intermembrane docking reactions are regulated by membrane curvature

Biophysical Journal Volume 101 December 2011 2693–2703 2693

Intermembrane Docking Reactions Are Regulated by Membrane Curvature

Andreas H. Kunding,†‡§6* Michael W. Mortensen,†‡6 Sune M. Christensen,†‡§6 Vikram K. Bhatia,†‡§

Ivan Makarov,†‡ Ralf Metzler,k and Dimitrios Stamou†‡§{*†Bionanotechnology and Nanomedicine Laboratory, Department of Neuroscience and Pharmacology, ‡Nano-Science Center, §LundbeckFoundation Center for Biomembranes in Nanomedicine, and {Center for Pharmaceutical Nanotechnology and Nanotoxicology, University ofCopenhagen, Copenhagen, Denmark; and kPhysik Department, Technical University of Munich, Munich, Germany

ABSTRACT The polymorphism of eukaryotic cellular membranes is a tightly regulated and well-conserved phenotype. Recentdata have revealed important regulatory roles of membrane curvature on the spatio-temporal localization of proteins andin membrane fusion. Here we quantified the influence of membrane curvature on the efficiency of intermembrane dockingreactions. Using fluorescence microscopy, we monitored the docking of single vesicle–vesicle pairs of different diameter(30–200 nm) and therefore curvature, as mediated by neuronal soluble N-ethylmaleimide-sensitive factor attachment proteinreceptors (SNAREs) and streptavidin-biotin. Surprisingly, the intermembrane docking efficiency exhibited an ~30–60 foldenhancement as a function of curvature. In comparison, synaptotagmin and calcium accelerate SNARE-mediated fusion in vitroby a factor of 2–10. To explain this finding, we formulated a biophysical model. On the basis of our findings, we propose thatmembrane curvature can regulate intermembrane tethering reactions and consequently any downstream process, includingthe fusion of vesicles and possibly viruses with their target membranes.

INTRODUCTION

The process of vesicle docking on other membranes is a vitalbiological reaction because it precedes all membrane fusionevents. Thus, any factors that modulate the docking reactionwill de facto propagate to downstream processes suchas membrane trafficking or neurotransmission. Becausesystematic variation of the experimental factors that affectvesicle docking and fusion is challenging in cell-basedassays, investigators have devised a wealth of in vitro assaysto dissect the mechanism of membrane fusion (1,2). In themajority of in vitro studies of intermembrane reactions,researchers relied on ensemble-based measurements inwhich two distinct populations of fusogenic vesicles weremixed, and subsequently monitored the onset of the fusionreaction by applying time-lapse spectroscopy (e.g., fluores-cence dequenching or Forster resonance energy transfer) ofthe intensity signal (3–5). Despite its merits, this approach islimited to monitoring only the end-point of the reaction,i.e., membrane fusion. Consequently, information regardingthe initial docking stage is inevitably lost, which rendersinterpretation of a kinetic curve less straightforward (forexample, did the experimental variable affect only the dock-ing step or the fusion step, or both?).

To overcome this challenge, investigators devised a newgeneration of experiments that, in contrast to ensemblemeasurements, allow them to study single vesicles directlyby applying fluorescence microscopy (6–10). Docking and

Submitted March 29, 2011, and accepted for publication September 29,

2011.6Andreas H. Kunding, Michael W. Mortensen, and Sune M. Christensen

contributed equally to this work.

*Correspondence: [email protected] or [email protected]

Editor: Axel T. Brunger.

� 2011 by the Biophysical Society

0006-3495/11/12/2693/11 $2.00

fusion can be monitored independently, thus enablinga more detailed understanding of the complete intermem-brane reaction pathway. For example, it was found thatneuronal synaptotagmin-1 (syt), a soluble N-ethylmalei-mide-sensitive factor attachment protein receptor (SNARE)-interaction partner, influenced both docking and fusion ina calcium-dependent manner (6). So far, researchers havefocused their attention on reproducing and refining the resultsfrom the ensemble-based fusion assays, thus resolving themechanics of membrane fusion to an unparalleled extentbut leaving the mechanics of docking unresolved.

Here we present a biophysical model (along with data insupport of the model) that describes the vesicle-dockingprocess in detail and reveals a substantial energetic barrierthat exclusively depends on membrane shape. We employedtime-resolved fluorescence microscopy to monitor thekinetics of single small unilamellar vesicles (SUVs) under-going docking on apposed membranes of different geome-tries. We measured the shape of the apposing membraneswith a precision of ~5 nm from their fluorescence intensitysignal (11–14), which enabled us to correlate the SUV dock-ing kinetics with membrane curvature. We measured thereaction kinetics as a function of membrane curvatureradius for two distinct docking-mediators (receptor/ligand),NeutrAvidin (NAv)/biotin and neuronal SNAREs, both ofwhich exhibit size-dependent docking. We found that,depending on the intermembrane geometry, the dockingefficiency could be increased up to 60 times for otherwisechemically identical vesicles.

Up to now, the putative regulatory roles of membranecurvature in lipid (15) and protein (16) sorting, as well asmembrane fusion efficiency (17), have been rationalizedby its influence on intrabilayer structure. In this work, we

doi: 10.1016/j.bpj.2011.09.059

mailto:[email protected]

mailto:[email protected]

http://dx.doi.org/10.1016/j.bpj.2011.09.059





A B

Ene

rgy

Distance

RC

UB

RkBT

1.0

0.8

0.6

0.4

0.2

0.0

Pro

babi

lity

1208040R (nm)

PA

PB

PD

FIGURE 1 Impact of membrane curvature on SUV docking. (A) A sketch

illustrating the docking process. An SUV from the bulk under Brownian

motion probes the potential energy landscape of the immobilized docking

partner. (B) The two dominant contributions to the docking efficiency

(black) are depicted as a function of the SUV radius. PA and PB are plotted

2694 Kunding et al.

show how this curvature also modulates the long-rangeinteractions between membranes. The curvature-dependentdocking kinetics we documented originates from the curva-ture dependence of both long-range repulsive intermem-brane forces and receptor/ligand membrane abundance.The dramatic influence of membrane curvature on dockingkinetics even surpasses the response of protein-mediatedmembrane fusion in vitro, i.e., a 2–10-fold acceleration offusion in the presence of synaptotagmin/Ca2þ (18–20).This led us to hypothesize that membrane curvature maybe relevant in vivo, where, for example, vesicles and organ-elles of different sizes or shapes may exhibit different dock-ing curvature preferences, thus imparting an additional layerof regulation in the efficiency of vesicle fusion.

