VOL. 15, 785-795 (1976)
BIOPOLY MERS
Ultrasonic Absorption in Aqueous Solution of Lysozyme HIROSHI KANDA,* NOR10 OOKUBO, HARUHIKO NAKAJIMA, YASUKO SUZUKI,** MICHIO MINATO, TAKURO IHARA, and YASAKU WADA, Department of Applied Physics, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, Japan
Synopsis The titration curve of ultrasonic absorption a t 2.82 MHz in aqueous solutions of lysozyme measured by Zana and Lang [J. Phys. Chem., 74, 2734 (1970)] is theoretically analyzed. The maxima a t pH 3 and pH 11 are describable with proton-transfer reactions of dissociable carboxyl and amino groups by assuming that volume changes due to the reactions are 2.3 and 5.2 cm3/mole, respectively, which are appreciably smaller than those of simple amino acids. The remaining, pH-independent excess absorption over solvent is measured a t frequencies ranging from 3 to 150 MHz. The absorption is ascribed to the internal loss of protein. The complex compressibility Fp - iypof lysozyme molecule is cm2/dyne from the increcm2/dyne and /3”p = 4.3 X evaluated as Fp = 7.2 X ments over solvent in absorption as well as in sound velocity.
INTRODUCTION As a result of experimental investigation^,'-^ it has been well established that the ultrasonic absorption in an aqueous solution of protein consists of pH-dependent and pH-independent absorptions and the pH-dependent part is ascribed in proton-transfer reactions of carboxyl and amino groups. The conclusion, however, has not yet been reached at present on the mechanism of the pH-independent absorption. The aim of this paper is, first, to analyze the pH-dependent absorption of aqueous lysozyme reported by Zana and Langl and to evaluate parameters of proton-transfer reactions in the protein. Secondly, this paper describes experimental results on the frequency dependence of the pH-independent absorption in aqueous lysozyme. By comparing the data with those in aqueous h e m ~ g l o b i nit, ~is suggested that the absorption arises mostly from the bulk property of the protein molecule rather than the surface property. The complex compressibility of the lysozyme molecule is determined from sound velocity and absorption in lysozyme solution. * Present address: Central Laboratory, Hitachi Ltd., Kokubunji, Tokyo, Japan.
** On leave from Research Institute for Polymers and Textiles, Sawatari, Kanagawa-ku, Yokohama, Japan. 785
0 1976 by John Wiley & Sons, Inc.
786
KANDA, SUZUKI, A N D WADA
EXPERIMENTAL The sample of hen egg white lysozyme in a powdered form, supplied by Seikagaku Kogyo Co., was purified six times by recrystallization. The protein was dissolved in 0.2M NaC1. The protein concentration was determined by weighing the protein after removing water from the solution for three days under vacuum a t 3OoC because the as-received, crystalline sample included an appreciable amount of crystalline water. A solution a t a concentration of 4 g protein in 100 ml 0.2M NaCl was used for absorption measurements. The absorption was found to vary linearly with protein concentration at least up to 5 g/100 ml a t the neutral pH range. Sound velocity and density were measured in the concentration range up to 3 g/100 ml, keeping the salt concentration constant. The sound velocity a t 1 MHz was measured with an ultrasonic interferometer and the density with a pycnometer of 25 ml in volume. The accuracy of velocity measurement was checked for pure water to be within 0.1%. Two techniques were employed for absorption measurements. The absorption of ultrasonic waves at frequencies higher than 50 MHz was measured with the light diffraction technique, using the Bragg reflection of a He-Ne laser light beam by the sound wave. Details of the apparatus have been described el~ewhere.