Partial Molar Heat Capacities at Chosen Temperatures in the Range

Apr 5, 2012 - Partial Molar Heat Capacities at Chosen Temperatures in the Range. (298.15 to 328.15) K and Partial Molar Volumes at 298.15 K of...
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Partial Molar Heat Capacities at Chosen Temperatures in the Range (298.15 to 328.15) K and Partial Molar Volumes at 298.15 K of N-Acetyl-N′-methyl-L-α-amino Acid Amides in Aqueous Solution Sylwia Belica,* Katarzyna Łudzik, and Bartłomiej Pałecz* Department of Physical Chemistry, University of Łódź, 90-236 Łódź, Pomorska 165, Poland ABSTRACT: The heat capacities and the densities have been measured for aqueous solutions of N-acetyl-N′-methylglycinamide, N-acetyl-N′-methyl-L-α-alaninamide, N-acetyl-N′-methylL-α-valinamide, N-acetyl-N′-methyl-L-α-leucinamide, N-acetylN′-methyl-L-α-serinamide, N-acetyl-N′-methyl-L-α-threoninamide, and N-acetyl-N′-methyl-L-α-histidinamide. These results have been used to calculate the contributions of the amino acid side chains to the partial molar heat capacities and the partial molar volumes. The results were compared with literature data obtained for similar systems.

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INTRODUCTION The complicated structure of proteins containing many miscellaneous functional groups unusually hinders the interpretation of thermodynamic examinations of these biomolecules. Therefore, to know the behavior of proteins, one can study model compounds such as amino acids,1−7 small peptides,8−13 and also methyl amides of N-acetyl-L-α-amino acids represented by the general formula: CH3−CO−NH−CαHR−CO−N′H−CH314−19 where R represents the amino acid side substituents. The amides of amino acids contain in their structure an amino acid segment placed between two peptide bonds that border on nonpolar methyl groups on both sides. Ionic groups in the molecules of these compounds, derivatives of L-α-amino acids, have been eliminated. In many research centers, studies have been carried out to determine the contributions of particular functional groups of the amino acid side chain of model molecules to thermodynamic parameters such as standard partial molar volume and standard partial molar heat capacity.20,21 Based on the said chain contributions, some workers expected that it can be used to calculate Cop of protein in a hypothetical extended state in water.22 That is why it is important to determine the precise value of amino acid side chain contributions to examine properties like heat capacity or volume. In the present paper, the standard partial molar volumes and heat capacities of the methyl amides of N-acetyl-L-α-amino acids were determined by means of densimetric measurements and differential scanning calorimetry (DSC). The results obtained were used to determine the contributions of amino acid side substituents to the values of the thermodynamic functions determined.

N-acetyl-N′-methyl-L-α-serinamide, N-acetyl-N′-methyl- L-αthreoninamide, and N-acetyl-N′-methyl-L-α-histidinamide (Table 1), purchased from Bachem (all mass fraction purity 0.99), were dried for 72 h under reduced pressure at 298.15 K. The water used in the experiments was deionized and distilled three times and degassed under vacuum. The aqueous solutions examined were prepared by weight using a Mettler AE240 balance within the precision 1·10−5 g and have contained from 0.04000 to 0.40000 with the uncertainty of 2·10 −5 moles of N-acetyl-N′-methyl- L-αamino acid amides per kilogram of water. The heat capacity of aqueous solutions under a constant pressure was measured by means of a MicroDSCIII calorimeter from SETARAM. Measurements were carried out in a “batch” type cell made of Hastelloy C276 stainless steel with a volume of about 1 cm3 within the temperature range of (293.15 to 333.15) K. A change in the cell volume was neglected as the measurements were performed at temperatures lower than 358.15 K. Heat capacity, cp, was measured by the continuous method using a reference23 and a scanning rate of 0.35 K·min−1. The accuracy of the calorimetric measurement was checked by determining the specific heat capacity of water. In the range of examined temperatures the obtained results differed from literature data by less than 0.003 J·g−1·K−1 (0.07 %) and water was used as the reference substance, where the specific heat capacity value was taken from the paper of Zabransky and co-workers.24 The cp values for each temperature were calculated from the cp = f(T) function, by interpolation. Using a procedure described widely by Goralski et al.,23 the

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EXPERIMENTAL SECTION The substances used for investigations: N-acetyl-N′-methylglycinamide, N-acetyl-N′-methyl-L-α-alaninamide, N-acetyl-N′methyl-L-α-valinamide, N-acetyl-N′-methyl-L-α-leucinamide, © 2012 American Chemical Society

Received: November 30, 2011 Accepted: March 22, 2012 Published: April 5, 2012 1423

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Table 1. Names, Abbreviations, and Structures of N-Acetyl-N′-methyl-L-α-amino Acid Amides Examined and Discussed in This Work

o capacities in an infinitely dilute solution, Cp,2 , were determined for the systems under investigation:

uncertainty in the cp values can be estimated to be smaller than 0.20 %. The density of the aqueous solutions of the methyl amides of N-acetyl-L-α-amino acids was measured by means of a DMA 5000 densimeter from Anton Paar with an accuracy of 5·10−6 g·cm−3 at a temperature of 298.15 K. The density of outgassed water was measured before each measurement series, and the result obtained was compared with the table value.25 The discrepancies between reference and experimental data were smaller than 0.005 %.

