Imaging of single molecule diffusion

Proc.Natl. Acad. Sci. USA Vol.93,

pp.

2926-2929,

April

1996

Biophysics

Imaging

of

single

molecule

diffusion

(fluorescence

microscopy/single

dye

detection/time-resolved

imaging/quantal

fluorescence/lipid

bilayers)

TH.

SCHMIDT,

G. J.

SCHUTZ,

W.

BAUMGARTNER,

H. J.

GRUBER,

AND H.

SCHINDLER

Institute forBiophysics, UniversityofLinz,4040Linz,Austria

Communicated

by George

Feher,

University

of

California,

San

Diego,

LaJolla, CA,December18, 1995

(received

for

review

August

14,

1995)

ABSTRACT Inrecent

years

observations at the level of

individual atoms and molecules became

possible

by

micros-copy

and

spectroscopy.

Imaging

of

single

fluorescence mole-cules has been achieved but has so far been restricted to molecules intheimmobile state. Here we

provide

methodology

forvisualization of the motion of individualfluorescent mol-ecules. It is

applied

to

imaging

ofthediffusional

path

of

single

molecules ina

phospholipid

membrane

by

using

phospholip-ids

carrying

one rhodamine

dye

molecule. For this

method-ology,

fluorescence

microscopy

wascarried to a

sensitivity

so

that

single

fluorescent molecules illuminated for

only

5 ms

were resolvable at a

signal/noise

ratio of 28.

Repeated

illu-minations

permitted

direct observation of the diffusional

motion ofindividualmolecules witha

positional

accuracy

of

30 nm. Such

capability

has

fascinating potentials

in bio-science-for

example,

tocorrelate

biological

functions of cell membranes with

movements,

spatial

organization,

and stoi-chiometries of individual

components.

The ultimate

goal

of

high-sensitivity

detection schemes is

observationonthe

single

moleculelevel.Thiscameinto reach

by

theinvention of

scanning

probe

microscopy

(1,

2),

which has

since

brought

awealth of new

insights (3).

Optical

methods allowed fordetection of

single

atoms

(4).

Theeffective

light

conversioninfluorescent molecules made it

possible

todetect

single

fluorophores

in

liquids

by

confocal fluorescence

mi-croscopy

(5-8)

andto

perform high-resolution spectroscopy

of

single

dye

moleculesatlow

temperature

(9-12).

The firsttrue

imaging

of

single dye

molecules

by optical

means wasachieved

by scanning

near-field

optical

microscopy (13).

Thismethodis

unique

in

reaching

a

spatial

resolution of 14

nm,

muchbelow the

optical

diffraction limitbut restricted inits

application

to

immobile

objects.

Very

recently,

single

fluorescence labeled

myosin

molecules onimmobilized actin filamentswere

imaged

by

conventional

microscopy

andilluminationtimes of seconds

(14).

Itwould be of interest for

many

applications, especially

in

bioscience,

to extend

microscopy

to visualization of

single

fluorophores

in motion. To our

knowledge,

such

imaging

has notbeen

reported

todate. Here weshowthat the motion of

single dye

molecules canbe visualized

by

conventional

fluo-rescence

microscopy

by

extending

the time resolution into the millisecond

range.

For

this,

weused

epifluorescence

micros-copy

with

argon-ion

laser excitation and

imaging

onto a

highly-sensitive liquid-nitrogen-cooled

CCD-camera.

Optical

parts

were

carefully

selected to achieve an

efficiency

for the detection ofemitted fluorescence as

high

as

3%,

while

scat-tered

light

wasblocked

effectively.

Fordemonstration of the

potentials

of

observing

individual mobile moleculeswe have chosenafluorescence-labelled

lipid

inafluid

lipid

membrane

as a most

appropriate

system.

It

uniquely permitted

to use results obtained at

high

surface densitiesof labelled

lipid

for

Thepublicationcostsofthis articleweredefrayedinpartbypagecharge payment.This articlemusttherefore beherebymarked"advertisement"in accordance with 18 U.S.C.§1734solelytoindicate this fact.

quantitative

controlin

identifying

isolated

signals

with

single

fluorescence-labelled

lipids

observedatlow surface densities.

