Download ac nanocalorimeter for measuring heat capacity of biological

REVIEW OF SCIENTIFIC INSTRUMENTS
VOLUME 74, NUMBER 9
SEPTEMBER 2003
ac nanocalorimeter for measuring heat capacity of biological
macromolecules in solution
Haruhiko Yaoa) and Kenji Ema
Department of Condensed Matter Physics, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro-ku,
Tokyo 152-8551, Japan
Harumi Fukada and Katsutada Takahashi
Laboratory of Biophysical Chemistry, Graduate School of Agriculture and Biological Sciences,
Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
Ichiro Hatta
Department of General Education, Fukui University of Technology, 3-6-1 Gakuen, Fukui 910-8505, Japan
共Received 14 November 2002; accepted 29 June 2003兲
A precise calorimeter has been developed to measure the heat capacity of a small amount of liquid
using a novel ac calorimetric method in which the effect of heat loss from a sample cell is corrected
using the phase of the ac temperature. The sample cell is made of a fine glass tube, whose outer
surface is plated with a nickel film as an ac heater. The ac temperature of the sample is detected
precisely with a microbead thermistor attached to the middle of the tube. The resistance of the
thermistor is measured with an ac Wheatstone bridge which is composed of resistors with a low
temperature coefficient of ⫾1 ppm/K. The unbalance ac signal of the bridge is measured with a
lock-in amplifier. To reduce the drift of measured values caused by the variation of room
temperature, the amplifier and measuring instruments with temperature coefficients of ⬎1 ppm/K
are kept at constant temperature. Moreover, the gain of the amplifier is calibrated at every measuring
point. Consequently, the heat capacity of 10 ␮l liquid can be determined with an extremely high
sensitivity of ⫾0.001%, which corresponds to heat capacity changes of ⫾300 nJ/K. A test of the
performance was made of the heat capacity measurement during thermal denaturation of lysozyme
dissolved in buffered solution. This method is particularly useful for studying thermal properties of
biological macromolecules in solution, since the heat capacity of macromolecules can be measured
with a 10 ␮g sample. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1602958兴
lution using a small amount of sample 共⬇10 ␮l兲 on the basis
of previous ac microcalorimetry for liquid samples.3,4
I. INTRODUCTION
To understand the thermostability of biological macromolecules, proteins and nucleic acids, the study of their heatcapacity function has attracted a great deal of interest because one can obtain a thermodynamic description and
prediction of their native state, denatured state and, in some
cases, intermediate state which is often found to exist during
unfolding. However, experimental determination of the heatcapacity function is difficult because it requires measurement
of the heat capacity of the molecules in very dilute solution.
For example, in the case of proteins, a concentration as dilute
as 0.1 wt % is required to avoid aggregation after unfolding.
Currently the heat capacity of biological macromolecules can
be measured most precisely with a highly sensitive differential scanning calorimeter 共DSC兲 working under an adiabatic
principle,1,2 but the accuracy is still not good enough to get a
quantitative thermodynamic description of biological macromolecules. Furthermore, DSC requires a large amount of
sample 共0.3–1 ml兲. Therefore, we tried a different approach
to solve the above problems. Here, we describe a new ac
nanocalorimeter which was developed for measurement of
the heat capacity of biological macromolecules in dilute so-
II. PRINCIPLE OF ac NANOCALORIMETRY
In ordinary ac calorimetry, when the amount of a sample
is very small, the experimental error caused by heat loss at a
sample is substantially large. High-resolution ac
microcalorimetry4 is a novel and useful method by which to
measure the heat capacity of a small sample with extremely
high precision notwithstanding the presence of heat loss,
whose contribution is corrected. Since a detailed description
of the principle is given elsewhere,4 we describe it only
briefly.
