Heat capacities of solid, globular proteins

Macromol. Chem. Phys. 197,3791-3806 (1996) 3791

Heat capacities of solid, globular proteins

Ge Zhang, Stina Gerdes, Bernhurd Wunderlich*

Division of Analytical and Chemical Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6197; and Department of Chemistry, University of Tennessee, Knoxville, TN 37996- 1600

(Received: February 19, 1996; revised manuscript of May 17, 1996)

SUMMARY: In an ongoing effort to understand the thermodynamic properties of proteins, solid-

state heat capacities of poly(amino acid)s of all 20 naturally occurring amino acids and 4 copoly(amino acid)s were previously determined using our Advance THermal Analysis System (ATHAS). Recently, poly(L-methionine) and poly(L-phenylalanine) were further studied with new low-temperature measurements from 10 to 340 K. In addition, an analysis was performed on literature data of a first protein, zinc bovine insulin dimer Cs08H7s201s$\7130S12Zn. Good agreement was found between experiment and calculation. In the present work, we have investigated four additional anhydrous globular proteins, a- chymotrypsinogen, P-lactoglobulin, ovalbumin, and ribonuclease A. The heat capacity of each protein was measured from 130 to 420 K with differential scanning calorimetry, and the data were analyzed with both the ATHAS empirical addition scheme and a fitting to computations using an approximate vibrational spectrum. For the solid state, agreement between measurement and computation scheme could be accomplished to an average and root mean square percentage error of 0.5 3.2% for a-chymotrypsinogen, -0.8 2.5% for P-lactoglobulin, -0.4 f 1.8% for ovalbumin, and -0.7 f 2.2% for ribonuclease A. With these calculations, it was possible to link the macroscopic heat capacities to their microscopic causes, the group and skeletal vibrational motion. For each protein one set of parameters of the Tarasov function, @, and @,, represent the skeletal vibrational contributions to the heat capacity. They are obtained from a new optimization procedure [a-chymotrypsinogen: 631 K and 79 K (number of skeletal vibrators N, = 3005); P-lactoglobulin: 582 K and (79 K) (N, = 2 188); ovalbumin: 651 K and (79 K) (N, = 5008) and ribonuclease A: 717 K and (79 K) (Ns = I574), respectively]. Enthalpy, entropy, and Gibbs free energy can be derived for the solid state.

Introduction

The Advanced THermal Analysis System (ATHAS) has been developed in our laboratory for the evaluation of the thermal properties of linear macromolecules and related compounds, and to maintain a critically evaluated data bank'). As a result of these efforts, detailed thermodynamic information exists now for over 200 linear macromolecules and related small molecules. As building blocks for the study of proteins, the heat capacities of poly(amino acid)s of all 20 naturally occurring amino acids and four copoly(amino acid)s have been measured and The agreement was 22% or better for both the homopolymers and the copolymers. Furthermore, literature heat capacity data of a first protein, zinc bovine insulin dimer C508H7520,5~,30S12Zn, have been described with the ATHAS and agreed to 0.01 f 3.1% with measurement5). The present work is another step towards full thermodynamic characterization of proteins.

0 1996, Hiithig & Wepf Verlag, Zug CCC 1022- 1352/96/$10.00

3792 G. Zhang, S . Gerdes, B. Wunderlich

The ATHAS permits to link the macroscopic heat capacity to its microscopic cause. At low temperature, this cause is the vibrational motion. As the temperature increases, large-amplitude motion is initiated in the form of conformational motion (internal rotation) and, for small molecules, also translation and rotation. Often this large-amplitude motion begins at a well-defined phase transition (melting, glass transition, or disordering transition). A more gradual beginning of such large-amplitude motion in the amorphous phase of some poly(amino acid)s seems also possible, as was suggested earlier". Recently, it could be shown that more complicated molecules, particularly those which display mesophases, may even gain large-amplitude motion in the crystalline state at temperatures far below the disordering transitions7).

To achieve a full characterization, the measured low-temperature heat capacities are first fitted to an approximate vibrational spectrum, as described in more detail below. Then, the heat capacities are calculated for the whole temperature range, using the fitted skeletal plus the group vibrational spectra. At high temperatures the computed heat capacities can then be compared to the measured heat capacities to detect the onset of transitions and large-amplitude motion.

