Added Mass Effect on Immobilizations of Proteins ... - ACS Publications

Feb 19, 2009 - Thus, the added mass effect was dependent on proteins but independent of the immobilized amount (40−60% coverage in this study)...
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Anal. Chem. 2009, 81, 2268–2273

Added Mass Effect on Immobilizations of Proteins on a 27 MHz Quartz Crystal Microbalance in Aqueous Solution Hiroyuki Furusawa,† Tomomitsu Ozeki,† Mizuki Morita,‡ and Yoshio Okahata*,† Department of Biomolecular Engineering, Tokyo Institute of Technology and SENTAN, JST, 4259 Nagatsuda, Midori-ku, Yokohama 226-8501, Japan, and Department of Biotechnology, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo, 113-8657, Japan During the immobilization process of proteins onto an Ausurface of a 27 MHz quartz crystal microbalance (QCM) in aqueous solutions, apparent large frequency changes (∆Fwater) were observed compared with those in the air phase (∆Fair) due to the interaction with surrounding water of proteins. On the basis of an energy-transfer model for the QCM, the apparent added mass in the aqueous solution [(-∆Fwater)/(-∆Fair) - 1] could be explained by frictional forces at the interface of proteins with aqueous solutions. When [(-∆Fwater)/(-∆Fair) 1] values for various proteins were plotted against values relating to the friction (antimobility), such as values of the molecular weight divided by the sedimentation coefficient (Mw/s), the inverse of the diffusion coefficient (1/D), and the volume divided by the surface area (volume/surface area ) apparent radius) of proteins, there were good linear correlations. Thus, observations of the larger ∆Fwater than ∆Fair for protein immobilizations on the QCM can be simply explained by the friction effect at the interface between proteins and the aqueous solution. Thus, QCM would be a mass sensor based on mechanical oscillation motion even in aqueous solutions. The piezoelectric quartz crystal microbalance (QCM) is a very sensitive mass-measuring device and has been used as a mass sensor in the air phase. When an elastic thin film was deposited on the QCM plate in the air phase, the frequency change can be surmised using a Sauerbrey’s equation (eq 1) that consists with experimental observations,1-4

-∆Fair )

2F02 A√Fqµq

∆m

(1)

* Corresponding author. E-mail: [email protected]. Fax: +81-45-9245836. † Tokyo Institute of Technology and SENTAN. ‡ The University of Tokyo. (1) Sauerbrey, G. Z. Z. Phyz. 1959, 155, 206–222. (2) Buttry, D. A.; Ward, M. D. Chem. Rev. 1992, 92, 1355–1379. (3) Janshoff, A.; Galla, H.-J.; Steinem, C. Angew. Chem., Int. Ed. 2000, 39, 4004–4032. (4) Marx, K. A. Biomacromolecules 2003, 4, 1099–1120.