The thermal system of an ac nanocalorimeter is shown in
Fig. 1. The sample cell is made of a fine tube which can be
filled with a liquid sample. The sample tube passes through a
box filled with thermal exchange gas. Both ends of the tube
are in thermal contact with the box that acts as a heat bath
共sink兲. A thin heater is deposited on the surface of the tube
and an oscillating heat flux q 关 exp(i␻t)⫹1兴 is generated at the
surface per unit length of the tube. Hereafter, we refer to the
tube filled with liquid as a sample. According to the analysis
in Ref. 4, the complex ac temperature of the middle part of
the sample ⌬T * is
a兲
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© 2003 American Institute of Physics
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Rev. Sci. Instrum., Vol. 74, No. 9, September 2003
ac nanocalorimeter for liquids
FIG. 1. Thermal model of an ac nanocalorimeter. A rod-like sample is
placed in a box filled with gas. The temperature of both ends is fixed at T
⫽0. Oscillating heat flux q 关 exp(i␻t)⫹1兴 is supplied to the sample per unit
length of the sample. C: Heat capacity of the sample per unit length; Λ:
thermal diffusivity of the sample; K: conductance of heat loss at the surface
of the sample per unit length.
because, even if conductance K is large, heat capacity C can
be obtained exactly by measuring amplitude ⌬T and phase
␾.
The absolute value of the heat capacity of liquid is determined by calibrating the calorimeter using reference liquid, such as pure water. The procedure is explained as follows. When the tube is filled with sample liquid having
specific heat capacity c s (T) and density ␳ s (T), the heat capacity of the sample at temperature T is given by
V 共 T 兲 ␳ s 共 T 兲 c s 共 T 兲 ⫹C t 共 T 兲 ⫽
⌬T * ⫽⌬T exp共 ⫺i ␾ 兲 ⫽
q 共 1⫺ ␣ 兲
,
i ␻ C 共 1⫺ ␤ 兲 ⫹ 共 K⫹ ␥ 兲
共1兲
where ⌬T is the amplitude of the ac temperature, ␾ is the
phase difference between the ac temperature and the ac heat
flux, C is the heat capacity of the sample per unit length of
the sample, K is the thermal conductance between the sample
surface and the bath and
␣ ⫽ ␣ ⬘ ⫹i ␣ ⬙ ⫽ 共 sinh冑共 K/ ␻ C⫹i 兲共 l/l 0 兲 2 /2兲 ⫺1 ,
␤ ⫽ 共 a/a 0 兲 4 /12,
共2兲
␥ ⫽ ␻ C 共 a/a 0 兲 2 /4,
are correction terms for the thermal diffusion length and dimensions of the sample.
If the tube length l is ⬃20 times longer than the thermal
diffusion length of the sample in longitudinal direction
l 0 (⬅ 冑2Λ/ ␻ , Λ is the thermal diffusivity of the sample in
the longitudinal direction兲, the correction term ␣ will be
within 0.001%. Then, the middle part of the sample can be
regarded as an infinite tube. This condition determines the
low-frequency limit of operating frequency ␻. On the other
hand, if the inner radius of tube a is ⬃10 times smaller than
the thermal diffusion length of liquid a 0 (⬅ 冑2D/ ␻ , D is the
thermal diffusivity of the liquid兲, ␤ will be within 0.001%.
Then, the sample composed of the tube and liquid can be
regarded thermally as a uniform rod. This condition determines the high-frequency limit of ␻. The frequency ␻ is
chosen in order that both ␣ and ␤ can be neglected. Then, the
complex ac temperature ⌬T * is given by
⌬T * ⫽⌬T exp共 ⫺i ␾ 兲 ⫽
q
.
i ␻ C⫹ 共 K⫹ ␥ 兲
共3兲
If K⫹ ␥ is small, phase ␾ is close to ␲/2. It is worth noting
that C and K⫹ ␥ in Eq. 共3兲 can be separated using the phase
␾ as
C⫽
q
sin ␾
␻ ⌬T
共4兲
and
K⫹ ␥ ⫽
q
cos ␾ ,
⌬T
共5兲
since C and K⫹ ␥ are quadrature and in-phase components
with respect to the ac heat flux. This relation is quite useful
4165
qs
sin ␾ s ,
␻ ⌬T s
共6兲
where V(T) is the inner volume of the tube per unit length
and C t (T) is the heat capacity of the tube per unit length.
