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A differential ac calorimeter for biophysical studies
ANALYTICAL
BIOCHEMISTRY
121.55-61
A Differential
AC Calorimeter
G. S. DIXON,S. Department
(1982)
of Physics,
for Biophysical
Studies’
G. BLACK, C. T. BUTLER,* AND A. K. Oklahoma
State
Received
University,
July
Stillwater,
Oklahoma
JAIN~ 74078
17, 1981
A differential ac calorimeter has been developed to investigate the phase transition behavior of liquids of biological interest, especially suspensions of liposomes and other model membranes. The sensitivity of the calorimeter is independent of the temperature scan rate and scan direction. Therefore, the heat capacity can be measured during heating scans, cooling scans, and at constant mean temperature. Thus, the time-dependent behavior of the heat capacity can be measured. A rather massive sample cell has been used to minimize problems with hermetically sealing the cell and maintaining a constant thermal path between the heater and thermometer. As the heat capacity of this cell is large compared to that of the sample, a differential method has been used to remove the heat capacity of the cell. Results are presented for heating, cooling, and quasi-isothermal studies of the main phase transition in dimyristoylphosphatidylcholine liposomes. Heating scans at 3”C/h are in excellent agreement with conventional scanning calorimetry. Cooling scans exhibit a supercooling of up to 0.5”C at this transition, confirming the first-order nature of the transition. Quasi-isothermal measurements for up to 20 min in the transition region show that there is no observable, instrumental distortion of the transition at these iow scanning rates.
In recent years calorimetric studies have become an important probe of biological systems that undergo phase transitions. This has been especially true of biological membranes ( 1) and related synthetic systems based on lipid multilayers (2-4). Calorimetry is advantageous in these studies in being noninvasive and measuring a bulk property of the system. Hence, the questions of microscopic location and possible perturbing influence that complicate the use of molecular probes do not arise for calorimetry. Although the heat capacity of a system is an equilibrium property, the conventional methods used to study biological samples, namely differential scanning calorimetry and differential thermal analysis, are essentially measurements of the transient re-
sponse of the system to changes in temperature. The sensitivity of these instruments is, thus, tied directly to the rate at which the temperature is scanned. This limits the temperature resolution of these instruments near a phase transition, and at high scan rates raises questions of possible distortion of the calorimetric behavior in the transition region. Moreover, heat conduction problems in most cases limit these instruments to use in heating scans. In this paper we describe a calorimeter based on the ac method introduced by Sullivan and Seidel (5) for the study of solids and which has been successfully applied to a variety of solid-state phase transitions (6,7). The ac method is steady state and capable of temperature resolution in excess of a millidegree. It consists in measuring the thermal response of the sample to periodic heat pulses. The sensitivity of the apparatus is, thus, independent of the rate at which the mean temperature of the sample is scanned.
’ Supported by NSF Grant PCM 78-13752. ’ Visiting Scientist from Department of Physics, Virginia Commonwealth University, Richmond, Va. ’ Present address: McDonnell-Douglas Corp., Houston, Tex.
55
0003-2697/82/050055-07$02.00/O Copyright 0 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
56
DIXON
The operation in a cooling cycle is no different from that in a heat cycle. It is also possible to hold the mean temperature of the sample fixed and measure changes in heat capacity as a function of time. This allows one to check for possible distortions in the calorimetric event that might arise from an excessive scan rate, to search for kinetic behavior on a time scale larger than the period of the heat pulses, and, as Sullivan and Seide1 (5) have demonstrated in solids, to detect the variation of the heat capacity as a function of time-varying conditions imposed on the sample or its environment. By the use of a differential technique this calorimeter avoids some of the problems that have attended other recent applications of the ac method to organic liquids. To our knowledge this is the first time the ac calorimetry technique has been incorporated in a differential instrument.
ET AL.
This has a sinusoidal solution T = Taceiw’
with i = (-1)“’
[21
and
T,, = -iQ,,(wC)-I/[
1 + i(wJ’]
[ 31
where ?-b = RC is the sample-to-bath relaxtime. If orb B 1, this reduces to
ation
Tat = -iQa/wC.
