Parameter Estimation as a Problem in Statistical Thermodynamics

Jul 8, 2010 - Studying Protein Motions. Resolving Multiple Time Scales ... Field-Swept vs. Time Domain ... Figure: Blümich Prog. in NMR Spec. 19:331–417 ...
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Studying Protein Motions Dialogues with Data Summary Thanks

Parameter Estimation as a Problem in Statistical Thermodynamics Keith A. Earle1,2

David J. Schneider3,4

1 Department of Physics University at Albany, SUNY 2 ACERT Cornell University 3 USDA 4 Department

of Plant Pathology Cornell University

Thursday, 8 July 2010 1 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Outline

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Studying Protein Motions Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

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Dialogues with Data Building a Probability Distribution Function What can you do with your PDF? Putting Geometry and Statistical Mechanics to Work

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Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Outline

1

Studying Protein Motions Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

2

Dialogues with Data Building a Probability Distribution Function What can you do with your PDF? Putting Geometry and Statistical Mechanics to Work

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Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

T4 Lysozyme ACERT and Hubbell group collaboration

Figure: Dynamic modes: global and local 4 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Sensitivity of EPR Frequency-dependent windows

Figure: Dynamic processes cover many decades in rate 5 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Hamiltonian

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Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Field-Swept vs. Time Domain

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Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

A Third Way Stochastic Excitation

Figure: Blümich Prog. in NMR Spec. 19:331–417 (1987)

Magnetic resonance absorption is non-negative and normalized Can be treated as a probability density function Leads to statistical geometry 8 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Derivative vs Absorption Representation

Applied magnetic field 9 T 9 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

High field gives g and A resolution

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Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Outline

1

Studying Protein Motions Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

2

Dialogues with Data Building a Probability Distribution Function What can you do with your PDF? Putting Geometry and Statistical Mechanics to Work

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Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Dynamics

Isotropic part of spin interactions give line positions Anisotropic part of spin interactions give line widths 12 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Collect spectra over a range of Frequencies Generate a data matrix

Figure: 131 R2 in ficoll solution

Zhang, et al., J. Phys. Chem. 114(16):5503–5521. 13 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Complex, Heterogeneous Systems The Blind Monk Problem

Figure: Simultaneous multifrequency line shape analysis: Many blind monks, pooling their knowledge, can learn a lot about the elephant.

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Studying Protein Motions Dialogues with Data Summary Thanks

Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

Eliminate Unnecessary Detail

Figure: Tame the elephant, but don’t overwhelm the science

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Studying Protein Motions Dialogues with Data Summary Thanks

Building a Probability Distribution Function What can you do with your PDF? Putting Geometry and Statistical Mechanics to Work

Outline

1

Studying Protein Motions Resolving Multiple Time Scales Interpreting Magnetic Resonance Spectra

2

Dialogues with Data Building a Probability Distribution Function What can you do with your PDF? Putting Geometry and Statistical Mechanics to Work

16 / 40

Studying Protein Motions Dialogues with Data Summary Thanks

Building a Probability Distribution Function What can you do with your PDF? Putting Geometry and Statistical Mechanics to Work

Start with a simple model

Figure: Simulation of an exchange-narrowed multiplet with noise

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Studying Protein Motions Dialogues with Data Summary Thanks

Building a Probability Distribution Function What can you do with your PDF? Putting Geometry and Statistical Mechanics to Work

Analytical Expression for Lineshape In the absence of noise, the line shape has the following form: 1 p(ω|θ)= π(2I+1)