Only few measurements of heat capacities of anhydrous proteins exist in the literature'-''), however, there is a broad array of papers examining the thermal properties of hydrated proteins and protein solutions. The main effort is centered around the helidcoil transition and the heat and cold denaturation. It has been shown".") that the denaturation effect gets smaller and occurs at higher temperatures with decreasing hydration. Many authors think that the denaturation effect arises from protein-water interactions rather than from changes of the protein itself. In order to clarify such questions quantitatively, it is crucial to establish proper reference "base- lines" from heat capacity measurements of anhydrous proteins. For example, the heat capacity of hydrated collagen has a complicated temperature dependence that is very difficult to interpret without a reference based on the heat capacity of the anhydrous form which has a much clearer temperature dependen~e'~).

In this research, heat capacities at constant pressure, C,, were measured for four relatively simple anhydrous globular proteins, a-chymotrypsinogen, P-lactoglobulin, ovalbumin, and ribonuclease A. The temperature range was 130-420 K. The experimental C,, data for each protein, including low-temperature data in the literature for a-chymotrypsinogen'), were then fitted separately to functions of an approximate vibration frequency spectrum, so that the vibrational component of the heat capacities could be computed at any temperature. An improved fitting method, applicable to all polymers, was used for this task5). In addition, we have analyzed the protein heat capacity using the ATHAS emprirical addition scheme.

Experimental part The four proteins were selected to test our analysis and fitting methods because of

their well established structure and stability. A11 samples were purchased from Sigma Chemical Company and used without further purification. Bovine a-chymotrypsinogen is of type I1 (amino acids AA = 245, molar weight M = 25646 Da), six times crystallized and lyophilized; 8-Iactoglobulin from bovine milk (AA = 162, M = I8 367 Da) is three times crystallized and lyophilized; chicken ovalbumin of grade VII (AA = 385, M =

Heat capacities of solid, globular proteins 3793

42750 Da), crystallized and lyophilized; and ribonuclease A of type I-A from bovine pancreas (AA = 124, M = 13690 Da), five times crystallized, salt fractionated and chro- matically purified. The proteins were packaged with drying agent and stored frozen.

Sample masses, ranging from 5 to 15 mg, were measured on a Cahn 28 Electrobalance that is accurate to d.001 mg. Aluminium sample pans with a weight range of 25.3 2 0.05 mg were used.

The measurements were carried out on two different instruments. The low-temperature data from 130 to around 270 K were made on a dual sample differential scanning calori- meter (DSDSC), a TA Instruments 2100 Thermal Analyzer with a 912 DSDSC cooled with liquid nitrogen, as described earlier'3-'5). Runs of a baseline and a sapphire (A120g), as a standard, were made to calibrate all measurements. Experiments from 220 to 420 K were made on a Perkin-Elmer (PE) DSC-7 with a mechanical refrigeration accessory. Dry nitrogen gas was allowed to flow through the DSC cell at a rate of 20 mumin. In addition, the instrument is equipped with a dry box assembly, necessary to avoid signal instability due to drafts or changes in room temperature. Low pressure dry nitrogen gas is kept flowing at constant rate through the dry box to prevent condensation of atmospheric moisture. Each sample run was immediately followed by a baseline run with an empty pan and sapphire standard (A1,0,) run so that each trace is individually calibrated under the same experimental conditions. The standard heat capacity for sapphire was taken from ref.16). Each run on the PE DSC was divided into three sections to minimize effects of non-linear change of the isotherms. The heating rate used on both instruments was 10 Wmin.

Prior to each actual measurement, a heating run was performed to demoisturize the sample by heating to and holding at 120°C until no more water loss was detected (steady baseline and no further mass loss). By using this high-temperature drying, the sample should show no lowering of the glass transition due to water. The analysis can then serve as a baseline for future studies of the effect of even small amounts of water since any mobility introduced into the protein gives a quantitative response to the heat capacity [=I1 J/(K mol of mobilized molecular grouping)]. The data reported here are an average of at least three separate measurements.

Calculations

The ATHAS computation scheme is briefly explained as follows: The vibrational spectra of solid polymers are separated into group and skeletal vibrations (N = 3 x total number of atoms = Ng + N,). The number and types of group vibrations, N g , are derived by inspection of the chemical structure, and are then represented by a series of single frequencies and/or box-distributions over narrow frequency ranges. These frequencies can be taken from normal-mode calculations on isolated chains that are fitted to experimental IR and Raman frequencies of the macromolecule or suitable low molecular mass analogues. All approximate group vibrational frequencies that are relevant to the current study of poly(amino acid)s and proteins were collected by Roles et al.3). The remaining number of skeletal vibrations, N, , are not well represented by present day normal-mode calculations. The skeletal vibrations are thus approximated. A quadratic increase in frequency distribution from zero to vg , as found for isotropic solids, is assumed to describe the lowest (acoustic) vibrations. They account mainly for the intermolecular vibrations (Debye model). The skeletal vibrations of somewhat higher frequency, due mainly to intramolecular vibrations, are represented by an adjacent box distribution for the frequencies from


