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Langmuir 2007, 23, 11684-11692
Thermodynamic and Real-Space Structural Evidence of a 2D Critical Point in Phospholipid Monolayers Lars K. Nielsen Radiometer Medical, ÅkandeVej 21, DK-2700 Brønshøj, Denmark
Thomas Bjørnholm Nano-Science Center and Department of Chemistry, UniVersity of Copenhagen, DK-2100 Copenhagen Ø, Denmark
Ole G. Mouritsen* MEMPHYS-Center for Biomembrane Physics, Department of Physics and Chemistry, UniVersity of Southern Denmark, DK-5230 Odense M, Denmark ReceiVed June 4, 2007. In Final Form: August 22, 2007 The two-dimensional phase diagram of phospholipid monolayers at air-water interfaces has been constructed from Langmuir compression isotherms. The coexistence region between the solid and fluid phases of the monolayer ends at the critical temperature of the transition. The small-scale lateral structure of the monolayers has been imaged by atomic force microscopy in the nm to µm range at distinct points in the phase diagram. The lateral structure is immobilized by transferring the monolayer from an air-water interface to a solid mica support using LangmuirBlodgett techniques. A transfer protocol that ensures preservation of the structure during the transfer has been established. The lateral structure reflecting the density fluctuations has been visualized and quantitatively characterized as the monolayer passes through a series of first-order phase transitions and ultimately approaches a critical point. The critical behavior inferred from the thermodynamic as well as the structural data is found to be consistent with the 2D Ising universality class. Additional results are presented demonstrating the presence of striped phases and coexisting domains in binary mixtures.
I. Introduction When spread on an air-water interface, amphiphilic molecules like phospholipids form monomolecular layers,1 called Langmuir films, whose bulk-phase equilibria lend themselves to twodimensional thermodynamic investigations by measurement of the relationship between surface area and surface pressure using a film balance.2 The lateral structure and organization of Langmuir layers have been studied extensively by a range of techniques, notably fluorescence microscopy3,4 and synchrotron X-ray scattering.5 Whereas scattering studies permit structural analysis of solid phases of the film at the molecular scale, fluorescence microscopy provides insight into the lateral organization of both fluid and solid phases on the µm and super-µm scales. It has been proposed that phospholipid monolayers at the airwater interface can be poised to a critical point3,4 by varying the temperature and surface pressure of the monolayer confined in a Langmuir trough. However, depending on the symmetries of the involved phases, the line of first-order transitions may actually end in a tricritical point. At critical points, molecular-scale interactions built up to macroscopic length scales, and the correlation of the critical fluctuations becomes long-ranged. The theory of critical phenomena6 predicts that systems at critical * To whom correspondence should be addressed. E-mail: ogm@ memphys.sdu.dk. URL: www.memphys.sdu.dk. (1) Knobler, C. M.; Schwartz, D. K. Curr. Opin. Colloid Interface Sci. 1999, 4, 46. (2) Albrecht, O.; Gruler, H.; Sackmann, E. J. Phys. (Paris) 1978, 39, 301. (3) Knobler, C. M. Science 1990, 249, 870. (4) McConnell, H. M. Annu. ReV. Phys. Chem. 1991, 42, 171. (5) Kaganer, V. M.; Mo¨hwald, H.; Dutta, P. ReV. Mod. Phys. 1999, 71, 779.
points display universal behavior described by scaling invariance and certain power laws associated with universal exponents. Universality implies that critical-point phenomena can be similar in magnetism, superconductivity, liquid-vapor transitions, and quark-confinement in the early universe.7 At a critical point, the system develops strong fluctuations on scales from molecules to the size of the entire system and there is no characteristic length scale. If these fluctuations could be visualized in real space, they are predicted to display a power-law distribution of sizes characterized by a universal exponent.8 In an attempt to cover the length-scale gap between optical microscopy and scattering techniques, scanning-probe techniques have been applied to lipid layers transferred onto solid supports. A substantial amount of work has been carried out to elucidate the fluctuations and the lateral structure of solid-supported aqueous bilayers9-11 because these systems are good models of biological membranes.12 Less work has been reported on solid-supported lipid monolayers in the dry state.8,13 An inherent assumption underlying this approach is that the monolayer structure during transfer can be fixated and remain essentially unperturbed by the transfer process. Reports of both the success14 and failure15 of (6) Goldenfeld, N. Renormalization group in critical phenomena; AddisonWesley: Reading, PA, 1999. (7) Stanley, H. E. ReV. Mod. Phys. 1999, 71, S358. (8) Nielsen, L. K.; Bjørnholm, T.; Mouritsen, O. G. Nature 2000, 404, 352. (9) Santos, N. C.; Castanho, M. A. Biophys. Chem. 2004, 107, 133. (10) Richter, R. P.; Be´rat, R.; Brisson, A. R. Langmuir 2006, 22, 3497. (11) Dufreˆne, Y. F.; Lee, G. U. Biochim. Biophys. Acta 2000, 1509, 14. (12) Mouritsen, O. G. Life - as a Matter of Fat. The Emerging Science of Lipidomics; Springer-Verlag: Heidelberg, Germany, 2005. (13) Sanchez, J., Badia, A. Thin Solid Films 2003, 440, 223. (14) Karg, P.; Petrov, A. G.; Sackmann, E.; Wunderlich, A. J. Mol. Electron. 1990, 6, 21.