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where ∆Fair is the measured frequency change in the air phase (Hz), F0 the fundamental frequency of the quartz crystal (Hz), ∆m the mass change (g), A the electrode area (cm2), Fq the density of quartz (g cm-3), and µq the shear modulus of quartz (dyn cm-2). Recently, applications of QCM in aqueous solutions have been interested and utilized as a tool for in situ measurements of biomolecular interactions2-4 and as a biosensor, such as an immunosensor.5 However, in the employment of QCM in aqueous solutions, the deviation from ideal Sauerbrey behavior has been observed experimentally.6-9 These observations can be interpreted by the sensitivity of QCM to the viscosity (hydration) of the aqueous solution and/or to the viscoelasticity (softness) of the adsorbed material, which would result in the apparent added mass and the lost mass on QCM responses, respectively.7-10 The difficulty of a quantitative interpretation of these experimentally observed deviations from the ideal mass would limit the precise mass detection of the QCM. To understand the apparent mass, referred to as “acoustic mass”, on the QCM in aqueous solution, a frequency change of the QCM in aqueous solution (∆Fwater) has been compared with the “optical mass” obtained by optical techniques such as surface plasmon resonance8,10,11 and “the viscous property” monitored from the impedance (QCM-Z),12 the electrically equivalent circuit resistance (R-QCM),13 or the energy dissipation (QCMD) of a quartz oscillator.7,10,14 On the other hand, as the simplified approach for detection of a dry mass on a QCM plate, we (5) (a) Kurosawa, S.; Park, J.-W.; Aizawa, H.; Wakida, S.; Tao, H.; Ishihara, K. Biosens. Bioelectron. 2006, 22, 473–481. (b) Rahman, M. A.; Shiddiky, M. J.; Park, J. S.; Shim, Y. B. Biosens. Bioelectron. 2007, 22, 2464–2470. (c) Shen, Z.; Yan, H.; Parl, F. F.; Mernaugh, R. L.; Zeng, X. Anal. Chem. 2007, 79, 1283–1289. (6) Rickert, J.; Brechet, A.; Go ¨pel, W. Anal. Chem. 1997, 69, 1441–1448. (7) Voinova, M. V.; Jonson, M.; Kasemo, B. Biosens. Bioelectron. 2002, 15, 835–841. (8) Su, X.; Wu, Y.-J.; Knoll, W. Biosens. Bioelectron. 2005, 21, 719–726. (9) Ozeki, T.; Morita, M.; Yoshimine, H.; Furusawa, H.; Okahata, Y. Anal. Chem. 2007, 79, 79–88. (10) Bingen, P.; Wang, G.; Steinmetz, N. F.; Rodahl, M.; Richter, R. P. Anal. Chem. 2008, 80, 8880–8890. (11) Laschitsch, A.; Menges, B.; Johannsmann, D. Appl. Phys. Lett. 2000, 77, 2252–2254. (12) (a) Beck, R.; Pittermann, U.; Weil, K. G. Ber. Bunsen-Ges. 1988, 92, 1363– 1368. (b) Johannsmann, D. Phys. Chem. Chem. Phys. 2008, 10, 4516–4534. (13) Cho, N.-J.; D’Amour, J. N.; Stalgren, J.; Knoll, W.; Kanazawa, K.; Frank, C. W. J. Colloid Interface Sci. 2007, 315, 248–254. (14) Larsson, C.; Rodahl, M.; Ho ¨o ¨k, F. Anal. Chem. 2003, 75, 5080–5087. 10.1021/ac802412t CCC: $40.75  2009 American Chemical Society Published on Web 02/19/2009

demonstrated to obtain -∆Fair in the air phase after drying the mass-deposited QCM in the aqueous solution (-∆Fwater).9 Thus, ∆Fwater could be expressed as a function of a real mass change (∆m) (eq 2) by using the value of [(–∆Fwater)/(–∆Fair)] and eq 1. -∆Fwater )

-∆Fwater 2F02 ∆m -∆Fair A F µ √q q

(2)

We have reported that there was a linear correlation between ∆Fwater and ∆Fair in the case of adsorption experiments of biomolecules such as proteins, DNAs, and polysaccharides on a 27 MHz QCM.9 Values of ∆Fwater/∆Fair for various proteins showed a proper constant from 2 to 4.6,9 Thus, ∆Fwater for protein-deposited QCM was 2-4 times larger than ∆Fair due to the complex rheology of vibration in aqueous solution. However, it is important to interpret such a large difference between ∆Fwater and ∆Fair in terms of meaningful physical properties. We should note that the apparent mass behavior is also observed in an ultracentrifugal analysis of proteins in aqueous solution, in which a deviation from the real mass is interpreted by two factors such as buoyancy and friction based on the wellestablished physical law. The sedimentation velocity (v) divided by the centrifugal field strength (ω2r) in aqueous solution, called the sedimentation coefficient (s), is proportional to the real mass (Mw) that is multiplied by the buoyancy factor (1 -v¯Fl) and that is divided by the frictional coefficient fric (eq 3), s)

Mw(1 - v¯Fl) v ) 2 fric ωr

(3)

