Zero-Mode Waveguides for Single-Molecule g g Analysis at High ...
Zero-Mode Waveguides for Single-Molecule g g Analysis at High ...
Zero-Mode Waveguides for Single-Molecule g g Analysis at High ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Zero</strong>-<strong>Mode</strong> <strong>Waveguides</strong> g <strong>for</strong> <strong>Single</strong>-<strong>Molecule</strong><br />
g<br />
<strong>Analysis</strong> <strong>at</strong> <strong>High</strong> Concentr<strong>at</strong>ions<br />
Cha Seoncheol<br />
Sogang University, Department of Physics, Soft M<strong>at</strong>ter Optical Spectroscopy
Review<br />
Fluorescence Correl<strong>at</strong>ion Spectroscopy<br />
APD<br />
Transsmittance<br />
10 1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
DM570<br />
BA575<br />
TMR<br />
400 500 600 700<br />
Wavelength(nm)<br />
Laser Source<br />
Autocorrel<strong>at</strong>ion function<br />
< δ Ft () δFt ( + τ)<br />
><br />
G(<br />
τ ) =<br />
2<br />
< Ft () >
Review<br />
Fluorescence Correl<strong>at</strong>ion Spectroscopy<br />
APD<br />
APD<br />
Transmittancee<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
02 0.2<br />
0.0<br />
DM570<br />
BA575<br />
TMR<br />
400 500 600 700<br />
Wavelength(nm)<br />
Laser Source<br />
Cross Correl<strong>at</strong>ion function<br />
< δδ F F1 () t δδ F F2 ( t + ττ<br />
) ><br />
G(<br />
τ ) =<br />
< F() t >< F () t ><br />
1 2
Review<br />
Fluorescence Correl<strong>at</strong>ion Spectroscopy<br />
P.Schwille., Biophysics Textbook Online (2001).
Review<br />
<strong>Single</strong> <strong>Molecule</strong> Spectroscopy<br />
Considering 1n mol/L solution<br />
0.2μm V eff = π 3/2 r 0 2 z0 ~ 10fL<br />
3μm<br />
1n mol/L · V eff · N a ~ 6<br />
roughly six per volume element<br />
In 100pm ~ 1nm range,<br />
This method is able<br />
to show single molecule dynamics
Why<br />
Limit<strong>at</strong>ion of FCS
Why<br />
Previous approaches to overcome limit<strong>at</strong>ion of FCS<br />
T. E. Starr, N. L. Thompson, Biophys. J. 80, 1575 (2001).<br />
F. de Lange et al., J. Cell Sci. 114, 4153 (2001).
Review<br />
<strong>Single</strong> <strong>Molecule</strong> Spectroscopy<br />
V eff ~ 1fL<br />
0.2μm<br />
3μm μ<br />
V eff ~ <strong>at</strong>to~zeto liter<br />
KTS K.T.Samiee, i et t al., l Bi Biophys. ph J J. 88 88, 2145 (2005).<br />
(2005)
How<br />
Setup<br />
60x w<strong>at</strong>er immersion<br />
(NA ( = 1.2) )<br />
488nm circularly<br />
polarized light
How<br />
<strong>Zero</strong> <strong>Zero</strong>-<strong>Mode</strong> <strong>Mode</strong> Waveguide (Example)<br />
a<br />
y z<br />
a<br />
x<br />
Perfect conductor<br />
��<br />
⎧⎪E⎫⎪ ⎨ ⎨�� ⎬<br />
⎪⎩B⎪⎭ 2 2<br />
( ∇ + μεω μεω ) = 0<br />
��<br />
⎧ ⎫<br />
2 2 2 ⎪E ⎫⎪<br />
[ ∇ t + ( μεω − k )] ⎨�� ⎬=<br />
0<br />
⎪⎩B⎪⎭ �� ��<br />
Exyzt ( , , , ) = Exye ( , )<br />
�� ��<br />
Bxyzt ( , , , ) = Bxye ( , )<br />
2 2 2<br />
μεω −k≡ γ > 0 By B.Cs<br />