~ The absorption a t 3,9, and 15 MHz was measured with a resonant reverberation method. The acoustic part of the apparatus was essentially similar to that of the pulse method with transmitting and receiving transducers. The specimen solution was put in the gap between two parallel X-cut quartz plates, both being resonant a t 3 MHz and 1.5 cm in diameter. The parallelism of two crystals was finely adjusted so as to get a maximum echo when the apparatus was operated as a pulse echo equipment. The gap ranged from 1to 2 cm and was adjusted with a micrometer screw to be n times of half wavelength where n is an integer. This adjustment was performed by obtaining a minimum decay rate as will be described later. The acoustic energy a t a resonant frequency was supplied to the specimen by one crystal, and after establishment of standing waves, the energy supply was stopped and the decay of the acoustic energy was detected by the other crystal. A purely exponential decay with a minimum decay rate was observed when the gap was appropriately set. The exponential decay of the received signal was compared on the oscilloscope screen with a decay curve generated by a CR circuit and the decay rate D was determined. The decay rate is related with the absorption coefficient a of the specimen by6
D=au+D,
(1)
where u is the second velocity of the solution and D , is the surface decay rate. D , was determined from the measurement for pure water with the
ULTRASONIC ABSORPTION IN LYSOZYME
787
140 N"
120-
0
-? I5
-
p-
-0
100-
8000
'0 5 LO-':y-.Loo-
wx
6o 20
-
:--------
0 1
3
5
7
91113
PH Fig. 1. Ultrasonic absorption titration curve of aqueous solution of lysozyme: 2.8 MHz, 25OC, 0.2M NaCl, protein concentration: 1.04 g/100 ml. Circles represent data by Zana and Lang.' Solid curve represents calculated values by assuming the absorption is the , sum of three contributions; solvent absorption, pH-independent absorption ( A c u l p ) ~and absorption due to proton-transfer reactions.
same resonant mode (i.e., the same value of n) as for the solution. This technique requires a relatively small amount of solution, 10-20 ml in our case, and a short measuring time. All the measurements were made a t 25°C.
pH-DEPENDENT ABSORPTION Ultrasonic absorption a t 2.82 MHz in aqueous solutions of lysozyme, P-lactoglobulin, and bovine serum albumin was measured by Zana and Langl as a function of pH. The results show that the excess absorption over solvent is the sum of well-defined two maxima, a t pH 3 and pH 11 for lysozyme, respectively, and pH-independent background absorption. The maxima are usual in amphoteric electrolytes such as amino acids7lo and protein^,^,^ and have been attributed to proton-transfer reactions of carboxyl and amino groups. In Figure 1 circles give experimental values of the absorption a t 2.82 MHz for lysozyme in 0.2M NaCl (protein concentration = 1.04 g/100 ml) by Zana and Lang.' The absorption maxima a t pH 3 and pH 11 are, respectively, attributed to proton-transfer reactions:
+ H30+ * -COOH + H20 -NH3+ + OH- * -NH2 + H20
-COO-
(2)
We shall analyze the data following Hussey and Edmonds7 who analyzed the absorption data of aqueous glycine. The absorption ( A ~ ~ / f 2 ) ~ t due to these reactions is given by the well-known equation1'
where f is the frequency of ultrasonic wave (w denoting 27rf), p is the density of solution, u is the sound velocity in solution, R is the gas con-
KANDA, SUZUKI, AND WADA
788
. TABLE1 Parameters of Protolytic Groups of Lysozyme
Groups
Number of group in a molecule
pK
sec-' mole-'
a-Carboxyl p,yCarboxyl 7-Carboxyl Imidazolium a-Amino €-Amino Phenolic hydroxyl
1 6 1 1 1 6 1
3.5 4.3 6.0 6.8 7.8 10.7 9.95
4.0 x 1010 4.0 X 10'' 4.0 x l o L o 2.4 x 10'O 3.5 x 10'0 2.4 x 1010 -
kf,
A kh.