where v¯ is the partial specific volume, Fl the solution density, ω the angular velocity, and r the distance from the center of rotation. Equation 3 indicates that when a smaller v for a molecule than that expected from the known molecular weight is observed due to the shape and/or interaction with aqueous solution, we would incriminate mainly a smaller v as a large apparent friction fric (antimobility). We had better consider hydrodynamic effects (antimobility) as an apparent added mass for proteins rocking back and forth on the oscillating QCM, similar to the sedimentation of proteins under a centrifugal field in aqueous solutions. In this paper, we describe that values of [(-∆Fwater)/(-∆Fair) - 1] obtained from immobilization of various proteins on a 27 MHz QCM can be related with parameters of antimobility, such as the molecular weight divided by the sedimentation coefficient (Mw/s), the inverse of the diffusion coefficient (1/D) obtained from ultracentrifugal analyses, and also the apparent radius of proteins calculated from the protein database. If the added mass of [(-∆Fwater)/(-∆Fair) - 1] can be understood in terms of convincing physical properties and be calculated from parameters that are easily available to a database for proteins, QCM can be used as a simple mass sensor even in aqueous solutions. EXPERIMENTAL SECTION Reagents. Lysozyme (from chicken egg white), myoglobin (from equine heart), proteinase K (from Tritirachium album),

Figure 1. (A) Schematic illustrations of AFFINIX Q4 with four 500 µL cells equipped with a 27 MHz QCM plate at the bottom of each cell. (B) Procedure of measurements for both ∆Fwater and ∆Fair. (C) Illustration of the time course during protein immobilization on a QCM plate both in air and water phases.

pepsin (from porcine stomach mucosa), and IgG (from human serum) were purchased from Sigma-Aldrich Japan, Co. (Tokyo, Japan). Apo-ferritin (from equine spleen) was purchased from CALBIOCHEM (Tokyo, Japan). Glucose oxidase (from Aspergillus niger) was purchased from Tokyo Chemical Industry Co. Ltd. (Tokyo, Japan). Catalase (from bovine liver) was purchased from GE Healthcare UK Ltd. (Buckinghamshire, England). We purchased 1-ethyl-3-[3-(dimethylamino)propyl]carbodiimide (EDC) from DOJINDO, Co. (Kumamoto, Japan). HSA (human serum albumin), N-hydroxysuccinimide (NHS) were purchased from Wako Pure Chemical Industries, Ltd. (Osaka, Japan). Avidin (from egg white) and all other reagents were purchased from Nacalai Tesque Inc. (Kyoto, Japan). All reagents were used without further purification. 27 MHz QCM (AFFINX Q4) Apparatus. AFFINIX Q4 was used as a QCM instrument (Initium Co. Ltd., Tokyo, Japan: http:// www.initium2000.com) (Figure 1A). The QCM instrument had four 500 µL cells that were equipped with a 27 MHz QCM plate (60 µm thickness and 8.7 mm diameter of a AT-cut shear-mode quartz plate and an area of 5.7 mm2 of the Au electrode) at the bottom of each cell, a stirring bar, and a temperature controlling system.9,15 The Sauerbrey’s equation (eq 1) was applied for the AT-cut shear mode QCM in the air phase.1 When F0 is the fundamental frequency of the quartz crystal (27 × 106 Hz), A the electrode area (5.7 mm2), Fq the density of quartz (2.65 g cm-3), and µq the shear modulus of quartz (2.95 × 1011 dyn Analytical Chemistry, Vol. 81, No. 6, March 15, 2009

