Chaotic Inertia Weight Particle Swarm Optimization for PCR Primer Design

Transcription

1 Chaotc Inerta Weght Partcle Swarm Optmzaton for PCR Prmer Desgn Cheng-Hue Yang Department of Electronc Communcaton Engneerng, Natonal Kaohsung Marne Unversty Kaohsung, 811, Tawan Yu-Hue Cheng Department of Electronc Engneerng, Natonal Kaohsung Unversty of Appled Scences Kaohsung, 807, Tawan L-Yeh Chuang Department of Chemcal Engneerng & Insttute of Botechnology and Chemcal Engneerng, I-Shou Unversty Kaohsung, 840, Tawan and Cheng-Hong Yang Department of Electronc Engneerng, Natonal Kaohsung Unversty of Appled Scences Kaohsung, 807, Tawan ABSTRACT In order to provde feasble prmer sets for performng a polymerase chan reacton (PCR) experment, many prmer desgn methods have been proposed. However, the majorty of these methods requre a long tme to obtan an optmal soluton snce large quanttes of template DNA need to be analyzed, and the desgned prmer sets usually do not provde a specfc PCR product sze. In recent years, partcle swarm optmzaton (PSO) has been appled to solve many problems and yelded good results. In ths paper, a logstc map s proposed to determne the value of nerta weght of PSO (CIWPSO) to desgn feasble prmers. Accuraces for the prmer desgn of the Homo sapens RNA bndng motf proten 11 (RBM11), mrna (NM_144770), and the Homo sapens G proten-coupled receptor 78 (GPR78), mrna (NM_080819) were calculated. Fve hundred runs of PSO and the CIWPSO prmer desgn method were performed on dfferent PCR product lengths and the dfferent methods of calculatng the meltng temperature. A comparson of the accuracy results for PSO and CIWPSO prmer desgn showed that CIWPSO s superor to the PSO for prmer desgn. The proposed method could effectvely fnd optmal or near-optmal prmer sets. Keywords: Polymerase chan reacton (PCR), prmer desgn, partcle swarm optmzaton (PSO), chaos 1. INTRODUCTION A feasble prmer set s requred before performng polymerase chan reactons (PCR). The PCR method s used for fast mass duplcaton of DNA sequences [1] and s a common technology appled n the bomedcal and botechnology feld. Before a PCR experment can be successfully performed, a prmer set has to be desgned. In prmer desgn numerous constrants, such as the length, length dfference, GC content, meltng temperature (T m ), dfference of meltng temperature (T m-dff ), GC clamp, dmer, harpn and specfcty of a prmer par need to be consdered, and large quanttes of template DNA need to be analyzed. Manually desgnng prmers s unsutable due to the complexty of the processes nvolved. Consequently, desgn of feasble prmer sets usng automatc computaton s preferable. Many prmer desgn methods have been proposed to date for the desgn of feasble prmer sets. Kämpke et al. desgn prmers usng dynamc programmng [2]. Ths allows for desgnng multple prmers for multple target DNA sequences. However, the method requres a relatvely long tme to obtan a sutable prmer set. Chen et al. used thermodynamc theory to evaluate the ftness of prmers to develop the web-based tool PDA for prmer desgn [3] and Wu et al. proposed a genetc algorthm (GA) mtatng nature s process of evoluton and genetc operatons on chromosomes n order to acheve optmal solutons [4]. Hseh et al. developed an effcent algorthm usng automatc varable fxng and automatc redundant constrant elmnaton to tackle the bnary nteger programmng problem assocated wth the mnmal prmer set (MPS) selecton problem [5]. Wang et al. employed a greedy algorthm to generate a MPS specfcally annealed to all open readng frames (ORFs) n a gven mcrobal genome, thus mprovng the 44 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 11 - NUMBER 3 - YEAR 2013 ISSN:

2 hybrdzaton sgnals of mcroarray experments [6]. Mura et al. developed an algorthm that dentfes the specfcty-determnng subsequence (SDSS) of each prmer and examnes ts unqueness n the target genome [7]. We have prevously presented a memetc algorthm (MA) [8] and partcle swarm optmzaton (PSO) method [9] to search for feasble prmers. Durng the past decade, PSO has been appled to all knds of problems and yelded promsng results. PSO, developed by Kennedy and Eberhart n 1995 [10], s a populaton-based stochastc optmzaton technque that smulates the socal behavor of organsms, such as brds n a flock, and descrbes an automatcally evolvng system. However, many studes n the lterature report the premature convergence of PSO and that the process may get trapped n a local optmum easly when handlng complex multmodal problems [11-14]. Chaos has ergodc and stochastc propertes, and contans elements of certanty. By followng chaotc orbts, a global optmum or a good approxmaton may eventually be reached wth hgh probablty n a dynamc system. In ths paper, we use a logstc map to determne the value of nerta weght of PSO named (CIWPSO) to mprove the performance of the prmer desgn. Dfferent PCR product lengths and meltng temperature calculatons are used to compare the performances of PSO and CIWPSO. 2. PROBLEM DEFINITION The prmer desgn problem s defned n ths secton. Let T D be the template DNA sequence, whch s made up of base-nuclec acd codes of the DNA,.e., A, T, C, or G. T D can then be defned as follows: TD = { B B ' A' or ' T' or 'C' or 'G', Ζ } (1) where, B represents the base-nuclec acd sequence made up of the base-nuclec acd codes of the DNA; s the ndex of the poston on T D, and Z represents the regon of postve ntegers. The prmer desgn problem now conssts of fndng a par of sub-sequences n T D for correspondng constrants. One sub-sequence s called the forward prmer and the other s called the reverse prmer. The forward prmer and the reverse prmer are defned as follows: Pf = { B B {'A', 'T', 'C', 'G'}, Fs Fe TD, Ζ } (2) Pr = { B B {' A', ' T', ' C', 'G'}, Rs Re TD, Ζ } (3) where, P f s the forward prmer, and F s and F e denote the start ndex and the end ndex of P f n T D. P r s the reverse prmer, and R s and R e denote the start ndex and the end ndex of P r n T D. Together, P f and P r are called a prmer par. The ant-sense sequence of B s called B. Ths ant-sense sequence B s the reverse of the complementng sequence of B. In Fg. 1, the length of the template DNA s T l, the mnmum PCR product length s P mn, the maxmum PCR product length s P max, the start poston of the forward prmer s F s, the length of the forward prmer s F l, the PCR product length between the forward prmer and the reverse prmer s P l, the length of the reverse prmer s R l, the random range of F s s F s _ Range, and the length from F s to the template DNA end s P Range. Now, a vector gven by F s, F l, P l and R l can determne a prmer par. We defne ths vector P v as: P v = (F s, F l, P l, R l ) (4) In order to determne the reverse prmer start ndex, we use the followng equaton: R s = F s P l -R l (5) The forward prmer (P f ) and the reverse prmer (P r ) can both be obtaned through P v. Ths vector P v s the prototype of a partcle n the PSO, and later sectons wll use P v to perform PSO prmer desgn. Table 1 summarzes the parameters used n Fg PRIMER DESIGN METHOD The flowchart of the proposed method s shown n Fg. 2. The separate processes of 1) ntalzaton of partcle swarm, 2) determnaton of ntal nerta weght, 3) evaluaton of ftness value, 4) judgment of termnaton condton, 5) fndng pbest and gbest, 6) updatng of nerta weght usng chaos, and 7) updatng of velocty and poston of each partcle, are descrbed below. Parameter F s F l P l R l F s_ Range P mn P max P Range T l Fg. 1. Parameters of the template DNA and prmer set TABLE I. PARAMETERS USED IN FIGURE1. Descrpton Start poston of the forward prmer Length of the forward prmer PCR product length between forward prmer and reverse prmer Length of the reverse prmer Random range of F s Mnmum PCR product length Maxmum PCR product length Length from F s to the template DNA end Length of template DNA ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 11 - NUMBER 3 - YEAR

