quantum chemical modeling of enzymatic methyl transfer...

Quantum Chemical Modeling of

Enzymatic Methyl Transfer

Reactions

Polina Georgieva

Department of Theoretical Chemistry

Royal Institute of Technology

Stockholm, Sweden, 2008

Thesis for Philosophy Doctor degree

Department of Theoretical Chemistry

School of Biotechnology

Royal Institute of Technology

Stockholm

Sweden 2008

c© Polina Georgieva

ISBN 978-91-7415-171-8 pp i-ix, 1-51

ISSN 1654-2312

TRITA-BIO-Report 2008:26

Printed by Universitetsservice US-AB,

Stockholm

Sweden 2008

Abstract

In this thesis, quantum chemistry, in particular the B3LYP density functional method,

is used to investigate a number of methyl transfer enzymes. Quantum chemical

methodology is today a very important tool in the elucidation of properties and reac-

tion mechanisms of enzyme active sites. The enzymes considered in this thesis are the

S-adenosyl L-methionine-dependent enzymes - glycine N-methyltransferase, guanidi-

noacetate methyltransferase, phenylethanolamine N-methyltransferase, and histone

lysine methyltransferase. In addition, the reaction mechanism of the DNA repairing

enzyme O6-methylguanine methyltransferase is studied.

Active site models of varying sizes were designed and stationary points along the

reaction paths were optimized and characterized. Potential energy surfaces for the

reactions were calculated and the feasibility of the suggested reaction mechanisms

was able to be judged. By systematically increasing the size of the models, deeper

insight into the details of the reactions was obtained, the roles of the various active

site residues could be analyzed, and, very importantly, the adopted modeling strategy

was evaluated.

i

Acknowledgements

I have spent a few wonderful years in the Theoretical Chemistry group in Stockholm,

Sweden. During those lovely years I had the fortune that Docent Fahmi Himo was

my supervisor. Under his guidance, helpfulness, and encouragement I have learned a

lot about science and life. I cannot find words to express my gratitude and happiness

of working with him. Thank you Fahmi, thank you for everything.

I would like to express my gratitude to Prof. Hans Agren for accepting me in the

Theoretical Chemistry group and for providing a warm working environment. Grati-

tude goes also to all the people who took care of the computer technical problems,

administrative staff and the librarians without whom this thesis would not have been

possible.

I would like to acknowledge the people with whom I had the pleasure to work

- Kathrin, Jing Dong, Tommaso, Robin, Peter, Chen, and Liao. Thank you for

the discussions during our internal seminars and for the fun we had together. Over

the years the theoretical chemistry group guided by Prof. Hans Agren expanded a

lot. Right now there are people who I do not know personally, but I would like to

thank some present and former colleagues who made my time here more pleasant -

Yasen, Oscar, Luca, Viviane, Katja, Freddy, Elias, Emil. I had a special connection

and friendship to a former member of the group, Ivo. Thank you for the joys and

inspirations, thank you for changing my life, thank you..... Rest in peace.

I would like to thank the person who believed in me some years ago, opened my

eyes for science and gave me much support, Prof. Alia Tadjer from the University

of Sofia, Bulgaria. I will be forever grateful for everything I have learned and for the

positive and valuable life guidings.

Thanks to the friends that have been by my side during the years. Warm thanks

to my family - Valentin and Monica. Thank you Valentin for your love and support,

thank you for being by my side every day through the last years. Special thanks to

my daughter Monica for her love. I am infinitely grateful to you, with all my heart.

Thanks to my father, mother, and my brother who love me, and have been on my

side all the time. Thank you!

iii

List of Papers

• I. Methyl Transfer in Glycine N-Methyltransferase. A Theo-

retical Study.

Polina Velichkova, Fahmi Himo,

J. Phys. Chem. B 109 (16), 8216 –8219 (2005).

• II. Theoretical Study of The Methyl Transfer in Guanidinoac-

etate Methyltransferase.

Polina Velichkova, Fahmi Himo,

J. Phys. Chem. B 110 (1), 16 –19 (2006).

• III. The Reaction Mechanism of Phenylethanolamine N-Methyl-

transferase: A Density Functional Theory Study.

