t).Measurement is carried out to the quantum bit of the 2N in individuality and generates scale-of-two, and convert scale-of-two solution to correspondence direction solution form.Rule is as follows: the direction value of 00 correspondence is 1, represents direction upwards; The direction value of 01 correspondence is i, represents direction to the right; The direction value of 10 correspondences is-1, represents that direction is downward; The direction value of 11 correspondences is-i, represents direction left.A final 2N binary bits converts N number of direction value (because last amino acid is directionless, therefore N number of direction is set to 0) to; Wherein direction value 1 ,-1, i ,-i be all plural numbers, i is imaginary unit.
3rd step: check and repair direction and separate population moveDirect (t).The configuration that direction is separated representated by individuality is checked whether to there is loop (i.e. invalid configuration), its basic thought carries out accumulation calculating to one section of direction value any in the solution of direction, if 0 expression exists loop, and last direction value is conflict point, need repair this point.Check whether for invalid configuration idiographic flow as shown in Figure 2, its detailed process is as follows:
(1) direction inputting a protein configuration is separated;
(2) defining variable i=2, wherein i represents the subscript of gal4 amino acid;
(3) judge whether i is less than or equal to HP lattice point number, in this way, stop checking; Otherwise carry out next step;
(4) variable k is set, is worth for i-1;
(5) the continuous direction value between k and i lattice point is added up;
(6) judge accumulated value, if 0, represent that i lattice point direction and k lattice point direction clash, and i is conflict point, exports i value; Otherwise, continue next step;
(7) judge k, if be less than 1, then before representing i, possessive case point checks complete, goes to (9); Otherwise, continue next step;
(8) k is from subtracting 1, goes to (5) and performs another section of HP lattice point conflict inspection;
(9) i is from adding 1, goes to (3).
After finding conflict, adopt rollback method to repair direction solution according to rreturn value i, namely attempt other 3 directions of amendment conflict point i, see and can manage conflict; As cannot, then return back to previous point (i-1) attempt repair.
4th step, the fitness value (energy value of configuration) of all individualities in calculated direction solution population moveDirect (t), namely configuration is not connected but adjacent H is multiplied by-1 to number.As shown in Figure 3, its detailed process is as follows:
(1) arranging variable count is 0, for recording connected but not adjacent H to number; Variable j=0 is HP lattice point subscript;
(2) judge whether j is less than HP lattice point number-3, if not, then fitness value is count* (-1), exports this value and stops algorithm; Otherwise, continue next step;
(3) judge whether j lattice point is H lattice point, in this way, continues next step; Otherwise j, from adding 1, goes to (2);
(4) arrange variable k=j+2, k represents HP lattice point subscript;
(5) judge whether k is less than HP lattice point number, in this way, continues next step; Otherwise j, from adding 1, goes to (2);
(6) judge whether k lattice point is H lattice point, if so, continues next step; Otherwise k adds 1, go to (5);
(7) direction value between k and j lattice point is added up;
(8) judge accumulated value be whether 1 ,-1, i or-i, in this way, show k lattice point and j lattice point be the adjacent but disjunct H in space to lattice point, then count is from adding 1; Then k is from adding 2, goes to (5); Wherein direction value 1 ,-1, i ,-i be all plural numbers, i is imaginary unit.
5th step, compares individuality, preserves the Fitness value and individual direction solution that have minimum energy in population with bestSoFar.
6th step, judges whether the energy whether evolutionary generation reaches maximum algebraically or current optimum individual is open minimum energy, if meet, stops; Otherwise continue next step.
