Langmuir 1996,11,3083-3091
3083
Measurement of Forces between Surfaces Composed of Two-DimensionallyOrganized, Complementary and Noncomplementary Nucleobases Peter Berndt,? Kazue Kurihara,S and Toyoki Kunitake*># Molecular Architecture Project, Research Development Corporation of Japan, Kurume Research Park, Kurume 830, Japan Received February 10, 1995. In Final Form: May 2, 1995@ Langmuir-Blodgett films of amphiphiles with an orotic acid (Oro, uracil-like) headgroup or a complementary adenine (Ade) headgroup were deposited onto mica surfaces and investigated by surface force measurement. Interactions between both complementary (Oro-Ade)and noncomplementary (AdeAde, Oro-Oro) nucleobase pairs were studied. The LB films showed functional features of the nucleobase headgroups. Electrolyte-dependent electrostatic repulsion was found at pH's close to the pKa of the headgroups. In the absence of strong electrostatic forces, Le., Oro-Ade and Oro-Oro combinations at pH 5.6, weak long-range attraction was detected. At close distances strong attractive forces made the surfaces jump into a contact position. "he adhesive force between the complementary layers was found to be 100 mNIm, while the values between the noncomplementary pairs were ca. 50 mN/m and 250 f 50 mNlm for Ade-Ade and Oro-Oro, respectively. "he force profiles found between nucleobase surfaces are made of two components. One is observed at ca. 100-20 nm and changes its intensity drastically dependingon conditions. This force is found both for complementary and for noncomplementary surfaces and is similar to the very long range attraction reported for hydrophobic surfaces (Claesson et al., 1988,1994;Kurihara et al., 1990, 1992;Evans, 1993). The other, appearing at around 20 nm, is characteristic of complementary pairs and remains unchanged for pH changes and by salt (KBr) addition. These forces may have an important bearing on interaction mechanisms involved in molecular recognition and supramolecular assembling in biological systems.
between strands of DNA molecules by osmotic pressure measurements.12J3 However, forces that bring together nucleobase pairs from separated states have not been elucidated. It is necessary to conduct the direct measurement of surface forces on model systems that mimic certain aspects of the nucleobase interaction and that are simple enough to allow potentially theoretical treatment of the data. In the last few years, several groups have succeeded in synthesizing monolayer-forming amphiphilic compounds that bear nucleobase h e a d g r o ~ p s . l ~Investigations -~~ conducted in our laboratories showed that monolayers of these nucleobase-modified lipids could bind complementary nucleobases from aqueous subphases e f f i ~ i e n t l y . ~ ~ , ~ ~ ~ ~ In contrast, the pair formation of nucleobases through hydrogen bonding is usually not detectable in bulk water
Introduction Nucleobase interactions occupy a special position among the fundamental biological molecular interactions. The high but not yet ultimate specificity of base-base pairing in nucleic acids has proved to be one of the most efficient mechanisms of accumulating, storing, reproducing, and evolving genetic information. Understanding of all the principles of the base-base interaction is, however, not yet achieved.l Thus, until recently, exact values of the binding energy of hydrogen bonding in regular base pairs and mismatches have been subject to intense study.2-6 Progress in this field has been achieved recently with molecular dynamics simulation with large sets ofwater molecules mimicking the aqueous environment and exact quantum chemical calculations of base-base pairing e n e r g i e ~ . ~ ~A~ strong -'l hydration force caused by the phosphate backbones has been found Present address: Department of Chemical Engineering and Material Science,University ofMinnesota,Minneapolis,MN 55455+
0132.
*Present address: Department of Applied Physics, School of Engineering, Nagoya University, Chikusa-ku, Furo-cho, Nagoya 464-01, Japan. !Present address: Department of Chemical Science and Technology, Faculty of Engineering, Kyushu University, Fukuoka 812, Japan.
Abstract published in Advance A C S Abstracts, July 1, 1995. (1)Fersht, A. R. Trends Biochem. Sci. 1987,12,301-304. (2)SantaLucia, J.; Kierzek, R.; Turner, D. H. Science 1992,256, 217-219. (3)SantaLucia, J.; Kierzek, R.; Turner, D. H. J. Am. Chem. SOC. 1991 113, 4313-4322. (4)Pranata, J.;Wierschke, S. G.; Jorgensen, W. L. J. Am. Chem. SOC. 1991,113,2810-2819. ( 5 ) Williams, D. H.; Cox, J. P. L.; Doig, A. J.;Gardner, M.; Gerhard, U.; Kaye, P. T.; Lal, A. R.; Nicholls, I. A,; Salter, C. J.; Mitchell, R. C. J . Am. Chem. SOC.1991,113,7020-7030. (6)Zieba, K.; Chu, T. M.; Kupke, D. W.; Marky, L. A. Biochemistry 1991,30,8018-8026. (7) Sim. F.: St-Amant.A,: Pauai, I.; Salahub, D. R. J.Am. Chem. SOC. 1992,114;4391-4400. @
'
d
(8)Doig, A.D.; Williams, D. H. J.Am. Chem. SOC.1992,114,338343. (9)Jorgensen, W.L.; Pratana,J. J. Am. Chem. SOC.1990,112,20082010. (10)Jeong, K. S.;Tijivikua, T.; Muehldorf, A.; Deslongchamps, G.; Famulok, M.; Rebek, J. J. Am. Chem. SOC.1991,113,201-209. (ll)Novoa, J. J.; Whangbo, M.-H. J.Am. Chem. SOC.1991, 113, 9017-9026. (12)Anthony-Cahill, S. J.;Benfield, P. A.; Fairman, R.; Wasserman, Z. R.; Brenner, S. L.; Stafford,W. F., 111;Altenbach,C.; Hubbell, W. L.; Degrado, W. F. Science 1992,255,979-983. (13)Rau,D. C.;Lee, B.;Parsegian,V. A. Proc. Natl. Acad. Sci. U.S.A. 1984,81,2621-2625. (14)Ahlers,M.; Ringsdorf, H.; Rosemeyer,H.; Seela,F. Colloid Polym. Sci. 1990,268,132-142. (15)Honda, Y.; Kurihara, K.; Kunitake, T. Chem. Lett. 1991,681684. (16)Piantadosi, C.; Marasco, C. J. J.;Morris-Natschke, S. L.; Meyer, K. L.; Gumus, F.; Surles, J. R.; Ishaq, K. S.; Kucera, L. S.; Iyer, N.; et al. J.Med. Chem. 1991,34,1408-1414. (17)Shea, R. G.; Marsters, J. C.; Bischofierger, N. Nucleic Acids Res. 1990,18,3777-3783. (18)Hong, C. I.; Kirisits, A. J.; Nechaev, A,; Buchheit, D. J.; West, C. R. J.Med. Chem. 1990,33, 1380-1386. (19)Hong, C. I.; An, S. H.; Buchheit, D. J.;Nechaev, A.; Kirisits, A. J.; West, C. R.; Berdel, W. E. J. Med. Chem. 1986,29,2038-2044. (20)Kawahara, T.; Kurihara, K.; Kunitake, T. Chem. Lett. 1992, 1839-1842.