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cm-2), a 0.62 ng cm-2 mass increase per 1 Hz of frequency decrease is expected in the air phase. Immobilization of Proteins onto a 27 MHz QCM Plate. Proteins were covalently immobilized onto the QCM plate as follows.9,15 To the cleaned bare Au electrode, 3,3′-dithiodipropionic acid was immobilized, and then carboxylic acids were activated as N-hydroxysuccinimidyl (NHS) esters with 1-ethyl-3-[3-(dimethylamino)propyl]carbodiimide (EDC) on the surface. The QCM cell was filled up by a buffer solution optimized for each protein as follows: lysozyme, 20 mM HEPES-Na, pH 7.5, 200 mM NaCl; calmodulin, 10 mM HEPES-Na, pH 7.2, 100 mM NaCl; myoglobin and proteinase K, 5 mM citrate-Na, pH 6.0, 150 mM NaCl; pepsin, 1 mM citrate-Na, 1 mM phosphate-Na, 1 mM borate-Na, pH 3.0, 25 mM NaCl; avidin, milli Q water; HSA, 20 mM HEPES-Na, pH 7.5, 200 mM NaCl; BSA, 20 mM HEPES-Na, pH 7.5, 200 mM NaCl; glucose oxidase, 50 mM acetic acid-Na, pH 5.2; human IgG, PBS; catalase, 20 mM HEPES-Na, pH 7.5, 200 mM NaCl; apo-ferritin, 20 mM HEPES-Na, pH 7.5, 200 mM NaCl; each ribosome, 10 mM HEPES-K, pH 7.3, 100 mM NH4Cl, 5 mM Mg(OAc)2, 0.5 mM CaCl2. After a protein was injected in the NHS-activated cell, immobilization behaviors of the protein reacted with the activated esters were followed by frequency decreases (-∆Fwater) with time. After reactions had reached equilibrium, reaction media were aspirated after washing with Milli Q water several times, and the QCM plate was kept in dried air on silica gels to obtain Fair1 values. ∆Fair values were calculated by subtracting Fair0 values of 3,3′-dithiodipropionic acid-coated QCM in the air phase (parts B and C of Figure 1). Immobilization experiments to obtain (-∆Fwater)/(-∆Fair) values for proteins were repeated at least four times with changing immobilized amounts of proteins. Ultracentrifugal Analyses of Proteins. Sedimentation velocity experiments were performed in an Optima XL-I analytical ultracentrifuge (Beckman-Coulter) with an eight hole An-50Ti rotor. Proteins were beforehand dialyzed against buffer solutions, and the dialysate was used as the reference solution. Sedimentation velocity data were acquired at an absorbance at 280 nm of 0.1 with a rotor speed of 50 000 rpm at 20 °C and then analyzed using the SEDFIT program. Calculation of Surface Areas and Volumes for Proteins. The surface areas and volumes of proteins were calculated from the structural data obtained in the Protein Data Bank (PDB)16 and Protein Quaternary Structure (PQS)17 databases using the computer program VOLBL, which is an analytical method based upon the alpha shape theory.18 Proteins were measured as being (15) (a) Nishino, H.; Nihira, T.; Mori, T.; Okahata, Y. J. Am. Chem. Soc. 2004, 126, 2262–2265. (b) Nishino, H.; Murakawa, A.; Mori, T.; Okahata, Y. J. Am. Chem. Soc. 2004, 126, 14752–14757. (c) Nihira, T.; Mizuno, M.; Tonozuka, T.; Sakano, Y.; Mori, T.; Okahata, Y. Biochemistry 2005, 44, 9456–9461. (d) Takahashi, S.; Matsuno, H.; Furusawa, H.; Okahata, Y. Anal. Biochem. 2007, 361, 210–217. (e) Furusawa, H.; Takano, H.; Okahata, Y. Org. Biomol. Chem. 2008, 6, 727–731. (f) Takahashi, S.; Akita, R.; Matsuno, H.; Furusawa, H.; Shimizu, Y.; Ueda, T.; Okahata, Y. ChemBioChem 2008, 9, 870–873. (g) Furusawa, H.; Takano, H.; Okahata, Y. Anal. Chem. 2008, 80, 1005–1011. (h) Takahashi, S.; Matsuno, H.; Furusawa, H.; Okahata, Y. J. Biol. Chem. 2008, 283, 15023–15030. (16) Bernstein, F. C.; Koetzle, T. F.; Williams, G. J. B.; Meyer, E. F., Jr.; Brice, M. D.; Rodgers, J. R.; Kennard, O.; Shimanouchi, T.; Tasumi, M. J. Mol. Biol. 1977, 112, 535–542. (17) Henrick, K.; Thornton, J. M. Trends Biochem. Sci. 1998, 23, 358–361. (18) Liang, J.; Edelsbrunner, H.; Fu, P.; Sudhakar, P. V.; Subramanian, S. Proteins 1998, 33, 1–17.

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enveloped by the molecular surface (MS),19 which is defined as the surface accessible to the probe sphere (probe radius ) 1.4 Å). The computed surface area was that of the outside surface, and the computed volume was corresponding to the sum of both volumes of the space filling and the inaccessible cavities in proteins. Protein structural data of 2LYZ, 1CLL, 1DWR, 1IC6, 4PEP, and 1GPE in the PDB database and 1AVD, 1E78, 7CAT, and 1IER in the PQS database were applied in this study. Prior to computation, all water molecules were removed from the structural data. RESULTS AND DISCUSSION Added Mass on QCM Employment in Aqueous Solution. QCM is a mass-sensitive device based on mechanical oscillation motion. Frequency changes of the thin elastic or inelastic filmdeposited QCM can be surmised using an energy-transfer model.20-22 Frequency changes (-∆F) can be interpreted simply by the kinetic energy (∆Et) transferred from the vibrating quartz crystal as eq 4, -∆F ∆Et ) F 2Eq

