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Evidence for Gravity’s Influence on Molecules at a Solid-Solution Interface Newton C. Fawcett,* Richard D. Craven, Ping Zhang,† and Jeffrey A. Evans Department of Chemistry and Biochemistry, The University of Southern Mississippi, Hattiesburg, Mississippi 39406 Received October 22, 2003. In Final Form: April 15, 2004 Yoshimoto et al. [Anal. Chem. 2002, 74, 4306-4309] reported that a quartz crystal microbalance or QCM changed its response to sucrose solutions according to its angle of immersion. The effect was tentatively attributed to gravity-caused stress on the viscous interface between the oscillator and the bulk solution. The present work reports results from QCM experiments carried out so that any effect of gravity on the interfacial region would be magnified. This permitted use of a lower-frequency, less-sensitive QCM. Molecules of DNA were tethered to a functionalized QCM surface and then extended in steps, via sandwich hybridization, to produce DNA of uniform and known length. This feature allowed both the effect of QCM immersion angle and the relationship between frequency and molecular length to be investigated simultaneously. Comparison of acoustic wave damping at 0° and 180° immersion angles offers compelling evidence that the interfacial region expands when the active face of the QCM is down and contracts when it is up. This is apparently a consequence of the interfacial region being more dense than the bulk solution. The results are consistent with (a) slow gravity-driven movement of molecules away from a down-facing QCM, (b) rapid hybridization-driven movement away from an up-facing QCM, and (c) a QCM frequency response that decreases according to a simple exponential function of the tethered molecules’ radius of gyration.
Introduction Will molecules at a solid-solution interface be so overwhelmed by thermal energy that they will be unaffected by gravity? From the kinetic gas theory, one can easily calculate that the thermal, or kT, energy of ideal gases at 25 °C exceeds the potential energy of gravity by a factor of 106-107. This fact is used to rationalize why gases do not settle. Though the calculation of thermal kinetic energy for condensed states is far more difficult, the same argument is used to rationalize why solutes do not settle from homogeneous solution. Consider, however, molecules trapped on a surface by adsorption or chemical bonds but otherwise solvated. The situation now is complicated not only by a density gradient across the interface but also by a large, immobilization-caused decrease in entropy. Asking whether kT energy in the interfacial region will preclude any noticeable effect of gravity is equivalent to asking whether the thickness of the interface region will depend on the position of the interface relative to the gravitational field. There is already evidence suggesting molecules at an interface are affected by gravity. For example, solvated molecules of DNA on the surface of a microcantilever deflect the cantilever downward in the direction of the gravitational field when their mass is increased through hybridization.1 Recently, Yoshimoto et al. found that a quartz crystal microbalance (QCM) changed its response to sucrose solutions as a function of immersion angle.2 It was suggested that angular dependence of the QCM signal was due to gravity-caused variation in stress on the interface region between the bulk sucrose solution and * Corresponding author. E-mail:
[email protected]. Tel: 601-266-4703. Fax: 601-266-6075. † Present address: Reichhold, Inc., Durham, NC 27703. (1) Fritz, J.; Baller, M. K.; Lang, H. P.; Rothuizen, H.; Vettiger, P.; Meyer, E.; Guntherodt, H.-J.; Gerber, C. L.; Gimzewski, J. K. Science 2000, 288, 316-318. (2) Yoshimoto, M.; Kurosawa, S. Anal. Chem. 2002, 74, 4306-4309.