So So, this equ<strong>at</strong>ion has the modes .<br />
± i( kz−ωt) ± i( kz−ωt) Jackson (1999)
How<br />
<strong>Zero</strong> <strong>Zero</strong>-<strong>Mode</strong> <strong>Mode</strong> Waveguide (Example)<br />
y z<br />
a<br />
x<br />
2<br />
[ ∇ t + γγm ] ψψm<br />
= 0<br />
2 2 2<br />
∇ + k m = μεω μ m −γγ<br />
m<br />
Define<br />
From B.Cs<br />
1 1<br />
k = 2π<br />
−<br />
λ λ<br />
a 2 2<br />
m<br />
Perfect conductor<br />
ω<br />
m<br />
2<br />
m<br />
=<br />
γ =<br />
λλ<br />
m<br />
~<br />
γ m<br />
με<br />
2π<br />
m<br />
2<br />
a<br />
a<br />
2 2<br />
For longer wavelength (λm>a) are evanescent<br />
and their intensity decays exponentially<br />
along the length z of the guide<br />
I( z) ∝ e<br />
ikz<br />
Jackson (1999)
How<br />
<strong>Zero</strong> <strong>Zero</strong>-<strong>Mode</strong> <strong>Mode</strong> Waveguide (Example)<br />
y z<br />
a<br />
x<br />
Perfect conductor<br />
For circular waveguide case,<br />
1 1<br />
k = 2 − 2<br />
λ 1.7d<br />
I( z) ∝ e<br />
ikz<br />
Jackson (1999)
How<br />
<strong>Zero</strong> <strong>Zero</strong>-<strong>Mode</strong> <strong>Mode</strong> Waveguide<br />
For<br />
Real Metal (Skin depth Effect)<br />
-> Solving by Numerical Method
Calcul<strong>at</strong>ion<br />
Coupling Efficiency<br />
radi<strong>at</strong>ive r<strong>at</strong>e of a dipole<br />
∝ density of photonic st<strong>at</strong>es available <strong>for</strong> emission<br />
Approxim<strong>at</strong>ion : k r(z) ~ p(z)<br />
k kr ( z ) p ( z )<br />
Qz ( ) = ≈<br />
k ( z) + k p( z) + C<br />
r nr<br />
constant such th<strong>at</strong><br />
Q(0) equals the quantum yield<br />
p(z) : Averaging over all dipole orient<strong>at</strong>ions yields
Calcul<strong>at</strong>ion<br />
Effective Volume<br />
p( z)<br />
Sz ( ) = Izpz ( ) ( )<br />
p( z) + C<br />
V<br />
eff<br />
∫<br />
∫<br />
4<br />
2<br />
3 2<br />
π d ( Szdz ( ) ) 1.56πLλ<br />
= =<br />
2<br />
2 2<br />
4 S ( z) dz λ − 36L<br />
3 2<br />
1.56πLλ<br />
Veff | L= 14m ~ | 2 2 L= 14m<br />
~14zl<br />
λ −<br />
36L
Calcul<strong>at</strong>ion<br />
Correl<strong>at</strong>ion Function<br />
1-Dimensional Diffusion<br />
∞<br />
2<br />
2 −υ<br />
Dτ<br />
G( ) ∝ ∫ ( S( z)cos( z) dz) e d<br />
υ ∫<br />
τ υ υ<br />
L<br />
b by perfect f t conductor d t approxim<strong>at</strong>ion i ti<br />
τ d<br />
π τd τd 2 τd 1/2 d erf ( R)<br />
τ<br />
− τ<br />
G( τ ) = G0[ ((1−2 ) e erfc(<br />
− ( ) )) −<br />
] 2 2<br />
4 ττ ττ ππ<br />
ττ ττ<br />
(1 + R )<br />
K.T.Samiee, et al., Biophys. J. 88, 2145 (2005).
Results<br />
Correl<strong>at</strong>ion Function<br />
N<br />
R110dCTP : Rhodamine green + dCTP G(0)<br />
=<br />
2<br />
( N + B )<br />
Free parameter is only waveguide diameter in fits<br />
<strong>Zero</strong>-<strong>Mode</strong> Waveguide increases<br />
temporal resolution significantly
Results<br />
Correl<strong>at</strong>ion Function
Results<br />
Correl<strong>at</strong>ion Function
Change language