ARTICLE pubs.acs.org/Langmuir
Control of Effect on the Nucleation Rate for Hen Egg White Lysozyme Crystals under Application of an External ac Electric Field H. Koizumi,* S. Uda, K. Fujiwara, and J. Nozawa Institute for Materials Research, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ABSTRACT: The effect of an external ac electric field on the nucleation rate of hen egg white lysozyme crystals increased with an increase in the concentration of the precipitant used, which enabled the design of an electric double layer (EDL) formed at the inner surface of the drop in the oil. This is attributed to the thickness of the EDL controlled by the ionic strength of the precipitant used. Control of the EDL formed at the interface between the two phases is important to establishing this novel technique for the crystallization of proteins under the application of an external ac electric field.
’ INTRODUCTION It is important to determine the 3D structures of protein molecules in order to achieve structure-guided drug design and controlled drug delivery; therefore, the establishment of novel techniques for the crystallization of proteins is necessary. Much research has been focused on controlling the nucleation of protein crystals under the application of an electrostatic or current-injection field.114 In previous work,111 a dc voltage was used to apply an electrostatic or current-injection field to a protein solution, and the nucleation rate of lysozyme crystals was found to decrease for all cases. Mirkin et al. observed the reduction in the induction time for the nucleation of cytochrome c by applying a dc current-injection field.12 Hou and Chang have observed the rapid increase in the crystal size of lysozymes by applying an ac current-injection field.13 Similarly, Revalor et al. also reported a decrease in nucleation time and an increase in growth kinetics by using a trypsin inhibitor under a dc currentinjection field.14 However, the control of the nucleation rate for protein crystals is not yet satisfactory under the application of an electrostatic or current-injection field. Here, we emphasize that the electrostatic field is applied to a protein solution in our experiments. In addition, the effect of an external electric field on the nucleation rate has not been theoretically analyzed to date. Therefore, we have attempted to provide a solution from a thermodynamic perspective.15 The effect of an external electric field on the nucleation rate is determined by the magnitude of the difference in the electrical permittivity between the liquid and solid phases.1518 That is, almost all previous research observed a decrease in the nucleation rate of lysozyme crystals because the electrical permittivity of the solid is greater than that of the liquid.111 The electrical permittivity of a liquid or solid is dependent on the imposed frequency, as shown in Figure 1a. We have succeeded in obtaining both an increase and a decrease in the nucleation rate of hen egg white (HEW) lysozyme crystals15 by r 2011 American Chemical Society
changing the frequency of the applied electrostatic field, as shown in Figure 1a, so that the electrical permittivity of the liquid is greater than that of the solid. This principle can also explain why the crystal size of lysozymes rapidly increases by applying an ac currentinjection field.13 Accordingly, this crystallization technique can be used to both increase and decrease the nucleation rate for protein crystals by changing the frequency of the applied electric field. More recently, we observed that the nucleation rate increased with an increase in the frequency of the applied external electric field (800 V/cm) in the range of 1 to 5 MHz before slightly decreasing at 6 MHz, dropping significantly at 7 MHz, and finally being reduced to a nucleation rate close to that observed without an external electric field at 8 and 9 MHz.19 Such a phenomenon has also been observed by Hou and Chang,13 which is that the voltage required for protein crystallization is the smallest at around 5 MHz. These phenomena can be explained by the stability of the electric double layer (EDL) formed at the interface between two phases. We have revealed that the strength of the external electric field necessary to control the nucleation rate is ∼104 V/cm,19 which is greater than that used in the experiment (800 V/cm) by 2 orders of magnitude. In our experimental system, a drop of protein solution is surrounded by paraffin oil; therefore, a large electric potential gradient can be expected to be generated at the inner surface of the drop in the oil, as shown in Figure 1b. It is considered that such a high electric field strength could be sustained in the electric double layer (EDL) formed at the inner surface of the drop and therefore the disappearance of the effect of the external electric field on the nucleation rate could suggest that the EDL becomes unstable at higher frequency. Moreover, Received: March 28, 2011 Revised: May 26, 2011 Published: June 09, 2011 8333
dx.doi.org/10.1021/la2010985 | Langmuir 2011, 27, 8333–8338
Langmuir
ARTICLE
Figure 1. (a) Schematic diagram of the predicted dependence of the electrical permittivity of a protein solution and protein crystals on the frequency of the applied electric field. (b) Schematic diagram of the electric potential distribution in the experimental system.
