Finals

Systems approach to fundamental limitations in nano-scale interrogation

Tathagata De

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Organization: A new paradigm of sample profile estimation  Model based sensor-loss detection  Dynamic study of surface morphology of live cells 

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How SPM works

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Surface Profile estimation

Utilizing Observer based solution of H∞ controller, we may estimate sample profile at infinite bandwidth

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AFM: Systems Viewpoint

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Compromise between regulation and profile estimate

 Actual

objective is to estimate sample profile (d)  Does regulation serves that purpose? 7

Existing wisdom

 Use

control effort as image  It works in low frequency. Why?  Is there a fundamental limit on bandwidth of imaging? 

We will answer these question from systems viewpoint

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Contact mode: Piezo input for image

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Limitations of actuation signal

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Result

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Problem Formulation: with Estimation in mind…

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A New Estimate Signal for SampleProfile

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Observer based solution of regular H∞ problem

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Error in profile estimation

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Estimation error

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State estimation error:

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Strictly proper plant yields zero estimation error

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Proof: Contd…

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Special Structure Zero Error

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To show Zinf and L2inf has the claimed form:

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To show solution of ARE is zero

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Hamiltonian is upper triangular

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Uniqueness of ARE solution

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Solution of 2ndARE is zero

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Strictly proper plant yields zero estimation error

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Maps from uncertainties

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Remarks on robustness:

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Conventional vs New Estimate

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Conventional vs New Estimate

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Conventional vs New Estimate

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Conventional vs New Estimate

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Summary  Image

reconstruction is cast as a disturbance estimation problem  Better images by tapping new signals  All implementations are done in our lab and all presented results are verified experimentally

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Sensor Reliability

Model Based solution for sensor loss detection

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Background of the problem  Relevant

to Intermittent Contact Mode AFM operation  High Q of cantilever  Long transients  Loss of tip-sample interaction  Sensor output is spurious

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Difficulty of the problem  When

only source of information (cantilever sensor) is malfunctioning, how do you detect that?  Corrupted image may look similar to non-corrupted one.  No direct way to verify fidelity of the image

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How SPM works

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Dynamic Mode Operation

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Amplitude Modulation AFM Operation

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Experimental Demonstration of sensor loss in AM-AFM

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Sensor Loss: Why difficult to sense?

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Approach to solve the problem  Build

an observer for nominal model of cantilever  When cantilever is interacting with the surface, it will settle at an effective model  Difference between nominal model and effective model will indicate presence of tip sample interaction  When interaction disappears, cantilever follows nominal model 51

Schematic of the detection scheme

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Main Concept: Model Mismatch

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Nominal Model and Equivalent model:

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Experimental Demonstration of sensor loss

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Imaging a Square Profile in AM-AFM

2 1 0 ­1 ­2

2

4

µs

6

8

1

x 10

4

0.5 0 ­0.5 ­1 5.8

6

6.2 6.4 6.6 6.8 µs 4 x 10 60

Imaging a triangular profile 2 0 ­2 5

µs

10

15

x 10

4

2 0 ­2 6

8

µs

10 4 x 10 61

Indistinguishable from Amplitude based imaging 2

1

Normalized Parameter

Normalized Parameter

1.5

1 

0.5

0 

0

­0.5

­1

­1

­1.5 58

60

62

ms

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66

68

80

90

100

ms

110

120

130

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Main Concept: Model Mismatch

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Reliability Index

2

1

Normalized Parameter

Normalized Parameter

1.5

1 

0.5

0 

0

­0.5

­1

­1

­1.5 58

60

62

ms

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80

90

100

ms

110

120

130

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Experimental Detection of Sensor Loss

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Increase of Sensor Loss with Scanning speed 2

2

1

1

0

0

­1

­1

­2 5

6

7

µs

8

9

2

10 4 x 10

­2 5

1

0

0

­1

­1 1

1.2

1.4 µs

1.6

1.8

x 10

6

6

6.5

1.195 µs

1.2

µs

2

1

­2

5.5

­2 1.185

1.19

x 10

7

4

1.205

x 10

6

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Monotonic Dependence of var(e) with tip-sample separation