0743-746319512411-3083$09.00/0 0 1995 American Chemical Society
Berndt et a2.
3084 Langmuir, Vol. 11, No. 8, 1995 because of competitive binding of water molecules. This intriguing phenomenon at the interface is not limited to nucleobase-containing lipid monolayers, but has been observed for monolayers with other hydrogen-bonding headgroups.15r21 The monolayer surface must provide unique, favorable environments for these interactions. In the present study, we prepared an adenine-containing amphiphile (Ade, 1) as a complementary counterpart of the uracil-like orotate amphiphile (Oro, 2). The latter
n
2 (Oro)
.O
U
monolayer has been found to bind adenine derivatives in a highly specific,cooperative manner.2oTheir interactions were investigated directly by surface forces measurement.23 This method is useful to investigate characteristics of these nucleobase-functionalizedsurfaces, as it is capable of molecular resolution, and according to the Deryaguin approximation (eq l), it yields the surface interaction energy as a function of distance.24 This study must have an important bearing on the long-range attraction between hydrophobic surfaces, because the charge density and the hydrophobicity of the surfaces can be regulated by changing pH. The origin of long-range attraction between hydrophobic surfaces, which extends sometimes to a separation close to 250 nm,25is one of the important questions that are not solved in surface science.26 To our knowledge, the dependence of force profiles on surface fimctionalities between complementary and noncomplementary pairs has been studied for the first time, with surface force m e a ~ u r e m e n t . ~ ~
Experimental Section Materials. The preparation of orotate amphiphile 2 was described previously.20Dioctadecyldimethylammonium bromide was purchased from Sogo Pharmaceutical Co. Thymidine derivatives were obtained from Sigma Co. Inorganic salts were e ofreagent grade from Wako Chemicals. All commercial reagents were used without further purification. Spreading solvents for monolayers were of spectrograde (Kishida Chemicals). Water was deionized and distilled twice by a Nanopure I1 and FI-streem 48D glass still system (Barnstead). The water had a specific resistance of more than 17 MOcm (prior to distillation). Prior (21)Ikeura, Y.; Kurihara, K.; Kunitake, T. J. Am. Chem. SOC.1991, 113,7342-7350. (22)Kurihara, K.; Ohto, K ; Honda, Y.; Kunitake, T. J. Am. Chem. SOC.1991,113,5077-5079. (23)Preliminary accounts of this work Bemdt, P.; Kurihara, K.; Kunitake, T. InFinn1 Report ofKunitakeMolecularhhitecture Projects, JRDC, Kurume 1992,45-47;Proceedingof65thAnnual SpringMeeting, Chemical Society o f JaDan, 1993. 2D443. (24)Israelachili, J.-N., Intermolecular and surface Forces, 2nd ed.; Academic Press: London, 1989. (25)(a) Kurihara, K.; Kato, S.;Kunitake, T.Chem. Lett. 1990,15551558.(b) Kurihara, K.; Kunitake, T.; Higashi, N.; Niwa, M. Thin Solid Films 1992,210f211,681-684.(c) Kurihara, K.; Kunitake, T. J . Am. Chem. SOC.1992,114, 10927-10933. (26)Tsao, Y.-H.; Evans, D. F.; Wennerstrom, H. Science 1993,262, 547-550. (27)Recently interactions between complementary and noncomplementary nucleotide monolayers were also measured by another group: Pincet, F.; Perez, E.; Bryant, G.; Lebeau, L.; Mioskowski, C. Phys. Rev. Lett. 1994,73,2780-2783.
to surface force measurement, freshly distilled water was deaerated with a water stream pump. DidodecylN-[3-(6-Aminopurin-9-yl)propionyl]-~-glutamate. Ditetradecyl L-glutamateZ8(1 g, 1.85 mmol) and 9-[2[@-nitrophenyl)carbonyl]ethyl]adenine14(0.6g, 1.85mmol)were dissolved in a minimum volume of chloroform and dimethylformamide (2:1, ca. 10 mL), and a few droplets of triethylamine were added. The mixture was stirred for 10 h, until thin layer chromatography indicated completion of the reaction. The product was filtered off and purified by recrystallization from ethanol until the yellow color of p-nitrophenol had virtually vanished. It was then dissolved in hexandchloroform (70:30, v/v) and applied on a column with silica gel 60. Impurities running at the solvent front were washed out with hexand chloroform (30:70, v/v), and the product was eluted with chlorofodmethanol (95:5, v/v). Rechromatography with the latter solvent system yielded a colorless powder of 1: yield 60%; mp 71 "C; 'H 600-MHz NMR (CDCl3) 6 0.85(t, 6 H, CH3), 1.25 1.96 and 2.12 (m, (m, 44 H, CHz), 1.65 (m, 4 H, RCH~CHZCOO), 2H, COOCH2CH2CHNHCO), 2.44 (t, 2 H, COOCH&H&HNHCO), 2.81 (t, 2 H, COCH~CHz-adenine(Nl)),3.68 (dd, 1 H, COOCHNH), 4.06 and 4.18 (tt, 4 H, RCH2CH2COO),4.5 (t, 2 H, COCHzCHz-adenine(Nl)),6.4 (m, 1H, CHNHCOCHz),7.93 (s, 1H, adenine, H-C(8)), 8.54 (s, 1H, adenine, H-C(3)); IR (KBr) 2916 and 2848 (CH), 1735 (C=O ester), 1685 and 1540 (C=O amide), 1607 and 1510 (adenine), 1467 (CH) cm-'. Anal. Calcd for C4&20&: C, 67.39; H, 9.95; N, 11.53. Found: C, 67.55; H, 9.94; N, 11.46. Monolayer Studies. A computer-controlled film balance system, FSD5O (US1System, Fukuoka), was used for measuring surface pressure as a function of molecular area (pressure-area isotherms). The trough size was 150 x 600 mm, the compression rate was varied from 6 to 48 m d m i n , and the temperature was maintained at 20.0 f 0.1 "C unless otherwise indicated. The solvents used for spreading monolayerswere mixtures ofhexand CHC13/methanol(6:3:1,by volume) for adenine amphiphile 1 and CHCldmethanol (9:1, v/v) for orotate amphiphile 2 and dioctadecyldimethylammoniumbromide. Monolayers were spread over pure water. The incubation time before starting compression was varied in the range 3-30 min, and the spreading volume was varied from 80 to 200 pL in order to ensure equilibrium conditions. n-A isotherms were not affected by changes in the incubation time or spreadingvolume. Absorption measurements at the surface of monolayers were carried out as