Polina Georgieva, Michael McLeish, Fahmi Himo,

Manuscript

• IV. Quantum Chemical Modeling of Enzymatic Reactions: The

Case of Histone Lysine Methyltransferase.

Polina Georgieva, Fahmi Himo,

Manuscript

• V. Density Functional Theory Study of The Reaction Mecha-

nism of The DNA Repairing Enzyme Alkylguanine Alkyltrans-

ferase.

Polina Georgieva, Fahmi Himo,

Chem. Phys. Lett. 463, 214 – 218 (2008).

v

Abbreviations and Acronyms

Abbreviation Description Definition

DFT Density Functional Theory page 3

SAM S-adenosyl L-methionine page 4

GNMT Glycine N-methyltransferase page 4

GAMT Guanidinoacetate methyltransferase page 4

HKMT Histone methyltransferase page 4

PNMT Phenylethanolamine N-methyltransferase page 4

MGMT O6-methylguanine methyltransferase page 4

TST Transition State Theory page 4

QC Quantum Chemistry page 5

QM Quantum Mechanics page 5

B3LYP Becke 3 parameter Lee-Yang-Parr Func-

tional

page 7

PDB Protein Data Bank page 16

ZPVE Zero-Point Vibrational Effect page 18

PCM Polarizable continuum model page 18

SAH S-adenosylhomocysteine page 20

ATP Adenosine triphosphate page 20

GAA Guanidinoacetate page 26

PEA Phenylethanolamine page 31

AGT Alkylguanine alkyltransferase page 39

vii

Amino Acids Abbreviations

1-Letter Symbol 3-Letter Symbol Full Name

A Ala Alanine

C Cys Cysteine

D Asp Aspartate

E Glu Glutamate

F Phe Phenylalanine

G Gly Glycine

H His Histidine

I Ile Isoleucine

K Lys Lysine

L Leu Leucine

M Met Methionine

N Asn Asparagine

P Pro Proline

Q Gln Glutamine

R Arg Arginine

S Ser Serine

T Thr Threonine

V Val Valine

W Trp Tryptophan

X Xaa Any Residue

Y Tyr Tyrosine

ix

Contents

Contents 1

1 Theoretical Background 5

1.1 Density Functional Theory, DFT . . . . . . . . . . . . . . . . . . . 51.2 B3LYP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1 Performance of B3LYP . . . . . . . . . . . . . . . . . . . . 71.3 Reaction Rates and Transition State Theory . . . . . . . . . . . . . 91.4 Enzyme Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Modeling of Enzymatic Reactions 15

2.1 Modeling Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Modeling of Methyl Transfer Reactions 19

3.1 SAM-dependent Enzymes . . . . . . . . . . . . . . . . . . . . . . . 213.1.1 Glycine N-methyltransferase, GNMT (Paper I) . . . . . . . 213.1.2 Guanidinoacetate Methyltransferase, GAMT (Paper II) . . 263.1.3 Phenylethanolamine N-methyltransferase, PNMT (Paper III) 303.1.4 Histone Lysine Methyltransferase, HKMT (Paper IV) . . . 35

3.2 Other Methyl Transfer Enzymes . . . . . . . . . . . . . . . . . . . 393.2.1 O6-Methylguanine Methyltransferase, MGMT (Paper V) . 39

4 Conclusions 45

Bibliography 47

1

Introduction

Enzymes are the catalytic machines of life. Basically all chemical transformations

that take place in the organisms are catalyzed and controlled by specific enzymes.

Thus, failure of the function of certain key enzymes can lead to serious diseases. In

fact, many medicines work by blocking the function of some target enzyme. Due to

their specificity and selectivity properties, enzymes are today also used as synthetic

tools in large-scale industry processes to produce chemicals. It is thus of enormous

importance that one develops a detailed understanding of how these fascinating ma-

chines are able to catalyze their reactions. This understanding can, in the long run,

have far-reaching consequences. It can, for instance, allow for the rational design of

new drug compounds that will have improved selectivity and potency properties. It

can also make possible the design of bio-mimetic catalytic complexes for industrial

applications.

To this end, theoretical chemistry is today providing a number of computational

techniques capable of addressing and solving a wide range of problems in many di-

verse fields. It has proved its usefulness in many different research areas, ranging

from traditional chemistry, such as synthesis and analysis, to modern fields, such as

material science and drug development. Because the field heavily depends on compu-

tational power, it has, like other computational fields, benefited from the enormous

advancement in computer speed. Computers are becoming faster and cheaper every

day, and thus more and more complicated problems can be tackled.

