Thermodynamics of unfolding of the α-amylase inhibitor tendamistat

J. Mol. Biol.

(1992)

223,

769-779

Thermodynamics of Unfolding of the ar-Amylase Inhibitor Tendamistat Correlations

Between

Accessible

Michael Institut

fiir

Renner,

Surface Hans-Jiirgen

Area and Heat Capacity Hinz”f

Physikalische Chemie der Westfilischen WilhelmsSchloJplatz 417, 4400 Miinster, Germany

Universit&

M. Scharf and J. W. Engels Institut

fiir

Organ&he

Chemie der Universittit D-6000 Frankfurt/Main,

Frankfurt,

Niederurseler

Hang

Germany

(Received 6 May 1991; accepted 30 August 1991) Unfolding of the small a-amylase inhibitor tendamistat (74 residues, 2 disulfide bridges) has been characterized thermodynamically by high sensitivity scanning microcalorimetry. To link the stability parameters with structural information we use heat capacity group parameters and water accessible surface areas to calculate the change in heat capacity on unfolding of tendamistat. Our results show that both the group parameter and surface area approaches provide a reasonable, though not perfect, basis for AC, calculations. When using the experimentally determined temperature-independent heat capacity increase of 2.89 kJ mall’ K- ’ tendamistat exhibits convergence of thermodynamic parameters at about 140X, in agreement with recent predictions of the temperature at which the hydrophobic hydration is supposed to disappear. Despite the apparent support of this new view of the hydrophobic effect, there are inconsistencies in the interpretation of the thermodynamic parameters and these are addressed in the Discussion. The specific stability of tendamistat is similar to that of modified bovine pancreatic trypsin inhibitor, with only two of the native three disulfide bridges intact. This observation confirms our previous conclusion that disulfide bridges affect significantly the enthalpy and entropy of unfolding. The recent study by Doig & Williams provides additional convincing support for this conclusion. The predictive scheme proposed by these authors permits a fair estimate of the Gibbs free energy and enthalpy changes of these two proteins.

Keywords: tendamistat;

unfolding;

thermodynamics;

1. Introduction Tendamistat is a small golbular protein, 74 amino acid residues long, having a molecular mass of 7952 Da. Its precise three-dimensional structure both in solution and in the single crystals has been determined by nuclear magnetic resonance (n.m.r.$) studies and X-ray diffraction analysis (Billeter et al., 1989; Pflugrath et al., 1986). Figure 1 shows the sequence (Aschauer et al., 1981) and the three7 Author to whom all correspondence should be addressed. 8 Abbreviations used: n.m.r., nuclear magnetic resonance; BPTI, bovine pancreatic trypsin inhibitor; DSC, density scanning calorimetry; ASA, accessible surface area.

accessible

surface

area; heat capacity

dimensional structure (Kline et al., 1986) of the protein. Tendamistat contains two non-overlapping disulfide bridges between Cysl l-Cys27 and Cys45-Cys73. The tertiary structure is characterized by two B-pleated sheets each consisting of three antiparallel strands (Kline & Wiithrich, 1985). The independently determined n.m.r. and crystal coordinates are very similar and for the interior practically identical. Subtle differences in the degree of disorder become apparent only for residues near the solvent-exposed surface of the molecule, where lattice forces may favor increased order in the crystal as compared with the free protein in solution. Tendamistat is a tight-binding cl-amylase inhibitor. The dissociation constant is hard to determine

769 0022-2836/92/030769-11

$03.00/O

0

1992 Academic

Press Limited

770

M. Renner

et al

m? Thr Thr Ual Ser Glu Pro

ThrEeu

TY~

Gin

Ser

Cys

Ual

s S Cys Gly g flsn fW~laGln Thr

Ser TPP fir3 TY~ Ser

Ual LYS

Ual Ual

ASP

S

TyrlrgAla Figure structure

His GUY His Glu His

1. Primary (Aschauer et al., 1981) and tertiary is based on set 1 of 7 n.m.r. structures deposited

accurately, but its. order of magnitude is 10-l’ M. The isoelectric point of the protein is at pH 4.35 (Vertesy et al., 1984). An intriguing feature of polypeptide inhibitors is their stability towards proteolytic cleavage and denaturant, or temperature induced unfolding. In several cases stability results from a high degree of covalent linkage by disulfide bridges. These disulfide bonds increase stability predominantly by improving van der Waals’ interactions in the native stat’e. This was demonstrated by the large decrease in the transition enthalpy for bovine pancreatic trypsin inhibitor (BPTI) analogs that lacked the 14-38 disulfide bond (Moses & Hinz, 1983; Schwarz et al., 1987; States et al., 1987). It is of prime importance from a biochemical and biotechnological point of view to characterize the thermodynamic basis of protein stability. Small globular proteins are particularly useful paradigms, since many larger proteins have been found to consist of structural domains resulting from the repeated occurrence of a few types of building block (Baron et aZ., 1991). These structural modules often turn out to fold independently or in co-operation with a few other domains. A second reason for our preference for small proteins is the fact that the molecular interpretation of the thermodynamic paramet,ers is probably least ambiguous due to the small size, the availability of high resolution structures, the reversibility of the