10.1021/la7016352 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/11/2007
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this assumption exist where the structure of the monolayers at the air-water interface is either preserved or modified as a result of the transfer process. A delicate interplay between the composition of the Langmuir film, the composition of the subphase, and the nature of the solid support controls the structure of the transferred monolayer. A preservation of the fluid phase has been reported to be the biggest problem during the transfer. Condensation of the fluid phase into small sub-µm islands has repeatedly been observed. The fluctuations in lipid monolayers both in terms of density and composition serve as a fundamental physical mechanism of laterally structuring lipid films. This mechanism may be of seminal importance for a deeper understanding of small-scale domain formation particularly in lipid bilayers which are models of biological membranes.12 Lipid bilayers are known to exhibit a rich variety of lateral structures and domains on various length scales.11,16-19 Similarly, it is becoming clear that lipid domains occur in active biological membranes where they act as platforms for biological function20 and enzymatic activity.21,22 Furthermore, a number of studies of lipid monolayers and bilayers, e.g., including cholesterol, have revealed critical-point behavior in mixtures.23 In the present paper we establish the two-dimensional phase diagram of monolayers of saturated phospholipids, specifically di-myristoyl-phosphatidylcholine (DMPC), and we use this diagram as a starting point for imaging critical fluctuations. For comparison, some results will also be reported for monolayers made of a similar lipid, di-palmitoyl-phosphatidylcholine (DPPC), which has fatty-acid chains that are two carbon atoms longer. We have developed a protocol that allows us to transfer the monolayer at different points in the phase diagram without damage. This transfer protocol enables us to capture and visualize the lateral monolayer structure in the range from nm to µm using atomic force microscopy (AFM). This range of length scales is demonstrated to provide a window to probe critical fluctuations which can be measured quantitatively. Some preliminary results of our work were already reported in refs 8 and 24. In the present paper, we provide a full account of our investigations. In addition, we present results for the coexistence of phases of different symmetry, such as striped and hexagonal phases in DPPC monolayers, and coexisting domains in monolayers made from mixtures of DMPC with DSPC (di-stearoyl-phosphatidylcholine). II. Materials and Methods A. Langmuir and Langmuir-Blodgett Films. All monolayers were prepared on a commercial Langmuir trough (KSV 5000, KSV Ltd., Finland) enclosed in a box that improves temperature control and allows high humidity around the trough. The trough was placed in a room with temperature control which allowed the trough to have (15) Lee, K. Y. C.; Lipp, M. M.; Takamoto, D. Y.; Ter-Ovanesyan, E.; Zsadzinski, J. A. Langmuir 1998, 14, 2567. (16) Bagatolli, L. A. Biochim. Biophys. Acta 2006, 1758, 1541. (17) Veatch, S. L.; Keller, S. L. Biochim. Biophys. Acta 2005, 1746, 172. (18) Keller, D.; Larsen, N. B.; Møller, I. M.; Mouritsen, O. G. Phys. ReV. Lett. 2005, 94, 025701-1. (19) Rinia, H. A.; De Kruijff, B. FEBS Lett. 2001, 504, 194. (20) Jacobson, K.; Mouritsen, O. G.; Anderson, G. W. Nat. Cell Biol. 2007, 9, 7. (21) Nielsen, L. K.; Balashev, K.; Callisen, T. H.; Bjørnholm, T. Biophys. J. 2002, 83, 2617. (22) Leidy, C.; Linderoth, L.; Andresen, T. L.; Mouritsen, O. G.; Jørgensen, K. Biophys. J. 2006, 90, 3165. (23) Keller, S. L.; Anderson, T. G.; McConnell, H. M. Biophys. J. 2000, 79, 2033. Keller, S. L.; McConnell, H. M. Phys. ReV. Lett. 1999, 82, 1602. Keller, S. L. J. Phys.: Condens. Matter 2002, 14, 4763. Veatch, S. L.; Keller, S. L. Phys. ReV. Lett. 2002, 89, 268101-1. (24) Nielsen, L. K.; Bjørnholm, T.; Mouritsen, O. G. J. Phys.: Condens. Matter 2000, 12, 309.