sec-'
1.2 x 107 2.0 X lo6 4.0 x lo4 1.2 x l o 2 2.2 x lo4 1.1 x 107 -
v,
cm3/mo1e 2.3 2.3 2.3 5.2 5.2 5.2
-
stant, T is the absolute temperature, n is the number of group in a protein molecule, AV is the volume change in one-mole reaction, and r is the relaxation time. The subscript i denotes the species of protolytic group. For an ideal solution, r is given by the equation,
r-1 =
1 a(l-a)Cp
+-c1
(4)
and r is written in the form,
where C , is the molar concentration of protein, C is that of H30+ or OH- for acid or base, respectively, and kf and k b are forward and backward rate constants of reactions in Eq. (2), respectively, and a is the degree of dissociation. For a lysozyme solution, the value of pK of each dissociable group has been estimated from the potentiometric titration curve14 as listed in Table I, and from the pK we calculated a as a function of pH for each group. The values of k f in Table I were obtained by assuming that kf is equal to that of respective amino acids7-10 and the values of k b were estimated from k f and pK. This is acceptable because kf of the protontransfer reaction may not be affected seriously by the surrounding as is evidenced by the fact that kf of amino acids does not depend so much on the species. The value of kf of phenolic hydroxyl group has not been reported in literature and the contribution of this group was neglected in this calculation. However, this does not affect the result seriously because the lysozyme contains only a single dissociable phenolic hydroxyl group.12 For obtaining a best fit of the calculated absorption titration curve to the observed one, values of AV were chosen as listed in Table I, which are considerably smaller than those for g l y ~ i n e A , ~V = 6 and 25 cm3/ mole for carboxyl and amino groups, respectively. This may be accept-
ULTRASONIC ABSORPTION IN LYSOZYME
789
able because hydration of COO- and NH3+ groups in the protein may be appreciably hindered by surrounding atomic groups of the protein. If we might assume that k f is smaller in protein than in amino acids on account of any effect of surrounding atomic groups in the protein, T would be longer and thus A V would be smaller because, a t 2.82 MHz, 07 is always less than unity. The soli\d curve in Figure 1 is drawn by assuming that ( A a / f 2 )is the sum of three contributions: solvent absorption, pH-independent ab, ( A a / f 2 ) p t . The calculated curve reproduces well sorption ( A a / f 2 ) ~and the two maxima around pH 3 and pH 11.
pH-INDEPENDENT ABSORPTION In the following, we shall discuss the origin of pH-independent absorption, ( A a / f 2 ) ~ .The excess absorption of sound in solutions of small particles is due to scattering of sound by the particle, viscous and transport processes occurring at the interrmal face of nonhomogeneities, as well as to the intrinsic absorption in the particle.13J4 The excess absorption due to the scattering of sound is given by the equation,I3
=a$(34f2a3[1 - - (Ps -P sP
”)
(6) 2Pp + P s where 4 is the volume fraction of particle, a is the radius of particle, P and p are adiabatic compressibility and density, respectively. Here subscripts s and p stand for solvent and particle, respectively. In the present case of lysozyme ( a = 17.2 A and pp = 1.34 g/cm3) a t a frequency of 2.82 MHz, (Aa/f2)scatterwas calculated to be much smaller than the observed value, even if we assume pp = 0 in Eq. (6). The excess absorption due to the viscous drag effect arising from relative motion of particle and solvent and that due to thermal transport process between particle and solvent are:14 scatter
+(pp-ps)2]
and
where q is the shear viscosity, c is the specific heat at constant pressure, d is the thermal expansion coefficient, and K is the thermal conductivity. These two absorptions also were estimated to be negligibly small in our case. In evaluating the thermal transport loss, values of specific heat, thermal expansion coefficient, and thermal conductivity of lysozyme are necessary, which have not been reported in literature. We made an estimation of the upper limit of the absorption with ‘reference to those
790
KANDA, SUZUKI, AND WADA
1
10 FREQUENCY
102
(MHz)
Fig. 2. Excess ultrasonic absorption over solvent divided by concentration in weight per volume in aqueous lysozyme at 25OC. Closed circles represent data of the present work and open circles data by 1n0ue.l~ Dashed curve represents a single relaxation curve which fits to high-frequency data.