(Kline et al., 1986) structure of tendamistat: in the Brookhaven Protein Data Bank.

the

tertiary

unfolding transitions and the actual or foreseeable tractability of energy data by theoretical ealculations (Dill, 1990a,b). In the present study we determined the thermodynamic unfolding characteristics of tendamistat, by high sensitivity scanning microcalorimetry (DSC) and correlated it with the changes in the accessible surface area (ASA) associated with thermal unfolding. The calculat’ions showed a good agreement between experiment’al and estimated partial molar heat capacities of the native and unfolded state of the protein. This result demonstrates that accessible surface area calculations provide an important empirical link between structural and thermodynamic parameters.

2. Materials and Methods (a) Materia1.s Tendamistat (HOE467) was isolated from Stre@onLyces tendae 4158 and purified according to the procedure of Vertesy et al. (1984). Protein concentra,tion was determined using an absorption coefficient A:sbq, = 16.1 at et al., 1984). The molar mass of La = 276 nm (Vertesy the protein, M = 7952 g/mol, was calculated from the amino acid sequence (Aschauer et al., 1981). Before each measurement a,11 samples were routinly dialyzed to equilibrium using 2 x 1 1 of the respective buffer for 8 h. Spectrapor 6 NWCO 2000 dialysis tubing that has a eutoff limit of M = 2500 was employed. The buffer consisted

Thermodynamics

of Unfolding

of 10 mnr-sodium phosphate, 10 m&r-NazSG, and the pH was adjusted with the use of a WTW pH digi 510 pHmeter (Wissenschaftliche Technische Werkstatten, Weilheim, Germany). Before starting the dialysis, oxygen was removed from the buffer by bubbling nitrogen through the solution.

(b) Methods The temperature dependence of the apparent specific heat capacity was determined using a Privalov type DASM-4 adiabatic, differential scanning microcalorimeter. For automatic data collection the instrument is connected via a multiplexer to a 6 digit Keithley 192 DMM voltmeter serving as analog-to-digital converter. Heat capacity and temperature readings were made every 91 deg. K using a personal computer. Each protein run was preceded by a calibration run employing equilibrium buffer-filled sample and reference cells. Electrical calibration was performed using a 50 PW signal for 5 min. Measurements were made from 20 to 110°C. The majority of measurements were made with a heating rate of 1 K/min. Smaller or higher heating rates did not affect the results. For numerical evaluation of the transition enthalpies, AH”, transition temperatures, T,, and the denaturational heat capacity changes, AC,, from the experimental heat capacity versus temperature curves several methods have been employed that differ from each other by the form of the baseline that underlies the transition peak. One program generates a straight line connecting the start and end points of the transition peak, the other extrapolates the pre- and postdenaturational heat capacity functions into the transition region and applies a step function equal to AC, at T,. Thereby one obtains a direct value for the heat capacity change on unfolding from the individual transition curve. This value was compared with the AC, value determined from the pH induced variation with temperature of the transition enthalpy, and both were found to be identical within error limits of 15%. As a third possibility a program based on the thermodynamic analysis of sequential transitions was employed (Freire & Biltonen, 1978). All 3 analyses yielded essentially identical results for the transition enthalpies and transition temperatures. The van’t Hoff enthalpies at T, were calculated from the calorimetric data according to the equation for a 2-state transition: WdT,)

= 4RTi

C,(Tm) AH”(T,)’

where C&T,) is the molar excess heat capacity at T, and AH”(T,) the corresponding molar calorimetric transition enthalpy. R is the gas constant (8.314 J/(mol K). (i) Calculation of the heat capacity difference, A;C,(T), from group parameters (method 1) Following a recent suggestion by Makhatadze & Privalov (1990) we calculated the heat capacity of the unfolded state of tendamistat, C:(t), by heat capacity increments based on the amino acid composition of the protein. At each temperature the heat capacity of the denatured state, C,“, can be represented by an equation of the type: C; = C&NH,)

+ (N-

1) x C,(-CHCONH-) +C,(-CHCOOH)+

5 C&R,), k=l

(2)

of Tendamistat

771

where C&-NH,) is the heat capacity contribution of the N terminus, C,(-CHCOOH) that of the C terminus, C&-R,) refers to the heat capacity contribution of the side-chain of the kth amino acid, and C,(-CHCOrVH-) is the heat capacity contribution of the peptide group. To obtain numerical values for the group contributions to heat capacity as a continuous function of temperature we applied a least-squares fitting routine to the C, parameters, which were listed in Table 5 of Makhatadze & Privalov (1990) for 6 selected temperatures. The function used for fitting was a 3rd degree polynomial: C:(t) =axt3+bxt2+cxt+d

(kJ/(molK))

(3) and the resulting coefficients a, b, c and d for the equations of all group contributions are summarized in Table 1. t is the temperature in “C. As heat capacity function of the native state, C:(t), we used the linear predenaturational calorimetric heat capacity and extrapolated the values into the transition region. The resulting equation for C!(t) of tendamistat is: C:(t) = 0048 x t + 11805

(kJ/(mol

K)).