v3 to vI . They are representative of vibrations in a one-dimensional continuum. To obtain quantitative values for the limiting frequencies v3 and vl , one fits the skeletal heat capacity to a Tarasov function. The frequencies vl and vg are usually expressed as the corresponding theta temperatures, 0, , and 03, where hv/k = 0 with h and k representing Plank’s and Boltzmann’s constants”). The parameter O3 is most sensitive in the 0-50 K temperature region, while O1 is most sensitive in the 100-300 K region”, 19). The resulting approximate vibrational spectrum, consisting of group and skeletal vibrations, is then inverted to give the heat capacity at constant volume C,,. To convert the experimental Cp to C,, and vice versa, one can use the well- known thermodynamic relationships. Since expansivity and compressibility are, however, not known for these proteins, one needs to use the modified Nerst-Linde- mann approximation that was proven applicable for polymers”):

C, - C, = 3RAo (C, TIT:)

where A, is often a universal constant [3.9 x (K mol)/J], and T i refers to an estimated equilibrium melting temperature, 573 K for all four Since Eq. (1) yields only a small correction (4% at 300 K), the precision of A, and T: does not need to be better than &30% to match the typical experimental precision. Further- more, the difference between Cp and C,, decreases rapidly with temperature, so that below 180 K its contribution to the heat capacity is less than 3.0% and Cp could be used directly for the preliminary evaluation of O1 and 0318).

For a-chymotrypsinogen, the low-temperature experimental heat capacities for 10-300 K, less group vibrational contribution, were analyzed as the skeletal portion (N , = 3 005) by fitting to the Tarasov function with adjustable O1 and 0,. The procedure is described next. For the other three samples, fitting was done only with an adjustable O1. Due to a lack of low-temperature C, data, 0, had to be set to an estimated value. Prior to all fits, the measured Cp is converted to C,

The optimization procedure for obtaining O1 and 0, of the Tarasov function is newly constructed from a standard routine for energy minimization. A 20 by 20 mesh, with 0, between 10 and 200 K, and O1 between 200 and 960 K, is evaluated for the least-square error of fitting the experimental Cp to the Tarasov function. Absolute and relative errors can be used as fitting criteria. An interpolation method is then employed to determine the global minimum between mesh points that corre- sponds to the best fit. Fig. 1 shows the results for a-chymotrypsinogen in a 3-D mesh plot. When the low temperature Cp is unavailable, but O3 can be estimated, this procedure can easily be adapted to fit only O1 while 0, is fixed. For the other three proteins studied in this paper, whose C, data are available only from 130- 420 K, the single parameter fitting approach is taken.

Besides the detailed interpretation of the heat capacity in terms of an approximate vibrational spectrum, a purely empirical addition scheme was also developed in our laboratory, based on group contributions of the chain elements21322). This treatment is particularly useful for the description of the heat capacity of solid copolymers (usually sufficiently accurate above 100 K) and for liquid polymers over the whole temperature range. A first test of this method for biopolymers was made for four


Fig. 1. Three-dimensional-mesh plot of the fitting of the experimental, skeletal heat capacity to a Tarasov function with parameters @, and @, (the minimum of the relative least-square percentage errors are indicated under the figure with fitting average error)

Optimization of Chymotrypsinogen

0, = 630.7 K 0, = 78.7 K error = 0.49 f 3.2 %

copolymers by simply adding the homopolymer heat capacities in the proper molar ratios of their compositional content4). This addition scheme calculations led to rms deviations from 1.6 to 3.1%, mostly lower than the expected experimental errors of about 3%4). With the thermodynamic data of all poly(amino acid)s readily avail- able2,3), proteins, which are practically random copolymers made of the twenty naturally occumng amino acids in the L-configuration, are ideal candidates for such an approach. Combining the C, contributions from all amino acids in polymeric form and in ratios as they occur in the protein, the heat capacities of various proteins can be approximated. The amino acid composition of the four sample proteins are given in Tab. 1. The amino acid composition for ovalbumin was obtained from ref.23) and for the other three proteins from the atlas of protein sequence 1967- 196gZ4’; all data were confirmed with the Swiss-Prot protein sequence database on the Internet25).