values for crystalline amino acids and similar substances, but the result was still much smaller than the observed absorption. We must look, therefore, for the origin of pH-independent absorption in the intrinisic property of the globular protein. Figure 2 illustrates the observed absorption of ultrasonic waves in the frequency range from 3 to 150 MHz in an aqueous solution of lysozyme, together with the data by Inoue,15 a t pH 5 where the contribution of proton-transfer reactions is negligible. The agreement of our data with those by Inoue is satisfactory while Inoue measured the absorption with the conventional pulse echo technique. The data a t frequencies above 10 MHz may be well fitted, as shown by a dashed curve, by a single relaxation process with a relaxation frequency located at 12 MHz, but the upswing of the absorption a t lower frequencies indicates a distribution of relaxation times as was found for aqueous bovine hemoglobin by Schneider et al.* Figure 3 compares the excess absorptions per wavelength A p for lysozyme and hemoglobin, both reduced to unit weight concentration, the latter being calculated from the data compiled by Schneider e t a1.4 It is found in Figure 3 that lysozyme and hemoglobin have an analogous behavior in the shape of absorption spectrum, whereas the magnitude is somewhat higher in hemoglobin than lysozyme. This fact suggests that, since the molecular surface area per unit mass is considerably larger for lysozyme than for hemoglobin because of a smaller size of the former, the absorption arises, a t least for the most part, from the bulk property of globular proteins rather than the surface property like the interaction between solvent and protein a t the interface.15J6 The increase of absorption per unit weight concentration with increasing molecular weight of globular proteins is also found in a series of data for lysozyme, ,&lactoglobulin, and bovine serum albumin by Zana and Lang.l Of course,
ULTRASONIC ABSORPTION IN LYSOZYME
- o l
791
_ _ --, Hb
__----
LYSOZYME
l0'l 1
'
' ' ' , . . . l
'
"
1
10 FREQUENCY
,
1
1
1
'
1o2 ( MHz)
'
' ' A J
103
Fig. 3. Excess absorption per wavelength at 25OC for lysozyme (solid curve) and hemoglobin (dashed curve), both reduced to unit concentration.
the role of the surface reaction cannot be completely discounted at this time because, in the case of linear polymers, the interaction of solvent molecules with the polymer has been evidenced to play an important role in the ultrasonic a b ~ o r p t i o n . ~Multiple mechanisms may exist simultaneously but the surface reaction may have a minor degree of effectiveness in the absorption in the frequency range 2-100 MHz for the globular protein. Effects of denaturants on the ultrasonic absorption of aqueous lysozyme were studied by Inoue15 and Minato et al.17 According to them, denaturation of lysozyme makes the absorption increase for various denaturants including urea, urea and Na2S03, 2-chloroethanol, LiBr, and guanidine-HC1. However, the increase in absorption with denaturing time is not in general parallel with the increase in viscosity which reflects the expansion of protein molecules. The time variations of excess absorption and reduced viscosity of lysozyme in 8.2M urea and 0.03M Na2S04 after mixing the protein in the denaturant are illustrated in Figure 4. The absorption reaches a final value within one minute but the viscosity continues to increase over a few hours. This indicates that the breakup of the internal structure seriously affects the absorption while subsequent scissions of S-S bondsla, which result in the expansion of molecule and the increase of molecular surface, do not.
COMPLEX COMPRESSIBILITY OF LYSOZYME T o summarize the discussion in the preceding section, the globular molecule of protein may be regarded as a viscoelastic particle and the absorption of sound in the protein solution arises for the most part from the internal loss of the particle. In this section, we shall estimate the compressibility of the lysozyme molecule as a complex quantity. When the solvent particle is much smaller than the wavelength of sound, the compressibility p of a solution is given by the equation,lg
792
KANDA, SUZUKI, AND WADA 120
I
I
1
60
120
180
.
1
240
TIME ( M I N I
Fig. 4. Time variations of ultrasonic excess absorption at 3 MHz (open circles) and reduced viscosity (closed circles) of lysozyme in aqueous urea (8.2M) and NaZS03 (0.03M)at 25OC. Protein concentration: 4 g/100 ml. Initial values before denaturation are Aa/P = 80 X wi7 sec2/cm and qred = 3.5 cm3/g.