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Cp ,2, ϕ = C po,2 + Scm2

In this equation, m2 describes the molality of the substance tested, and Sc determines the slope of a straight line. The o values of Cp,2 calculated, together with standard deviations and literature data, are given in Table 3. The heat capacities of the methyl amides of aliphatic N-acetyl-L-α-amino acids as a function of temperature are shown in Figure 1, while the temperature relationship of the heat capacities of the remaining amides tested is illustrated in Figure 2. These relationships are well-described by the quadratic equation. The values of heat capacity monotonically increase with increasing temperature, which indicates a lack of phase transitions within the temperature range investigated (Figures 1 and 2). The values of standard partial molar o heat capacities, Cp,2 , obtained by the experimental method under discussion for the methyl amides of N-acetylglycine, N-acetyl-L-α-alanine, N-acetyl-L-α-valine, and methyl amide of N-acetyl-L-α-leucine show a very good compatibility with literature data14 determined by the “step-by-step” method (Table 3; Figure 1). Diagram 3 shows the dependence of the standard molar heat capacity of the amides investigated on the number of CH2 groups in the aliphatic side chain

RESULTS AND DISCUSSION

The apparent molar heat capacity, Cp,2,ϕ, was determined from the following formula: Cp ,2, ϕ = M2cp +

1000(cp − c* p ,1) m2

(2)

(1)

where M2 is the molar weight of the solute, cp is the specific heat capacity of solution, c*p,1 is the specific heat capacity of water, and m2 is the molality of the solute. The Cp,2,ϕ values together with their uncertainties determined using the combination of standard uncertainties for complicated formulas are listed in Table 2. Using eq 2, the partial molar heat 1424

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Table 2. Apparent Molar Heat Capacities Cp,2,ϕ of Aqueous Solutions of N-Acetyl-N′-methyl Amino Acid Amides of Glycine, L-αAlanine, L-α-Valine, L-α-Leucine, L-α-Serine, L-α-Threonine, and L-α-Histidine in the Temperature Range (298.15 to 328.15) K; Estimated Uncertainties of Apparent Molar Heat Capacities Are in Parentheses Cp,2,ϕ/J·mol−1·K−1

m mol·kg

−1

298.15 K

303.15 K

308.15 K

0.04788 0.07153 0.09578 0.14390 0.19121

328.9 328.6 327.8 326.0 324.0

(2.3) (1.6) (1.2) (0.8) (0.6)

334.9 336.1 334.3 333.6 330.6

(2.3) (1.6) (1.2) (0.8) (0.6)

343.0 343.3 342.7 343.1 342.7

(2.3) (1.6) (1.2) (0.8) (0.6)

0.04476 0.05449 0.06826 0.09093 0.13756

431.0 429.7 431.5 429.6 427.5

(2.5) (2.0) (1.6) (1.2) (0.6)

436.8 437.5 437.5 437.0 434.7

(2.5) (2.0) (1.6) (1.2) (0.6)

444.0 444.1 442.3 442.9 442.4

(2.5) (2.0) (1.6) (1.2) (0.6)

0.06709 0.07607 0.07116 0.07867 0.08500 0.09044 0.10646 0.10882

581.7 583.9 581.6 582.0 583.9 582.8 579.9 580.5

(1.7) (1.5) (1.6) (1.4) (1.3) (1.2) (1.1) (1.0)

586.3 588.3 590.7 590.5 591.0 585.8 589.3 585.3

(1.7) (1.5) (1.6) (1.4) (1.3) (1.2) (1.1) (1.0)

592.9 595.9 597.0 597.2 597.1 594.1 596.7 593.4

(1.7) (1.5) (1.6) (1.4) (1.3) (1.2) (1.1) (1.0)

0.04635 0.05587 0.06999 0.09363 0.11292 0.14226

681.0 682.8 682.5 680.2 680.0 681.9

(2.4) (2.0) (1.6) (1.2) (1.0) (0.8)

683.5 684.7 684.3 682.6 682.2 684.4

(2.4) (2.0) (1.6) (1.2) (1.0) (0.8)

687.5 688.6 687.3 688.3 686.7 687.4

(2.4) (2.0) (1.6) (1.2) (1.0) (0.8)

0.05250 0.06334 0.07956 0.12778 0.28439 0.36582

383.1 392.7 392.7 377.2 370.9 386.3

(2.1) (1.8) (1.4) (0.9) (0.4) (0.3)

401.7 409.7 399.0 395.3 398.5 396.9

(2.1) (1.8) (1.4) (0.9) (0.4) (0.3)

412.3 424.0 420.0 416.6 415.5 413.4

(2.1) (1.8) (1.4) (0.9) (0.4) (0.3)

0.08836 0.11725 0.19176 0.23844 0.31179 0.38604 0.40626

472.0 471.0 468.5 469.4 467.5 467.0 464.0

(1.3) (1.0) (0.6) (0.5) (0.4) (0.3) (0.3)

484.4 488.0 481.0 484.8 476.8 476.6 482.0

(1.3) (1.0) (0.6) (0.5) (0.4) (0.3) (0.3)

501.6 500.7 496.9 499.1 496.1 493.9 493.3

(1.3) (1.0) (0.6) (0.5) (0.4) (0.3) (0.3)

0.05462 0.05509 0.06165 0.07774 0.09099 0.10903 0.13580 0.13767

595.6 594.5 600.5 595.1 596.7 598.8 598.5 597.9

(2.0) (2.0) (1.8) (1.4) (1.2) (1.0) (0.8) (0.8)

606.8 610.2 612.0 609.8 608.7 610.9 612.6 608.0

(2.0) (2.0) (1.8) (1.4) (1.2) (1.0) (0.8) (0.8)

621.8 618.1 620.9 621.4 619.4 622.5 621.0 624.6

(2.0) (2.0) (1.8) (1.4) (1.2) (1.0) (0.8) (0.8)