(4)

where F is the fundamental frequency, Eq the kinetic energy stored in the quartz oscillator vibration.20-22 When the elastic film was loaded as ∆m and vibrated at the same velocity (v) with the QCM shear velocity, ∆Et () (1/2)∆mv2) is directly proportional to ∆m, meaning Sauerbrey’s equation (eq 1).20-22 When the QCM was employed in aqueous solutions, ∆F should be affected by two factors: (1) the interaction with hydrodynamical water around the material as an apparent added mass due to the friction with surrounded water and (2) the viscosity (softness) of the material as an apparent lost mass due to the energy dissipation (∆Et would be decreased). When proteins were immobilized on a QCM in aqueous solution, we could focus only the above factor (1) of the hydrodynamical water but not the factor (2) of the viscoelasticity of the material, because globular proteins have been reported to be relatively rigid-like ice in compressibility measurements.23,24 Therefore, we measured the deviation ratio from the dry mass [(-∆Fwater)/(-∆Fair)] in the immobilization of various proteins onto the QCM plate in order to evaluate an added mass of each protein. Proteins were covalently bonded on the Au electrode of the QCM in buffer solutions by using an amine-coupling method with monitoring the frequency changes (∆Fwater). After the water phase was aspirated from the QCM cell, ∆Fair values were obtained in the dry air phase (Figure 1B,C). These processes for each protein were repeated several times with changing the immobilized protein amount. Typical plots of -∆Fwater against -∆Fair were shown in Figure 2 as examples of lysozyme (1.6), avidin (2.1), glucose oxidase (2.7), and apo-ferritin (4.0), where (19) Richards, F. M. Annu. Rev. Biophys. Bioeng. 1977, 6, 151–176. (20) Mecea, V. M. Sens. Actuators, A 1994, 40, 1–27. (21) Mecea, V. M.; Carlsson, J. O.; Bucur, R. V. Sens. Actuators, A 1996, 53, 371–378. (22) Lin, Z.; Ward, M. D. Anal. Chem. 1995, 67, 685–693. (23) Gekko, K.; Noguchi, H. J. Phys. Chem. 1979, 83, 2760–2714. (24) Gekko, K.; Hasegawa, Y. Biochemistry 1986, 25, 6563–6571.

quartz oscillator should be transferred to both the kinetic energy of adsorbed proteins and the frictional energy that will be dissipated through hydrodynamic water and/or as thermal energy. In this case, the frequency change (-∆Fwater) can be expressed by eq 6 (see the Appendix), ∆Fair mprotein ) F mq f ′ric ∆Fwater mprotein + F mprotein ) F mq

Figure 2. Linear plots of -∆Fwater against -∆Fair values for immobilization of 1, lysozyme (1.6); 5, avidin (2.1); 11, glucose oxidase (2.7); and 15, apo-ferritin (4.0) on a 27 MHz QCM plate. Protein numbers are correlated with those in Table 1. The numbers in parentheses indicate the slope [(-∆Fwater)/(-∆Fair)] of straight lines. -∆Fwater values were obtained at 20 °C in different buffer solutions depending on proteins (see Experimental Section). -∆Fair values obtained in the dry air phase on silica gel at 20 °C. The dotted line indicates the slope of 1 meaning no added mass in aqueous solutions.

