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Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
J. Chem. Thermodynamics 2002, 34, 319–336 doi:10.1006/jcht.2001.0855 Available online at http://www.idealibrary.com on
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin Karunakar Kar, Biju Alex, and Nand Kishorea Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai – 400 076, India
High sensitivity differential scanning calorimetry (d.s.c.) and uv-visible spectrophotometry have been used to study the thermal unfolding of α-chymotrypsin in presence of calcium chloride at pH = 2.8, 3.4, 5.0, 7.0, and 8.2. Quantitative thermodynamic parameters accompanying the thermal transitions have been evaluated. In the absence of calcium ions, the thermal denaturation of α-chymotrypsin is a reversible process giving a ratio of the van’t Hoff to calorimetric enthalpy of 0.92 at pH = 2.8. At pH values higher than 5.0, the thermal denaturations in the absence of calcium chloride were observed to be completely irreversible. In the presence of calcium chloride, α-chymotrypsin undergoes irreversible thermal denaturation and its thermal transitions are found to be scan-rate dependent fitting to the model N2 → I, yielding an average activation energy of (419 ± 16) kJ · mol−1 using different approaches at pH = 2.8. It is also observed that at pH = 2.8 and 3.4, calcium reduces the transition temperature of the protein. However, at pH = 5.0, 7.0, and 8.2, it stabilizes initially, and at higher concentrations the salt acts as a destabilizer of the native structure of α-chymotrypsin. The surface tension values of aqueous calcium chloride solutions were measured and it is observed that the role of surface tension of the medium is not c 2002 Published by Elsevier Science Ltd. dominant in providing thermal stability of this protein. KEYWORDS: α-chymotrypsin; differential scanning calorimetry; calcium; thermal denaturation; surface tension of aqueous calcium chloride
1. Introduction Calcium is biologically an important trace inorganic element. It activates many nonfunctional proteins to functional proteins by changing the conformation resulting in quenching of tryptophan fluorescence. Calcium interacts with a number of extracellular proteins to confer thermal stability, protection against autolysis, and is required for the activity of a number of enzymes. (1, 2) The existence of monomeric and polymeric forms of α-chymotrypsin in solution is well established and the dependence of the reversible association on the ionic strength of the a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/02
c 2002 Published by Elsevier Science Ltd.
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environment has also been well reported. (3–5) It has been reported that an increase in the ionic strength enhances the association of α-chymotrypsin in the acid pH region. The effect of calcium on the monomer–dimer equilibria in terms of the dimerization constant has been reported in the literature. (6) However, the thermal denaturation of this protein in the presence of calcium and its mechanism of denaturation, and quantitative thermodynamics parameters accompanying the thermal transitions are scarce in the literature. In this paper, we report the systematic quantitative thermal denaturation of α-chymotrypsin in the presence of calcium chloride at various pH values using differential scanning calorimetry (d.s.c.) and uv-visible spectrophotometry. The effect of calcium chloride on the surface tension of water has also been correlated with the results available from the thermal denaturation study.
2. Experimental The α-chymotrypsin was procured from Sigma Chemical Company, U.S.A., with its activity as an enzyme reported as 40–60 units per mg protein and used without further purification. The stock solution of the protein was prepared by extensive dialysis of α-chymotrypsin at T = 277 K in respective buffers. At pH = 2.8 and 3.4, 20 · 10−3 mol · dm−3 glycine–HCl; at pH = 5.0, 20 · 10−3 mol · dm−3 acetic acid–sodium acetate; at pH = 7.0, 10 · 10−3 mol · dm−3 HEPES (N-2-Hydroxyethylpiperazine-N-2ethanesulphonic acid); and at pH = 8.2, 5 mmol · dm−3 HEPES solutions were used as buffer. Acetic acid, sodium acetate, glycine, and HEPES were also sigma products. Calcium chloride was obtained from E. Merck (India). The purity of each of these compounds stated by the supplier as mass fraction was greater than 0.99. The pH reported is that of the dialysate buffers determined on a standard control dynamics pH meter at room temperature. Water used for preparing all the solutions was double distilled and deionized using Cole-Parmer research cartridge resins. The concentration of protein was determined spectrophotometrically on a Shimadzu double-beam spectrophotometer (uv0.1% = 2.0. (7) 265) using molar absorptivity, E 280 nm DIFFERENTIAL SCANNING CALORIMETRY
The micro-d.s.c. from SETARAM, France was employed for all calorimetric scans at pH = 2.8. The capacity of the reference and the sample cells of the calorimeter is 1 cm3 . All the samples were degassed for about 10 min before being scanned at the heating rate of interest. Any loss of water during the degassing process was made up by adding an appropriate amount of degassed water. The volume of the solution containing protein or protein and calcium chloride was held fixed at 0.85 cm3 , and the weight of the solutions in the sample and reference cells was always matched. The reference solution was the buffer when the experiment was performed with buffer, or buffer plus calcium chloride when the measurements were made in the presence of salt. All the thermal scans were base line subtracted, and corrected for the thermal lag of the calorimeter using the Tian equation. The reversibility of the calorimetric scans was checked by heating the sample to a temperature slightly above the transition temperature, cooling immediately and then reheating.
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
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The corrected calorimetric data were analyzed by the EXAM program of Kirchhoff, (8) which, for reversible transitions allows least square fits of the data to a two state model including base lines: C p (T ) = (1−α){Ba + Ba0 (T −Tm )}+ N {1H (T )2 /RT 2 }F(α)+α{Bb + Bb0 (T −Tm )}. (1) Here, N is the number of moles of co-operative units per mole of α-chymotrypsin in the sample cell that can be varied as one of the parameters of the fit or held fixed at some pre-determined value and α is the molar fraction of the reaction. The first and the last product parts of the above equation represent pre- and post-transition base lines. The thermodynamic parameters accompanying the endotherm: T1/2 , the temperature where the transition is half complete; 1Hcal , 1C p , respectively the calorimetric enthalpy and heat capacity of denaturation at T = T1/2 ; and N values were determined using an iterative nonlinear fit of the above equation using analytical derivatives and holding the baseline parameters fixed. The van’t Hoff enthalpies for reversible transitions 1HvH were calculated using the following equation (9) : 1HvH = (A RT 21/2 Cex,1/2 )/1Hcal ,
(2)
where the Cex,1/2 is the excess over the base line value of apparent specific heat at T1/2 , R is the gas constant and A = 4.0 for a two state process involving neither association nor dissociation. The deviation of the ratio of the van’t Hoff to calorimetric enthalpy (β), which can also be expressed as inverse of N , (10) may vary significantly from unity if there is some degree of aggregation in either the initial or final state or both, and variation in domain interactions during the multidomain proteins denaturation reaction. (11) For irreversible calorimetric transitions, Tm represents the temperature at which the excess heat capacity has the maximum value. UV-VISIBLE SPECTROPHOTOMETRY
The thermal denaturation experiments on α-chymotrypsin at pH = 3.4, 5.0, 7.0, and 8.2 were carried out using an uv-265 Shimadzu double-beam spectrophotometer. Thermal unfolding of the protein was examined by observing the absorbance at 293 · 10−9 m as a function of temperature. The reference cell contained buffer when the measurements were made in buffer or buffer plus calcium when the thermal denaturation was carried out in the presence of calcium. The temperature of the cuvettes was maintained by circulating water around them from a Plasto Crafts (LTB-20) water bath. The temperature stability in the cuvettes was observed to be ±0.1 K. Heating of the solutions in the cuvette was started at a temperature that was below the thermal transition and continued to a temperature higher than the complete transition. The heating rate of the water around the cuvettes was 0.32 K · min−1 . The reversibility of the thermal transitions recorded for the proteins was checked by reheating the protein solution that was heated to a temperature just past the denaturation in the first heating and cooled. The temperature was increased in steps of 1 K and enough time was given for the thermal equilibrium. The concentration of the α-chymotrypsin in each experiment was fixed at 0.135 · 10−3 mol · dm−3 for d.s.c. experiments and 0.2 · 10−4 mol · dm−3 for uv-visible experiments.
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The evaluation of the thermodynamic parameters obtained from the spectroscopic measurements is generally based upon the temperature dependence of the equilibrium constant of a suitable denaturation mechanism. However, if the process under investigation is irreversible, laws of equilibrium thermodynamics cannot be applied. The data obtained in these measurements were fitted to the EXAM program of Kirchhoff. (8) In the reversible unfolding, the transition temperature, calormetric and van’t Hoff enthalpies of unfolding were evaluated. If the thermal transition was observed to be irreversible, 1Hcal represents the total heat absorbed during the irreversible denaturation process. SURFACE TENSION MEASUREMENTS
The surface tension of the calcium chloride–water solutions was measured by drop weight method. (12) The desired temperature was obtained by circulating water through the glass jacket around the Stalagnometer using a Cole-Parmer Polystat constant-temperature circulator. With this arrangement, the stability of the temperature was within 0.1 K. Maximum care was taken to avoid the vibration of the capillary during the measurements. For each liquid, 35 drops of the solution were collected in a pre-weighed dry vial. After collection of the solution in the vial, it was immediately capped to avoid any evaporation, and then weighed on a Sartorius MP-2004 digital balance having a readability of 0.01 mg.