the QCM surface.3 In this paper, we address the specific question of whether the thickness of an interfacial region at the boundary between a solid and a solution is affected by gravity using experiments designed to magnify any such effect. The QCM alone, despite its name, is not influenced by gravity. It oscillates, sending an acoustic wave into nearby matter. When used in contact with solution, it responds according to how well that matter’s inertia is coupled to its own. The coupling decreases exponentially with distance according to the viscoelastic property of the interfacial fluid layer between the QCM surface and the bulk solution.4-8 Consequently, matter nearer the QCM surface has greater influence on its resonance frequency than matter further away. If molecules trapped at a QCMsolution interface change their position relative to the surface, the QCM responds accordingly. This feature makes the QCM particularly suited to observing changes in the spatial distribution of molecules in the interface region. The present results, together with those of Yoshimoto et al.,2,3 offer compelling evidence for a gravity-driven compression and expansion of the interfacial region on the QCM according to whether the active surface of the QCM is up or down. Since so much of modern biology and chemistry involves consideration of interfaces, gravity’s effect on these interfaces may turn out to have rather wide-reaching implications. The present experiments also demonstrate, for the first time, an empirical relationship between the QCM frequency shift and the radius of gyration of molecules tethered to its surface. (3) Yoshimoto, M.; Nishikanbara, M.; Shigenobu, K. Instrum. Sci. Tech. 2003, 31 (2), 109-119. (4) Kanazawa, K. K.; Melroy, O. R. IBM J. Res. Dev. 1993, 37 (2), 157-171. (5) Benes, E. J. Appl. Phys. 1984, 56 (3), 608-626. (6) Ward, M. D.; Buttry, D. A. Science 1990, 249, 1000-1007. (7) Rajakovic, V. L.; Biljana, A. C.; Ghaemmaghami, V.; Kallury, M. R.; Kipling, A. L.; Thompson, M. L. Anal. Chem. 1991, 63, 615-621. (8) Ha, T. H.; Kim, K. Langmuir 2001, 17, 1999-2007.
10.1021/la030390d CCC: $27.50 © 2004 American Chemical Society Published on Web 07/07/2004
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Figure 1. Stepwise increase of DNA length via DNA sandwich hybridization. The 90:10 mole ratio poly(ethylene-co-acrylic acid) crystal coat was on the order of 103 Å thick. Base-strand and target sequences were from Lambda phage and were commercially synthesized. The base sequence was modified at its 5′-end by addition of a C12-alkyl tail terminating in -NH2. The base was tethered by reaction of its terminal -NH2 group with surface carboxylate to form an amide link to the polymer coat using aqueous, carbodiimide chemistry. Hybridization was carried out in steps. First, strand-1 was added, then strand-2, then strand-1 again, etc. Each hybridization corresponds to a frequency plateau in either Figure 2 or Figure 4. Hybridization steps were continued until no further change in QCM frequency could be detected.
Experimental Method Materials and Reagents. Five MHz, AT-cut, biconvex quartz crystals, 15.2 mm diameter, polished to 15×) to drive the hybridization reaction, see Figure 1, to completion. When the 50-mer entered the flow cell, as evidenced by a sudden drop in the crystal’s frequency, flow was stopped and hybridization was allowed to continue until the frequency stabilized again. Excess 50-mer was then flushed from the cell with buffer. After 5 min of flow, the pump was again stopped to allow the frequency to stabilize. Buffer flow was restarted, and then the entire 50-mer injection and hybridization procedure was repeated using strand-2 in place of strand-1. This process of alternately (11) Gagnon, D. R.; McCarthy, T. J. J. Appl. Polym. Sci. 1984, 29, 4335.