P = P s O - 4) + Pp4
(9) where subscripts s and p denote solvent and particle (protein) and the quantity without subscript that of solution. When the solute particle is viscoelastic, Pp in Eq. (9) should be replaced by a complex quantity P*p
P*p = Kp - iP”p
(10)
and therefore Eq. (9) is written in the form
P*
= PS(1 - 4)
+ P*p4
(11)
which is related with the complex sound velocity u * as u* = (l/pP*)1’2
(12)
Since u * is by definition
_1- -_ 1_ u*
u
.Aa 1-
w
we get, by combining Eqs. (10)-(13), for A a u / w 1
BIOPOLY MERS
Ultrasonic Absorption in Aqueous Solution of Lysozyme HIROSHI KANDA,* NOR10 OOKUBO, HARUHIKO NAKAJIMA, YASUKO SUZUKI,** MICHIO MINATO, TAKURO IHARA, and YASAKU WADA, Department of Applied Physics, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, Japan
Synopsis The titration curve of ultrasonic absorption a t 2.82 MHz in aqueous solutions of lysozyme measured by Zana and Lang [J. Phys. Chem., 74, 2734 (1970)] is theoretically analyzed. The maxima a t pH 3 and pH 11 are describable with proton-transfer reactions of dissociable carboxyl and amino groups by assuming that volume changes due to the reactions are 2.3 and 5.2 cm3/mole, respectively, which are appreciably smaller than those of simple amino acids. The remaining, pH-independent excess absorption over solvent is measured a t frequencies ranging from 3 to 150 MHz. The absorption is ascribed to the internal loss of protein. The complex compressibility Fp - iypof lysozyme molecule is cm2/dyne from the increcm2/dyne and /3”p = 4.3 X evaluated as Fp = 7.2 X ments over solvent in absorption as well as in sound velocity.
INTRODUCTION As a result of experimental investigation^,'-^ it has been well established that the ultrasonic absorption in an aqueous solution of protein consists of pH-dependent and pH-independent absorptions and the pH-dependent part is ascribed in proton-transfer reactions of carboxyl and amino groups. The conclusion, however, has not yet been reached at present on the mechanism of the pH-independent absorption. The aim of this paper is, first, to analyze the pH-dependent absorption of aqueous lysozyme reported by Zana and Langl and to evaluate parameters of proton-transfer reactions in the protein. Secondly, this paper describes experimental results on the frequency dependence of the pH-independent absorption in aqueous lysozyme. By comparing the data with those in aqueous h e m ~ g l o b i nit, ~is suggested that the absorption arises mostly from the bulk property of the protein molecule rather than the surface property. The complex compressibility of the lysozyme molecule is determined from sound velocity and absorption in lysozyme solution. * Present address: Central Laboratory, Hitachi Ltd., Kokubunji, Tokyo, Japan.
** On leave from Research Institute for Polymers and Textiles, Sawatari, Kanagawa-ku, Yokohama, Japan. 785
0 1976 by John Wiley & Sons, Inc.
786
KANDA, SUZUKI, A N D WADA
EXPERIMENTAL The sample of hen egg white lysozyme in a powdered form, supplied by Seikagaku Kogyo Co., was purified six times by recrystallization. The protein was dissolved in 0.2M NaC1. The protein concentration was determined by weighing the protein after removing water from the solution for three days under vacuum a t 3OoC because the as-received, crystalline sample included an appreciable amount of crystalline water. A solution a t a concentration of 4 g protein in 100 ml 0.2M NaCl was used for absorption measurements. The absorption was found to vary linearly with protein concentration at least up to 5 g/100 ml a t the neutral pH range. Sound velocity and density were measured in the concentration range up to 3 g/100 ml, keeping the salt concentration constant. The sound velocity a t 1 MHz was measured with an ultrasonic interferometer and the density with a pycnometer of 25 ml in volume. The accuracy of velocity measurement was checked for pure water to be within 0.1%. Two techniques were employed for absorption measurements. The absorption of ultrasonic waves at frequencies higher than 50 MHz was measured with the light diffraction technique, using the Bragg reflection of a He-Ne laser light beam by the sound wave. Details of the apparatus have been described el~ewhere.