3. Results and discussion Figure 1 represents the excess heat capacity against temperature plots for α-chymotrypsin at pH = 2.8 in 20 · 10−3 mol · dm−3 glycine–HCl buffer, and in the presence of 50 · 10−3 mol · kg−1 calcium chloride. The transition temperature of the unfolding of chymotrypsin in 20 · 10−3 mol · dm−3 glycine–HCl buffer is observed at T1/2 = 321.6 K which is in excellent agreement with the literature. (7) The ratio of van’t Hoff enthalpy to calorimetric enthalpy was observed to be 0.92 indicating the adherence of the denaturation reaction to two-state Native Denatured mechanism. Figure 2 represents a set of thermal unfolding curves for α-chymotrypsin in the absence and presence of calcium chloride as monitored using a uv-visible spectrophotometer. A wide range of pH values were selected: pH = 2.8, 3.4, 5.0, 7.0, and 8.2. The concentration range of calcium chloride covered in both the differential scanning calorimetric and spectrophotometric measurements was 25 · 10−3 mol · dm−3 to 3 mol · dm−3 . The thermodynamic parameters obtained for α-chymotrypsin from a series of calorimetric and spectrophotometric experiments are summarized in tables 1 and 2. In the calorimetric measurements, the T1/2 values have an experimental error of ±0.1 K and calorimetric enthalpy 1Hcal values have a deviation of 3 per cent including errors in sample preparation, calibration constant and reproducibility. The error in the spectrophotometric measurements was 0.1 K on Tm , which is the temperature at the mid-point of the transition. In the absence of calcium, the thermal stability of α-chymotrypsin was found to increase with an increase in the pH of the solution from pH = 2.8 to 3.4. This result is consistent with that reported by Privalov et al. (7) However, when the pH of the solution is further raised to pH = 5.0 and to pH = 8.2, the transition temperature of α-chymotrypsin falls (figure 3). The thermal unfolding of α-chymotrypsin
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
323
TABLE 1. Thermodynamic parameters associated with the thermal unfolding of 0.135 · 10−3 mol · dm−3 α-chymotrypsin at pH = 2.8 in the absence and presence of CaCla2 determined using d.s.c. The scan-rate of the d.s.c. was 0.5 K · min−1 Ca2+ 10−3 mol · dm−3
Tm K
1Hcal
1C p
kJ · mol−1
kJ · K−1 · mol−1
0
321.6 ± 0.4
588 ± 10
10.3 ± 3.0
25
317.8 ± 0.4
552 ± 15
—
50
316.9 ± 0.6
553 ± 12
—
75
315.6 ± 0.7
620 ± 15
—
a Each value in this table is an average of three or four measurements.
at pH = 2.8 and 3.4 was found to be reversible, hence the data are amenable to application of equilibrium thermodynamics at these pH values. At higher pH values, the thermal transitions were observed to be irreversible. The activity of α-chymotrypsin is very sensitive to pH. Chymotrypsin catalyzed reactions have bell-shaped pH-rate profiles. For example, the pH-rate profile of N -acetyl-L-tryptophan amide catalyzed by α-chymotrypsin at T = 298.15 K shows a maximum at pH ≈ 8.5. (13) In the present study, the transition temperature of α-chymotrypsin decreases between pH = 5 to 7 beyond which up to pH = 8.2 there is a marginal increase. Since chymotrypsin is a protease that is active over the range of pH = 5.0 to 8.2, as the temperature is increased above the onset of the unfolding transition but still below the transition temperature, both native and denatured forms of the enzyme exist. Therefore the thermal transition profiles will be affected since the active enzyme will start degrading the unfolded chymotrypsin, thus contributing to the irreversibility of the transitions. Also it is known (14) that α-chymotrypsin at pH = 2.3 in the presence of 0.1 mol · dm−3 NaCl exists in a predominantly monomeric state, and the association reaction of α-chymotrypsin increases until a maximum is nearly reached at pH = 4.4 beyond which the tendency to associate falls. In the present study, the calorimetric transitions were observed to be reversible at pH = 2.8 in the absence of CaCl2 . Another factor that contributes to the irreversibility with rise in the pH of solution in the absence of CaCl2 is the greater extent of association of the protein. It is also reported that above pH = 6, α-chymotrypsin undergoes aggregation of a higher order than the monomer–dimer. (15) In the presence of calcium chloride, all the thermal transitions were irreversible; hence we have reported only the Tm values for these cases. Figure 4 shows the alternation of the transition temperature which is widely considered as a protein stability index {1T = T1/2 or Tm (α-chymotrypsin + Ca2+ (aq) ) − T1/2 or Tm (α-chymotrypsin + buffer)}, upon addition of varying concentrations of calcium chloride. It is seen in this figure that at pH = 2.8 and 3.4, calcium reduces the thermal stability of the protein. However, at pH = 5.0, 7.0, and 8.2, calcium is initially observed to increase the transition temperature, thus imparts thermal stabilization to α-chymotrypsin at low concentration (figure 4). At these three pH values, the plot of 1T against concentration of calcium ions in solution shows a maxima.
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K. Kar, B. Alex, and N. Kishore 103
CpE / (kJ . K –1 . mol –1)
a
– 10 52.5
b
CpE / (kJ . K –1 . mol –1)
(a)
– 5.1 297
(b)
T/K
336
FIGURE 1. d.s.c. scans of the thermal denaturation of 0.135 · 10−3 mol · dm−3 α-chymotrypsin in the absence {figure 1(a)} and presence {figure 1(b)} of CaCl2 plotted against temperture: (a) of 50 · 10−3 mol · dm−3 calcium chloride at pH = 2.8: , experimental points; ——, theoretical fit; (b) rescan of (a).
◦
The order of the thermal stabilization is the following: pH = 7.0 (1T = 15.4) > pH = 8.2 (1T = 12.0) > pH = 5.0 (1T = 3.6). The concentrations of calcium at which stabilization imparted to α-chymotrypsin is maximum, are (500 · 10−3 , 150 · 10−3 , and 500 · 10−3 ) mol · kg−1 at pH = 5.0, 7.0, and 8.2 respectively. In a multi-component system containing α-chymotrypsin, water and calcium chloride, the interactions that could govern the shifting of the N D equilibrium include those
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin 1.2
325
a
Fraction Denatured
1.0 0.8 0.6 0.4 0.2 0.0 290
1.2
300
310
320 T/K
330
340
350
300
310
320
330
340
350
b
Fraction Denatured
1.0 0.8 0.6 0.4 0.2 0.0 290
T/K
FIGURE 2. Thermal denaturation profiles of α-chymotrypsin plotted against temperature in the absence {figure 2(a): , pH = 3.4; , pH = 5.0; 4, pH = 7.0; O, pH = 8.2} and presence of calcium chloride {figure 2(b): pH = 7.0: , 0; , 25; 1, 50; O, 150; ♦, 500; +, 1000; ×, 2000 · 10−3 mol · kg−1 }.
◦
◦
between calcium chloride and water, calcium chloride and protein, and water and protein. The binding constant of Ca2+ (aq) to bovine α-chymotrypsin has been reported (16) as (1.4 ± 0.3) · 104 at pH = 6 with unit stoichiometry of the binding reaction. For serine proteases, the structure of trypsin with one bound calcium has been determined to a
326
K. Kar, B. Alex, and N. Kishore 330 328 326
T1/2 / K
324 322 320 318 316 314 2
3
4
5
pH
6
7
8
9
FIGURE 3. Variation of the transition temperature of α-chymotrypsin plotted against pH of the solution. 20 15
∆T 1/2
10 5 0 –5 – 10 0
500
1000
1500
2000
2500
3000
3500
10 3 . mol . kg –1
FIGURE 4. Change in the temperature of denaturation {1T = T1/2 or Tm (α-chymotrypsin + Ca2+ aq ) − T1/2 or Tm (α-chymotrypsin + buffer)} plotted against molality: pH = 3.4; H, pH = 5.0; ∇, pH = 7.0; , pH = 8.2.