An estimation of the errors in these measurements has been made by calculating a conventional standard deviation, 6, from the square sum of the deviations of the individual data points from the average value at each temperature (in percent), with n temperatures and a runs.

To compare the calculated data with the measured data, a standard deviation is computed from the percentage difference between the average of the measured data and the calculated data.


Tab. 1 . Composition of the proteins analyzed

Amino acid a-Chymotryp- P-Lactoglobulin Ovalbumin Ribonuclease sinogen M=25646Da M = 18367 M=42750 M = 13690

alanine arginine asparagine aspartic acid cysteine glutamine glutamic acid glycine histidine isoleucine leucine lysine methionine phenylalanine proline serine threonine tryptophan tyrosine valine Total

Results

22 4

15 8

I0 10 5

23 2

I0 19 14 2 6 9

28 23 8 4

23 245

14 3 5

11 5 9

16 3 2

10 22 15 4 4 8 7 8 2 4

10 162

35 15 17 14 6

15 33 19 7

25 32 20 16 20 14 38 15 3

10 31

385

12 4

10 5 8 7 5 3 4 3 2

10 4 3 4

15 10 0 6 9

124

The four proteins investigated in this study are a-chymotrypsinogen, p-lactoglobulin, ovalbumin and ribonuclease A. Their heat capacities were measured from 130 to 420 K and calculated over this range with the addition scheme using data from poly(L-amino and the vibrational computation scheme described above. The results are shown in Tabs. 2-5 and in Figs. 2-5 . For the four proteins, we report a standard deviation of 2.5, 1.7, 2.0, and 2.5% for the measurements done on the PE DSC 7 and of 8.3,5.7,7.7, and 4.8% for measurements done on the DSDSC, respectively. The higher standard deviations of the latter measurements is probably due to the lack of dry box assembly to protect the cells from outside moisture and changes in atmosphere around the cell. The measured experimental results are listed in Tabs. 2-5 at regular temperature intervals. Figs. 3-5 contain the recommended (averaged) experimental C,.

The calculated results are shown as curves in Fig. 2 for a-chymotrypsinogen and Fig. 3 for p-lactoglobulin, Fig. 4 for ovalbumin and Fig. 5 for ribonucleasxe A. The figures contain also the experimental data for comparison. The values of 0, and 03, as evaluated by fitting to the Tarasov functions, are for a-chymotrypsinogen: 631 K and 79 K; p-lactoglobulin: 582 K and (79 K); ovalbumin: 651 K and (79 K) and ribonuclease A: 717 K and (79 K), respectively. The values in parenthesis are esti-


Tab. 2. Experimental heat capacities in M/(K - mol) for chymotrypsinogen

Temperature Perkin-Elme la) TA Instrumentsa) Data from ref.” in K DSC 7 DSDSC (Hutchens)

10.00 0.48 1 15.00 1.114 20.00 1.871 25.00 2.700 30.00 3.557 35.00 4.397 40.00 5.213 45 .00 5.997 50.00 6.769 55.00 7.524 60.00 8.256 70.00 9.612 80.00 10.838 90.00 12.018

100.00 13.102 110.00 14.185 120.00 15.216 130.00 16.224 140.00 17.222 150.00 18.199 160.00 19.175 170.00 20.151 180.00 21.139 190.00 22.115 200.00 23.102 210.00 24.100 220.00 27.49 25.087 230.00 28.50 26.075 240.00 29.52 27.073 250.00 30.59 28.081 260.00 3 1.47 29.122 270.00 32.54 30.152 280.00 33.27 31.204 290.00 33.46 32.277 300.00 34.43 33.360 3 10.00 35.44 34.433 320.00 36.32 330.00 37.32 340.00 38.07 350.00 38.97 360.00 40.71 370.00 42.05 380.00 43.09 390.00 44.21 400.00 45.00 4 10.00 45.30 420.00 45.98 a) The standard deviation in the Perkin-Elmer and TA Instruments data is 2.5% and

8.3%, respectively.

16.77 18.84 19.96 21.57 22.26 22.33 24.15 24.53 26.65 26.85 29.33 31.61 30.86

3798 G. Zhang, S. Gerdes, B. Wunderlich

Tab. 3. Experimental heat capacities in kJ/(K - mol) for lactoglobulin ~ ~~~

Temperature Perkin-Elmera) TA Instrumentsa) in K DSC 7 DSDSC

130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420

19.266 20.356 21.318 22.035 22.644 23.234 23.637 24.369 24.983 25.639 26.235 26.872 27.663 28.274 28.864 29.732 30.576 31.446 32.249 33.062 33.915

12.317 12.858 13.601 14.726 15.635 16.429 17.059 17.802 18.565 19.537 20.058 20.5 16 20.872 21.746 23.386

a) The standard deviation in the Perkin-Elmer and TA Instruments data is 1.7% and 5.7%, respectively.

