Download What is Hidden Markov Method (HMM)?

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smFRET
Single molecule FRET
Reminder about FRET
R↓ E↑
R↑ E↓
http://bio.physics.illinois.edu/
sm FRET data
Imaging (Single Molecules) with very good S/N
(at the cost of seeing only a thin section very near the surface)
Total Internal Reflection (TIR) Microscopy
Free dyes don’t contribute background
TIR- ( > c)
Exponential
decay
dp=(l/4p)[n12sin2i) - n22]-1/2
For glass (n=1.5), water (n=1.33):
TIR angle = >57°
Penetration depth = dp = 58 nm
With dp = 58 nm , can excite sample and not much background.
Experimental Setup: Imaging Single Molecules
Total Internal Reflection Microscopy
Prism TIR (Wide-field)
Objective TIR (Wide-field)
Sample
Objective (NA=1.49)
Excite donor-only
(or can use two
wavelength, i.e. ALEX)
Dichroic
Laser
Filter
Lens
CCD
Detector
Objective: + somewhat higher
collection efficiency,
(-) autofluorescence of objective
Lots of approximations
q
A
__
qD
In fact IDID/qD : IAIA/qA
Often, though not always, use FRET to say that A is closer than B
Assuming that k2 doesn’t change too much.
smFRET on Telomeric DNA
Folded
[G-quadruplex: 6- telomeric sequence (TTAGGG)4] 
Telomeres: single-stranded ends of DNA.
Fold up to make sure not recognized as
double-stranded breaks.
Unfolded
G-quadruplex: at
least 3G, repeated
4 times
G-quadruplex “hides” the double-stranded break of DNA
G-Quadruplex DNA
Salt stabilizes G-quadruplex
Excite 1 wavelength,
look at D-only and A-only.
At given [salt] will have stochastic (random) amount of Energy Transfer
HMM Analysis
How fast transitions occur
Determine the average transition state between two conformations.
Assume Markov state where probability per unit time depends only on current state
the lifetime of each state is exponential.
Process is hidden because we don’t observe FRET state, but rather the fluorescence
What is Hidden Markov Method (HMM)?
Hidden Markov Methods (HMM) –powerful statistical data analysis methods
initially developed for single ion channel recordings – but recently extended to
FRET on DNA, to analyze motor protein steps sizes – particularly in noisy traces.
What is a Markov method?
the transition rates between the states are independent of time.
Why is it called Hidden?
Often times states have the same current, and hence are hidden.
Also, can be “lost” in noise.
What is it good for?
Can derive signals where it appears to be only noise!
Lec 17: 4/2010, Physics 498: http://courses.physics.illinois.edu/biop401/lecturesSP10.htm
Hidden Markov Models
An impressive feature of combining Hidden Markov & Maximum Likelihood models is
the ability to extract signal from noise. Indeed, they are often called Hidden Markov
Methods because the observable (ionic current, or position in the case of molecular
motors) is often hidden in the noise.
a.
c.
b.
Use of Hidden Markov Methods to analyze single ion channel recordings. a)
Ideal current vs. time, showing ion channel transitions with two different
conductivities and forward and backward rate constants of 0.3 and 0.1. B)
Data of (a) added to white noise such that noise level = signal level. C)
Extraction of kinetic parameters using HMM from noisy data in b, showing
kinetic constants can be recovered. (Venkataramanan et al., IEEE
Transactions, 1998, Part I.)
The End