•,
pH = 2.8;
◦,
resolution of 0.18 nm and the calcium ligands were identified. (17) It has been reported (18) that most likely Ca(II) binding sites are in essentially identical places on chymotrypsin and trypsin. In trypsin, the calcium ion is co-ordinated by six ligands at the edges of an
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
327
TABLE 2. Thermodynamic parameters associated with the thermal unfolding of 0.2 · 10−4 mol · dm−3 αchymotrypsin at pH = 3.4, 5.0, 7.0, and 8.2 in the absence and presence of CaCla2 determined using a uvvisible spectrophotometer Ca2+ 10−3 · mol · dm−3
Tm K
pH = 3.4 0
329.4
25
325.3
50
323.0
150
321.3 pH = 5.0
0
325.5
25
328.9
500
329.1
1000
328.3
1500
326.1 pH = 7.0
0
315.1
25
328.0
50
329.6
150
330.5
1000
328.4
2000
320.4
3000
309.7 pH = 8.2
0
316.4
25
324.5
500
328.4
1000
326.7
1500
324.6
2000
320.2
a Each value in this table is an average of three or four measurements.
octahedron. Four ligands form a loop of the protein, Glu70 and Glu80 are co-ordinated with their side chain carboxylate groups, and Asn72 and Val75 are co-ordinated with the
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K. Kar, B. Alex, and N. Kishore
CpE / (kJ . K –1 . mol –1)
15 kJ . K –1 . mol –1
300
T/K
340
FIGURE 5. Excess heat capacity profile plotted against temperature for thermal denaturation of α-chymotrypsin at pH = 2.8 and heating rate of 0.5 K · min−1 in the presence of 100 · 10−3 mol · kg−1 calcium chloride.
backbone carboxyls. The remaining ligands are water molecules that are also hydrogen bonded to Glu70 and Glu77 respectively. (17) Also, the Ca2+ binding site is located far from the active site. (17) Figure 1(b) shows the thermal denaturation curve of α-chymoptrypsin in the presence of 50 · 10−3 mol · kg−1 Ca2+ (aq) at pH = 2.8. The mid-point of the transition was found to be lower than that of the protein in the absence of Ca2+ indicating that Ca2+ has reduced the thermal stability of α-chymotrypsin. Further, at this pH = 2.8, on increasing the concentration of Ca2+ , the transition temperature was found to decrease. In the presence of 0.100 mol · dm−3 Ca2+ , there appears to a strong post-transition aggregation of the protein as reflected by the disturbed behaviour of the d.s.c. profile after the transition (figure 5). Therefore in these cases, we have not calculated the area under the curve. Upon re-heating the solution of α-chymotrypsin in the presence of all concentrations of Ca2+ studied, no transition was observed indicating that the thermal denaturation of α-chymotrypsin under these conditions is irreversible. The increase in the ionic strength of the solution due to addition of calcium chloride even at pH = 2.8 leads to irreversible thermal transitions. This result is consistent with the enhancement of dimerization constant of α-chymotrypsin with an increase in the ionic strength. (14) For applying the equilibrium thermodynamic model to the thermal studies, an essential requirement is that there should be thermodynamic equilibrium in the sample under investigation throughout the temperature-induced unfolding process. The criteria for equilibrium are generally judged from the reproducibility of the d.s.c. trace in a second heating of the sample. If the second thermogram shows no thermal effect, thermodynamic functions for the process such as changes in entropy and reaction Gibbs function cannot be extracted from the first trace. However, it has also been shown that the thermogram of
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
329
the thermal denaturation of several proteins can be interpreted in terms of the van’t Hoff equation in spite of the calorimetric irreversibility. (19) In the calorimetric experiments, the calorimetric enthalpy of transition is obtained by calculating the area under the C p,ex against T profile. Therefore, we have reported the transition temperature T1/2 and calorimetric enthalpies 1Hcal for the measurements performed using d.s.c. However, evaluation of enthalpy of denaturation in spectroscopic measurements is done from the temperature dependence of the equilibrium constant. For this, the reversibility of the thermal transition must be ensured. Therefore, if the transitions are irreversible, we have reported only Tm values. Experiments were done on thermal unfolding of 0.135·10−3 mol · dm−3 α-chymotrypsin in the presence of 0.025 mol · dm−3 calcium chloride at scanning rates of (0.2, 0.4, 0.5, and 0.6) K · min−1 to check whether the process under investigation was under kinetic control. Figure 6 shows the d.s.c. traces obtained at different scanning rates. The thermodynamic parameters accompanying the thermal transitions at these four scan-rates are given in table 3. It is clear from figure 6 that the transition temperature of α-chymotrypsin in the presence of 25 · 10−3 mol · dm−3 Ca2+ is scan-rate dependent even after correcting for the instrumental response time. The reversibility of the calorimetric transitions was checked at each scan-rate. No transition was obtained in the second heating in all these cases. These results suggest that the denaturation process of α-chymotrypsin in the presence of calcium chloride is under kinetic control, and the interpretation of calorimetric data in terms of equilibrium thermodynamics cannot be carried out. The process taking place in the calorimetric cells fits to the following two-state process: k
N2 → I,
(3)
where N is the native state, and I is the final state arrived at irreversibly from the unfolded one, k is a first-order kinetic constant which changes with the temperature according to the Arrhenius equation. A mathematical elaboration (20) of the model given above allows the calculation of activation energy of the kinetic process in different ways as discussed below. Method A: The rate constant of the reaction at a temperature T can be obtained by using (20) k = νC p /(qT − q),
(4)
where ν, C p , qT , and q are respectively, the scan-rate of the calorimeter, excess heat capacity above the base line, total heat absorbed or evolved in the process and heat change at a given temperature T . The energy of activation E a can be obtained from the values of k at several temperatures by using the Arrhenius equation, k = A · e−E a /RT .
(5)
Figure 7(a) shows the plot of log k against 1/T using the data obtained at four scan-rates. A dimer value of (411±7) kJ · mol−1 for the energy of activation has been calculated from this Arrhenius plot.
330
K. Kar, B. Alex, and N. Kishore 80 4
CpE / (kJ . K –1 . mol –1)
60 3 40
2
20
1
0 313
323
T/K
FIGURE 6. Excess heat capacity plotted against temperature of 0.135 · 10−3 mol · dm−3 α-chymotrypsin at pH = (2.83: 1, 0.2; 2, 0.4; 3, 0.5; 4, 0.6) K · min−1 . TABLE 3. Thermodynamic parameters associated with the scan-rate dependent thermal unfolding of 0.135 · 10−3 mol · dm−3 α-chymotrypsin in the presence of 25 · 10−3 mol · dm−3 CaCla2 at pH = 2.8 Scan-rate K · min−1
Tm K
1Hcal kJ · mol−1 638 ± 17
0.2
316.3 ± 0.3
0.4
317.2 ± 0.2
552 ± 6
0.5
317.5 ± 0.4
552 ± 12
0.6
318.4 ± 0.5
516 ± 9
a Each value in this table is an average of three or four measurements.
Method B: The dependence of heat evolved or absorbed as a function of temperature can be expressed as (20) ln[ln{qT /(qT − q)}] = E a /R[1/Tm − 1/T ].
(6)
According to this model, a plot of ln[ln(q/(qT − q))] versus 1/T should lead to straight lines, and the slope of each line at every scan-rate should yield the value of −E a /R. Using the data at four scan-rates studied, the plot generated is shown in figure 7(b) and the average
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
331
– 11
– 0.87 a
c
ln k
ln(ν / Tm2)
– 12
– 13
– 6.58 – 0.85
– 14 31.35 31.40 31.45 31.50 31.55 31.60
b
ln[ln {qT / (qT-q)}]
104 . 1 /Tm/ K –1
– 5.10 3.12
103 . 1 /T / K –1
3.23
◦
FIGURE 7. Arrhenius plot including k data from the four scan-rates used {figure 7(a)}: N, 0.2; , 0.4; , 0.5; , 0.6 K · min−1 . (b) Plots of ln [ln{qT /(qT − q)}] against 1/T : symbols are same as those used in (a). (c) Values of ln(ν/Tm2 ) versus 1/Tm .
•
activation energy thus obtained is (414 ± 8) kJ · mol−1 . In addition, the x-axis intercept of these plots should yield the values of Tm . The values of Tm thus obtained are (318.9, 317.8, 316.4, and 316.1) K at the scan-rates (0.6, 0.5, 0.4, and 0.2) K · min−1 respectively. The values obtained experimentally at these four scan-rates are respectively (318.4, 317.5, 317.0, and 316.3) K, which are in excellent agreement with those calculated from the plots, thus supporting the validity of model assumed. Method C: The two-state kinetic model of denaturation also predicts that the temperature corresponding to the maximum of the heat capacity, changes according to the following relation (20) : ν/Tm2 = A/E a · e−E a /RT m .
(7)
Thus a plot of ln ν/Tm2 against 1/Tm should result in a straight line with a slope equal to −E a /R. From the plot {figure 7(c)} the calculated activation energy is (432 ± 10) kJ · mol−1 .
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K. Kar, B. Alex, and N. Kishore
Method D: The activation energy can be calculated (20) from the heat capacity at the maximum of the trace C m p 2 E a = (e RC m p Tm )/qT .