Subscripts s and t denote the sample liquid and tube, respectively. Prior to or subsequent to the above measurement, the
amplitudes of ac temperatures are measured at the same temperature T for the case where the tube is filled with air as
well as for the case where the tube is filled with reference
liquid. When the sample cell is filled with air, the heat capacity of the sample is determined by
V 共 T 兲 ␳ a 共 T 兲 c a 共 T 兲 ⫹C t 共 T 兲 ⫽
qa
sin ␾ a ,
␻ ⌬T a
共7兲
where ␳ a (T) and c a (T) are the density and heat capacity of
air. Similarly, when the tube is filled with reference liquid of
known heat capacity c r (T) and density ␳ r (T), we obtain
V 共 T 兲 ␳ r 共 T 兲 c r 共 T 兲 ⫹C t 共 T 兲 ⫽
qr
sin ␾ r ,
␻ ⌬T r
共8兲
where subscript r stands for reference. Therefore, the volume
heat capacity of the liquid ␳ s (T)c s (T) can be obtained as the
following:
␳ s共 T 兲 c s共 T 兲 ⫽
q s sin ␾ s /⌬T s ⫺q a sin ␾ a /⌬T a
q r sin ␾ r /⌬T r ⫺q a sin ␾ a /⌬T a
⫻ 关 ␳ r 共 T 兲 c r 共 T 兲 ⫺ ␳ a 共 T 兲 c a 共 T 兲兴
⫹ ␳ a共 T 兲 c a共 T 兲 .
共9兲
This relation holds independent of the leakage conductances
(K s , K a , and K r ). The absolute value of heat capacity can
be obtained exactly by measuring both the amplitudes and
phases of the ac temperatures.
III. DESIGN AND OPERATION
Figure 2 shows a block diagram of an ac nanocalorimeter. The sample cell is made of a borosilicate-glass capillary
tube which has an inner radius a of 0.26 mm, a wall thickness of 40 ␮m and a length l of 5 cm. The internal volume of
the tube is about 10 ␮l. Both ends of the capillary tube extend out of the side walls of a copper box 共heat bath兲 and are
connected to external glass tubes which lead to the outside of
the calorimeter to supply liquid samples. The box is filled
with air. As a heater, a nickel film (R heater⬇12 ⍀) is deposited on the outer surface of the tube with electroless plating
followed by electroplating. The heater is connected to an
arbitrary wave form generator 共AWG兲 board 共Microscience
Co., MDA2798BPC兲 through a voltage-to-current converter.
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4166
Yao et al.
Rev. Sci. Instrum., Vol. 74, No. 9, September 2003
FIG. 2. Schematic of a sample cell and block diagram of the ac nanocalorimeter. A: Thin glass capillary tube coated with nickel; B: microbead thermistor, C: external glass tubes, D: lead wires, E: voltage divider.
Stable ac heat flow of 0.05 Hz is generated by putting constant ac current through the heater in order that the resistance
variation of wires and connectors does not affect the magnitude of the power generated. Since amplifiers inside the converter and AWG have small but unremovable dc offsets, they
are added to an ac current, i.e., I 0 cos(␻t/2)⫹⌬I offset . This
produces an ac heat flow, R heater关 I 20 (cos ␻t⫹1)/2
2
⫹⌬I offsetI 0 cos(␻t/2)⫹⌬I offset
兴 , which is distorted with
respect
to
the
␻/2-frequency
component,
R heater⌬I offsetI 0 cos(␻t/2). Since distortion affects precise determination of the ac temperature, another wave form of ac
current, 兩 I 0 cos(␻t/2) 兩 , was adopted to reduce distortion.
When dc offset current, ⌬I offset , is added to the modified ac
current, i.e., 兩 I 0 cos(␻t/2) 兩 ⫹⌬I offset , it generates ac heat
2
flow, R heater关 I 20 (cos ␻t⫹1)/2⫹⌬I offsetI 0 兩 cos(␻t/2) 兩 ⫹⌬I offset
兴.