Langmuir, Vol. 23, No. 23, 2007 11685 the same temperature as the surroundings thus minimizing any temperature gradient. 1,2-Dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-di-stearoylphosphatidylcholine (DSPC), or mixtures of DMPC and DSPC (Avanti Polar Lipids, Alabaster, AL) were dissolved in n-hexane: methanol (95:5) to a concentration between 0.6 and 1 mg/mL. The spreading from the hexane solution is much less vigorous and improves reproducibility of the isotherms compared to spreading from a chloroform solution. The lipids were spread on a pure MilliQ (Millipore Corporation, Bedford, MA) water subphase or on a subphase containing NaCl (99.99%, Aldrich). The subphase was allowed to reach the desired temperature (within 0.2 °C), controlled by circulating water, before spreading the lipids. High relative humidity (>90%) was achieved by decorating the inside of the box with “wet curtains” in the form of wet paper towels. Before compression of the monolayer, 15-30 min were allowed for solvent evaporation. Langmuir isotherms were obtained at various temperatures by lateral compression of the films. The monolayers were compressed at a constant speed of less than 0.01 nm2/molecule/min to a final surface pressure in the solid-fluid coexistence region. After reaching the desired pressure, the monolayers were allowed to equilibrate for at least 30 min. For the preparation of Langmuir-Blodgett films, freshly cleaved mica was used as solid support for the monolayers. A mica piece was immersed in the subphase either horizontally or vertically prior to the spreading of the phospholipids. Horizontally oriented substrates were manually aligned with the water surface. The monolayers were then transferred to the mica support at a constant speed of 1 mm/ min. The transfer protocol developed will be described in detail in Sec III.B. After the transfer, the supported monolayer was immediately mounted in the AFM and imaging was initiated. B. Atomic-Force Microscopy. A Nanoscope IIIa system (Digital Instruments, Santa Barbara, CA) was used for all imaging. Cantilevers with oxide sharpened silicon nitride tips (NanoProbes, Santa Babara, CA) with a nominal spring constant of 0.06 N/m were used for scanning. All imaging was carried out in contact mode with a loading force of less than 500 pN, and the force was constantly kept at a minimum by manual adjustment of the set point. The temperature is controlled by thermostating the entire monolayer rather than using an AFM temperature stage. In order to ensure that the transfer of the monolayer was successful resulting in a uniform monolayer, at least two macroscopically different regions were scanned on each sample. C. Image Analysis. In order to allow quantitative analysis of the AFM images, the color images were transformed to binary images by automatic locating the edges of the domains25 and assigning black to solid-phase domains and white to fluid-phase domains. For images of discrete domains, all domains touching the boundary of the image frame were not used in the statistical analysis.
III. Results A. Langmuir Isotherms. The isotherms of phospholipid monolayers made of DMPC and DPPC are shown in Figures 1 and 2, respectively. Upon compression at appropriate temperatures, both types of monolayer undergo a first-order phase transition from a fluid liquid-extended (LE) phase to a solid liquid-condensed (LC) phase, corresponding to a chain-ordering (condensation) process as illustrated schematically in Figure 1. At low temperatures, a coexistence region between these phases exists as indicated by the near-horizontal regions of the isotherms. This phase behavior is most clear in the case of DMPC, and we shall therefore restrict our subsequent analysis of the phase diagram to this case. The condensation is manifested macroscopically in a change, ∆A, in the film area across the coexistence region corresponding to a concomitant change in film thickness. (25) Using NIH-Image, see http://rsb.info.nih.gov/nih-image.
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Figure 3. The lateral compressibility, κ(A)in eq 1, for the isotherm of DMPC at 12 °C. The kinks in the compressibility are used as an indication of the borders of the coexistence region (marked by arrows). Figure 1. Isotherms (lateral pressure Π vs mean molecular area A) and phase diagram of a DMPC lipid monolayer at the air-water interface. The curves from a to c correspond to increasing temperatures, ranging from 12 to 20 °C in steps of one degree. The critical point at a temperature Tc is indicated by a dot. The region inside the dotted lines is the solid-liquid coexistence region, separating the solid, liquid-condensed (LC) phase to the left and the liquid (liquid expanded) (LE) phase to the right. Above the critical point as marked by the critical temperature, Tc, the two phases are identical.
Figure 4. log-log plot of the width of the coexistence region for DMPC lipid monolayers as a function of reduced temperature, (Tc - T)/Tc. The critical temperature is Tc ) 20 °C. The data are derived from the isotherms in Figure 4. The solid line is the theoretical prediction for the 2D Ising model which shows that the data for the monolayer closest to the transition is consistent with the power-law behavior pertaining to the universality class of the 2D Ising model.
Figure 2. Isotherms (lateral pressure Π vs mean molecular area A) for a DPPC lipid monolayer at the air-water interface. The approximate location of the critical point at a temperature Tc is indicated by a dot.