Tab. 4. Experimental heat capacities in H/(K * mol) for ovalbumin

Temperature Perkin-Elmer") TA Instrumentsa) in K DSC 7 DSDSC

130 140 150 160 170 180 190 200

27.818 28.1 30.485 32.125 33.573 35.775 38.451 38.581


Tab. 4. continued


210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420

44.241 46.448 48.192 49.48 1 51.278 52.914 54.057 55.486 57.012 58.879 60.569 61.706 63.537 65.598 68.055 69.638 72.21 74.156 75.316 76.743

40.072 42.776 45.282 46.223 49.23 5 1.955


Tab. 5. Experimental heat capacities in kJ/(K * mol) for ribonucfease A


130 140 150 160 170 180 190 200 210 220 230 240 250 260

13.784 14.314 14.978 15.478 15.812

7.945 7.912 8.779 9.652

10.448 11.09 11.547 12.023 12.32 12.924 13.405 13.674 14.263 15.187


Tab. 5. continued

Temperature Perkin-Elmef) TA Instrumentsa) in K DSC 7 DSDSC

270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420

16.276 16.49 16.84 17.234 17.717 18.215 18.985 19.534 19.999 20.553 21.114 21.572 22.008 22.637 23.247 23.833

16.078


mated based on available information on other proteins and poly(amino acid)s. The average and root mean square percentage errors of the fits are 0.5 * 3.2% for a-chymotrypsinogen, -0.8 * 2.5% for /3-lactoglobulin, -0.4 * 1.8% for ovalbumin, and -0.7 * 2.2% for ribonuclease A. For comparison, the results from the addition scheme, using the known heat capacities calculated for the poly(amino acid)s, are also given in Figs. 2-5 (dotted lines).

Discussion The new experimental heat capacities by DSC for the four proteins as shown in

Figs. 2-5 are compared to the calculated results from 0-600 K (solid lines: vibrational computation; dotted lines: empirical addition, respectively). The heat capacity of all samples gradually increases over the whole temperature interval studied. Of the proteins investigated, only the heat capacity of anhydrous a-chymotrypsinogen has been the subject of an earlier study”. The result of that study, by Hutchens et al., is in agreement with our calculated and measured data as shown in Fig. 2. For all of the three data sets for a-chymotrypsinogen, the two sets between DSC 7 and DSDSC agree to better than 25% in the common range of temperature with the average, close to the limit acceptable for the two instruments; *IS% between DSC 7 data and those from Hutchens; *2.5% between DSDSC data and those from Hutchens. For /3-lactoglobulin and ovalbumin, the error between the two sets of experimental data is *2.5% with the average. For ribonuclease A, the error between the two sets of experimental data is *3.5% with the average. As an approximation, a curve averaged


Heat Capacity of Chymotrypsinogen A

" i ~ - cp CPCalC(ATHAS) addtion CalC

5180 E 5 % 2

v Q

b = c 2 A Cp e v (OSDSC)

2a 0 Cpeq(OSC7) r

10 0 Cp exp (Hutchens)

0 0 100 200 300 400 500 '390

Temperature [1(1

Fig. 2. Heat capacity of a-chymotrypsinogen: experimental data from the literature'), open circles; Cp, by DSDSC, filled triangles; Cp by DSC 7, open diamonds; calculated data from the vibration spectrum, solid line; addition scheme using the computed heat capacities for poly(amino acid)s, dotted line

Heat Capacity of Bovine Lactoglobulin

50 I 45 -

40 - - 8 35 - E

r Y

30 -

g 25 - 020- 0,

1%-

10 -

5 -

r

0 50 100 150 200 250 300 350 400 450 500 550 600

T=nperabrS I1(1

Fig. 3. Heat capacities of /I-lactoglobulin: average Cp by DSDSC and DSC 7, open circles; calculated data from the vibrational spectrum, solid line; addition scheme using the computed heat capacities for poly(amino acid)s, dotted line

