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

1. (HiddenMM) Analysis: Can see signal with a lot of noise (con’t).2. SHRImP- Super High Resolution Imaging with Photobleaching.

1. Homework assigned #6 (assigned last Friday; due Monday, 4/12 in class.

2. This Wednesday: in class quiz on “take-home messages” : won’t be solely fill in the blanks.

3. Next Monday 4/12: Klaus Schulten birds and magnetotaxis

4. Next Wednesday 4/14: VMD (computer analysis)

Today’s Announcements

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!

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.

Two general points: Notice that correlations between states are inherent in the topology and rate constants. (For example, if state B can only be reached through State A, then the presence of state B would indicate that state A should be found in some time before State B.) Furthermore, like the histogram method mentioned, multiple states (conformations) with the same signal (e.g. multiple open states with the same ionic conductance, or multiple closed states) can be detected via statistical analysis from their lifetime distributions.

Outline con’t: Making a Markov Process

Hidden Markov ModelsAn 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.

b.

c.

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.)

Multiple algorithms for finding best pathways.

There are multiple ways to do HMM. The Viterbi algorithm is what QuB uses to idealize the data (IDL command) but Viterbi is not a guaranteed global optimum since it is a selected pathway through the data, but its much faster than the alternative, the point likelihood. The alternative is to do the maximum point likelihood (MPL command) that optimizes the parameters (amplitude and rates) over the selected data.

Molecular motors can be modeled like ion channels

Conceptually a transition between a closed and open state in an ion channel corresponds to a molecular motor taking a step. A transition between one closed ion channel state and another closed state corresponds to a conformational change within the motor that does not lead to a step – e.g. hydrolysis of ATP into ADP + Pi in kinesin. These states can potentially be detected because they affect the kinetics (stepping rate and /or distribution). Hence, an important aspect of this analysis is that we may be able to discover the presence of new conformational states, likely associated with nucleotide states. In addition, if motors walk in a hand-over-hand mechanism, and there is an asymmetry between the two heads – e.g. a step where “left foot” goes forward, vs. “right foot” goes forward – and one tends to overwinds the coiled-coiled stalk, and the other tends to underwind the stalk, then this may show up in the stepping kinetics. This is analogous to an ion channel with multiple states of equal conductance.

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

Vinculin-tagged dEosFP

Magnified PALM imageTIRF image

Comparative TIRF and PALM imagesPALM

G. H. Patterson et al., Science 297, 1873 -1877 (2002) Photo-active GFP

Wild-type GFP T203H GFP: PA-GFP

Photoactivatable variant of GFP that, after intense irradiation with 413-nanometer light, increasesfluorescence 100 times when excited by 488-nanometer light and remainsstable for days under aerobic conditions

Native= filled circle

Photoactivated= Open squares

Photoactivation and imaging in vitro

G. H. Patterson et al., Science 297, 1873 (2002)

Breaking the Rayleigh criteria: 1st method• Can we achieve nanometer resolution?• i.e. resolve two point objects separated by d << /2?

SHRIMP

Super High Resolution IMaging with Photobleaching

P1P2

SHRImP on DNA(Super-High Resolution Imaging with Photobleaching)

100

200

300

400

500

600

700

800

900

0200

400600

8001000

0

200

400600

800

-100

0

100

200

300

400

500

600

700

0200

400600

8001000

0

200

400

600

800

-100

0

100

200

300

400

500

600

0200

400600

8001000

0

200

400

600

800

Utilizing Photobleaching for Colocalization

- =

Time (sec)

0 20 40 60 80 100 120 140

Inte

gra

ted

in

ten

sity (

co

un

ts)

35000

40000

45000

50000

55000

Additional knowledge: 2 single dyesWhen one dies, fit remaining PSF accurately;

then go back and refit first PSF.

Separation = 329.7 ± 2.2 nm Separation = 324.6 ± 1.6 nm

Control: DNA Molecule End-to-End Separation

•DNA labeled Cy3 on 5’ end, hydridized.•Flowed over coverslip coated with nitrocellulose to prevent adverse photophysical interaction of dye with glass•DNA binds non-specifically to NC surface•*DNA is stretched by fluid flow to 150% extension (Bensimon, Science, 1994).

Conventional resolution: 300 nmUnconventional resolution: few nm!

Measured Distance

10.7 ± 1.0 nm

13.0 ± 0.5 nm

30-mer

17.7 ± 0.7 nm51-mer

Sample

40-mer

Gordon et al. PNAS, 2003

DNA Replication: made with very high fidelity

Is each mutation independent of the another mutation?

How does mutation rate depend on time?

Assume mutations accrue at constant ratei.e. probability of mutation time.If each mutation is independent, then probability of:2 mutations = t2

..6 mutations =

t3

t6

Since Probability (cancer) ~ t6, likely that cancer caused by average of six mutations

3 mutations =

Note: This assumes that you get 6 mutations “all of a sudden,” that is, within a certain period of time, that gives you cancer. For example: If you get a mutation with a rate of 1/year, then after 2 years you have 2 mutations, after 3 years you have 3 mutations , etc. But if the body cleans up the mutation (within the time it takes you to get 6 mutations—in this case, 6 years), these don’t likely cause cancer. It’s only if you “all of a sudden” get the 6 mutations, that it causes cancer. In this case the rate at which the body “cleans up” the mutation is important.

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.