Application of theoretical chemistry techniques to study enzyme catalysis is not

a recent developments. However, the use of accurate quantum chemical methods to

model enzyme active sites and reactivities is a quite recent field. The most important

reason for this development is the advances that density functional theory (DFT) has

made. DFT, and in particular hybrid functionals such as B3LYP, has made it possible

to treat, quite accurately, far larger systems than is possible with ab initio methods.

This has paved the way for wider applications, such as enzyme catalysis.

Theoretical studies of enzyme reactions provide excellent complement to the ex-

perimental studies. It also provides some advantages. For example, it is possible to

locate and characterize short-lived intermediates (and transition states), something

3

4 CONTENTS

that is very challenging to do with the current experimental techniques. Also, it

is possible to investigate hypothetical mechanistic scenarios and to provide detailed

information and break-down of various effects contributing to the reactivity of the

system.

The field of computational enzymology is a highly interdisciplinary one, on the in-

terface between several traditional research fields, such as biochemistry, organic chem-

istry, inorganic chemistry, physical chemistry, molecular biology, quantum physics, and

computational sciences. Knowledge in all these areas is a prerequisite for successful

research.

In this thesis, DFT is used to study a number of methyl transfer enzymes. This

class of enzymes catalyzes a number of very vital reactions, in many cases related to

brain and nerve activity. The enzymes considered in this thesis are the S-adenosyl L-

methionine-dependent (SAM) enzymes glycine N-methyltransferase (GNMT), guani-

dinoacetate methyltransferase (GAMT), phenylethanolamine N-methyltransferase

(PNMT), and histone lysine methyltransferase (HKMT). Another enzyme, that is not

SAM-dependent, is studied also, namely the DNA repairing enzyme O6-methylguanine

methyltransferase (MGMT).

The thesis is organized in the following way: First, the theoretical methods, in

particular DFT, are briefly described in Chapter 1. Transition state theory (TST) and

enzyme kinetics are also briefly outlined in this chapter, due to their fundamental role

in making connections between theory and experimental measurements. Chapter 2

introduces the modeling approach used in this thesis to investigate enzyme reac-

tions. In Chapter 3, the main results of our studies on the methyltransferases are

summarized. Finally, in Chapter 4 some general conclusions are given.

Chapter 1

Theoretical Background

Quantum chemistry (QC) is a wide research field concerned with the general use

of the laws of quantum physics to study chemical problems. It encompasses many

diverse sub-fields, ranging from pure mathematical development och tools, to high-

end applications. This thesis deals with studying enzyme reaction mechanisms using

the tools of quantum chemistry.

One major reason for this becoming possible is the qualitative and quantitative

advances in density functional theory (DFT). With help of DFT methods, it is now

possible to treat quite large systems with reasonable accuracy and speed, which has

lead to more and more realistic models of enzyme active sites.

This chapter provides a very brief background to DFT. In particular, the hybrid

B3LYP functional and its performance are discussed. Also, brief accounts of transition

state theory and enzyme kinetics are given. These topics are very important in order

to relate the theoretical calculations to the experimental measurements.

1.1 Density Functional Theory, DFT

Explaining enzymatic reaction mechanisms that involve bond making and breaking

requires good description of the enzyme system at atomic level. The mathemati-

cal expressions that describe a molecular system are defined in quantum mechanics

(QM) [1, 2, 3]. The most important parameter is the wave function from the time-

independent Schrodinger equation, HΨ = EΨ, where Ψ is the wave function that

completely determine given physical system, H is the Hamiltonian operator that rep-

resents the energy of the system as a sum of kinetics and potential energy, and E is

the energy of the system obtained as an eigenvalue to the Hamiltonian. The equa-

tion cannot be solved exactly for systems larger than two particles. Since the real

chemical systems are quite complicated, solving the Schrodinger equation for them

5

6 CHAPTER 1. THEORETICAL BACKGROUND

requires approximations.

