New Perturbation Model for Prediction of Amino Acid and Peptide Activity Coefficients

Transcription

1 Iranan Journal of Chemcal Engneerng Vol. 9, No. 2 (Sprng), 2012, IAChE Resea rch note New Perturbaton Model for Predcton of Amno Acd and Peptde Actvty Coeffcents M. R. Dehghan 1, E. Saleh 1,2, A. R. Fazlal 2 1- Thermodynamcs Research Laboratory, School of Chemcal Engneerng, Iran Unversty of Scence and Technology, Tehran, Iran 2- Department of Chemcal Engneerng, Faculty of Engneerng, Arak Unversty, Arak, Iran Abstract In ths work, a new thermodynamc model based on the perturbaton theory s presented. A new hard spheres equaton of state as a reference term s appled to correlate the actvty coeffcent of amno acds and peptdes n bnary aqueous solutons. The new hard sphere equaton of state has been recently proposed by Dehghan and Modarress [11] and has been appled for dfferent theores and showed excellent capablty. In ths model dpole-dpole and Lennard-Jones nteractons are consdered. The results have been compared wth smlar models and t s shown that applcaton of the new hard spheres equaton of state has caused an mprovement n the results of perturbaton model. Keywords: Actvty Coeffcent, Hard Sphere, Perturbaton Model, Amno Acd 1. Introducton In recent years, producton of bochemcals and pharmaceutcal materals has sgnfcantly ncreased. The hgh cost of separaton and concentraton of bomolecules from dlute aqueous soluton (whch can be as hgh as 90% of ther total manufacturng cost [1]) has encouraged researchers to fnd new methods for purfcaton of these solutons. Fractonal precptaton and crystallzaton methods are often used for separaton and concentraton of the bomolecules [1]. In ths regard, thermodynamc studes such as expermental and theoretcal studes for correlaton and predcton of actvty coeffcent of amno acds as the smplest bomolecules are valuable. Thermo physcal propertes are essental factors n the desgn of the separaton processes such as crystallzaton, dstllaton and lqud-lqud extracton. Durng the past decades, many scentsts have focused on determnaton of actvty coeffcents of amno acds as well as peptdes n aqueous solutons by expermental and theoretcal studes [2-12]. In 1989, local composton model (NRTL) was used by Chen et al. [2] Correspondng author: m_dehghan@ust.ac.r 34

2 Dehghan, Saleh, Fazlal for predcton of phase parttonng and amno acd solublty. After that, conventonal thermodynamc models ncludng group contrbuton methods, Wlson, UNIQUAC and UNIFAC models were used by Nass [6], Peres et al. [7], Jn et al. [8] and Gupta et al. [9], Pnho et al. [10], Kuramoch et al. [11] respectvely. Recently, the perturbaton theory has also been ncorporated nto the amno acd systems by Khoshkbarch and Vera [12] to correlate the actvty coeffcents of amno acds and peptdes n the aqueous solutons. In ths work, we present a new two parametrc model based on perturbaton theory for predcton of amno acds and peptdes actvty coeffcents. In ths model a new hard sphere equaton of state s used as a reference system. Ths hard sphere equaton of state was recently proposed by Dehghan and Modarress [13] and has shown sgnfcant ablty n comparson wth other hard sphere equaton of states. 2. Theory of the model The perturbaton theory was ntally developed by Zwanzg [14] and was extended to lquds by Barker and Henderson [15]. In ths theory, the total nteracton energy of the system s dvded nto two reference and perturbaton contrbutons. The perturbaton theory has the advantage of ncorporatng varous types of nteractons easly. In our model dfferent forms of nteractons have been consdered. In ths work a prmtve perturbaton model has been utlzed to gnore the hydrogen bondng between solvent and solute. However, the amno acds, and especally peptdes, are the chan lke molecules; nevertheless, n ths model they have been consdered as hard spheres contanng dpole moments just for the smplcty of the model. Based on these assumptons, the resdual chemcal potental of the amno acds can be defned as follows: R EF r r r kt kt kt PER (1) Where the superscrpts REF. and PER. denote the contrbutons of the reference and perturbaton term, respectvely. k s Boltzmann constant ( JK -1 ) and T s the absolute temperature. Generally hard sphere equatons of state are used as reference term. There are several hard sphere equatons of state n the lterature, n ths paper we have focused on usng a new hard spheres equaton of state whch was recently presented by Dehghan and Modarress [13]. We have utlzed ths Hard sphere EOS because of ts unque abltes. Ths hard sphere equaton of state was bult based on new hghly optmzed molecular dynamcs smulaton data. It s capable of meetng both the low densty and closed packed lmts of compressblty factor [13]. In ths model, the compressblty factor for pure hard spheres s presented as follows: Z [ p ]/(1 ) 11 4 (2) Where æ s equal to í 0 /í (í 0 s the occuped volume by hard spheres and í s the total volume). The mathematcal equaton for æ s defned as Eq. (3): Iranan Journal of Chemcal Engneerng, Vol.9, No. 2 35