[41
It is this simple, inverse relationship between the heat capacity and the ac temperature that one strives to obtain in an actual experiment. A real material has a finite thermal conductivity K and, therefore, it is necessary to consider how the temperature oscillation propagates through the slab. This is governed by the heat conduction equation [51
REVIEW
OF ac CALORIMETRY
The method of ac calorimetry has been described in detail by several authors (5,7). Here, we present a brief discussion of two examples which illustrate the operation of the technique in an ideal case and the difficulties that must be surmounted to use it for the study of liquids. First, consider a slab-like sample of heat capacity C and infinite thermal conductivity connected through a thermal resistance R to a heat reservoir maintained at constant temperature To. The heat capacity C includes not only that of the specimen of interest, but also that of the sample cell, heater, thermometer, and any other addenda. To simplify the algebra, let temperature be measured on a relative scale with To = 0. Let the slab be heated sinusoidally at a rate Q = QOeiw’.The temperature of the slab is governed by the differential equation 1T +Q-;.
T
where 77= K/C~ is the thermal diffusivity with c the specific heat of the sample and p its density. Here, it has been assumed that heat losses through the sides of the slab are negligible, so that the problem is one of onedimensional heat flow from front to back. Solving this equation subject to the same boundary conditions as in the first example, one finds that the sample will be uniformly heated provided its thickness is small compared to a characteristic length l,, = (2n/ w)“‘. Other small corrections arising from finite heater-to-sample and thermometer-tosample relaxation times have been treated by Sullivan and Seidel (5). While a slab-like geometry of the sample cell simplifies a discussion of the technique, it is not a necessary condition for the operation of an ac calorimeter. The essential physical parameters are the following. (i) The dimensions of the sample should be small compared to lo in order to obtain uniform heating. (ii) The sample-to-bath relaxation time should be long compared to the
DIFFERENTIAL
57’
AC CALORIMETER
period of the temperature wave to maximize the amplitude of the temperature oscillations. (iii) Similarly, the heater-to-sample and thermometer-to-sample relaxation times should be short compared to the period so that the temperature wave is efficiently driven and detected. The major experimental difficulty in applying ac calorimetry to liquids arises from their low thermal diffusivity. This is typically one to two orders of magnitude smaller than is found in crystalline solids, and limits the characteristic thermal length 1,. For example, in water the thermal diffusivity ? = 1.5 X 10e3 cm2/s yielding lo = (5 X 10e2/ w1i2) cm. At a frequency of 1 Hz this gives lo = 200 pm. This is to be compared to a characteristic length of 5 mm in aluminum at the same frequency. Uniform heating of the liquid can be assured only if very thin samples (8,9) or long periods (10) (I-10 min) are used. For a single thin-layer sample, one can use only a small sample volume, and a large addendum correction can be avoided only through the use of very thin walls for the sample cell. In our hands such cells have proven difficult to seal reliably. Others (9) have noted such cells’ sensitivity to variation in the thermal pathlength caused by fluctuations in the ambient pressure or by thermal expansion. The long-period method leads to inconveniently long data acquisition times. This is of concern with biological specimens that may be subject to deterioration. The differential ac calorimeter described here avoids the difficulties noted above. The sample is contained in an aluminum cell in which the liquid is arranged in a number of layers each of thickness small compared to 4,. These are arranged so that the limiting characteristic thermal length is that of the aluminum rather than the liquid sample. This cell is rigid, easy to seal, and can hold a larger volume than is conveniently accommodated in a single thin-layer appropriate to frequencies near 1 Hz. Data acquisition is, thus, rapid; and the heat capacity of the