Gravity and Solid-Solution Interfaces hybridizing to strand-1 and strand-2 was repeated until an attempted hybridization yielded e1 Hz change in frequency. These experiments were carried out on eight different PEAA substrates estimated to range from 40 to 1050 Å in average thickness. In four of the eight experiments, data was collected in both up- and down-orientations of the cell using the same crystal, the same amount of tethered base-strand, and the same substrate thickness. Regeneration of the Sensing Surface and Cell Inversion. Of the four sandwich hybridization experiments done in both up- and down-orientations, three were done in up-down order, and one in down-up order. This necessitated that the multistep-hybrids on the crystals be denatured so that the crystals could be used again in another orientation. The hybrid was denatured by passing 3 mL of room-temperature water through the cell with a 10 s pause at ∼0.5 mL increments, and as a result the frequency rose to a value within a few Hertz of the original frequency before hybridization. The crystal was then removed from the cell and dried under nitrogen, and its frequency was redetermined (dry) to ascertain that the amount of base-strand tethered to the crystal had not changed significantly. The crystal was then remounted in the inverted cell, the buffer flow was started, and the entire sandwich hybridization procedure was repeated, beginning with the equilibration step, in the new orientation. Control Experiments. Three types of control experiments were performed. In the first, an injection of strand-2 in the second step was repeated in the third instead of injecting strand-1. The second injection of strand-2 produced no significant change in frequency. This was followed by the normal injection of strand-1 again and then strand-2 in the usual alternation. The second control experiment consisted of collecting sandwich hybridization data in reverse order, down first and then up. The third control experiment consisted of changing the fluid in the cell in the absence of tethered macromolecule. Three sets of these experiments were done. The crystals used in the first two sets had PEAA on their surfaces but no DNA attached. A bare crystal was used in the third set of control experiments. In first set, successive injections of water and glycerol solutions were carried out with the cell in each of two orientations, 0° and 180°. In the second set, water and buffer injections were alternated in each of the two cell orientations. In the third set, injections alternated between 0.01 and 0.1 M NaCl using a bare crystal with no PEAA on it and cell orientations of 0°, 90°, and 180°. The frequency was recorded continuously, and the changes in the equilibrium frequency produced by the various liquids were noted separately for each cell orientation.
Results and Discussion In the discussion that follows, the down-orientation of the QCM is equivalent to the 0° immersion angle of Yoshimoto et al.,2,3 and the up-orientation is equivalent to the 180° immersion angle. All data are for one face of the QCM in contact with liquid and the other in contact with air. Rather than comparing frequency shifts directly between up- and down-orientations, the frequency response within a series of events in the up-orientation is compared to the response within an identical series of events in the down-orientation. This precluded any possibility that a repositioning of the oscillator leads between up and down QCM positions or mounting and demounting of the crystal could influence the results. Details of the Procedure. The 25-mer base-strand shown in Figure 1 was tethered to a 12 mm2 polyethyleneco-acrylic acid coating on one side of the microbalance using chemistry that strongly favors attachment via the 5′-end of the oligo.12 Each hybridization experiment was begun with a dry sensing surface. We adapted a common procedure in DNA biochemistry, that of repetitive, quan(12) Zhang, P.; Fawcett, N. C.; Evans, J. A.; Hurt, T.; Harvey, K. G.; Craven, R. D. Anal. Biochem. 2000, 282, 218-226.
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titative, sandwich hybridization13 as explained in the experimental section and illustrated in Figure 1. While the phenomena investigated have nothing to do with DNA per se, DNA was chosen for two reasons: (a) the chemistry for specific 5′-end attachment to a surface was already established, and (b) sandwich hybridization affords tethered molecules all of the same accurately known length, and that length may be incremented by accurately known amounts. Two partially complementary, target strands of 50-mer ss-DNA (strand-1 and strand-2) were used as illustrated. This permitted a sandwich hybrid to be built up stepwise on the QCM by alternating between target strands. Each