313.15 K AcGlyNHCH3 349.6 (2.3) 350.0 (1.6) 349.6 (1.2) 350.6 (0.8) 350.9 (0.6) AcAlaNHCH3 448.0 (2.5) 447.7 (2.0) 450.6 (1.6) 450.6 (1.2) 448.4 (0.6) AcValNHCH3 598.7 (1.7) 599.0 (1.5) 600.2 (1.6) 601.1 (1.4) 600.4 (1.3) 599.5 (1.2) 599.4 (1.1) 599.4 (1.0) AcLeuNHCH3 690.1 (2.4) 691.3 (2.0) 690.9 (1.6) 690.3 (1.2) 689.6 (1.0) 691.1 (0.8) AcSerNHCH3 427.2 (2.1) 435.2 (1.8) 435.7 (1.4) 429.4 (0.9) 433.6 (0.4) 425.6 (0.3) AcThrNHCH3 515.9 (1.3) 515.4 (1.0) 513.8 (0.6) 515.5 (0.5) 513.7 (0.4) 513.2 (0.3) 512.9 (0.3) AcHisNHCH3 634.0 (2.0) 628.9 (2.0) 631.6 (1.8) 629.5 (1.4) 635.5 (1.2) 630.5 (1.0) 637.1 (0.8) 631.6 (0.8)

in accordance with Savage and Wood's convention,26 where CH 3 groups correspond to 1.5 CH 2 , while CH = 0.5 CH2. The elongation of the side alkyl chain of the compounds investigated brings about an increase in the

318.15 K

323.15 K

328.15 K

357.0 358.4 359.1 358.2 360.0

(2.3) (1.6) (1.2) (0.8) (0.6)

360.1 361.7 361.6 361.4 363.0

(2.3) (1.6) (1.2) (0.8) (0.6)

365.8 366.7 367.2 369.7 369.1

(2.3) (1.6) (1.2) (0.8) (0.6)

453.6 453.6 453.3 453.9 453.5

(2.5) (2.0) (1.6) (1.2) (0.6)

457.5 458.3 457.3 458.2 458.0

(2.5) (2.0) (1.6) (1.2) (0.6)

459.8 462.9 462.4 461.2 461.5

(2.5) (2.0) (1.6) (1.2) (0.6)

603.9 600.5 602.0 603.7 602.0 601.4 601.9 602.7

(1.7) (1.5) (1.6) (1.4) (1.3) (1.2) (1.1) (1.0)

605.2 604.7 605.5 604.7 604.8 604.1 604.6 605.1

(1.7) (1.5) (1.6) (1.4) (1.3) (1.2) (1.1) (1.0)

606.5 608.0 608.1 608.2 608.7 606.5 608.1 607.0

(1.7) (1.5) (1.6) (1.4) (1.3) (1.2) (1.1) (1.0)

691.6 692.3 692.3 691.5 691.7 692.4

(2.4) (2.0) (1.6) (1.2) (1.0) (0.8)

693.1 694.7 694.8 693.4 693.6 694.8

(2.4) (2.0) (1.6) (1.2) (1.0) (0.8)

695.9 696.8 696.9 695.8 697.5 696.4

(2.4) (2.0) (1.6) (1.2) (1.0) (0.8)

440.5 444.3 442.1 445.9 441.6 436.3

(2.1) (1.8) (1.4) (0.9) (0.4) (0.3)

448.5 460.0 447.4 458.6 446.4 454.9

(2.1) (1.8) (1.4) (0.9) (0.4) (0.3)

458.1 474.6 453.8 466.6 460.0 470.3

(2.1) (1.8) (1.4) (0.9) (0.4) (0.3)

526.2 525.7 524.3 524.2 523.6 522.6 522.5

(1.3) (1.0) (0.6) (0.5) (0.4) (0.3) (0.3)

534.9 531.3 534.1 530.9 531.5 530.1 532.2

(1.3) (1.0) (0.6) (0.5) (0.4) (0.3) (0.3)

540.4 543.0 541.5 542.4 540.5 542.8 539.0

(1.3) (1.0) (0.6) (0.5) (0.4) (0.3) (0.3)

640.4 637.0 642.3 638.0 640.8 637.5 638.9 643.6

(2.0) (2.0) (1.8) (1.4) (1.2) (1.0) (0.8) (0.8)

648.2 652.0 651.7 648.2 646.7 654.0 650.6 650.9

(2.0) (2.0) (1.8) (1.4) (1.2) (1.0) (0.8) (0.8)

657.3 659.5 657.0 656.4 656.4 660.5 660.0 656.0

(2.0) (2.0) (1.8) (1.4) (1.2) (1.0) (0.8) (0.8)

o , of the methyl standard partial molar heat capacity, Cp,2 amides of N-acetyl- L -α-amino acids in the following sequence AcGlyNHCH3 < AcAlaNHCH3 < AcValNHCH3 < AcLeuNHCH3 (Figure 3). The free term of the equation

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Table 3. Partial Molar Heat Capacities at Infinite Dilution of Aqueous Solutions of N-Acetyl-N′-methyl Amino Acid Amides of Glycine, L-α-Alanine, L-α-Valine, L-α-Leucine, L-α-Serine, L-α-Threonine, and L-α-Histidine in the Temperature Range (298.15 to 328.15) K Cop,2/J·mol−1·K−1 T/K 298.15 303.15 308.15 313.15 318.15 323.15 328.15 a

AcGlyNHCH3 330.1 ± 329.6a 336.8 ± 343.3 ± 349.1 ± 346.0a 356.9 ± 359.9 ± 364.7 ± 360.7a

0.3 1.1 0.3 0.3 0.9 0.7 0.8

AcAlaNHCH3 432.6 ± 432.8a 438.8 ± 444.4 ± 448.6 ± 448.9a 453.6 ± 457.5 ± 461.1 ± 460.6a