addendum is removed by the use of a matching differential reference cell. In differential operation the reference cell has a heat capacity C, due to the addenda alone while the sample cell has a heat capacity C, + C,, where C, is the heat capacity of the sample. If C, is small compared to C,, then the differential ac temperature between the two cells will be, ignoring the phase factor, ATa, = (Qc&)G/Cf). [61 Expressed as a fraction of the ac thermal response of a single ceI1, (AWITac
= G/G
7
t71
and C, can be measured by any convenient technique. Note that this last expression has the advantage of removing the amplitude Q0 of the heat transported through the sample. This is useful since a portion of the applied power is normally lost to the surroundings as radiation. DESIGN
OF THE CALORIMETER
The sample cell for our differential ac calorimeter is shown in cross section in Fig. 1. The cell consists of a cylindrical aluminum body fitted with a demountable top and bottom, also of aluminum. These are hermetically sealed to the body by 0 rings mounted on the body. The sample space is a series of concentric grooves each 300 pm wide and 250 pm deep, comprising a total volume of 7.7 j.J. With this arrangement all of the sample is well within 1, of the aluminum parts of the cell in all directions. The distance from heater to thermometer is 1 mm, suitably smaller than lo for aluminum for frequencies of 1 Hz and smaller. The heater is a 100-R thick-film resistance heater obtained from Dale Electronics. It is attached to the top of the cell by a thin layer of epoxy. To insure that both the sample cell and the reference cell are driven with the same phase, their heaters are connected in series. This series combination is driven sinusoidally by a digital frequency synthesizer
58
DIXON
B
0
s
FIG. 1. Cross-section diagram of a sample cell. B, Aluminum bottom cap; D, thermistor; F, aluminum body; G, O-ring gasket; H, thick-film chip resistor; S, screw; T, aluminum top cap; V, sample volume.
(Monsanto Model 3 100A) at a typical frequency of 0.2 Hz and typical amplitude of 5 v. The resulting temperature oscillations are detected with a microbead thermistor epoxied to the bottom of each cell. Each thermistor has a nominal resistance of 5 k!J at 25°C and were obtained from Omega Engineering. These are connected as shown in Fig. 2 to obtain the differential temperature oscillations. The differential signal is amplified by a PARC Model 113 preamplifier and detected by an Ithaca Model 391A lockin amplifier. The circuit can also be reconnected to obtain the signal from each cell separately. Miniature coaxial cable has been used wherever possible to minimize electrical pickup from the heater circuit. A separate thermometer is used to detect the mean temperature of the sample cell. This is a type E (chromel-constantan) thermocouple attached to the bottom of the sample cell and referenced to an ice bath. This thermal emf4 is amplified by a Keithley 4 Abbreviations used: emf, electromotive force; DMPC, dimyristoylpbosphatidylcholine.
ET AL.
Model 140 nanovolt amplifier and detected by a Keithly Model 5900 digital voltmeter. Both the mean temperature and the amplitude of the ac response of the cell are collected and analyzed by a dedicated microcomputer. With this arrangement the temperature resolution is limited by the amplitude of the ac response, typically
DIFFERENTIAL
Differential Calor ISee
1T
Frequency Synthesizer
imeter Detai
I
59
AC CALORIMETER
If
b-i
OTac
ac
Ret I Signal
FIG. 2. Schematic diagram of the calorimeter system showing the signal paths (top) and a detail of the differential calorimeter (bottom). T, The signal from the thermometer; I.,, the sinusoidal heating signal to the heater chips; AT., the difference between the ac temperature for the reference cell and that for the sample cell; H,, the heater chip resistor for the reference cell; T,, the thermistor detector for the reference cell; R, a l-MQ decade resistance unit.
sive amounts of epoxy are used in attaching the heaters and thermometers. In order that any residual phase difference not degrade the signal of interest, the lockin amplifier should be adjusted to maximize the signal from the sample cell alone rather than the differential signal from two cells. When this is done, the residual phase shift can only limit the cancellation of the thermal response of the addenda and will not atten-
tuate the signal from the thermal response of the sample. Subtraction of any remaining addendum response can be handled in software by the microcomputer. EXPERIMENTAL
PROCEDURE
To demonstrate the application of this calorimeter to biochemical systems, we have studied the gel-to-liquid-crystal phase tran-
DIXON
ET AL.