(8)
Using this equation for the four traces shown in figure 6, an average activation energy of (419 ± 7) kJ · mol−1 is obtained. The above methods involve different approximations and experimental information. It is seen that the above methods applied to the data obtained in the present study provide excellent agreement between the results obtained for the energy of activation. The average value of the activation energy employing the methods A to D is (419 ± 16) kJ · mol−1 of dimer. Thus by this excellent agreement, we have shown that the d.s.c. thermograms for the thermal denaturation α-chymotrypsin can be interpreted in terms of a kinetic k
process N2 → I, where k is a first-order kinetic constant that changes with temperature as described by the Arrhenius equation. It is possible that more complex models may represent a first-order kinetic process, for example, the irreversible thermal denaturation of α-chymotrypsin might be k1
k3
N2 D → I. k2
(9)
Here, I is a final state irreversibly arrived at from the unfolded state. It is assumed that all the processes are first order, that k3 k2 at any moment, most of the D molecules will be converted to I instead of returning to N through the process D N2 . If the sample of α-chymotrypsin in the d.s.c. cells is heated only up to the mid-point of the transition, followed by immediate cooling, a rescanning of the sample still shows the peak. However, the height of the transition is much lower than the transition in the first heating. This indicates that the process is irreversible before the complete denaturation, thus supporting the proposed irreversible model N2 → I. Effect of surface tension The values of surface tension of aqueous calcium chloride solutions measured by drop weight method have been reported in table 4. The surface tension of water was found to increase linearly with the concentration of calcium chloride as shown in figure 8. Figure 9 shows the variation of 1T as a function of change in the surface tension of water at various pH values. It is seen in this figure that at pH = 5.0, 7.0, and 8.2, the thermal stability index of the protein passes through a maximum followed by a decrease. However, at pH = 2.8 and 3.2, the thermal stability of the protein falls sharply with the surface tension. It is generally observed (21) that the compounds that lead to a positive increase in the surface tension, give a negative preferential interaction parameter, (∂m 3 /∂m 2 ). Here, m 2 and m 3 represent the molalities of protein and co-solvent respectively. Negative values of the preferential interaction parameters indicate the preferential exclusion of the co-solvent molecules from the protein surface. (21) It has been shown using rigorous thermodynamic analysis that the effect of sugars such as sucrose, (22) glucose and lactose (23) on the surface
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
333
88 86
10 3 . σ / (N . m –1)
84 82 80 78 76 74 72 0
1000
2000 3000 103 . mol . kg –1
4000
5000
FIGURE 8. Surface tension plotted against molality of aqueous calcium chloride at T = 298.15 K.
tension of water has been the main force responsible for the stabilization of the proteins and their preferential interactions. Although we have observed a positive slope of surface tension versus concentration of CaCl2 , the present results do not show a linear relationship between the increase in the surface tension of water and the alteration in the thermal stability of the protein. The results are clearly pH dependent. As seen in figure 3, at pH = 2.8 and 3.42, CaCl2 reduces the thermal stability of the protein at all concentrations studied. However, at pH = 7.0 and 8.2, CaCl2 initially enhances the thermal stability followed by destabilization at higher concentrations. These observations suggest that in this case the role of surface tension of the medium is not dominant in providing thermal stability to this protein. Breslow and Guo (24) and Timasheff and co-workers (12, 25) have proposed that the free energy of cavity formation in water to accommodate the exposed groups of proteins upon denaturation is proportional to the increase in surface tension of water by different solvent additives. On the other hand, it has also been reported that amino acids and salts, (12) urea and guanidinium chloride have been found to increase the surface free energy of water (24) and are also preferentially bound to proteins at high concentrations. (26) We have no doubt that the thermal transitions observed in the presence of calcium using uv-visible spectrophotometry are due to the unfolding of protein give the similar results to those observed by us using d.s.c. at pH = 2.8 as reported in this paper. A clear cooperative endotherm on the d.s.c. is proof of the thermally induced unfolding reaction of the protein. Moreover, the aggregation of the protein is an exothermic reaction. The plot in figure 2, which shows the shape of the transition profile at pH = 3.4 in the absence of calcium (reversible reaction) and in the presence of calcium (irreversible reaction), is indicative of the unfolding reaction of the protein. An increase in the optical density for
334
K. Kar, B. Alex, and N. Kishore 18 16 14 12 10 ∆T 1/ 2 / K
8 6 4 2 0 –2 –4 –6 –8 0
2
4 6 10 3 . ∆σ / (N . m –1)
8
10
FIGURE 9. Plot of the change in thermal stability of α-chymotrypsin against the change in surface tension of water in the presence of calcium chloride: O, pH = 7.0; ♦, pH = 5.0; 4, pH = 8.2; , pH = 2.8; , pH = 3.4.
◦
TABLE 4. Results of surface tension on aqueous calcium chloride at T = 298.15 K M (mol · kg−1 )
σ (10−3 · N · m−1 )
0.05
73.2
0.20
73.8
0.50
74.7
1.00
76.3
2.00
77.7
3.00
83.6
5.00
87.3
some proteins with a rise in temperature showing the thermal denaturation transition has also been reported in the literature. (27, 28)
4. Conclusions The thermal denaturation of α-chymotrypsin in the absence of calcium chloride follows the two-state reversible denaturation mechanism at pH = 2.8 and 3.4. However, at pH = 5.0, 7.2, and 8.2, the thermal denaturation of the protein is irreversible. The effect of calcium
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
335
towards the thermal stability of α-chymotrypsin has been found to be pH dependent. At pH = 2.8 and 3.4, calcium reduces the transition temperature of the protein. At pH = 5.0, 7.0, and 8.2, calcium chloride was initially found to be a stabilizer of the protein at lower concentrations, but at higher concentration the salt acted as a destabilizer. All the thermal transitions of the protein in the presence of calcium chloride were observed to be irreversible, thus restricting the application of equilibrium thermodynamics to the analysis of the irreversible data. Under the condition where calcium chloride induces irreversible calorimetric transition, the scan-rate analysis provide energy of activation of (419 ± 16) kJ · mol−1 for the process which the protein follows under kinetic control. An excellent match between the experimental and calculate transition temperatures, and the activation energy values calculated by different methods support that the thermal k
denaturation of α-chymotrypsin in the presence of calcium chloride follows the N2 → I mechanism. Calcium chloride has been observed to increase the surface tension of water at all the concentrations studied. These results suggest that in this case the role of surface tension of the medium is not dominant in providing thermal stability to this protein. Financial support from Department of Science and Technology, India is gratefully acknowledged. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
Hendrix, T.; Griko, Y. V.; Privalov, P. L. Biophys. Chem. 2000, 84, 27–34. Zahnley, J. C. J. Inorg. Biochem. 1981, 15, 67–78. Winzor, D. J.; Scheraga, H. A. Biochemistry 1963, 2, 1263–1267. Shiao, D. D. F.; Sturtevant, J. M. Biochemistry 1963, 8, 4910–4917. Anue, K. C.; Timasheff, S. N. Biochemistry 1971, 10, 1609–1617. Shearwin, K. E.; Winzor, D. J. Biochim. Biophys. Acta 1990, 1038, 136–138. Privalov, P. L.; Khechinashvilli, N. N. J. Mol. Biol. 1974, 86, 665–684. Kirchhoff, W. H. EXAM, US Department of Energy, Thermodynamics Division, National Institute of Standards and Technology. Gaithersburg: USA, MD. Sturtevant, J. M. Annu. Rev. Phys. Chem. 1987, 38, 463–488. Ginnsburg, A.; Zolkiewski, M. Biochemistry 1991, 30, 9421–9429. Brandts, J. F.; Hu, C. Q.; Lin, L-N.; Mas, M. T. Biochemistry 1989, 28, 8588–8596. Kita, Y.; Arakawa, T.; Lin, T-Y.; Timasheff, S. N. Biochemistry 1994, 33, 15178–15189. Hess, G. P. Chymotrypsin—Chemical Properties and Catalysis. The Enzymes. Boyer, P.: editor. Academic Press: 1971, 213–244. Anue, K. C.; Timasheff, S. N. Biochemistry 1971, 10, 1609–1617. Rao, M. S. N.; Kegeles, G. J. Am. Chem. Soc. 1958, 80, 5724–5729. Chiancone, E.; Drakenberg, T.; Teleman, O.; Forsen, S. J. Mol. Biol 1985, 185, 201–207. Bode, W.; Schwager, P. J. Biol. Chem. 1975, 98, 693–717. Adebodun, F.; Jordan, F. Biochemistry 1989, 28, 7524–7531. Hu, C. Q.; Sturtevant, J. M. Biochemistry 1987, 26, 178–182. Sanchez, J. M.; Lopez-L, J. L.; Cortijo, M.; Mateo, P. L. Biochemistry 1988, 27, 1648–1652. Timasheff, S. N. Preferential Interactions of Water and Cosolvents with Proteins: Protein– Solvent Interactions. Gregory, R. N.: editor. Marcel Dekker Inc: New York. 1995, 445–482. Lee, J. C.; Timasheff, S. N. J. Biol. Chem. 1981, 256, 7193–7201. Arakawa, T.; Timasheff, S. N. Biochemistry 1982, 21, 6536–6544. Breslow, R.; Guo, T. Proc. Natl. Acad. Sci., USA 1990, 87, 167–169. Lin, T-Y.; Timasheff, S. N. Protein Sci. 1996, 5, 372–381.