strand overlapped the next by a 25-base tract. The result was a tethered, nicked ds-DNA with a 25-base ss-DNA distal end. It was essential that each hybridization be driven to completion. This was accomplished by using a large excess (>15×) of mobile strand at high concentration. After the frequency stabilized, excess, nonhybridized DNA was expelled from the cell with additional buffer. Hybridizations to strand-1 and strand-2 were continued until, upon further hybridization, no decrease in frequency resulted. After each series of sandwich hybridizations, the hybridized DNA was denatured with distilled water to return the sensing surface to its original state with only the ss-DNA base-strand remaining attached. Then the resonance frequency of the dried crystal was checked to make certain that the amount of base-strand on the QCM surface had not changed significantly. After this, in the experiments where comparable data were to be collected for a different cell orientation, the cell was inverted. The experiment in each orientation began with the crystal’s surface in the same physical state, that is, dry with the same amount of base-strand attached. Beginning with a dry crystal each time not only allowed any loss of DNA probe from the QCM surface to be detected but also permitted us to observe any orientation effect on the time needed for the frequency to stabilize after hydrating the surface. The Nature of the PEAA QCM Coating. PEAA has properties ideally suited to tethering DNA to the QCM.14 From its routine use, we have learned that nonspecific binding of DNA in buffer to PEAA does not occur.10 The PEAA surface is somewhat hydrophobic (receding water contact angle ) 56°). Weak adsorption of ss-DNA occurs if the DNA is dried on the surface of the PEAA. In an experiment using DNA labeled with 32P, the DNA, after being dried on PEAA, desorbed completely when washed with buffer at 40 °C. There is evidence for ss-DNA lying down on a hydrophobic surface with its negatively charged phosphate groups upward.15 This is likely the preferred position of ss-DNA when dried on a PEAA surface. Slight swelling of PEAA takes place when exposed to aqueous solutions. Scanning electron microscopy showed that the thickness of a 5 µm PEAA film increased 16% in going from 25% to 95% relative humidity. The Control Experiments. One control experiment consisted of making identical changes in the viscositydensity product of the cell solution in each cell orientation and comparing the resulting frequency shifts. Using crystals with only a thin polyethylene-co-acrylic acid layer and no DNA on their surfaces, water and two concentrations of sodium phosphate buffer were sequentially injected into the cell in both orientations. The QCM’s (13) Keller, G. H.; Manak, M. M. DNA Probes; Stockton Press: New York, 1993; pp 238-247. (14) Chong, K. T.; Su, X.; Lee, E. J. D.; O’Shea, S. J. Langmuir 2002, 18, 9932-9936. (15) Bustamante, C.; Dunlap, D. D. Nature 1989, 342, 204-206.
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frequency was, of course, different for water and each buffer concentration, but the cell’s orientation affected the frequency shifts between concentrations by e1 Hz, which is at the level of the standard deviation. In another control experiment, water and a dilute glycerol solution were injected into the cell. As with the control experiment that used water and buffer, the frequency shift in going from water to glycerol solution showed no dependence on cell orientation. In still another control, using a bare gold electrode, cell injections were alternated between 0.01 and 0.1 M NaCl in three orientations of the cell: up, down, and 90°. The average frequency difference between NaCl solutions was 1.8 ( 0.57 Hz, but the effect of cell orientation on the result was only 0.1 ( 0.1 Hz. Again, the signal due to QCM orientation was insignificant. Yoshimoto et al.,2,3 on the other hand, reported a significant orientation effect in experiments analogous to our control experiments using sucrose solutions of increasing concentration, higher frequency crystals, and an impedance analyzer. They observed an orientation effect on what was apparently an interfacial region consisting of adsorbed aqueous sucrose. The sensitivity of their experiments was greatly aided by the use of higher frequency, 9 and 30 MHz crystals. In the present experiments, failure to detect a small orientation effect in the control experiments was very likely a result of the much less sensitive apparatus used. Once DNA was tethered to the QCM, however, the cell’s orientation had a significant and consistent effect on the QCM signal. Another control, in one of the up-experiments, consisted of injecting strand-2 twice in succession. No significant shift resulted from the second