as red and green lines, respectively. Curves were constructed with the

following parameters: RC ¼ inf., d ¼ 2 nm, ACS ¼ 2 nm2, N0 ¼ 2,

[Naþ] ¼ 100 mM, rL ¼ 1.0 mol %, and rR ¼ 10.0 mol% (see also Table

S3). The membrane charge was set to 40.0 and 10.0 mol % of negatively

charged lipids, corresponding to surface potentials of 204 mV and 51 mV,

respectively.

MATERIALS AND METHODS

Vesicle preparation

We prepared SUVs by applying the thin-film rehydration technique. Lipids

dissolved in chloroform were mixed in the desired ratio, followed by evap-

oration of the solvent under nitrogen flow, thus producing a thin lipid film

on the side of the glass vessel. The film was stored in vacuum for 2 h to

remove residual solvent and then gently rehydrated in the appropriate buffer

to a total lipid concentration of 1.0 g/l to form a vesicle suspension. The

suspension was thoroughly vortexed and subjected to five freeze/thaw

cycles before it was extruded through polycarbonate membranes with

a pore diameter of 50 nm (SUV50 or SUVSLB; see Table S1 in the Support-

ing Material) or 200 nm (SUV200; Table S1) via a pressurized extrusion

device (Northern Lipids, Burnaby, British Columbia, Canada). Details

about the SNARE-reconstitution protocol and lipid compositions can be

found in the Supporting Material and Table S2.

Microscopy

All fluorescence micrographs were acquired with an inverted confocal

microscope (TCS SP5; Leica, Solms, Germany) with an oil immersion

objective HCX PL APO, �100 magnification, and numerical aperture

1.4. Images were typically acquired at a resolution of 1024 � 1024 pixels,

physical pixel size of 60� 60 nm2, and a temporal resolution of 0.5 frame/s.

Laser light wavelengths of 458 nm, 543 nm, and 633 nm were used to excite

vesicles labeled with DiO, DiI, and DiD, respectively. The emitted fluores-

cence signal was collected with photomultiplier tubes. We measured the

axial point-spread function of the objective by operating the microscope

in reflection mode, and used it to calibrate the SUV size and NAv density.

For additional information about the materials and experimental methods

used, see the Supporting Material.

THEORY

Biophysical model of SUV docking

For simplicity, we model the docking process as two distinctsteps: 1), a SUV is brought into proximity to its complemen-tary surface (here defined as the binding distance d); and 2),tether complexes are formed upon contact, as sketched inFig. 1 A.

Intermembrane proximity

Due to a variety of intermembrane forces (21), there is anenergy cost associated with bringing a SUV close to any

Biophysical Journal 101(11) 2693–2703

other membrane surface. The three most prominent interac-tion potentials are the hydration repulsion (UH) (22), the vander Waals attraction (UV) (23), and the electrostatic double-layer repulsion (UE) (24). Evaluating the sum of thethree potentials at the binding distance d provides the totalenergy barrier (UB) associated with bringing two curvedmembranes into apposition, which in turn provides theprobability to surmount this barrier (PA) only by thermalmotion, i.e.,

PA ¼ exp

�� UHðdÞ þ UVðdÞ þ UEðdÞ

kBT

�¼ exp

�� UB

kBT

�;

(1)

where kB and T are the Boltzmann’s constant and the abso-lute temperature, respectively. Functional expressions forUH, UV, and UE are provided below. For the hydration repul-sion (UH) we have (25):

UHðdÞ ¼ 2p BlHRRC

Rþ RC

exp

�� d

lH

�; (2)

where B and lH are two phenomenological constants thatdescribe the potential energy profile (Table S3). The vander Waals attractive force exhibits a longer interaction rangethan the hydration repulsion, and for a pair of vesicles theinteraction energy (UV) is given as (23):

UVðdÞ ¼ �AHðdÞ6

"RRC

Rþ RC

�1

dþ 2t� 1

dþ tþ 1

d

�

� ln

dðd2tÞðdþ tÞ2

!#; (3)

Size-Dependent Vesicle-Docking Kinetics 2695

where t is the bilayer thickness and AH is the nonretardedHamaker constant given as (21):

AHðdÞ ¼ 2kd A0 expð�2kdÞ þ A1; (4)

where k is the inverse Debye-screening length, and A0 andA1 are the zero-frequency and dispersion contribution tothe Hamaker constant, respectively. Lastly, the electrostaticdouble-layer repulsion (UE) between lipid bilayers thatpossess charged headgroups assumes the following profile(24):

UEðdÞ ¼ εε0RRC

4ðRþ RCÞ�2JJC ln

�1þ expð�kdÞ1� expð�kdÞ

�

þ �J2 þJ2C

�lnð1� expð�kdÞÞ

�; (5)

where J and JC represent the surface potentials of the two
apposing membranes, e is the dielectric constant of thebuffer, and e0 is the permittivity of vacuum. The surfacepotentials are calculated as ε ¼ 2qc=ALHεε0k, where q isthe electronic charge, ε0 is the molar fraction of chargedlipid in the membrane, and ALH is the lipid headgroup area.
The expression for PA contains parameters relating to allexternal environmental factors (e.g., buffer ionic strength,temperature, and membrane composition), but of impor-tance, all of the terms carry an intrinsic size-dependent pre-factor ðRRC=ðRþ RCÞÞ that originates from the Derjaguin