In this case, the second term, R heater⌬I offsetI 0 兩 cos(␻t/2) 兩 , has
␻ and its higher harmonic components and does not include
␻/2 component. The distortion due to ⌬I offset is much smaller
than that in the former case.
To detect the temperature of the sample, a microbead
thermistor 共Victory Engineering Corp. 45A401C, diameter
0.125 mm, 50 k⍀兲 was adhered to the middle part of the tube
with GE 7031 varnish using a stereomicroscope. The thermistor was calibrated in a temperature range of 0–100 °C
with a platinum resistance thermometer 共Rosemount,
146MA100F兲 embedded in the bath when the ac heat power
was turned off. The resistance of the thermistor is measured
by the ac Wheatstone bridge method. The advantages to operating the bridge at ac rather than dc are that input noise can
be reduced by narrow-band amplification and that thermal
electromotive force 共emf兲 is removed. The bridge is composed of two fixed resistors 共1 k⍀兲, one programmable variable resistor, and the thermistor. The bridge is balanced when
the resistance of the variable resistor is equal to that of the
thermistor. The fixed resistors are high stability resistors 关Alpha Electronics, MCZ series, temperature coefficient 共TC兲 of
resistance: ⫾1 ppm/K兴. The variable resistor is composed of
MCZ resistors and relays 共Matsushita Electric Works, TF212V兲 which are switched by a computer using a digital output board 共Contec Co., PO-48B共98兲兲. The range of the vari-
able resistor is 98.5 ⍀–166 k⍀ with 0.1 ⍀ resolution. The
bridge is driven at 20 Hz using an oscillator 共Japan Circuit
Design OSC-16B, TC of amplitude ⬍25 ppm/K兲 and the
excitation voltage is 0.4 V.
The amplitude of the bridge’s unbalance signal 共20 Hz兲
is modulated by the ac temperature of the sample 共0.05 Hz兲.
It is detected with an analog lock-in amplifier 共EG&G
PARC, 5209, gain stability: 200 ppm/K typically兲. As a reference phase signal, the synchronous digital output 共20 Hz兲
of the oscillator is supplied to the amplifier. The output of the
amplifier oscillates at the ac heating cycle. It is read every
0.25 s for five heating cycles with an 8 21 digit multimeter
共Advantest 6581D, TC of reading: ⫾1 ppm/K兲 that is synchronized with the ac heating using the 0° and clock signals
of the AWG board. Four hundred read points are sent to the
computer.
Since a sensitivity of ⫾0.001% is close to the TCs of
measuring instruments, the lock-in amplifier, the oscillator,
the AWG board and the voltage-to-current converter are kept
at 26.0⫾0.1 °C in a low-temperature incubator 共Tokyo
Rikakikai Co., LTI-601SD兲. To calibrate the gain of the
lock-in amplifier and the amplitude of the excitation voltage,
the voltage is divided with a voltage divider 共resistance ratio:
1 k⍀/125 k⍀兲 composed of MCZ resistors. Then, it is amplified with the lock-in amplifier at the same gain used for
measuring the unbalance signal of the bridge and is measured with the multimeter. Thus, the TCs of the amplifier and
the oscillator are corrected and do not affect the sensitivity of
the measurement.
The amplitude and the phase of the ac temperature are
determined by fitting the following function to the data
points:
T 共 t 兲 ⫽A cos ␻ t⫹B sin ␻ t⫹C⫹Dt⫹Et 2 ,
共10兲
where A cos ␻t⫹B sin ␻t is the ac temperature component
and C⫹Dt⫹Et 2 is the baseline. The quadratic form of the
baseline is chosen for the case where the bath temperature is
disturbed during measurement. The absolute temperature of
the sample is determined by averaging the data points.