described e l s e ~ h e r eusing , ~ ~ a multichannel spectrophotometer. Deposition of Alternating Layers for FTIR Spectroscopy. Deposition of monolayersfor FTIR spectroscopyonto goldcovered (100 nm, vapor-deposited) glass slides was conducted in the vertical mode using a computer-controlled film balance (FSD50)and lifter (FSD21)system (US1System). Four different films were deposited as follows: eight layers of the orotate amphiphile starting with a downstroke deposition and finishing with an upstroke deposition (Or0 layer); eight layers of the adenine amphiphile (Ade layer); deposition of an Oro layer downstroke followed by an Ade layer upstroke (this sequence was repeated four times, complementary Oro-Ade layer); deposition of a double Oro layer followed by deposition of a double Ade layer (this sequence was repeated two times, noncomplementary Oro-Ade layer). Ade and Or0 layers were transferred at a surface pressure of 30 mN/m and a deposition rate of 20 mdmin. The transfer ratios of the amphiphiles were found t o be between 0.75 and 1.0 for both Ade and Oro. Preparation of LB Films on Mica Surfaces. Deposition of monolayers onto mica sheets glued to silica lenses was performed in the vertical mode. First, dioctadecyldimethylammonium bromide was transferred in the upstroke mode at a surface pressure of 35 mN/m and a deposition rate of 10 mm/ min. After 30 min, a layer ofAde (or Oro) was transferred in the downstroke mode onto the deposited layer of dioctadecyldimethylammonium bromide, at a surface pressure of 30 mN/m and a deposition rate of 2-10 mndmin. The transfer ratios of the (28)Asakuma, S.;Okada, H.; Kunitake, T. J. Am. Chem. SOC.1991, 113,1749-1755. (29)Yanagi, M.; Tamamura, H.; Kurihara, K.; Kunitake, T. Lungmuir 1991,7,167-172.
Langmuir, Vol. 11, No. 8, 1995 3085
Forces between Nucleobase Surfaces amphiphiles were found to be 1.2 f 0.3 for dioctadecyldimethylammonium bromide and between 0.75 and 1.0 for both Ade and Oro. After deposition, the lenses were transferred under water and mounted into the water-filled surface force apparatus. Surface Force Measurements. Surfaw force measurements were carried out employing a "Mark 4" (ANUTECH, Australia) apparatus. Detailed description of the apparatus, the measurement procedures, and the mathematical formalism employed can be found in the r e f e r e n c e ~ . ~ ,Briefly, 3 ~ , ~ ~the distance between the surfaces mounted as crossed cylinders was measured by multiple beam interferometry with an accuracy of up to 0.5 nm. The forces were determined with a detection limit of 10-'-10-* N from the deflection of a double-cantilever spring (on which one of the surfaces is mounted). In accordance with the Deryaguin approximation (eq 11,measured forces Fwere normalized by the geometric mean radius R of the surfaces, yielding a value proportional to the free energy EOof interaction of the surfaces.
'
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Surface Area (nm'/molecule)
Figure 1. Surface pressure-area (n-A) isotherms of adenine amphiphile 1 on pure water at various temperatures. The temperature was maintained within f0.1"C, and the compression speed was 24 m d m i n .
P'
- = 2zE0 R The zero value for the force was set as the force at large distances between the surfaces where no interactions were expected. As our measurements were intended to detect extremely weak forces, care had to be taken for the exact determination ofthis value. We used a least-squares routine for finding a distance range where the second derivative of the measured spring movement was close to 0. From this range we derived the spring movementidistance proportional factor and tested it for yielding zero force at distances far away from the surface but different from the calibration range. Time drifts were excluded by averaging data for several in-out movements without bringing the surfaces into contact during the measurement run and by the use of various approaching speeds of the motor drive. Electrolyte or substrate solutions were added sequentially. After each addition, forces were measured immediately as well as after incubation periods of 0.5-2 h, in order to assure equilibrium conditions. Due to solubility limits for certain nucleobase substrates, we used a peristaltic pump to exchange the subphase in the apparatus at high nucleobase substrate concentrations. Pumping was carried out at 50 mumin with at least a %fold volume replacement. Routinely we examined the contact position of the fringes derived from bare mica sheets before deposition of the amphiphiles. In independent tests we determined that exact optical alignment assures reproducibility of this position within a few angstroms on the spectrophotometer scale. However, in special cases we infused the apparatus with methanol (2-3 L)in order to dissolve the amphiphiles deposited on the surface and replaced the liquid with water again. This allowed us to make a layer thickness estimate at the same spot that was used for the force measurement. Model Calculations. Electrostatic repulsion between charged surfaces in 1:lelectrolyte solution was simulated employing the classical Poisson-Boltzmann equation,
where ~ ( xis) the surface potential as a function of distance x , e is the elementary charge, E is the dielectric permittivity of the solution, k is the Boltzmann constant, T is the absolute temperature, and K is the Debye length as defined by eq 3,
(3) where ei is the number density and zi the valency of the ith ion. Different boundary conditions were invoked (constant charge, (30)Christenson, H.K.;Israelachvili, J. N.; Pashley, R. M. SPE Reservoir Eng. 1987,5, 155-165. (31)Israelachvili, J.N.Nature 1971,229,85-86.
constant potential, and charge regulation). A simple numerical procedure as first described by Chan, Pashley, and White32was used for the calculation.