Lz

Lxy

Lxy

Fa

5

4

3

2

1

0

Fre

quen

cy

1.00.80.60.40.20.0EC

SUV50Immobilized

SUV501.6

1.2

0.8

0.4

0.0

Fre

quen

cy

543210Pixels

SUV50

wxwy

R + δR

RC + δ

RC

δRCA

A B

D E F

FIGURE 2 Quantification of SUV concentration. (A) Sketch of the contact are

radius RCA, which lies in a plane perpendicular to the center-to-center line betwe

remaining inside a rectangular box during the microscope acquisition time of a sin

eccentricity values of the particles are changed by their movement. Scale bars are

the immobilized SUV50 population. The discrepancy between widths along the

Distribution of EC-values obtained from a diffusing SUV50 population (green)

the eccentricity threshold applied to all experiments, i.e., ECT ¼ 0.75. The fra

with EC < ECT. (F) Accumulated number of SUVs diffusing inside the field of v

values greater than ECT. The black line indicates a linear fit to the curve with slop

beads with R ¼ 18 nm. The Pearson sample correlation coefficient (C) was cal

approximation. In Fig. 1 B we plot PA for a range of SUVsundergoing docking onto a planar substrate-supported lipidbilayer (SLB; i.e., RC ¼ N) under our experimental condi-tions. It can be seen that PA is a monotonously decreasingfunction of R, mainly due to the contribution from UE.

Bond formation

We now turn to calculating the probability to form bonds(PB) upon contact. In contrast to PA, PB does not dependon environmental parameters but on intrinsic molecularproperties that govern the binding process. Here we useone characteristic parameter, the binding cross section(ACS), to exclusively determine binding efficiency. Wedefine ACS in terms of the binding probability (PR,L) ofa single receptor/ligand pair. If the pair occupies an areaA < ACS, then a bond will be formed with PR,L ¼ 1; other-wise, if A > ACS, then PR,L ¼ ACS /A. Using this definition,we can model the bond-formation process as a randomprocess wherein NR receptors attempt to bind to NL ligandswith PR,L chance to succeed per bond.

From geometry we arrive at a closed expression for thecontact area (see sketch in Fig. 2 A):

AC ¼ pR2CA

¼ pðRþ dÞ2 sin2 arccos

ðRþ dÞ2þR2þ 2RðRC þ dÞ2ðRþ dÞðRþ RC þ dÞ

!!:

(6)

st-moving

6

4

2

0

Par

ticle

s (x

103 )

6004002000Frame no.

SUV50

ECT = 0.75

NFRAME = 11.5 ± 0.1

18171615141312M

easu

red

conc

. (nM

)

181716151413Nominal conc. (nM)

C = 0.98

Slow-moving

Lz

Lxy

Lxy

C

G

a between two apposing SUVs. The contact area is defined by the circle of

en the SUVs. (B and C) Sketch of a diffusing particle (B) escaping and (C)

gle particle. The corresponding micrographs are shown to illustrate how the

300 nm. (D) Distribution of wx and wy obtained from a calibration sample of

x- and y-axes is due to a minor aberration of the microscope objective. (E)

and the same population, but immobilized (red). The dashed line indicates

ction of missed detections (FMD) corresponds to the part of the red curve

iew during an experiment. The SUVs were selected to exhibit eccentricity

e NFRAME. (G) Correlation between the measured concentration of colloidal

culated to be 0.98.


2696 Kunding et al.

For the limiting case of an SUV in contact with an SLB,the area is AC ¼ pdð2Rþ dÞ. We denote the number of avail-able tether molecules in the apposing membrane as NR;L ¼rR;LAC, where rR;L is the membrane density and subscriptsR and L denote the receptor and ligand, respectively. Asshown in the Supporting Material, PB is calculated as

PB ¼ 1� 1

2

erf

�N0 � xRffiffiffi

2p

sR

�� erf

�� xRffiffiffi

2p

sR

�

1� erf

�� xRffiffiffi

2p

sR

�666664

þerf

�N0 � xLffiffiffi

2p

sL

�� erf

�� xLffiffiffi

2p

sL

�

1� erf

�� xLffiffiffi

2p

sL

�777775;

(7)

where xR,L ¼ NR,L PL,R ¼ ACrRrLACS and sR;L ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixR;Lð1� rL;RACSÞ

p. In contrast to PA, then PB is an

increasing function of R (Fig. 1 B). This is because greaterradii result in greater contact areas, thus increasing the like-lihood that at least N0 bonds will form upon contact. Thedocking probability (PD) is now found as the joint proba-bility that a vesicle will approach its complementarymembrane at the binding distance (PA) and simultaneouslyform minimum N0 bonds upon contact (PB), i.e.,

PDðR;RCÞ ¼ PAðR;RCÞ � PBðR;RCÞ: (8)

Because PD is a composite of an increasing anda decreasing function, it experiences a global maximumvalue, suggesting a particular set of R and RC to be thebest-suited geometry for efficient docking (Fig. 1 B). Wefind it interesting to speculate that this biophysical effectmight provide a passive targeting mechanism in vivo, andcould explain the fact that trafficking vesicles exhibit char-acteristic diameters depending on which pathway they areupholding (26,27).

Measuring SUV docking probabilities

We now describe how one can directly obtain values for PD

from particle-tracking experiments for freely diffusingSUVs docking onto immobilized SUVs and an SLB. Westart by noting that the number of diffusing SUVs that areimpinging onto the surface of an immobilized vesicle(NDIF) is given as (28,29):

NDIF ¼ 2pDðRþ RCÞCVt; (9)

where D is the diffusion coefficient of the SUV, RC is theradius of the diffusing SUV, R is the radius of the immobi-lized SUV, CV is the bulk SUV concentration, and t is timeelapsed. A similar expression can be obtained for an SLB(see Supporting Material):


NDIF ¼ 3DASLBC4=3V t; (10)

where ASLB is the area of the SLB. The docking probabilityis inversely proportional to NDIF, i.e., a high PD-value leadsto a short time elapsed before docking, whereas a low PD-value gives rise to an extended time duration before dock-ing. For a docking experiment, we collect two observables:the total number of docked SUVs (ND) and the docking timeduration. Our goal is now to convert these observables to thedocking probability. We start by considering the case ofSUV/SLB docking.