At the end of the coexistence region, the surface pressure increases upon further compression until the monolayer eventually collapses into a multilayer structure without any sign of an additional phase transition. The critical point at a temperature Tc marks the upper terminus of the coexistence region between the LC and LE phases. At this point, the two phases become indistinguishable (∆A f 0) and critical density (thickness) fluctuations prevail. DMPC monolayers prepared at temperatures above Tc were found to collapse at relatively low densities. On the basis of the collection of isotherms presented in Figure 1, we have constructed the two-dimensional phase diagram of the DMPC monolayer. The phase diagram is indicated by a dotted line in Figure 1. The phase boundaries were determined by locating kinks in the lateral compressibility
κ)-
1 ∂A A ∂Π T
( )
(1)
as illustrated in Figure 3, marking the beginning and the end of the plateau region. At 20 °C, there are no longer two discernible peaks in κ, and we thus take this temperature to approximate the critical temperature (Tc) of the transition. All isotherms were run
both as compression and expansion isotherms. For the barrier speeds employed, the hysteresis was negligible small. The determination of the width of the coexistence region is therefore accurate. A plot of the width, ∆A,of the coexistence region in DMPC monolayers as a function of reduced temperature (Tc - T)/Tc is shown in Figure 4. The data suggests that the approach to criticality is described by a power law
∆A ∼
( )
Tc - T β , T f Tc Tc
(2)
A fit to the four data points closest to the critical point yields an exponent value of β ) 0.135 ( 0.015 which is close to the exact value 1/8 for the 2D Ising model. Hence this finding is consistent with the lipid monolayer being in the universality class of the 2D Ising model. B. Transfer Protocol. In order to perform an investigation of the lateral, small-scale structure of the lipid monolayers using AFM, a transfer protocol is required that effectively captures the equilibrium monolayer structure as it appears on the air/water interface. The by far most intensively studied phospholipid monolayers reported in the literature are monolayers of DPPC which have been structurally characterized in the coexistence region by a number of microscopy techniques including fluorescence microscopy and Brewster angle microscopy as well
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Figure 5. Four AFM images obtained for DPPC monolayers in in the coexistence region at T ) 20 °C, transferred onto different solid supports (gray scale 2 nm). A. vertical transfer onto glass from a pure water subphase. The monolayer structure is practically invisible. Although some structural features can be discerned, the overall quality of the image does not allow assessment of any small-scale structures. B. Horizontal transfer onto mica from a pure water subphase. A well-defined structure is clearly visible with bean-shaped solid domains. However, condensation in the fluid phase has taken place thus altering the structure compared to that of the native Langmuir film. C. Vertical transfer from a 0.1 M NaCl subphase. No condensation in the fluid phase is observed but the edges of the solid bean-shaped domains appear disturbed by the transfer. D. Horizontal transfer from 0.1 M NaCl subphase. No condensation is observed in the fluid phase. Hence, he solid bean-shaped domains, when compared to to observations by fluorescence microscopy, appear to be undisturbed and well-defined by this transfer protocol.
as scanning probe microscopy. Many different domain morphologies have been reported.5,26 The most common domain shape is the so-called bean shape that always shows up when the monolayer is compressed slowly. In the low-pressure end of the coexistence region, the monolayer consists of condensed-phase bean-shaped domains surrounded by a homogeneous expanded phase. We have used this distinct monolayer morphology observed for DPPC as a bench mark for our transfer protocol. This means that the transfer of a DPPC monolayer in the coexistence region should in a reproducible manner resemble the many images recorded by fluorescence microscopy under similar conditions, both qualitatively in terms of domain shapes and quantitatively in terms of domain sizes. We have investigated the structure of a number of DPPC monolayers transferred both horizontally and vertically onto different hydrophilic solid supports including glass, quartz, silicon (26) Weis, R. M. Chem. Phys. Lipids 1991, 57, 227.
dioxide, and mica. For the subsequent analysis by AFM, it quickly became clear that mica was the support of choice. Because of its flatness, mica provides an excellent contrast between the LC and the LE phases in the AFM images. Microscope glass slides and quartz slides both have too rough a surface structure to allow assessment of the nm-scale features of the monolayers as illustrated in Figure 5A. On mica supports we have experienced condensation of the fluid phase as illustrated in Figure 5B in the case of transfer from a pure water subphase. Despite the well-defined solid domain which is transferred successfully, the fluid phase structure is changed into a network of solid-like strings with fluid-like inclusions. This condensation of the fluid phase in the transferred film is consistently observed when the monolayer is transferred from a pure water subphase onto the mica support. In the horizontal orientation as the mica supports get close to the monolayer it appears to jump into contact with the substrate leading to a sudden
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Figure 6. Pattern formation observed by AFM of lipid monolayers of DMPC approaching a critical point, corresponding to the points on the monolayer isotherms a-c in Figure 1, corresponding to T ) 12, 17, and 20 °C. The light regions represent lipid domains of the solid monolayer phase (LC) within the (dark) liquid monolayer phase (LE). The two types of domains have different heights and can therefore be imaged in the microscope. The size of the images is 6 µm × 6 µm (gray scale 2 nm).