MATERIALS AND METHODS

Phospholipid

Membranes.The

lipids

palmitoyloleoylphos-phocholine

(POPC,

Avanti Polar

Lipids)

and

N-(6-tetrameth-

ylrhodaminethiocarbamoyl)-1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine, triethylammonium

salt

(TRITC

DHPE;

T-1391,

Molecular

Probes)

wereusedwithout further

purifica-tion.

Lipid

monolayers

were

generated

atthe

air/buffer

interface

(buffer;

100mM

NaCl/10

mM

NaH2PO4,

pH

7.5)

in a

monolayer

trough

(Mayer

Feintechnik,

Gottingen,

Germany)

and heldat30

mN/m

surface

pressure.

Lipid bilayers

were

deposited

onto

0.17-mm-thick

glass

substrates

by

a

Langmuir-Blodgett technique

(15).

Beforeuse thesubstrates werecleaned with chromic acid and

extensively

washedin water.For

bilayer

formationaPOPC

monolayer

onthe

glass

substratewas

horizontally

apposed

to a

POPC

monolayer

atthe

air/buffer

interface

containing

TRITC

DHPE at a defined molar ratio. The molar ratio

[TRITC

DHPE]/[POPC]

wasvaried between6.5 x

10-9

and6.5 x

10-4

mol/mol,

which

yielded

a

range

of surface

density

of TRITC

DHPEfrom

10-2

to

103

dyes//Im2,

assuming

0.63

nm2

surface

area

per

lipid

(16).

The

lipid bilayer

onthe substratewas

pushed

through

the

air/buffer

interface and

clamped

underwater to an

open quartz

cell of 10,tm

optical

path length

(136QS, Hellma).

This cellwasmountedonthe

microscope

stage.

Fluorescence

Microscopy.

We used a Zeiss

microscope

(Axiovert 135-TV) equipped

withax100

objective

(Neofluar;

numerical

aperture

=

1.3,

Zeiss).

For

excitation,

the514-nm line ofan

Ar+

laser

(Innova

306,

Coherent) running

in

TEMoo

mode was

coupled through

an

acoustooptic

modulator

(1205C-1; Isomet)

intothe

epiport

of the

microscope.

A

A/4-plate

provided

circular

polarized

excitation

light. Using

a

defocusing

lens

(f

= 100

mm)

in front of the dichroic mirror

(515DRLEXT02;

Omega)

theGaussian excitation

profile

was set to6.1 ±0.8

Am

full-width-at-half-maximum

(FWHM)

and 57 + 15

kW/cm2

meanexcitation

intensity.

Illumination time for each

image

shownwas5 ms. After

long-pass

filtering

(570DF70

Omega

andOG550-3

Schott)

the fluorescencewasdetected

by

a

liquid-nitrogen-cooled

CCD-camera

(AT200,

4

counts/pixel

read-out

noise;

Photometrix) equipped

withaTH512B

chip, (512

x 512

pixel,

27

/m2

pixel

size;

Tektronix).

The

point-transfer

function of the

microscope

wasfound to be

adequately

described

by

a two-dimensional Gaussian

intensity

distributionofwidth pTF=

0.42

pum FWHM,

asdetermined from

images

of 30-nm fluores-centbeads

(Molecular Probes).

Thus,

the diffraction-limitedarea is

ir/4 FpTF2

=0.14

/m2.

The widthof the

intensity

profiles

found

for

single

molecules r=0.48+ 0.08 ,m FWHMwas

larger

than

FpTF

wherethe additional

broadening

could be accountedfor

by

molecular diffusion. For data

acquisition,

the CCDwasusedas

a

storage

device,

such that 12 successive

images

of 40x40

pixels

could be taken

by

using

a frameshift

procedure

allowing

for Abbreviations: TRITC DHPE,

N-(6-tetramethylrhodaminethiocar-bamoyl)-1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine,

tri-ethylammonium

salt; POPC,

palmitoyloleoylphosphocholine;

FWHM,

Proc. Natl. Acad. Sci. USA 93

(1996)

2927

repetition

ratesof

up

to 140

images

per

s. Thecamera

provided

trigger pulses

for the

acoustooptic

modulator for

repeated

illu-minations,

while theslow shutter of the camera was held

open

during

the whole illumination

sequence.

