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thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 1: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics
Page 2: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics
Page 3: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics
Page 4: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics
Page 5: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics
Page 6: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics
Page 7: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics
Page 8: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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GEM4 Summer School 2006Cell and Molecular Mechanics in BioMedicineAugust 7–18, 2006, MIT, Cambridge, MA, USA

“Reactions”,Energy Landscapes

& KineticsPat Doyle

[email protected] Engineering Dept.

MIT

Page 9: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Key References

• Mechanics of Motor Proteins & the Cytoskeleton,J. Howard

• Biophysical Chemistry, C. Cantor and P. Schimmel

• Mechanical Processes in Biochemistry, Bustamante etal., Ann. Rev. Biochem., 73, 705-748, 2004

• Brownian Motion in a Field of Force and the DiffusionModel of Chemical Reactions, H.A. Kramers, Physica, 4,284-304, 1940

Page 10: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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“Reactions”

Fisher, Marszalek & Fernandez, Nature 2000

Binding of TAT box-binding protein

Titin unfolding

RNA unfolding

Receptor-ligand

DNA-protein

Bustamante et al. 1997

Page 11: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Diffusion Limited Reactions

Page 12: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

5Geometry matters…

Some details….

Page 13: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 14: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 15: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 16: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 17: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 18: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 19: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Page 20: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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First Passage Time

Need to input U(x) to solve…..

Page 21: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Relaxation time of a damped spring

Exponential Effect of Barrier Height

Page 22: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Details of Derivation…

Page 23: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Things that Affect Energy Landscapes

• Force (pulling/pushing, rate)• Enzymes (catalysts)• Salt, pH• “additives” (protein drug stabilization)• ….

Page 24: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

17Strick, Allemand, Bensimon, Croquette, Ann. Rev. Biophys. 2000

Two State Example: Protein Unfolding

Page 25: thua ie d - Amazon S3...1 GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7–18, 2006, MIT, Cambridge, MA, USA “Reactions”, Energy Landscapes & Kinetics

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Force Changes the Energy Landscape

Bustamante et al., Ann. Rev. Biochem. 2004