RESULTS
20
21 22 23 TEMPERATURE
24
25
[“Cl
FIG. 3. Excess 0.4 Hz ac heat capacity of DMPC multilayers on heating through the transition temperature at 1 m ‘C/s (A) and on cooling at the same rate (0).
sition in dimyristoyl phosphatidylcholine liposomes. DMPC (Lot No. 8 1003 1) was obtained from Calbiochem. This preparation was found to be homogeneous by thin-layer chromatography and was used without further purification. The suspensions were prepared by heating the lipid in water to a temperature above the transition temperature and then shaking the mixture to disperse the lipids. The suspensions were then degassed, reheated to above the transition temperature, and held overnight in an ice bath. The samples were subsequently transferred to the calorimeter vessel and held at 10°C for 1 h before beginning the initial scan. In the experiments reported here the cells were heated at a frequency of 0.4 Hz with a resulting ac thermal response of amplitude 0.5 m “C. The temperature was scanned through the phase transition at a rate of 3”C/h and subsequently cooled at the same rate.
Figure 3 displays the result of successive heating and cooling scans on a 100 mg/ml sample. The sharp peak with full width at half maximum of 0.2”C agrees well with measurements by conventional differential scanning calorimetry (2,ll). The enthalpy change at the transition is obtained by using Eq. [ 71 and numerically integrating the peak in the ac heat capacity. This yields 5.0 kcal/ mol in excellent agreement with the results of conventional experiments. On cooling the peak is shifted to a temperature 0.5”C lower than on heating. This is to be expected for supercooling at a firstorder phase transition. The peak is also broadened slightly. The heating peak was reproducible from sample to sample to f12%. Of this uncertainty 3% could be attributed to the statistical scatter in the data, and the remaining 9%, to the uncertainty in filling the sample cell with small aliquots of an inhomogeneous sample. The cooling peak showed much greater variability. It was typically smaller than the heating peak and yielded an apparent enthalpy change of as little as 40% of that observed on heating. Both the heating and cooling features were reproducible in successive runs on the same sample. It is reasonable to expect that the establishment of large ordered regions on cooling may proceed at a much slower rate than does the melting of the acyl chains on heating and that the nucIeation of ordered regions would depend on the residual impurity concentration in the sample. Support for this view is provided by deuterium NMR on dipalmitoylphosphatidylcholine in which it is found that a mixed phase persists below the phase transition on cooling ( 12). A detailed ac calorimetry study of these phenomena has been carried out and is reported elsewhere (13). In addition to scanning slowly through this transition, the temperature was also held fixed +O.O2”C at selected points in the transition region. There was no observable change
DIFFERENTIAL
in the specific heat, apart from that associated with the uncertainty in temperature, for times up to 20 min. This clearly indicates that the slow scan rate used here does not distort the shape or position of the specific heat peaks. This result suggests that this lack of distortion would also apply to conventional scanning calorimetry studies at similar scan rates. In the present experiments both the heating and cooling peaks were found to be stable, and thus in the transition region any conversion between the state attained on cooling and that on heating must require hours to achieve at fixed temperature. REFERENCES 1. Melchior, D. L., Morowitz, and Tsong, T. Y. (1970) 219, 114-22.
H. J., Sturtevant, J. M., Biochim. Biophys. Acta
AC
61
CALORIMETER
2. Chapman, D. (1975) Quart. Rev. Biophys. 8, 185235. 3. Mabrey, S., and Sturtevant. J. M. (1976) Proc. Nat. Acad. Sci. USA 73, 3862-3866. 4. Mountcastle, D. B., Biltonen, R. L., and Halsey, M. J. (1978) Proc. Nat. Acad. Sci. USA 75, 4906-49 10. 5. Sullivan, P. F., and Seidel, G. (1968) Phys. Rev. 173, 679. 6. Ashman, J., and Handler, P. (1969) Phys. Rev. Lett. 23, 642-644. 7. Schwartz, P. (1971) Phys. Rev. B 4, 920-929. 8. Smaardyk, J. E., and Mochel, J. M. (1978) Rev. Sci. Instrum. 49, 988. 9. Tanasijczuk, 0. S., and Oja, T. (1978) Rev. Sci. Instrum. 49, 1978. 10. Schantz, C. A., and Johnson, D. L. (1978) Phys. Rev. A 17, 1504-1512. 11. Suurkuusk, J., Lentz, B. R., Barenholz, Y., Biltonen, R. L., and Thompson, T. E. (1976) Biochemistry 15, 1393. 12. Davis, J. H. (1979) Biophys. J. 27, 339-358. 13. Black, S. G.. and Dixon, 20, 6740-6744.