the numbers in parentheses indicate slopes [(-∆Fwater)/(-∆Fair)]. Although slopes are different for each protein, -∆Fwater linearly increased with the increase of -∆Fair (the dry mass). Thus, the added mass effect was dependent on proteins but independent of the immobilized amount (40-60% coverage in this study). In experiments using reflectometry and QCM-D, the similar results for a binding behavior of streptavidin or avidin onto a biotinylated supported lipid bilayer have reported (“acoustic mass”/“optical mass” ) 2.0 (streptavidin), 2.3 (avidin), respectively).10 We obtained (-∆Fwater)/(-∆Fair) values for 15 proteins, and results were summarized in Table 1, together with other parameters. To examine the effect of the added mass on observations of binding behaviors of proteins onto a QCM plate, we compared sensorgrams during immobilization of human serum albumin (HSA) onto an Au-plate of the QCM and SPR. The sensorgramshapes obtained from the two methods well overlapped each other (see Figure S1 in the Supporting Information). This suggests that both sensorgrams should be equivalent kinetically, because a general kinetic analysis requires a time course of the ratio of a signal at a time to a maximal signal not the absolute amount. This fact consists with previous reports that an apparent added mass does not impair the qualitative analysis of the kinetics.8,25 The ∆m value calculated from -∆Fwater using eq 2 was corresponding to that from resonance units (RU) of SPR signal in the error range of 20%. Comparison with Sedimentation Experiments of Proteins. We noted that the effect of friction between proteins vibrating with the QCM plate and the aqueous phase is similar to the friction between precipitating proteins and the aqueous phase during ultracentrifugation. The frequency change in the air (-∆Fair) can be given by eq 5 simply. When there is a frictional force at the interface of a protein in liquid, a part of the energy stored in the (25) Keller, C. A.; Kasemo, B. Biophys. J. 1998, 75, 1397–1402. (26) Tyn, M.; Gusek, T. W. Biotechnol. Bioeng. 1990, 35, 327–338.

(5)

(6)

where mq and mprotein are the mass of quartz and the total mass of adsorbed proteins per unit area, respectively, and f ′ric the frictional coefficient per unit mass, which was defined for this study. The apparent mass ratio [(-∆Fwater)/(-∆Fair)] is given as eq 7 from eqs 5 and 6. -∆Fwater f ′ric ) 1+ -∆Fair F

(7)

In comparison with eqs 3 and 7, we presumed that the apparent added mass [(-∆Fwater)/(-∆Fair) - 1] should be proportional to the molecular weight divided by the sedimentation constant (Mw/s), because the buoyancy factor of proteins could be a constant. Thus, -∆Fwater Mw - 1 ) C1 -∆Fair s

(8)

where C1 is constant. As shown in Figure 3, there was a good linear correlation between [(-∆Fwater)/(-∆Fair) - 1] obtained from QCM and Mw/s obtained from ultracentrifugul experiments of various proteins. A correlation coefficient (r) and χ2 (the sum of the squared error between the original data and the calculated linear fit) were obtained to be 0.931 and 0.866, respectively, showing the closer to one of r and the lower χ2 indicating the better linear correlation. This result suggests that the apparent added mass [(-∆Fwater)/(-∆Fair) - 1] would mainly come from the friction between vibrating proteins and aqueous solution. The parameter of Mw/s can be also interpreted as an inverse of sedimentation velocity per unit mass, indicating the antimobility of proteins in aqueous solution. As another parameter indicating the friction, the inverse of the diffusion coefficient (1/D) of proteins in aqueous solutions is known as the Stokes-Einstein relation (eq 9),

fric )

kbT D

(9)

where kb is Boltzmann’s constant, T the absolute temperature, and D the diffusion coefficient. We compared the apparent added mass with D values referred from several sources.26 A good linear correlation between [(-∆Fwater)/(-∆Fair) - 1] and 1/D was also found in Figure 4 (r ) 0.846 and χ2 ) 1.201). Thus, the apparent added mass [(-∆Fwater)/(-∆Fair) - 1] of proteins could be predictable using the diffusion coefficient D, Analytical Chemistry, Vol. 81, No. 6, March 15, 2009

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Table 1. Comparison of Apparent Mass Ratios [(-∆Fwater)/(-∆Fair)] with Various Physical Properties of Proteins no.

proteins (PDB ID)

apparent mass ratioa (-∆Fwater)/(-∆Fair)

Mwb/ kDa

sedimentation coefficientc/S

diffusion coefficientc/ 10-11 m2 s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

lysozyme (2LYZ) calmodulin (1CLL) pepsin (4PEP) myoglobin (1DWR) avidin (1AVD)e HSA (1E78)e BSA proteinase K (1IC6) catalase (7CAT)e human IgG glucose oxidase (1GPE) 30S ribosome, E. coli 70S ribosome, E. coli 50S ribosome, E. coli apo-ferritin (1IER)e