disappearance of the water covering the substrate. The jump into contact may lead to a condensation of the fluid phase due to the rapid water flow and a resulting close contact with the substrate. The high surface charge density of mica and the presence of a permanent dipole of the phospholipids suggest that the jump into contact may be electrostatic in nature. Screening of the electrostatic force by addition of 0.1 M of the simple electrolyte NaCl to the subphase effectively eliminated the jump into contact and as expected leads to a satisfactory transfer of the monolayer preserving both LC- and most importantly LE-phase characteristics. In Figure 5C is shown the result of a vertical transfer from a 0.1 M NaCl subphase. No condensation in the fluid phase is observed, but the edges of the solid bean-shaped domains appear to be disturbed by the transfer. Finally, the result of the successful horizontal transfer of a DPPC monolayer at 20 °C in the coexistence region is shown in Figure 5D. No condensation is observed in the fluid phase and the solid bean-shaped domains appear to be undisturbed and well-defined. Films prepared at super-critical conditions are found to be unstable at high pressures as previously reported2 and are therefore not imaged. On the basis of the accordance between AFM and fluorescence microscopy imaging of the solid domains and their size and shape, we conclude that our transfer protocol is a reliable procedure to capture the lateral structure of the monolayer. C. Phase Structure of DMPC. The lateral structure of DMPC monolayers taken at three different points in the phase diagram (Figure 1) was investigated with AFM by use of the established transfer protocol described above. The lateral structure was analyzed at sub-critical, near-critical, and critical conditions corresponding to points a, b, and c in Figure 1, respectively. As mentioned above, monolayers prepared at super-critical temperatures were found not to be stable and are therefore not included in the analysis. Typical AFM images at sub-critical, near-critical, and critical conditions are shown in Figure 6. These images show a pattern of domains of height variations corresponding to the thickness difference between the LE and LC phases of 0.40.6 nm. Hence, we interpret these images as an indication of a monolayer structure with domains of one phase within the other. Near the critical point these domains are expected to be dynamic and strongly fluctuating when the monolayer is at the air-water interface but they are “caught in the act” and immobilized during the transfer process. The AFM pictures in Figure 6 reveal that there is indeed a lateral structure on a smaller scale, and that the development of this structure, as the critical point is approached, has the qualitative as well as quantitative features of passing from a region of phase separation to a region of critical fluctuations in terms of lateral thickness variations. At sub-critical conditions, corresponding to point a in Figure 1, the film consists of a majority background phase (LE in Figure 6a) with phase-separated domains of the
Figure 7. Domain distribution function, P(n), as a function of domain area, n, for monolayers of DMPC at two different temperatures.
other phase (LC). These domains are large and compact and they have a characteristic size corresponding to a broad maximum in the domain-size distribution function, P(n) as shown in Figure 7 for T ) 12 °C. n is the measured area of the domains. As the critical point is approached, Figure 6b at T ) 17 °C, corresponding to point b in Figure 1, shows that there is a proliferation of small-size domains. At the same time, the morphology of the domains changes to more ramified shapes due to the decrease of the line tension near criticality. There is no longer a characteristic length scale, and the domain-size distribution approaches a power law. Due to the poor statistics of the domain distribution function, it is not possible to clearly demonstrate to power law and extract the value of the corresponding exponent. Very close to the critical point, Figure 6c, the film structure becomes very ramified due to the critical fluctuations and the domain pattern is percolative and effectively bicontinuous, as clearly illustrated in the large 25 µm × 25 µm frame in Figure 8. For comparison, the corresponding image in the case of DPPC near its critical point is also shown in Figure 8. It is noticed that domains of many different sizes are present for both types of monolayers.
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Figure 8. Pattern formation observed by atomic force microscopy of lipid monolayers of DMPC and DPPC near their respective critical point. The size of the images is 25 µm × 25 µm (gray scale 2 nm).
