bending mechanics and organization in biological membrances

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Bending Mechanics andMolecular Organizationin Biological Membranes

Jay T. Groves

Department of Chemistry, University of California, Berkeley, California 94720;email: [email protected]

Annu. Rev. Phys. Chem. 2007. 58:697717

First published online as a Review in Advance onJanuary 2, 2007

TheAnnual Review of Physical Chemistryis online athttp://physchem.annualreviews.org

This articles doi:10.1146/annurev.physchem.56.092503.141216

Copyright c2007 by Annual Reviews.All rights reserved

0066-426X/07/0505-0697$20.00

Key Words

lipid, curvature, force transduction, interferometry, fluorescence

Abstract

The underlying structure of cell membranes consists of a highlyheterogeneous fluid lipid bilayer. Within this milieu, complexes of

proteins transiently assemble and dissolve in the performance ofthe functions of life. The length scales of these coordinated spatia

rearrangements can approach the size of the cell, itself, enablingdirect visualization in some cases with tantalizing clarity. There has

been much interest in the physical driving forces responsible for the

assembly of organized structures in cell membranes. Cholesterol-mediated miscibility phase separation within the lipid bilayer has

attracted enormous attention over the past decade. This, however,

is not the only ordering principle at play. In the following sections, Ireview recent experimental observations of bending-mediated forcetransduction and molecular organization in lipid membranes. These

results have emerged largely from new experimental methodologieswhich are discussed in parallel.

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INTRODUCTION

The two-dimensional character of cell membranes allows bending into three-dimensional shapes, which can lead to curvature gradients along the membrane.

The constituents of membranes (as individual lipid or protein molecules, as wellas extended organizations such as phase-separated domains) may exhibit differential

responses to curvature. Consequently, curvature gradients could provide a driving

force for the spatial sorting of membranes into patterns of composition that bothreflect and potentially feed back onto the membrane geometry (14).

Over molecular length scales, relationships between membrane curvature andmolecular structure are well known. Membrane binding proteins and protein assem-

blies have intrinsic, minimum energy shape and thus naturally congregate in suitablycurved regions of the membrane. Correspondingly, curved protein structures tend to

bend the membrane until the bending strain energy is equalized between the lipid andprotein components of the complex. Recent reviews (5, 6) discuss the importance of

these and other mechanisms. The relative sizes of the hydrophobic and hydrophilicregions of lipid molecules can also lead to curvature preferences, at least within one

leaflet of the bilayer. Composition asymmetry between the two leaflets can lead to

bilayer membranes with a net intrinsic curvature. Complex behavior can arise inmixed systems, with curvature and composition both becoming spatially modulatedin coordination (710).

At length scales well beyond molecular dimensions, other mechanisms of cur-

vature coupling may arise. For example, components or domains in the membranewithout any intrinsic curvature of their own may nonetheless be selectively driven

along gradients of curvature. Bending rigidity differences between domains createdifferential driving forces and a preferred spatial arrangement with minimum strain

energy. Recent experimental observations specifically reveal such driving forces, andare discussed further below (10, 11). A general overview of the material properties of

membranes and consequential relationships between curvature and spatial organiza-

tion has been provided in a recent review (12).In the following sections, I review a collection of recent imaging and manipula-

tion experiments that probe bending-mediated interactions in membranes. Although

this work is broadly inspired by the potential roles of membrane bending-mediatedmechanisms of force transduction and controlled spatial organization in living cells,

it emphasizes reconstituted lipid bilayer systems in which precise physical measure-

ments can be made. I hope this material contributes to a foundation of understandingthe mechanical properties of cell membranes and facilitates extrapolation to the com-

plex environment within living cells.

MEMBRANE TOPOGRAPHY IMAGING

The ability to image membrane topographical features down to the nanometer scale iscritical to the study andunderstanding of membrane curvature andbending-mediated

processes. Reflection interference contrast microscopy (RICM) has been the domi-nant method of imaging topographical features of membranes near surfaces for over

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a decade, and its applications have been reviewed (13). More recently, fluorescenceinterference contrast (FLIC) imaging has emerged as a powerful alternative to RICM

(14, 15). Additionally, intermembrane Forster resonance energy transfer (FRET) hasbeen adapted to resolve molecular-scale topographical features with subnanometer

resolution (1618). I discuss applications of these newly emergent fluorescence tech-niques to membrane topographical imaging below.