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26. Arakawa, T.; Timasheff, S. N. Biochemistry 1984, 23, 5912–5923. 27. Lee, L. L-Y.; Lee, J. C. Biochemistry 1987, 26, 7813–7819. 28. Arakawa, T.; Bhat, R.; Timesheff, S. N. Biochemistry 1990, 29, 1924–1931. (Received 9 January 2001; in final form 16 April 2001)
WE-286
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin Karunakar Kar, Biju Alex, and Nand Kishorea Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai – 400 076, India
High sensitivity differential scanning calorimetry (d.s.c.) and uv-visible spectrophotometry have been used to study the thermal unfolding of α-chymotrypsin in presence of calcium chloride at pH = 2.8, 3.4, 5.0, 7.0, and 8.2. Quantitative thermodynamic parameters accompanying the thermal transitions have been evaluated. In the absence of calcium ions, the thermal denaturation of α-chymotrypsin is a reversible process giving a ratio of the van’t Hoff to calorimetric enthalpy of 0.92 at pH = 2.8. At pH values higher than 5.0, the thermal denaturations in the absence of calcium chloride were observed to be completely irreversible. In the presence of calcium chloride, α-chymotrypsin undergoes irreversible thermal denaturation and its thermal transitions are found to be scan-rate dependent fitting to the model N2 → I, yielding an average activation energy of (419 ± 16) kJ · mol−1 using different approaches at pH = 2.8. It is also observed that at pH = 2.8 and 3.4, calcium reduces the transition temperature of the protein. However, at pH = 5.0, 7.0, and 8.2, it stabilizes initially, and at higher concentrations the salt acts as a destabilizer of the native structure of α-chymotrypsin. The surface tension values of aqueous calcium chloride solutions were measured and it is observed that the role of surface tension of the medium is not c 2002 Published by Elsevier Science Ltd. dominant in providing thermal stability of this protein. KEYWORDS: α-chymotrypsin; differential scanning calorimetry; calcium; thermal denaturation; surface tension of aqueous calcium chloride
1. Introduction Calcium is biologically an important trace inorganic element. It activates many nonfunctional proteins to functional proteins by changing the conformation resulting in quenching of tryptophan fluorescence. Calcium interacts with a number of extracellular proteins to confer thermal stability, protection against autolysis, and is required for the activity of a number of enzymes. (1, 2) The existence of monomeric and polymeric forms of α-chymotrypsin in solution is well established and the dependence of the reversible association on the ionic strength of the a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/02
c 2002 Published by Elsevier Science Ltd.
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environment has also been well reported. (3–5) It has been reported that an increase in the ionic strength enhances the association of α-chymotrypsin in the acid pH region. The effect of calcium on the monomer–dimer equilibria in terms of the dimerization constant has been reported in the literature. (6) However, the thermal denaturation of this protein in the presence of calcium and its mechanism of denaturation, and quantitative thermodynamics parameters accompanying the thermal transitions are scarce in the literature. In this paper, we report the systematic quantitative thermal denaturation of α-chymotrypsin in the presence of calcium chloride at various pH values using differential scanning calorimetry (d.s.c.) and uv-visible spectrophotometry. The effect of calcium chloride on the surface tension of water has also been correlated with the results available from the thermal denaturation study.
2. Experimental The α-chymotrypsin was procured from Sigma Chemical Company, U.S.A., with its activity as an enzyme reported as 40–60 units per mg protein and used without further purification. The stock solution of the protein was prepared by extensive dialysis of α-chymotrypsin at T = 277 K in respective buffers. At pH = 2.8 and 3.4, 20 · 10−3 mol · dm−3 glycine–HCl; at pH = 5.0, 20 · 10−3 mol · dm−3 acetic acid–sodium acetate; at pH = 7.0, 10 · 10−3 mol · dm−3 HEPES (N-2-Hydroxyethylpiperazine-N-2ethanesulphonic acid); and at pH = 8.2, 5 mmol · dm−3 HEPES solutions were used as buffer. Acetic acid, sodium acetate, glycine, and HEPES were also sigma products. Calcium chloride was obtained from E. Merck (India). The purity of each of these compounds stated by the supplier as mass fraction was greater than 0.99. The pH reported is that of the dialysate buffers determined on a standard control dynamics pH meter at room temperature. Water used for preparing all the solutions was double distilled and deionized using Cole-Parmer research cartridge resins. The concentration of protein was determined spectrophotometrically on a Shimadzu double-beam spectrophotometer (uv0.1% = 2.0. (7) 265) using molar absorptivity, E 280 nm DIFFERENTIAL SCANNING CALORIMETRY
The micro-d.s.c. from SETARAM, France was employed for all calorimetric scans at pH = 2.8. The capacity of the reference and the sample cells of the calorimeter is 1 cm3 . All the samples were degassed for about 10 min before being scanned at the heating rate of interest. Any loss of water during the degassing process was made up by adding an appropriate amount of degassed water. The volume of the solution containing protein or protein and calcium chloride was held fixed at 0.85 cm3 , and the weight of the solutions in the sample and reference cells was always matched. The reference solution was the buffer when the experiment was performed with buffer, or buffer plus calcium chloride when the measurements were made in the presence of salt. All the thermal scans were base line subtracted, and corrected for the thermal lag of the calorimeter using the Tian equation. The reversibility of the calorimetric scans was checked by heating the sample to a temperature slightly above the transition temperature, cooling immediately and then reheating.
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
321
The corrected calorimetric data were analyzed by the EXAM program of Kirchhoff, (8) which, for reversible transitions allows least square fits of the data to a two state model including base lines: C p (T ) = (1−α){Ba + Ba0 (T −Tm )}+ N {1H (T )2 /RT 2 }F(α)+α{Bb + Bb0 (T −Tm )}. (1) Here, N is the number of moles of co-operative units per mole of α-chymotrypsin in the sample cell that can be varied as one of the parameters of the fit or held fixed at some pre-determined value and α is the molar fraction of the reaction. The first and the last product parts of the above equation represent pre- and post-transition base lines. The thermodynamic parameters accompanying the endotherm: T1/2 , the temperature where the transition is half complete; 1Hcal , 1C p , respectively the calorimetric enthalpy and heat capacity of denaturation at T = T1/2 ; and N values were determined using an iterative nonlinear fit of the above equation using analytical derivatives and holding the baseline parameters fixed. The van’t Hoff enthalpies for reversible transitions 1HvH were calculated using the following equation (9) : 1HvH = (A RT 21/2 Cex,1/2 )/1Hcal ,
(2)
where the Cex,1/2 is the excess over the base line value of apparent specific heat at T1/2 , R is the gas constant and A = 4.0 for a two state process involving neither association nor dissociation. The deviation of the ratio of the van’t Hoff to calorimetric enthalpy (β), which can also be expressed as inverse of N , (10) may vary significantly from unity if there is some degree of aggregation in either the initial or final state or both, and variation in domain interactions during the multidomain proteins denaturation reaction. (11) For irreversible calorimetric transitions, Tm represents the temperature at which the excess heat capacity has the maximum value. UV-VISIBLE SPECTROPHOTOMETRY
The thermal denaturation experiments on α-chymotrypsin at pH = 3.4, 5.0, 7.0, and 8.2 were carried out using an uv-265 Shimadzu double-beam spectrophotometer. Thermal unfolding of the protein was examined by observing the absorbance at 293 · 10−9 m as a function of temperature. The reference cell contained buffer when the measurements were made in buffer or buffer plus calcium when the thermal denaturation was carried out in the presence of calcium. The temperature of the cuvettes was maintained by circulating water around them from a Plasto Crafts (LTB-20) water bath. The temperature stability in the cuvettes was observed to be ±0.1 K. Heating of the solutions in the cuvette was started at a temperature that was below the thermal transition and continued to a temperature higher than the complete transition. The heating rate of the water around the cuvettes was 0.32 K · min−1 . The reversibility of the thermal transitions recorded for the proteins was checked by reheating the protein solution that was heated to a temperature just past the denaturation in the first heating and cooled. The temperature was increased in steps of 1 K and enough time was given for the thermal equilibrium. The concentration of the α-chymotrypsin in each experiment was fixed at 0.135 · 10−3 mol · dm−3 for d.s.c. experiments and 0.2 · 10−4 mol · dm−3 for uv-visible experiments.
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The evaluation of the thermodynamic parameters obtained from the spectroscopic measurements is generally based upon the temperature dependence of the equilibrium constant of a suitable denaturation mechanism. However, if the process under investigation is irreversible, laws of equilibrium thermodynamics cannot be applied. The data obtained in these measurements were fitted to the EXAM program of Kirchhoff. (8) In the reversible unfolding, the transition temperature, calormetric and van’t Hoff enthalpies of unfolding were evaluated. If the thermal transition was observed to be irreversible, 1Hcal represents the total heat absorbed during the irreversible denaturation process. SURFACE TENSION MEASUREMENTS
The surface tension of the calcium chloride–water solutions was measured by drop weight method. (12) The desired temperature was obtained by circulating water through the glass jacket around the Stalagnometer using a Cole-Parmer Polystat constant-temperature circulator. With this arrangement, the stability of the temperature was within 0.1 K. Maximum care was taken to avoid the vibration of the capillary during the measurements. For each liquid, 35 drops of the solution were collected in a pre-weighed dry vial. After collection of the solution in the vial, it was immediately capped to avoid any evaporation, and then weighed on a Sartorius MP-2004 digital balance having a readability of 0.01 mg.