Table 1. Solubility, Ceq, of Tetragonal HEW Lysozyme Crystals at 20 °C When NiCl2 Was Used As a Precipitant, Ionic Strength I, and Driving Force, Δμj0, for Nucleation without an External Electric Field at Each Concentrationa NiCl2
0.31 M
0.5 M
1.05 M
solubility, Ceq ionic strength, I
16.2 mg/mL 0.93
7.5 mg/mL 1.5
16.2 mg/mL 3.15
driving force for
3.03 kJ/mol
4.89 kJ/mol
3.03 kJ/mol
nucleation, Δμj0 a
The solubility of tetragonal HEW lysozyme crystals was measured by Li et al.23
Gagnon and Chang have shown experimentally and theoretically that the formation of the EDL between the gas and liquid phases occurs at even a few megahertz,20 which is consistent with the observation of protein crystallization.13,19 We have also observed that the effect of the external electric field on the nucleation rate increase with an increase in the cation valence of the precipitant used.21 In general, the thickness of the EDL, λ, is dependent on the electrical permittivity, εL, and the ionic strength, I, of the drop of protein solution according to22 λ2 ¼
εL kT 8πq2 I
ð1Þ
1 2
∑i mi z2i
ð2Þ
and I ¼
where k is Boltzmann’s constant, T is the absolute temperature, q is the charge of a proton, mi is the molar concentration, and zi is the valence of the precipitant ion. An increase in the precipitant cation valence causes an increase in the ionic strength, and the EDL that formed at the inner surface of the drop is thinner. Therefore, the external electric field strength sustained in the EDL increases with increasing valence of the precipitant cation if the potential drop in the EDL is constant for a certain external electric field. Accordingly, a larger precipitant cation valence causes a greater effect of the external electric field on the nucleation rate. From these results,19,21 we have suggested that the EDL could play an important role in the change in the nucleation rate under the application of an external electric field. It should be noted that the effect of the external electric field on the
nucleation rate also changes according to the precipitant concentration if such a high electric field strength can be sustained in the EDL. The solubility of tetragonal HEW lysozyme crystals was shown to have an extreme value when cations with a valence of greater than 2 were employed as a precipitant.23,24 The solubility of tetragonal HEW lysozyme crystals has a minimum value at 0.5 M, which is 7.5 mg/mL at 20 °C when NiCl2 is used as a precipitant.23 The addition of NiCl2 within 0.5 M induces a decrease in the solubility of tetragonal HEW lysozyme crystals and vice versa over 0.5 M; therefore, the solubility of 0.31 and 1.05 M solutions at 20 °C is 16.2 mg/mL,23 as shown in Table 1. The driving force, Δμj, for nucleation is generally related to the solubility, Ceq, as expressed by the following equation Δμj ¼ kT ln
C Ceq
ð3Þ
where C is the bulk concentration, k is Boltzmann’s constant, and T is the absolute temperature. The nucleation rate is expressed as a function of Δμj (eq 9), and it is therefore expected that the nucleation rate for 0.31 and 1.05 M solutions would be the same if the kinetic term was constant. However, it is predicted that the nucleation behavior under an electric field would be different between 0.31 and 1.05 M, according to the magnitude of the ionic strength of the precipitant used. In this report, the effect of the external electric field on the nucleation rate is controlled by the design of the EDL formed at the inner surface of the drop, using precipitants with different concentrations.