Atestof the mechanical

stability

(17)

ofour

apparatus

was

carriedout

by taking

consecutive

images

of fluorescent latex

spheres

(30

nm;

Molecular

Probes)

immobilized on a

coverslip.

Analysis

ofthe

positions

of the

spheres

gave

no indication for resolvable mechanical drifts ona time scale of seconds. The

positions

of the

spheres

were Gaussian distributed with a

standard deviation of 12

nm,

which

compares

wellwith 15

nm,

the

uncertainty

of determination of their

position by

Gaussian fits.

RESULTS AND DISCUSSION

Fig.

1A shows fluorescence

images

of a

(6.8

x

6.8)

/zm2

membrane area forthe

highest,

intermediate,

andlowest

dye

density

applied

in this

study.

From these

images,

the mean

signal

in an areaof4

pum2

atthe

image

centerwasdetermined and divided

by

the number of

dye

molecules withinthis area. Ameanvalue of

(172

±

15)

counts

per

dye

moleculewasfound for six

dye

densities

covering

the

range

from 10 to

103

dyes/p.m2.

This value

represents

a

quantitative

prediction

for the

intensity

ofan

image

ofan isolated labeled

lipid.

At 10

dyes/p.m2

a critical

density

is reached for which one

dye

molecule,

on

average,

is found

per

diffraction-limited areaof

10

dyesl/m2

10-2

dyes/pm2

I

A 210ms 245ms

I

280ms ±40nm

a

ii = (168±25) counts r = (0.48±0.08)pm _ + residues &. 9Sf jsh p' w

FIG.1.

Images

offluorescence-labeled

lipids

ina

lipid

membrane. The

samples

wereilluminated for 5mswitha

Gaussian-shaped

laser beam of 6.1 ,um width and 57

kW/cm2

meanexcitation

intensity.

(A)

Fluorescence

images

forthreesurfacedensitiesof labeled

lipid.

The

images

show

amembraneareaof 6.8 x 6.8

g,m2.

Color

scaling (blue

=0;red=60

counts)

isidentical for the three

images

presented.

Image

intensity

at103

dyes/,2m2

wasdivided

by

60.

(B)

Sequence

of nine

images

oftwolabeled

lipids

observedatlowestsurface

density

ina5.4x5.4

tum2

membrane area,takenevery35ms.

(C)

Subimage

ofa2.4x2.4

uIm2

membranearea

showing

the

peak

marked

by

*inB.Thenonlinear

least-squares

fitof

atwo-dimensional Gaussian

profile

(18)

tothe

peak yielded

theindicated values for fluorescence

intensity

ii,widthandtwo-dimensional

position

with theirrespectiveconfidence limits

(see

Materials and

Methods).

Residuesof thefitcomparewith

background

noise.

10°

dyes/pm'

A

B

Oms 35ms 70ms

C

4

*

Biophysics:

Schmidt

et

al.

i,

t

Proc.Natl. Acad. Sci. USA 93

(1996)

the

microscope. Images

at this

density

werecharacterized

by

large

fluctuationsofthe

intensity

as shownin

Fig.

1A. For still lower

dye

densities,

intensity

fluctuations occurred as isolated

peaks

as shown for

10-2

dyes/p.m2

in

Fig.

1A. Such isolated

peaks

were

considerably

more intense thanthe

background.

This is shown for two isolated

peaks

in the

sequence

of

images

presented

in

Fig.

1B. The

sequence

was obtained from con-secutive illuminations of the same membrane area

lasting

5 ms

at 35-ms intervals. Three

parameters

of such

peaks,

their

intensity

ii,

width

F,

and

position

inthe membrane

plane

were obtained from

fitting

Gaussian

profiles

to the

peaks

(18).

Note

that theGaussian

profile properly

matches the

point-transfer

function of the

optics

used

(see

alsoMaterials and

Methods).

Such

analysis

is

exemplified

in

Fig.

1C

(for

the

signal

marked

by

* in

Fig.

1B).

Itsfluorescence

intensity,

il,

throughout

the

sequence

is

plotted

in

Fig.

2

(Inset). Appropriate

summation of

theintensities

including

theirvariances

yields

the

probability-density

distribution of

peak

intensity

as shown in

Fig.

2

(19).