1.1 0.8 0.8 1.3 0.3 0.6 1.3

AcValNHCH3 586.1 ± 588.8a 591.6 ± 596.7 ± 599.4 ± 597.8a 603.3 ± 605.2 ± 607.4 ± 607.3a

2.3 5.1 4.1 1.3 2.6 0.9 1.3

AcLeuNHCH3 682.8 ± 683.2a 684.2 ± 688.5 ± 690.5 ± 689.3a 691.2 ± 693.7 ± 696.3 ± 694.9a

AcSerNHCH3

AcThrNHCH3

AcHisNHCH3

1.4

388.1 ± 5.0

473.1 ± 0.9

594.9 ± 2.2

1.3 0.8 0.9

403.6 ± 3.3 419.8 ± 2.9 433.2 ± 3.0

487.6 ± 2.9 503.8 ± 0.9 516.2 ± 0.6

608.5 ± 2.2 618.6 ± 1.8 629.6 ± 3.1

0.5 1.0 0.8

444.2 ± 1.9 453.5 ± 4.6 461.7 ± 4.9

526.2 ± 0.3 534.5 ± 1.4 542.7 ± 1.4

639.9 ± 2.6 649.0 ± 2.7 657.9 ± 2.0

Liu et al.14

Figure 2. Temperature dependences of the partial molar heat o of the N-acetyl-N′-methyl amino acid amides of L-αcapacities Cp,2 serine, L-α-threonine, and L-α-histidine at infinite dilution.

Figure 1. Temperature dependences of the partial molar heat o of the N-acetyl-N′-methyl amino acid amides of glycine, capacities Cp,2 L-α-alanine, L-α-valine, and L-α-leucine, at infinite dilution; □, from ref 14; ⧫, this work (MicroDSCIII).

of a straight line (Figure 3) determines the contribution made by the main chain (skeleton) CH3−CO−NH−CαH− CO−NH−CH3 of the amides investigated to the values of the heat capacities determined (Table 4). The contribution of the CH2 group made to the total value of heat capacity is determined by the slope of straight line (Figure 3), which amounts to 85.9 (J·K−1·mol−1) at a temperature of 298.15 K. For comparison, the value of an analogous contribution of a

o Figure 3. Standard partial molar heat capacities Cp,2 of the N-acetyl-N′methyl amino acid amides of glycine, L-α-alanine, L-α-valine, and L-α-leucine as a function of number of groups CH2 in the side chain at 298.15 K.

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Table 4. Contributions of the CH2 Group Derived from Aliphatic Side Chains and Contributions of the Main Chain (CH3−CO−NH−CαH−CO−NH−CH3) to the Heat Capacities of N-Acetyl-N′-methyl Amino Acid Amides of Glycine, L-α-Alanine, L-α-Valine, and L-α-Leucine in the Temperature Range (298.15 to 328.15) K o Cp,2 /J·K−1·mol−1

T/K 298.15

303.15 308.15 313.15 318.15 323.15 328.15 a

CH2 85.9 ± 89.3a 90b 88c 83.1d 84.8 ± 84.3 ± 83.4 ± 83.1d 81.7 ± 81.3 ± 81.0 ± 77.5d

main chain 3.3

293.1 ± 9.7

3.1 3.0 3.0

301.0 ± 9.3 307.6 ± 8.8 313.4 ± 8.8

2.8 3.3 2.9

321.6 ± 8.2 325.3 ± 9.1 330.0 ± 8.5

Figure 5. Standard partial molar heat capacities Cpo of the main chain (CH3−CO−NH−CαH−CO−NH−CH3) of aliphatic N-acetyl-N′methyl amino acid amides as a function of temperature.

Hedwig et al. 14 have proposed a method for the determination of the heat capacity of amino acid side substituents consisting of determining the difference between the values of partial molar heat capacities, Cpo, of the methyl amides of N-acetyl-L-α-amino acids and the value of C po of the methyl amide of N-acetylglycine (AcGlyNHCH3). According to Hedwig, this difference corresponds to the contribution made by the amino acid side substituent R to the total heat capacity value of the compound under investigation. The authors14 assume in their model that the contribution of the skeleton of methyl amides is the same as that of the methyl amide of Nacetylglycine. In our opinion, the contributions made by side substituents can be determined using the heat capacity values of the main chain of the amide investigated obtained from the previously discussed correlation (Figure 3) for 298.15 K and the remaining temperatures (Table 4). Using the following equation:

Della Gatta et al.27 bNichols et al.29 cRoux et al.30 dHakin et al.31

CH2 group determined for the amides of N-acetyl-L-αamino acids (with an unblocked terminal NH2 group) at a temperature of 298.15 K amounts to 89.3 (J·K−1·mol−1).27 The contributions of the CH2 group and the main chain of the aliphatic methyl amides of N-acetyl-L-α-amino acids made to the heat capacities for all of the temperatures tested are listed in Table 4 and shown in Figures 4 and 5. The increase in temperature causes a drop in the heat capacity of CH2 brought into the global heat capacity value of the amide investigated (Figure 4), while the heat capacity values of the

C po(R) = C po,2(CH3CONH−CαH(R)−CONHCH3) − C po,2(CH3CONH−CαH−CONHCH3)