Interferometric imaging techniques, such as RICM and FLIC,intrinsicallyrequirea planar interface for their performance. Intermembrane FRET is greatly facilitated

in a planar configuration as well. Thus exploring membrane topographical structuresby these techniques requires a planar configuration in which the membrane is also

relatively free to adopt three-dimensional shapes. Supported membranes, which canbe assembled by the adsorption and fusion of small unilamellar vesicles with silica

substrates, are planar, exhibit relatively unhindered lateral fluidity, and are widelyused as model membrane systems (1922). However, the ability of a supported mem-

brane to bend away from the supporting substrate is severely restricted owing to

strongly attractive van der Waals forces. A second membrane may be deposited ontop of a preformed supported membrane, either by the rupture of a giant unilamel-

lar vesicle (GUV) (17, 18, 23, 24) or by a combination of Langmuir-Blodgett andLangmuir-Schaeffer monolayer-transfer techniques (25, 26). In either case, the sec-

ond membrane in this supported intermembrane junction exhibits enhanced freedomto form three-dimensional structures and has proven to be a useful model system for

studies of membrane topographical bending effects. The GUV rupture method canalso produce extremely weak adhering junctions, here referred to as Type2 (23), which

likely cannot be produced by the monolayer-transfer methods. Figure 1illustratesintermembrane FRET and FLIC images of the two junction types.

FRET occurs between membranes, which have been doped with complementaryfluorescent probes, when the intermembrane spacing is comparable with the Forster

distance for the probe pair (5 nm). Quantitative analysis of FRET efficiency pro-

vides measurement of intermembrane spacing with subnanometer precision (1618).Figure 2 depicts a general schematic for the interpretation of intermembrane FRET.

The rate,kT, of nonradiative energy transfer from a donor to a population of accep-tors, which are distributed in an offset plane, is given by

kT =R 602Dz4

, (1)

where is the concentration of acceptor molecules, R0 is the Forster distance[5 nm for the Texas Red-NBD (7-nitrobenz-2-oxa-1,3-diazol-4-yl) pair (27)], Dis the fluorescence lifetime of the donor in the absence of acceptors, and z is the

separation distance between the donor and the plane of acceptors. Two leaflets ofthe bilayer membrane result in two planes of acceptors, separated from each other

by 4 nm. The NBD chromophore on the commonly used, tail-labeled NBDPC(NBD-phosphatidylcholine) preferentially localizes in the glycerol/upper-chain re-

gion of the membrane (28); it can be taken to occupy a single plane for analysis. Weobtain the total FRET efficiency,E, by summing up the different transfer pathways,

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Figure 1

Forster resonance energytransfer (FRET) andfluorescence interferencecontrast (FLIC) images ofType 1 and Type 2supported intermembrane

junctions. Schematics of thetwo junction types areillustrated inaandb,respectively. Type 1junctions are characterizedby close membraneapposition (severalnanometers) and efficientintermembrane FRET.(c) Fluorescence from TexasRed fluorophores in theupper membrane (left) andthe corresponding FRET

quenching footprint inNBD fluorophores in thelower membrane (right). Nointermembrane FRET isobserved in Type 2 junctions(d), which have much largerintermembrane spacings(3060 nm). (e,f) FLICimages of both junctiontypes, with correspondingthree-dimensional plots(g,h). Thermal fluctuationsof the membrane (5 nm inamplitude) are readilyvisible by FLIC in Type 2junctions.

denoted with primes:

E =k T + k

T+

1D + kT + k

T+

. (2)

Analysis of FRET efficiency using Equations 1 and 2 directly provides the separation

distance between probe molecule planes up to approximately 10 nm. Beyond thisdistance, interference techniques are more useful.

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z r

Figure 2

Schematic illustration of the intermembrane Forster resonance energy transfer (FRET)configuration. A single probe molecule in one membrane can, in general, resonantly transferenergy with one of multiple probes in the other membrane. This leads to a fourth-powerdependence of FRET efficiency with intermembrane spacing (z), in contrast to the canonicalsixth-power dependency generally encountered for one-to-one molecular FRET between adonor and an acceptor.