Depending on the desired accuracy, the approximations made in wave function-

based methods can be more or less sophisticated. In general, to obtain the high

accuracy needed to describe reaction energy profiles one has to use methods that are

quite expensive from computational point of view. Therefore, one is limited to treat

only relatively small systems.

An alternative way to express the energy of the system is by its electron den-

sity instead of the wave function [4, 5]. The method that uses electron density to

determine molecular properties is DFT.

The foundations of this theory lie on the two fundamental Hohenberg-Kohn the-

orems [6], which state that the ground state electron density of a system uniquely

determines the external potential, and that the density-dependent functional obeys

the variational principle. The first theorem implies that the ground state energy is

uniquely defined by the electron density, while the second means that the calculated

energy is higher than or equal to the true ground state energy. Mathematically, one

can thus express the total energy as a functional of the density:

Etot[ρ] = T [ρ] + Vee[ρ] + Vne[ρ], (1.1)

where ρ is electron density, T is the kinetic energy of the electrons, Vee is the

electron-electron repulsion, and Vne is the nuclear electron attraction. The first two

terms are independent of the nuclear position and represent the density functional,

F [ρ] = T [ρ] + Vee[ρ].

Etot[ρ] = F [ρ] + Vne[ρ], (1.2)

The problem with the Hohenberg-Kohn formalism is that the exact form of the

density functional F [ρ] is not known. It is known that it exists and connect energy

with a given electron density. The Kohn-Sham formalism gives a practical solution to

this problem by introducing an orbital-based scheme [7]. This approach divides the

kinetic energy of the system in two parts, one is the kinetic energy of non-interacting

system TS [ρ] and the rest is a residual kinetic part, TC [ρ], T [ρ] = TS [ρ] + TC [ρ].Introduction of the reference system gives the possibility larger part of the terms in

equation 1.2 to be calculated exactly. For example the kinetic energy functional of

non-interacting electrons is known exactly and this energy should be the same as in the

real interacting system. The second term in equation 1.2 contains classical Coulomb

interaction J [ρ] and residual non-classical part such as exchange, correlation, and

self-interaction Encl[ρ], Vee[ρ] = J [ρ] + Encl[ρ]. With this approaches equation 1.2

is reformulated as:

F [ρ] = TS [ρ] + J [ρ] + EXC [ρ] (1.3)

where EXC represents the difference in kinetic energy between the real system

and a system of non-interacting electrons plus the non-classical part of electron-

1.2. B3LYP 7

electron interaction. This term is called exchange-correlation functional and contains

all unknowns, and must be approximated. This is the biggest challenge in DFT

method, finding sufficiently accurate density functionals.

1.2 B3LYP

The most popular functionals in DFT are the hybrid functionals [5, 4] which introduce

parts of the Hartree-Fock exchange in the functional. Usually the parameters of the

functionals are fitted to reproduce some set of observables. The most widely used

functional in this category is Becke’s three parameter functional (B3LYP) [3], which

in general form can be written as:

FB3LY PXC = (1−A)FSlater

X + AFHFX + BFBecke

X + (1−C)F V WNC + CFLY P

C (1.4)

where FSlaterX is the Dirac-Slater exchange, FHF

X is the Hartree-Fock exchange

term, FBeckeX is the gradient part of the exchange functional of Becke [8, 9, 10,

11], F V WNC and FLY P

C are the correlation functionals of Vosko, Wilk, and Nusair

[12] and Lee, Yang, and Parr [13, 14] respectively. The parameters A, B and

C are related to the Hartree-Fock exchange and Coulomb correlation. They were

determined empirically by Becke [8, 9, 10, 11], and have the values of A = 0.20,

B = 0.72, and C = 0.81.

1.2.1 Performance of B3LYP

The use of approximations in the methods directly leads to errors in the obtained

results. In the present thesis we apply B3LYP functional to study enzyme reaction

mechanisms. The reason for this choice of B3LYP is the accuracy of the method

combined with its computational cost. Comparison between computational results

and experimental data assess the accuracy of a certain theoretical method. In case

of enzyme reaction mechanism, errors in the energies and geometrical parameters are

of interest.