G. S. ( 198 I ) Biochemistry
BIOCHEMISTRY
121.55-61
A Differential
AC Calorimeter
G. S. DIXON,S. Department
(1982)
of Physics,
for Biophysical
Studies’
G. BLACK, C. T. BUTLER,* AND A. K. Oklahoma
State
Received
University,
July
Stillwater,
Oklahoma
JAIN~ 74078
17, 1981
A differential ac calorimeter has been developed to investigate the phase transition behavior of liquids of biological interest, especially suspensions of liposomes and other model membranes. The sensitivity of the calorimeter is independent of the temperature scan rate and scan direction. Therefore, the heat capacity can be measured during heating scans, cooling scans, and at constant mean temperature. Thus, the time-dependent behavior of the heat capacity can be measured. A rather massive sample cell has been used to minimize problems with hermetically sealing the cell and maintaining a constant thermal path between the heater and thermometer. As the heat capacity of this cell is large compared to that of the sample, a differential method has been used to remove the heat capacity of the cell. Results are presented for heating, cooling, and quasi-isothermal studies of the main phase transition in dimyristoylphosphatidylcholine liposomes. Heating scans at 3”C/h are in excellent agreement with conventional scanning calorimetry. Cooling scans exhibit a supercooling of up to 0.5”C at this transition, confirming the first-order nature of the transition. Quasi-isothermal measurements for up to 20 min in the transition region show that there is no observable, instrumental distortion of the transition at these iow scanning rates.
In recent years calorimetric studies have become an important probe of biological systems that undergo phase transitions. This has been especially true of biological membranes ( 1) and related synthetic systems based on lipid multilayers (2-4). Calorimetry is advantageous in these studies in being noninvasive and measuring a bulk property of the system. Hence, the questions of microscopic location and possible perturbing influence that complicate the use of molecular probes do not arise for calorimetry. Although the heat capacity of a system is an equilibrium property, the conventional methods used to study biological samples, namely differential scanning calorimetry and differential thermal analysis, are essentially measurements of the transient re-
sponse of the system to changes in temperature. The sensitivity of these instruments is, thus, tied directly to the rate at which the temperature is scanned. This limits the temperature resolution of these instruments near a phase transition, and at high scan rates raises questions of possible distortion of the calorimetric behavior in the transition region. Moreover, heat conduction problems in most cases limit these instruments to use in heating scans. In this paper we describe a calorimeter based on the ac method introduced by Sullivan and Seidel (5) for the study of solids and which has been successfully applied to a variety of solid-state phase transitions (6,7). The ac method is steady state and capable of temperature resolution in excess of a millidegree. It consists in measuring the thermal response of the sample to periodic heat pulses. The sensitivity of the apparatus is, thus, independent of the rate at which the mean temperature of the sample is scanned.
’ Supported by NSF Grant PCM 78-13752. ’ Visiting Scientist from Department of Physics, Virginia Commonwealth University, Richmond, Va. ’ Present address: McDonnell-Douglas Corp., Houston, Tex.