’ THEORETICAL BACKGROUND Effect of an External Electric Field on the Nucleation Rate. The chemical potential of the jth species in a liquid, μjL(E), and that of a solid, μjS(E), modified by an external electric field is expressed by eqs 4 and 5,1519,21 assuming that the electric field is constant, whereas the electrical permittivity varies with composition in terms of the derivative of electrostatic energy
1 j DεL j j μLðEÞ ¼ μLð0Þ þ ΩL Eh L2 j 2 DXL
ð4Þ
1 j DεS j j μSðEÞ ¼ μSð0Þ þ ΩS Eh S2 j 2 DXS
ð5Þ
and
8334
dx.doi.org/10.1021/la2010985 |Langmuir 2011, 27, 8333–8338
Langmuir
ARTICLE
where μjL(0) and μjS(0) represent the chemical potentials for zero electric field, εL and εS are the electrical permittivities, XjL and XjS are the molar fraction concentrations, ΩjL and ΩjS are the molar volumes, and EL and ES are the strengths of the external electric field, all for the liquid and solid, respectively. From eqs 4 and 5, Δμj0(E) for nucleation under the application of an electric field can be expressed as j
j
j
Δμ0ðEÞ ¼ μLðEÞ μSðEÞ
¼
j Δμ0
1 j 2 DεL j 2 DεS þ ΩL EL j ΩS ES j 2 DXL DXS
! ð6Þ
where Δμj0 is the driving force for nucleation in the absence of an external electric field (= μjL(0) μjS(0)). The conservation of dielectric flux holds at the interface between the liquid and solid: εS ES ¼ εL EL
ð7Þ
Combining eqs 6 and 7 gives j Δμ0ðEÞ
¼
j Δμ0
2 ! 1 DεS 2 j DεL j εL þ ΩL j ΩS E 2 εS DXSj L DXL
ð8Þ
The nucleation rate in the absence of an external electric field, N(0), can generally be expressed as follows25 ! 16πυc 2 γ3 Nð0Þ ¼ N0 exp f ðθÞ ð9Þ j 3kTðΔμ0 Þ2 and f ðθÞ ¼
ð1 cos θÞ2 ð2 þ cos θÞ 4
ð10Þ
where N0 depends on the diffusion of the solute in the solution (kinetic term),26 υc is the specific volume of the molecule, γ is the interfacial free energy, k is Boltzmann’s constant, f(θ) is the shape factor for nucleation varying from 0 to 1, and θ is the wetting angle. The nucleation rate under an external electric field, N(E), can be described using the expression for the driving force for nucleation, Δμj0(E), in place of Δμj0 in eq 9. Therefore, the driving force for nucleation under an external electric field, Δμj0(E), can also be calculated on the basis of the change in the nucleation rate, with and without an external electric field, as we have previously described in detail:19 0 1 NðEÞ 16πυc 2 γ3 f ðθÞ@ 1 1 A ð11Þ ln ¼ j j 3kT Nð0Þ ðΔμ0 Þ2 ðΔμ0ðEÞ Þ2 In our calculation, the shape factor f(θ) is unity, the reason for which is detailed in our previous report.19 Thus, the required strength of the external electric field, EL, can be estimated on the basis of the calculated driving force, Δμj0(E), for nucleation under an external electric field using eqs 8 and 11. Role of the Electric Double Layer. In the experiment, a drop of protein solution is immersed in low-density paraffin oil (F = 0.860.89 g/m3), as shown in Figure 2. The relative permittivity of the drop of protein solution is approximately 70, and that of paraffin oil is approximately 2; therefore, the bulk solution is electrically conductive and the distribution of the electric potential in a drop of the bulk solution is flat, as illustrated in Figure 1b,
Figure 2. Schematic illustration of the “containerless” batch setup with electrodes placed on both sides of a drop of solution.