(3)

we determined the contributions made by the amino acid side substituents including that made by the proton being a side substituent of the methyl amide of N-acetylglycine to the total value of the partial molar heat capacity of all of the amides investigated. The values of the contributions of the amino acid side substituents of the amides of glycine, alanine, valine, leucine, serine, threonine, and histidine obtained are listed in Table 5. The heat capacity values of aliphatic substituents decrease with increasing temperature, while the heat capacities of polar amino acid substituents increase with increasing temperature (Table 5). The value of partial molar heat capacity of the statistic OH group of the methyl amide of N-acetyl-L-α-serine was obtained subtracting the partial molar heat capacities of the main chain and statistic CH2 group from the value of the partial molar heat capacity of a serine amide (Table 6). Similarly, the contribution of OH group to the value of the partial molar heat capacity of threonine derivative was calculated subtracting from the partial molar heat capacity of the methyl amide of N-acetyl-L-α-threonine the partial molar heat capacities of the main chain and two CH2 groups. The heat capacities values of OH group obtained for these

Figure 4. Standard partial molar heat capacities Cpo of the CH2 group in the side chains of aliphatic N-acetyl-N′-methyl amino acid amides as a function of temperature.

main chain increase with increasing temperature (Figure 5). The dependences of partial molar heat capacities on temperature for the derivatives of serine, threonine, and histidine (Figure 2) are very well-described by secondary polynomials. The values of Cop under discussion monotonically increase with no points of discontinuity, which indicates a lack of phase transitions within the temperature range investigated. The additional CH2 group of threonine amide brings about an increase in the partial molar heat capacity value compared to serine amide (Figure 2, Table 3). 1427

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o Table 5. Contributions to Heat Capacities of Amino Acids Side Chains (Cp,2 (−R)) of N-Acetyl-N′-methyl Amino Acid Amides of Glycine, L-α-Alanine, L-α-Valine, L-α-Leucine, L-α-Serine, L-α-Threonine, and L-α-Histidine in the Temperature Range (298.15 to 328.15) K o Cp,2 (−R)/J·K−1·mol−1

T/K

−Gly (−H)

−Ala (−CH3)

−Val (−C3H7)

−Leu (−C3H9)

−Ser (−CH2OH)

−Thr (−C2H4OH)

−His (−C4H6N2)

298.15

389.8 353.6e 436.2f

93.5

178.5

300.3

383.9 380.7 376.2 343.3e 417.4f 371.0 368.2 366.2 334.2e 407.2f

186.8 196.8 203.1

307.7 311.6 316.5

34.4 34.6

290.8 289.5 285.1 251.8e 329.2f 281.8 277.8 277.3 246.6e 319.2f

102.8 112.8 120.1

318.15 323.15 328.15

139.5 103.2e 157c 178d 183.5f 138.0 136.6 134.2 102.9e 171.6f 133.3 132.1 131.0 99.9e 163.9f

293.1 259.2e 339.5f

303.15 308.15 313.15

37.0 41.55a 45b 67c 90d 36.1 35.5 34.7

124.9 128.0 130.0

206.9 209.0 211.0

320.6 323.5 326.2

a Hakin et al.31 calculated from amino acid data. bHedwig et al.32 calculated from peptide derivative data. cNichols et al.29 calculated from aliphatic molecule data. dRoux et al.30 calculated from aliphatic molecule data. eLiu et al.14 data for methyl amides of N-acetyl-L-α-amino acids. fHakin and Hedwig33 calculated from N-acetyl amino acid amides.

apparent molar volume of the component, V2,ϕ, were calculated from the following equation:

Table 6. Standard Partial Molar Heat Capacities of o Functional Groups (Cp,2 ) of N-Acetyl-N′-methyl Amino Acid Amides Derivatives of L-α-Serine, L-α-Threonine, and L-α-Histidine in the Temperature Range (298.15 to 328.15) K o Cp,2

T/K 298.15

303.15 308.15 313.15 318.15 323.15 328.15

−1

o Cp,2

of OH group

−1

J·K ·mol

AcSerNHCH3 7.7 −4a 12b 19.3c 17.9 28.8 36.9 26.7c 42.6 46.5 49.4 27.2c

−1

−1

J·K ·mol

AcThrNHCH3 8.5 −4a 12b 19.3c 17.0 27.8 35.5 26.7c 41.3 46.1 51.4 27.2c

V2, ϕ =

M2 1000(ρ*1 − ρ) + ρ m2ρρ*1

(4)

where M2 is the molar weight of solute, ρ*1 is the density of pure solvent (water), and ρ is the density of amide solution with molality m2. The value of the partial molar volume of solute, V2o, in an infinitely dilute solution, was determined from the following equation:

of imidazole ring J·K−1·mol−1 AcHisNHCH3 214.5

V2, ϕ = V 2o + SV m2

222.8 227.5 233.3

(5)

where SV is the slope of the straight line. The values of V2o determined and their standard deviations are listed in Table 8 together with literature data. The dependence of the standard partial molar volumes V2o of the methyl amides of N-acetyl-L-α-amino acids with an alkyl side substituent in water on the number of CH2 groups26 is shown in Figure 6. The dependence was described with the equation of a straight line, in which the free term determines the contribution made by the main chain (CH3−CO−NH−CαH−CO−NH−CH3) and the slope of straight line describes the contribution made by the CH2 group. To determine the partial molar volumes of the amide side substituents, the value of the standard partial molar volume of the amide main chain, determined from the dependence shown in Figure 6, was subtracted from the standard partial molar volumes of the methyl amides of Nacetyl-L-α-amino acids. So the values of partial molar volumes of the amino acid side groups of the methyl amides of N-acetylL-α-amino acids such as glycine, L-α-alanine, L-α-valine, L-αleucine, L-α-serine, L-α-threonine, and L-α-histidine obtained in accordance with the equation:

238.3 242.0 245.6

a

Nichols et al.29 calculated from aliphatic molecule data. bRoux et al.30 calculated from aliphatic molecule data. cHakin et al.31 calculated from amino acid data.