Figure 10. log-log plot of the structure factor, S(q) in eq 4, for DMPC and DPPC monolayers very close to their respective critical temperatures (cf. also Figure 8). Figure 9. Structure factor, S(q) in eq 3, for DMPC monolayers for temperatures below, near, and at the critical temperature.
with x = 1. The data is therefore consistent with critical-point behavior6 which in general is described by
Near the critical point (point c in Figure 1), a calculation of the domain distribution function from the images becomes unreliable due to insufficient statistics. A quantitative analysis of the AFM images is more conveniently achieved through the circularly averaged structure factor calculated by two-dimensional fast-Fourier-transform as
S(q) ∼ [ξ-2(T) + q2]-x
S(q) ) N-1 |
∑j Fj exp(-i2πqrj)|2
(3)
where Fj ) 0, 1 is the pixel density of the LC phase in the binary image and rj is the spatial coordinate of the jth pixel. q ) |q b| is the length of a two-dimensional wave-vector and N is a normalization factor. The data presented for S(q) away from criticality were typically averaged over a large number (20-30) of 6 µm × 6 µm images. The data for S(q) in the critical region were obtained from large 25 µm × 25 µm images and only a few were needed to obtain reliable averages. The results of the structure-factor analysis are shown in Figure 9 which shows that at sub-critical conditions S(q) has a peak at finite q corresponding to the presence of a characteristic domain size. As the critical point is approached, the peak in S(q) moves toward the origin. The critical behavior is analyzed in Figure 10 which shows that at the critical point, the structure factor scales as a power law
S(q) ∼ q-2x
(4)
(5)
with an exponent x ) 1 - η/2. η is the critical exponent of the correlation function.6 ξ(T) is a correlation length that describes the range of the correlations of the fluctuations. At a critical point, the correlation length diverges ξ f ∞.6 Considering the accuracy of the data and the fact that η ) 1/8 for the 2D Ising model, the results in Figure 10 are for both DMPC and DPPC consistent with the critical point in both of these two-dimensional systems belonging to the universality class of the 2D Ising model.6 D. Other Examples of Lipid Organization in Monolayers. In this section, we shall take a brief look at two additional examples of lateral lipid organization which have not received the same experimental attention as the results presented in the previous sections. The results are however interesting because they confirm previous theoretical predictions.27,28 1. Coexistence of Hexagonal and Striped Phases. Figure 11 shows an AFM image of a DPPC monolayer transferred in the coexistence region at 33 °C. Two distinct super-structures of solid domains are visible in the image. One is an almost hexagonal pattern of circular domains which are interconnected by stripes. The diameter of the circular domains is ∼17 µm, whereas the stripes have a width of ∼2 µm. The interplay between on the one side in-plane electrostatic repulsion between dipoles forced together in the solid domains and on the other side the line tension (27) Andelman, D.; Brochard, F.; Joanny, J.-F. J. Chem. Phys. 1987, 86, 3673. (28) McConnel, H. M. Proc. Natl. Acad. Sci. U.S.A. 1987, 86, 3452.
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Figure 11. DPPC monolayer transferred at 33 °C (gray scale 2 nm). The image size is 50 µm × 50 µm. Two distinct super-structures are seen. One with hexagonally packed circular shaped domains which is interconnected by a striped phase. These super-structures in the monolayer are a result of the competition between electrostatic forces and line tension.
of the domains determines the overall super-structure. The total free energy of the domains is given by
Ftot ) Fel + Fλ
(6)
where Fel is the dipole energy and Fλ ) pλ is the line tension energy given as the domain perimeter p times the line tension λ. Examples of both hexagonal packed circular domains and the striped phase have been seen earlier in fluorescence microscopy experiments.29-31 A striped phase was observed when cholesterol was introduced to lower the line tension between the fluid and solid phases in the monolayer. Striped phase formation in the present case stems from the reduction of the line tension by the increased temperature. Coexistence of the hexagonal and striped phases has not previously been demonstrated in experiments for single-component phospholipid monolayers but has been predicted from theory.27,28 The theory also predicts that the characteristic radius and width of the phases should be of the same size (McConnell, personal communication). This is not the case for the image presented in Figure 11 where the average radius of the circular domains is about four times the width of the stripes. Although the structure shown is reproducible, additional experiments are needed to establish whether the structure represents the equilibrium structure of the monolayer at the air-water interface. 2. Small Scale Domains in Mixed Monolayers. When two phospholipids with different tail lengths are spread on the airwater interface and compressed, they are expected to phase separate because of the line tension arising from the mismatch in the carbon chain lengths.32 Computer simulations on simple (29) Rice, P. A.; McConnell, H. M. Proc. Natl. Acad. Sci. U.S.A. 1989, 86, 6445. (30) Seul, M. Physica A 1990, 168, 198. Seul, M.; Andelman, D. Phys. ReV. Lett. 1990, 64, 1903. (31) Radhakrishnan, A.; McConnell, H. M. Biophys. J. 1999, 77, 1507. (32) Jørgensen, K.; Sperotto, M. M.; Mouritsen, O. G.; Ipsen, J. H.; Zuckermann, M. J. Biochim. Biophys. Acta 1993, 1152, 135.