To regulate the temperature of the bath, a glass-bead
thermistor 共Shibaura Electronics, PB3-41E兲 with precise sensitivity is embedded in the bath. It comprises one arm of the
ac Wheatstone bridge driven at 10 Hz by the internal oscillator of a lock-in amplifier 共EG&G PARC, 5209兲. Its unbalance signal is detected with the lock-in amplifier and is fed to
a temperature controller 共Shimaden Co., SR52-6V兲 which
regulates its output in order that the signal may become null.
The output is amplified with a power supply 共Takasago Co.,
GP060-3兲 and is applied to a kapton-insulated flexible heater
共Omega Engineering Co., KH108/10兲 wound around the
bath. The outer jacket of the calorimeter is immersed into a
stainless-steel Dewar vessel filled with a polyethylene
glycol/water mixture, which is cooled to ⫺20 °C with an
immersion cooler 共Tokyo Rikakikai Co., ECS-50兲. The operationing temperature range of the calorimeter is currently
0–100 °C, because pure water is used as the reference liquid.
In a temperature scan, the bath temperature is changed
stepwise. After confirming that the bath temperature is stable
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Rev. Sci. Instrum., Vol. 74, No. 9, September 2003
ac nanocalorimeter for liquids
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to within ⫾0.1 mK at the measuring temperature, the bridge
for the sample temperature is balanced and the gains of the
amplifier and the excitation voltage are calibrated. Then, the
temperature of the sample and the ac heating power measured with the multimeter. The input of the multimeter is
selected using a scanner 共Hewlett Packard, 34970A兲. After
completing the measurement, the temperature of the bath is
changed for the next measurement point.
To consider the effects of thermal diffusion length and
operating frequency, we derive the equation of ␳ s c s including the correction terms from Eq. 共1兲:
␳ sc s⫽
q s sin ␾ s /⌬T s ⫺q a sin ␾ a /⌬T a
共 ␳ c ⫺ ␳ ac a 兲
q r sin ␾ r /⌬T r ⫺q a sin ␾ a /⌬T a r r
冋
再冉
冉
FIG. 3. Temperature dependence of the volume heat capacity of the 0.1
wt % lysozyme solution 共closed circles兲 and the glycine buffer 共crosses兲.
Ct
⫻ 1⫹ 共 ␤ s ⫺ ␤ r 兲 ⫺ 共 ␣ s⬘ ⫺ ␣ r⬘ 兲 ⫹
V ␳ rc r
⫻
␤s
⫻ 1⫺
冊冉
冊
␳ rc r
␳ rc r
⫺ ␤ r ⫺ ␣ s⬘
⫺ ␣ r⬘ ⫹ 共 ␤ a ⫺ ␣ a⬘ 兲
␳ sc s
␳ sc s
␳ rc r
␳ sc s
冊冎册
⫹ ␳ ac a ,
共11兲
where ␣ s⬘ and ␤ s are correction terms when the tube is filled
with sample liquid, ␣ r⬘ and ␤ r are correction terms when the
tube is filled with reference liquid, and ␣ a⬘ and ␤ a are correction terms when the tube is filled with air. In the present
cell, the inner radius is larger than one tenth of the thermal
diffusion length of sample liquid, because the tube may become clogged with protein samples after denaturation if the
radius is less than ⬃0.25 mm. However, the difference in
thermal diffusion length between protein dilute solution and
water is small, so correction terms ␣ s⬘ , ␣ r⬘ , ␤ s and ␤ r in Eq.
共11兲 cancel each other. When the tube is filled with water, the
thermal diffusion length a 0 ⫽0.93 mm at 0.05 Hz. This yields
␤ r ⫽5.1⫻10⫺4 . On the other hand, the effective thermal diffusion length of the tube filled with water l 0 ⫽1.1 mm at 0.05
Hz, and relaxation time K/C⬇16 s. Thus, ␣ r⬘ ⬇⫺4
⫻10⫺10. When the tube is filled with air, the thermal diffusion length a 0 ⫽11 mm and the effective thermal diffusion
length l 0 ⫽2.2 mm at 0.05 Hz. Thus, ␤ a ⫽2.7⫻10⫺8 and
␣ ⬘a ⬇9⫻10⫺6 . When sample liquid is protein dilute or buffer
solution, the difference in thermal diffusion length a 0 between the sample liquid and water is of the order of 0.3%.
