Protein Structure Prediction using 2D HP Lattice Model Based on Integer Programming Approach

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1 212 International Congre on Informatic, Environment, Energy and Application-IEEA 212 IPCSIT vol.38 (212) (212) IACSIT Pre, Singapore Protein Structure Prediction uing 2D HP Lattice Model Baed on Integer Programming Approach Sayantan Mandal a, Nanda Dulal Jana b a,b Department of Information Technology National Intitute of Technology National Intitute of Technology, Durgapur Wet Bengal 71329, INDIA a pikuayantan@gmail.com, b nanda.ana@gmail.com Abtract. To predict tructure of protein from primary amino acid equence i computationally difficult. Protein fold on a lattice called conformation predict a native confirmation which ha maximum topological hydrophobic contact. In i paper we addre Integer Programming approach to predict protein tructure uing 2D quare HP lattice. We propoed meod at bound e conformational pace where protein equence are folded and dicard e ymmetric conformation. The propoed meod applied on ome benchmark equence of protein. The experimental reult how e efficiency and effectivene of e propoed meod. Keyword: Protein tructure prediction, Integer programming, HP lattice model, Bioinformatic, Hydrophilic hydrophobic amino acid, Protein 1. Introduction A protein i a equence formed by combination 2 amino acid. Amino acid are characterized by polar (hydrophilic) and non polar (hydrophobic) baed on it reidue. Thee amino acid are connected to each oer wi peptide bond to form a protein equence [5]. Protein equence are folded on lattice wi non overlapping amino acid chain. Thee elf avoiding conformation produced native tructure which have minimum energy configuration [2]. The native tructure i e 3D tructure of e protein equence. We need to know e native protein tructure o at we can find out e function of at protein tructure. There are many optimization algorim ued to predict e native confirmation of a protein. Again taking determinitic approach will take long time a e earch pace i huge, and earching in each and every folding in at earch pace take lot of time. In i work protein tructure prediction i formulated by integer programming meod. Confirmation pace contain huge number of confirmation for a protein. Finding e native confirmation from i pace take lot of time. Therefore it i neceary to bound e earch pace and dicard e ymmetric confirmation from at pace. Here we ued backtracking meod to avoid non-overlapping amino acid. Thi concept helped a lot in reducing time to find e native confirmation. 2. HP lattice model HP lattice model wa introduced by Dill [1] in The different type of 2 amino acid are categorized in hydrophobic (H) and hydrophilic (P) depending on affinity toward water. The HP lattice model ha ome advantage for PSP, ee are:

2 (i) Two amino acid are aid to be conecutive if peptide bond (covalent bond) occur between two amino acid. When ere i a contact between two non conecutive hydrophobic (H) amino acid take place en it caue reduction of free energy of e reultant molecule. So, protein reache ground tate, when number of non conecutive hydrophobic amino acid contact i maximize. (ii) Two hydrophobic (H) amino acid adacent on lattice form an H-H contact. (iii) Hydrophobic (H) amino acid cluter in middle and hydrophilic amino acid urrounding e cluter [4]. (iv) Each confirmation i a graph where at each vertex reide amino acid and edge denote peptide bond. (v) In i model even amino acid i alway contact wi odd amino acid a adacent on-lattice and vice vera. (vi) In 2D HP quare lattice model any amino acid except firt and lat amino acid, ha two peptide bond (adacent on equence) and maximum of two topological contact (adacent on lattice). HP lattice model of e optimized protein equence HPHPPHHPHPPHPHHPPHPH. Black circle (white circle) are hydrophobic (hydrophilic) amino acid. Continuou line repreent polypeptide bond and e dotted line denote H-H contact. Here maximum H-H contact i 9. Fig 1: optimized 2D HP lattice model Fig 2: Baic flowchart for earching feaible folding 3. Previou Work Protein tructure prediction uing Integer programming in [6], it take much longer time for mall equence. It earched many invalid folding make e program run for much more time. It alo checked folding which are valid but oe folding don t give optimum reult at any cot. In [6] ome algorim place a particular amino acid by defining ditance or range in lattice from centre coordinate of eir lattice model. In at way it reduce placing of an amino acid in impoible location. But till ere remain many invalid folding. 4. Meodology 4.1. Integer programming formulation of PSP In i ection we repreent a maematical model of protein tructure in 2D HP lattice model. The maematical formulation can be decribe in e following manner Obective: Maximize e number of H-H contact.