SUV/SLB

Initially, we assume that the SUV population is monodis-perse with radius R. Our experimental observables are thetotal number of SUVs docked to the SLB (ND) and theexperimental time duration (t). The docking probability isobtained by dividing ND with the total number of SUVsthat impinge onto the SLB during the experiment. Thus,using Eq. 10, we arrive at

PD ¼ ND

NDIF

¼ ND

3DASLBC4=3V t

: (11)

We now adapt a more realistic scenario by replacing themonodisperse population with a polydisperse one. Withf(R) we denote the normalized size distribution function ofthe SUV population and can thus modify Eq. 10 to obtainNDIF as a function of R:

NDIFðRÞ ¼ 3DASLBð f ðRÞCVÞ4=3t; (12)

where CV indicates the average bulk concentration of SUVs.Thus, we can immediately obtain PD as a function of R,applying Eqs. 11 and 12:

PDðRÞ ¼ NDðRÞNDIFðRÞ ¼ NDðRÞ

3DASLBð f ðRÞCVÞ4=3t: (13)

SUV/SUV

The SUV/SUV scenario differs from the SUV/SLB experi-ment in one important aspect: Each time a diffusing SUVdocks onto an immobilized vesicle, the local membraneenvironment is perturbed, thus creating correlationsbetween successive docking events. For example, PD forthe first docking event is different from that for the nextevent, because a smaller area of the immobilized SUV’smembrane is accessible for docking and the electrostaticpotential is changed by the presence of the previous dockedSUV. Hence, to circumvent this experimental challenge, wedecided to only record the time duration to the first dockingevent (t1) for each immobilized SUV. Thus, the experi-mental observables in this case are t1, ND, and the total


number of immobilized SUVs that are available for docking(NI). As a first approximation, we can obtain PD simply bycalculating the average docking probability of all immobi-lized SUVs:

PD ¼ 1

NI

XNI

i¼ 1

1

NiDIF

¼ 1

NI

XNI

i¼ 1

1

2pDðRþ RCÞCVti1

: (14)

Here, the index i runs over all immobilized SUVs thatexperienced a docking event during the experimental timeframe. However, we chose to apply a more accuratemaximum likelihood (ML) approach to also take into accountthe SUVs on the sample, which did not experience a dockingevent due to the finite time span of the experiment.

To implement the ML approach, we assume the dockingto be a random process, and thus the probability to observe

a docking after t1 is PDð1� PDÞNDIFðt1Þ�1. Conversely,the probability to observe an immobilized SUV, whichdid not experience docking during the experiment, is

ð1� PDÞNDIFðTÞ. Here, NDIF(T) indicates the total number ofunsuccessful docking attempts that impinge on the immobi-lized SUV during the experimental time duration T (cf.Eq. 9). If we consider the entire immobilized population,we can calculate the joint probability (PJ) to observe thatparticular sequence of docking events:

PJðPDÞ ¼Y

Docked SUVs

PDð1� PDÞ2pDðRþRCÞCVti1�1

�Y

Non-docked SUVs

ð1� PDÞ2pDðRþRCÞCVT: (15)

PJ is a function of PD, and it is thus straightforward toobtain an accurate value for PD by plotting PJ from 0 to 1and locate the maximum, i.e., the PD-value that maximizesthe likelihood of obtaining these particular experimentalobservables.

RESULTS AND DISCUSSION

Online measurements of SUV concentration

To use Eqs. 13 and 15 to measure the docking probabilities,it is necessary to know the bulk concentration of diffusingSUVs. As a first approximation, we could use the nominalvalue of CV as estimated from the SUV preparation proce-dure and the volume of the sample. Nevertheless, due tothe extrusion process, significant amounts of lipids are lostduring the preparation (i.e., adsorption on surfaces andextrusion filters), and as a result of sample handling, theCV-values might even differ among identically preparedsamples. Furthermore, in the case of SUV/SLB experi-ments, the docking reaction might be diffusion-limited,thus inducing concentration gradients to build up adjacentto the SLB. For these two reasons, we do not consider itsufficiently accurate to simply estimate CV based on lipid

mass and sample volume. Instead, we developed a schemeto convert the number of detectable diffusing SUVs toCV-values, thus enabling an online measurement of concen-tration, while simultaneously recording docking events.

In a typical docking experiment, we consider an SUV tobe docked if its center position does not change >5 pixelsfor three consecutive frames. For each frame, we thus parti-tion all detected particles into two categories: docked anddiffusing. If we also know the detection volume (depth offield) of the microscope (VD), we can calculate CV as

CV ¼ NFRAME

VD

¼ NFRAME

AFWLZ

; (16)

where NFRAME is the average number of diffusing SUVs perframe. We have replaced VD with the sum of the field-of-view area (AFW) and the confocal detection length alongthe z-axis (Lz). The latter can be evaluated by measuringthe microscope point-spread function (see Eq. S9).However, many SUVs diffuse too rapidly to be detectableon a microscope image, and thus we have to modify Eq.16 to also include the fast-moving particles:

CV ¼ 1

FD

NFRAME

AFWLZ

; (17)

where FD represents the probability that an SUV willmove slowly enough to become detectable. The totalamount of SUVs that are present during an exposure is thusNFRAME/FD.We can consider slow-moving particles to residein a rectangular box of height Lz and widths Lxy during thetime (tP) it takes for the confocal microscope to acquire animage of the particle. A fast-moving particle will breakout of the imaginary box during the time span tP and thusappear elongated, as illustrated in Fig. 2, B andC. In the Sup-porting Material we show that FD is calculated as

FD ¼ erf�axy

�þ exp��a2

xy

�� 1

axy

ffiffiffip

p!2

��erfð2azÞ

þ exp��4a2

z

�� 1

2az

ffiffiffip

p�; (18)

where axy ¼ Lxy=ffiffiffiffiffiffiffiffiffiffiffi4 DtP

pand az ¼ Lz=

ffiffiffiffiffiffiffiffiffiffiffi4 DtP

pare charac-

teristic parameters that relate particle diffusion to the micro-scope acquisition time.