with an electric field of almost zero. However, an EDL with a large electric potential gradient is formed at the inner surface of the drop in the oil,19 as shown in Figure 1b. A decrease in electric potential of ∼1 mV in an ∼1-nm-thick EDL would generate an external electric field of ∼104 V/cm, which is comparable to the value calculated analytically (∼104 V/cm). Equation 1 shows that the thickness of the EDL, λ, is dependent on the electrical permittivity, εL, and ionic strength, I, of the drop of protein solution. It should be noted that the thickness of the EDL is determined by the ionic strength, I, of the drop of solution, assuming that the electrical permittivity, εL, of the drop is almost the same for all precipitants used. The ratio of the EDL thickness for 0.5 and 1.05 M solutions, λ1.05 M/0.5 M, when NiCl2 is used as a precipitant is described using ionic strengths of 0.5 M, I0.5 M, and 1.05 M, I1.05 M, as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=I1:05 M λ1:05 M=0:5 M ¼ ð12Þ 1=I0:5 M The strength of the electric field, E, is given by E µ 1/λ. Therefore, the resulting electric field strength can be evaluated on the basis of the ionic strength of the precipitant used.
’ EXPERIMENTAL SECTION HEW lysozyme was purchased from Seikagaku Kogyo Co. Ltd., which was purified by repeated crystallization (six times) and then lyophilized. Solutions of 114 mg/mL HEW lysozyme and 0.62, 1.0, and 2.1 M NiCl2 were prepared and mixed in equal volumes. The prepared solutions were passed through a filter with a pore size of 0.20 μm to remove any foreign matter or large protein aggregates. The resulting solutions, containing 57 mg/mL HEW lysozyme and 0.31, 0.5, and 1.05 M NiCl2 at pH 4.5, were used in the crystallization experiments. Crystallization experiments were conducted at 17 ( 0.2 °C using the containerless batch method developed by Chayen.27 As shown in Figure 2, a drop of solution is suspended between two oil layers, a bottom layer of high-density oil and a top layer of low-density oil, such that the drop of solution is not in contact with the container walls. In this experiment, fluorinert (F = 1.68 g/m3) and paraffin (F = 0.860.89 g/m3) were used as high- and low-density oils, respectively. The distance between the electrodes was 0.5 cm, and the drop of solution was 10 μL in volume. An external ac electric field of 800 V/cm was applied at 1 MHz. Crystals were nucleated in drops of solution with and without the application of an external electric field and were observed using an optical microscope after 24 h. Table 1 summarizes the ionic strength, I, and driving force, Δμj0, for nucleation without an external electric field for each concentration. The ionic strength was calculated using eq 2, assuming that the precipitant 8335
dx.doi.org/10.1021/la2010985 |Langmuir 2011, 27, 8333–8338
Langmuir
ARTICLE
crystallization experiments were performed at 7 ( 0.2 °C for the 1.05 M concentration. The driving force, Δμj0, for nucleation at 7 °C in the absence of an external electric field for 1.05 M is discussed later.
Figure 3. Distribution of crystals in a drop when NiCl2 was used as a precipitant with and without the application of an external electric field at 17 °C in the case of NiCl2 at (a) 0.31, (b) 0.5, and (c) 1.05 M. (d) Distribution of crystals in a drop when 1.05 M NiCl2 was used as a precipitant, with and without the application of an external electric field at 7 °C. was completely ionized in solution. Δμj0 for nucleation in the absence of an external electric field was estimated using eq 3, assuming that the solubility was almost the same between 17 and 20 °C. Furthermore,