3 Subect to: Aignment: Each amino acid mut occupy one lattice point. Non-overlapping: No two amino acid may hare e ame lattice point. Connectivity: Every two amino acid at are conecutive in e protein equence mut occupy adacent lattice point. Therefore, e obective i to maximize e H-H contact and obtain e feaible olution, atifying e contraint, e aignment, non-overlapping and e connectivity. We conider a protein equence of n amino acid Xiki e K amino acid of e equence at ( i, ) poition on e 2D HP lattice model { 1 if K amino acid at ( i, ) i hydrophobic Let Xik if K amino acid i polar K i i K amino acid placed at (i,) { 1 if K amino acid i placed at point( i, ) Let Ki oerwie Y iku = 1 if bo Kiand K ' i( + 1) bo are hydrophobic, i.e. check between k node and node above it Y ikr = 1 if bo Kiand K '( i 1) bo are hydrophobic, i.e. check between k node and node right ide of it. + So, we need to maximize H-H bond Maximie Z = Yiku + Yikr k, i, Non-Overlapping K i 1 i, Connectivity Let K amino acid i placed at i,, o K i = 1, en, K+ 1 + K+ 1 + K+ 1 + K+ 1 = 1 ( i+ 1) i( + 1) i 1 i( 1) 4.2. Bound area for earch While earching all e feaible folding make algorim to run for long time. To reduce runtime we will bound e earching area, o at folding are compact and earching i done in defined bounded area. We know at hydrophobic amino acid form e inner core and polar amino acid urround at inner core of at amino acid and hence form a compact tructure. For example many tructure like which form traight graph or double line graph (for big leng erie) it i obviou at it will not give maximum HH contact, o we can dicard em. Structure wi many amino acid reide wiout any neighbour amino topologically connected are alo dicarded a it doen t form compact tructure. We have bounded e region uing e formula P= 2( n+ 3) where n i e leng of amino acid. Leng and bread of e conformational pace i P Propoed Meodology We will et 1 t amino acid at center of e lattice(n,n) and 2 nd one ut right of it (N+1,N). Fixing em will avoid rotational ymmetry. We follow a equence for traveral like i Up Right Down Left, let call i rule URDL rule. Each amino acid will have i et of rule one after anoer. If one amino acid i moved to new node on lattice en i rule will apply form tart for at amino acid. There will be a pointer to track current working node at i to be placed. Now according to e rule 3 rd amino acid will move up