3 New Perturbaton Model for Predcton of Amno Acd and Peptde Actvty Coeffcents 1 3 (3) 2 In the above equaton ó and ñ are the sze parameter and number densty respectvely. Applyng pure hard sphere compressblty factor, the resdual Helmholtz free energy A r, and the chemcal potental, ì r, can be determned as Eq. (5) and (6) respectvely. [,, ] Z 1 p d NkT 0 r, HS A T V N (4) The result of a combnaton of Eq. (2) and (4) has been presented as follows [13]: r, HS A [ T, V, N ] NkT (1 ) (1 ) (1 ) ln(1 ) kt A ( A NkT ( ) NkT r, HS r, HS r, HS T, V, j (5) (6) The perturbaton term of chemcal potental n our model has been defned usng an equaton based on Barker-Henderson theory [15]. Accordng to Tepel-Gubbns [16] the chemcal potental term can be calculated utlzng Eq. (7): Per HS 2 4 u ( r ) g ( r ) r dr (7) In whch; r, u(r), and g HS (r) are ntermolecular dstance, ntermolecular potental and radal dstrbuton functon, respectvely. Dfferent types of ntermolecular nteractons can be consdered. In ths work the most mportant ones such as dpole-dpole and dsperson nteracton energes have been consdered. Lenard-Jones model has been employed for consderng dsperson energy (Eq. (8)). Dpole-dpole nteractons have been defned as Eq. (9) [17]. u u 12 6 ( ) 4 L J r 12 6 D D (8) r r 4 D 3(4 ) ktr 0 r 2 6 (9) Where, å, D, å 0 and å r are depth potental well, dpole moment, permttvty of vacuum and relatve delectrc constant, respectvely. Combnng Eq. (8) and (9) the perturbaton part n resdual chemcal potental wll be derved as Eq. (10). 4 r, Per 8 3 D 4 [ ] (4 ) kt 0 r (10) In the above equaton ñ s number densty. Unsymmetrcal actvty coeffcent of soluton, ã, s related to the resdual chemcal potental accordng to Eq. (11): d ln (11) kt d In whch s chemcal potental of component n deal soluton. Resdual chemcal potental of amno acd s presented as follows: 36 Iranan Journal of Chemcal Engneerng, Vol. 9, No. 2

4 Dehghan, Saleh, Fazlal kt r A HS PER ln ln ln (12) A A A Soluton densty s a necessary physcal property data n calculaton of amno acd and peptde actvty coeffcents and ts accuracy s mportant. Although n prevous models pure solvent densty was appled as soluton densty, n ths work Eq. (13-14) proposed by Mshra-Ahluwala [18] was employed to predct soluton densty m. M d m / d V 0 S m v. 0 (13) (14) Where m and M are the molalty and molecular weght of amno acd, respectvely, and d 0 s densty of pure water at expermental condton. 3. Parameter estmaton In the presented model there are two adjustable parameters, sze and depth of potental well parameters, whch should be determned based on avalable expermental data on actvty coeffcent. Dpole moments of amno acds and peptdes are constant values. Dpole moments cannot be measured expermentally [17] and must be calculated through quantum mechancal approach. Usually, modelng softwares such as Hyperchem molecular modelng can be used for ths purpose [12]. The estmaton of parameters s a very mportant procedure, because ts results wll affect the predctablty of the model. In order to avod the local optmzaton nstead of global optmzaton, Davdon-Fletcher- Powell (DFP) [13] algorthm was used to avod the method of drect nverson of Hessan matrx. DFP s a well known procedure whch approxmates the nverse Hessan matrx to fnd the global mnmum. Adjustable parameters were determned through mnmzaton of objectve functon. Objectve functon was defned as follows: OF n 1 exp cal 2 n (15) Avalable expermental data on actvty coeffcent s molalty based whle calculated actvty coeffcents are based on mole fracton, n ths regard Eq. (16) s used to change the expermental actvty coeffcent from molalty based to mole fracton based. ( x ) ( m ) ln ln ln( M s m ) (16) In whch M s s molecular weght of solvent. The superscrpts x and m denote the molalty and the mole fracton base actvty coeffcents, respectvely. Fnally, devaton of the presented model from the expermental data was calculated usng root mean square devaton (RMSD) as shown below: RMSD n 1 exp cal ( ) n (17) Where ã exp s the expermental value of actvty coeffcent, ã cal s the calculated Iranan Journal of Chemcal Engneerng, Vol.9, No. 2 37