55
0003-2697/82/050055-07$02.00/O Copyright 0 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
56
DIXON
The operation in a cooling cycle is no different from that in a heat cycle. It is also possible to hold the mean temperature of the sample fixed and measure changes in heat capacity as a function of time. This allows one to check for possible distortions in the calorimetric event that might arise from an excessive scan rate, to search for kinetic behavior on a time scale larger than the period of the heat pulses, and, as Sullivan and Seide1 (5) have demonstrated in solids, to detect the variation of the heat capacity as a function of time-varying conditions imposed on the sample or its environment. By the use of a differential technique this calorimeter avoids some of the problems that have attended other recent applications of the ac method to organic liquids. To our knowledge this is the first time the ac calorimetry technique has been incorporated in a differential instrument.
ET AL.
This has a sinusoidal solution T = Taceiw’
with i = (-1)“’
[21
and
T,, = -iQ,,(wC)-I/[
1 + i(wJ’]
[ 31
where ?-b = RC is the sample-to-bath relaxtime. If orb B 1, this reduces to
ation
Tat = -iQa/wC.
[41
It is this simple, inverse relationship between the heat capacity and the ac temperature that one strives to obtain in an actual experiment. A real material has a finite thermal conductivity K and, therefore, it is necessary to consider how the temperature oscillation propagates through the slab. This is governed by the heat conduction equation [51
REVIEW
OF ac CALORIMETRY
The method of ac calorimetry has been described in detail by several authors (5,7). Here, we present a brief discussion of two examples which illustrate the operation of the technique in an ideal case and the difficulties that must be surmounted to use it for the study of liquids. First, consider a slab-like sample of heat capacity C and infinite thermal conductivity connected through a thermal resistance R to a heat reservoir maintained at constant temperature To. The heat capacity C includes not only that of the specimen of interest, but also that of the sample cell, heater, thermometer, and any other addenda. To simplify the algebra, let temperature be measured on a relative scale with To = 0. Let the slab be heated sinusoidally at a rate Q = QOeiw’.The temperature of the slab is governed by the differential equation 1T +Q-;.
T
where 77= K/C~ is the thermal diffusivity with c the specific heat of the sample and p its density. Here, it has been assumed that heat losses through the sides of the slab are negligible, so that the problem is one of onedimensional heat flow from front to back. Solving this equation subject to the same boundary conditions as in the first example, one finds that the sample will be uniformly heated provided its thickness is small compared to a characteristic length l,, = (2n/ w)“‘. Other small corrections arising from finite heater-to-sample and thermometer-tosample relaxation times have been treated by Sullivan and Seidel (5). While a slab-like geometry of the sample cell simplifies a discussion of the technique, it is not a necessary condition for the operation of an ac calorimeter. The essential physical parameters are the following. (i) The dimensions of the sample should be small compared to lo in order to obtain uniform heating. (ii) The sample-to-bath relaxation time should be long compared to the
DIFFERENTIAL
57’
AC CALORIMETER
period of the temperature wave to maximize the amplitude of the temperature oscillations. (iii) Similarly, the heater-to-sample and thermometer-to-sample relaxation times should be short compared to the period so that the temperature wave is efficiently driven and detected. The major experimental difficulty in applying ac calorimetry to liquids arises from their low thermal diffusivity. This is typically one to two orders of magnitude smaller than is found in crystalline solids, and limits the characteristic thermal length 1,. For example, in water the thermal diffusivity ? = 1.5 X 10e3 cm2/s yielding lo = (5 X 10e2/ w1i2) cm. At a frequency of 1 Hz this gives lo = 200 pm. This is to be compared to a characteristic length of 5 mm in aluminum at the same frequency. Uniform heating of the liquid can be assured only if very thin samples (8,9) or long periods (10) (I-10 min) are used. For a single thin-layer sample, one can use only a small sample volume, and a large addendum correction can be avoided only through the use of very thin walls for the sample cell. In our hands such cells have proven difficult to seal reliably. Others (9) have noted such cells’ sensitivity to variation in the thermal pathlength caused by fluctuations in the ambient