3 802

Ovalbumin Heat Capacw

160

140 - 120 - - = 5 100-

z 80-

E .g 60- 8 5 4 0 - I

20 - 0 -

30 -

25 -

Y * a 20 - 6 0 1 5 - B 1 0 -

0

Q, = 651 K @, = 78.7 K

5 -

G. Zhang, S. Gerdes, B. Wunderlich

.:" ... .. .... cp addition

Fig. 4. Heat capacities of ovalbumin: average Cp by DSDSC and DSC 7, open circles; calculated data from the vibrational spectrum, solid line; addition scheme using the computed heat capacities for poly(amino acid)s, dotted line. In this plot the contributions of the skeletal and the group vibrations to C,, as well as C,, are also indicated as an example

Heat Capacity of Ribonuclease A

35

Q, = 717 K


over all experimental data is compared to the calculation results and used as recommended experimental data in the ATHAS data bank.

A small, seemingly systematic deviation of ovalbumin Cp from the calculated vibrational heat capacity may exist at temperatures above about 350 K (see Fig. 4). This could be the beginning of some large-amplitude motion, denaturation, or even decomposition, It is to be resolved pending further investigation. Care has been taken to rule out possible instrument effects by dividing up the measuring sequence into two temperature ranges to minimize the effect of non-linear change of the isotherms.

An earlier attempt to calculate the heat capacity of a-chymotrypsinogen had been madez6). These data can, however, be rejected since the author has used the Debye model that is inappropriate for linear polymers. Indeed, these calculations deviate from the measured heat capacities by hundreds of percent. From the ATHAS computation, the parameters O1 and 0, of the Tarasov equation fitted for a-chymotrypsinogen are 630.7 K and 79 K with an error of 0.5 t 3.2%. They are comparable to 599 K and 79 K for bovine zinc insulin, the first protein studied by this method5). The common value of O3 obtained for both proteins indicates the possibility that proteins are not so different at very low temperature in terms of the vibrational heat capacity parameter 0,. Although O1 and 0, should not be affected much by the exact amino acid sequence of a protein, they ought to be related to the same parameters, O1 and 03, of its composing amino acids in polymeric form. To support this argument, the average of 0, is 73 K for the 5 poly(amino acid)s analyzed to date at low temperature, polyglycine (0, = 91 K), polyalanine (58 K), polyvaline (65 K), polymethionine (83 K) and polyphenylalanine (67 K)2,5327). Based on the above, the 0, value of 79 K was chosen as an estimate for the other three proteins for which now low temperature experimental Cp were available. In this case, a single parameter version of the fitting program is employed to optimize the Tarasov function. The fitting results are good, as indicated by the combination of average and root mean square percentage error. For the solid state, agreement with the measurement from 130 to 420 K could be accomplished to -0.8 i 2.5% for p-lactoglobulin, -0.4 * 1.8% for ovalbumin, and -0.7 i 2.2% for ribonuclease A. Although O1 fitted with 0, fixed may differ some with values based on fitting from low temperature Cp, it is a good approximation for the temperature range of most interest, 200-500 K. The small discrepancies in 0, will not be surprising, since the values had to be estimated from limited low temperature measurements available for other proteins and poly(amino acid)s. The expected deviations in O1 can also be linked to the limited low temperature data for the measurements. The largest sensitivity in the O-to- C, inversion is at the point of inflection of the Tarasov function at about 014 to 01 5**’. Even for a O1 of 400 to 550 K, one expects higher accuracy at about 100 K, still somewhat below the current experimental temperature range for three of the four protein samples. At higher temperatures the sensitivity of the inversion decrease and approaches zero above the 0 temperature as C, approaches N, x R (Dulong-Petit’s rule). In the future, we intend to make more low temperature experiments on selected poly(amino acid)s and proteins to test these conjectures.

Since the number of proteins is unlimited, our goal is to search and predict intrin- sic relationships between a protein’s structural information and physical properties

3804 G. Zhang, S. Gerdes, 3. Wunderlich

by selectively studying representative samples. For example, this current study attempts to link the macroscopic heat capacity of proteins to its microscopic structural cause, the group and skeletal vibrational motion.