To calibrate particle motion, we imaged a sample of im-mobilized vesicles and fitted the intensity distributions ofindividual particles to 2D Gaussian functions of thefollowing form to obtain the particle eccentricity (EC):

Gðx; yÞ ¼ IBG þ A exp

� x2Rw2

x

� y2Rw2

y

!: (19)


R

RC

A

CTime to first docking event

RC =

R

B

Neutravidin/Streptavidin

PLL-g-PEG-biotin

Biotinylatedlipid

PLL-g-PEG

30

20

10

0

4003002001000Time (s)

t1

30

20

10

0I R

OI (

IU)

4003002001000Time (s)

t1

D

FIGURE 3 Measurements of single-vesicle-docking kinetics on

membranes of variable curvature obtained by time-resolved fluorescence

microscopy. (A) Vesicles with a coat of NAv and of various radii were im-

mobilized on a glass substrate functionalized with biotin conjugates of

polyethylene glycol. Extruded, monodisperse SUVs with DOPE-biotin

included in the membrane were allowed to dock onto their surface-immo-

bilized partners. Surface-attached and diffusing SUVs contained 2.0 mol

% of the lipophilic fluorescent probe DiD-C18. (B) Docking reactions

between a SLB functionalized with NAv and a polydisperse population of

biotinylated diffusing SUVs labeled with DiD-C18. Membranes of fixed

curvature (RC) are labeled in green, and membranes of variable curvature

are labeled in red. The red SUV population remained the same in both

SUV/SUVand SUV/SLB experiments. (C) False-colored micrograph series

after docking events at the site of two immobilized SUVs from the setup in

panel A. (D) Time-resolved intensity signal extracted from the micrograph

sequences in C showing bleaching of an immobilized SUV and then dock-

ing of another SUV from solution after time (t1), as indicated by an arrow.

2698 Kunding et al.

Here xR ¼ (x� x0) cosq � (y� y0) sinq and yR ¼ (x� x0)sinq � (y � y0) cosq, where x0 and y0 are the particle centercoordinates and q is the angle of rotation relative to thex-axis. IBG is the background intensity, A is the signal ampli-tude, and wx and wy are the widths along the x- and y-axis,respectively. We thus define eccentricity as the ratio ofy-width to the x-width, i.e., EC ¼ wy/wx (see Fig. 2 D).

Next, we imaged and extracted EC-values for a sample offreely diffusing vesicles. Not surprisingly, the diffusingvesicles exhibited lower EC-values than the immobilizedones (Fig. 2 E). We set a threshold eccentricity value(ECT) of 0.75 to distinguish between fast- and slow-movingparticles. In this way, we consider a slow-moving (detect-able) particle to exhibit an EC-value > ECT, whereasa fast-moving (nondetectable) particle exhibits EC-values <ECT. The result of this classification is shown in Fig. 2 F asa graph of the cumulated count of detectable particles for asequence of fluorescence micrographs. We obtained a valuefor NFRAME as the slope of the graph.

However, as shown in Fig. 2 E, even completely immobi-lized particles can exhibit EC-values < ECT due to noise. Tocorrect for this, we introduce the parameter FMD, which isthe fraction of missed detections, i.e., slow-moving particlesthat due to noise are not detected. FMD is directly obtainedfrom the EC distribution of immobilized vesicles by inte-grating the part of the graph to the left of ECT. Eq. 17 isthus recast as

CV ¼ 1

FDð1� FMDÞNFRAME

AFWLz

: (20)

To validate Eqs. 18 and 20, we prepared five solutions offluorescence-labeled, 36-nm-diameter colloid beads, forwhich the particle concentration was known in advancefrom the manufacturer’s specifications. We imaged a refer-ence sample of immobilized beads and also acquired time-lapse micrograph sequences of freely diffusing colloids.Setting an ECT-value of 0.75 allowed us to extract NFRAME

and calculate FD, thus evaluating the particle bulk concen-tration (Fig. 2 G). For the five samples tested, we founda good agreement between the nominal and the measuredparticle concentration, yielding a Pearson sample correla-tion coefficient of 0.98.

Quantification of the reaction efficiencyfor SUV/SUV and SUV/SLB docking

To quantify how nanoscale membrane curvature influenceda docking reaction, we applied two distinct experimentalassays involving fluorescence-labeled SUVs, as sketchedin Fig. 3, A and B. In one assay, we functionalized SUVsof various sizes (and thus curvatures) with a coat of fluores-cence-labeled NAv, and subsequently immobilized them ona polyethylene-glycol-passivated glass substrate. Next, weinitiated docking by adding a biotinylated SUV population


(SUV50) with a narrow size distribution and average radiusof RC ¼ 28 nm (as obtained from dynamic light scattering).In the second assay, we docked a polydisperse population ofbiotinylated SUVs (SUV200) on an SLB functionalized withNAv. In this way we were able to compare docking reactionsbetween SUVs of various radii (R ¼ 20–150 nm) andanother surface of fixed complementary curvature at eitherRC ¼ 28 nm or RC ¼ N.

We measured the kinetics for docking reactions thattook place between two highly curved SUV membranes,as sketched in Fig. 3 A. The low density of immobilizedNAv-coated SUVs on the surface enabled us to resolvesingle vesicles, and thus we were able to follow the dockingreaction by monitoring the fluorescence intensity trajectoryat the site of individual SUVs, as shown in Fig. 3 C.