Figure 12. AFM image of the compositional lateral structure of a mixed monolayer of DMPC and DSPC (image size 250 nm × 250 nm, gray scale 1 nm). The image demonstrates that domain formation can occur on the nm scale. The section through the image shows that the height difference between the two types of domains are 0.4 nm in good agreement with the length difference between the acyl chains of the two different lipid species.
lattice-gas-type models show that both density fluctuations as discussed above close to a critical point as well as compositional fluctuations may occur in two-component systems of phospholipids.24,32 Such compositional variations have been observed in a monolayer consisting of a 1:1 mixture of DMPC and DSPC as shown in Figure 12. The mixing of the two lipids occurs with domains which are below 25 nm in width. This observation is in accord with findings on other lipid mixtures using neutron diffraction and AFM.33 The height difference between the domains in Figure 12 is 0.4 nm in good agreement with the difference in length of the fully extended chains of the two different lipid species. The difficulty of establishing two-dimensional phase diagrams for mixed systems directly from the compression isotherm severely limits the conclusions that can be drawn from results obtained with AFM alone regarding the similarity of the structure observed and the one expected at the air-water interface. We shall therefore only conclude that small scale domain formation does indeed occur in mixed phospholipid monolayers. We expect the fluctuating domains to be of fluid character. (33) Gliss, C.; Clausen-Schaumann, H.; Gu¨nther, R.; Odenbach, S.; Randl, O.; Bayerl, T. M. Biophys. J. 1998, 74, 2443.
2D Critical Point in Phospholipid Monolayers
IV. Discussion The nature and order of the main phase transition in phospholipid monolayers has been a subject of much debate. Based on the Gibbs phase rule, which can be applied in two dimensions, the surface pressure should remain constant in the transition region because all available degrees of freedom have been used. The isotherms presented in Figure 1 and those reported by many other investigators do not have a constant surface pressure in the transition region but exhibit a finite slope. Trace amounts of impurities, kinetic effects due to the constant compression speed, and uncontrolled humidity may indeed lead to nonhorizontal isotherms. Pallas and Pethica34 showed in a classical and very careful study of DPPC monolayers that the surface pressure stays constant in the transition region within experimental error thus providing strong evidence for the transition to be of first order. At densities beyond the LE-LC phase transition, the presence of a higher-order transition has been reported2 where lipid chains change from a tilted to a nontilted upright configuration. This second transition has been observed in phospholipid monolayers at low temperatures as a kink in the isotherm at high densities. The presence of this transition in phospholipid monolayers is often not observed,35 and our data show no evidence of such a transition. We are however not able to rule out the existence of a LC-solid crystalline (SC) transition but we do not expect it to have any influence on the data analysis presented. Based on the assumption that the LE-LC phase transition is of first order and that the critical point is not tricritical due to influence of a second transition at higher densities, it is reasonable to consider the transition within the framework of the twodimensional Ising model. The fit to the data in Figure 3 illustrates the consistency with the 2D Ising universality class for which the exact value of the exponent is β ) 1/8. Due to inherent limitations in the experiment, we are not able to approach the critical point with very high precision. We are thus not able to predict the value of the exponents with high accuracy but merely show that the data is consistent with exponent of the 2D Ising universality class. Termination of the coexistence loop in a critical point as shown in Figure 2 is in conflict with the data of Crane et al.35 These authors reported the persistence of the phase coexistence without any termination at higher temperatures. The persistence was obtained by a tenfold increase of the heating rate. Coexistence of the two phases and the termination of the coexistence region in a critical point are both equilibrium phenomena that can be hidden due to kinetic effects. All isotherms presented in Figure 2 are run at the same slow compression speed that assures that the experiment is done as close to equilibrium as possible. Moreover, the analysis of the structure factor in Figure 10, in terms of S(q) ∼ [ξ-2(T) + q2]-x with an exponent x close to one for both DMPC and DPPC, is consistent with the critical point in these two-dimensional systems being in the universality class of the 2D Ising model.6 Similarly, the general trend in the domain size distribution function, P(n), as the critical point is approached, cf. Figure 7, is in accord with P(n) approaching a power-law distribution. Since we have not determined experimentally the underlying symmetries of the various phases of our system, we wish to stress that our data and the results of the analyses for all practical purposes are consistent with the monolayer system exhibiting critical-point-like behavior. We cannot rule out that a closer (34) Pallas, N. R.; Pethica, B. A. Langmuir 1985, 1, 509. (35) Crane, J. M.; Putz, G.; Hall, S. B. Biophys. J. 1999, 77, 3134.