Results and Discussion Monolayer and Deposition Properties of Ade Amphiphile and Oro Amphiphile. Adenine amphiphile 1 contains two myristoyl chains in its tail portion. At 20 "C it spreads out over water to give a monolayer that undergoes several phase transitions upon compression. When compressed with a speed of less than 12 mnd min, a liquid expanded phase is formed at surface areas of about 0.95 nm2/molecule,which undergoes transition to a two-phase region at ca. 0.60nm2/moleculeand builds a condensed phase with a limiting area of slightly less than 0.40nm2/molecule. At compression speeds equal to or larger than 24 "Imin, the limiting area is reduced to ca. 0.35 nm2/molecule (Figure 1). All deposition procedures were carried out at compression rates of 6 or 12 mm/min. With increasing temperature the expanded phase becomes even more pronounced. A condensed phase cannot be formed at 40 "C. Absorption spectra of monolayer 1 at the air-water interface showed a slight shift ofthe absorption maximum of the adenine headgroup from 258 nm (solution) to 262 nm during compression. This shift may indicate n-n stacking interaction of the headgroups or at least a nonrandom orientation of the adenine headgroup in the monolayer. The monolayer can readily be transferred to various substrates (glass, gold, silver, mica). The amphiphile always forms Y-type layers. At transfer pressures in the range 30-40 mN/m the transfer ratios to mica surfaces and mica surfaces rendered hydrophobic with dioctadecyldimethylammoniumbromide are as high as 0.75- 1.0. The n-A isotherm of monolayer 1 changes distinctively in the presence of nucleobase substrates. After spreading over solutions containing more than 0.5 mM thymidine, the transition between the two-phase region and the condensed phase becomes less steep, and the transition starts at higher surface areas. Correspondingly, the absorption maximum of the nucleobase headgroup is shifted to values as high as 264 nm, with the spectral shift occurring at surface areas of ca. 0.6 nm2/molecule. In FTIR and ESCA experiments we have found that thymidine, thymine, or thymidine 5'-monophosphate in (32)Chan, D.Y.C.; Pashley, R. M.; White, L.R. J.Colloid Interface Sci. 1980,77,283-285.
Berndt et al.
3086 Langmuir, Vol. 11, No. 8, 1995
I
1
/
split peaks
1750/1790
I!i 3,,,
1
,
Ade-Oro
m
I 3600
3200
zaoo
: 2000
4 1600
1200
BOO
Wavenumber (cm”) Figure 2. Fourier transform infrared spectra of LangmuirBlodgett films composed of eight monomolecular layers: (a) orotate (Oro)film; (b) adenine (Ade) film; (c)alternating AdeOro film; (d)nonalternatingAde-Oro film. “Alternating“layers are LB films deposited with different types of headgroups but identical tails approaching each other, whereas in “nonalternating” layers only identical headgroups were in contact. Schematic illustrations of the respective films are included. Important spectral differences are marked by arrows.
the subphase are incorporated into the adenine amphiphile in the form of LB films. All these observations show that adenine monolayer 1 at the air-water interface is capable of interacting with dissolved nucleobase substrates. The substrate binding can be detected at nucleobase concentrations of below 10 mM. Therefore, the binding is at least several orders of magnitude stronger than the corresponding interaction in bulk solution. Monolayer and binding properties of orotate amphiphile 2 have been described in a recent paper.20 In brief, when spread over pure water, the amphiphile forms a monolayer that possesses a condensed phase with a limiting area of 0.4 nm2/molecule and a high collapse pressure of about 50 mN/m. LB films formed from the monolayer spread over the aqueous adenine contain adenine. The binding isotherms for adenine and its derivatives are sigmoidal, indicating a cooperative, multiple site interaction during the binding process. Interaction of the Ade-Oro Layers in LB Films: FTIR Observation. The interactions between the complementary and noncomplementary nucleobase monolayer surfaces were examined with FTIR spectroscopy (Nicolet, Model 170, reflection absorption method) as shown in Figure 2. LB films of the orotate monorayer contain Oro-Oro pairs that are hydrated or bound together by hydrogen bonds, as indicated by the V N H peaks a t 3086 and 3200 cm-’ 33
(Figure 2a). The headgroups in an LB film of Ade form similar hydrogen bonds with hydrating water molecules or adenine groups of the opposite layer as indicated by the absence of the monomeric V N H peak at 3600 cm-l and the presence of a peak at 3200 cm-’ (Figure 2b). Both spectra show the presence of carboxyl groups at 1750 cm-l. The spectrum of Ade shows absorption bands at 1685, 1610, and 1540cm-’ that can be attributed to the amide I band, the aromatic ring of the adenine headgroup, and the amide I1 band, r e ~ p e c t i v e l y . ~ ~ Alternating Ade-Oro layers were prepared either as layers where the hydrophilic headgroups of different amphiphiles approached each other (this LB film contains only Ade-Oro contacts, Figure 2c) or as layers where the hydrophobic tails of different amphiphiles were in contact (leavingonly Ade-Ade or Oro-Oro headgroup interactions, Figure 2d). Whereas the spectrum of an LB film that contains contacts between identical amphiphile headgroups (Figure 2d) is close to the sum of the amphiphile spectra taken separately, the spectrum where complementary headgroups approach each other is different (Figure 2c). Most important are the differences in the YNH region where the shoulder attributed to the NH stretching of the orotate imide group (3086 cm-l) disappears and in the vco (1750 cm-l) region where the carbonyl peak is split into two separate peaks (Figure 2c). These spectral alterations can be explained as a result of the formation of hydrogen bonds between the orotate imide and a nitrogen atom from the adenine headgroup as well as between the adenine amino group and the orotate carbonyls. A number of other spectral shifts (e.g., from 1610 to 1635 cm-l and from 1685 to 1690 cm-l) indicate even more complex structural alterations in the headgroup regions of the amphiphile layers. Stepwise Repulsion between Surfaces of Ade Monolayers in Pure Water. Forces between Ade surfaces were investigated in the usual manner after transferring the mica lenses covered with the Ade layers under water to the apparatus. Force curves were recorded either by decreasing the distance between the layers at a constant speed with the fine motor or by stopping the drive at every data point. Care was taken to monitor “first approach” experiments by changing the measured surface spot several times during the experiment. Typical force-distance dependencies for the Ade surface in pure water are shown in Figure 3. We could not detect forces reaching out beyond ca. 150 nm. Therefore, the zero force was usually set to the range between 200 and 300 nm. The surfaces could be brought into a contact position that was 14 f2 nm apart from the contact position of the bare mica sheets before deposition, or after removal of the layers with methanol and refilling of the apparatus with water. The thickness ofthe inner layer corresponded roughly to the size of two double layers of an amphiphile with 3-4-nm length. This was a reasonable estimate for the thickness of the deposited layers. In the following, we give all distance estimates relative to the contact position of the amphiphile surfaces rather than relative to the mica surfaces. As shown by the inset in Figure 3, avery weak repulsive force appeared from ca. 150 nm, and it reached approximately 250 pN/m at 50-nm separation. At separations closer than 28 nm, a steep, stepwise increase in force with a periodicity of ca. 7 nm was found (Figure 3a). At each step, the surfaces jumped into the position of the next inside step after overcoming the force barrier for the current step. When the surfaces were separated after (33) Kyogoku, Y.;Lord, R. L.;Rich, A. J.Am. Chem. SOC.1967,89, 496-504.