injection, showing that the hybridization reaction had, as intended, been driven to completion by the first injection and that DNA was not binding nonspecifically. Yet another control consisted of doing the experiment in reverse order: down first and then up. This showed that the results were independent of the order in which the data were collected. Frequency Response Dependence on Radius of Gyration. A typical example of what was seen for stepwise sandwich hybridization of DNA on the QCM is shown in Figure 2. Here, the upper graph was obtained with the sensing surface of the QCM up, and the lower graph with it down. Each successively lower frequency plateau in Figure 2 corresponds to an increase in DNA length by the same amount. In both orientations, the plateau frequencies decline exponentially; however, the number of DNA segments needed to reach the point of no further response differed with orientation. When the active surface was up, 10 additions to the length of the DNA could be detected, while only 7 could be detected with the surface down. This indicates that with the QCM up, the DNA layer was less lossy or the DNA lay closer to the QCM surface, or both. Note that a linear decrease in frequency with mass, commonly seen for mass layers of constant thickness on the QCM, is not seen in these experiments. Instead, the frequency decreases as a negative exponential power of the reciprocal square root of mass. This is the response expected when the thickness of an inelastic layer on the QCM increases in proportion to mass.16 In a lossy medium, such as a dilute aqueous solution of DNA, the acoustic wave propagated from the QCM damps exponentially with distance. Consequently, the load of each volume element on the oscillator should also decrease exponentially with distance. Therefore, the frequency versus time data in Figure 2 were fit to the following exponential decay function:
f ) a(exp-b/x)
(1)
Figure 2. Frequency change versus time for stepwise extensions of upward- and downward-oriented molecules. Solid and open arrows indicate additions of target strand-1 and strand-2, respectively. The time axis starts after ∼1 and ∼4 h equilibration times for up- and down-data, respectively. Data were acquired at ambient temperature on the QCM with ∼35 ng of basestrand attached, of which about 70% is active. Biconvex, ATcut, 5 MHz quartz wafers were used. Buffer was degassed, pH 7.0, 0.1 M phosphate; flow rate ) 37.5 µL/min; target injection ) >40 pmol/5 µL; cell flush time after hybridization ) 5 min; flow was stopped during hybridization.
where f is the total frequency shift relative to an initial frequency measured with only the ss-DNA base-strand present on the QCM, and x is distance from the QCM surface. Since the radius of gyration, Rg, for either ss- or ds-DNA is given by lxN,17,18 where N is the number of segments of characteristic length l, xN was substituted for x, and b′ ) b/l was substituted for b in eq 1 to get eq 2.
f ) a(exp-b′/xN)
(2)
The value of N was set equal to the number of 50-bp DNA segments tethered to the QCM via sandwich hybridization. The down-trace plateau frequencies in Figure 2 are described by eq 2, as can be seen in Figure 3. The up-data, however, show a slight oscillation about the regression line. Figure 4 is analogous to Figure 2 but was obtained using another crystal with its polymer substrate only ∼1/7 as thick (Table 1, 40 Å data). The data from Figure 4 were also fit to eq 2, as shown in Figure 5. Slight oscillation about the regression line is apparent in data collected with the QCM up using the thinnest, and hence most sensitive, substrate (Figure 5). The reason for oscillation is unknown, but its regularity argues against it being caused by a chance occurrence. The oscillation seen in Figure 5 has a period corresponding to 14, 50-bp segments of DNA. At 3.4 Å per bp, one estimates a period length of 2 × 103 Å, which is 4 times the persistence length of 450-530 Å for ds-DNA.19,20 The other up-data also show (16) Muramatsu, H.; Kimura, K. Anal. Chem. 1992, 64, 2502. (17) Chan, V.; Graves, D. J.; McKenzie, S. E. Biophys. J. 1995, 69, 2243-2255. (18) Tinoco, I., Jr.; Sauer, K.; Wang, C. Physical Chemistry Principles and Applications in Biological Sciences, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 1985; pp 576-596. (19) Hagerman, P. J. Annu. Rev. Biophys. Biophys. Chem. 1988, 17, 265-286. (20) Bustamante, C.; Marko, J.; Siggia, E.; Smith, S. Science 1994, 265, 1599.
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Figure 3. Plateau frequencies from Figure 2 versus the number of 50-mer DNA segments added. The regression curves are the result of fitting the data to eq 2. 2 ) up; b ) down. Error bars correspond to the 95% confidence band of the fit superimposed on the experimental points.