~ The absorption a t 3,9, and 15 MHz was measured with a resonant reverberation method. The acoustic part of the apparatus was essentially similar to that of the pulse method with transmitting and receiving transducers. The specimen solution was put in the gap between two parallel X-cut quartz plates, both being resonant a t 3 MHz and 1.5 cm in diameter. The parallelism of two crystals was finely adjusted so as to get a maximum echo when the apparatus was operated as a pulse echo equipment. The gap ranged from 1to 2 cm and was adjusted with a micrometer screw to be n times of half wavelength where n is an integer. This adjustment was performed by obtaining a minimum decay rate as will be described later. The acoustic energy a t a resonant frequency was supplied to the specimen by one crystal, and after establishment of standing waves, the energy supply was stopped and the decay of the acoustic energy was detected by the other crystal. A purely exponential decay with a minimum decay rate was observed when the gap was appropriately set. The exponential decay of the received signal was compared on the oscilloscope screen with a decay curve generated by a CR circuit and the decay rate D was determined. The decay rate is related with the absorption coefficient a of the specimen by6
D=au+D,
(1)
where u is the second velocity of the solution and D , is the surface decay rate. D , was determined from the measurement for pure water with the
ULTRASONIC ABSORPTION IN LYSOZYME
787
140 N"
120-
0
-? I5
-
p-
-0
100-
8000
'0 5 LO-':y-.Loo-
wx
6o 20
-
:--------
0 1
3
5
7
91113
PH Fig. 1. Ultrasonic absorption titration curve of aqueous solution of lysozyme: 2.8 MHz, 25OC, 0.2M NaCl, protein concentration: 1.04 g/100 ml. Circles represent data by Zana and Lang.' Solid curve represents calculated values by assuming the absorption is the , sum of three contributions; solvent absorption, pH-independent absorption ( A c u l p ) ~and absorption due to proton-transfer reactions.
same resonant mode (i.e., the same value of n) as for the solution. This technique requires a relatively small amount of solution, 10-20 ml in our case, and a short measuring time. All the measurements were made a t 25°C.
pH-DEPENDENT ABSORPTION Ultrasonic absorption a t 2.82 MHz in aqueous solutions of lysozyme, P-lactoglobulin, and bovine serum albumin was measured by Zana and Langl as a function of pH. The results show that the excess absorption over solvent is the sum of well-defined two maxima, a t pH 3 and pH 11 for lysozyme, respectively, and pH-independent background absorption. The maxima are usual in amphoteric electrolytes such as amino acids7lo and protein^,^,^ and have been attributed to proton-transfer reactions of carboxyl and amino groups. In Figure 1 circles give experimental values of the absorption a t 2.82 MHz for lysozyme in 0.2M NaCl (protein concentration = 1.04 g/100 ml) by Zana and Lang.' The absorption maxima a t pH 3 and pH 11 are, respectively, attributed to proton-transfer reactions:
+ H30+ * -COOH + H20 -NH3+ + OH- * -NH2 + H20
-COO-
(2)
We shall analyze the data following Hussey and Edmonds7 who analyzed the absorption data of aqueous glycine. The absorption ( A ~ ~ / f 2 ) ~ t due to these reactions is given by the well-known equation1'
where f is the frequency of ultrasonic wave (w denoting 27rf), p is the density of solution, u is the sound velocity in solution, R is the gas con-
KANDA, SUZUKI, AND WADA
788
. TABLE1 Parameters of Protolytic Groups of Lysozyme
Groups
Number of group in a molecule
pK
sec-' mole-'
a-Carboxyl p,yCarboxyl 7-Carboxyl Imidazolium a-Amino €-Amino Phenolic hydroxyl
1 6 1 1 1 6 1
3.5 4.3 6.0 6.8 7.8 10.7 9.95
4.0 x 1010 4.0 X 10'' 4.0 x l o L o 2.4 x 10'O 3.5 x 10'0 2.4 x 1010 -
kf,
A kh.