7th step: t is upgraded for quantum population, rotated by variable angle distance and carry out quantum evolution, as shown in Figure 4, detailed process is as follows:
(1) input quantity daughter chromosome scale-of-two solution x, and variable i=0 is set, i represents the subscript of quantum bit Qubit;
(2) judging whether i is less than Qubit sum, if not being, stopping; Otherwise continue next step;
(3) judge whether the fitness value of optimum individual scale-of-two solution b is greater than the fitness value of current individual x, carries out next step, otherwise arrange angular distance if satisfy condition
be 0, go to (6);
(4) judge whether i-th of optimum individual binary string b is 0, and whether i-th of current individual x be 1.If meet, then current individual i-th Qubit will be to | 0> deflects, and angular distance
go to (6); Otherwise continue next step;
(5) judge whether i-th of b is 1, and whether i-th of x be 0.If meet, then current individual i-th Qubit will be to | 1> deflects, and angular distance
otherwise, angular distance
be 0;
(6) formula is utilized
calculate the anglec of rotation, wherein k chooses arbitrary constant between [2,10],
represent the angular distance of trying to achieve above;
(7) according to anglec of rotation θ
icarry out rotation to Qubit to evolve;
(8) i adds 1, goes to (2), carries out next Qubit angular distance and evolves;
Utilize process that current population is evolved towards optimum solution bestSoFar, thus obtain quantum population of new generation.
8th step: measure quantum population of new generation, produce new direction solution population, process is as described in second step.
9th step: separate population to direction and repair, process is as described in the 3rd step.
Tenth step: the fitness value of population is separated in the direction calculating a new generation, and process is as described in the 4th step.
11 step: by individual assignment minimum for fitness value in a new generation's individuality and bestSoFar to bestSoFar.
12 step, judges whether satisfied traction condition, if meet travel direction traction, calculates fitness value, bestSoFar and direction is separated optimum individual in population and is saved in bestSoFar.The traction condition of this method is: optimum individual nearly 10 generations did not change or every 30 generations.The overall thought of direction traction for straight chain in configuration is become folding chain, thus increases the adjacent H that is not connected as far as possible to number.Go to the 6th step.
The present invention tests the protein sequence that amino acid number is 20,24,25,36,48,50,60,64,85, and all can find disclosed corresponding minimum energy configuration, compare with other secondary protein structure prediction methods (genetic algorithm, difference algorithm and particle cluster algorithm), method of the present invention searches the time less spent by minimum energy, and efficiency is higher.These characteristics fully demonstrate the search capability of the inventive method and by force, are not easily absorbed in local optimum and efficiency advantages of higher.
Interpretation
In order to the high efficiency of the inventive method is described, better two class methods of performance (difference algorithm, particle cluster algorithm) is at present selected to carry out contrast test.The population scale that institute of the present invention extracting method is chosen is 30 (difference algorithm and particle cluster algorithm select 100), amino acid quantity elects 20,24,25,36,48,50,60,64,85 as, and maximum evolutionary generation experimentally scale is formulated (as 20,24,25,36 was 500 generations; 48,50,60,64 and 85 was 800 generations).In experimentation, 3 kinds of algorithms perform 25 times respectively, by adding up the average minimum energy value in per generation, can obtain the evolution comparative result (as shown in Figure 5) of three kinds of algorithms.For simplicity, this only show amino acid scale be 24,48,85 comparison diagram (scale of the scale of Fig. 5 a to be the scale of 24, Fig. 5 b be 48, Fig. 5 c is 85; ).In 3 width figure, straight line is difference algorithm, dotted line is particle cluster algorithm, propose QEA method in two the present invention of being scribed ss.Easily find out from figure, the inventive method first finds disclosed minimum energy than other two kinds of algorithms; Although particle cluster algorithm is lower than quantum evolutionary algorithm in the average minimum energy in some stage, and decline rate is very fast, but not as this method is stablized in speed of convergence, particularly in later stage average minimum energy lower than this method, on the whole, on algorithm performance lower than this method; Although difference algorithm finally also have found disclosed minimum energy value, can find out from average minimum energy figure its travelling speed and speed of convergence minimum.In sum, in three kinds of algorithms, the overall performance of this method is best.
Table 1 further illustrates three kinds of methods in the effect different protein sequences being found to minimum energy simultaneously.The scale that in table, secondary series (Size) is protein sequence, 3rd row (E*) are disclosed minimum value, third and fourth, the five row energy-minimum that searches out of corresponding three kinds of methods respectively, wherein the average minimum energy value after execution 25 times is shown in Avg list, represents the number of times finding minimum in 25 times in parenthesis.