3. Results and discussion Figure 1 represents the excess heat capacity against temperature plots for α-chymotrypsin at pH = 2.8 in 20 · 10−3 mol · dm−3 glycine–HCl buffer, and in the presence of 50 · 10−3 mol · kg−1 calcium chloride. The transition temperature of the unfolding of chymotrypsin in 20 · 10−3 mol · dm−3 glycine–HCl buffer is observed at T1/2 = 321.6 K which is in excellent agreement with the literature. (7) The ratio of van’t Hoff enthalpy to calorimetric enthalpy was observed to be 0.92 indicating the adherence of the denaturation reaction to two-state Native Denatured mechanism. Figure 2 represents a set of thermal unfolding curves for α-chymotrypsin in the absence and presence of calcium chloride as monitored using a uv-visible spectrophotometer. A wide range of pH values were selected: pH = 2.8, 3.4, 5.0, 7.0, and 8.2. The concentration range of calcium chloride covered in both the differential scanning calorimetric and spectrophotometric measurements was 25 · 10−3 mol · dm−3 to 3 mol · dm−3 . The thermodynamic parameters obtained for α-chymotrypsin from a series of calorimetric and spectrophotometric experiments are summarized in tables 1 and 2. In the calorimetric measurements, the T1/2 values have an experimental error of ±0.1 K and calorimetric enthalpy 1Hcal values have a deviation of 3 per cent including errors in sample preparation, calibration constant and reproducibility. The error in the spectrophotometric measurements was 0.1 K on Tm , which is the temperature at the mid-point of the transition. In the absence of calcium, the thermal stability of α-chymotrypsin was found to increase with an increase in the pH of the solution from pH = 2.8 to 3.4. This result is consistent with that reported by Privalov et al. (7) However, when the pH of the solution is further raised to pH = 5.0 and to pH = 8.2, the transition temperature of α-chymotrypsin falls (figure 3). The thermal unfolding of α-chymotrypsin
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
323
TABLE 1. Thermodynamic parameters associated with the thermal unfolding of 0.135 · 10−3 mol · dm−3 α-chymotrypsin at pH = 2.8 in the absence and presence of CaCla2 determined using d.s.c. The scan-rate of the d.s.c. was 0.5 K · min−1 Ca2+ 10−3 mol · dm−3
Tm K
1Hcal
1C p
kJ · mol−1
kJ · K−1 · mol−1
0
321.6 ± 0.4
588 ± 10
10.3 ± 3.0
25
317.8 ± 0.4
552 ± 15
—
50
316.9 ± 0.6
553 ± 12
—
75
315.6 ± 0.7
620 ± 15
—
a Each value in this table is an average of three or four measurements.
at pH = 2.8 and 3.4 was found to be reversible, hence the data are amenable to application of equilibrium thermodynamics at these pH values. At higher pH values, the thermal transitions were observed to be irreversible. The activity of α-chymotrypsin is very sensitive to pH. Chymotrypsin catalyzed reactions have bell-shaped pH-rate profiles. For example, the pH-rate profile of N -acetyl-L-tryptophan amide catalyzed by α-chymotrypsin at T = 298.15 K shows a maximum at pH ≈ 8.5. (13) In the present study, the transition temperature of α-chymotrypsin decreases between pH = 5 to 7 beyond which up to pH = 8.2 there is a marginal increase. Since chymotrypsin is a protease that is active over the range of pH = 5.0 to 8.2, as the temperature is increased above the onset of the unfolding transition but still below the transition temperature, both native and denatured forms of the enzyme exist. Therefore the thermal transition profiles will be affected since the active enzyme will start degrading the unfolded chymotrypsin, thus contributing to the irreversibility of the transitions. Also it is known (14) that α-chymotrypsin at pH = 2.3 in the presence of 0.1 mol · dm−3 NaCl exists in a predominantly monomeric state, and the association reaction of α-chymotrypsin increases until a maximum is nearly reached at pH = 4.4 beyond which the tendency to associate falls. In the present study, the calorimetric transitions were observed to be reversible at pH = 2.8 in the absence of CaCl2 . Another factor that contributes to the irreversibility with rise in the pH of solution in the absence of CaCl2 is the greater extent of association of the protein. It is also reported that above pH = 6, α-chymotrypsin undergoes aggregation of a higher order than the monomer–dimer. (15) In the presence of calcium chloride, all the thermal transitions were irreversible; hence we have reported only the Tm values for these cases. Figure 4 shows the alternation of the transition temperature which is widely considered as a protein stability index {1T = T1/2 or Tm (α-chymotrypsin + Ca2+ (aq) ) − T1/2 or Tm (α-chymotrypsin + buffer)}, upon addition of varying concentrations of calcium chloride. It is seen in this figure that at pH = 2.8 and 3.4, calcium reduces the thermal stability of the protein. However, at pH = 5.0, 7.0, and 8.2, calcium is initially observed to increase the transition temperature, thus imparts thermal stabilization to α-chymotrypsin at low concentration (figure 4). At these three pH values, the plot of 1T against concentration of calcium ions in solution shows a maxima.
324
K. Kar, B. Alex, and N. Kishore 103
CpE / (kJ . K –1 . mol –1)
a
– 10 52.5
b
CpE / (kJ . K –1 . mol –1)
(a)
– 5.1 297
(b)
T/K
336
FIGURE 1. d.s.c. scans of the thermal denaturation of 0.135 · 10−3 mol · dm−3 α-chymotrypsin in the absence {figure 1(a)} and presence {figure 1(b)} of CaCl2 plotted against temperture: (a) of 50 · 10−3 mol · dm−3 calcium chloride at pH = 2.8: , experimental points; ——, theoretical fit; (b) rescan of (a).
◦
The order of the thermal stabilization is the following: pH = 7.0 (1T = 15.4) > pH = 8.2 (1T = 12.0) > pH = 5.0 (1T = 3.6). The concentrations of calcium at which stabilization imparted to α-chymotrypsin is maximum, are (500 · 10−3 , 150 · 10−3 , and 500 · 10−3 ) mol · kg−1 at pH = 5.0, 7.0, and 8.2 respectively. In a multi-component system containing α-chymotrypsin, water and calcium chloride, the interactions that could govern the shifting of the N D equilibrium include those
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin 1.2
325
a
Fraction Denatured
1.0 0.8 0.6 0.4 0.2 0.0 290
1.2
300
310
320 T/K
330
340
350
300
310
320
330
340
350
b
Fraction Denatured
1.0 0.8 0.6 0.4 0.2 0.0 290
T/K
FIGURE 2. Thermal denaturation profiles of α-chymotrypsin plotted against temperature in the absence {figure 2(a): , pH = 3.4; , pH = 5.0; 4, pH = 7.0; O, pH = 8.2} and presence of calcium chloride {figure 2(b): pH = 7.0: , 0; , 25; 1, 50; O, 150; ♦, 500; +, 1000; ×, 2000 · 10−3 mol · kg−1 }.
◦
◦
between calcium chloride and water, calcium chloride and protein, and water and protein. The binding constant of Ca2+ (aq) to bovine α-chymotrypsin has been reported (16) as (1.4 ± 0.3) · 104 at pH = 6 with unit stoichiometry of the binding reaction. For serine proteases, the structure of trypsin with one bound calcium has been determined to a
326
K. Kar, B. Alex, and N. Kishore 330 328 326
T1/2 / K
324 322 320 318 316 314 2
3
4
5
pH
6
7
8
9
FIGURE 3. Variation of the transition temperature of α-chymotrypsin plotted against pH of the solution. 20 15
∆T 1/2
10 5 0 –5 – 10 0
500
1000
1500
2000
2500
3000
3500
10 3 . mol . kg –1
FIGURE 4. Change in the temperature of denaturation {1T = T1/2 or Tm (α-chymotrypsin + Ca2+ aq ) − T1/2 or Tm (α-chymotrypsin + buffer)} plotted against molality: pH = 3.4; H, pH = 5.0; ∇, pH = 7.0; , pH = 8.2.