Figure 4. Frequency change versus time for stepwise extensions of upward- and downward-oriented molecules on a QCM that was coated with PEAA approximately 1/8 the thickness of the PEAA on the QCM used to acquire the data of Figure 2. All other factors were similar to those for Figure 2 except that ∼44 ng of base segments were tethered to the QCM.
oscillation, but this becomes progressively less evident as the substrate thickness increases. The down-data in Figure 3 fit eq 2 well, but the downdata in Figure 5 collected on a more sensitive substrate fit less well. The nature of the constants a and b in eq 2 was not explored, but it seems reasonable that a may be related to the total frequency shift for DNA long enough to reach the point at which the acoustic wave has damped to zero amplitude, that is, the theoretical maximum shift, and b may incorporate the elastic properties of the medium and the reciprocal characteristic segment length, 1/l. If so, and assuming all other factors for the two orientations are equal, the b values shown in Figures 3 and 5 are consistent with R being less in the up-orientation than in the down-orientation. Equation 2 could, of course, be transformed to obtain a straight line for the down-data. Exponentially decaying frequency shifts have been seen in other work10 but have not always been recognized.21 (21) Okahata, Y.; Matsunobu, Y.; Ijiro, K.; Mukae, M.; Murakami, A.; Makino, K. J. Am. Chem. Soc. 1992, 114, 8299-8300.
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The Frequency Stabilization Time. In addition to a greater number of DNA length extensions that could be observed with the cell up, the time needed for the frequency to stabilize to a change of less than 1 Hz in 5 min was much less with the QCM up than with it down. This is, indeed, very difficult to explain based on any previously known phenomenon involving the QCM. Beginning with a dry surface, the time needed to hydrate the DNA and for the DNA to reach physical equilibrium, as judged by the frequency changing by 4 h with it facing down. Whereas in the control experiments, which were done in the absence of DNA, the time needed for the frequency to stabilize was independent of cell orientation and well under an hour. Comparison of Up- and Down-Data. The successive, sandwich-hybridization experiment of Figure 2 was repeated seven more times on different PEAA-coating thicknesses. By estimation of the area of the QCM’s electrode covered by PEAA and from its dry mass and density, the thickness of the PEAA coating was estimated. Results on different PEAA substrate thicknesses are summarized in Table 1. Shown in the table are absolute values of the total frequency shift after extending the DNA length to the point of no further frequency change. A ∼280 Å thick PEAA coating was used to acquire data for Figure 2, and a thin ∼40 Å PEAA coating was used for Figure 4. Table 1 shows that regardless of the PEAA coating thickness, whenever data were acquired in both orientations, the up-facing QCM always allowed more DNA length extensions to be observed. In the last two columns of Table 1 are the ratio of the first two frequency shifts, ∆f1/∆f2, for sequential hybridization to strand-1 and strand-2, respectively. With the QCM up, ∆f1 is less than ∆f2, but with the QCM down, ∆f1 is greater than ∆f2, as would be predicted by eq 2. The ratio of 2.8 shown for data acquired on a very thick PEAA substrate is unreliable, because on a thick substrate the acoustic energy is mostly absorbed in the PEAA before it enters the DNA-occupied layer. This causes a small total shift and the barely detectable shift for the first addition of strand-2. Because the picomoles of base-strand attached differ from crystal to crystal (Table 1, column 2), the experimental frequency shifts in columns 5 and 6 were normalized by dividing by the moles of base-strand. The normalized shifts in columns 7 and 8 depend exponentially on the polymer coating thickness. Clearly, up and down hybridization data can only be compared if the substrate thickness remains constant, and a thin substrate is required for maximum sensitivity.10 The most interesting features of the data in Table 1 and in Figures 2 and 4 are (a) the greater number of DNA length extensions observed when the QCM is up and (b) the smaller value for ∆f1 compared to ∆f2 seen only in the up-data. Why could more length extensions be seen with the QCM’s sensing surface up, and why did the initial length extension of DNA with the QCM up result in a smaller shift than the next extension, when normal exponential decay, according to eq 2, would require just the opposite relationship? And finally, why was the time needed for the frequency to stabilize radically different for up and down QCM orientations? We will address each of these questions in turn, starting with the last. After addition of buffer to a dry DNA layer on the QCM, >4 h was needed for the frequency to stabilize with the QCM down but only about 1 h was needed with the QCM up. If gravity does not affect the interface region, these times should not differ, but nevertheless they do, and dramatically so. In fact, the slow upward drift of the