sec-'
1.2 x 107 2.0 X lo6 4.0 x lo4 1.2 x l o 2 2.2 x lo4 1.1 x 107 -
v,
cm3/mo1e 2.3 2.3 2.3 5.2 5.2 5.2
-
stant, T is the absolute temperature, n is the number of group in a protein molecule, AV is the volume change in one-mole reaction, and r is the relaxation time. The subscript i denotes the species of protolytic group. For an ideal solution, r is given by the equation,
r-1 =
1 a(l-a)Cp
+-c1
(4)
and r is written in the form,
where C , is the molar concentration of protein, C is that of H30+ or OH- for acid or base, respectively, and kf and k b are forward and backward rate constants of reactions in Eq. (2), respectively, and a is the degree of dissociation. For a lysozyme solution, the value of pK of each dissociable group has been estimated from the potentiometric titration curve14 as listed in Table I, and from the pK we calculated a as a function of pH for each group. The values of k f in Table I were obtained by assuming that kf is equal to that of respective amino acids7-10 and the values of k b were estimated from k f and pK. This is acceptable because kf of the protontransfer reaction may not be affected seriously by the surrounding as is evidenced by the fact that kf of amino acids does not depend so much on the species. The value of kf of phenolic hydroxyl group has not been reported in literature and the contribution of this group was neglected in this calculation. However, this does not affect the result seriously because the lysozyme contains only a single dissociable phenolic hydroxyl group.12 For obtaining a best fit of the calculated absorption titration curve to the observed one, values of AV were chosen as listed in Table I, which are considerably smaller than those for g l y ~ i n e A , ~V = 6 and 25 cm3/ mole for carboxyl and amino groups, respectively. This may be accept-
ULTRASONIC ABSORPTION IN LYSOZYME
789
able because hydration of COO- and NH3+ groups in the protein may be appreciably hindered by surrounding atomic groups of the protein. If we might assume that k f is smaller in protein than in amino acids on account of any effect of surrounding atomic groups in the protein, T would be longer and thus A V would be smaller because, a t 2.82 MHz, 07 is always less than unity. The soli\d curve in Figure 1 is drawn by assuming that ( A a / f 2 )is the sum of three contributions: solvent absorption, pH-independent ab, ( A a / f 2 ) p t . The calculated curve reproduces well sorption ( A a / f 2 ) ~and the two maxima around pH 3 and pH 11.
pH-INDEPENDENT ABSORPTION In the following, we shall discuss the origin of pH-independent absorption, ( A a / f 2 ) ~ .The excess absorption of sound in solutions of small particles is due to scattering of sound by the particle, viscous and transport processes occurring at the interrmal face of nonhomogeneities, as well as to the intrinsic absorption in the particle.13J4 The excess absorption due to the scattering of sound is given by the equation,I3
=a$(34f2a3[1 - - (Ps -P sP
”)
(6) 2Pp + P s where 4 is the volume fraction of particle, a is the radius of particle, P and p are adiabatic compressibility and density, respectively. Here subscripts s and p stand for solvent and particle, respectively. In the present case of lysozyme ( a = 17.2 A and pp = 1.34 g/cm3) a t a frequency of 2.82 MHz, (Aa/f2)scatterwas calculated to be much smaller than the observed value, even if we assume pp = 0 in Eq. (6). The excess absorption due to the viscous drag effect arising from relative motion of particle and solvent and that due to thermal transport process between particle and solvent are:14 scatter
+(pp-ps)2]
and
where q is the shear viscosity, c is the specific heat at constant pressure, d is the thermal expansion coefficient, and K is the thermal conductivity. These two absorptions also were estimated to be negligibly small in our case. In evaluating the thermal transport loss, values of specific heat, thermal expansion coefficient, and thermal conductivity of lysozyme are necessary, which have not been reported in literature. We made an estimation of the upper limit of the absorption with ‘reference to those
790
KANDA, SUZUKI, AND WADA
1
10 FREQUENCY
102
(MHz)
Fig. 2. Excess ultrasonic absorption over solvent divided by concentration in weight per volume in aqueous lysozyme at 25OC. Closed circles represent data of the present work and open circles data by 1n0ue.l~ Dashed curve represents a single relaxation curve which fits to high-frequency data.