’ RESULT AND DISCUSSION Figure 3ac shows the crystal distributions in drops when NiCl2 was used as a precipitant, with and without the application of an external electric field, at 17 °C in the case of 0.31, 0.5, and 1.05 M solutions, respectively. Let us first focus on the nucleation behavior without an external electric field. As shown in Figure 3b, the nucleation rate for the 0.5 M solution was the greatest. The nucleation rates for the 0.31 M (Figure 3a) and 1.05 M (Figure 3c) solutions were almost the same and were smaller than that for the 0.5 M solution. As shown in Table 1, these results reflect the magnitude of Δμj0 for nucleation without an external electric field, as estimated from the solubility of tetragonal HEW lysozyme crystals in the solution. In contrast, the nucleation behavior with an external electric field was different among the NiCl2 precipitants with different concentrations. The external electric field had little effect on the nucleation rate when 0.31 M NiCl2 was used as a precipitant, and the nucleation rate for 0.5 and 1.05 M NiCl2 increased under the application of an external electric field. In particular, the nucleation rate for the 1.05 M solution was greater than that for the 0.31 M solution, despite the almost equal nucleation rates for 1.05 and 0.31 M without an external electric field. This is consistent with the magnitude of the ionic strength for 0.31 and 1.05 M solutions, as shown in Table 1. The effect of the external electric field on the nucleation rate increased with an increase in the ionic strength of the precipitant used, which supports the idea that a high electric field strength can be sustained in the EDL formed at the inner surface of the drop. Figure 3b shows that the number of crystals per drop increased from 3 to 7 on average when 0.5 M NiCl2 was used as a precipitant; the nucleation rate was 2.3 times greater with an external electric field than without. However, in the case of the 1.05 M solution, the number of crystals per drop increased from 0 to 1 on average, and a comparison of the increase in the nucleation rate with and without an external electric field could not be made. Therefore, the nucleation rate for the 1.05 M solution with and without an external electric field was also observed at 7 °C. Figure 3d shows the crystal distributions in drops when 1.05 M NiCl2 was used as a precipitant, with and without the application of an external electric field, at 7 °C. The number of crystals per drop increased from 1 to 6 on average; therefore, the nucleation rate with an external electric field was 6 times greater than that without. Therefore, the effect of the external electric field for the 1.05 M solution was significantly greater than that for the 0.5 M solution (2.3 times), assuming that the temperature difference (17 °C (Figure 3b) and 7 °C (Figure 3d)) does not have a noticeable effect on the kinetics for nucleation. Consequently, the order for the effect of the external electric field on the nucleation rate was 1.05 M > 0.5 M > 0.31 M. In general, the electrical permittivity of the liquid, εL, slightly decreased upon increasing the concentration of the precipitant in the solution.28 This suggests that the magnitude of the difference in the electrical permittivity between the liquid and solid is smaller with increasing concentration of the precipitant used when the electrical permittivity of the liquid, εL, is larger than that of the solid, εS; therefore, it is predicted that the effect of the 8336
dx.doi.org/10.1021/la2010985 |Langmuir 2011, 27, 8333–8338
Langmuir
ARTICLE
Table 2. Parameters Used to Calculate the Strength of the External Electric Field Necessary to Cause an Increase in the Nucleation Ratea,b εδ
Ωjδ 3
protein solution, δ = L protein crystal, δ = S
∂εδ/∂Xjδ
(m /mol)
(C /N m )
(C2/N m2)
102
6 1010
5 1010
2
10
10
2
2
2.6 10
4 109
The interfacial free energy, γ, was measured by Vekilov et al.31 Subscripts L and S denote liquid and solid, respectively. b γ = 1 mJ/m2, υc = 1026 m3. a
