MSI, MScBIOINFO

2012

Molecular simulations of enzyme reactivityMixing all concepts together

Jordi Villà i Freixa

jordi.villa@upf.edu // cbbl.imim.esPrograma de Recerca en Informàtica Biomèdica

Universitat Pompeu FabraBarcelona

Barcelona, January 2012

MSI, MScBIOINFO

2012

Outline

Enzymes

1 Table of contents

2 Enzymes accelerate biochemical reactionsKinetic dataEnzyme reactivityGround state destabilization or TS stabilization?Electrostatic stressDesolvationDynamical effects in enzyme reactivityNear attack conformationsQuantum effects are also negligible in generalCatalysis by preorganized environment

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Enzymes accelerate biochemical rate constants,but up to some extend

[Bruice, 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Enzymes accelerate biochemical rate constants,but up to some extend

[Bruice, 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Putting kinetic data into context

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Putting kinetic data into context

E + L EL EL‡

!g‡cage

!g‡cat

!g‡p

!g‡w

L + L' LL' (LL')‡

!Gbind

EL‡

EL

LL'

(LL')‡

L + L'

E + L

!G

figure 1

JPC, feature article

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

What models have been proposed so far?

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

What models have been proposed so far?

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

What models have been proposed so far?

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

What models have been proposed so far?

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Linear free energy relationships

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Linear free energy relationships

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Linear free energy relationships

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Even metaloenzymes do not just depend on theelectronic structure

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

QM/MM

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

The empirical valence bond method

C1H11 O1

C1H11

R

R'C5

C6N1

C2

C3C4

R

R'

O1L1

H6

H5

H2

L2L1 L2

benzyl alcoholatebenzaldehyde NADH NAD+

RS 2RS 2

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

The empirical valence bond method

C1H11 O1

C1H11

R

R'C5

C6N1

C2

C3C4

R

R'

O1L1

H6

H5

H2

L2L1 L2

benzyl alcoholatebenzaldehyde NADH NAD+

RS 2RS 2

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

The empirical valence bond method

E1, E2

C1H11 O1

C1H11

R

R'C5

C6N1

C2

C3C4

R

R'

O1L1

H6

H5

H2

L2L1 L2

benzyl alcoholatebenzaldehyde NADH NAD+

RS 2RS 2

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

The empirical valence bond method

E1, E2

C1H11 O1

C1H11

R

R'C5

C6N1

C2

C3C4

R

R'

O1L1

H6

H5

H2

L2L1 L2

benzyl alcoholatebenzaldehyde NADH NAD+

RS 2RS 2

∣∣∣∣ E1 − V H12H12 E2 − V

∣∣∣∣ = 0

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

The empirical valence bond method

E1, E2V1, V2

C1H11 O1

C1H11

R

R'C5

C6N1

C2

C3C4

R

R'

O1L1

H6

H5

H2

L2L1 L2

benzyl alcoholatebenzaldehyde NADH NAD+

RS 2RS 2

∣∣∣∣ E1 − V H12H12 E2 − V

∣∣∣∣ = 0

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

The EVB: an intensively used method forenzyme reactivity studies

[Warshel and Weiss, 1980, Åqvist and Warshel, 1993,Kim et al., 2000, Villà and Warshel, 2001, Luzhkov, 2001,Bjelic, 2007, Sonnenberg and Schlegel, 2007,Higashi and Truhlar, 2008, Vardi-Kilshtain et al., 2009]Markus relationship:

∆GTS =(∆G + λ)2

4λ

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

[Via et al., 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

[Glennon et al., 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Reactivity in the Ras/RasGAP system

[Glennon et al., 2000,Allin and Gerwert, 2001]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Electrostatics: YES, but.. stress??

[Warshel et al., 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Electrostatics: YES, but.. stress??

[Warshel et al., 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Electrostatics: YES, but.. stress??

[Warshel et al., 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Electrostatics: YES, but.. stress??

[Warshel et al., 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

or creating a non-polar environment?

[Warshel et al., 2000]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

What about dynamics?

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

What about dynamics?

0 10 20 30 40 50-300

-250

-200

-150

-100

0 10 20 30 40 50-200

-150

-100

-50

0

NADH/B

NAD+/BH-

water

protein

Electrostatic fluctuations in LADH

εneutral

εion pair

εion pair

εneutral

O

H

H

N

CONH2

HZn

2+

NAD+BH-

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

What about dynamics?

-80 -60 -40 -20 0 20 40 60 80-300

-250

-200

-150

-100

-50

0

50

100

150

200

-80 -60 -40 -20 0 20 40 60 80-300

-250

-200

-150

-100

-50

0

50

100

150

200

Solvent coordinate !"elec / kcal/mol

Solvent coordinate !"elec / kcal/mol

Sol

ute

coor

dina

te !