FLIC is achieved by positioning the sample near a reflective interface. For sup-ported membrane junctions, one can easily accomplish this by using oxidized silicon

wafers in which the oxide layer provides a controllable transparent spacer and thesilicon/silicon-oxide interface provides a reasonably good reflector. The reflection

coefficient,rf, is 0.46 at 645 nm. The incident excitation light and its counterprop-agating reflection create an optical standing wave near the surface. The intensity of

the excitation is thus a function of distance from the reflective interface (Figure 3).Because interference is in the near field, even incoherent light, such as from a mer-

cury arc lamp, is perfectly suitable for FLIC excitation. Emitted fluorescent pho-

tons also exhibit a self-interference, which is angular in nature but has an identical

z(nm)

Bulk water

Trapped water

l(z)

100

0

Figure 3

Schematic of membranetopography imaging byfluorescence interferencecontrast (FLIC). Reflectionof excitation light off thereflectivesilicon/silicon-oxideinterface creates an opticalstanding wave with a staticintensity profile,I(z). The

fluorescence intensity ofprobes in the membrane is afunction of their verticalposition in the standingwave excitation.



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z-dependence as the standing wave intensity, except at the fluorescence emissionwavelength. We can compute the fluorophore height from the observed fluorescence

intensity, which enables topographical mapping of the membrane surface. Maximallyprecise interpretation of FLIC requires integration over the excitation and emission

spectral bands, as well as the angular spread of incident and collected light (deter-mined by the excitation and emission numerical apertures of the imaging configura-

tion). Alternatively, we can make a relatively simple interpretation, assuming normallight propagation, and monochromatic excitation and emission lines. In this case, the

fluorescence intensity,IF, is approximated by

IF

(1 rf)

2 + 4rfsin2

ex

2

(1 rf)

2 + 4rfsin2

em

2

. (3)

The arguments, ex and em, are given by (4ex)(nwz + n0z0) and (4em)(nwz +

n0z0), respectively. Indices of refraction for water (1.33) and silicon oxide (1.46) are

represented bynw andn0,z is the height above the oxide surface, and z0 is the ox-ide thickness. The excitation and emission wavelengths, ex and em, are 560 and

645 nm, respectively, when using the Texas Red fluorophore. This approximation has

a maximum error of2 nm over the distance range of typical supported membranejunction experiments (575 nm), compared with more involved calculations that in-clude the angular spread of incident and collected light, as well as spectral bandwidth

(14, 15, 29, 30).

PROTEIN SORTING AT INTERMEMBRANE JUNCTIONS

Several studies of the intercellular synapses between immune cells suggest that me-

chanical bending of the membrane can drive protein sorting and influence signaltransduction events. Such bending effects can manifest at the molecular level, at

which intermembrane protein complexes of differing sizes become mutually repul-

sive as a result of the mechanical deformations of the membrane they induce (3134).This mechanism amounts to a size exclusion effect and is illustrated in the context of

the T cellimmunological synapse inFigure 4(12, 35).We have employed FLIC imaging of supported intermembrane junctions to study

the strength and efficacy of membrane bending-mediated size exclusion as a mech-anism of protein sorting (24, 36). In these experiments, antibodies were bound to

ligands that had been incorporated into the first supported membrane. The anti-body layer, which was typically studied at coverage densities of 0.5 times the max-

imum density, consisted of freely diffusing proteins prior to the deposition of thesecond membrane. After the rupture of a GUV onto this protein-covered supported

membrane, protein patterns with characteristic length scales spontaneously emerged

within the intermembrane junction. FLIC images of membrane topography illustratethat the membrane structure is reflective of the protein patterns (Figure 5). Further-more, the consistent 14 2-nm height of the membrane topographical features sug-

gests that the orientation of the antibody is with the Fc domain facing away from the

interface, based on the known structure of these proteins from crystallographic data.

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Figure 4

(a) Schematic drawing of animmunological synapsebetween a T cell and anantigen presenting cell(APC). (b) Fluorescenceimage of the synapse

illustrating the positions ofT cell receptor (TCR)(green) and lymphocytefunction associated antigen(LFA) (red). Cognateligands on the APC, majorhistocompatibility complex(MHC), and intercellularadhesion molecule (ICAM)are organized into acomplimentary structure.TCR-MHC andLFA-ICAM complexes have

preferred intermembraneseparations of 15 and42 nm, respectively. Thusmembrane bending energyis reduced by segregatingthe complexes (c).