3 ftness functon, and the produced ftness value s mnmzed. A prmer length between 16 bps and 28 bps s consdered feasble for a PCR experment [4]. If a prmer s longer, ts specfcty may be hgher, and a relatvely hgh T m s requred. On the other hand, a relatvely short prmer may have a decreased specfcty. Hence, nether a prmer that s too long nor too short s sutable. We dd not nclude the length constrant n the ftness functon, because F l and R l are always lmted between the mnmum length and the maxmum length of the prmer under the constrants. The ftness value s provded by the followng ftness functons, whch are made up of Len dff (P v ), T m (P v ), T mdff (P v ), GC proporton (P v ), GC clamp (P v ), dmer(p v ), harpn(p v ) and specfcty(p v ), each of whch s descrbed below: Fg. 2. Flowchart of the proposed algorthm for PCR prmer desgn. 1) Intalzaton of partcle swarm Intally, ten partcles P v = (F s, F l, P l, R l ) are randomly generated as an ntal partcle swarm wthout duplcates. F s s randomly generated between 1 and (T l -P mn 1). F l s randomly generated between the mnmum length of the prmer and the maxmum length of the prmer. In the present study, the mnmum length of the prmer was set to 16 bps and the maxmum length of the prmer was set to 28 bps. In order to lmt the PCR product length, we dd not select P l = R e -F s 1, but nstead randomly generated P l between P mn and P max. R l was randomly generated n the same way as F l. Each partcle s gven a velocty (v). Ths velocty s randomly generated wthn 0~1. 2) Determnaton of ntal nerta weght Chaos s hghly senstve to ts ntal condtons. Small dfferences n the ntal condtons yeld wdely dvergng outcomes and can make long-term predcton mpossble [15]. Ths nerta weght s subsequently updated and fne tuned by a chaotc map. In ths paper, we ntalze an nerta weght equal to 0.8 whch s commonly used n other studes, to test the performance of CIWPSO. 3) Evaluaton of ftness value A ftness functon s used to evaluate the ftness value of each partcle n order to check whether the canddate prmers satsfy the desgn constrants or not. The prmer desgn constrants are used as estmated values for the Ftness( = 3 * ( Lendff ( GCproporton( GCclamp( ) 10 * ( Tm( Tmdff ( dmer( harpn( ) 50 * specfcty( (6) The weghts of components n the ftness functon are 3, 10 and 50 based on ther mportance. A larger weght ndcates that the constrant s more mportance. The weghts are can be adapted freely by users to dfferent condtons. A prmer length of 16 to 28 bps s consdered feasble for a PCR experment s consdered between 16 and 28 bps [4]. If a prmer s longer, ts specfcty may be hgher, and a relatvely hgh T m s requred. On the other hand, a relatvely short length decreases the specfcty. Hence, nether a prmer that s too long nor too short s sutable. In ths study, the prmer length s not consdered n the ftness functon snce the random values of F l and R l always satsfy the constrants. A prmer length dfference less than or equal to 3 bps of dfference for the forward prmer and the reverse prmer s consdered optmal [4]. The Len dff (P v ) functon s used to check ths condton. The Tm(P v ) functon s used to check whether the meltng temperature of a prmer par s between 50 o C and 62 o C. The Tm dff (P v ) functon checks whether the T m dfference between the forward and reverse prmer exceeds 5 o C, as a lower T m dfference ndcates a better prmer par. In ths study, the meltng temperatures (T m ) of prmers are calculated by the Wallace formula [16]. The computatonal formula for T m s: Tm W ( P) = (#G#C)*4(#A#T)*2 (7) where, P represents the forward prmer or reverse prmer, #G represents the number of G, #C represents the number of C, #A represents the number of A and # T represents the number of T. The suffx W represents the 46 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 11 - NUMBER 3 - YEAR 2013 ISSN:

4 formula whch was proposed by Wallace. Furthermore, a more elaborate equaton proposed by Bolton and McCarthy [17] that takes the onc strength, G and C content and the length of the prmer nto account was s also used n ths study. Tm BM ( P) = (log 10[Na ]) (8) 0.41 * (GC content) - 675/ P where, P represents a prmer and P represents the length of prmer P; [Na ] s the molar salt concentraton. The suffx BM represents the formula whch was proposed by Bolton and McCarthy. The GC proporton (P v ) functon s appled to evaluate the GC proporton n a prmer. It calculates the rato of nucleotde G and C that appear n a prmer. An approprate GC proporton n a prmer should be n the range of 40-60%. The GC clamp (P v ) functon s used to check whether the 3 termnal end of a prmer s G or C. It ensures that the prmer has a tghtly localzed hybrdzaton bond. Furthermore, the dmer(p v ) functon s used to check whether the forward prmer and the reverse prmer anneal to each other or anneal to themselves. The harpn(p v ) functon s used to check f a prmer anneal to tself. The annealng of prmers s detrmental to the PCR experment. Fnally, the specfcty(p v ) functon s used to judge whether the prmer reappears tself n the template DNA sequence, and thus t ensures the specfcty of the prmer. The PCR experment s more easly successful f the prmer s specfc whch means t s annealed to specfc poston of the template sequence. 4) Judgment of termnaton condton The proposed method s termnated when gbest has acheved the best poston,.e., ts ftness value s 0, or when a maxmum number of generatons have been reached. When the termnaton condton s reached, gbest s the optmal soluton for the prmer desgn n the respectve run. 5) Fndng pbest and gbest One of the characterstcs of PSO s that each partcle has a memory of ts own best experence. Ths s true for CIWPSO as well. Each partcle needs to fnd ts personal best poston and velocty (called pbest), and all partcles must determne the global best poston and velocty (called gbest). If the ftness of a partcle P v s better than the ftness of pbest n the prevous generaton, pbest wll be updated to P v n the generaton. If the ftness of a partcle P v s n turn better than gbest n the prevous generaton and s the best one n the generaton, gbest wll be updated to P v. Based on pbest and gbest, each partcle adjusts ts drecton n the generaton. 6) Updatng of nerta weght usng chaos In PSO, the nerta weght s used to balance the global and local search ablty. A large nerta weght facltates a global search whle a small nerta weght facltates a local search [18]. In order to adjust the search ablty, the nerta weght s changed dynamcally usng a chaotc system. In ths paper, we propose a logstc map to generate chaotc sequence for updatng nerta weght. The logstc map used to determne the value of nerta weght s descrbed by: w ( t 1) = 4.0 w( t) (1 w( t)), w( t) (0,1) (9) where the value of w at (t1)th teraton s represented by w(t1). 7) Updatng of velocty and poston of each partcle In each generaton, the partcles wll change ther poston and velocty. Equatons (20) and (21) gve the updatng formulas for each partcle. v p = w v c1 r1 ( s s g c r ( s s ) 2 2 ) (10) s = s v (11) In equatons (10) and (11), v s the updated velocty of the th partcle; v s the velocty of the th partcle; c 1 and c 2 are the acceleraton coeffcents; w s the nerta weght; r 1 and r 2 s a number whch s randomly generated wthn 0~1; s p s the g personal best poston of the th partcle; s s the global best poston of the partcles; s s the poston of the th partcle; s s the updated poston of the th partcle. In order to avod a partcle overshootng the lmts of F s, F l, P l and R l when beng updated, we use a random process to reset the poston of an unavalable partcle based on the prmer constrants. 4. RESULTS AND DISCUSSIONS Data sets and envronment The template sequence of the Homo sapens RNA bndng motf proten 11 (RBM11), mrna (NM_144770), and the Homo sapens G proten-coupled receptor 78 (GPR78), mrna (NM_080819) were tested wth PSO and the proposed method CIWPSO for prmer desgn. Fve man parameters, namely the number of teratons (generatons), the number of partcles, the nerta weght w, and the acceleraton coeffcent c 1 and c 2 were set n the PSO and CIWPSO prmer desgn methods for the computatonal smulatons. These values were set ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 11 - NUMBER 3 - YEAR