1.6 ± 0.1 1.8 ± 0.2f 1.8 ± 0.1 2.1 ± 0.2 2.1 ± 0.1 2.3 ± 0.1 2.4 ± 0.1f 2.4 ± 0.1 2.5 ± 0.1 2.6 ± 0.2 2.7 ± 0.1 3.2 ± 0.1 3.3 ± 0.1 3.5 ± 0.1 4.0 ± 0.2

14.3 16.2 34.5 16.9 54.9 65.4 66.5 28.9 227.6 150 127.9 788 2143 1355 476.3

1.9 2.0 3.0 1.9 4.3 4.5 4.4

11.1 9.0 8.7 10.5 6.0 6.0 6.1

11.2 7.0 8.0 30 70 50 17.1

4.3 3.9 4.1

3.6

90 048

surface aread/Å2

volumed/Å3

5 645 8 086 12 019 6 669 19 448 26 895

16 008 17 767 40 627 20 638 65 511 70 562

9 436 58 609

34 436 286 278

35 790

153 888

a

892 314 b

The experimental condition is described in the Experimental Section in this paper. The errors represent the standard error. Molecular weight (Mw) of each protein was calculated from the amino acid content. c Data from the experiment or several sources including ref 26. d Surface areas and volumes of proteins were calculated from the structural information of the Protein Data Bank using the computer program, VOLBL. e These data were obtained from PQS. f These data were quoted from ref 9.

Figure 3. Linear plots of the apparent added mass [(-∆Fwater)/ (-∆Fair) - 1] obtained from QCM experiments against the molecular weight divided by the sedimentation constant (Mw/s) of proteins obtained from ultracentrifugal experiments. The linear correlation was obtained to be r ) 0.931 and χ2 ) 0.866 with a slope of (8.8 ( 0.36) × 10-5 S from a least-squares analysis. 1, lysozyme; 2, calmodulin; 3, pepsin; 4, myoglobin; 5, avidin; 6, HSA; 7, BSA; 9, catalase; 10, human IgG; 11, glucose oxidase; 12, 30S ribosome; 13, 70S ribosome; 14, 50S ribosome; and 15, apo-ferritin.

Figure 4. Linear plots of the apparent added mass [(∆Fwater)/(∆Fair) - 1] obtained from QCM experiments against the inverse of the diffusion constant (1/D) of proteins obtained from several sources.26 The linear correlation was obtained to be r ) 0.846 and χ2 ) 1.201 with a slope of (7.8 ( 0.56) × 10-11 m2 s-1 from a least-squares analysis. 1, lysozyme; 2, calmodulin; 3, pepsin; 4, myoglobin; 5, avidin; 6, HSA; 7, BSA; 9, catalase; 10, human IgG; 11, glucose oxidase; and 15, apo-ferritin.

which is available from ultracentrifugal experiments, dynamic light scattering (DLS) experiments, and protein database including calculable prediction.26 Therefore, the dry mass of proteins on QCM (-∆Fair) could be predicted from the frequency change in aqueous solution (-∆Fwater) using the diffusion coefficient (D). Comparison with Structural Properties of Proteins. We also tried to obtain the correlation between [(-∆Fwater)/(-∆Fair) - 1] values and accessible parameters of protein database without carrying measurements. Surface areas and volumes of proteins, which can be calculated from the database such as PDB, could be candidates as parameters related to the friction of proteins in aqueous solution. When [(-∆Fwater)/ (-∆Fair) - 1] values for proteins were plotted against the computed surface areas or the computed volumes, there were not good linear relations (r ) 0.459, χ2 ) 3.285 and r ) 0.857,

χ2 ) 7.218, respectively), showing the lower r and the higher χ2 values (see Figure S2 in the Supporting Information). While, there was a good linear correlation (r ) 0.925 and χ2 ) 0.600) between [(-∆Fwater)/(-∆Fair) - 1] and values of the volume divided by the surface area (volume/surface area) (Figure 5). Since the structural value of (volume/surface area) can be assumed to be an apparent radius of the spherical proteins, this linear correlation can be explained from Stokes’ law. Thus, the frictional coefficient fric is proportional to hydrodynamic radius rH of particles, which is also referred to as the Stokes radius or a gyration radius (eq 10),

