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

€

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

€

Ckcat t( ) =δk t( )δk 0( )δk 0( )δk 0( )

=CE t( )

€

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