Thus, ␤ s ⬇5.1⫻10⫺4 and ␣ s⬘ ⬇⫺4⫻10⫺10. Since the difference in heat capacity between the sample liquid and water is
of the order of 0.6% and C t /V ␳ r c r ⬇0.13, Eq. 共9兲 holds to
within an accuracy of 0.001%. However, in the case where
the sample liquid is n-heptane or ethanol, a 0 ⬇0.72 mm and
l 0 ⬇1.2 mm at 0.05 Hz. Thus, ␤ s ⬇1.4⫻10⫺3 and ␣ s⬘
⬇10⫺9 . The accuracy of Eq. 共9兲 becomes 0.1% as a result.
In the case where the thermal diffusion length of the sample
liquid is different from that of the reference liquid, the appropriate inner radius is one tenth the thermal diffusion
length.
IV. PERFORMANCE OF THE APPARATUS
Heat capacity in thermal denaturation of lysozyme in
dilute solution was measured to test the performance of the
present ac nanocalorimeter. Hen egg-white lysozyme 共MW
14 307兲 was purchased from Seikagaku Kogyo Co. 共recrystallized six times兲. Lysozyme solution was prepared by dissolving an appropriate amount of lysozyme in glycine buffer
( pH 3.0, glycine 50 mM, KCl 0.1 M兲. The concentration of
lysozyme was 0.1 wt %. Then, the sample was dialyzed
against the buffer at 4 °C for 24 h. The dialyzate was
changed three times during dialysis.
The measurement results of the volume heat capacity of
the lysozyme solution and the buffer are shown in Fig. 3. The
calorimeter was calibrated using water 关resistivity: 18.2
M⍀/cm2, purified with an ultrapure water purification system
共Advantec Toyo Co., CPW-100兲兴 as the reference liquid.
Since the heat capacity differences between the lysozyme
solution and the buffer are extremely small, it is hard to
distinguish them on this ordinate scale. The amplitudes of ac
temperatures in these measurements were less than 0.55 K.
The partial molar heat capacity of lysozyme, c pr , is determined by
c pr⫽M
冋
册
100⫺w pr
v buf共 C sol⫺C buf兲 ⫹ v prC sol ,
w pr
共12兲
where C sol is the measured volume heat capacity of protein
solution, C buf is the measured volume heat capacity of buffer,
M is the molecular weight of the protein, w pr is the concentration of the protein in wt %, v pr is the partial specific volume of the protein and v buf is the specific volume of the
buffer. To calculate the molar heat capacity of lysozyme,
reported values of the partial specific volume of lysozyme5
were used. The specific volume of the buffer was measured
with a high-precision density meter 共Anton Paar,
DMA5000兲. Figure 4 shows the partial molar heat capacity
of lysozyme calculated on the basis of Eq. 共12兲 using the
results of the heat capacity measurement given in Fig. 3. The
excess heat capacity associated with thermally induced denaturation is clearly seen in the plot with the midpoint temperature of denaturation being around 65 °C. The heat capacity
difference between native and denatured states was also
clearly seen. The error bars in Fig. 4 correspond to ⫾0.001%
of the volume heat capacity of the lysozyme solution. Therefore, the heat capacity differences were measured within an
extremely high sensitivity of ⫾0.001%, which is one decade
higher than that in high-resolution ac calorimetry
共⫾0.01%兲.4,6,7
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4168
Yao et al.
Rev. Sci. Instrum., Vol. 74, No. 9, September 2003
FIG. 4. Temperature dependence of the molar heat capacity of lysozyme in
the thermal denaturation. The error bars show ⫾0.001% of the heat capacity
of the lysozyme solution.