The observed protein patterns do not represent equilibrium configurations. Pre-sumably, the equilibrium state would be a flat membrane junction from which all

proteins had been excluded. In most experiments there was a large area to which theprotein could escape, and the mechanical strain energy in the membrane is clearlyminimized when it is not bent. Nonetheless, characteristic length scales for the pro-

tein patterns were observed. This has been attributed, in part, to a kinetic processwhereby the protein is plowed over the surface by the second membrane as it ad-

heres. The protein is driven into densely packed regions until it ultimately jams, andthe force generated by membrane bending strain is no longer sufficient to drive the

process. This interpretation is supported by the observation of the reduced lateralmobility of the protein in the dense domains within the junction. Although this is

likely to occur in some cases, it is not the only plausible mechanism that determinesthe final pattern.

We have analyzed observed protein patterns within model intermembrane junc-tions in terms of the thermal fluctuation spectrum of the membrane just prior to

touch down (37). These results suggest that coupling of membrane fluctuations to

protein mobility may also contribute to the final pattern. Coordination of timescalesbetween protein lateral mobility with the length and timescales of membrane thermal



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Figure 5

A supported intermembrane junction in which antibodies are bound to the lower membrane.Fluorescence interference contrast (FLIC) imaging of the upper membrane revealstopographical features (a) that reflect the distribution of fluorescently labeled antibodies (b). Aschematic of the structure is illustrated in c, and a three-dimensional topography mapcalculated from a marked region of the FLIC data is plotted in d.

fluctuations is required for patterning to occur. Only membrane modes that are slowenough to couple to protein mobility drive intermembrane protein patterns. How-

ever, the long wavelength modes that proved most important in these experiments

are not likely to exist in live cell membranes owing to the enhanced stiffness providedby coupling to the cytoskeleton. Nonetheless, similar processes may possibly occur

in live cells but on different length scales.

MEMBRANE BENDING FLUCTUATIONS

Intercellular junctions create a complex environment in which a variety of collec-

tive molecular motions, over relatively long length scales, can become coupled toindividual molecular interactions (35). The kinetic on rate for binding of an in-

tercellular receptor-ligand pair, for example, is intimately associated with the local

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geometrical configuration of the two membranes and their fluctuations (32). Accu-rate models of membrane thermal fluctuationdynamics are thus essential components

of an effective description of macromolecular interactions at membrane interfaces.The spatiotemporal topography of the relatively free upper membrane of a Type

2 junction (see Figure 1) has been imaged by FLIC microscopy with diffractionlimited lateral spatial resolution and 2-nm topographical resolution at five frames

per second (Figure 6) (38). Using this technique to perform spatiotemporal thermal

Figure 6

(a) Time series offluorescence interferencecontrast (FLIC) images ofthe upper membrane in aType 2 supportedintermembrane junction,along with correspondingthree-dimensionaltopography plots. (b) Spatialcorrelation function of

fluctuation displacement.The solid line represents thebest fit of the experimentaldata to Equation 5.



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b

20

10

(nm2)

0

0 0.5 1.0

Figure 6

(Continued)

fluctuation spectroscopy, investigators have observed strong hydrodynamic damping

of thefluctuation timescale (10,000-fold)when themembranesare near an interface.Quantitative comparison between these measurements and theoretical descriptions

of confined hydrodynamic effects, which have been developed based on Oseen in-

teraction kernels (3942), provided experimental confirmation of the models. Such

hydrodynamic damping effects are likely to exist in junctions between living cells, inwhich they may dominate the binding kinetics of membrane receptor proteins.It is convenient to describe the membrane bending energy and hydrodynamic in-

teractions based on Fourier decompositions. However, such mode analysis requireswell-defined boundary conditions and has not been easily implemented in the in-

terpretation of FLIC data. An alternative analytical strategy based on spatial andtemporal correlation functions has proven effective. The free-energy functional of a

fluctuating membrane can be approximated by

F

A

dr

1

2(2h(r))2 +

1

2h(r)2

, (4)

where is the bending rigidity, is the spring constant for an ad hoc harmonic

confinement potential,Ais the area of the system, and h(r) is the local displacementfrom the average height at positionr. The membrane in a Type 2 junction is held

in place by occasional pinning sites; the collective effect of these is incorporated viathe ad hoc potential. We can eliminate this term if we include the specific boundary

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conditions and utilize a more sophisticated computation strategy to determine theactual mode spectrum (43).