amides are similar (Table 6). Similarly, the partial molar heat capacity value of the imidazole ring of histidine derivative was obtained subtracting the partial molar heat capacities of the main chain and CH2 group from the partial molar heat capacity of the methyl amide of N-acetyl-L-α-histidine (Table 6). The density values determined for the aqueous solutions of the methyl amides of N-acetylglycine, N-acetyl-L-α-alanine, N-acetyl-Lα-leucine, N-acetyl-L-α-serine, N-acetyl-L-α-threonine, and Nacetyl-L-α-histidine at a temperature of 298.15 K are listed in Table 7. Based on the density values, the apparent molar volumes of these substances were calculated together with their uncertainties determined using the combination of standard uncertainties for a complex formula (Table 7). The values of

V o(R) = V 2o(CH3CONH−CαH(R)−CONHCH3) − V 2o(CH3CONH−CαH−CONHCH3) 1428

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Table 7. Densities ρ and Apparent Molar Volumes V2,ϕ in Aqueous Solutions of N-Acetyl-N′-methyl Amino Acid Amides of Glycine, L-α-Alanine, L-α-Valine, L-α-Leucine, L-α-Serine, L-α-Threonine, and L-α-Histidine at 298.15 K; Estimated Uncertainties of Apparent Molar Volumes Are in Parentheses ρ

m2 mol·kg

−1

0.04565 0.05924 0.07804 0.09293 0.09870 0.15303 0.16149 0.17655 0.18888

0.01068 0.02402 0.03619 0.05311 0.06442 0.07609

g·cm

V2,ϕ −3

AcGlyNHCH3 0.998056 0.998352 0.998754 0.999062 0.999177 1.000320 1.000495 1.000791 1.001043 AcValNHCH3

0.997221 0.997425 0.997609 0.997865 0.998038 0.998216

ρ

m2 −1

cm ·mol 3

mol·kg

−1

V2,ϕ −3

g·cm

cm ·mol−1 3

AcAlaNHCH3 109.17 109.00 108.92 108.98 109.05 108.96 108.96 109.05 109.06

157.35 157.33 157.33 157.32 157.27 157.25

(0.11) (0.09) (0.06) (0.05) (0.05) (0.03) (0.03) (0.03) (0.03)

0.02067 0.04272 0.07510 0.10312 0.12255 0.14310 0.18164

0.04684 0.08312 0.09402 0.10067 0.10798 0.11565 0.12996 0.14144 0.16128

(0.47) (0.21) (0.14) (0.10) (0.08) (0.07)

AcSerNHCH3

0.14009 0.16553 0.18573 0.21538 0.23063 0.24848 0.26722 0.28365 0.31580 0.33292 0.37123

1.001848 1.002670 1.003355 1.004317 1.004920 1.005462 1.006090 1.006642 1.007686 1.008224 1.009314

125.54 125.74 125.66 125.75 125.30 125.50 125.45 125.40 125.40 125.45 125.84

(0.04) (0.03) (0.03) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.01)

0.03827 0.04755 0.04924 0.05453 0.05796 0.06518 0.06820 0.07517 0.07826 0.09152 0.09190 0.09948 0.11257 0.11878

AcHisNHCH3 0.998760 0.999201 0.999284 0.999470 0.999649 0.999989 1.000138 1.000413 1.000586 1.001157 1.001164 1.001492 1.002024 1.002276

165.48 164.88 164.73 165.71 165.22 164.93 164.72 165.22 164.75 164.97 165.08 165.15 165.54 165.68

(0.13) (0.11) (0.10) (0.09) (0.09) (0.08) (0.07) (0.07) (0.06) (0.06) (0.06) (0.05) (0.05) (0.04)

0.01090 0.01491 0.02341 0.03554 0.04981 0.06044 0.07489 0.08032 0.08444 0.09798 0.10498 0.12043 0.13453 0.14157 0.15386

0.997447 0.997844 0.998437 0.998944 0.999278 0.999644 1.000362 AcLeuNHCH3 0.997650 0.998122 0.998230 0.998343 0.998407 0.998565 0.998750 0.998921 0.999112 AcThrNHCH3 0.997424 0.997550 0.997823 0.998224 0.998675 0.999039 0.999482 0.999667 0.999799 1.000197 1.000410 1.000879 1.001359 1.001557 1.001957

126.15 126.25 126.10 126.07 126.18 126.17 125.94

(0.24) (0.12) (0.07) (0.05) (0.04) (0.04) (0.03)

173.67 173.57 173.91 173.60 173.87 173.31 173.30 173.13 173.55

(0.11) (0.06) (0.05) (0.05) (0.05) (0.04) (0.04) (0.04) (0.03)

142.38 142.54 142.43 142.01 142.16 141.74 142.04 141.88 141.87 142.22 142.28 142.40 142.07 142.23 142.10

(0.46) (0.34) (0.21) (0.14) (0.10) (0.08) (0.07) (0.06) (0.06) (0.05) (0.05) (0.04) (0.04) (0.04) (0.03)

of the statistic OH group of the methyl amide of N-acetyl-Lα-serine was obtained by subtracting the partial molar volumes of the main chain and statistic CH2 group from the partial molar volume of serine amide (Table 10). Similarly, the partial molar volume of OH group of the

are listed in Table 9. The value of the contribution of CH2 group obtained for the amides with alkyl substituent that amounts to 16.10 cm3·mol−1 is very compatible with the value of the statistic CH2 group obtained for tripeptides (15.9 cm3·mol−1).28 The value of the partial molar volume 1429

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Table 8. Standard Partial Molar Volumes (V2o) N-Acetyl-N′methyl Amino Acid Amides of Glycine, L-α-Alanine, L-αValine, L-α-Leucine, L-α-Serine, L-α-Threonine, and L-αHistidine at 298.15 K V2o substances AcGlyNHCH3

AcAlaNHCH3

AcValNHCH3 AcLeuNHCH3

AcSerNHCH3 AcThrNHCH3 AcHisNHCH3 a

cm3·mol−1 109.04 ± 109.20a 108.93b 126.22 ± 126.25a 122.87b 157.37 ± 157.37a 173.95 ± 174.35a 174.75b 125.61 ± 142.24 ± 164.86 ±

0.07

0.07

0.02 0.30

Figure 6. Standard partial molar volumes V2o of the N-acetyl-N′-methyl amino acid amides of glycine, L-α-alanine, L-α-valine, and L-α-leucine as a function of number of groups of CH2 in the side chain at 298.15 K.

