Today’s take-home lessons(i.e. what you should be able to answer at end of lecture)

1. Super-resolution microscopy—STORM, PALM, SHRImP, SHREC microscopy (gets resolution << /2)

2. 1- vs. 2-photon Microscopy3. Hidden Markov Method (HMM) Analysis

1. Read ECB: Will assign later today (for real!).2. Homework assigned (later) today (for real!).

Today’s Announcements

Can we achieve nanometer resolution?i.e. resolve two point objects separated by d <</2?

Idea: 1) Make Point-Spread Function smaller << /2 2) Make one temporally or permanently disappear, find

center (via FIONA) and then reconstruct image.

Super-resolutionBreaking the classical diffraction limit

Basics of Most Super-Resolution MicroscopyInherently a single-molecule technique

Huang, Annu. Rev. Biochem, 2009

Bates, 2007 Science

STORM STochastic Optical

Reconstruction Microscopy

PhotoActivation Localization Microscopy (F)PALM(Photoactivatable GFP)

1 m1 m 1 m

PALM TEM

Mitochondrial targetingsequence tagged with mEOS

TIRF

Patterson et al., Science 2002

You get automatic confocal detection with 2-photon microscopy

emission

1p

two-photonOne-photon

wavelength

Inte

nsity

2p

Simultaneous absorption of two photonsReasonable power if use pulsed laser

Two-Photon MicroscopyInherently confocal, long wavelength (less scattering)

One photon

Inherent spatial (z-) resolutionLow light scattering

Single-color excitation with multiple emission colors

objective

two photon

Advantages of Two-Photon MicroscopyCan we excite with 2-Photon Excitation?

Q-dots with 1-P & 2P

Advantages of Qdots:Brightness, LongevityMultiple colors with single excitationSingle molecule sensitivity for 1P

Disadvantages of Qdots:Blinking, Size, Difficulty of Labeling

Single Molecule sensitivity has not been shown for Q-dots at RT & in water-based solutions

Zipfel, Nat. Biotech., 2003

2-Photon Widefield Excitation of Single Quantum Dot

• Blinking and emission intensity – laser power plot prove that it is single Qdots and 2-photon excitation

Qdot585 in M5 buffer, no deoxygenation, <P> = ~220 W/cm2 , 30 msec/frame, scale bar 1 um

449 mW46 mW

Suppression of Blinking and Photobleaching by Thiol-group Containing Reductants

• Similar with under 1-photon excitation, small thiol-group containing reductants, such as DTTDTT and BMEBME, can sufficiently, though not completely, suppress Qdot’s blinking

• Large thiol-containing molecule like glutathione, carboxylic reductant like TCEP and Trolox do not work well

• Thiol-containing ligands may help passivate the Qdot surface

100 mM DTT

Qdot655, 1800 W/cm^2, 30 msec/frame, 30 sec

Myosin V labeled on the Head

37 nm

q655

2-P FIONA localization = 1.6 nm

-200

0

200

400

600

800

1000

1200

1400

2

4

68

1012

1416

18

24

68

1012

1416

Z D

ata

X D

ata

Y Data

3D Graph 1

Myosin V, 2 uM ATP, 100mM DTT, 50msec exposure time, 655Qdot labeled on head, widefield 2-photon excitation (840nm) and TIR 1-photon excitation (532nm)

0 2 4 6 8 10 12 14 16 18-600

-500

-400

-300

-200

-100

0

100

Myosin V Localization, 655nm Qdot Labeled on Head, 2P excitation Myosin V Steps, Student's T-test Fitting Myosin V Localization, 655nm Qdot Labeled on Head, 1P excitation Myosin V Steps, Student's T-test Fitting

Dis

pla

ce

me

nt

(nm

)

Time (sec)

Myosin V walking, 1P and 2P excitationCargo binding domain walks 37 nm

1-P

2-P

Zhang, unpublished

REGULAR FLUORESCENCE MICROSCOPY

A lot of autofluorescen

ce

TWO-PHOTON Q-DOT EXCITED FLUORESCENCE MICROSCOPY

MDA-MB-468 Cells. 1nM QD (EB:SQ=1:1)

Overlay of cells’ brightfield images (red) and fluorescence (green)

Individual EGF Receptors in Single Breast Cancer Cells

Eli Rothenberg at UIUC; Tony Ng and Gilbert Fruhwirth @ King's College School of Medicine & Dentistry, London

TWO-PHOTON Q-DOT EXCITED FLUORESCENCE MICROSCOPY

REGULAR FLUORESCENCE MICROSCOPY

MDA-MB-468 Cells. 1nM QD (EB:SQ=1:1)

Rendered 3D Images

Individual EGF Receptors in Single Breast Cancer Cells

Eli Rothenberg at UIUC; Tony Ng and Gilbert Fruhwirth @ King's College School of Medicine & Dentistry, London