(4)

The difference function: A;C,(t)

= C;(t) - C;(t)

between the heat capacity of the denatured and native state is the temperature dependent heat capacity change associated with unfolding of tendamistat. (ii) Calculation of the hydration heat capacity difference, A$$“‘(t), from accessible surface areas (method 2) A method to determine the molar hydration heat capacity change, AgCy, is based upon the empirical finding of a linear relationship between heat capacity and accessible surface area of hydrophobic moieties in aqueous solution (Gill & Wadsii, 1976; Olofson et al., 1984; Jolicoeur et al., 1986; Privalov & Gill, 1988; Doig & Williams, 1991). Thus, knowledge of the accessible surface area of groups in both the native and unfolded state provides a possibility of calculating, for a particular temperature, the heat capacity change resulting from the exposure of groups to water upon denaturation according to the equation AECy

= C AAXAi X Acp, ii 1 where AAXA, is the change in the accessible surface area of each_amino acid of type i in the protein upon unfolding, and AC .(J/(mol K ASA,)) refers to the corresponding change iLlthe group contribution to the hydration heat capacity of amino acid i per unit of accessible surface area (Makhatadze & Privalov (1990); Table 7). This AC, value is considered to account for more than 80 o/0 of the experimental heat capacity change (P. L. Privalov, personal communication). Summation over all amino acids in the protein results in the theoretical overall molar change in hydration heat capacity A$y. We calculated AASAi for unfolding of tendamistat using eqn (7) from the difference between the AAXAf’ values, which are the accessible surface area parameters for denatured proteins given by Miller et al. (1987), and the AXA? values that were obtained from accessible surface area calculations employing the program ACCESS by Richards (1985). Both the n.m.r. and X-ray co-ordinates of tendamistat deposited in the Brookhaven Data Base File were used for the ASA” calculations of the native state. AASA, = t j=l

(ASA;-

ASA;).

(7)

ill.

772

Renner

et al.

Table CoefJicients for the heat capacity Group

-57.75

Met

-4579

His Ala Gin

-S526

GI y Ser A3l-l

Glu Thr LYS TY~ Phe Val Leu Ile TOP CYS Argb Arg’ LJd

Lys’

-NH, + -CH,COOH -CHCONH-

b x IO3

a x lo6

PI-0

Asp

polynomial of the denatured state c -2.488

24.71 13.83 23.25 -0064 -3.844 0035

1.10 lo-95 -5637 1.045 1.241 4211 -6.763

0569 -0718 0200 -0716 -0.669 -0,645 -0.204 -0*2os

1.999

3989 327.8 386.8 407.8 4744 221.6 1846

-0.669

1999

7.443 4.568

-3.844 -51.37 -10.73 -21.22 1877 -665s -571

187,8 41.18 68.22 -74.35 157.4 14.59

I642 692 83.4 746 68.0 1653 197.5 328.0 3143

0.925

5065 0350 -0.3647

10%

212.4 177.9

0.744 0.765 -0215 0,245

-0.351 -2.421 -@362 8-814 -1.781 7.548

9.427 -2208 -3.544 -28.88 0.6418 2.452 -3.544

2262 2046

- 1.497 - 1.699 -0.4391

- 2.998

-1494

d

1,033

295.9 205.9

2.140 -1.365 6.178 0757

3169

- 192.6 -0.017

C;(t) = at3 + bt2 + ct + d has been derived from the heat capacity parameters given in Table Makhata,dze & Privaiov (1990) for selected temperatures. t is in “C, C:(I) is given in J/(moi K).

The index i refers to the classification of the groups of the amino acid into aliphatic, backbone, glycine type or aromatic moieties (Makhatadze & Privalov, 1990), and the sum is over all amino acidsj that contribute to the type i. In the case of polar amino acids the summation for the polar contributions, e.g. the OH group of serine, extends only over the number of the particular type of polar amino acid present in the protein. This restriction results from the fact that polar amino acids cannot be grouped into a common class as can be, for example, aromatic amino acids. Each polar ammo acid must therefore be treated separately. Following the procedure of Shrake $

5 of

Rupley (1973) hetero-atoms and carbon atoms bonded to 2 or more hetero-atoms are classed as polar. The AC,,,,i parameters given by Makhatadze & Privalov (1990) were approximated by a polynomial of 3rd degree (eqn (8)) to obtain a continuous function of temperature (in “C), AC, i(l):

4cp i(t) =uxt3ibxt2+cxtfd (J/(mol

K asA,)).