We can evaluate the spatial correlation of fluctuation displacements, separated bydistancer, as follows:

h(0)h(r) =1

A qh(q )h(q )J0(qr)

=1

A

q

kB T

q 4 + J0(qr), (5)

whereh(q) is the amplitude in the mode of wave vector q, andJ0is a Bessel functionof the first kind (38, 44). Experimentally determined spatial correlation functions

represent the sum of correlations in all modes. The smallest wave vector, q = q0,is the dominant frequency and is roughly related to the effective system size, L, by

A = L2 = 4 2/q02. Figure 6b illustrates an experimental spatial correlation functionalong with the corresponding fit to Equation 5. It is essential to specifically measure

the system size in each case to interpret the fluctuation dynamics.We can express the fluctuation temporal autocorrelation function as the sum of

its Fourier modes:

h(r, 0)h(r, t) =1

A

q

kB T

q 4 + e w(q )t, (6)

wherew(q) is the temporal relaxation frequency of the fluctuation mode with wave

vector q. For each mode, a Langevin equation type calculation gives a relaxationfrequency by

w (q ) = (q )(q 4 + ), (7)

where(q) is the Oseen interaction kernel (4042, 45). This kinetic coefficient de-

scribes hydrodynamic interactions within the surrounding media. By determining

the spatial dimensions and membrane elastic properties (q0,) from the spatial cor-relation analysis of each membrane region studied, one can determine (q) from the

corresponding temporal autocorrelation functions.Figure 7aplots an experimentaltemporal autocorrelation function and its corresponding fit to Equation 6. Figure 7b

plots measurements of(q0) for 50 different membrane regions, at various averageintermembrane separation distances, z.

CURVATURE-MEDIATED SUPERSTRUCTURE FORMATION

Miscibility phase separation is widely thought to play a significant role in the lateral

organization of cell membranes (46, 47). So-called membrane rafts refer to the more

ordered of the two phases that emerge below the miscibility transition temperatureof the mixture, which generally contains cholesterol, and saturated and unsaturated

phospholipids. These structures can be readily formed in reconstituted membranesand visualized by fluorescence microscopy (9, 48). Fluorescently labeled probe lipids

usually partition preferentially into one of the two phases, providing good contrastfor imaging.



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30

20

10

0

0 2 4 6

(nm2)

t(s)

(nm)

1/

(q0

)(Nsm3)

(InverseOseeninte

ractionkernel)

a

b

109

108

107

106

105

104

30 40

Free membrane model

Confined water model

50

V

Figure 7

(a) Time autocorrelationfunction of normaldisplacement of membranefluctuations. (b) Plot ofexperimentally determinedOseen interaction kernels,

1/(q), and averageintermembrane spacing, z,of each membrane region(open circles). Valuescalculated from confined(solid blue line) and free(dashed orange line)hydrodynamic dampingmodels are plotted forcomparison. Confinementproduces a dramatic slowingof fluctuation timescaleswithout impacting the

time-independent spatialmode spectra.

Demixing in the multicomponent liquid membrane is primarily driven by thedifferential pair interaction energies between the various components. Complex for-

mation between cholesterol and lipids may complicate the phase diagram, but the

fundamental basis of miscibility phase separation is unchanged (47). In the absenceof long-range forces, the minimum energy configuration consists of single large

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Figure 8

Ordered superstructures in phase-separated giant unilamellar vesicles. The membrane consistsof a roughly 1:1:1 ternary mixture of saturated lipids, unsaturated lipids, and cholesterol. Afluorescent probe lipid is doped into the mixture at1 mol%, and its differential partitioningbetween the phases provides contrast for fluorescence microscopy. All the vesicles in thisimage were prepared simultaneously from the same mother lipid mixture. The diversity ofsuperstructures illustrates the sensitivity of the system to small perturbations and the intrinsicdifficulty in preparing homogeneous populations of vesicles. Stripe patterns (lower left) seem tobe stabilized by interaction with the underlying substrate. This may be a result of the need tobalance anisotropic forces resulting from the stripe superstructure.