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fric ) 6πηrH

(10)

friction between proteins vibrating with the QCM plate and aqueous solutions should be considered. The frequency change in the air (-∆Fair) can be expressed by a simple equation using the kinetic energy stored in the quartz oscillator (Eq) and the t transferred energy to adsorbed proteins (∆Eprotein ) referred to 20-22 as eqs 4 and A1. 1 t m v 2 m -∆Fair ∆Eprotein 2 protein m protein ) ) ) F 2Eq mq 1 2 2 mqvm 4

Figure 5. Linear plots of the apparent added mass [(∆Fwater)/(∆Fair) - 1] obtained from QCM experiments against the computed volume divided by the computed surface area (volume/surface area) of proteins. The linear correlation was obtained to be r ) 0.925 and χ2 ) 0.600 with a slope of 0.32 ( 0.018 Å-1 from a least-squares analysis. 1, lysozyme; 2, calmodulin; 3, pepsin; 4, myoglobin; 5, avidin; 6, HSA; 8, proteinase K; 9, catalase; 11, glucose oxidase; and 15, apo-ferritin.

t where Eq and ∆Eprotein are the energy stored in the quartz oscillator and the energy transferred from the quartz to proteins, respectively, and vm is the maximum velocity. When there is a frictional force at the interface of proteins in aqueous solution, a part of the energy stored in the quartz oscillator should be transferred to both the kinetic energy of the immobilized proteins and the frictional energy that will be dissipated through hydrodynamic water and/or as thermal energy. In this case, the frequency change (-∆Fwater) can be expressed by eq A2,

where η is the viscosity of liquids. The good linear correlation shown in Figure 5 means that the apparent radius (volume/surface area) could be a related parameter with the frictional force between the protein surface and aqueous solution. CONCLUSION There were good linear correlations between the apparent added mass [(-∆Fwater)/(-∆Fair) - 1] for various proteins obtained on a 27 MHz QCM and various parameters relating to the friction (antimobility) of proteins in aqueous solution such as the values of the molecular weight divided by the sedimentation coefficient (Mw/s), the inverses of the diffusion coefficient (1/D), and the values of the volume divided by the surface area (volume/surface area). Thus, the frequency decrease of protein immobilizing on a QCM plate (-∆Fwater) increases with increasing their apparent radiuses due to the increase of the friction parameter with aqueous solution. In other words, the dry mass of proteins (-∆Fair) can be calculated from -∆Fwater and other parameters such as Mw/s, 1/D, and the apparent radius of proteins. Thus, QCM would be a mass sensor based on mechanical oscillation motion even in aqueous solutions. ACKNOWLEDGMENT The authors acknowledge the help of Prof. Fumio Arisaka for discussion of ultracentrifugal analysis. We thank Prof. Takuya Ueda for providing the E. coli ribosome sample. We thank Mayu Komatsu, Tatsuya Koyanagi, Ken-ichiro Namazuda, Yukihiko Kudo, and Shuntaro Takahashi for helping with the QCM experiments. This work was partially supported by SENTAN, Japan Science and Technology Corporation (JST), and by a Grantin-Aid for Science Research from the Japan Society for the Promotion of Science. APPENDIX Here, we explain a frequency change of the protein-immobilized QCM in aqueous solution, where the effect of the

(A1)

t t -∆Fwater ∆Eprotein + ∆Efriction ) F 2Eq

∫

T 1 2 -∆Fwater 2 mproteinv + 0 (vf ′ricmprotein)v dt ) F 1 2 mqv2 4

(A2)

t where v ) V0 cos ωt exp (-ar2/re2), ∆Eprotein the frictional energy for the periodical time ) T, f ′ric the frictional coefficient per unit mass, V0 the velocity at the electrode center, ω the angular frequency (ω ) 2πF), r the radial position, re the electrode radius, and a is a constant. Here, vf ′ricmprotein means the frictional force and v dt means the distance. When T is 1/F () 2π/ω),

T

∫

T

(vf ′ricmprotein)(v dt) ) f ′ricmprotein

0

∫v

2

dt

0

[V0 exp(-ar2 ⁄ re2)]2 2F v2 ) f ′ricmprotein 2F ) f ′ricmprotein

(A3)

Combining eqs A2 and A3, the frequency change with the frictional force in aqueous solution is expressed as eq 6 in the text. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review November 14, 2008. Accepted January 28, 2009. AC802412T Analytical Chemistry, Vol. 81, No. 6, March 15, 2009

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