Basis Set

The accuracy of a method depends, apart from the approximation of the methods

itself, also on the choice of a basis set used in the calculations [2, 3]. A basis set

is a set of functions centered on the different atoms in the molecule. In DFT the

basis set is used to describe the Kohn-Sham orbitals. Most of the commonly used

basis sets are composed of Gaussian functions. Common additions to the basis sets

are polarization and diffuse functions. Usually, a medium-sized basis set is used for

geometry optimization. In this thesis all geometry optimizations are performed by

using Pople double-ζ basis set, 6-31G(d,p). The core orbitals are presented by one


function composed of 6 Gaussians. The valence orbitals are treated with two func-

tions, one of which is composed of 3 and the other one of 1 Gaussians. Additionally p-

and d- polarization functions are added. These functions introduce some additional

flexibility important while considering accurate representation of bonding between

the atoms. For accurate evaluation of the energy a larger triple-ζ basis set is used,

6-311G+(2d,2p).

Accuracy on Geometries

The accuracy of B3LYP with respect to geometrical parameters was tested against the

standard G2 benchmark set of molecules [15, 16]. The G2 set includes 55 molecules

for which very accurate experimental data is available. As mentioned above, the

accuracy of the B3LYP calculations depends on the choice of basis set. The smallest

basis set which is recommended for calculations is 6-31G* or equivalent of double-ζ

quality. Comparison with experimental data reveals that this basis set works quite

well for geometry optimizations, see Table 1.1.

error 6-31G* 6-311+G(3df,2p)

average 0.013 0.008Bond Lengths,(A)maximum 0.055 0.039

average 0.62◦ 0.61◦Bond Angles, (◦)maximum 1.69◦ 1.85◦

average 0.35◦ 3.66◦Dihedral Angles, (◦)maximum 0.63◦ 6.61◦

average 5.18 2.20Atomization Energy, (kcal/mol)maximum 31.50 8.40

Table 1.1: Mean absolute errors of B3LYP on the G2 benchmark test set [15, 16, 17].

Using a very large basis set, as 6-311+G(3df,2p) [15, 16], contributes very little

to the geometry accuracy. The B3LYP functional performs thus very well in terms

of geometries.

1.3. REACTION RATES AND TRANSITION STATE THEORY 9

Accuracy on Energies

The average error in atomization energies of B3LYP on the G2 test set using the

6-31G* basis set is calculated to be 5.18 kcal/mol (Table 1.1) [17], while using

the much larger 6-311+G(3df,2p) basis set yields a much smaller error of only 2.2

kcal/mol. This is an outstanding performance, comparable to the most accurate ab

initio methods.

Another evaluation of B3LYP has been performed on the G3 test set [18, 19],

which includes many more molecules, see Table 1.2. The calculations are single-

points using B3LYP/6-311+G(3df,2p) on MP2/6-31G(d) geometries, and corrected

for zero-point vibrations by HF/6-31G(d) scaled by 0.89. The results show, again,

that B3LYP achieves quite high accuracy.

Energies Mean Absolute Deviation, (kcal/mol)

Enthalpies of Formation 4.63

Ionization Energies 3.83

Electron Affinities 2.99

Proton Affinities 1.39

All 4.11

Table 1.2: Mean absolute deviation of B3LYP on the G3 test set [19].

This, together with the favorable scaling of the method, make B3LYP an at-

tractive tool in the study of enzymes reaction mechanism, which is the topic of the

present thesis [20, 21].

1.3 Reaction Rates and Transition State Theory

The present thesis deals with studying the catalytic reaction mechanism in enzymes.

This process involves continuous chemical and potential energies changes and it is

characterized by reaction rates. A reaction rate defines how fast particular reaction

takes place, i.e. how quickly reactants change into products. Some of the important

quantities used in the characterization of reactions, in general and for the case of

enzymes, are defined in Figure 1.1.


E + S

ES

TS

EP

E + P

reactantsreactants

productsproducts

TS

S

P

uncatalyzed chemical reaction enzyme catalyzed chemical reaction

ΔG �

ΔG �

ΔG0

Relative

Energies

R e a c t i o n C o o r d i n a t e

Figure 1.1: Schematic free energy profile for uncatalyzed and enzyme catalyzed chemicalreactions.