The number of skeletal vibrations is given by the total number of degrees of free- dom less all group vibrations, computed from the corresponding poly(amino acid)s. Given the amino acid composition of a protein, a computer program has been pre- pared to compute its N, , M and also collect the group vibrational spectrum for the protein from a database constructed for all 20 poly(amino acid)s. The values for N, are: for a-chymotrypsinogen, N , = 3005; for /.?-lactoglobulin, N, = 2188; for ovalbumin, N, = 5008; and for ribonuclease A, N, = 1574. Not explicitly included in the above consideration are changes in the poly(peptide) chain ends (-H and --OH groups), and inter-chain or intra-chain bonds like the S-S substitutions for the S-H bonds when two cysteine groups combine into cystine. At present we estimate the heat capacity from these changes to be much less than the experimental error because of the very large number of vibrators. Besides correcting for these changes, efforts are also underway to assess effects due to buffer salts, complex groups, and water, common or necessary in other proteins. New measurements on appropriate proteins and model compounds are in the planning stage, so that ultimately a quick assessment of heat capacity, and with it the thermodynamic properties of any unknown protein, is possible. For example, the well known globular horse myoglo- bin, with iron protoporphynn IX as heme group, is being studied with several of the usual biological buffer substances present in the solid state to better understand its thermal stability. Further steps that are in the proposal stage are the connection to the partial molar functions in concentrated solutions, the connection to heats of formation, and the evaluation of additional low temperature heat capacities which could bring information about secondary and tertiary structure.

Compared to the earlier fitting method to obtain the 0 temperaturesgs lo), the new optimization procedure of Fig. 1 is more efficient, since both Q1 and 0, are obtained in a single run. In addition, the fitting is directly linked to the error in C,. In the previous fits the condition was to achieve a constant value of Q1 over a chosen temperature range. The new approach is relatively simple, i. e., the directly evaluated percentage least square error of all data in the chosen temperature interval is calculated. With the help of interpolation, the minimum point between the mesh points is found as shown in Fig. 1. This plot with one unique global minimum proves also the physical relevance of the two-parameter description. Also, it remains to establish the changes in @-values if absolute errors are used instead of percentage errors. The absolute errors would be of advantage for the optimization of the integral properties (H, S, and G), while the percentage error is useful for the assessment of the heat capacity as a function of temperature (see Figs. 2-5).

In earlier papers in this ~ e r i e s ~ - ~ ) it has been shown that our calculations of the heat capacities of poly(L-amino acid)s agree well with measurements and also that these heat capacities are additive for simple co-polymers of these poly(amino acid)s. The present work supports that this simple and direct ATHAS empirical addition scheme used to predict heat capacities for co-poly(amino acid)s can be extended to proteins. Minor differences between these calculated and measured Cp existed from


100 to 150 K for bovine insulin5). For the present analysis of a-chymotrypsinogen, no such differences exist, even down to 10 K, where skeletal vibrations dominate. For the other three proteins, the additional results are also satisfactory, as can be seen from Figs. 3-5. Thus, given its amino acid composition, it is possible to estimate the heat capacity of any anhydrous protein.

With the knowledge of heat capacities from absolute zero of temperature, it becomes also possible to calculate the thermodynamic functions enthalpy H , entropy S, and Gibbs free energy G:

H = H o + CpdT J S = SO + / ( C p / T ) dT

( 3 )

(4)

G = H - T S ( 5 )

The computation center of the ATHAS data bank is set up to calculate the functions H, S and G from the computed C,. The function H is calculated as H - Ho, where Ho can be linked to the heat of formation at 298.15 K via Q. (3). The entropy at zero kelvin, So, is taken as zero for perfect crystals (third law entropy). The Gibbs free energy, the measure of thermal stability, is then calculated according to Eq. (5). These functions can serve as a beginning for the understanding of the thermody- namics of biopolymers like proteins. The data tables and corresponding curves, as well as tables of the computed Cp and the recommended experimental C,, for the proteins can be inspected and reproduced from the ATHAS data bank available through the World Wide Web on the Internet').

Conclusions

In the present study, the experimental data on heat capacities of four proteins, a- chymotrypsinogen, P-lactoglobulin, ovalbumin and ribonuclease A, have been measured from 130-420 K, and values for the two parameters O1 and O3 of the Tarasov equation have been obtained. With the established connection between existing information on the vibrational spectra and heat capacity, the latter can be more reli- ably calculated from both group and skeletal vibrational contributions. The variation of the 0 temperatures from polymer to polymer is correlated so that, in case of miss- ing data, first approximations can also be estimated from the extensive tabulation in the ATHAS data bank. More importantly, we have extended the ATHAS framework derived mainly from synthetic polymers to four more proteins. With both structural and energetic information available, progress should be possible towards a thermodynamic characterization of proteins and other biopolymers.


Acknowledgments: This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant * DMR 90-00520 and Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research C o p . for the U.S. Department of Energy, under contract number DE-AC05-960R22464.