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examination may actually reveal that the endpoint of the coexistence region is actually a tricritical point. In order to get beyond the resolution of an optical microscope and take advantage of scanning probe methods, a transfer of the monolayers from the air-water interface to a solid support is necessary. In the present context, the main focus of the transfer has been to capture the state of the monolayer as it is at the air-water interface and to preserve its structure on the solid support. This is not an easy task, and several investigations dealing with the transfer process itself have been made. Parameters that can affect the structure of the monolayer during the transfer from the air-water interface to a solid support include the type of support and its orientation, the speed of support withdrawal from the interface, drainage of the subphase from the support, changes in monolayer structure due to changes in the properties of the subphase at the meniscus between support and the air-water interface, condensation of the monolayer on the support, as well as epitatic coupling between monolayer molecular lattice and support lattice. A universal transfer protocol does not exist since the significant parameters of the transfer process can vary according to the specific system in question. Thus, a reliable experimental protocol has to be established by experiment for every system under consideration. Specific problems for the transfer of phosphatidylcholines in the coexistence region include flow disturbances caused by the unidirectional subphase flow, as the substrate is pulled through the interface in a vertical orientation. Inspection by AFM often shows lateral and vertical channel structures that presumably arise due to drainage of the film. Reducing the transfer speed can lower this effect. The properties of the meniscus at the point of contact between the hydrophilic solid support and the air-water interface may also influence the success of the deposition of the monolayer. During initial stages of film spreading and compression, the height of the meniscus on a mica support has been shown to change, leading to deposition of molecules long before the desired surface pressure is reached.36 Changing the substrate orientation to horizontal will allow the flow to proceed in all directions, and a meniscus is only formed at the very end of the transfer process, which should improve the transfer. Preservation of the characteristics of the LE-phase has been reported to be problematic as is also illustrated in Figure 5. During or shortly after the transfer, the fluid phase condenses into a network structure that is not found on the air-water interface. The same type of network structure has been observed by fluorescence microscopy in good agreement with the image shown in Figure 5B where the discrimination is based purely on height differences. Similar condensation phenomena have been reported in other systems.37 Our observation that a jump into contact occurs when a mica support approached the monolayer horizontally and that this jump can be reduced by adding a simple electrolyte indicates that electrostatic forces between the monolayer and the substrate are also important.38 Considering the details of our experiments, the electrostatic attraction appears to arise from the interaction of the layer of dipoles formed by the phospholipids with the high surface charge density of mica. Tsao et al.39 investigated the details of such an attraction. A prerequisite for an attractive force between a charged surface and a layer of dipoles is that the dipole layer is heterogeneous as is the case in the coexistence region of DMPC. The length scale of the attractive interaction is given by the smallest of the domain size and the Debye screening (36) Yaminsky, V. V.; Nylander, T.; Ninham, B. W. Langmuir 1997, 13, 1746. (37) Sikes, H. D.; Schwartz, D. K. Langmuir 1997, 13, 4704. (38) Jensen, M. H.; Morris, E. J.; Simonsen, A. C. Langmuir 2007, 23, 8135 . (39) Tsao, Y.-H.; Evans, D. F.; Wennerstro¨m, H. Science 1993, 262, 547.
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length.39 In pure water, the Debye screening length is approximately 1 µm, and in 100 mM NaCl, it drops to approximately 1 nm thus significantly reducing the range of the charge dipole interaction.
V. Conclusion Domain formation in lipid monolayers is interesting for cell biology because monolayers are simple model systems of the lipid-bilayer component of cell membranes.12 The rich polymorphism and the level of detail to which the thermodynamic parameters are under control make monolayers especially attractive as model systems. High-resolution structural information about the monolayers can be obtained using AFM but the experimental details of the transfer to a solid substrate needed for the AFM analysis are of utmost importance. Once a transfer protocol is established, the structure and domain formation from several nanometers to a few micrometers can be assessed in a systematic manner. The equivalent of the LE-LC transition in monolayers is the main phase transition in lipid bilayers. Various functions supported
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by lipid bilayers,12,40 e.g., lipase activity and binding of proteins, have been correlated with lipid-domain formation in the nanometer range that is controlled by the underlying phase transition in the bilayer. Biological membranes contain a large number of different lipid species which under physiological conditions have been surmised to be organized heterogeneously in the form of domains or “rafts”20 in the membrane plane. The principles underlying this organization remain largely unknown. The results presented in the present paper suggest that fluctuations in physical properties of the lipid bilayer, e.g., in density or composition, constitute one possible and general physical mechanism for lipid-domain formation in biomembranes. Acknowledgment. MEMPHYS - Center for Biomembrane Physics is supported by The Danish National Research Foundation. Nano-Science Center is supported by the Danish Research Councils. Dr. Adam Cohen Simonsen is thanked for a critical reading of the manuscript. LA7016352 (40) Heimburg, T. R. Thermal Biophysics of Membranes; Wiley-VCH: Berlin, 2007.