By fitting linear functions to the linear portion of heat
capacity data points both in native and denatured states, the
difference in heat capacity between native and denatured
states at the denaturation temperature, ⌬C p,d , was determined to be 7.0⫾1.0 kJ K⫺1 mol⫺1 at 65 °C. This value
agrees with the values obtained by DSC 共6.0– 6.6
kJ K⫺1 mol⫺1, seen in Fig. 5 of Ref. 8兲. On the other hand,
the absolute values of heat capacity did not agree well with
the values obtained by DSC, for example, 20 kJ K⫺1 mol⫺1 at
30 °C, seen in Fig. 7 of Ref. 2. The disagreement is presumably due to the poor reproducibility of the heat capacity values 共⫾0.01% of the heat capacity of solution兲 upon refilling
the sample cell. It is probably caused by the formation of
small air bubbles in the liquid upon refilling, since the
bubbles reduce V(T) effectively in Eqs. 共6兲 and 共8兲. A similar problem has been reported in DSC.2 To reduce air
bubbles, pressure is applied to the cell in DSC. However,
since the error caused by refilling is almost constant during a
temperature scan, it does not affect the values of ⌬C p,d and
the area of the excess heat capacity peak. To improve determination of the absolute value of the heat capacity, it is probably necessary to dissolve air bubbles in sample and reference liquids, e.g., by degassing them.
The area of the excess heat capacity peak is taken as the
area limited from above by the heat capacity curve, and from
below by the fitted linear functions extrapolated to the
middle of the transition temperature.8 The area of the excess
heat capacity peak was determined to be 3.0
⫻102 kJ mol⫺1 , be much smaller than the denaturation enthalpy, ⌬H d , measured by DSC (5.1⫻102 kJ mol⫺1 at T d
⫽65 °C, seen in Fig. 7 of Ref. 8兲. The discrepancy between
the results obtained by ac and dc calorimetry is most probably due to the fact that folding and unfolding of lysozyme
are slower processes compared with the measuring frequency
of 0.05 Hz 共time constant: 3.2 s兲 and cannot follow the temperature oscillations. In fact, a kinetic study of guanidine
induced unfolding or refolding of lysozyme revealed that the
time constant of these two processes is of the order of 20–50
s.9 It seems probable to think that the comparison of studies
by ac and dc methods on other proteins provides more information about the kinetic feature of protein folding and unfolding.
In multistate transitions of proteins, broad excess heat
capacity peaks overlap each other. At present, the heat capacity peaks are separated by deconvolution analysis. A distinct
feature of the ac method is that the overlapping peaks can be
separated by changing the measuring frequency if the time
constants of transitions among native, intermediate and denatured states are different. Therefore, the dynamic heat capacity measurement in multistate transitions of proteins is a
goal of the present ac nanocalorimetry.
ACKNOWLEDGMENTS
The authors would like to thank Dr. Akikazu Maesono
for his invaluable discussions. This work was partly supported by a Grand-in-Aid for Science Research 共Grant No.
09780598兲 from the Ministry of Education, Science and
Culture of Japan, and a Creative and Fundamental R&D
Program, which is entrusted to the Japan Small Business
Corporation by the New Energy and Industrial Technology
Development Organization.
P. L. Privalov, Pure Appl. Chem. 52, 479 共1980兲.
G. Privalov, V. Kavina, E. Freire, and P. L. Privalov, Anal. Biochem. 232,
79 共1995兲.
3
H. Yao and I. Hatta, Jpn. J. Appl. Phys., Part 2 27, L121 共1988兲.
4
H. Yao, K. Ema, and I. Hatta, Jpn. J. Appl. Phys., Part 1 38, 945 共1999兲.
5
K. Gekko and Y. Hasegawa, J. Phys. Chem. 93, 426 共1989兲.
6
J. E. Smaardyk and J. M. Mochel, Rev. Sci. Instrum. 49, 988 共1978兲.
7
K. Ema and H. Yao, Thermochim. Acta 304Õ305, 157 共1997兲.
8
P. L. Privalov and N. N. Khechinashvili, J. Mol. Biol. 86, 665 共1974兲.
9
C. Tanford, K. C. Aune, and A. Ikai, J. Mol. Biol. 73, 185 共1973兲.
1
2
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