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Table 1. Data Acquired for DNA Sandwich Hybridization on 8 Different Thicknesses of PEAA Substrates for Up- and Down-Orientations of the QCM Liquid Cell, Including Data from Figures 2 and 4 Acquired on 280 and 40 Å Substrates, Respectively PEAAa
base-strandb
(D)
(pmol)
max no. of strand additionsc up down
1050 830 740 480 280 120 70 40
6.5 10.1 7.6 2.6 2.7 3.2 2.7 0.99
4 6 7 7 10 10 nd 20
ndh 2 nd nd 7 5 3 10
total ∆f,d (Hz) up down -4.9 -21.6 -20.8 -16.8 -33.1 -59.7 nd -86.6
nd -4.1 nd nd -23.9 -51.2 -42.9 -68.2
∆f × pmol-1 of base-strande (Hz pmo l-1) up down -0.75 -2.14 -2.74 -6.46 -12.26 -18.66 nd -87.47
nd -0.41 nd nd -8.85 -16.00 -15.89 -68.89
(∆f1 ÷ ∆f2)f up down 0.50 0.36 0.40 0.52 0.64 0.26 nd 0.32
nd 2.8g nd nd 1.03 0.97 0.95 1.21
a PEAA thickness estimated from area and density (F ) 0.9498 g mL-1 at 23 °C). b Calculated from the frequency shift due to tethering of base-strand to the QCM; measured dry. c Number of DNA strand additions that resulted in a frequency shift. d Sum of shifts from all strand additions. e The sum of shifts from all strand additions normalized to the pmol of base-strand. f Ratio of the frequency shift from the first strand addition to that for the second strand addition. g Subject to large relative error due to thick substrate. h Not determined.
Figure 5. Plateau frequencies from Figure 4 versus the number of 50-mer DNA segments added. The regression curves are the result of fitting the data to eq 2. 2 ) up; b ) down. Error bars correspond to the 95% confidence band of the fit superimposed on the experimental points.
frequency seen in the down-orientation would be consistent with slow, gravity-aided desorption accompanied by gravity-aided movement of the DNA away from the surface. Although desorption of the DNA undoubtedly occurs in an hour’s time on an upward-facing QCM, in this orientation gravity would act to keep the DNA near the surface and the frequency stabilization time would be limited to that needed to hydrate the DNA. With the QCM up, the DNA should not need to move away from the surface until it hybridizes. To hybridize, however, assuming the DNA is initially lying on the QCM surface, it would have to “stand up”. (Or perhaps a more colorful and accurate picture would be one of moving from a reclining position to a slouch.) Its center of mass would be moved away from the surface, which would cause an increase in frequency. The expected decrease in frequency accompanying the initial sandwich hybridization step would then be reduced (made less negative) by the amount of frequency increase caused by the DNA standing up away from the surface. This model for DNA’s behavior at the interface is consistent with experiment and explains both the shorter frequency stabilization time and the less negative than expected initial frequency shift seen only in the uporientation. This seems very strong evidence, indeed, for the DNA remaining closer to the up QCM surface while it is being hydrated. One can see the foregoing model for DNA behavior at the interface manifested in the entirety of the experimental
data when the initial and second hybridization-frequency shifts are compared. Table 1 shows that in the upexperiments the relationship between initial and second shifts was ∆f1 < ∆f2, whereas ∆f1 > ∆f2 is expected if the hybridizing DNA is already positioned away from the surface, as seen for down-data. The ∆f1 < ∆f2 relationship characteristic of the up-data is less evident in Figure 3 than in the corresponding raw trace of Figure 2. This is because, for ease in comparing Figures 3 and 5, both figures have been plotted on the same scale. The raw data in Figure 2, however, clearly show that even on a thicker substrate the first frequency shift in the up-data is smaller than the second shift. The smaller initial shift is very evident in the up-trace in Figure 