(8) The coefficients of eqn (8) for all amino acids are listed in Table 2. The equation for the temperature dependence of the overall heat capacity change that should be compared

Table 2 CoefJicients for the hydration heat capacity polynomial unit of surface accessible area for constituent Group

axlo’

Aliphatic Aromatic

-05771 -0.1421

-CHCONHGlY

Met His Ser ASIl

Asp Qln GlU LYS TYr Ag Thr Trp

“C.

The data used for fitting A4 is given in J mol-’

L?LFp= at3 + bt2 + ct + d per groups of proteins

bx105 1.289 4.055 -1.167 -2.779 -3.948

2.702

- 1.108 1.786

e x IO3 -5657 -6.611 13.31

-0.8355 -1.713 -1.371

3979

- 2%99 11.45 16.01 15.57 9.289 9.176 -2014 -0709

-W324 -3542

02689

3.310

4-204 -3.398 8-440

are the parameters K-!d-‘.

-1.082 2.745 -2.075

in Table

7 of Makhatadze

0.2965 -4.135

-2.508 -6.480 -0.614

-0.7820 -13.79

1.349 -1.226

3859

I.052 2.441 -0.7445

-4144

2.260

2032

- 14.47

1.140

d

- 1.814 - 0.4392 -0.7780

- 1.229 -0-0423 --o-4367

11.19

- 1.067

-15.78 -6322

& Privalov

3.858

(1990).

1 refers

to

qf Unfolding

Thermodynamics

101 20

I 40

I 60

I 80

I 100

I 120

qf Tendamistat

I 2

60L 0

d

14c

773

I 4

Figure 2. Calorimetric transition curves of tendamistat in 10 mM-sodium phosphate, 10 mM-Na,SO,: a, pH 2; b, pH 3; e, pH 7.

AC, is:

A;Cy(t)

= c AAXA,

x AC,, i(t).

(9)

(iii) Calculation of thermodynamic stability Stability of tendamistat, AGO(T) was calculated from the experimental transition enthalpies at T,, AHo( the transition temperatures, T,, and the heat capacity changes AC, using the following equations: T

AH”(T)

= AH”(T’,) +

ACp dT (kJ/mol); s T”,

AS’(T)

s

T AC T dT J/(mol K),

= Aso(

(10)

(11)

Tm

&‘j’“(T’)

=

Figure 3. Variation

with pH of the calorimetrically determined transition temperature, T,,,. The bell-shaped curve has been calculated by using eqn (15) and the parameters given in Table 3.

ducibility after cooling and reheating of the same sample. The transition curves show an increase of heat capacity after unfolding. Plotting the transition temperatures as a function of pH results in the graph shown in Figure 3. The bell-shaped profile of this plot illustrates the different influence of the H+ concentration below and above the isoelectric point of the protein. Between pH 2 and approximately pH 5 the T, value of tendamistat increases with increasing pH, whereas between pH 5 and pH 8 it decreases with increasing pH. The two sigmoidal branches of the bell-shaped T, versus pH curve can each be quantitatively described by an equation of the form:

(12)

7,

T, =

m

AGO(T) = AH”(T)-AS”(T) AC”(T)

= AH”(T,)

x

x T (kJ/mol),

(13)

[ m 1 1- f

xTxln%

8

PH

f (“Cl

with the experimental

I 6

+AC,(T,)

+AC,(T,)x(T,-T).

(14)

Eqn (13) was used for calculation of stability employing the temperature dependent AgC, values that resulted from eqn (5) or (9). Eqn (14) was used for AG” calculations based on the constant AC&T,) value. T refers to absolute temperature.

(15)

which is an equation for a titration curve having an inflection point at pK and a corresponding transition temperature T,, pK. The limiting transition temperatures at low and high pH are T,,,,, and T,, high, respectively. The continuous line in Figure 3 is the result of a non-linear least-square fit of the experimental T, values to equation (15). The parameters obtained from the fitting procedures for the two pH ranges have been summarized in Table 3.

Table 3 Parameters

3. Results The variation with temperature of the apparent molar heat capacity of tendamistat solutions at three pH values is illustrated in Figure 2. Increase of pH results in a strong increase of stability as indicated by the shift in transition temperature from 68.3”C at pH 2 to 81.6”C at pH 7. The transitions are reversible by the criterion of > 95 y. repro-

T m, low + T,, high X 10pHppK (“C), 1+ 10PHPPK

pa-range

for the pH dependence temperature

of the transition

T,, lOw(“C)

l-5

640

5-8

93.0 & 0.7

+ 1.5

The values were derived 2 branches of the bell-shaped using eqn (15).

PK 93.3+e9 77.9+ 1.0

from non-linear T, ZI~WUS pH

2.68+@10 f?54+0.11

least-square profile shown

fits of the in Fig. 3

774

M. Renner

et aB

200

/ 2

-2.01 0

I 4

I 6

I 0

I IO

w Figure 4. Proton flux An involved in unfolding of tendamistat as a function of pH. The curve has been obtained by numerical differentiation of the T,,, versus pH function employing eqn (16) a.nd the AH and T, values corresponding to the respective pH.