domains of each of the phases. This minimizes the interface between the phases.In GUVs, domains can often be observed to coalesce over time and achieve this type

of configuration. However, stably ordered superstructures of stripes and hexagonallyordered domain lattices can also be observed (Figure 8) (9, 10). Such patterns are

ubiquitous in nature when opposing forces (e.g., attraction at short range and repul-sion at long range) lead to periodic modulation of an internal order parameter, such as

orientation or composition (49). Similar patterns are well known in lipid monolayers

(50). In the case of monolayers at the air-water interface, long-range electrostaticdipole-dipole interactions are responsible for the interdomain repulsion that ulti-mately drives the formation of ordered superstructures. Dipole-dipole interactions,

although still present, are greatly attenuated in lipid bilayers owing to the electrostaticscreening from ions in the water on both sides of the membrane (51). Observation of

ordered superstructures in bilayer membranes begs the question, what is the origin

of the long-range repulsive interaction between domains?One possible explanation lies in the membrane curvature induced by the domains,

themselves. In two-dimensional fluids able to adopt three-dimensional shapes, theperimeter-to-area ratio of a circle is not fixed. Local mechanical equilibrium requires

that line tension and curvature bending strain balance, defining an equilibrium con-

figuration with the domain bulging out of the plane of the membrane. The phaseboundary is not a hinge region; thus the membrane normal varies nearly continuouslyacross this interface (9, 52). As a result, the puckered shape of a domain sets a con-

straint on the surface normal of the membrane along its boundary. Correspondingly,the other phase region surrounding the domain is also deformed. As two domains near

each other, the intervening membrane is bent into a saddle shape, with progressively



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higher curvature as it deforms against the boundary condition of meeting the surfacenormals of the approaching domains. This does not necessarily imply that ordered

superstructures represent equilibrium configurations; it only provides a long-rangerepulsive force that could drive the formation of and stabilize such structure irrespec-

tive of the global equilibrium. The use of RICM to image the topography of domainarrays reveals domain curvature as described above (Figure 9).

Figure 9

(a) Time sequence offluorescence imagesillustrating the transitionfrom a strip domainpattern to a hexagonallyordered array of circulardomains.(b) Correspondingreflection interferencecontrast microscopy(RICM) imagesillustrating thetopography of thesuperstructuredmembranes. Each domainis puckered out of themembrane (the directionis ambiguous), and theyapparently repel oneanother. (c) Schematic ofthe membrane domainpositions and topographyas inferred from thefluorescence and RICMimages. The direction of

domain curvature isambiguous in this data set.(Y. Kaizuka, unpublisheddata.)

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By tracking the relative positions of domains in particularly well-ordered lat-tices over time, one can estimate the magnitude of the repulsive forces.Figure 10a

illustrates a highly monodisperse and well-ordered array of domains. Figure 10billustrates traces of domain center movements from a time series of images for a

representative set of domains. By compiling positions of all domains throughout thetime series, one can construct the radial pair distribution function, g(r), for the lat-

tice (Figure 10c). This example consists of 200-nm-diameter domains configuredinto a hexagonal lattice with 700-nm interdomain spacing. Despite the crystalline

structure of the domain array, the membrane is, itself, fluid. The structure is sta-bilized by interdomain repulsions. A close view of the first peak in g(r) (side graph

inFigure 10c) reveals a Gaussian distribution of interdomain separation distances.This provides a measure of the potential of mean force:w(r) = kBTln(g(r)), the

curvature of which, (2w(r)/r2), can be interpreted as an effective spring constant

for displacement of a domain from its equilibrium position within its constellationof neighbors. Various factors, such as the polydispersity of domain diameter and im-

age resolution, can broaden the measurement ofg(r). Therefore, the effective springconstant determined for this array, 790kBTm21, represents a rough estimate of

the magnitude of interaction forces between domains.