High Accuracy Organelle Tracking in Pigment Cells(with non-fluorescent objects)

Xenopus Melanophores with Melanin-Filled Dark Melanosomes

Aggregated Melanosomes(+ Caffeine)

Borisy et al., Curr. Biol., 1998

Dispersed Melanosomes (+ Adrenalin)

~20 min.

kinesin-2, dynein, myosin VKinesin

Dynein

bFIONA: Molecular Motors in Action“Normal” 8 nm steps

Kinesin 2

Dynein

Kural, PNAS, 2007

1 vs. 2 kinesins dragging a cargo (in vivo)

• 1 kinesin: 1 cargo

8 nm 8 nm

8 nm

2 kinesin: cargo4 nm

Two kinesins operate simultaneously in vivoMust use Hidden Markov Method to see

Two kinesins (+2 Dyneins), in vivo, are moving melanosome

Unlikely due to microtubule motion because fairly sharply spiked around ±4-5 nm

Syed, unpublished

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?Why is it called Hidden?

What is it good for?

Simple model (non-HMM) applied to ion channels

C O←→

In general, N exponentials indicate N open (or closed) states. Hence the number of open (closed) states can be determined, even if they have the same conductance. In addition, the relative free energies of the open vs. closed two states can be determined because the equilibrium constant is just the ratio of open to closed times and equals exp(-G/kT).

Transitions between one or more closed states to one or more open states.

(From Venkataramanan et al, IEEE Trans., 1998 Part 1.)

Model (middle) of a single closed (C) and open (O) state, leading to 2 pA or 0 pA of current (middle, top), and a histogram analysis of open (left) and closed (right) lifetimes, with single exponential lifetimes. In both cases, a single exponential indicates that there is only one open and one closed state. Hence the simple model C O is sufficient to describe this particular ion channel.

Histogram: Not all information used

For example, if a channel happens to be closed for a long time, does that tell you something about how long it will then be open? The simplest kinds of models that can utilize these correlations are known as Markovian models, where the basic assumption is that there are a small number of distinct channel states and that the transition rates between the states are independent of time.

The Markov property states that the probability distribution for the system at the next step (and in fact at all future steps) only depends on the current state of the system, and not additionally on the state of the system at previous steps.

(Non-Markovian models postulate a large number of states where the dynamics can be described by diffusion or fractals.)

Makes no use of correlations; add Markov processes.

Examples of Markov ProcessesExample 1: Random walk on the number line where, at each step, the position may change by +1 or −1 with equal probability. From any position there are two possible transitions: to the next or previous integer. The transition probabilities depend only on the current position, not on the way the position was reached. For example, if the current position is 5, then the transition to 6 has a probability of 0.5, regardless of any prior positions.

Example 2: Dietary habits of a creature who eats only grapes, cheese or lettuce, and whose dietary habits conform to the following (artificial) rules: it eats exactly once a day; if it ate cheese yesterday, it will not today, and it will eat lettuce or grapes with equal probability; if it ate grapes yesterday, it will eat grapes today with probability 1/10, cheese with probability 4/10 and lettuce with probability 5/10; finally, if it ate lettuce yesterday, it won't eat lettuce again today but will eat grapes with probability 4/10 or cheese with probability 6/10. This creature's eating habits can be modeled with a Markov chain since its choice depends on what it ate yesterday, not additionally on what it ate 2 or 3 (or 4, etc.) days ago. One statistical property one could calculate is the expected percentage of the time the creature will eat cheese over a long period.

Example 3: A series of independent events—for example, a series of coin flips—does satisfy the formal definition of a Markov chain. However, the theory is usually applied only when the probability distribution of the next step depends non-trivially on the current state.

http://en.wikipedia.org/wiki/Markov_chain

General Outline: Making a Markov Process

Then the model’s parameters are chosen and optimized. For example, in an ion channel with N states, each state has its ionic current (e.g. 2 pA), initial state probability (e.g. starts off in open state) and transition rates to all other states (an N x N matrix). These parameters are then optimized to give the most likely fit to the actual data. So-called maximum-likelihood methods are used to find and evaluate the parameters; when comparing different models, a “likehood-ratio” test is used.

First the number of states and the connectivity between these states are chosen. For example, a simple ion channel model might involve two closed states (closed and inactive) and one open state, and the open state can only transition into the inactive form.

A cartoon showing two possible models. B represents some inactivation due to a drug (lidocaine). (Horn, Biophys. J. 1983)

A cartoon showing three possible gates in the Shaker channel: (1) the S6 gate; (2) the pore gate; and (3) the N-type inactivation gate. (Zheng, JCB, 2010)

Class evaluation1. What was the most interesting thing you learned in class today?

2. What are you confused about?

3. Related to today’s subject, what would you like to know more about?

4. Any helpful comments.

Answer, and turn in at the end of class.