Forces between Nucleobase Surfaces
20000
E 16000
%
e
5.12000 v
L
8000 4000
0
,/
3.
24000 n
Langmuir, Vol. 11, No. 8, 1995 3087
-
I
11 “:” -
‘p- * [ a
--------
-
20
40
60
80
100
120
‘\
Distance (nm)
-
- -
I
-4000
’
0
10
20
30
40
50
Distance ( n m ) Figure3. Stepwiseincreaseof forcesbetween surfacescovered with adenine monolayers in pure water at a room temperature (21 f 1 “C). Each Curve in the main chart (a, x; b, A; c, +) represents the first approach onto the surfaces in independent experimental setups. Arrows representjump-in portions of the force curve caused by strong attractive forces. The inset shows the 12 point weighted sliding averageof 1286 data points in the range between 20 and 120 nm accumulated in more than 20 different experiments.
having been brought into the contact position, theyjumped out from this position. In order to measure the adhesive forces at each separate step position, we moved the surfaces inside, stopping the movement just after the surfaces jumped into the next step level, and separated the surfaces again until they jumped out to a far distance. Adhesive forces were different for jumps from different step levels. In a typical run,they were estimated to be ca. 50 mN/m for the innermost step and 4 and 0.25 mN/m for the following outer steps. Excellent reproducibility was observed for the position of the steps in different runs and different experiments (see curves a, b, and c in Figure 31, but a rather poor reproducibility was found for the height of the force barriers between the steps even between consecutive experimental runs. However, steps were observed in all experiments regardless of the time between individual I-lNiS.
After several hours, the amplitude of the steps grows, and the resolution of jumps between the steps becomes lower. When the measurement was carried out for more than 24 h, we could observe a distorted fringe shape a t the contact position, with several “spikes”reaching out of the fringes for some 5- 10 nm. In this situation forces a t far distances ( ~ 5nm) 0 were not predictable, and in several experiments long-range attraction could be observed. The stepwise increase of the force close to the surface of the adenine amphiphile can be explained by assuming mobile monolayers. As the layer is transferred in an ordered, highly compressed state, dissipative processes tend to reduce the surface pressure and the degree of ordering of the monolayer. These relaxation processes are common to noncrystalline, weakly charged monolayers and LB films, especially if they contain only a few layer^.^^-^^ In our case, we have to assume that amphiphile molecules that are pushed out from the layer will not dissolve, but form micelles or similar aggregates (Figure 4). Upon compression, these aggregates are confined in the narrow space between the surfaces. When the separation approaches a multiple of the aggregate (34) Rothberg,L.; Higashi, G. S.;Allara, D. L.; Garoff,S. Chem.Phys. Lett. 1987, 133, 67-72. (35) Schwartz, D. K.; Garnaes, J.; Viswanathan, R.; Zasadzinski, J. A. N.Science 1992,257,508-511. (36) Skita,V.; Richardson, W.; Filipkowski, M.; Garito, A.; Blasie, J. K. J. Phys. (Paris) 1986,47, 1849-1855.
21 nm
14 nm
7 nm
Figure4. Schematicillustrationsof the mechanismof micellar readsorptionto the adenine amphiphilesurface.The relaxation process leads to expulsion of amphiphile molecules from the surface monolayer.These molecules form micelles that readsorb due to the strongly attractive headgroup- headgroup interaction. The interactingsurface is maximizedby micelle clustering. In the experiment, three dominant force barriers with a step size of 7 nm can be detected. ,
size (7nm), steric repulsion is built up. The force turns to attraction (due to van der Waals forces)after the micelles rearrange or are pressed back into the layer. The pulloff force of 50 mN/m (correspondingto a surface energy ys of 5.3 mN/m from FIR = 3ny,) is close to the pulloff force between bare mica in pure water (20-40 mN/m).37 Smaller pulloff forces a t outer steps may reflect the area of surfaces in contact. As the layers are separated again, uneven disruption of the monolayer, fast relaxation of the lateral pressure, and readsorption can restore the step phenomenon quickly. Upon repetition the surface tends to get more and more rough, until macroscopic distortions become evident. Similar phenomena can be expected for all monolayers that are sufficiently mobile and where readsorption of desorbed materials is facilitated by the lack of headgroup repulsion. Crystallinity and ordering in fluorocarbon amphiphile layers have been found to decrease dramatically with the charge state of the h e a d g r ~ u p .If~ mono~ layers of an ionic fluorocarbon amphiphileare discharged after addition of electrolyte, they build step structures very similar to the ones found in our experiment^.^^ Long-Range Attractive Forces between Or0 Surfaces in Pure Water. When investigated immediately (within 30 min) after deposition, the forces between the Or0 surfaces are attractive and detectable at distances over 100 nm (Figure 5). The attractive force is weak, but increases as the surfaces approach each other. From about 50 nm the surfaces jump into the contact position. The adhesive force between the surfaces is estimated to be 250 f50mN/m. The range of the attractive force increases slightly with time, and after 2-3 h attractive forces can be detected at separations of 120-150 nm. Further incubation (’6 h) of the layers leads to a pronounced change in the force curve (Figure 5). The distance where an attractive force can be detected decreases from ca. 100 nm to ca. 50-30 nm. In the close vicinity of the surface we can again detect a stepwise increase of the force similar to that found with the adenine amphiphile (not shown in the figure). Further incubation leads to an increase in the distance range where the steps (37) Kkkicheff,P.;Christenson, H. IC;Ninham, B. W. Colloids Surf. 1989,40,31-41. (38) Jacquemain, D.; Wolf, S. G.; Leveiller, F.;Lahav, M.; Leiserowitz, L.; Deutsch, M.; Yjaer, K.; Als-Nielsen,J. J. Am. Chem.Soc. 1990,112, 7724-7736. (39) Islaerachvili,J. N.; Pashely, R. M. J. Colloid Interface Sci. 1984, 98,500-514.
Berndt et al.