MEMBRANE CURVATURE MODULATIONWITH PATTERNED SUBSTRATES

Exploration of the relationships between membrane curvature and local chemical

composition requires experiments that apply precisely defined mechanical deforma-tions to membranes with well-understood phase behavior. Lipid bilayers comprising

ternary mixtures of cholesterol and lipids with unsaturated and saturated fatty acid

tails are well studied and provide a good model system (9, 48, 53). These phasesseparate at temperatures below a miscibility transition temperature into coexisting

liquid-ordered (Lo) and liquid-disordered (Ld) phases, enriched in saturated and un-saturated acyl chain lipids, respectively. The experimental strategy is based on the use

of solid substrates on which precisely defined patterns of curvature have been fab-ricated. Supported membranes can then be assembled onto these curved substrates,

allowing the physical characterization of the ways in which the fluid membrane re-sponds to the imposed curvature constraints.

Experiments reveal that membrane deformation directs the positioning of LoandLd domains; the Lo phase is preferentially localized at regions of low curvature.

Figure 11illustrates the experimental geometry. The substrate consists of continu-ously alternating high and low curvature contours with a one-dimensional periodicity

(in this case, of 2 m). The upper membrane is uniform in composition immediately

after GUV rupture. Phase separation then occurs, as Loand Lddomains nucleate andgrow. Thekey observation is that liquid-ordered membrane domains becomesituated

at, and elongated along, plateaus of lower curvature as imposed by the underlyingsubstrate (Figure 11b). Fluorophores in the lower bilayer are FRET donors to upper-

membrane probes. Intermembrane FRET confirms conformal contact between theupper and lower membranes; the lower bilayer fluorescence signal is the inverse of



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Figure 10

Estimation of the mean force between domains from the radial pair distribution function. (a) Arepresentative section of a fairly monodisperse domain lattice. (b) Domain motion, relative to

the central domain (open circle), during the trajectory analyzed. (c) Radial pair distributionfunction (r0marks the domain diameter, which is the center-to-center separation distance atwhich two domains would come into contact. (Side graph) The first peak ing(r) is enlarged,and the dotted red line traces a parabolic fit of ln(g(r)), which is the effective potential of themean force,w(r).

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Figure 11

(a) A topographicallypatterned quartz substrate(gray) and lower (green) andupper (red) lipidmembranes. (b) Atomicforce micrograph (AFM) ofthe underlying substrate(left). Fluorescence andForster resonance energytransfer (FRET) images ofthe upper and lower bilayersare shown in the middle andthe right panel, respectively.(c) Preferential localizationof Lodomains at regions oflow membrane curvature.Vertically averagedfluorescence of the upper

membrane, whichcorresponds to the Loprobability, is plotted (top)in registry with thevertically averaged substratetopography from AFM data(middle), and thecorresponding curvature(bottom).



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that of the upper membrane, indicating continuous intermembrane contact. Averag-ing the fluorescence intensity (F) of the upper membrane along the substrate stripe

direction provides a measure of the relative probability of Lomembrane composition(P = 1 F/Fmax, whereFmaxis the maximal value ofF) as a function of lateral po-

sition (Figure 2a). The similarly stripe-averaged substrate topography (from atomicforce microscopy) and the magnitude of the local curvature indicate a correspondence

between domain position and curvature.These results suggest that curvature patterning can be a general method of in-

ducing organization in soft two-dimensional fluid systems, including living cells.A significant corollary of the observation of curvature-driven domain ordering is

that deformation of the membrane provides mechanical coupling between mem-brane components, even in an entirely fluid system. The cellular cytoskeleton and

membrane should thus be considered together as the mechanical network for forcetransmission within living cells.

CONCLUSIONS AND OUTLOOK

A hallmark characteristic of the cell membrane environment is that large-scale fea-tures of the system can feed back onto and modulate the behavior of molecular-scale

chemical interactions. Much attention has been directed toward composition organi-zation within thetwo-dimensionalsurface of the membrane. Additionally, it is becom-

ing apparent that there are a number of mechanisms by which the three-dimensionalshape and curvature of membranes produce driving forces that also contribute to this

organization. Although conceptual ideas of curvature coupling can be traced backdecades, newexperimentalstrategies areopening avenues to quantitative evaluationof

such phenomena. Extension of many of these strategies to the direct manipulation and

analysis of living-cell membrane systems can be expected in the not too distant future.