5 to 100, 10, 0.8, 2 and 2, respectvely. Fve hundred runs were performed wth the PSO and CIWPSO prmer desgn methods, wth PCR product lengths n 150~300 bps, 500~800 bps and 800~1000 bps, and a T m calculated by the Wallace formula and the Bolton and McCarthy formula. The smulated envronment used a Pentum 4 CPU 3.4 GHz and 1GB of RAM under Mcrosoft Wndows XP SP3. Comparson of the prmer desgn results The results of the PSO and CIWPSO prmer desgn methods for the Homo sapens RNA bndng motf proten 11 (RBM11), mrna (NM_144770), and the Homo sapens G proten-coupled receptor 78 (GPR78), mrna (NM_080819) wth dfferent product lengths are shown n Table II and Table III, respectvely. Average accuraces of 79.8 % and 84.3% were reached when the CIWPSO prmer desgn method wth the Wallace formula was used to desgn NM_ and NM_ for dfferent product lengths. However, the average accuraces only got up to 68.0% and 64.6% when PSO was used under the same crcumstances. The accuraces of the CIWPSO prmer desgn method are thus 12.3% and 23.2% hgher than for PSO prmer desgn method for the two template sequences. Furthermore, the average accuraces reached 75.3% and 73.3% when CIWPSO was used wth T m calculaton by the Bolton and McCarthy formula. The average accuraces only got up to 57.3% and 39.8% when PSO was used under these condtons. The accuraces of the CIWPSO prmer desgn method were thus 18.0% and 33.5% hgher than the accuraces of the PSO prmer desgn method for the two template sequences. The CIWPSO prmer desgn method also outperformed the PSO prmer desgn method n terms of the average runnng tme wth dfferent T m calculatons. The computatonally smulated results show that the performance of the proposed CIWPSO method s superor to the performance of PSO for the prmer desgn problem. The proposed chaos effect for nerta weght Chaos s a determnstc, random process found n non-lnear system. It s greatly senstve to ts ntal condtons. Small dfferences n ntal condtons yeld wdely dvergng outcomes makng long-term predcton mpossble [15]. Mathematcally, chaos may be consdered a source of randomness snce ts smple determnstc dynamcal behavor. In ths study, we propose a logstc map to generate chaotc sequences for updatng the nerta weght. The proposed chaotc map behaves chaotcally n (0, 1). Snce chaos possesses elements of certanty, ergodcty, and stochastc propertes, t was ntroduced to control the movement of the partcles. Ths allowed us to eventually reach a good approxmaton of optmal results wth hgh probablty. TABLE II. ACCURACY AND RUNNING TIME FOR THE PSO AND CIWPSO PRIMER DESIGN METHODS. COMPUTATIONALLY SIMULATED RESULTS FOR THE HOMO SAPIENS RNA BINDING MOTIF PROTEIN 11 (RBM11), MRNA (NM_144770) USING THE WALLACE FORMULA AND BOLTON AND MCCARTHY FORMULA WITH PCR PRODUCT LENGTHS IN 150 ~ 300 BPS, 500~800 BPS AND 800~1000 BPS. A, ACCURACY (%); T, RUNNING TIME (MS). BOLDFACE INDICATES HIGHEST VALUES. T m formula and prmer Wallace's formula Bolton and McCarthy formula desgn methods PSO CIWPSO PSO CIWPSO PCR product length a (%) t (ms) a (%) t (ms) a (%) t (ms) a (%) t (ms) 150~300 bps ~800 bps ~1000bps average TABLE III. ACCURACY AND RUNNING TIME FOR THE PSO AND CIWPSO PRIMER DESIGN METHODS. COMPUTATIONALLY SIMULATED RESULTS FOR THE HOMO SAPIENS G PROTEIN-COUPLED RECEPTOR 78 (GPR78), MRNA (NM_080819) USING THE WALLACE FORMULA AND BOLTON AND MCCARTHY FORMULA WITH PCR PRODUCT LENGTHS IN 150 ~ 300 BPS, 500~800 BPS AND 800~1000 BPS. A, ACCURACY (%); T, RUNNING TIME (MS). BOLDFACE INDICATES HIGHEST VALUES. T m formula and prmer Wallace's formula Bolton and McCarthy formula desgn methods PSO CIWPSO PSO CIWPSO PCR product length a (%) t (ms) a (%) t (ms) a (%) t (ms) a (%) t (ms) 150~300 bps ~800 bps ~1000bps average SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 11 - NUMBER 3 - YEAR 2013 ISSN:

6 5. CONCLUSION Prmer desgn has become an mportant ssue over the last decade. The qualty of prmers always nfluences whether a PCR experment s successful or not. To date, many prmer desgn methods and tools have been developed, but most of these are neffcent or fall short of desgnng optmal prmers pars for PCR experments. PSO s consdered an effcent algorthm wdely appled to solve varous optmzaton problems. However, PSO tends to get trapped n a local optmum easly when appled to complex problems. In ths study, we propose a logstc map embedded n PSO to mprove the performance of the prmer desgn. The proposed CIWPSO desgns optmal prmers wth prmer constrants, such as prmer length, prmer length dfference, GC proporton, PCR product length, meltng temperature (T m ), meltng temperature dfference (T m-dff ), GC clamp, dmers (ncludng cross-dmer and self-dmer), harpn and specfcty used to apprase the ftness values. Each constrant was gven a sutable weght based on ts sgnfcance. Through the evoluton of a ftness functon, feasble prmer sets could always be obtaned usng the CIWPSO method. The prmer desgn results show that dfferent methods of T m calculaton affect the sze of the prmer length and the meltng temperature. A shorter prmer length and lower temperature value were obtaned when Wallace formula was used to calculate Tm, whereas a longer prmer length and a hgher temperature value were obtaned when the Bolton and McCarthy formula was used to calculate Tm. The computatonally smulated results ndcate that the proposed method can desgn optmal or near-optmal prmer sets. The CIWPSO prmer desgn method could be a valuable tool for bologsts and researchers nvolved n related research felds. ACKNOWLEDGMENTS Ths work s partly supported by the Natonal Scence Councl n Tawan under grant NSC E REFERENCES [1] K. B. Mulls and F. A. Faloona, "Specfc synthess of DNA n vtro va a polymerase-catalyzed chan reacton," Methods Enzymol, vol. 155, pp , [2] T. Kämpke, M. Kennger, and M. Mecklenburg, "Effcent prmer desgn algorthms," Bonformatcs, vol. 17, pp , Mar [3] S. H. Chen, C. Y. Ln, C. S. Cho, C. Z. Lo, and C. A. Hsung, "Prmer Desgn Assstant (PDA): A web-based prmer desgn tool," Nuclec Acds Res, vol. 31, pp , Jul [4] J. S. Wu, C. Lee, C. C. Wu, and Y. L. Shue, "Prmer desgn usng genetc algorthm," Bonformatcs, vol. 20, pp , Jul [5] M. H. Hseh, W. C. Hsu, S. K. Chu, and C. M. Tzeng, "An effcent algorthm for mnmal prmer set selecton," Bonformatcs, vol. 19, pp , Jan [6] J. Wang, K. B. L, and W. K. Sung, "G-PRIMER: greedy algorthm for selectng mnmal prmer set," Bonformatcs, vol. 20, pp , Oct [7] F. Mura, C. Uematsu, Y. Sakak, and T. Ito, "A novel strategy to desgn hghly specfc PCR prmers based on the stablty and unqueness of 3'-end subsequences," Bonformatcs, vol. 21, pp , Dec [8] C. H. Yang, Y. H. Cheng, L. Y. Chuang, and H. W. Chang, "Specfc PCR product prmer desgn usng memetc algorthm," Botechnology progress, vol. 25, pp , [9] C. H. Yang, Y. H. Cheng, H. W. Chang, and L. Y. Chuang, "Prmer Desgn wth Specfc PCR Product usng Partcle Swarm Optmzaton," Internatonal Journal of Chemcal and Bomolecular Engneerng, vol. 3, pp , [10] J. Kennedy and R. Eberhart, "Partcle swarm optmzaton," IEEE Internatonal Conference on Neural Networks, vol. 4, pp , [11] F. Van den Bergh and A. P. Engelbrecht, "A cooperatve approach to partcle swarm optmzaton," IEEE Transactons on Evolutonary Computaton, vol. 8, pp , [12] J. J. Lang, A. K. Qn, P. N. Suganthan, and S. Baskar, "Comprehensve learnng partcle swarm optmzer for global optmzaton of multmodal functons," IEEE Transactons on Evolutonary Computaton, vol. 10, pp , [13] X. Yang, J. Yuan, J. Yuan, and H. Mao, "A modfed partcle swarm optmzer wth dynamc adaptaton," Appled Mathematcs and Computaton, vol. 189, pp , [14] S. T. Hseh, T. Y. Sun, C. C. Lu, and S. J. Tsa, "Effcent populaton utlzaton strategy for partcle swarm optmzer," IEEE Trans Syst Man Cybern B Cybern, vol. 39, pp , Apr [15] S. H. Kellert, In the wake of chaos: Unpredctable order n dynamcal systems: Unversty of Chcago Press, [16] R. B. Wallace, J. Shaffer, R. F. Murphy, J. Bonner, T. Hrose, and K. Itakura, "Hybrdzaton of synthetc olgodeoxyrbonucleotdes to ph ch 174 DNA: the effect of sngle base par msmatch," Nuclec Acds Res, vol. 6, pp , Aug [17] J. Sambrook, E. F. Frtsch, and T. Manats, Molecular clonng: Cold Sprng Harbor Laboratory Press Cold Sprng Harbor, NY, [18] Y. Sh, R. C. Eberhart, E. Team, and I. N. Kokomo, "Fuzzy adaptve partcle swarm optmzaton," Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton, vol. 1, pp , May ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 11 - NUMBER 3 - YEAR