Table 1
Easily find out from table, the present invention is when protein sequence is 60,64,85, and minimum energy mean value is higher than particle cluster algorithm, namely finds the number of times of open minimum value higher.Therefore, all can find out from table 1 and Fig. 5, the method in the present invention is better than other two kinds of algorithms from efficiency.
Claims (3)
1., based on the protein HP model solution method of variable angle distance QEA algorithm, it is characterized in that, the concrete steps of described method are as follows:
Steps A, initialization quantum population Q (t), wherein t is evolutionary generation, and initial value is 0;
Step B, measures quantum population Q (t), and generate direction and separate population moveDirect (t), body represents a configuration one by one;
Wherein measure the quantum bit in quantum population, generate binary bits, if be 00, corresponding direction value is 1, represents direction upwards; If be 01, corresponding direction value is i, represents direction to the right; If be 10, corresponding direction value is-1, represents that direction is downward; If be 11, corresponding direction value is-i, represents direction left; And then produce direction solution population; Wherein direction value 1 ,-1, i ,-i be all plural numbers, i is imaginary unit;
Step C, checks that direction is separated, judges whether that closed loop appears in configuration; If there is closed loop, then configuration is invalid, utilizes the reparation of rollback method;
Described configuration occurs that closed loop refers to: separate according to direction and calculate any one section of direction value sum, if 0, then illustrate that closed loop appears in this configuration, this configuration is invalid;
The reparation of described rollback method refers to: make conflict point select other direction, if conflicted with still having, selects other directions above; If all directions are attempted all, still cannot repair, then return back to previous point, reparation be carried out to this point and attempts, until form an effective configuration;
Step D, calculates fitness value to population moveDirect (t); Described calculating fitness value refers to: search black ball connected but spatially not adjacent on this configuration chain to number by direction solution, described black ball is multiplied by-1 to number, obtains fitness value, this fitness value is the energy of this configuration;
Step e, preserves the optimum solution bestSoFar in population moveDirect (t); Namely described optimum solution is the individuality of minimum energy;
Step F, judges whether optimum solution bestSoFar is that disclosed minimum value or t reach maximum algebraically, if meet, then termination algorithm; Otherwise, continue next step;
Step G, adopts variable angle distance Quantum rotating gate evolvement method, upgrades Q (t), generate quantum population of new generation;
Step H, evolutionary generation t adds 1;
Step I, measures quantum population Q (t), generates direction of new generation and separates population moveDirect (t);
Step J, checks that direction is separated, judges whether configuration occurs closed loop; If there is closed loop, then configuration is invalid, utilizes the reparation of rollback method;
Step K, calculates fitness value to population moveDirect (t);
Step L, by the optimum solution assignment in bestSoFar and moveDirect (t) to bestSoFar;
Step M, judges whether satisfied traction condition, if meet, then draws population moveDirect (t), and calculates fitness value, by the optimum solution assignment in bestSoFar and moveDirect (t) to bestSoFar; Go to step F;
Described traction condition refers to that optimum individual 10 generation did not change or every 30 generations; If meet this traction condition, then all configurations are drawn.
2. the protein HP model solution method based on variable angle distance QEA algorithm according to claim 1, is characterized in that, in described steps A, initialization quantum population, make measure quantum bit time be 0 or 1 probability be 1/2.
3. the protein HP model solution method based on variable angle distance QEA algorithm according to claim 1, it is characterized in that, in described step G, variable angle distance strategy refers to and adopts angular distance to adjust the anglec of rotation, before rotation, first direction will be separated the form that population changes into binary bits, recycling variable angle distance carries out quantum rotation evolution; Described anglec of rotation θ
jrepresent, calculate according to following formula:
The arbitrary constant of normal distribution between [2,10] that in formula, k chooses; J is quantum bit sequence number, and j is natural number;
represent a jth quantum bit in quantum chromosomes
and ground state | 0> and | the angular distance between 1>;
calculated by following formula:
In formula, α
jand β
jfor
probability amplitude; x
jfor
measured value 0 or 1; b
jfor a jth bit value 0 or 1 of current optimum scale-of-two solution b; ∧ is for shipping calculation.
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