•,
pH = 2.8;
◦,
resolution of 0.18 nm and the calcium ligands were identified. (17) It has been reported (18) that most likely Ca(II) binding sites are in essentially identical places on chymotrypsin and trypsin. In trypsin, the calcium ion is co-ordinated by six ligands at the edges of an
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
327
TABLE 2. Thermodynamic parameters associated with the thermal unfolding of 0.2 · 10−4 mol · dm−3 αchymotrypsin at pH = 3.4, 5.0, 7.0, and 8.2 in the absence and presence of CaCla2 determined using a uvvisible spectrophotometer Ca2+ 10−3 · mol · dm−3
Tm K
pH = 3.4 0
329.4
25
325.3
50
323.0
150
321.3 pH = 5.0
0
325.5
25
328.9
500
329.1
1000
328.3
1500
326.1 pH = 7.0
0
315.1
25
328.0
50
329.6
150
330.5
1000
328.4
2000
320.4
3000
309.7 pH = 8.2
0
316.4
25
324.5
500
328.4
1000
326.7
1500
324.6
2000
320.2
a Each value in this table is an average of three or four measurements.
octahedron. Four ligands form a loop of the protein, Glu70 and Glu80 are co-ordinated with their side chain carboxylate groups, and Asn72 and Val75 are co-ordinated with the
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K. Kar, B. Alex, and N. Kishore
CpE / (kJ . K –1 . mol –1)
15 kJ . K –1 . mol –1
300
T/K
340
FIGURE 5. Excess heat capacity profile plotted against temperature for thermal denaturation of α-chymotrypsin at pH = 2.8 and heating rate of 0.5 K · min−1 in the presence of 100 · 10−3 mol · kg−1 calcium chloride.
backbone carboxyls. The remaining ligands are water molecules that are also hydrogen bonded to Glu70 and Glu77 respectively. (17) Also, the Ca2+ binding site is located far from the active site. (17) Figure 1(b) shows the thermal denaturation curve of α-chymoptrypsin in the presence of 50 · 10−3 mol · kg−1 Ca2+ (aq) at pH = 2.8. The mid-point of the transition was found to be lower than that of the protein in the absence of Ca2+ indicating that Ca2+ has reduced the thermal stability of α-chymotrypsin. Further, at this pH = 2.8, on increasing the concentration of Ca2+ , the transition temperature was found to decrease. In the presence of 0.100 mol · dm−3 Ca2+ , there appears to a strong post-transition aggregation of the protein as reflected by the disturbed behaviour of the d.s.c. profile after the transition (figure 5). Therefore in these cases, we have not calculated the area under the curve. Upon re-heating the solution of α-chymotrypsin in the presence of all concentrations of Ca2+ studied, no transition was observed indicating that the thermal denaturation of α-chymotrypsin under these conditions is irreversible. The increase in the ionic strength of the solution due to addition of calcium chloride even at pH = 2.8 leads to irreversible thermal transitions. This result is consistent with the enhancement of dimerization constant of α-chymotrypsin with an increase in the ionic strength. (14) For applying the equilibrium thermodynamic model to the thermal studies, an essential requirement is that there should be thermodynamic equilibrium in the sample under investigation throughout the temperature-induced unfolding process. The criteria for equilibrium are generally judged from the reproducibility of the d.s.c. trace in a second heating of the sample. If the second thermogram shows no thermal effect, thermodynamic functions for the process such as changes in entropy and reaction Gibbs function cannot be extracted from the first trace. However, it has also been shown that the thermogram of
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
329
the thermal denaturation of several proteins can be interpreted in terms of the van’t Hoff equation in spite of the calorimetric irreversibility. (19) In the calorimetric experiments, the calorimetric enthalpy of transition is obtained by calculating the area under the C p,ex against T profile. Therefore, we have reported the transition temperature T1/2 and calorimetric enthalpies 1Hcal for the measurements performed using d.s.c. However, evaluation of enthalpy of denaturation in spectroscopic measurements is done from the temperature dependence of the equilibrium constant. For this, the reversibility of the thermal transition must be ensured. Therefore, if the transitions are irreversible, we have reported only Tm values. Experiments were done on thermal unfolding of 0.135·10−3 mol · dm−3 α-chymotrypsin in the presence of 0.025 mol · dm−3 calcium chloride at scanning rates of (0.2, 0.4, 0.5, and 0.6) K · min−1 to check whether the process under investigation was under kinetic control. Figure 6 shows the d.s.c. traces obtained at different scanning rates. The thermodynamic parameters accompanying the thermal transitions at these four scan-rates are given in table 3. It is clear from figure 6 that the transition temperature of α-chymotrypsin in the presence of 25 · 10−3 mol · dm−3 Ca2+ is scan-rate dependent even after correcting for the instrumental response time. The reversibility of the calorimetric transitions was checked at each scan-rate. No transition was obtained in the second heating in all these cases. These results suggest that the denaturation process of α-chymotrypsin in the presence of calcium chloride is under kinetic control, and the interpretation of calorimetric data in terms of equilibrium thermodynamics cannot be carried out. The process taking place in the calorimetric cells fits to the following two-state process: k
N2 → I,
(3)
where N is the native state, and I is the final state arrived at irreversibly from the unfolded one, k is a first-order kinetic constant which changes with the temperature according to the Arrhenius equation. A mathematical elaboration (20) of the model given above allows the calculation of activation energy of the kinetic process in different ways as discussed below. Method A: The rate constant of the reaction at a temperature T can be obtained by using (20) k = νC p /(qT − q),
(4)
where ν, C p , qT , and q are respectively, the scan-rate of the calorimeter, excess heat capacity above the base line, total heat absorbed or evolved in the process and heat change at a given temperature T . The energy of activation E a can be obtained from the values of k at several temperatures by using the Arrhenius equation, k = A · e−E a /RT .
(5)
Figure 7(a) shows the plot of log k against 1/T using the data obtained at four scan-rates. A dimer value of (411±7) kJ · mol−1 for the energy of activation has been calculated from this Arrhenius plot.
330
K. Kar, B. Alex, and N. Kishore 80 4
CpE / (kJ . K –1 . mol –1)
60 3 40
2
20
1
0 313
323
T/K
FIGURE 6. Excess heat capacity plotted against temperature of 0.135 · 10−3 mol · dm−3 α-chymotrypsin at pH = (2.83: 1, 0.2; 2, 0.4; 3, 0.5; 4, 0.6) K · min−1 . TABLE 3. Thermodynamic parameters associated with the scan-rate dependent thermal unfolding of 0.135 · 10−3 mol · dm−3 α-chymotrypsin in the presence of 25 · 10−3 mol · dm−3 CaCla2 at pH = 2.8 Scan-rate K · min−1
Tm K
1Hcal kJ · mol−1 638 ± 17
0.2
316.3 ± 0.3
0.4
317.2 ± 0.2
552 ± 6
0.5
317.5 ± 0.4
552 ± 12
0.6
318.4 ± 0.5
516 ± 9
a Each value in this table is an average of three or four measurements.
Method B: The dependence of heat evolved or absorbed as a function of temperature can be expressed as (20) ln[ln{qT /(qT − q)}] = E a /R[1/Tm − 1/T ].
(6)
According to this model, a plot of ln[ln(q/(qT − q))] versus 1/T should lead to straight lines, and the slope of each line at every scan-rate should yield the value of −E a /R. Using the data at four scan-rates studied, the plot generated is shown in figure 7(b) and the average
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
331
– 11
– 0.87 a
c
ln k
ln(ν / Tm2)
– 12
– 13
– 6.58 – 0.85
– 14 31.35 31.40 31.45 31.50 31.55 31.60
b
ln[ln {qT / (qT-q)}]
104 . 1 /Tm/ K –1
– 5.10 3.12
103 . 1 /T / K –1
3.23
◦
FIGURE 7. Arrhenius plot including k data from the four scan-rates used {figure 7(a)}: N, 0.2; , 0.4; , 0.5; , 0.6 K · min−1 . (b) Plots of ln [ln{qT /(qT − q)}] against 1/T : symbols are same as those used in (a). (c) Values of ln(ν/Tm2 ) versus 1/Tm .
•
activation energy thus obtained is (414 ± 8) kJ · mol−1 . In addition, the x-axis intercept of these plots should yield the values of Tm . The values of Tm thus obtained are (318.9, 317.8, 316.4, and 316.1) K at the scan-rates (0.6, 0.5, 0.4, and 0.2) K · min−1 respectively. The values obtained experimentally at these four scan-rates are respectively (318.4, 317.5, 317.0, and 316.3) K, which are in excellent agreement with those calculated from the plots, thus supporting the validity of model assumed. Method C: The two-state kinetic model of denaturation also predicts that the temperature corresponding to the maximum of the heat capacity, changes according to the following relation (20) : ν/Tm2 = A/E a · e−E a /RT m .
(7)
Thus a plot of ln ν/Tm2 against 1/Tm should result in a straight line with a slope equal to −E a /R. From the plot {figure 7(c)} the calculated activation energy is (432 ± 10) kJ · mol−1 .
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K. Kar, B. Alex, and N. Kishore
Method D: The activation energy can be calculated (20) from the heat capacity at the maximum of the trace C m p 2 E a = (e RC m p Tm )/qT .