ACKNOWLEDGMENTS

I would like to thank the many coworkers who have participated in this work. I espe-cially acknowledge the following people for their direct contributions to the present

article: Raghu Parthasarathy, Yoshi Kaizuka, Sharon Rozovsky, Cheng Han Yu, AmyWong, and Frank Brown. R.P. also painted the watercolor illustrations. Financial

support has been provided by the DOE, the NIH, the NSF, the Burroughs Well-come Career Award in the Biomedical Sciences (to J.T.G.), the Miller Foundation

Fellowship (to R.P.), and the Beckman Young Investigators Award (to J.T.G.).

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Annual Review

Physical Chemi

Volume 58, 2007Contents

Frontispiece

C. Bradley Moore xvi

A Spectroscopists View of Energy States, Energy Transfers, and

Chemical Reactions

C. Bradley Moore 1

Stochastic Simulation of Chemical KineticsDaniel T. Gillespie 35

Protein-Folding Dynamics: Overview of Molecular Simulation

Techniques

Harold A. Scheraga, Mey Khalili, and Adam Liwo 57

Density-Functional Theory for Complex Fluids

Jianzhong Wu and Zhidong Li 85

Phosphorylation Energy Hypothesis: Open Chemical Systems and

Their Biological Functions

Hong Qian

113

Theoretical Studies of Photoinduced Electron Transfer in

Dye-Sensitized TiO2Walter R. Duncan and Oleg V. Prezhdo 143

Nanoscale Fracture Mechanics

Steven L. Mielke, Ted Belytschko, and George C. Schatz 185

Modeling Self-Assembly and Phase Behavior in

Complex Mixtures

Anna C. Balazs 211

Theory of Structural Glasses and Supercooled LiquidsVassiliy Lubchenko and Peter G. Wolynes 235

Localized Surface Plasmon Resonance Spectroscopy and Sensing

Katherine A. Willets and Richard P. Van Duyne 267

Copper and the Prion Protein: Methods, Structures, Function,

and Disease

Glenn L. Millhauser 299

ix


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Aging of Organic Aerosol: Bridging the Gap Between Laboratory and

Field Studies

Yinon Rudich, Neil M. Donahue, and Thomas F. Mentel

Molecular Motion at Soft and Hard Interfaces: From Phospholipid

Bilayers to Polymers and Lubricants

Sung Chul Bae and Steve Granick

Molecular Architectonic on Metal Surfaces

Johannes V. Barth

Highly Fluorescent Noble-Metal Quantum Dots

Jie Zheng, Philip R. Nicovich, and Robert M. Dickson

State-to-State Dynamics of Elementary Bimolecular Reactions

Xueming Yang

Femtosecond Stimulated Raman Spectroscopy

Philipp Kukura, David W. McCamant, and Richard A. Mathies

Single-Molecule Probing of Adsorption and Diffusion on SilicaSurfaces

Mary J. Wirth and Michael A. Legg

Intermolecular Interactions in Biomolecular Systems Examined by

Mass Spectrometry

Thomas Wyttenbach and Michael T. Bowers

Measurement of Single-Molecule Conductance

Fang Chen, Joshua Hihath, Zhifeng Huang, Xiulan Li, and N.J. Tao

Structure and Dynamics of Conjugated Polymers in Liquid Crystalline

SolventsP.F. Barbara, W.-S. Chang, S. Link, G.D. Scholes, and Arun Yethiraj

Gas-Phase Spectroscopy of Biomolecular Building Blocks

Mattanjah S. de Vries and Pavel Hobza

Isomerization Through Conical Intersections

Benjamin G. Levine and Todd J. Martnez

Spectral and Dynamical Properties of Multiexcitons in Semiconductor

Nanocrystals

Victor I. Klimov

Molecular Motors: A Theorists PerspectiveAnatoly B. Kolomeisky and Michael E. Fisher

Bending Mechanics and Molecular Organization in Biological

Membranes

Jay T. Groves

Exciton Photophysics of Carbon Nanotubes

Mildred S. Dresselhaus, Gene Dresselhaus, Riichiro Saito, and Ado Jorio

bending mechanics and organization in biological membrances

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