Experimental methods in Biophysics

Lecture 1: Techniques for observing single molecules

Outline• Lecture 1: Techniques for optical detection of

individual biomolecules

Localizing single molecules

Tracking single molecules in concentrated solutions

Measuring dynamics in single molecules

• Lecture 2: Techniques for imaging single molecules in crowded environments

• Lecture 3: Techniques for manipulating single biomolecules

Distribution-useful if population is

heterogeneous.

time

Time trajectory-useful if the dynamics is

not synchronizable

Ultimate Sensitivity

Why study single molecules

• At most one molecule per detection volume

• Signal > Background

Laser

wavelength

S1

S0

T1

laser

fluorescence

kR

ISC

kISC

1-10 nsec

<1%

How to optically detect single molecules?

Life history of an excited state electron in a

luminescent probe

Localizing Single molecules with high resolution

Image of a point source

Will a geometrically perfect lens generate a mathematical point

focus image from a point source?

What is the size of the blur spot or Point Spread Function (PSF)?

D = 0.61λ/NA

D = center to zero distance

Numerical aperture

Numerical Aperture and PSF

D = 0.61λ/NA

Accuracy and Resolution

Accuracy: minimum distance or volume that one can locate a

particle’s position within a certain time period. Current state of

the art = 1 nm accuracy in 1–500 ms.

Resolution: minimum distance or volume that can be measured

between two (identical) particles in a given period of time. For

visible fluorescence in the far-field, it is λ/2 or 200–300 nm.

However, with modern super-resolution methods, the optical

resolution is 8–25 nm.

Fluorescence Imaging with One Nanometer Accuracy

(1.5 nm, 1-500 msec)

Fluorescence from a single dye

Width = λ/2NA

0

40

80

120

160

200

240

280

05

1015

2025

510

1520

25

Photo

ns

X DataY axis

Prism-type TIR 0.2 sec integration

Z-Data from Columns 1-21

center

width

Enough photons (signal to noise)…Center determined to 1 nm.

Center ≈ width/√N

Accuracy depends on how well you can locate the center of the

fluorescence distribution.

Important Parameters in determining accuracy

1. Number of photons (Signal) must be high. Center of PSF can be

located to within width/√N.

2. Size of detection pixel. If pixel is too large, you cannot resolve the

PSF. If pixel is too small, the signal-to-noise ratio diminishes and the

PSF may become anisotropic.

3. Background noise from the detector or from the sample must be low.

The former can be essentially eliminated with electron multiplying

charge coupled devices (EMCCDs). Autofluorescence can be greatly

minimized using Total Internal Reflection Microscopy

4. Photobleaching time of the fluorophore must be large

Total Internal Reflection microscope

Wide-field

Objective TIR

Laser

Objective

Filter

Dichroic

Sample

CCD

Detector

Lens

Wide-field, Prism-type,

Total Internal Reflection

Microscope

Sample

Laser

Objective

Filter

CCD

Detector

Lens

Calculating Super-Accuracy

Goal is to determine the center, or mean value of the distribution, μ=(x0, y0), and its

uncertainty, standard error of the mean (σμ). σμ tells you how well you can localize the

fluorophore.

Relation between σμ and the number of collected photons (N), the pixel size of the

imaging detector (a), the standard deviation of the background (b), and the width of the

distribution (standard deviation, si, in direction i) in two dimensions is given by

22

2222 812

Na

bs

N

a

N

s ii

i

where the index i refers to the x or y direction. The first term is the photon noise, the

second term is the effect of finite pixel size of the detector, and the last term is the effect

of background

Accuracy from a single dye

0

40

80

120

160

200

240

280

05

1015

2025

510

1520

25

Photo

ns

X DataY axis

Prism-type TIR 0.2 sec integration

Z-Data from Columns 1-21

center

width

PSF of an individual Cy3 dye with an integration time of 0.5 s. N=14,200 photons, a=86

nm, b=11, sy=122 nm, sx=125 nm. The expected σμ is 1.24 nm in each direction.

Photon noise only leads to σμ=1.02 nm, pixelation increases σμ to 1.04 nm, and

background noise increases σμ to 1.24 nm.

22

2222 812

Na

bs

N

a

N

s ii

i

Myosin V (Kinesin): Hand-over-hand or Inchworm?