The T, versus pH profiles can be used for the calculation of the prot,on flux, AR, linked to the unfolding reaction according to equation (16):

dTn d(pW

1

T =-

An x 2.303 x TkR AHG)

.

(16)

T, and AH(T,) are the transition temperature and the corresponding transition ent.halpy at a given pH, R = 8.3144 J/(mol K) is the gas constant (dT,/d(pH)), is the slope of the T, W~SUS pH curve and An = nD-nN is the number of protons released (An > 0) or absorbed (An < 0) in the unfolding reaction: N = D+ An[H+]. (17) The graphical representation of the numerical differentiation is shown in Figure 4. The number of protons involved in the unfolding reaction has been plotted versus the pH value of the solution. Maximal stability as judged from the T, versus pH profile (Fig. 3) coincides with the absence of proton flux, Maximal proton exchange occurs at the pH values corresponding to the inflect’ion points of the curve in Figure 3. In the acidic range at pH 2.68, approximately 1.7 protons are absorbed, while unfolding at pH 667 is associated with the release of about one Hf. These numbers reflect the overall proton flux due to pK shifts of all ionisable groups. Figure 5 exhibits the variat’ion with temperature of t,he calorimetrically determined transition enthalpy AH”. Transition temperatures were varied by changes in pH, as shown in Figure 3. A linear regression analysis was used for the determination of the temperature dependence of AH” with the result given in equation (18): in which

AH“ = 2.89 x t + 38.23 (kJ/mol); t is the temperature in “C.

(18)

100 60

I 70

4 80 f PC)

I 90

J 100

Figure 5. Temperature dependence of the molar calctrfmetric transition enthalpy, AH in 10 miw-sodium phosphate, IO mM-Na,SO, buffer. pH values were carefully adjusted before each measurement and controlled after the measurement.

According to Hess’s law, the slope of the curve represents ACP, the molar heat capacity change on unfolding. The numerical value AC, = 2*89( &O*Sl) kJ/(mol K) coincides within + 15% with the AC, values obtained from the single transition curves.

(a) Calculation

of the temperature

dependence

of AC,

Figure 6 shows a comparison of heat capacity functions of tendamistat normalized to 1 g of protein. The continuous curve a is the beat capacity function of the unfolded state calculated from equation (3) and the parameters in Table 1. Curve b gives three heat capacity functions of the native state, c!(t). The broken line is the experimental specific heat capacity of native tendamistat extrapolated linearly t’o high temperatures, the continuous and broken curves represent calculated heat capacity functions based on n.m.r. and X-ray coordinates, respectively. Curve c shows the difference functions Aic,(t) resulting from application of equation (5). The broken-double-dotted curve parallel to the temperature axis represents the temperature-independent specific heat capacity change AEcr = 6363 J/(g K) that has been obtained from t,he molar value given in equation (18) by division by the molar mass of 7952. The temperature range, in which AEcr can be calorimetrically determined, is from 64 to 93 “C. Inspection of Figure 6 (broken line) shows that the experimental AC, value is practically identical with the mean value of the calculated heat ca.pa,city change in this temperature range. Since the accurate determination of AC, is extremely difficult, any extrapolation beyond the accessible temperature range is problematic. Table 4 summarizes the ASA parameters for native and

Thermodynamics

of Unfolding

of Tendamistat

Water-accessible

775 Table 4 surface areas for

native ASA Group

-0.5 -100

-50

0

50

1 100

I 150

200

f PC) Figure 6. Specific heat capacity functions of tendamistat Curves a: c:(t), unfolded protein: the function c:(t) was calculated by using eqn 3 and the coefficients in Table 1. Curves b: Native protein, (- - - -) experimental; (.....) c:(t) function based on the equation c:(t) = c:(t)-Aicr(t) using the X-ray co-ordinates for the estimat,e of Agcy according to eqn (9). (p 1 43) based on the same equation but using the n.m.r. coordinates. Curves c: (- - - -) c:(t) -c:(t), (broken line in c:(t)--!(t) (continuous line in (b)); (b)). ( p) (-..-..-) average constant specific A;c, = 0.363 J/(g K). The vertical bars indicate the temperature range in which AC, can be determined by calorimetry.

denatured tendamistat. Inspection of Table 4 shows that the differences between the crystal and solution structure of native tendamistat result in small AASA differences, which in turn show up in the dotted and continuous curves in Figure 6; b. It is, however, obvious that these differences are much smaller than the differences between the linearly extrapolated experimental C!(t) curve (broken line) and the calculated curves. The major difference is the larger slope of the experimental curve. However, more important than this difference is the remarkable observation that also the calculated heat capacity of the native state is practically a linear function of temperature in the temperature range from 10 to 120°C. This result is not trivial, since both the heat capacity of the denatured state shown in Figure 6, curves a, and the heat capacity difference AEc,(t) given in Figure 6, curves c, are non-linear functions of temperature. The differences in the slope between the experimental and calculated C:(t) functions are perhaps not too surprising if one considers the simplifying assumptions that enter the derivation of the Agcy(t) functions. The method based on the AASA calculations assumes a temperature independent ASAN parameter for the native state when calculating the ACP,i values at various temperatures.