3088 Langmuir, Vol. 11, No. 8, 1995 ___
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120 140 160 180 200 Distance (nm)
Figure 6. Forces between the surfaces of orotate layer 2 in pure water at 21 f 1 "C. Arrows representjump-in portions of the force curve caused by strong attractive forces. The range of the detected attractive force initially increases with the incubation time. Further incubation longer than ca. 6 h leads to a step phenomenon similar t o the one observed with Ade amphiphile.
can be found, to 25 nm. Although jumps cannot be seen anymore, the forces at separations about 50 nm are still clearly attractive. The Oro surface a t the neutral pH is another example of a surface that features very long range attraction. Similar long-range attractive forces have been described in the literature for hydrophobic layers of a hydrocarbon and a fluorocarbon amphiphile in water and in ethylene glyco1,26~39-41 for those of polymerized ammonium amphiphile layers.25 The pulloff force for the Oro-Oro contact (250 f 50 mN1 m) is close to the values reported for hydrophobic surface^.^^^^^ The Oro layers were deposited on the hydrophobic surface of dioctadecylammonium bromide films; thus one might suspect that the interactions measured were actually those between hydrophobic ammonium layers. However, this was not the case. The existence of the orotate layers was ascertained by charging the surface at higher pH as shown in the following section. ElectrostaticRepulsion Depending on Acid/Base Equilibrium of Nucleobase Groups. Monolayer surfaces ofAde and Oro amphiphiles can be treated as charged surfaces because of weak acid (Oro) or weak base (Ade) headgroups. The force curves for these monolayers should resemble those for mineral surfaces (e.g., the mica surface in electrolyte) or other surfaces where the electrostatic properties are governed by the so-calledcharge regulation m e ~ h a n i s m . ~This ~ , ~charging ~ phenomenon is used to understand the differences in force profiles for the Ade and Oro layers. The pH of pure water in the apparatus is usually determined by a weak buffer made up of dissolved carbonic acid and dissociated ions from the oxide layer on the wall. Although it is not easy to estimate the exact pH value by ordinary laboratory methods, we can choose pH 5-6 as a reasonable estimate. This is only 1-2 pH units away from the pKaofthe adenine headgroup, but more than 3-4 pH units apart from the pKa of the orotate head in the Oro layer. Our calculations show that the electrostatic force predicted for the Oro amphiphile in pure water would be in the range of just several micro(40)Pashely, R.M.; McGuiggan, P. M.; Ninham, B. W.; Evans, D. F. Science 1985,229,1088-1089. (41)(a) Claesson, P. M.; Blom, C. E.; Herder, P. C.; Ninham, B. W. J. Colloid Interface Sci. 1986,114, 234-242. (b) Claesson, P. M.; Christenson, H. K. J.Phys. Chem. 1988,92,1650-1655.(c) Parker, J. L.; Claesson, P. M. Langmuir 1994,10,635-639. (42)Pashley, R. M. J. Colloid Interface Sci. 1981,83, 531-546. (43)Pashley, R.M.; Israelachvili, J. N. J.ColloidlnterfuceSci. 1984, 97,446-455.
0
10
40
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20
Distance (nm)
Figure 6. Theoretical force profiles for the Ade surface at different pH values in an aqueous subphase containing a 0.5 mMconcentrationof a 1:1 electrolyte.The inset showsthe extent of dissociation of the headgroup. 5000
40001 30001
hi
~
___
7 I
x pure water A PH 4 8 . 0 5 mM KNO,
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I
pH 3 5 , 0 5 mM KNO, o 24 hat pH3 5 0 5 mM KNO, "mipedcnan
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Figure 7. Forces between adenine surfaces at 21 f 1 "C.Forces were first measured in pure water. Then KNo3 was added to give a concentration of 0.5 mM, and the pH was set to 4.8 by
adding mo3.Forces were measured several times over a period of 2 h. Finally, the pH was set to 3.5 by further addition of HN03.Forces were measured over a period of 2 h and after 24 h. Arrows representjump-in portions of the force curve caused by strong attractive forces. Note the absence of jumps for the force profiles in the electrolytesolution.Thick solid lines describe theoretical curves obtained following procedures described in the Appendix. newtonslmeter and therefore escape detection with the current surface force apparatus. However, the electrostatic repulsion should become measurable in the pH range close to the pKa of the headgroup (Figure 6). In order to prove this feature we examined the behavior of the weak acidhase headgroups at different pH and salt concentrations and compared the theoretical prediction (Figure 6 and Appendix) with the experimental results. The Adenine Amphiphile. Addition of KBr or KN03 (0.5mM) at neutral pH did not influence the forces between Ade surfaces (data not shown). However, when the pH of KN03 solutions had been set to the desired value with HN03, we could observe changes in the force curves as shown in Figure 7. At pH 4.8, the repulsion increased in the distance range 25-50 nm but decreased at distances larger than 50 nm in good agreement with the theoretical prediction. Moreover, the stepwise increase of the force with "jump-ins" (as clearly noticeable in the pure water phase, see Figure 3) vanished at this pH, and the force increased monotonously, except for one or two steps at a close distance that could be observed shortly after addition ofthe electrolyte. As the pH was lowered to 3.5, the range and extent of the monotonous force increased further, and steps could not be observed any more. However, the force profile was not stable at this pH. After more than 10 h, a long-range attractive force appeared, and the contact position changed, suggesting dissolution of the outer amphiphile layer. An obvious explanation for this observation is that the increased charge of the headgroup causes an increase in the repulsive force between the two surfaces. This force
Forces between Nucleobase Surfaces
Langmuir, Vol. 11, No. 8, 1995 3089
Ii pure water
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S 4000 a
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Figure 8. Forces between orotatesurfaces at 21 i1 “C. Forces
were first measured in pure water, and then the pH was set to 8.9 with KOH and forces were measured immediately.After these measurements, KBr solution was added to give an electrolyte concentration of 2 mM, and the forceswere measured again. Arrows represent jump-in portions of the force curve caused by strong attractive forces. Note the absence of jumps for the force profiles in electrolyte solution. acts also on the amphiphile micelles that are adsorbed to the surface at neutral pH’s and leads to their dispersion in the aqueous subphase, a process we can clearly observe as quick disappearance of the step phenomenon. The layer becomes unstable at pH 3.5, as the lateral repulsion ofthe charged headgroups exceeds even the hydrophobic forces that keep the amphiphile tail in the monolayer. This results in dissolution of the outer layer, which is evident by the “negative” distance values (relative to the outer headgroup layer) for the force profile after prolonged incubation at pH 3.5 (Figure 7). The Or0 Surfaces. Forces between the Oro surfaces were measured before and after succeeding addition of KOH and KBr. The force profile was found to be altered at a high pH value (pH 8.9, as shown in Figure 8). Instead of the attraction characteristic of the Ora layer at the neutral pH (see Figure 51, we found a pronounced repulsion between the surfaces. The repulsion decreased when KBr was added at a concentration of 2 mM, indicating that the repulsion is truly of electrostatic origin. The decay length of the repulsive force was close to the Debye length expected from the electrolyte concentrations used. Interactions of Ade Monolayers with Soluble Nucleobase Derivatives. It was attempted to monitor nucleobase binding to Ade or Oro surfaces with the surface force measurement using charge neutralization and/or alteration of the structural forces in the close vicinity of the surface. However, 10 mM thymidine (at pH 7.0) in the aqueous phase showed no apparent influence on forces between Ade surfaces. Similarly, the presence of thymidine 5’-monophosphate (0.2-2 mM) or thymine (2 mM) did not alter the force profile. These results may appear contradictory with nucleobase binding by the Ade monolayer on water (see above) and related data.21,22The efficiency of the substrate binding depends on the physical state of monolayers, and monolayers with pronounced molecular recognition capability on the water surface may not be necessarily effective as LB films. In the same vein, adenosine was not bound onto LB films of Oro am~hiphile.~~ Attractive Forces between Complementary Surfaces of Adenine Amphiphile and Orotate Amphiphile. Subsequently, we examined the interaction between surfaces with complementary headgroups. The Oro amphiphile was deposited onto a pair of mica sheets as usual, and the Ade amphiphile was deposited onto a third mica sheet obtained from the same cutout. By measuring forces between two Oro-covered mica sheets we were able to confirm the integrity of the monolayer surface immediately before examining the interactions (44) Kawahara, T.; Kurihara, K.; Kunitake, T. Unpublished data.