This distribution has a maximum at

i\

= 154 counts with a standard deviationoj = 53counts. The value of

Ti

was found

to be

representative

ofatotal of >104

peaks analyzed

for a

large

numberof

membranes,

from which

(ij)

= 173±20counts

per

dye

molecule was determined. The latter value is in

excellent

agreement

withthe

prediction

of172 counts

per

dye

molecule obtained at

high

surface densities. This

provides

confidence that the isolated

peaks

observed

originate

from

individual fluorescence-labeled

lipids.

The

uncertainty

of each

intensity

value

(Fig.

2

Inset,

error

bars)

is

fully

accounted for

by

statistical errors due to shot

noise,

pixelation,

anddiffusionasverified

by

simulations. The additional variation of the

intensity

from

image

to

image

is attributed to variations of the

angle

between the electric field andthe transition

dipole

momentof the

molecule,

likely

due

to surface

corrugations

asseen in force

microscopy images

of the

glass

surfaces used.

300. x103 12 _xx3₃ 200. * 10.-

100

.c

*

Abackground

0 8 0 0

a

_

/

\

image#

66 44 Cu 1 2 0 100 200 300 400 counts

FIG. 2.

Unitary

fluorescence

intensity

of

single

fluorescence-labeled

lipid

molecules. The

probability-density

distributionof

single

molecule fluorescence

intensity

is shown. The

probability-density

distributioniscalculated from data shown in theInsetas a superpo-sition ofnormalizedGaussians,each

entering

atiiwithawidth

given

by

theerrorbar.For

comparison,

the

probability-density

distribution ofthe

background

noise is shown.

(Inset)

Fluorescence

intensity

of the molecule marked

by

*in

Fig.

1Basit

progressed throughout

the

image

sequenceasdetermined

by

Gaussian fits

(Fig.

1C).

Thetwo

lipid

molecules observed in

Fig.

1B

undergo

motion

asit is

apparent

from the lateral shifts of the

peaks

inthe

image

sequence.

The

position

of a

single

molecule

during

each

illuminationwasdetermined from Gaussianfits

(Fig.

1C).

The

uncertainty

was 30

nm,

on

average,

which is 7 times smaller

than the diffraction limited width of the

optics

used. This

positional

accuracy

allowed us to visualize the

trajectory

of

individual

fluorophore

movements for timeintervalsof 35 ms as shown in

Fig.

3 for the two molecules in

Fig.

lB. The

observed

displacements

of the

lipids

conforms with two-dimensionalBrownian diffusioninthe membrane.

Analysis

of

trajectories

of531 individual molecules showed that the

di-rection of diffusional

steps

of

simultaneously

observed mole-cules were uncorrelated. The

mean-square

displacement

(MSD) (20),

and the time

lag

(tlag)

yielded

the

expected

linear

relationship

asshownin

Fig.

3

(Inset).

Using

the relation

MSD=

4Dlattlag

(21),

the

lipid

motion ischaracterized

by

the lateral diffusionconstant

Dlat

=

(1.42

+

0.13)

X

10-8

cm2/s.

Thisvalueisinfair

agreement

with

Dlat

=(0.77

+

0.13)

x10-8

cm2/s

determined

by

us at the

highest

surface

density

of

103

dyes/p.m2

from

experiments

using

the fluorescence

recovery

after

photobleaching

(FRAP) technique (22)

with a

spot

diameter of 3 p.m. The two methods

analyze

diffusion at

different

length

scales:33

pm

in our FRAP

experiments

and

-0.3 p.m in the

single

molecule

experiments.

Thefactor of2

differencein

Dlat

is consistentwith the

general

finding

that

Dlat

values for

lipids

decrease with

increasing

length

scale of the method used

(23).

The time

period

of

following

the

trajectory

of a

single

moleculewaslimited

by

photobleaching

of the

fluorophor (24,

25).

Photobleaching

wascharacterized

by

a

quantum

efficiency

for

photobleaching

of (b - 2

10-6,

as determined from a

sample

with

103

dyes/p.m2

and also estimated from

single

molecule data. This

quantum

efficiency agrees

with values

reported

for rhodamine

bleaching ranging

between

4b

=

10-5

and

10-7

(26,

27).

About 4000counts werecollectable froma

single

labeled

lipid

before

bleaching

occurred. This

corre-sponds

to an overall illumination time of -120 ms at the

excitation

intensity

of57

kW/cm2

usedin this

study.