5 New Perturbaton Model for Predcton of Amno Acd and Peptde Actvty Coeffcents actvty coeffcent by Eq. (12), and n s number of data. 4. Results and dscusson In Fg.1 and 2, the actvty coeffcent of dfferent amno acds such as amno butyrc acd, alanne, hydroxporlne and threonne have been correlated usng a new model. It can be seen that the presented model could correlate the expermental values effcently. In Fg. 3 the same results have been presented for peptdes. As t s shown, the overall fttng s qute good and from the results t can be concluded that the appled modfcatons have mproved the fttng procedure. In Tables 1 and 2, calculated values for sze parameter and depth potental well have been presented. All adjusted values are n the acceptable range. Ths subject can be referred to the appled physcally meanngful assumptons n ths model. The obtaned results have been compared wth other models such as those presented by Khoshkbarch and Vera [12], Mortazavmanesh et. al.[19], Chen et al.[5], Gupta et al.[9] and fnally Pnho[10]. Calculated RMSD ndcates that ths model can correlate expermental data more accurately than the other ones. Table 2 shows that the presented model could correlate the actvty coeffcent of peptdes accurately. In the case of amno acds, the average RMSD n the present work s 0.34 whle for other models such as Khoshkbarch, Mortazavmanesh, Chen, Gupta, Hedemann and Pnho t s 0.89, 0.6, 1.51, 7.85 and 8 respectvely. Smlar results have been obtaned for peptdes. It s worth mentonng that n ths work just two adjustable parameters have been utlzed for correlaton. Meanwhle, t can be concluded that applyng new hard sphere equaton of state as well as modfcaton on soluton densty (as other researchers used densty of pure water) mproved the results of perturbaton theory n comparson wth other smlar models. Fgure 1. Actvty coeffcent of amno acds versus ther molaltes (all expermental data used were output from Fasman [20]) 38 Iranan Journal of Chemcal Engneerng, Vol. 9, No. 2

6 Dehghan, Saleh, Fazlal Fgure 2. Actvty coeffcent of amno acds versus ther molaltes (all expermental data used were output from Fasman [20]) Fgure 3. Actvty coeffcent of peptdes versus ther molaltes, (all expermental data used were output from Fasman [20]) Iranan Journal of Chemcal Engneerng, Vol.9, No. 2 39

7 New Perturbaton Model for Predcton of Amno Acd and Peptde Actvty Coeffcents Table 1. Calculated ó, å/k and RMSD from Correlaton of Amno Acds expermental Actvty Coeffcents 100 (6) 100 (5) 100 (4) 100 (3) 100 (2) 100 (1) ó10^10 (m) å/k(k) Amno acd Alanne o á-amno n-butyrc acd Glycne Hydroxyprolne Prolne Serne Threonne Average rmsd (1) Calculated n ths work; (2) Khoshkbarch-Vera [12]; (3) Mortazav manesh et al. [19]; (4) Chen et al. [5]; (5) Gupta and Hedemann [9]; (6) Pnho [10] Table 2. Calculated ó, å/k and RMSD from Correlaton of Peptdes Expermental Actvty Coeffcents. 100 (5) 100 (4) 100 (3) 100 (2) 100 (1) ó10 10 (m) å/k(k) Peptde Alanylalanne Alanylglycne Glycylalanne Glycylglycne Tr-glycne Average rmsd (1) Calculated n ths work; (2) Khoshkbarch-Vera [12]; (3) Mortazav manesh et al. [19]; (4) Chen et al. [5]; (6) Pnho [10] 5. Conclusons In ths work a new model based on perturbaton theory was developed for correlaton of expermental actvty coeffcents of amno acds and peptdes. In our model a new hard sphere equaton of state was used as a reference system. Dpoledpole and dsperson nteractons were consdered as perturbaton terms. In order to mprove the accuracy of the model an emprcal equaton was used for predcton of soluton densty. The results of ths work were compared wth prevous works and t was shown that the presented model was successful n correlaton of the expermental data. Ths subject can be referred to the followng tems: frst of all, applcaton of new hghly optmzed molecular dynamcs 40 Iranan Journal of Chemcal Engneerng, Vol. 9, No. 2