pressure or by thermal expansion. The long-period method leads to inconveniently long data acquisition times. This is of concern with biological specimens that may be subject to deterioration. The differential ac calorimeter described here avoids the difficulties noted above. The sample is contained in an aluminum cell in which the liquid is arranged in a number of layers each of thickness small compared to 4,. These are arranged so that the limiting characteristic thermal length is that of the aluminum rather than the liquid sample. This cell is rigid, easy to seal, and can hold a larger volume than is conveniently accommodated in a single thin-layer appropriate to frequencies near 1 Hz. Data acquisition is, thus, rapid; and the heat capacity of the
addendum is removed by the use of a matching differential reference cell. In differential operation the reference cell has a heat capacity C, due to the addenda alone while the sample cell has a heat capacity C, + C,, where C, is the heat capacity of the sample. If C, is small compared to C,, then the differential ac temperature between the two cells will be, ignoring the phase factor, ATa, = (Qc&)G/Cf). [61 Expressed as a fraction of the ac thermal response of a single ceI1, (AWITac
= G/G
7
t71
and C, can be measured by any convenient technique. Note that this last expression has the advantage of removing the amplitude Q0 of the heat transported through the sample. This is useful since a portion of the applied power is normally lost to the surroundings as radiation. DESIGN
OF THE CALORIMETER
The sample cell for our differential ac calorimeter is shown in cross section in Fig. 1. The cell consists of a cylindrical aluminum body fitted with a demountable top and bottom, also of aluminum. These are hermetically sealed to the body by 0 rings mounted on the body. The sample space is a series of concentric grooves each 300 pm wide and 250 pm deep, comprising a total volume of 7.7 j.J. With this arrangement all of the sample is well within 1, of the aluminum parts of the cell in all directions. The distance from heater to thermometer is 1 mm, suitably smaller than lo for aluminum for frequencies of 1 Hz and smaller. The heater is a 100-R thick-film resistance heater obtained from Dale Electronics. It is attached to the top of the cell by a thin layer of epoxy. To insure that both the sample cell and the reference cell are driven with the same phase, their heaters are connected in series. This series combination is driven sinusoidally by a digital frequency synthesizer
58
DIXON
B
0
s
FIG. 1. Cross-section diagram of a sample cell. B, Aluminum bottom cap; D, thermistor; F, aluminum body; G, O-ring gasket; H, thick-film chip resistor; S, screw; T, aluminum top cap; V, sample volume.
(Monsanto Model 3 100A) at a typical frequency of 0.2 Hz and typical amplitude of 5 v. The resulting temperature oscillations are detected with a microbead thermistor epoxied to the bottom of each cell. Each thermistor has a nominal resistance of 5 k!J at 25°C and were obtained from Omega Engineering. These are connected as shown in Fig. 2 to obtain the differential temperature oscillations. The differential signal is amplified by a PARC Model 113 preamplifier and detected by an Ithaca Model 391A lockin amplifier. The circuit can also be reconnected to obtain the signal from each cell separately. Miniature coaxial cable has been used wherever possible to minimize electrical pickup from the heater circuit. A separate thermometer is used to detect the mean temperature of the sample cell. This is a type E (chromel-constantan) thermocouple attached to the bottom of the sample cell and referenced to an ice bath. This thermal emf4 is amplified by a Keithley 4 Abbreviations used: emf, electromotive force; DMPC, dimyristoylpbosphatidylcholine.
ET AL.
Model 140 nanovolt amplifier and detected by a Keithly Model 5900 digital voltmeter. Both the mean temperature and the amplitude of the ac response of the cell are collected and analyzed by a dedicated microcomputer. With this arrangement the temperature resolution is limited by the amplitude of the ac response, typically
DIFFERENTIAL
Differential Calor ISee
1T
Frequency Synthesizer
imeter Detai
I
59
AC CALORIMETER
If
b-i
OTac
ac
Ret I Signal
FIG. 2. Schematic diagram of the calorimeter system showing the signal paths (top) and a detail of the differential calorimeter (bottom). T, The signal from the thermometer; I.,, the sinusoidal heating signal to the heater chips; AT., the difference between the ac temperature for the reference cell and that for the sample cell; H,, the heater chip resistor for the reference cell; T,, the thermistor detector for the reference cell; R, a l-MQ decade resistance unit.