’) ATHAS data bank. For a recent description see: B. Wunderlich, Pure Appl. Chem. 67, 1019 (1995). For the data bank of experimental heat capacities see: U. Gaur, S.-F. Lau, H.-C. Shu, B. B. Wunderlich, M. Varma-Nair, B. Wunderlich, J. Phys. Chem. Re$ Data 10, 89, 119, 1001, 1051 (1981); 11, 313, 1065 (1982); 12, 29, 65, 91 (1983), and (1990), 20, 349-404 (1991). For detailed information see World Wide Web address on the Internet: http://funnelweb.utcc.utk.edu/-athas

2, K. Roles, B. Wunderlich, Biopolymers 31,477 (1991) 3, K. Roles, Y. Xenopoulos, B. Wunderlich, Biopolymers 33,753 (1993) 4, K. Roles, B. Wunderlich, J. Polym. Sci., Part B: Polym. Phys. 31,477 (1993) 5, Ge Zhang, B. V. Lebedev, B. Wunderlich, Jing-ye Zhang, J. Polym. Sci., Part B:

6 , A. Xenopoulos, K. Roles, B. Wunderlich, Polymer 34,2559 (1993) 7, A. Xenopoulos, J. Cheng, B. Wunderlich, Mol. Cryst. Liq. Cryst. 226, 87 (1993);

Y. Jin, J. Cheng, B. Wunderlich, S. Z. D. Cheng, M. A. Yandrasits, Polym. Adv. Tech- nol. 5,785 (1994); J. Cheng, Y. Jin, G. Liang, B. Wunderlich, H. G. Wiedemann, Mol. Cryst. Liq. Cryst. 213,237 (1992)

Polym. Phys. 33,2449 (1995)

*) J. 0. Hutchens, A. G. Cole, J. W. Stout, J. Biol. Chem. 244,26-32 (1969) 9, E. L. Andronikashvili, G. M. Mrevlishvili, G. Sh. Japaridze, V. M. Sokhadze,

lo) A. R. Haly, J. W. Snaith, BiopoZymers 10, 1681 (1971) K. A. Kvavadze, Biopolymers 15, 1991 (1976)

H. J. Hinz, C. Steis, T. Vogl, X. Meyer, M. Rinnair, R. Ledermiiller, Pure Appl. Chem. 65,947 (1993)

12) I. V. Sochava, 0. I. Smirnova, Food Hydrocolloids 6,513 (1993) 13) Y. Jin, B. Wunderlich, J. Therm. Anal. 36,765 (1990) 14) Y. Jin, B. Wunderlich, J. Therm. Anal. 36, 1519 (1990) 15) Y. Jin, B. Wunderlich, J. Therm. Anal. 38,2257 (1990) 16) D. C. Ginnings, G. T. Furukawa, J. Am. Chem. SOC. 75,522 (1953) 17) The nomenclature of 0 temperatures ( h v k ) for the characteristic frequencies (v) of

Einstein or Debye distributions has been in use since 1907 [A. Einstein, Ann. Phys. 22, 180 (1907)l. It should not be confused with the much later established 6-temperature for macromolecular conformations at which the excluded volume is compensated by intermolecular attraction

18) Yu. V. Cheban, S.-F. Lau, B. Wunderlich, Colloid Polym. Sci. 160,9 (1982) 19) S.-F. Lau, B. Wunderlich, J. Therm. Anal. 28,59 (1982) 20) R. Pan, M. Varma-Nair, B. Wunderlich, J. Therm. Anal. 35,951 (1989) *’) U. Gaur, M.-Y. Cao, R. Pan, B. Wunderlich, J. Therm. Anal. 31,421 (1986) 22) R. Pan, M.-Y. Cao, B. Wunderlich, J. Therm. Anal. 31, 1319 (1986) 23) R. Helig, R. Muraskowsky, C. Kloepfer, J. L. Mandel, Nucleic Acids Res. 10, 4363

24) M. 0. Dayhoff, R. V. Eck, “Atlas of Sequence and Structure”, National Biomedical

25) WWW address on the Internet: http://expasy.hcuge.ch/sprot/ 26) J. Edelmann, Biopolymers 32, 209 (1992) 27) A. Xenopoulos, B. Wunderlich, Polymer 31, 1260 (1990) 28) H. S. Bu, S. Z. D. Cheng, B. Wunderlich, J. Phys. Chem. 91,4179 (1987)

( 1982)

Research Foundation, ( 1967 -68)

Heat capacities of solid, globular proteins

Documents

Transcript of Heat capacities of solid, globular proteins