250 “im
150
200
250
Distance (nm)
Figure 9. Forces between noncomplementary surfaces of orotate (Oro) amphiphiles2 and those between complementary surfaces of adenine (Ade)amphiphile 1 and the Oro amphiphile in pure water at 21 f 1 “C.Forces were measured between two Oro surfaces several times. Thereafter,one of the Oro surfaces
was replaced by an Ade surface that was deposited onto a mica sheet cut from the same leaf of mica, and the forces were measured immediately. All measurements were completed within 30 min after deposition of the adenine amphiphile surface. Arrows represent jump-in portions of the force curve caused by strong attractive forces. Thick solid lines describe theoretical curves obtained by following procedures described in the Appendix. between complementary surfaces. All measurements were finished within 2-3 h after deposition in order to avoid micelle buildup. As described earlier, forces between Oro-Oro surfaces were attractive in pure water (Figures 5 and 9). The attractive force could be detected at distances longer then 50 nm. At about 10-15 nm separation, the force became larger than the countering force of the spring, and the surfaces jumped into the contact position. It should be noted that the actual jump distance depended on the steepness of the descent ofthe force curve andvaried from experiment to experiment. The adhesive force between two orotate surfaces was found to be 250 mN/m. The force curve measured between complementary AdeOro surfaces immediately after replacing one of the Oro surfaces with an Ade surface was found to be similar to the force-distance dependence between the symmetric layers. However, the jump distance increased (to 20 nm), and the adhesive force was significantly reduced (100 mN/ m). In order to obtain additional information on the forces between symmetric noncomplementary and complementary surfaces, we carried out an analogous experiment at pH 7 (Figure 10). Here, forces between the symmetric Oro-Oro layers became repulsive up to 10 nm. Attractive forces could the surfaces jump into contact position at separations shorter than 10 nm. As described earlier, the origin of the repulsive force was identified as the electrical diffused double layer force between identically charged headgroups. Replacement of one of the Oro surfaces with an Ade surface led to a distinctive change in the observed force-distance dependence. In this case, we could not detect attractive nor repulsive forces at distances larger than 25 nm, and the surfaces jumped into contact at distances close to 20 nm. Addition of KBr (0.5 mM) did not alter the force curve. These experiments show that the attractive force between complementary nucleobase surfaces is probably not homogeneous, but consists of at least two components. The long-range constituent (20 nm < D < 150 nm) is sensitive to the charge at the surface and other surface conditions (e.g., the time elapsed from the LB deposition), much like the very long range attractive forces found between certain hydrophobic s u r f a c e ~ . In ~ ~contrast, ~~~-~~ the attractive force a t distances smaller than 20 nm is
3090 Langmuir, Vol. 11, No. 8, 1995 200 150 100
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Berndt et al.
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Figure 10. Forces between noncomplementary surfaces of orotate (Oro) amphiphiles 2 (open x ) and those between complementary surfaces of adenine (Ade) amphiphile 1 and the Oro amphiphile (solid x ) at pH 7 and 21 f 1 "C. The pH was adjusted by addition of a trace of phosphate buffer to pure water.Forces were first measured between the two OK)surfaces. The Ade layer that was deposited onto a mica sheet that was cut from the same leaf of mica was then mounted into the apparatus, and the forces were measured immediately. After completion of the measurements in water, KBr was added to make up a 0. 5 mM concentration. Forces between Ade-Oro surfaces in the presence of KBr: (solid box).
characteristic of the complementary system and not sensitive to the charge on the Oro surface. The adhesive force between Oro-Oro layers (250 mN/ m) is similar to that reported for the above mentioned hydrophobic surfaces, indicating a basically hydrophobic character of the orotate surface in pure water. Because the long-range attractive component of the force between both symmetric and complementary surfaces exhibited similar characteristics in the distance range and sensitivities to surface conditions, they could be caused by the same mechanism as the submicron-rangeattraction found between these hydrophobic ~ u r f a c e s . ~The ~ , ~adhesive ~-~~ force between complementary pairs is smaller than typical values for hydrophobic surfaces (300-400 mN/m), suggesting that the actual area in contact is smaller in the complementary pair than in the noncomplementary one, or that surface characteristics between Or0 and Ade layers are fundamentally different. The origin of the long-range attraction has been under active discussion. Similar long-range attractive forces have been described in the literature for various hydrophobic 1ayers,23,26,39-41 as well as for modified hydrophobic layers of an ammonium amphiphile partially covered by dimethyldodecylphosphine oxide and for mica surfaces in divalent ion solutions at the isoelectric point.46 Recently, long-range attractive forces were detected between phospholipid surfaces in the presence of calcium ions.47 One common feature of these examples is that they are all electrically neutral (or near neutral) surfaces. The first two surfaces are clearly hydrophobic, whereas the last two are basically hydrophilic. It has been shown that the phospholipid surfaces in the presence of calcium ions are a mosaic ofhydrophilic and hydrophobic patches.47 These more recent results indicate that observations of the long-range attraction are not strictly limited to purely hydrophobic surfaces. Further theoretical and experimental work is necessary to understand this interesting phenomenon. An explanation for the attractive force observed at distances below 20 nm is more difficult. Indeed, attractive forces between complementary Ade-Oro surfaces may be anticipated simply because of the opposite sign of their surface charges. However, the difference of the electric (45)Herder, C.E.J. Colloid Interface Sci. 1991,143, 1-8. (46)Dunstan, D.E.Langmuir 1992,8,740-743. (47)Leckband,D.E.;Helm, C. A.; Israelachvili,J.Biochemistry 1993, 32, 1127-1140.