2 0 ­2 2

4

6

µs

8

10 4 x 10

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Correction of Sensor Loss: Dynamic Gain

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Imaging method for live cells Dynamic study of surface properties of Sacharomyces cerevisiae (yeast)

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AFM investigation of live cells

 Widely

studied problem  Animal cells are imaged regularly  Plant cells are difficult to anchor  Significant research is underway to prepare samples of plant cells for AFM imaging

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Challenges:  Yeast 

is a large cell

Surface structures are 0.1% of cell size

 Anchoring

is challenging

Live anchoring  Supply of nutrients  Strong holding for sustained imaging  Expose the whole surface to environment 



Membrane and reverse agar is ruled out

 Image

in Tapping mode

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Some prior reports in AFM imaging of yeast cells  François

Ahimou, Ahmed Touhami, Yves F. Dufrêne Yeast(2002); Volume 20, Issue 1, Pages 25-30  Contact mode image: poor height resolution

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Immobilization on gel surface  Biophys

J. 1995 December; 69(6): 2226– 2233. M Gad and A Ikai  Contact mode

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Effect of thermal and osmotic shock: Tapping mode (dried cells)

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Correlation of cell morphology with cell viability  Heat

shock (e.g. 50°C) for 30 min or longer they shrank dramatically and surface roughness increased  Cell viability dropped to 53%  Sorbitol-induced hyperosmotic stress affected cell viability and cell morphology

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Motivation of studying cell surface • Connection of morphology to intracellular processes • Effect of external stimuli • Cell growth and cell aging

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Objectives • High resolution quantitative imaging of cell surface • Study the effect of cell aging on surface properties • Growth rate • Roughness

• Establish surface properties as an alternate marker

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A new protocol for sample preparation  Direct

Agar Plating

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Live yeast on Agar

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Amplitude image

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A budding yeast cell with scar

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Na-Az treated yeast

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Change in Surface morphology Roughness Variation of Yeast Cell wall 90.0000 80.0000 70.0000 60.0000

nm

50.0000 40.0000 30.0000 20.0000 10.0000 0.0000

40

80

120

160

200

240

16.3916

20.7807

21.7007

23.8988

23.5842

24.7469

Az Treated Daughter Cell

7.8668

6.9516

6.9934

7.4788

Az Treated Mother Cell

13.8376

15.1664

13.0170

13.9182

Mother Cell

Daughter Cell (Pt I)

30.6591

27.1848

19.4313

19.2267

20.9675

27.6498

Daughter Cell (Pt II)

83.3070

71.5252

61.1228

51.1652

43.2768

39.3398

Tim e Elapsed (m in)

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Growth Rate: Viability after anchoring 60.0000

50.0000

40.0000

Mother Cell 30.0000

Daughter Cell Az Treated Mother Cell Az Treated Daughter Cell

20.0000

10.0000

0.0000

40

80

120

160

200

240

Mother Cell

0.0000

1.4433

3.0096

3.1180

2.9927

2.5898

Daughter Cell

0.0000

16.6815

27.1510

36.3821

42.7431

47.6870

Az Treated Mother Cell

0.0000

3.0033

0.6230

1.6173

Az Treated Daughter Cell

0.0000

6.6461

1.4960

5.0836

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Summary A

new anchoring method has been established  Sustained imaging for 12 hours  Live yeasts are imaged in tapping mode  First time Quantitative imaging 

Study of morphology

 Cells

are free to absorb nutrients from environment

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Conclusion:  High   

A new signal which gives unity map Analytically proved and experimentally verified Fundamental limitation imposed by closed loop dynamics is removed

 Real   

 

time probe loss detection

Long standing problem is solved using model of cantilever Improved scanning speed in dynamic mode Fundamental limitation imposed by Q is removed

 New 

Bandwidth profile estimation

sample preparation

A repeatable, non-invasive method to image plant cells First time quantitative imaging in tapping mode High resolution images and unique evolution of morphology 86

Thank you

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