Backbone Aliphatic Aromatic Glycine Trp CYS Asn Asp Gln Glu LYS &4rg Ser Thr TY~ His

ASA” 2886 4777 1054 595 27 276 69 290 273 308 48 321 180 224 258 98

denaturated

and

tendamistat from

ASAN 725 1382 441 220 28 63 0 213 77 280 4 323 90 420 204 106

n.m.r.

ASA

AASA

ASAN

2161 3395 613 375 -1 213 69 77 196 28 44 -2 90 -196 54 -8

from

769 1464 376 208 16 40 0 178 107 181 46 166 82 397 147 94

X-ray AASA 2117 3313 678 387 11 236 69 112 166 127 2 155 98 -173 111 4

The differences in the ASAN parameters for the native state reflect the differences between the surface atom co-ordinates in the crystal and in solution. ASAN parameters have been calculated using the program ACCESS (Richards, 1985) with the n.m.r. and X-ray based tendamistat co-ordinates. respectively, deposited in the Brookhaven Data Base File. ASAD values have been determined as described by Miller et al. (1987). AASA = ASAD - ASAN. ASA values are given in A2.

Although there is no simple procedure to obtain temperature-dependent ASAN parameters, it can be assumed that increase of temperature increases also the accessibility of residues in the native state. This would reduce the ASA difference between the unfolded and native state and lead to a stronger decrease of A#?Fd with temperature than observed in the present calculations. The overall result would be a better agreement between the A#?,,(t) functions in Figure 6; curves c: and, concomitantly, also better agreement between the experimental and calculated C:(t) functions. (b) Stability

of

tendamistat

An unambiguous measure of protein stability is the standard Gibbs free energy of unfolding, A@(t). We calculated the thermodynamic functions AH”(t) and AS’(t) for the temperature range from -50 to 150 “C using equations (13) and (14). The corresponding plots are shown in Figure 7. Continuous lines refer to thermodynamic parameters calculated on the basis of the constant A$Z,(T,) = 2.89 kJ/(mol K). The other line types refer to parameters calculated by using temperature dependent AC,, values. There are significant differences between the graphs as a result of the different AC, values. The temperature-independent AC, value leads to an unlimited increase of AH” and As” with temperature, which is certainly incorrect; while the use of the temperature-dependent AC, results in AH” and AS” curves that have an extremum. From a physical point of view the latter result is certainly

31. Renner 800

et al. relatively high conformational stability. Anothe: representative of this class is basic panereat,ic trypsin inhibitor (BPTI). These proteins have different functions, but conformational stability results from similar principles. The major stabilizing force appears to be t,he large favorable enthalpy resulting from the presence of disulfide bonds. This view, which is contrary to the long-held belief that disulfide bridges stabilize preferentially by reduction of the conformationa. entropy gain on unfolding, has found convincing support in studies on BPTI having two and three disulfide bonds (Schwarz et al., 1987). Recently it was also strongly supported by a study by Doig & Williams (1991) on the interdependence between the number of disulfide groups and the hydrophobic effect. (a) Group pcwameters and AASA values provide a reasonable basis for AC, calculations

-80 -100

-50

0

50

100

150

200

f (“C) Figure 7. Thermodynamic functions for tendamistat. Calculated on the basis of constant A$$(T,) = (-----) 289 kJ/(mol K): ( - - - - ) temperature dependent A$2,(t) based on method 1. eqn (5): ( -. - .) temperat’ure dependent A$,(t) based on method 2. eqn (9) (X-ray co-ordinat.es); (,....) temperat.ure dependent A$‘,(T,) ba,sed on method 2, eqn (9) (n.m.r. co-ordinat,es).

more realistic. The stability curve At”(t) is strongly affected by the dependence on temperature of AC,. Particularly at low temperature the AGO(t) function deviates significantly from that calculated with a constant AC,. The differences bet’ween 50 and 120°C are, however, negligible. Tendamistat shows maximal stability of 28.5 kJ/mol around 4*9”C, based on the stability curve calculated with the temperature dependent AC, according t,o method. 4. Discussion Tendamistat small protein