Bleaching

1,5 2,0 2,5 4,5 5,0 2,0- 2. 2,0 2,5 , 2, -25 E 4,0. 4,5. 1, -4,5 2,0 2,5 4,5 5,0 5 2,0 2,5 4,5 5,0

FIG. 3. Diffusion of

single lipid

molecules.

Trajectories

of the two-dimensional diffusion for the two

lipid

molecules in

Fig.

1B determined from 12successive

images.

(Inset)

MSDversustime

lag

calculatedfor 531

trajectories.

Observed

displacements

areconsistent withtwo-dimensional Brownian diffusion of the

lipids,

since thedata

Proc.Natl. Acad. Sci. USA 93

(1996)

2929 occurred in a

one-step process

for the

present

time resolution

of35

ms,

which is takenas anadditional

fingerprint

for

single

molecule observation

(14, 28).

Single

molecule

imaging

as described here can be

charac-terized

by

two

figures

of merit. The first is the

signal/noise

ratio for detectionof

single dye

molecules,

which isdefinedas

(S/N)

=

(i1)/rb,

where

o-b

is the standard deviation of the

background

intensity.

Itsdistributionisincluded in

Fig.

2for

comparison

and is characterized

by

a standard deviation of

ab = 6

counts,

essentially

due to CCD readout noise. This

yields

a

signal/noise

ratio of 28. The

high

reliability

for detection

using

a5-msilluminationtime

permitted

for

exper-imentsat

considerably

shorter illuminationtimes

(not shown).

For

example, single dye

moleculeswere still detectablewith

(S/N)

-3 at anillumination time of

only

0.5ms.Thesecond

figure

of merit is

given

by (iTl/o)2,

representing

the "stoichi-ometric resolution" of themethod. It describes its

potential

for the

study

of stoichiometries-for

example,

in

applications

to

biological

systems

by

theuseoffluorescence-labeled

ligands

like antibodies.

Considering

a

number,

n,of colocalized

flu-orescence-labeled

ligands,

the

intensity,

in,

and standard

de-viation, on,

oftheir fluorescence is

expected

to be

'n +

on =

nil

+

V/no1.

By

a

priori

knowledge

of the

unitary intensity

il,

the numbern canbe determinedas

long

astheerror

V-oil

is smaller thani1 orfornsmaller than

(1/oir)2.

Therefore,

(11/c)2

setsthe

limitin

determining

thenumber or

stoichiometry

ofcolocalized

dye

molecules.Fromthe values foundfor the

unitary

intensity

il

and for

r1,

the method

appears

to have the

potential

for a

stoichiometricresolution of

up

to n = 8molecules.

CONCLUSIONS

Single

lipid

molecules

carrying

one fluorescence label were

reliably

detected

by

conventional fluorescence

imaging

at millisecond time resolution.

Single dye images

showed

repro-ducibly

a

unitary

fluorescence

intensity

of 173 counts at the illumination conditions

applied.

Due to the

high image

con-trast,

given by

(S/N)

=

28,

small diffusional

steps

of individual

lipids

in the membrane

plane

could be resolved with 30-nm

precision. Trajectories

showed that

lipid

motion occurs

ran-dom with MSDs described

by

a lateral diffusion constantof

Dlat

= 1.42 X

10-8

cm2/s.

The

accuracy

in

detecting unitary

fluorescence intensities ledtothe definition ofastoichiometric resolution which describes a novel

potential

for

optical

mi-croscopy.

Since the method widensthe

application

range

of

single

molecule

microscopy

fromimmobiletomobile

systems,

onefield of

application

isbioscience-for

example,

the surface

of

living

cells. In

approaches

used so

far,

biological ligands

were

employed,

carrying many dye

molecules

(17,

18, 20, 22,

29,

30).

This allowed tovisualize

dynamical processes

occur-ring

at

living

cell surfaces.

However,

there is a need for fluorescence

microscopy,

which enables us to resolve

processes

both in time and at the

single

molecule level with stoichio-metric resolution. Such novel

insights

may

be obtained

by

the method

presented

using

monolabeled fluorescence

ligands

like

antibodiesorother

compounds

used

by

naturefor molecular

recognition.

This work was

supported by

the AustrianResearchFonds,

Project

S06607-MED.

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