4 direction, and o like at next amino acid will alo be placed in up direction till e lat amino acid i placed and pointer will point to N-1 node. Whenever lat amino acid i uccefully placed it mean we got one complete folding and calculate it HH contact. Now lat amino acid will move right according to rule and complete anoer folding. Now, lat node will try to place in e down direction wi repect to n-1 node, but ere i already N-2 node i placed o it will not place n amino acid in down direction and move to left direction according to rule and complete anoer folding. Now all e combination i completed, o it will backtrack one node back to N-2 amino acid and pointer point i node. Now e N-1 node i placed to right to N-2 node and pointer point to i node. Now a it got new coordinate e rule will be applicable from tart. Hence, N amino acid will be placed in e up direction wi repect to N-1 amino acid and complete anoer fold. In i way it keep on placing amino acid on lattice and check it HH bond. While placing we took many conideration about boundary. Flowchart hown in fig. 2 how e movement algorim Evaluating HH contact When we are getting valid folding on quare lattice model, we are checking for number of amino acid preent in e equence. We tart checking from firt amino acid and gradually move to lat amino acid. We firt check if at amino acid i hydrophobic or polar X ik = 1 If amino acid i polar en we check node in up direction and node in left direction. Y iku = 1 if bo K i and K i(+1) bo are hydrophobic, i.e. check between k node and node above it. Y ikr = 1 if bo K i and K (i+1) bo are hydrophobic, i.e. check between k node and node right ide of it. Let number of HH bond in amino acid ide chain= S Then number of amino HH bond in folding but not in chain: Total HH bond= ( iku ikr) Y + Y S i, When checking urrounding for even amino acid we will check it adacency wi odd amino acid dicarding all even amino acid and vice vera. 5. Reult and Dicuion In i ection, we explain e reult obtained by our propoed meod on variou benchmark equence [7] and compare i wi [6]. In table 1 how e benchmark equence wi leng and maximum H-H contact known to date. Seq No Sequence Seq. Len Max H-H 1 PHP 2 HPHP 4 HP 5 H PHP 2 HPHP 4 HP 5 HP 2 H 2 P PHP 2 HPHP 4 HP 5 HP 2 H 2 P 2 HP HPHP 2 H 2 PHP 2 HPH 2 P 2 HP H H 2 P 2 HP 2 HP 2 HP 2 HP 2 HP 2 H P 2 H P 2 HP 2 H 2 P 4 H 2 P 4 H 2 P 4 H Table 1: benchmark equence of PSP Seq No. Max HH bond >1 Hyun-uk Yoon [6] Propoed algorim IP1 Max IP2 Max time Max 4 >1hr 4 9 ec 4 min 6 >1hr 6 23min 6 hr 7 >1hr 7 12hr >1 hr 4 9 N/A N/A N/A N/A 36ec N/A N/A N/A N/A 5min N/A N/A N/A N/A 123min 8 Table 2: comparion In table 2 how e comparion of e reult wi our propoed meod. N/A repreent ey are not conidered i equence wi eir experiment. The maximum H-H contact obtained by [6] and propoed meod are ame, but time taken to evaluate e tructure by oer meod i le an e previou approach. They did not mention what wa e exact time taken to evaluate, ut mentioned greater an 1 hr. In i paper we give e exact time taken to evaluate tructure of e correponding equence.

5 It i clearly hown at time taken by i algorim i le an e algorim defined in IP1 or IP2. On 28 leng equence e time taken hown i greater an 1hr, but we took approx 12hr which i alo greater an 1hr but on leng 23 it alo hown time taken i greater an 1hr, o we can ay at time taken for leng 28 i more an 12hr. 6. Concluion and future work In i work, protein tructure prediction problem i formulated by Integer programming meod and propoed algorim wi bounded conformational earch pace predict e tructure of a protein. Many ymmetric tructure are alo been excluded from conformational earch pace. From e experimental reult it ha been hown at our propoed algorim i very effective and efficient in PSP. We would like to apply propoed algorim to cubic lattice by applying more parameter on i algorim. 7. Reference [1] Lau, K. and Dill, K. A., A lattice tatitical mechanic model of e conformation and equence pace of protein Macromolecule, vol. 22, pp , 1989 [2] Charle J. Eptein, Robert F. Goldberger, and Chritian B. Anfinen. The genetic control of tertiary protein tructure: Studie wi model ytem In Cold Spring Harbor Sympoium on Quantitative Biology, page , Vol. 28. [3] William E. Hart and Alana Newman. Protein Structure Prediction wi Lattice Model. 21 by CRC Pre. [4] Kit Fun Lau and Ken A. Dill. A lattice tatitical mechanic model of e conformation and equence pace of protein Macromolecule, 22: , [5] V Chandru, A DattaSharma, and V S A Kumar. The algorimic of folding protein on lattice. Dicrete Applied Maematic, 127(1): , Apr 23. [6] Hyun-uk Yoon. Optimization Approache to Protein Folding,Phd. Thei, School of Indutrial and Sytem Engineering,Georgia Intitute of Technology, December 26. [7] Thang N. Bui and Gnanaekaran Sundarra. An Efficient Genetic Algorim for Predicting Protein Tertiary Structure in e 2D HP Model, GECCO 5, June 25 29, 25, Wahington, DC, USA. [8] Wayne L. Winton, "Operation Reearch: Application and Algorim", Four Edition.