By measuring head (foot)-step size, can differentiate models

Hand-over-hand: Head (foot) takes 74 (16.6) nm steps

16 nm

Adapted from Hua, Chung, Gelles, Science, 20028 nm 8 nm

Inchworm: Head (foot) takes 37 (8.3) nm steps

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

0

5

10

15

20

25

30

35

40

duration between adjacent steps (sec)

num

ber

of

step

s

0 5 10 15 20 25

200

300

400

500

600

700

800

900

1000

MyoV steps

Time (Sec)

Positio

n (

nm

)

72 74 76 780

1

2

no. of

ste

ps

step size (nm)

nm

nm

Myosin V Steps

Steps: 75,0,75,0...

0 10 20 30 40 50 60 70 80 90 100

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

60 65 70 75 80 85 900

10

20

30

40 = 74.08 nm

= 5.25 nm

R2 = 0.99346

2 = 1.6742

Nmol

= 31

Nstep

= 227

histogram of 74-0 nm steps

step size (nm)

num

ber of

ste

ps

75.4 nm

82.4 nm

65.1 nm

83.5 nm

69.8 nm

64.2 nm

78.8 nm

70.0 nm

70.9 nm

79.1 nm

67.4 nm

68.8 nm

73.7 nm

70.7 nm

70.1 nm

68.9 nm

71.3 nm

72.0 nm

time (sec)

Pos

itio

n (n

m)

74 nm +/- 5nm

Strongly supports

hand-over-hand

Tracking single molecules in concentrated solutions

Detecting Single Molecules in reduced volume

Laurence, et. al. Science (2003), 299, 667 - 668

Conventional observation of single molecules require 10-12 to 10-9 M concentrations of

fluorophore in order to isolate individual molecules in solution. However, many enzymes

work at much higher ligand concentrations. Working at biologically relevant, micromolar

concentrations requires reduced observation volume. In addition, temporal resolution of

conventional approaches is often limited by the time it takes for molecules to diffuse out

of the observation volume, usually on the order of several hundred microseconds.

Confocal Microscopes TIR Microscopes Near Field Scanning Optical Microscopes

Solution: Zero Mode Waveguides (ZMW)

Zero Mode waveguides (ZMW

•Circular apertures fabricated on a thin layer of aluminum on a glass coverslip.

•ZMW exhibit a cut-off wavelength of λc=1.7d (where d is ZMW diameter), above which

no propagating guided modes exist in the metallic system.

• Light of wavelengths longer than λc decay exponentially along the length of the

aperture

•For smallest ZMW, the depth of decay is 10nm to 20nm. Effective volume is < 10-20 to

10-21 L

Zero-mode waveguides (ZMW)

Levene, et. al. Science (2003), 299, 682 - 686

How to measure dynamics of single molecules?

Fluorescence Resonance Energy Transfer

(FRET)

Fluorescence Resonance Energy Transfer (FRET):

conformational changes of single biomolecules

Distance dependent interactions between green and red light

bulbs can be used to deduce the shape of the scissors during

the function.

Energy

Transfer

DONOR ACCEPTOR

Energy transfer efficiency

6

0 )/(1

1

RRE

R0=50% transfer efficiency distance

3nm~7nm

“Spectroscopic Ruler”

AD

R0AD

D A 0 25 50 75 100

0.0

0.2

0.4

0.6

0.8

1.0

E

R (Å)

R0=50 Å

Fluorescence Resonance Energy Transfer

Calculating R0

Single Molecule Techniques; Paul Selvin and Taekjip Ha, CSHL Press

Choosing fluorophore pairs for FRET experiments

1. Photostable: Should emit millions of photons before photobleaching

2. Bright: high extinction coefficient and quantum yield

3. Show little to no intensity fluctuation

4. Excitable and emitting in visible wavelengths

5. Relatively Small

6. Commercially available in a form that can be conjugated to

biomolecules

Single RNA Folding via FRET

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500

Fluo

resc

ence

Time (sec)

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

1.2

EFR

ET=I

Acc

epto

r/(ID

onor+I

acce

ptor)

Time (sec)

FR

ET

Effic

iency

Folding Unfolding

Analyzing conformational dynamics with single

molecule FRET

Single Molecule Techniques; Paul Selvin and Taekjip Ha, CSHL Press