Interplay of theory and computations in science - Examples drawn from theoretical/experimental studies of
Reaction rates On-water catalysiorganic reactions Isotope fractionation Single-molecule fluctuations
Rudolph Marcus California Institute of Technology KITPC Workshop on Dynamics of Biomolecular Machinery Beijing August 6, 2009
ELECTRON TRANSFER MECHANISM
Reaction Coordinate
Free
Ene
rgy
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k = Ae−λ
4RT1+
ΔG°λ
⎛ ⎝ ⎜
⎞ ⎠ ⎟2
Rate Constant for Electron Transfer
Time-dependent Stokes Shift
Reaction Coordinate
Free
Ene
rgy
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Time-dependent Stokes Shift Calculated from Solvent Dielectric dispersion
Hsu, Song &RAM JPC 1997
Time-dependent Stokes Shift. Coumarin 343 in Water
Hsu, Song & RAM JPC B 1997.… Experiment
----- Theory, no adjustable parameters
Free Energy Surfaces
Protein Reorganization
AH~ 1017/s at low T
Klinman et al. 1999, 2004
RAM 2008/2009
Thermophilic Alcohol Dehydrogenase -
Oxidation of Benzyl Alcohol
Fluctuations in Catalysis Rate & Spectral DiffusionChloresterol oxidase oxidation of FAD
Using data of Xie et al., Science 1998. Prakash & RAM PNAS 2007
Equation relating Correlation Functions: Electrostatic Fluctuations at Active Site
Prakash & RAM PNAS 2007
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Ckcat t( ) =δk t( )δk 0( )δk 0( )δk 0( )
=CE t( )
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Ckcat t( ) =Cspectdiff t( ) =Crad t( ) =CE t( )
Fluctuations and Dielectric Dispersion
Prakash & RAM JPC B 2008
Fluctuations in Enzyme Catalysis & Dielectric Dispersion
Prakash & RAM PNAS 2007
Lipase catalyzed ester hydrolysis
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Fluctuations for galactosidase
Prakash & RAM 2008
Enzymes - Summary• When is the kinetic isotope effect H/D T- independent? • What does the breakpoint and pre-exponential factors
of rate constants for a thermophilic enzyme tell us about flexibility?
• When do different single molecule time-correlation functions agree for the same enzyme and why?
• When does one expect “normal” Arrhenius preexponential factors A for H transfer?
• Does one expect a small A for proton-coupled electron transfer?
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An On-Water Cycloaddition Reaction
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Sharpless et al. 2005
Solvent Conc. [M] Time to completion
Toluene 2 > 120 h
DMSO 2 36 h
MeOH 2 18 h
MeOH/H2O (3:1 homogeneous) 2 4 h
Neat liquids 4.53 48 h
on H2O (heterogeneous) 4.53 10 min
MeOH/H2O (1:1 heterogeneous) 4.53 10 min
on C6F14 4.53 36 h
Sharpless and co-workers, Angew. Chem. Int. Ed. 44, 3275 (2005)
Reaction Time Data
N
N
CO2Me
MeO2C
N
N
CO2Me
CO2Me
1 2 3
Ice Surface
http://www.lsbu.ac.uk/water/ice1h.html
Solvent Reaction time Experiment (s-1) TST (s-1)
Neat 48 h 4 10-6 5 10-7
Homogeneous 4 h 9 10-4 -
on H2O 10 min 0.5 0.2
TST Rate Constants Compared with Experimental Rates
Interfacial H-Bond formation is the key to the on-water rate acceleration
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Interaction of Theory, Computation & Experiment Not Discussed Here
•Mass-independent isotope effect in stratosphere
•Combustion/atmospheric reactions and RRKM
•Fluorescence blinking of semiconductor QDs
•Vibrational adiabaticty, born of computatiom