sive amounts of epoxy are used in attaching the heaters and thermometers. In order that any residual phase difference not degrade the signal of interest, the lockin amplifier should be adjusted to maximize the signal from the sample cell alone rather than the differential signal from two cells. When this is done, the residual phase shift can only limit the cancellation of the thermal response of the addenda and will not atten-
tuate the signal from the thermal response of the sample. Subtraction of any remaining addendum response can be handled in software by the microcomputer. EXPERIMENTAL
PROCEDURE
To demonstrate the application of this calorimeter to biochemical systems, we have studied the gel-to-liquid-crystal phase tran-
DIXON
ET AL.
RESULTS
20
21 22 23 TEMPERATURE
24
25
[“Cl
FIG. 3. Excess 0.4 Hz ac heat capacity of DMPC multilayers on heating through the transition temperature at 1 m ‘C/s (A) and on cooling at the same rate (0).
sition in dimyristoyl phosphatidylcholine liposomes. DMPC (Lot No. 8 1003 1) was obtained from Calbiochem. This preparation was found to be homogeneous by thin-layer chromatography and was used without further purification. The suspensions were prepared by heating the lipid in water to a temperature above the transition temperature and then shaking the mixture to disperse the lipids. The suspensions were then degassed, reheated to above the transition temperature, and held overnight in an ice bath. The samples were subsequently transferred to the calorimeter vessel and held at 10°C for 1 h before beginning the initial scan. In the experiments reported here the cells were heated at a frequency of 0.4 Hz with a resulting ac thermal response of amplitude 0.5 m “C. The temperature was scanned through the phase transition at a rate of 3”C/h and subsequently cooled at the same rate.
Figure 3 displays the result of successive heating and cooling scans on a 100 mg/ml sample. The sharp peak with full width at half maximum of 0.2”C agrees well with measurements by conventional differential scanning calorimetry (2,ll). The enthalpy change at the transition is obtained by using Eq. [ 71 and numerically integrating the peak in the ac heat capacity. This yields 5.0 kcal/ mol in excellent agreement with the results of conventional experiments. On cooling the peak is shifted to a temperature 0.5”C lower than on heating. This is to be expected for supercooling at a firstorder phase transition. The peak is also broadened slightly. The heating peak was reproducible from sample to sample to f12%. Of this uncertainty 3% could be attributed to the statistical scatter in the data, and the remaining 9%, to the uncertainty in filling the sample cell with small aliquots of an inhomogeneous sample. The cooling peak showed much greater variability. It was typically smaller than the heating peak and yielded an apparent enthalpy change of as little as 40% of that observed on heating. Both the heating and cooling features were reproducible in successive runs on the same sample. It is reasonable to expect that the establishment of large ordered regions on cooling may proceed at a much slower rate than does the melting of the acyl chains on heating and that the nucIeation of ordered regions would depend on the residual impurity concentration in the sample. Support for this view is provided by deuterium NMR on dipalmitoylphosphatidylcholine in which it is found that a mixed phase persists below the phase transition on cooling ( 12). A detailed ac calorimetry study of these phenomena has been carried out and is reported elsewhere (13). In addition to scanning slowly through this transition, the temperature was also held fixed +O.O2”C at selected points in the transition region. There was no observable change
DIFFERENTIAL
in the specific heat, apart from that associated with the uncertainty in temperature, for times up to 20 min. This clearly indicates that the slow scan rate used here does not distort the shape or position of the specific heat peaks. This result suggests that this lack of distortion would also apply to conventional scanning calorimetry studies at similar scan rates. In the present experiments both the heating and cooling peaks were found to be stable, and thus in the transition region any conversion between the state attained on cooling and that on heating must require hours to achieve at fixed temperature. REFERENCES 1. Melchior, D. L., Morowitz, and Tsong, T. Y. (1970) 219, 114-22.
H. J., Sturtevant, J. M., Biochim. Biophys. Acta
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G. S. ( 198 I ) Biochemistry