1010

1011

1012

Par

ticle

s / M

16012080400R (nm)

D E

6040200Frame

0

400

800

# S

UV

s

102

103

104

ND

IF

1208040R (nm)

t = 0.0 s 5.1 s 10.2 s 15.3 sC

A B 1.0

0.8

0.6

0.4

0.2

0.0

PJ

100806040200PD (x10

-6 )

2 mol% 10 mol%

4000

2000

0

Diff

usin

g S

UV

s

10000Time (s)

CV = 44.5 nM

CV = 29.9 nM

FIGURE 4 Docking efficiency measured for NAv-coated SUVs. (A)


Initially, the intensity from the membrane label 1,10-diocta-decyl-3,3,30,30-tetramethyl-indodicarbocyanine (DiD-C18)decreased exponentially as a footprint of photobleaching(Fig. 3 D). The moment a docking reaction took place, theDiD-C18 intensity increased abruptly due to the presenceof the docked SUV, which subsequently also underwentphotobleaching. From the intensity trajectories, we ex-tracted the docking time (t1), here defined as the timeelapsed until the occurrence of the first intensity peak (illus-trated with gray arrows in Fig. 3 D).

In analogy to our recently published work (29), we con-verted the list of t1-values into the number of unsuccessfuldocking attempts (NDIF) before docking. Briefly, wecounted the number of detectable diffusing SUVs that ap-peared during the entire experimental time course (Fig. 4 A)and converted this number to actual concentration (CV) byapplying Eq. 20. For SUV/SUV docking, we obtained thedocking efficiency (PD) from an ML fit to the t1 list accord-ing to Eq. 15 (Fig. 4 B). For SUV/SLB docking, we obtainedPD-values by recording and analyzing micrographsequences of the docking process (Fig. 4 C), and thus ex-tracted the total number of docked (ND) SUVs during theexperimental time as well as CV. We resolved both NDIF

and ND as a function of the SUV radius (Fig. 4, D and E),and thus calculated the docking efficiency as PD ¼ ND /NDIF according to Eq. 13.

Concentration measurement of single diffusing SUVs. The CV-values

were 44.15 0.1 nM (red line) and 29.85 0.1 nM (green line). Black lines

indicate a linear fit to the data. (B) Direct extraction of docking efficiency

(PD) by a global maximum-likelihood fit to the complete set of experiments

performed with SUVs displaying 2.0 mol % (red line) or 10 mol % (green

line) DOPE-biotin in the membrane. From Eq. 15 we found PD ¼ (2.2 5

0.6) � 10�5 and PD ¼ (4.4 5 0.5) � 10�5 for 2 mol % and 10 mol %

DOPE-biotin, respectively. (C) Confocal fluorescence micrograph sequence

displaying DiD-C18-stained diffusing biotinylated SUVs docking onto an

SLB presenting NAv. Red circles indicate diffusing SUVs probing the

SLB interface, and the green circle identifies a successfully docked vesicle.

Scale bar is 5.0 mm. (D) Distribution of SUV docking attempts (NDIF) expe-

rienced by the SLB resolved as a function of vesicle radius R. The inset

shows the number of diffusing SUVs for two different experiments with

[Naþ] ¼ 80 mM (red) and [Naþ] ¼ 120 mM (green) corresponding to

CV ¼ 0.10 nM and CV ¼ 0.21 nM, respectively. (E) The size distribution

of all SUVs that successfully docked after t ¼ 358 s normalized by the

average bulk concentration of SUVs (CV ) for direct comparison among

experiments. Docking reactions took place in buffers with [Naþ] ¼80 mM (green) and [Naþ] ¼ 120 mM (red).

Membrane ligand density and electrostaticscreening regulates docking efficiency

In Fig. 4 B we compare two SUV/SUV-docking experi-ments in which we increased the membrane density of1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(biotinyl)(DOPE-biotin) from 2 to 10 mol %. Not surprisingly, we ob-tained a corresponding increase from PD ¼ (2.2 5 0.6) �10�5 to PD ¼ (4.4 5 0.5) � 10�5. In Fig. 4 E we comparetwo SUV/SLB-docking experiments in which we decreasedthe counterion concentration of the buffer from 120 mM to80 mM but otherwise kept all settings identical. Mainly dueto the increased electrostatic repulsion in the 80 mM experi-ment, we observed a consistent decrease in ND. In particular,large SUVs (R> 120 nm)were not permitted to dock onto theSLB during the experimental time course of ~10 min. Fromthese four types of experiments, it is evident that both thedensity of receptors/ligands available in the SUV contactarea (AC) and the potential energy of establishing the inter-membrane junction affect the docking efficiency, in qualita-tive agreement with Eqs. 1 and 7 for PA and PB, respectively.

SUV/SLB-docking efficiency depends onmembrane curvature

From the data shown in Fig. 4, we can extract the full rela-tionship between SUV docking efficiency and membranecurvature, thus testing the predictions of Eq. 8. For the

case of SUV/SLB docking, we calculate PD(R) simply bydividing the docked SUV size distribution (Fig. 4 E) withthe docking-attempt size distribution (Fig. 4 D), i.e., Eq.13. The resulting docking efficiency profiles are shown inFig. 5 A for two different buffer ionic strengths. BothPD(R) profiles exhibit a clear trend of increasing efficiencyfor larger SUV radii; however, the measured PD-values areoverall smaller for the low ionic strength ([Naþ] ¼ 80 mM)than for the higher ionic strength ([Naþ] ¼ 120 mM),consistent with the predicted decrease of the potentialenergy barrier UB in Eq. 1.


0.5

0.4

0.3

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0.1

0.0

PD

1208040R (nm)

[Na+] = 120 mM

[Na+] = 80 mM

RC = inf. 35

30

25

20

15

10

5

0

PD (

x10-6

)

12010080604020R (nm)

RC = 28 nm

[Na+] = 120 mM

0.30

0.25

0.20

0.15

0.10

0.05

0.00

PD

706050403020R (nm)

RC = 33 nm

[Na+] + [K+] = 120 mM

20

15

10

5

0Den

sity

(x1

015 m

-2)

100806040200R (nm)

12

10

8

6

4

2

0

Act

ivat

ion

ener

gy (

k BT

)

12080400R (nm)

