Optimal probing strategies with applications to Biomolecular NMR

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Optimal probing strategies with applications to
Biomolecular NMR
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Protein NMR Spectroscopy
MSSRKVSRAHYDEDELASAANMSLVAEGHFRGMKELLSTMDLDTDANTIP
ELKERAHMLCARFLGGAWKTVPLEHLRISRIKGGMSNMLFLCRLSEVYPP
IRNEPNKVLLRVYFNPETESHLVAESVIFTLLSERHLGPKLYGIFSGGRL
EEYIPSRPLSCHEISLAHMSTKIAKRVAKVHQLEVPIWE
H
R
H
O
C
C
N
C
C
C
N
N
H
R
O
H
H
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One dimensional spectrum
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Random collisions with solvent molecules causes
stochastic tumbling of the protein molecules
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Optimal Control in Presence of Relaxation
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Constrained Bilinear Systems
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Relaxation Optimized Pulse Elements (ROPE)
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Experimental Results
Khaneja, Reiss, Luy, Glaser JMR(2003)
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Comparison
S
x
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Cross-Correlated Relaxation
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Optimal control of spin dynamics in the presence
of Cross-correlated Relaxation









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Khaneja et. al. Proc. Natl. Acad. Sci., 2003
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Proc. Natl. Acad. Sci. , Nov. 2003
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Broadband Control









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Broadband Control
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Experimental Results
T 271K J 193 Hz Proton Freq 750MHz Ka 193
Hz Kc .75 Ka Amax 67 J
Khaneja et. al. PNAS (2004)
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Groel Protein 800KDa
Room Temperature J 93 Hz Proton Freq
750Mhz Ka 446 Hz Kc 326 Hz
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Quadratic Control Systems and Semi-definite
Programming
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Optimal control in solid-state NMR
Challenges Powder Samples Sample
spinning/oriented samples Inhomogeneity Sample
heating Specific transfers in complicated spin
systems
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Optimal control in biological solid-state NMR
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Optimal Hamiltonian Identification
Find optimal ui(t) such that entropy in system
Hamiltonian is minimized at end of certain time T
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Intelligent Probing
Intelligent Probing
If output Y can be observed, choose n questions
x1, x2,, xn sequentially such that entropy of
channel is minimized. Each ci is characterized by
Pi ( y x )
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Collaborators
Steffen Glaser Burkhard Luy Frank Kramer Timo
Reiss Kyryl Kobzar Gerhard Wagner Dominique
Frueh Takuhiro Ito Niels Nielsen Astrid
Sivertsen Cindie Kehlet Morten Bjerring
Technische Universitaet Muenchen
Harvard Medical School
University of Aarhus
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Haidong Yuan Dionisis Stefanatos Brent Pryor Dan
Iancu Andrew Johnson Navin Khaneja Jr-Shin Li
NSF Career, Sloan, DARPA, AFOSR
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