external electric field on the nucleation rate is smaller according to an increase in the concentration of the precipitant used. However, the observed phenomenon indicates the inverse trend, which could imply that the change in the ionic strength has a larger influence on the nucleation rate than does the slightly change in the electrical permittivity. Here we discuss if the ratio of the nucleation rate (6 times greater with than without an external electric field for 1.05 M NiCl2) corresponds to the change in the thickness of the EDL associated with the ionic strength of the precipitant. First, let us evaluate the strength of the external electric field for the case of 1.05 M NiCl2. The parameters used for the calculation are listed in Tables 1 and 2. The dependence of the electrical permittivity on the protein concentration, (∂εδ)/(∂Xjδ), for the liquid and solid (δ = L or S) was estimated from the values measured by Pennock and Schwan29 and Takashima,30 respectively. The interfacial free energy, γ, was measured by Vekilov et al.31 The average increase in the number of crystals per drop, from 3 to 7, upon application of an external electric field for 0.5 M NiCl2 resulted in the calculation of a required electric field strength of 1.2 104 V/cm using eqs 8 and 11. The ionic strengths of the precipitant were calculated to be 1.5 and 3.15 for 0.5 M NiCl2 and 1.05 M NiCl2, respectively, as shown in Table 1. Thus, the ratio of the EDL thickness in the two solutions λ1.05 M/0.5 M, was estimated to be approximately 0.7 on the basis of eq 12. It should be noted that although crystallization experiments for 0.5 M (Figure 3b) and 1.05 M (Figure 3d) solutions were conducted at different growth temperatures, the difference in growth temperature (17 vs 7 °C) does not substantially change the results obtained using eq 12. It is therefore predicted that the electric field strength in the case of the 1.05 M solution will be 1.4 times greater than that for the 0.5 M solution, thus an effective electric field strength of 1.7 104 V/cm would be obtained. Second, Δμj0(E) for nucleation with an external electric field should also be estimated for the case of 1.05 M NiCl2 using eq 8. The ratio of the nucleation rate with and without an external electric field can then be obtained for 1.05 M NiCl2 by substituting the estimated Δμj0(E) into eq 11. To estimate Δμj0(E) for nucleation with an external electric field, Δμj0, nucleation at 7 °C without an external electric field was estimated for the case of 1.05 M NiCl2 because the solubility for a 1.05 M solution was not measured by Li et al.23 at 7 °C. For this, the kinetic term N0 in eq 9 is evaluated. Figure 3a,c shows that the distribution profile of the nucleation rate for the 0.31 M solution without an external electric field was almost the same as that for the 1.05 M solution without an external electric field at 17 °C. This suggests that the nucleation rate is dependent only on Δμj0, regardless of the precipitant concentration in the experimental range (i.e., it is expected that the kinetic term N0 in eq 9 is
constant). Therefore, N0 calculated for the case of 0.5 M NiCl2 can be applied to every condition for the NiCl2 precipitant. Δμj0 for nucleation at 7 °C without an external electric field in the case of 1.05 M NiCl2 was then estimated to be 4.78 kJ/mol by substituting N0 and the nucleation rate at 7 °C without an external electric field for 1.05 M NiCl2, N(0), into eq 9. As a result, the ratio of the nucleation rate with and without an external electric field for 1.05 M NiCl2 was evaluated to be 6.3 by substituting the estimated effective electric field strength (1.7 104 V/cm) and Δμj0 for nucleation without an external electric field (4.78 kJ/mol) into eqs 8 and 11. The estimated value is almost the same as that obtained from Figure 3d, which suggests that the difference in the effect of the external electric field on the nucleation rate can be attributed to the change in the thickness of the EDL due to the ionic strength of the precipitant. Therefore, the effect of the external electric field on the nucleation rate can be controlled by designing the EDL formed at the inner surface of the drop by changing the ionic strength of the precipitant used.