values for crystalline amino acids and similar substances, but the result was still much smaller than the observed absorption. We must look, therefore, for the origin of pH-independent absorption in the intrinisic property of the globular protein. Figure 2 illustrates the observed absorption of ultrasonic waves in the frequency range from 3 to 150 MHz in an aqueous solution of lysozyme, together with the data by Inoue,15 a t pH 5 where the contribution of proton-transfer reactions is negligible. The agreement of our data with those by Inoue is satisfactory while Inoue measured the absorption with the conventional pulse echo technique. The data a t frequencies above 10 MHz may be well fitted, as shown by a dashed curve, by a single relaxation process with a relaxation frequency located at 12 MHz, but the upswing of the absorption a t lower frequencies indicates a distribution of relaxation times as was found for aqueous bovine hemoglobin by Schneider et al.* Figure 3 compares the excess absorptions per wavelength A p for lysozyme and hemoglobin, both reduced to unit weight concentration, the latter being calculated from the data compiled by Schneider e t a1.4 It is found in Figure 3 that lysozyme and hemoglobin have an analogous behavior in the shape of absorption spectrum, whereas the magnitude is somewhat higher in hemoglobin than lysozyme. This fact suggests that, since the molecular surface area per unit mass is considerably larger for lysozyme than for hemoglobin because of a smaller size of the former, the absorption arises, a t least for the most part, from the bulk property of globular proteins rather than the surface property like the interaction between solvent and protein a t the interface.15J6 The increase of absorption per unit weight concentration with increasing molecular weight of globular proteins is also found in a series of data for lysozyme, ,&lactoglobulin, and bovine serum albumin by Zana and Lang.l Of course,
ULTRASONIC ABSORPTION IN LYSOZYME
- o l
791
_ _ --, Hb
__----
LYSOZYME
l0'l 1
'
' ' ' , . . . l
'
"
1
10 FREQUENCY
,
1
1
1
'
1o2 ( MHz)
'
' ' A J
103
Fig. 3. Excess absorption per wavelength at 25OC for lysozyme (solid curve) and hemoglobin (dashed curve), both reduced to unit concentration.
the role of the surface reaction cannot be completely discounted at this time because, in the case of linear polymers, the interaction of solvent molecules with the polymer has been evidenced to play an important role in the ultrasonic a b ~ o r p t i o n . ~Multiple mechanisms may exist simultaneously but the surface reaction may have a minor degree of effectiveness in the absorption in the frequency range 2-100 MHz for the globular protein. Effects of denaturants on the ultrasonic absorption of aqueous lysozyme were studied by Inoue15 and Minato et al.17 According to them, denaturation of lysozyme makes the absorption increase for various denaturants including urea, urea and Na2S03, 2-chloroethanol, LiBr, and guanidine-HC1. However, the increase in absorption with denaturing time is not in general parallel with the increase in viscosity which reflects the expansion of protein molecules. The time variations of excess absorption and reduced viscosity of lysozyme in 8.2M urea and 0.03M Na2S04 after mixing the protein in the denaturant are illustrated in Figure 4. The absorption reaches a final value within one minute but the viscosity continues to increase over a few hours. This indicates that the breakup of the internal structure seriously affects the absorption while subsequent scissions of S-S bondsla, which result in the expansion of molecule and the increase of molecular surface, do not.
COMPLEX COMPRESSIBILITY OF LYSOZYME T o summarize the discussion in the preceding section, the globular molecule of protein may be regarded as a viscoelastic particle and the absorption of sound in the protein solution arises for the most part from the internal loss of the particle. In this section, we shall estimate the compressibility of the lysozyme molecule as a complex quantity. When the solvent particle is much smaller than the wavelength of sound, the compressibility p of a solution is given by the equation,lg
792
KANDA, SUZUKI, AND WADA 120
I
I
1
60
120
180
.
1
240
TIME ( M I N I
Fig. 4. Time variations of ultrasonic excess absorption at 3 MHz (open circles) and reduced viscosity (closed circles) of lysozyme in aqueous urea (8.2M) and NaZS03 (0.03M)at 25OC. Protein concentration: 4 g/100 ml. Initial values before denaturation are Aa/P = 80 X wi7 sec2/cm and qred = 3.5 cm3/g.
P = P s O - 4) + Pp4
(9) where subscripts s and p denote solvent and particle (protein) and the quantity without subscript that of solution. When the solute particle is viscoelastic, Pp in Eq. (9) should be replaced by a complex quantity P*p
P*p = Kp - iP”p
(10)
and therefore Eq. (9) is written in the form
P*
= PS(1 - 4)
+ P*p4
(11)
which is related with the complex sound velocity u * as u* = (l/pP*)1’2
(12)
Since u * is by definition
_1- -_ 1_ u*
u
.Aa 1-
w
we get, by combining Eqs. (10)-(13), for A a u / w 1