(8)
Using this equation for the four traces shown in figure 6, an average activation energy of (419 ± 7) kJ · mol−1 is obtained. The above methods involve different approximations and experimental information. It is seen that the above methods applied to the data obtained in the present study provide excellent agreement between the results obtained for the energy of activation. The average value of the activation energy employing the methods A to D is (419 ± 16) kJ · mol−1 of dimer. Thus by this excellent agreement, we have shown that the d.s.c. thermograms for the thermal denaturation α-chymotrypsin can be interpreted in terms of a kinetic k
process N2 → I, where k is a first-order kinetic constant that changes with temperature as described by the Arrhenius equation. It is possible that more complex models may represent a first-order kinetic process, for example, the irreversible thermal denaturation of α-chymotrypsin might be k1
k3
N2 D → I. k2
(9)
Here, I is a final state irreversibly arrived at from the unfolded state. It is assumed that all the processes are first order, that k3 k2 at any moment, most of the D molecules will be converted to I instead of returning to N through the process D N2 . If the sample of α-chymotrypsin in the d.s.c. cells is heated only up to the mid-point of the transition, followed by immediate cooling, a rescanning of the sample still shows the peak. However, the height of the transition is much lower than the transition in the first heating. This indicates that the process is irreversible before the complete denaturation, thus supporting the proposed irreversible model N2 → I. Effect of surface tension The values of surface tension of aqueous calcium chloride solutions measured by drop weight method have been reported in table 4. The surface tension of water was found to increase linearly with the concentration of calcium chloride as shown in figure 8. Figure 9 shows the variation of 1T as a function of change in the surface tension of water at various pH values. It is seen in this figure that at pH = 5.0, 7.0, and 8.2, the thermal stability index of the protein passes through a maximum followed by a decrease. However, at pH = 2.8 and 3.2, the thermal stability of the protein falls sharply with the surface tension. It is generally observed (21) that the compounds that lead to a positive increase in the surface tension, give a negative preferential interaction parameter, (∂m 3 /∂m 2 ). Here, m 2 and m 3 represent the molalities of protein and co-solvent respectively. Negative values of the preferential interaction parameters indicate the preferential exclusion of the co-solvent molecules from the protein surface. (21) It has been shown using rigorous thermodynamic analysis that the effect of sugars such as sucrose, (22) glucose and lactose (23) on the surface
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
333
88 86
10 3 . σ / (N . m –1)
84 82 80 78 76 74 72 0
1000
2000 3000 103 . mol . kg –1
4000
5000
FIGURE 8. Surface tension plotted against molality of aqueous calcium chloride at T = 298.15 K.
tension of water has been the main force responsible for the stabilization of the proteins and their preferential interactions. Although we have observed a positive slope of surface tension versus concentration of CaCl2 , the present results do not show a linear relationship between the increase in the surface tension of water and the alteration in the thermal stability of the protein. The results are clearly pH dependent. As seen in figure 3, at pH = 2.8 and 3.42, CaCl2 reduces the thermal stability of the protein at all concentrations studied. However, at pH = 7.0 and 8.2, CaCl2 initially enhances the thermal stability followed by destabilization at higher concentrations. These observations suggest that in this case the role of surface tension of the medium is not dominant in providing thermal stability to this protein. Breslow and Guo (24) and Timasheff and co-workers (12, 25) have proposed that the free energy of cavity formation in water to accommodate the exposed groups of proteins upon denaturation is proportional to the increase in surface tension of water by different solvent additives. On the other hand, it has also been reported that amino acids and salts, (12) urea and guanidinium chloride have been found to increase the surface free energy of water (24) and are also preferentially bound to proteins at high concentrations. (26) We have no doubt that the thermal transitions observed in the presence of calcium using uv-visible spectrophotometry are due to the unfolding of protein give the similar results to those observed by us using d.s.c. at pH = 2.8 as reported in this paper. A clear cooperative endotherm on the d.s.c. is proof of the thermally induced unfolding reaction of the protein. Moreover, the aggregation of the protein is an exothermic reaction. The plot in figure 2, which shows the shape of the transition profile at pH = 3.4 in the absence of calcium (reversible reaction) and in the presence of calcium (irreversible reaction), is indicative of the unfolding reaction of the protein. An increase in the optical density for
334
K. Kar, B. Alex, and N. Kishore 18 16 14 12 10 ∆T 1/ 2 / K
8 6 4 2 0 –2 –4 –6 –8 0
2
4 6 10 3 . ∆σ / (N . m –1)
8
10
FIGURE 9. Plot of the change in thermal stability of α-chymotrypsin against the change in surface tension of water in the presence of calcium chloride: O, pH = 7.0; ♦, pH = 5.0; 4, pH = 8.2; , pH = 2.8; , pH = 3.4.
◦
TABLE 4. Results of surface tension on aqueous calcium chloride at T = 298.15 K M (mol · kg−1 )
σ (10−3 · N · m−1 )
0.05
73.2
0.20
73.8
0.50
74.7
1.00
76.3
2.00
77.7
3.00
83.6
5.00
87.3
some proteins with a rise in temperature showing the thermal denaturation transition has also been reported in the literature. (27, 28)
4. Conclusions The thermal denaturation of α-chymotrypsin in the absence of calcium chloride follows the two-state reversible denaturation mechanism at pH = 2.8 and 3.4. However, at pH = 5.0, 7.2, and 8.2, the thermal denaturation of the protein is irreversible. The effect of calcium
Thermodynamics of the interactions of calcium chloride with α-chymotrypsin
335
towards the thermal stability of α-chymotrypsin has been found to be pH dependent. At pH = 2.8 and 3.4, calcium reduces the transition temperature of the protein. At pH = 5.0, 7.0, and 8.2, calcium chloride was initially found to be a stabilizer of the protein at lower concentrations, but at higher concentration the salt acted as a destabilizer. All the thermal transitions of the protein in the presence of calcium chloride were observed to be irreversible, thus restricting the application of equilibrium thermodynamics to the analysis of the irreversible data. Under the condition where calcium chloride induces irreversible calorimetric transition, the scan-rate analysis provide energy of activation of (419 ± 16) kJ · mol−1 for the process which the protein follows under kinetic control. An excellent match between the experimental and calculate transition temperatures, and the activation energy values calculated by different methods support that the thermal k
denaturation of α-chymotrypsin in the presence of calcium chloride follows the N2 → I mechanism. Calcium chloride has been observed to increase the surface tension of water at all the concentrations studied. These results suggest that in this case the role of surface tension of the medium is not dominant in providing thermal stability to this protein. Financial support from Department of Science and Technology, India is gratefully acknowledged. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
Hendrix, T.; Griko, Y. V.; Privalov, P. L. Biophys. Chem. 2000, 84, 27–34. Zahnley, J. C. J. Inorg. Biochem. 1981, 15, 67–78. Winzor, D. J.; Scheraga, H. A. Biochemistry 1963, 2, 1263–1267. Shiao, D. D. F.; Sturtevant, J. M. Biochemistry 1963, 8, 4910–4917. Anue, K. C.; Timasheff, S. N. Biochemistry 1971, 10, 1609–1617. Shearwin, K. E.; Winzor, D. J. Biochim. Biophys. Acta 1990, 1038, 136–138. Privalov, P. L.; Khechinashvilli, N. N. J. Mol. Biol. 1974, 86, 665–684. Kirchhoff, W. H. EXAM, US Department of Energy, Thermodynamics Division, National Institute of Standards and Technology. Gaithersburg: USA, MD. Sturtevant, J. M. Annu. Rev. Phys. Chem. 1987, 38, 463–488. Ginnsburg, A.; Zolkiewski, M. Biochemistry 1991, 30, 9421–9429. Brandts, J. F.; Hu, C. Q.; Lin, L-N.; Mas, M. T. Biochemistry 1989, 28, 8588–8596. Kita, Y.; Arakawa, T.; Lin, T-Y.; Timasheff, S. N. Biochemistry 1994, 33, 15178–15189. Hess, G. P. Chymotrypsin—Chemical Properties and Catalysis. The Enzymes. Boyer, P.: editor. Academic Press: 1971, 213–244. Anue, K. C.; Timasheff, S. N. Biochemistry 1971, 10, 1609–1617. Rao, M. S. N.; Kegeles, G. J. Am. Chem. Soc. 1958, 80, 5724–5729. Chiancone, E.; Drakenberg, T.; Teleman, O.; Forsen, S. J. Mol. Biol 1985, 185, 201–207. Bode, W.; Schwager, P. J. Biol. Chem. 1975, 98, 693–717. Adebodun, F.; Jordan, F. Biochemistry 1989, 28, 7524–7531. Hu, C. Q.; Sturtevant, J. M. Biochemistry 1987, 26, 178–182. Sanchez, J. M.; Lopez-L, J. L.; Cortijo, M.; Mateo, P. L. Biochemistry 1988, 27, 1648–1652. Timasheff, S. N. Preferential Interactions of Water and Cosolvents with Proteins: Protein– Solvent Interactions. Gregory, R. N.: editor. Marcel Dekker Inc: New York. 1995, 445–482. Lee, J. C.; Timasheff, S. N. J. Biol. Chem. 1981, 256, 7193–7201. Arakawa, T.; Timasheff, S. N. Biochemistry 1982, 21, 6536–6544. Breslow, R.; Guo, T. Proc. Natl. Acad. Sci., USA 1990, 87, 167–169. Lin, T-Y.; Timasheff, S. N. Protein Sci. 1996, 5, 372–381.
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26. Arakawa, T.; Timasheff, S. N. Biochemistry 1984, 23, 5912–5923. 27. Lee, L. L-Y.; Lee, J. C. Biochemistry 1987, 26, 7813–7819. 28. Arakawa, T.; Bhat, R.; Timesheff, S. N. Biochemistry 1990, 29, 1924–1931. (Received 9 January 2001; in final form 16 April 2001)
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