can be grouped into the class of inhibitors having disulfide bridges and

It is characteristic of protein unfolding that t,he thermodynamic functions AH”(t) and AS’(t) are strongly temperature-dependent as a result of the heat capacity difference AC,(t) between the native and unfolded stat’e. Thus for a proper elucidation of the stability of proteins as a function of temperature knowledge of the AC,,(t) function is essential in a,ddition t,o the knowledge of reference values of AN” and AS”. All predict’ions of stability features such as cold denaturation temperature or maximal stability depend critically on the knowledge of the temperature course of AGO(t) as can be seen in Figure 7. The best experimental approach is the direct microcalorimetric measurement of AH”, T, and ACp. However. the transition temperature range, which can be covered by pW variation, is often rather limited. which renders difficult the experimenLa1 determination of changes in AC, with temperature. This is the reason for the iong-held claim that AC, is independent of temperature. It is therefore desirable to have a, possibility of estimating AC,(t) for temperatures outside the accessible temperature range. The two different methods employed in the present study provide results in fair agreement with the direct calorimetric measurement. One method uses experimental heat capacity group parameters of model compounds for the calculation of the heat capa,citv function of the unfolded state. In combination with the calorimetrically det’ermined heat capa,city of the native state the difference function A;C,(t) = C;(t) -C;(t) ca,n be calculated. The second method st.arts with the calculation of the ARC?(t) function on the basis of water-accessible surface areas. AECy(t) is then substracted from the heat capacity data C:(t) of the unfolded state to obt,ain the heat capacity of the nat’ive st~ate. The reliability of the procedure is rat,ed by the agreement of the caiculated heat capacity function of the nat,ive state with the linear experimental C:(t) curve. This approach is particularly interesting. since it provides a link between purely structurat and thermodynamic quantities. The experimental and calculated specific heat capacities of the native

Thermodynamics

qf Unfolding

state of tendamistat are shown in Figure 6, curves b. It is worth noting that the calculated heat capacity C:(t) is a practically linear function of temperature in the range 20 to 100°C. This agrees very well with the experimental finding obtained for tendamistat and many other proteins. The calorimetrically observed heat capacity function of the native state of tendamistat, shown in Figure 6, curve b, as a broken line, exhibits a larger slope than the calculated C:(t) functions. This may result from the fact that the AASA based A#$ values take only the hydration contribution into account and, moreover, do not consider the likely decrease in AASA with increasing temperature. The consequences of having AASA dependent on temperature have not been addressed yet. The assumption of a temperatureindependent AASA is, however, potentially problematic, as was recently also pointed out by Lee (1991), and future studies will have to be directed to clarifying this question. At present the differences between the C:(t) curves in Figure 6, curves c, should, however, not be overemphasized. Rather it is the fairly good correlation between the experimental and calculated values that should be stressed. After all, these empirical relations between ASA and heat capacity changes constitute, so far, the only link between structural and thermodynamic properties of proteins. They permit fairly good quantitative estimates of the important property ACr, which governs the temperature dependence of all thermodynamic functions and which cannot be estimated by any other theoretical approach. For quantitative results the changes in both the polar and non-polar accessible surface areas must be taken into account: as was done in the present study. Calculations that rely only on the hydrophobic contribution to AC, may lead to incorrect results. (b) Tendamistat

shows convergence of thermodynamic parameters at about 140°C

The recent discussions on hydrophobic interaction and protein stability (Privalov & Gill, 1988, 1989; Baldwin, 1986; Dill, 1990a,b; Creighton, 1990, 1991) focussed on similarities in the thermodynamic properties of proteins and the transfer of non-polar molecules from liquid to water. The remarkable finding was that for several proteins AC, vanished between 130 and 150°C and that this temperature range coincides with the temperature range in which the AS” of transfer of non-polar molecules becomes zero. The vanishing entropy change has been interpreted as being indicative of the disappearance of the characteristic water structure around hydrophobic moieties. At this temperature the solvation water is considered to assume properties no longer different from those of bulk water. The thermodynamics of unfolding of tendamistat supports this view of protein stability. Figure 6 (broken curves) shows that the heat capacity difference between the native and unfolded state of the protein disappears near 140°C. This convergence temperature is iden-

qf Tendamistat

777

tical with that observed with other proteins of considerably different structure (Privalov & Makhatadze, 1990), supporting the view that underlying molecular mechanisms may be of general nature. Although this result is apparently in line with the present interpretation of the hydrophobic effect as propagated by Privalov & Gill (1988, 1989), Murphy et al. (1990) and Privalov et al. (1990), some weaknesses of the model should not be overlooked. These have been most clearly discussed by Muller (1990). While the extrapolated AC, values for several proteins goes to zero between 130 and 150 “C, the AC,, value for transfer of non-polar model compounds does not vanish in this temperature range but retains 30% to 50% of the AC, value at 25°C (Crovetto et al., 1982; Makhatadze & Privalov, 1988). Thus, when the vanishing AS” value of transfer at around 140°C is interpreted as being indicative of the fact that water has lost its anomalous properties and is no longer hydrophobic, the positive AC, value for the transfer of hydrophobic model compounds at this temperature causes interpretative difficulties. First, AC, > 0 implies residual hydrophobic hydration and, secondly, in view of equation (ll), it renders AS” positive for temperatures higher than 140°C. Then, if a negative AS” value is characteristic for hydrophobic hydration, what is the interpretation of a positive AS” above 14O”CZ Does it mean that the anomaly caused by the presence of a hydrophobic moiety in water at low temperatures is reversed above 14O”CZ An analogous difficulty is envisaged in the interpretation of the extrapolated negative AC, value of tendamistat above approximately 140°C (Fig. 6, broken curve c). Therefore, at present’ one has to conclude in view of the inconsistencies that exist in the molecular interpretation of not only the thermodynamic but also the n.m.r. data (Muller, 1990) that there is no break in the solvation properties of water at about 140°C. More sophisticated models will have to be devised before a satisfactory, self-consistent picture of the hydrophobic effect is obtained. (c) Stability