4, which was acquired on the thinnest substrate. One must not compare absolute shift magnitudes between Figures 2 and 4 because the amounts of base segment tethered to the QCM are not the same for these two figures (see Table 1). When the thin-substrate data of Figure 4 are fit to eq 2, as shown in Figure 5, the initial shift in the up-data is so much smaller than the second that it causes the entire up-trace to lie above the down-trace. If the up-plateau frequencies in Figure 4 are corrected by shifting the entire up-trace downward by the amount of shift missing from the first step because of DNA standing away from the surface, the traces in Figure 5 assume their expected relationship. The up- and down-traces are then nearly coincident through the first 6 points with the up-data gradually diverging below the down-data (not shown). The divergence is cumulative, as predicted by the model. (The data acquired on thicker substrates, e.g., Figure 3, appear as expected, with the up-trace below the down. This is only because the effect of DNA standing away from the surface upon initial hybridization is less dramatic because of the reduced response slope on thicker substrates10 and because of a y-axis scale that further conceals the effect. The raw data, see Table 1, clearly show an effect of DNA moving from the surface in every initial hybridization shift acquired with the QCM up.) Let us next address the question of why more extensions of the DNA’s length can be observed with the QCM up. In both Figures 2 and 4, significantly more length extensions are observed with the QCM up. As noted in Table 1, this is a consistent pattern regardless of substrate thickness. Again, the results are readily explained by a model of the interface that takes gravity into account. In the up-orientation, the interface region compresses and is thus less thick. The DNA is then, on average, both closer to the surface and very slightly denser and more viscous, and hence slightly less lossy. Either positioning closer to
Gravity and Solid-Solution Interfaces
the surface or greater density-viscosity product alone would result in better coupling of the interface region’s inertia to the QCM. In the present case, it would seem these two factors act in consort, which explains why more DNA extensions can be seen with the QCM up. Regardless of orientation, the interface layer must have greater density than the bulk solution. Apparently, this interface layer attempts to “fall” through the less dense bulk solution toward an up-facing surface and away from a down-facing one. But, of course, the DNA is tethered. The best it can do with the QCM facing down is to stretch out some and move, on average, further from the surface, resulting in a somewhat less dense, more lossy interface. The entirety of the experimental results are consistent with and can be rationalized by this simple model that invokes gravity as the driving force for effects seen. Conclusion The present data are consistent with the orientation effect reported by Yoshimoto et al., who postulated that the effect may be due to the influence of gravity on the QCM-solution interface. Here, we have shown that a large orientation effect results from tethering solvated macromolecules to the QCM, and we have proposed a model to
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explain the effect. Altogether, the data present a convincing argument in favor of gravity acting on the interface region between solid and solution. A simple explanation for why gravity affects the interface region is that the interfacial solution layer is compelled to have a density different from the bulk density because of the molecules trapped there by chemical or physical bonds to the surface. The pioneering paper by Yoshimoto et al.2 demonstrated clearly and rather remarkably that gravity’s influence on even small, adsorbed molecules can be observed if lownoise measurements are made using higher-frequency QCMs. It is conceivable that with very sensitive apparatus it may even be possible to observe a gravity-driven distortion in the hydration spheres of adsorbed ions. Acknowledgment. For helpful discussion, we thank John Pojman, Douglas McCain, Peter Butko, Ras Pandey, Kay Kanazawa, and David Paul. We also thank David Paul for the design of our oscillator circuit and the National Institutes of Health and the United States Department of Agriculture for partial support of this work. One of us, R.D.C., also received support through the Sigma Xi Grants in Aid program. LA030390D