0.20 0.14 0.31

Table 10. Standard Partial Molar Volumes (V2o) of Groups of N-Acetyl-N′-methyl Amino Acid Amides of Glycine, L-αAlanine, L-α-Valine, L-α-Leucine, L-α-Serine, L-α-Threonine, and L-α-Histidine at 298.15 K

Liu et al.14 bLeslie and Lilley.34

V2o/cm3·mol−1 the main chain aliphatic amides

Table 9. Standard Partial Molar Volumes (V2o) of Amino Acid Side Chains of N-Acetyl-N′-methyl Amino Acid Amides of Glycine, L-α-Alanine, L-α-Valine, L-α-Leucine, L-α-Serine, L-α-Threonine, and L-α-Histidine at 298.15 K

101.4

V2o amino acid side chain, −R −Gly (−H) −Ala (−CH3)

−Val (−C3H7)

−Leu (−C3H9)

−Ser (−CH2OH) −Thr (−C2H4OH) −His (−C4H6N2) a

cm ·mol−1 3

7.64 10.7a 24.82 26.7a 17.1b 17.04c 55.97 48.2b 47.90c 72.55 65.2b 65.07c 24.21 17.1d 40.84 33.1d 63.46 57.0d

−CH2 aliphatic amides 16.09 16a 15.9b 15.56c 15.82d

−OH AcSerNHCH3 8.11 8.74e 11.6c 12a

−OH imidazole ring AcThrNHCH3 AcHisNHCH3 8.65 8.74b 11.6c

47.4

a

Roux et al.30 calculated from aliphatic molecule data. bMishra and Ahluwalia28 from several homologous series of compounds. cArakawa et al.35 from several homologous series of compounds. dPal and Chauhan.36 eHakin et al.31 calculated from amino acid data.

Roux et al.30 bLiu et al.14 cHakin and Hedwig.33 dLee et al.13 Figure 7. Standard partial molar heat capacities Cpo of the amino acid residues as a function of hydrophobic solvent accessible solute surface area22 AHb.

methyl amide of N-acetyl-L-α-threonine was calculated by subtracting the contribution of the main chain and the double contribution of CH2 group from the value of the partial molar volume of threonine amide. The values of partial molar volume of OH groups obtained for the amides under discussion are similar (Table 10). The value of the partial molar volume of the imidazole ring of histidine derivative (Table 10) was calculated by subtracting the partial molar volumes of the main chain and CH2 group from the partial molar volume of the methyl amide of N-acetyl-Lα-histidine.

■

CONCLUSIONS

In this paper new measurements of heat capacity and density of N-acetyl-N′-methyl-L-α-serinamide, N-acetyl-N′-methyl-L-αthreoninamide, and N-acetyl-N′-methyl-L-α-histidinamide have been reported, and for N-acetyl-N′-methylglycinamide, N-acetylN′-methyl-L-α-alaninamide, N-acetyl-N′-methyl-L-α-valinamide, and N-acetyl-N′-methyl-L-α-leucinamide experimental data have 1430