potential between the surfaces is small (on the order of 30 mV in 0.1 mM electrolyte solution, pH 71, and electrostatic forces should not exceed 300pN/m. Attractive forces of electrostatic origin should be detected as the difference in the forces measured between symmetric layers and complementary layers at any pH. In our experiments, we could not detect such a force, and trivial electrostatic effects cannot be adopted as the single explanation. Two more "exotic" effects may be cited as origins of the 20-nm attractive force component. First, a possible explanation could be found in a correlation between the polar headgroups of the amphiphiles that leads to a modification of the short-range ( e 5 nm) van der Waals component of the force.48 It has been shown that this component can theoretically lead to an attractive force decaying as D-5 in addition to the forces predicted by the Lifshitz theory. It was pointed out that "correlations between dipolar headgroups can give rise to attractions many times larger than the conventional van der Waals Second, the hydration layer may transmit the polarity of the surface headgroups over a certain distance. An attractive force may arise as hydration layers with opposite orientations approach each other. This would be the attractive counterpart to the well-known repulsive structural forces exhibited by the hydration spheres of counterions on mineral s ~ r f a ~ e or s ~symmetrical ~ , ~ ~ * ~phos~ pholipid layer^.^^!^^ Very recently, Perez et al. have measured interactions between nucleoside(thymidineand adenosine) monolayers by the surface force apparatus.27 Some parts of their results are similar to ours, and others are considerably different. They have demonstrated long-range attraction extending up to 60-nm separation distances. However, unlike our data, this long-range attraction has been found commonly for noncomplementary (thymidine-thymidine, adenosine-adenosine) and complementary (thymidineadenosine)systems. Significant differenceshave not been detected among interactions at separation ranges shorter than 20 nm. Instead, they have found larger pulloff forces of 110 mN/m for complementary pairs, compared with those for noncomplemenatry pairs, 43 mN/m for thymidine-thymidine and 50 mN/m for adenosine-adenosine. The value of the pulloff force for the complementary pair is similar to ours; however, the values for noncomplementary pairs are not consistent with between two sets of measurements. Because the two research groups use different functional groups (nucleobases and nucleosides), origins of these similarities and differences are not clear at the moment. Further investigations are required. Concluding Remarks. This paper describes the nature of the forces between symmetrical and complementary layers of nucleobase amphiphiles. There are two types of forces which overlap depending on distance ranges and other conditions. One is found at distances of ca. 100-20 nm and changes its intensity drastically depending on conditions. This force is found both for complementary and for noncomplementary surfaces and is similar to the very long range attraction reported for hydrophobic surfaces. The other appearing at around 20 nm is (48) Argillier, J. F.; Ramachandran, R.; Harris, W. C.; Tirrell, M. J. Colloid ZnteTface Sci. 1991, 146, 242-250. (49)Attard, P.; Mitchell, D. J.; Ninham, B. W.Biophys. J. 1988,53,
457-460. (50)Horn, R. G.;Smith, D. T. J.Non-Cryst. Solids 1990,120,72-81. (51)Parsegian, V.A.; Rand, R. P.; Rau,D. C. Chem. Scr. 1986,25, 28-31. (52)Marra, J.; Israelachvili, J. N. Biochemistry 1985, 24, 46084618.
Langmuir, Vol. 11, No. 8, 1995 3091
Forces between Nucleobase Surfaces characteristic of complementary pairs and remains unaffected by pH changes and in the presence of a salt (KBr). An important and unsolved question is what kind of long-range forces are involved in molecular recognition as well as in formation of supramolecular assemblies in biological systems. For example, how do complementary strands ofDNA find each other from a distance in solution? How does antigen find antibody? A random collision process does not appear to explain the efficiencies of these biological molecular recognitions. The forces observed in this work may have important bearing on the interaction mechanisms involved. The longer range component, which appears nonspecific though sensitive to environment, may work for bringing two species closer; and the short-range component can be effective for specificpairing and recognition. If nature utilizes these noncontact forces to bring about efficient and specific interactions, the process of biological molecular recognition would be quite different from that based on the simple collision theory. Homing-in of biological macromolecules may lead to exciting possibilities.
Acknowledgment. We thank Mr. T. Kawahara for his generous gift of Oro amphiphile and Mrs. K. Ohto for her capable technical assistance in FTIR and ESCA measurements. Appendix: Calculation of Charge Density and Surface Potential between Symmetrical Nucleobase Surfaees The adenine amphiphile surface contains an aromatic amino group capable of binding protons with a binding constant of pKi = 4.25. The local proton concentration at a surface immersed into electrolyte solution with a bulk proton concentration of CH+ and charged with an electrostatic potential ~0 is given by the Boltzmann distribution function:
(4) By definition, the extent of dissociation at the surface is given by the amount of the charged species relative to the total amount of dissociable headgroups. An obvious transformation leads to
We can estimate the charge density u on the surface as the product of the extent of dissociation and maximum charge density a,, (equivalent to the number of the adenine groups on the surface):
On the other hand, the charge density IJ on the surface is given by the Grahame equation,
(7) where Czici is the ionic strength of the electrolyte solution. Obviously, eqs 6 and 7 are sufficient to determine the charge density and the surface potential for any given pH and ionic strength. We solved the equations numerically with a program implementing a nonlinear Newton method. Figure 7 represents the results of the calculations for Ade amphiphile. The electrostatic repulsion between the Oro surfaces can be calculated in the same way by considering proton dissociation from the amphiphile headgroup with a pKi of 9.2. LA9501041