8 Dehghan, Saleh, Fazlal smulaton data n constructng the new hard sphere equaton of state (HS-EOS). Secondly, capablty of the appled HS-EOS, to meet low densty as well as closed packed lmts of compressblty factor. Results of the model denote that the effect of reference term and soluton densty n chemcal potental of amno acds s sgnfcant. Compared to smlar models, the modfcatons caused an mprovement n the results of the perturbaton model. Nomenclature A r Resdual chemcal potental d Soluton densty d 0 Densty of pure water D Dpole moment g HS (r) k m M M S n N OF Radal dstrbuton functon Boltzmann constant Molalty of amno acd Molecular weght of amno acd Molecular weght of solvent Number of data Number of spheres Objectve functon r Intermolecular dstance radal dstrbuton functon T Absolute temperature u(r) Intermolecular potental V Molar volume ã Actvty coeffcent å Depth of potental well å 0 Permttvty of vacuum å r Relatve delectrc constant r ñ ó Z P Resdual chemcal potental Number densty Sze parameter Compressblty factor References [1] Belter, P. A., Cussler, E. L. and Hu, W. S., Boseparton, John Wley, New York, (1998). [2] Dehghan, M. R., Modarress, H. and Bakhsh, A., "Modelng and predcton of actvty coeffcent rato of electrolytes n aqueous electrolyte soluton contanng amno acds usng artfcal neural network", Flud Phase Equlb, 244, , (2006). [3] Dehghan, M. R., Modarress, H. and Monrfar, M., "Measurement and modelng of mean actvty coeffcents of NaBr and amno acd n (Sodum Bromde+Potassum Phosphate + Glycne + water) at and K", J. Chem. Thermodynamcs, 37, , (2005). [4] Dehghan, M. R., Modarress, H. and Monrfar, M., "Measurement and modellng of mean actvty coeffcents of aqueous mxed electrolyte soluton contanng glycne", J. Chem. Thermodynamcs, 38, , (2006). [5] Chen, C. C, Zhu, Y. and Evans, L. B., "Phase parttonng of bomolecules, solubltes of amno acds", Botechnol. Prog., 5, 111, (1989). [6] Nass, K. K., "Representaton of the solublty behavor of amno acds n water", AIChE J., 34, , (1988). [7] Peres, A. M. and Macedo, E. A., "Representaton of solubltes of amno-acds usng the unquac modelfor electrolytes", Chem. Eng. Sc., 49, Iranan Journal of Chemcal Engneerng, Vol.9, No. 2 41

9 New Perturbaton Model for Predcton of Amno Acd and Peptde Actvty Coeffcents , (1994). [8] Jn-Chen, L., Ju-Fang, L. and Y-Gu, L., "Study on the actvty coeffcents and the solubltes of amno acds n water by the perturbaton theory", Flud Phase Equlb., 142, 67-82, (1998). [9] Gupta, R. B. and Hedemann, R. A., "Solublty models for amno acds and antbotcs", AIChE J., 36, 333, (1990). [10] Pnho, S. P., Slva, C. M. and Macedo, E. A., "Solublty of amno acds: A group contrbuton model nvolvng phase and chemcal equlbra", Ind. Eng. Chem. Res., 33, , (1994). [11] Kuramoch, H., Nortom, H., Hoshno, D. and Nagahama, K., "Measurements of solubltes of two amno acds n water and predcton by the UNIFAC model", Botechnol. Prog. 12, , (1996). [12] Khoshkbarch, M. K. and Vera, J. H., "A smplfed perturbed hard sphere model for the actvty coeffcents of amno acds and peptdes n aqueous solutons", Ind. Eng. Chem. Res., 35, , (1996). [13] Dehghan, M. R. and Modarress, H., "Modfed equaton of state for pure and hard sphere mxtures n mean onc actvty coeffcent calculatons by mean sphercal approxmaton model", J. Molec. Lquds, 142, 45-52, (2008). [14] Zwanzg, R.W., "Hgh-temperature equaton of state by a perturbaton method. I. nonpolar gases", J. Chem. Phys., 22, 1420, (1954). [15] Barker, J. A. and Henderson, D., "Perturbaton theory and equaton of state for fluds. II. A successful theory of fluds", J. Chem. Phys., 47, 4714, (1967). [16] Tepel, T. M. and Gubbns, K. E. "Thermodynamc propertes of gases dssolved n electrolyte solutons", Ind. Eng. Chem. Fundam., 12, 18, (1973). [17] Matland, G. C., Rgby, M., Smth, E. B. and Wakeham. W. A., Intermolecular forces, Clarendon Press, Oxford, (1981). [18] Mshraw, A. K. and Ahluwala, J. C., "Apparent molal volumes of amno acds, N-acetylamno acds, and peptdes n aqueous solutons", J. Phys. Chem., , (1984). [19] Mortazav-Manesh, S., Ghotb, C. and Taghkhan, V., "A new model for predctng actvty coeffcents n aqueous solutons of amno acds and peptdes", J. Chem. Thermodynamcs, 35, , (2003). [20] Fasman, G. D., Handbook of bochemstry and molecular bology, 3 rd ed., Physcal and Chemcal Data, CRC Press, Cleveland, Vol. 1, (1976). 42 Iranan Journal of Chemcal Engneerng, Vol. 9, No. 2