’ CONCLUSIONS The effect of the external electric field on the nucleation rate increased with an increase in the concentration of the precipitant used. A larger ionic strength of the precipitant resulted in a greater effect of the external electric field on the nucleation rate. This is attributed to the change in the thickness of the EDL formed at the inner surface of the drop, which is thinner with increasing ionic strength of the precipitant; therefore, a larger electric field strength can be sustained in the EDL with an increase in the ionic strength of the precipitant. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported in part by a grant-in-aid for young scientists (B) (grant no. 22760001) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. ’ REFERENCES (1) Taleb, M.; Didierjean, C.; Jelsch, C.; Mangeot, J.; Capelle, B.; Aubry, A. J. Cryst. Growth 1999, 200, 575–582. (2) Taleb, M.; Didierjean, C.; Jelsch, C.; Mangeot, J.; Aubry, A. J. Cryst. Growth 2001, 232, 250–255. (3) Nanev, C.; Penkova, A. J. Cryst. Growth 2001, 232, 285–293. (4) Charron, C.; Didierjean, C.; Mangeot, J.; Aubry, A. J. Appl. Crystallogr. 2003, 36, 1482–1483. (5) Mirkin, N.; Frontana-Uribe, B.; Rodriguez-Romero, A.; HernandezSantoyo, A.; Moreno, A. Acta Crystallogr. 2003, D59, 1533–1538. (6) Moreno, A.; Sazaki, G. J. Cryst. Growth 2004, 264, 438–444. (7) Penkova, A.; Gliko, O.; Dimitrov, I.; Hodjaoglu, F.; Nanev, C.; Vekilov, P. J. Cryst. Growth 2005, 275, e1527–e1532. (8) Penkova, A.; Pan, W.; Hodjaoglu, F.; Vekilov, P. Ann. N.Y. Acad. Sci. 2006, 1077, 214–231. (9) Hammadi, Z.; Astier, J.; Morin, R.; Veesler, S. Cryst. Growth Des. 2007, 7, 1472–1475. (10) Al-Haq, M.; Lebrasseur, E.; Choi, W.; Tsuchiya, H.; Torii, T.; Yamazaki, H.; Shinohara, E. J. Appl. Crystallogr. 2007, 40, 199–201. (11) Perez, Y.; Eid, D.; Acosta, F.; Marin-Garica, L.; Jakoncic, J.; Stojanoff, V.; Frontana-Uribe, B.; Moreno, A. Cryst. Growth Des. 2008, 8, 2493–2496. 8337
dx.doi.org/10.1021/la2010985 |Langmuir 2011, 27, 8333–8338
Langmuir
ARTICLE
(12) Mirkin, N.; Jaconcic, J.; Stojanoff, V.; Moreno, A. Proteins: Struct., Funct., Bioinf. 2008, 70, 83–92. (13) Hou, D.; Chang, H. Appl. Phys. Lett. 2008, 92, 223902. (14) Revalor, E.; Hammadi, Z.; Astier, J.; Grossier, R.; Garcia, E.; Hoff, C.; Furuta, K.; Okustu, T.; Morin, R.; Veesler, S. J. Cryst. Growth 2010, 312, 939–946. (15) Koizumi, H.; Fujiwara, K.; Uda, S. Cryst. Growth Des. 2009, 9, 2420–2424. (16) Uda, S.; Huang, X.; Koh, S. J. Cryst. Growth 2005, 281, 481–491. (17) Huang, X.; Uda, S.; Yao, X.; Koh, S. J. Cryst. Growth 2006, 294, 420–426. (18) Huang, X.; Uda, S.; Koh, S. J. Cryst. Growth 2007, 307, 432–439. (19) Koizumi, H.; Fujiwara, K.; Uda, S. Cryst. Growth Des. 2010, 10, 2591–2595. (20) Gagnon, Z.; Chang, H. Appl. Phys. Lett. 2008, 93, 224101. (21) Koizumi, H.; Uda, S.; Fujiwara, K.; Nozawa, J. J. Cryst. Growth 2010, 312, 3503–3508. (22) Sharp, K.; Honig, B. J. Phys. Chem. 1990, 94, 7684–7692. (23) Jie Li, S.; Matsuura, T.; Tanaka, H.; Nakagawa, A.; Tsukihara, T.; Ataka, M. J. Cryst. Growth 2005, 276, 222–229. (24) Benas, P.; Legrand, L.; Ries-Kautt, M. Acta Crystallogr. 2002, D58, 1582–1587. (25) Chernov, A. Modern Crystallography III. Crystal Growth; SpringerVerlag: Berlin, 1984. (26) Petsev, D.; Chen, K.; Gliko, O.; Vekilov, P. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 792–796. (27) Chayen, N. Protein Eng. 1996, 9, 927–929. (28) Buchner, R.; Hefter, G.; May, P. J. Phys. Chem. A 1999, 103, 1–9. (29) Pennock, B.; Schwan, H. J. Phys. Chem. 1969, 73, 2600–2610. (30) Takashima, S. J. Polym. Sci. 1962, 62, 233–240. (31) Vekilov, P.; Monaco, L.; Thomas, B.; Stojanoff, V.; Rosenberger, F. Acta Crystallogr. 1996, D52, 785–798.
8338
dx.doi.org/10.1021/la2010985 |Langmuir 2011, 27, 8333–8338