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(7) Sahin, M.; Yesil, Z.; Gunel, M.; Tahiroglu, S.; Ayranci, E. Interactions of Glycine with Polyethylene Glycol Studied by Measurements of Density and Ultrasound Speed in Aqueous Solutions at Various Temperatures. Fluid Phase Equilib. 2011, 300, 155−161. (8) Yan, Z.; Wanga, X.; Xing, R.; Wang, J. Volumetric and Conductometric Studies on the Interactions of Dipeptides with Sodium Acetate and Sodium Butyrate in Aqueous Solutions at T = 298.15 K. J. Chem. Thermodyn. 2009, 41, 1343−1349. (9) Liu, J. L.; Hakin, A. W.; Hedwig, G. R. Volumetric Properties of Tripeptides with Non-polar Side-chains: Partial Molar Volumes at T = (288.15 to 313.15) K and Partial Molar Expansions at T = 298.15 K of Some Peptides of Sequence gly−X−gly in Aqueous Solution. J. Chem. Thermodyn. 2009, 41, 1232−1238. (10) Guo, L.; Xu, L.; Ma, L.; Lin, R. Transfer Volumes of Small Peptides from Water to Aqueous Xylitol Solutions at 298.15 K. J. Solution Chem. 2009, 38, 383−389. (11) Palecz, B.; Belica, S.; Nowicka, B. The Enthalpies of Solution of Some Dipeptides in Aqueous Urea Mixtures at T = 298.15 K. J. Chem. Thermodyn. 2009, 41, 923−925. (12) Pal, A.; Chauhana, N.; Kumarb, S. Interactions of Tripeptide with Glucose in Aqueous Solutions at Various Temperatures: A Volumetric and Ultrasonic Study. Thermochim. Acta 2010, 509, 24−32. (13) Lee, S.; Shek, Y. L.; Chalikian, T. V. Urea Interactions with Protein Groups: A Volumetric Study. Biopolymers 2010, 93, 866−879. (14) Liu, J. L.; Hakin, A. W.; Hedwig, G. R. Amino Acid Derivatives as Protein Side-chain Model Compounds: The Partial Molar Volumes and Heat Capacities of Some N-Acetyl-N′-methyl Amino Acid Amides in Aqueous Solution. J. Solution Chem. 2001, 30, 861−883. (15) Hedwig, G. R.; Hoiland, H. Partial Molar Isentropic and Isothermal Compressibilities of Some N-acetyl Amino Acid Amides in Aqueous Solution at 298.15 K. Phys. Chem. Chem. Phys. 2004, 6, 2440−2445. (16) Nowicka, B.; Palecz, B.; Belica, S.; Piekarski, H. The Interactions between Some N-acetyl-N′-methyl-L-α-amino Acid Amides and Urea in Water at 298.15 K. Thermochim. Acta 2006, 448, 41−43. (17) Masman, M. F.; Lovas, S.; Murphy, R. F.; Enritz, R. D.; Rodriguez, A. M. Conformational Preferences of N-Acetyl-L-leucineN′-methylamide. Gas-Phase and Solution Calculations on the Model Dipeptide. J. Phys. Chem. A 2007, 111, 10682−10691. (18) Palecz, B.; Belica, S.; Piekarski, H.; Jozwiak, A. Studies of Homogeneous Interactions of N-acetyl-N′-methyl-L-α-amino Acid Amides in Water at 298.15 K. Thermochim. Acta 2009, 489, 1−4. (19) Belica, S.; Palecz, B.; Nowicka, B.; Piekarski, H.; Jozwiak, A. Studies of Heterogeneous Interactions between N-acetyl-N′-methyl-Lα-amino Acid Amides and Urea Molecules in Water at 298.15 K. Thermochim. Acta 2010, 501, 19−23. (20) Kharakoz, D. P. Partial Volumes and Compressibilities of Extended Polypeptide Chains in Aqueous Solution: Additivity Scheme and Implication of Protein Unfolding at Normal and High Pressure. Biochemistry 1997, 36, 10276−10285. (21) Liu, J. L.; Hakin, A. W.; Hedwig, G. R. Partial Molar Volumes and Heat Capacities of the N-acetyl Amide Derivatives of the Amino Acids Asparagine, Glutamine, Tyrosine, and Lysine Monohydrochloride in Aqueous Solution at Temperatures from T = 288.15 K to T = 328.15 K. J. Chem. Thermodyn. 2006, 38, 1640−1650. (22) Jolicoeur, C.; Riedl, B.; Desrochers, D.; Lemelin, L. L.; Zamojska, R.; Enea, O. Solvation of Amino Acid Residues in Water and Urea-Water Mixtures: Volumes and Heat Capacities of 20 Amino Acids in Water and in 8 Molar Urea at 25 °C. J. Solution Chem. 1986, 15, 109−128. (23) Goralski, P.; Tkaczyk, M.; Chorazewski, M. Heat Capacities of α,ω-Dichloroalkanes at Temperatures from 284.15 to 353.15 K and a Group Additivity Analysis. J. Chem. Eng. Data 2003, 48, 492−496. (24) Zabransky, M.; Ruzicka, V.; Majer, V.; Domalski, E. Heat Capacity of Liquids: Critical Review and Recommended Values. J. Phys. Chem. Ref. Data, Monograph No. 6; American Chemical Society: Washington, DC, 1996. (25) Kell, G. S. Precise Representation of Volume Properties of Water at One Atmosphere. J. Chem. Eng. Data 1967, 12, 66−69.

been compared with those from literature. The observation has been made that the elongation of the side alkyl chain of the compounds investigated brings about an increase in the standard partial molar heat capacities, Cop,2 (or the standard partial molar volumes, Vo2), of the methyl amides of N-acetyl-Lα-amino acids in the following sequence AcGlyNHCH3 < AcAlaNHCH3 < AcValNHCH3 < AcLeuNHCH3 (Figures 3 and 6), thus with increasing hydrophobicity. The standard partial molar heat capacity and the standard partial molar volumes of examined substances match up to the additive scheme, where the aliphatic group has a contribution to the heat capacity value of about 85.91 J·K−1·mol−1 and to the volume value about 16.09 cm3·mol−1 and the main chain 293.1 J·K−1·mol−1 and 101.4 cm3·mol−1 at 298.15 K. As it is given in the literature, the side chain contributions to o Cp,2 and V2o of the amino acids in principle are derived from the difference between the properties of each amino acid (or its derivatives) and glycine (side chain C−H; or its derivatives). It means that the contribution of the hydrogen atom (in glycine or its derivatives) is also subtracted and the side chain o contributions to Cp,2 and V2o values from literature could be smaller in comparison with the values from this paper (Tables 5 and 9). The side chain contributions given in this work are more precisely calculated because this contributions are obtained by subtracting the standard partial molar heat capacity (or the standard partial molar volume) values only of the main o chain from the standard partial molar heat capacity values, Cp,2 o (or the standard partial molar volume, V 2), of the amide o investigated. The correlation of Cp,2 values of the amino acid residues with hydrophobic solvent accessible solute surface area22 (Figure 7) with a slope of 282 J·K−1·mol−1·nm−2 is better (a correlation coefficient of 0.995) than that in literature for amino acids which confirms that N-acetyl-N′-methyl-L-α-amino acids are a convenient set of compounds to receive the amino acid side chain contribution to the values of the heat capacities.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (S.B.); [email protected] (B.P.). Notes

The authors declare no competing financial interest.

■

REFERENCES

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