" int /

kca

l/mol

Sol

ute

coor

dina

te !

" int /

kca

l/mol

water

protein

a)

b)

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Right, but perhaps the substrate is positioned torestrict its motions in a smart way...

[Shurki et al., 2002]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Right, but perhaps the substrate is positioned torestrict its motions in a smart way...

[Shurki et al., 2002]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Right, but perhaps the substrate is positioned torestrict its motions in a smart way...

[Shurki et al., 2002]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Contributions to the NAC effect

[Shurki et al., 2002]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Quantum effects in enzyme reactivity

Uq =P∑

k=1

12P

MΩ2∆x2k +

1P

U(xk )

C1H11 O1

C1H11

R

R'C5

C6N1

C2

C3C4

R

R'

O1L1

H6

H5

H2

L2L1 L2

benzyl alcoholatebenzaldehyde NADH NAD+

RS 2RS 2

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Quantum effects in enzyme reactivity

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Quantum effects in enzyme reactivity

0 5 10 15 20-2

-1.5

-1

-0.5

0!

!

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Quantum effects in enzyme reactivity

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

∆Gsol = ∆GQµ−∆Gµµ =

∆GQµ − 1

2∆GQµ = 12∆GQµ water

∆GQµ + 0 = ∆GQµ enzyme

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

[Barbany et al., 2003]

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Allin, C. and Gerwert, K. (2001).Ras catalyzes gtp hydrolysis by shifting negative charges from - to -phosphate as revealed bytime-resolved ftir difference spectroscopy.Biochemistry, 40(10):3037–3046.

Åqvist, J. and Warshel, A. (1993).Simulation of Enzyme Reactions Using Valence Bond Force Fields and Other Hybrid Quantum/ClassicalApproaches.93:2523–2544.

Barbany, M., Gutiérrez-de Terán, H., Sanz, F., Villà-Freixa, J., and Warshel, A. (2003).Pharmacophore approach for hapten design in catalytic antibodies generation.4:277–85.

Bjelic, S. (2007).Molecular Simulation of Enzyme Catalysis and Inhibition.Acta Universitatis Upsaliensis.

Bruice, T. C. Benkovic, S. J. (2000).Chemical basis for enzyme catalysis.39:6267–6274.

Glennon, T. M., Villà, J., and Warshel, A. (2000).How Does GAP Catalyze the GTPase Reaction of Ras? A Computer Simulation Study.39:9641–51.

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Higashi, M. and Truhlar, D. (2008).Electrostatically embedded multiconfiguration molecular mechanics based on the combined densityfunctional and molecular mechanical method.Journal of Chemical Theory and Computation, 4(5):790–803.

Kim, Y., Corchado, J., Villa, J., Xing, J., and Truhlar, D. (2000).Multiconfiguration molecular mechanics algorithm for potential energy surfaces of chemical reactions.The Journal of Chemical Physics, 112:2718.

Luzhkov, V. B. (2001).Empirical valence bond study of radical reactions: hydrogen atom transfer in peroxidation of phenol.Chemical Physics Letters, 345(3-4):345 – 352.

Shurki, A., Štrajbl, M., Villà, J., and Warshel, A. (2002).How Much Enzymes Really Gain by Restraining Their Reacting Fragments?124:4097–4107.

Sonnenberg, J. and Schlegel, H. (2007).Empirical valence bond models for reactive potential energy surfaces. II. Intramolecular proton transfer inpyridone and the Claisen reaction of allyl vinyl ether.Molecular Physics, 105(19):2719–2729.

Vardi-Kilshtain, A., Roca, M., and Warshel, A. (2009).The empirical valence bond as an effective strategy for computer-aided enzyme design.Biotechnology journal, 4(4):495–500.

MSI, MScBIOINFO

2012

Outline

EnzymesKinetics

Enzymereactivity

GSD/TSS

Electrostaticstress

Desolvation

Dynamics

NAC

Quantum

Summary

Via, A., Ferre, F., Brannetti, B., Valencia, A., and Helmer-Citterich, M. (2000).Three-dimensional view of the surface motif associated with the p-loop structure: cis and trans cases ofconvergent evolution.303(4):455–65.455–65.

Villà, J. and Warshel, A. (2001).Energetics and Dynamics of Enzymatic Reactions.J. Phys. Chem. B, 105:7887–907.

Warshel, A., Štrajbl, M., Villà, J., and Florián, J. (2000).Remarkable Rate Enhancement of Orotidine 5’-monophosphate Decarboxylase is Due to Transition StateStabilization rather than to Ground State Destabilization.39:14728–14738.

Warshel, A. and Weiss, R. (1980).An empirical valence bond approach for comparing reactions in solutions and in enzymes.Journal of the American Chemical Society, 102(20):6218–6226.