contribution

of disulfide

bonds

A comparison of the stabilities of the a-amylase inhibitor tendamistat, native trypsin inhibitor BPTI, and BPTI-RCOM, a BPTI analog that has only two disulfide bonds, affords some interesting insight into the nature of the stabilizing forces of the proteins. The essential difference between native BPTI and the other two proteins is the number of disulfide bridges. At 25°C this leads to a difference in AH” of 175 kJ/mol and a difference in AG” of 23 kJ/mol between native BPTI and tendamistat. Another comparison also supports the idea that the disulfide bonds are the crucial source of conformational stability for both proteins. BPTI-RCOM, which has the 14-38 sulfhydryl groups carboxymethylated and contains, therefore, only two disulfide bridges between residues 5-55 and 30-51, exhibits strikingly similar stability to that of tendamistat. The standard Gibbs free energy change

778

Diswljide Protein

Tendamistat BPTI-RCOMB

n,Rt 74 58

AHog

4 2 2

AHZII

(kJ/mol)

(kJ/mol)

122 i31

110 130

hds

Table 5 and thermodynccmic ACp§ (kJ/(mol

parameters ASog

AC,,, K))

(kJ/(mol

3.8 2.6

K))

(kJ/(mol

29 1.6

AXXll K))

(kJ/(mol

0.325 0.356

K))

AG”S (kJ/mol)

AGQ jkJ/mol)

25 25

28 26

0275 o-35

Comparison of experimental and calculated results for tendamistat, and BPTI-R,COM at 25°C. t Number of amino acids. $ Number of disulfide bridges. 5 Refers to ca!culated values. using eqns (8), (IO). (12) of Doig & Williams (1991). /I ex refers to experimental calorimetric data; the AG& of tendamistat has been calculated on the basis of the temperature dependent derived from group contributions by method 1. The value is 30.2 kJjmo1 when employing the constant AC&T,) = 2+39 kJ/(mol K). 7 Schwarz et al. (198i).

of unfolding, AC”, of BPTI-RCON is 26 kJ/mol of tendamistat is (4 J/g) at pH 5, and that, 28 kJ/mol (3.7 J/g). Doig & Williams (1991) give empirical relations to estimat,e thermodynamic paramet,ers for simple globular proteins on t,he basis of the total number of residues and the number of disulfide bridges. The values calculated using their equat’ions (8), (10) and (12) are summarized in Table 5 together with the corresponding experimental quantit’ies for BPTT-RCOM. Tt is not really surprising that, using their equations (8), (10) and (12), Doig & Williams (1991) reproduced the thermodynamic quantities, which were the basis of their parameters. A better test for the validity of the correla’tion is therefore the application of these equations to proteins that, were not in the data base that’ was employed for deriving the coefficient,s. Such proteins are tendamistat and BPTI-RCORI. It is noteworthy that’ also in these cases there is good agreement between the calculat’ed and experimental thermodynamic para,meters for both prot#eins. Only the calculated ACp values do not reproduce the experimental values very well. However. that is understandable in view of the limited data set of ACp values that is available for deriving the correlations and in view of the relatively large experimental error involved in t,he determination of these parameters. another important point must be ment,ioned in this context. Cont,ributions of disulfide bonds t,o AGO are not simplv additive. Removal of t,he 14-38 disulfide bondin RPTY decreases AG” bv 33 kJ/mol. which is considerably more than the estimated 13 kJ/mol of disulfide group (Pace et al., 1988). This becomes understandable, if one recalls the role of co-operativity in forming and maintaining protein structure (Prlvalov, 1979; Creighton. 1983, 1990: Dill et aZ., 1989; Baldwin & Eisenberg, 1987). Even though each amino acid contributes marginal binding energy, often an order of magnit’ude below thermal energy kT. co-operation of the interactions provides the required stability. Due to the short-range nature of t,he van der Waals’ interactions, removal of one disulfide group can be visualized to lower interaction energies co-operatively throughout’ the protein. Thus, one has to differentiate between the overall average contribution to stability per disui-

fide bond in intact proteins and the st’ability bation per disulfide bond removed. i-i.-J. Hinz and J. W. Engels gratefulir support from the DFG.

Ag(7’

pertur-

acknowmledge

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by R. Huber