SUV/SLB 120 mM SUV/SLB 80 mM

SUV/SUV 120 mM

SUV/SUV 120 mM

NAv/biotin

SNARE/syt

1.0

0.5

0.0

PJ

10-6

10-4

PD

A B

D

C

E

F

G

FIGURE 5 Vesicle-docking reactions are dramatically influenced by membrane curvature. (A) Efficiency profile of a NAv/biotin-mediated SUV/SLB-

docking reaction as a function of SUV radius for [Naþ] ¼ 120 mM (red markers) and [Naþ] ¼ 80 mM (green markers). Black lines indicate a global fit

of the data to Eq. 8 (for input parameters see Table S3). (B) Maximum-likelihood fit to extract PD for NAv/biotin-mediated SUV/SUV-docking reactions

shown for two immobilized SUV subpopulations with average radius 104 nm (red line) and 12 nm (green line). (C) Efficiency profile of a NAv/biotin-medi-

ated SUV/SUV-docking reaction as a function of SUV radius. The black line indicates a plot of Eq. 8 with the values of ACS and d obtained from the fits shown

in A and with a size-dependent NAv density as obtained from D. (D) Density profile of NAv bound to SUV membranes as a function of SUV radius. (E) Size-

dependent efficiency of a SNARE/syt-mediated SUV/SUV-docking reaction. The black line is a fit to Eq. 8. (F) False-color micrograph of an SUV/SUV

complex stably docked by the formation of SNARE/syt-complexes. The SUV originating from the bulk solution (green color) diffuses on the membrane

surface of the immobilized SUV (red). Scale bar is 500 nm. (G) Energy barriers associated with forming a stable intermembrane junction through docking

of SUVs is shown for NAv/biotin-mediated docking on SLB at [Naþ] ¼ 120 mM (red) and 80 mM (green), and for SUV/SUV docking at [Naþ] ¼ 120 mM

(blue). The curve in black corresponds to SNARE/syt-mediated docking of SUVs.

2700 Kunding et al.

The feature of increasing PD-values for larger SUVssuggests that the bond-formation process (PB) is the rate-limiting step of the docking reaction, i.e., smaller SUVshave less chance to create bonds upon contact. Of interest,by decreasing [Naþ] to 80 mM, we were able to enhancethe electrostatic repulsion and thus observed a maximumin the PD(R) profile at R ¼ 90 nm, suggesting a transitionfrom bond formation to SUV proximity as the rate-limitingstep, i.e., PA(R > 90 nm) < PB(R > 90 nm). To gain a moredetailed insight into the docking process, we conducteda global fit of the data in Fig. 5 A to Eq. 8 keeping d, ACS,and N0 as the only free parameters. From the global fit weobtained d ¼ 3.78 5 0.07 nm, ACS ¼ 2.8 5 0.6 nm2, andN0 ¼ 2.7 5 0.5. The binding distance of 3.78 nm agreeswell with published values on the molecular dimensionsof streptavidin (30), a homotetramer that is similar in struc-ture to NAv.

For the range of SUVs shown in Fig. 5 A, the contact areasspan 400–3600 nm2 corresponding to 5–42 NAv tetramerswithin (Table S3), thus yielding on average 10–84 bindingsites available for docking. However, the low ACS-value of2.8 nm2 corresponds to an optimal density of 0.2 NAv/nm2,


which is ~15 times larger than the experimental density ofbinding sites, thus supporting the notion that bond formationis indeed the rate-limiting step of SUV/SLB docking.

NAv-mediated SUV/SUV-docking efficiencydepends on membrane curvature

To further test the predictions of Eq. 8, we constructeda PD(R) profile for the data on SUV/SUV docking shownin Fig. 4 B. We first partitioned the immobilized populationof SUVs into bins depending on their size, and then appliedEq. 15 to each of the four subpopulations (Fig. 5 B). The re-sulting profile is shown in Fig. 5 C, which shows a consistentdecrease in docking efficiency as R increases. Of interest,the overall PD for a SUV docking with another SUV(RC ¼ 28 nm) is ~100,000 times smaller than that for thesame SUV docking onto a SLB (RC ¼ infinite). Our model,which predicted only an ~1000-fold decrease in dockingefficiency, could not immediately explain this large differ-ence. However, in all of our NAv-mediated docking experi-ments, we simultaneously measured the membrane NAvdensity using a fluorescence intensity calibration scheme


as described previously (12) and in the Supporting Material.In this way, we found that single SUVs bind NAv to a lesserextent than does an SLB (Table S3), most likely due todifferences in the membrane composition (i.e., the SLB con-tained four times less charged lipids than the SUVmembrane; Table S1). This difference in electrostatic poten-tial may modulate the interfacial concentration of NAv,resulting in a different membrane density. We also observedthat NAv binding to the biotinylated SUV membranes takesplace in a mildly (~3-fold) curvature-dependent manner(Fig. 5 D). By combining Eq. 8 with the measured NAv-density profile, i.e., rR ¼ rR(R), we obtained theoreticalPD-values that matched the magnitude of the experimentallyrecorded ones (Fig. 5 C, black line) and described the curva-ture dependence within uncertainties.

The efficiency of SNARE-mediated dockingdepends on membrane curvature

To investigate a more biologically relevant system, wereconstituted rat neuronal synaptobrevin, syntaxin, andSNAP-25 into SUVmembranes. The reconstitution protocolwe used is described in detail elsewhere (29,31) and was notchanged. We conducted experiments involving dockingbetween surface-immobilized SUVs displaying syntaxin/SNAP-25 and freely diffusing SUVs displaying synaptobre-vin. Upon addition of the water-soluble domain of syt andCa2þ, SUVs from the bulk successfully docked on theircounterparts at the surface, which allowed us to extractthe docking times and the corresponding PD(R) profileshown in Fig. 5 E. Again, we found a strongly size-depen-dent docking efficiency that exhibited a 34-fold decreasefrom R ¼ 16 nm to R ¼ 61 nm.

Stable SUV/SUV membrane junctions could only beformed in the presence of syt and Ca2þ, and were irrevers-ible on an experimental timescale. The docked synaptobre-vin-functionalized SUVs that did not undergo immediatefusion were able to execute a random walk on the surfaceof the immobilized syntaxin/SNAP-25 SUVs (Fig. 5 F),suggesting that the SNARE/syt-complex remained mobilein the membrane even after docking. According to previousstudies (9), a single SNARE complex is sufficient to mediatestable docking. This allowed us to set N0 ¼ 1 and conse-quently fit the PD(R) profile in Fig. 5 F to Eq. 8, and thusobtain values for d and ACS. Because the syt fragment weused here was previously shown to exhibit size-dependentbinding to SUV membranes (31), we used the publisheddensity profile of syt (reproduced in Fig. S1 B) to enablethe fitting.

The SNARE/syt system yielded a significantly smallerbinding distance (d ¼ 1.8 5 0.1 nm), as well as a greaterbinding cross section (ACS ¼ 60 5 25 nm2), comparedwith NAv. The d-value of 1.8 nm suggests that SNARE/syt-mediated docking is enabled only when the intermem-brane separation is comparable to the short axis of the

folded SNARE complex (~1–2 nm) (32). The surprisinglyhigh binding cross section indicates that SNARE/syt assem-bles 22 times more readily than NAv/biotin, which impliesthat fast association kinetics dominate the high SNARE-complex binding energy (~30 kBT), in contrast to the off-rate controlled binding energy of NAv/biotin.

We find it worthwhile to compare our results withprevious bulk experiments by Cypionka et al. (33) on thedocking and fusion kinetics of SNARE-functionalized vesi-cles. In their experiments, the authors compared the dockingrate (kD) between two complementary SUV populationswith an average radius of 15 nm with that of two othercomplementary populations with an average radius of50 nm. They concluded that the two kD-values were almostidentical, resulting in at least a threefold difference betweenthe corresponding PD-values due to the threefold greaterdiffusion of the smaller SUVs. In reality, even carefullyextruded SUV preparations exhibit a substantial degree ofpolydispersity as the extrusion filter pores get larger (13),which can mask any size-dependent effect measured in anensemble-based assay. However, to enable comparisonwith our results, we applied our experimentally obtainedvalues of d and ACS along with Eq. 8 to calculate PD

(15 nm, 15 nm) andPD (50 nm, 50 nm),which yielded a three-to fourfold difference depending on the exact electrostaticconditions (e.g., membrane composition and ionic strength).Consequently, our single-vesicle results are in good agree-ment with the previously published bulk experiments.

As shown in Fig. S2, A–C, we extracted, processed, andreplotted data from Grabner et al.’s (34) electrophysiolog-ical study of exocytosis in chromaffin cells. Of interest,Fig. S2 C shows an ~250–450% decrease in exocytic effi-ciency as the vesicle radius increased. Cell-based assaysthat cannot measure the biochemical composition of indi-vidual native vesicles cannot decouple the contributions ofmembrane curvature and vesicle composition on the dock-ing and fusion efficiency, and thus cannot establish theorigin of the trend underlying the data of Fig. S2 C.However, because this trend is qualitatively similar to ourin vitro data on SNAREs (Fig. 5 F), we suggest that itmay be an example of rate-limiting, curvature-sensitivedocking and its influence on fusion kinetics in vivo.

Comparison of docking mechanisms

We illustrate the differences in docking mechanism amongthe four different experiments presented in Fig. 5, A, C,and E, by converting the docking efficiency into activationenergy (EA), which indicates the minimum energy requiredto dock, where

EA ¼ �kBT lnðPDÞ ¼ �kBTðlnðPAÞ þ lnðPBÞÞ: (21)

The EA-values are shown in Fig. 5 G and span a widerange from ~1–12 kBT. EA is a composite of the repulsive


2702 Kunding et al.

potential experienced by the two opposing surfaces and thecombinatorial process of initiating receptor/ligand complex-ation. NAv/biotin-mediated SUV/SUV-docking reactionsare least probable and thus attain the highest EA-value,which is entirely due to the small number of availablebinding sites in the contact area combined with the lowACS-value. It is worth noting that due to the differences inNAv density on SUV and SLB membranes, the EA-valuesfor SUV/SUV docking do not asymptotically approach(for R / N) those of SUV/SLB docking. For SNARE/syt-mediated docking, the overall activation energy is lowbut exhibits a substantial increase with SUV size, whichwe mainly attribute to the size-dependent syt density.

CONCLUSION

The shape of cellular membranes is a tightly regulated andwell-conserved phenotype; however, to date, investigatorshave largely ignored the effects of membrane shape/curva-ture on biological functions that make this shape so criticalfor sustaining life. Recent data revealed putative regulatoryroles of membrane curvature in lipid (15) and protein (16)sorting, as well as membrane fusion efficiency (17). Herewe show that apart from influencing intrabilayer structure,curvature causes dramatic changes in the long-range inter-actions between membranes and thus in the membranedocking kinetics. The magnitude of the dependence of dock-ing rates on curvature that we observed in purified in vitrosystems (up to 5000% and energy barriers up to 12 kBT;Fig. 5, A–E) suggests that this mechanism may play animportant, heretofore unrecognized role in cellular biology.As shown here, however, docking rates can in principleeither increase or decrease with curvature depending ona number of molecular parameters (e.g., tether density,tether length, and surface charge), allowing for diversityand adaptability of this mechanism. Most importantly,long-range, membrane-shape-induced effects that cancontrol the yield of intermembrane tethering reactionswould de facto propagate to numerous downstream biolog-ical processes, including viral infection, membrane traf-ficking, neurotransmitter release at the synapse, and evenjuxtacrine signaling (35).

SUPPORTING MATERIAL

Additional materials,methods, and other details, and three tables and two

figures are available at http://www.biophysj.org/biophysj/supplemental/

S0006-3495(11)01238-0.

We thank H. T. McMahon and Sascha Martens for contributing the purified

synaptobrevin, SNAP-25, syntaxin, and syt.

This work was supported by the Danish Council for Independent Research;

the Danish Council for Strategic Research; the Lundbeck Foundation; the

University of Copenhagen programs of excellence BioScart, Single Mole-

cule Nanoscience, and UNIK-Synthetic Biology; and the European Union

program NEMOSLAB (FP6-2004-IST-4).


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intermembrane docking reactions are regulated by membrane curvature

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