For the uncatalyzed reaction, the barrier of the reaction is the relative free energy,

∆G6= of the reactant and the transition state. In the enzyme-catalyzed reaction, the

substrate, S, binds to the enzyme active site, E, and forms an enzyme-substrate

complex, ES. The ES goes through chemical steps to form an enzyme-product

complex, EP , which then releases the product, P , and free the enzyme. In this case

the reaction barrier is relative free energy between the enzyme-substrate complex,

ES and the transition state, TS.

Usually reaction rates are determined experimentally while potential energy sur-

faces and the relative energies between different states can be computed using the

quantum chemistry. A very powerful way to connect these two concepts is in terms

of classical transition state theory (TST)[22, 23, 24, 25]. TST assumes that once a

reaction passes through its reaction barrier it cannot go back again. Its postulates an

equilibrium (Boltzmann) energy distribution at all stable and unstable states along

the reaction coordinates, leading to the following expression for the rate constant k:

k =kBT

hexp

(−∆G6=

RT

), (1.5)

where k is the rate constant (s−1), kB is the Boltzmann’s constant (1.38 x

10−23J/K); h is the Planck’s constant (6.626 x 10−34Js); T is the absolute tempera-

1.4. ENZYME KINETICS 11

ture (298.15 K at room temperature); R is the universal gas constant (8.314JK−1mol−1);

and ∆G 6= corresponds to the Gibbs free energy of activation. The Gibbs free energy

of activation consists enthalpic, and entropic terms, ∆G 6= = ∆H 6= − T∆S 6=. The

rate constant becomes:

k =kBT

hexp

(∆S 6=

R

)exp

(−∆H 6=

RT

), (1.6)

Based on the Eyring equation 1.6, one can for example estimate that a reaction

with a rate constant of 1 s−1 at room temperature corresponds to a barrier of ca

18 kcal/mol. When the energy barrier decreases or increases with ca 1.4 kcal/mol,

the rate constant increases or decreases with one order of magnitude, respectively.

These are quite useful relations that one can use to quickly convert between rates

and energies. It is important to note that, due to the exponential nature of the

relationship, a calculated energy barrier with an error bar of ca 3 kcal/mol, which is

considered to be good, leads to an error in the rate of two orders of magnitude. It

is therefore not possible with the methods used in this thesis to determine accurate

reaction rates. Rather, the computed energies are used as a way to judge the energetic

feasibility of reaction mechanisms.

Considering the exponential dependence of activation energy and the accuracy of

B3LYP functional it is not possible to predict the rate constant accurately from the

computed barriers. However, comparison with experimentally defined rate constants

is suitable in order to evaluate the feasibility of a certain reaction mechanism. In

case of multistep mechanism, the reaction rate is defined by the transition state with

highest activation barrier. This step is a rate-limiting step.

It is also important to point out that the barriers calculated in this work correspond

only to the enthalpy part of equation 1.6. The entropic part is not calculated due to

the coordinate locking scheme used to model enzyme active sites, see Chapter 2.

1.4 Enzyme Kinetics

Enzyme kinetics studies the speed or rate of an enzyme-catalyzed reaction, and

factors that affect reaction rates [26]. Kinetics experiments can be analyzed in terms

of Michaelis–Menten formalism. In this framework, the enzyme action starts with

binding of the substrate, S, to the free enzyme, E, by forming an enzyme-substrate

complex, ES. This complex undergoes chemical transformation (passing through

a transition state, TS) to form enzyme-product complex, EP . The EP releases

the products, P and frees the enzyme for another round of catalysis. Laboratory

procedure traces changes in the concentration of either substrates or products to

determined the reaction rate constant.

The Michaelis–Menten framework gives a mathematical description that links

the reaction rate, kcat or v, and the substrate concentration, [S] using the following

scheme:


E + S

k+1

Àk−1

ES

kcat

−→ E + P (1.7)

The terms k+1, k−1 and kcat are rate constants. k+1 describes the association

of substrate and enzyme. k−1 characterizes the dissociation of the enzyme-substrate

complex, ES. kcat characterizes the conversion of ES to product, P . This gives the

following expression for the velocity, v:

v =vmax[S]

KM + [S](1.8)

where [S] is the substrate concentration, vmax is the velocity at maximum con-

centration of substrate when [S] À [E] and all the enzyme molecules are in form

ES, KM is the Michaelis – Menten constant presented as equilibrium constant:

KM =k−1 + kcat

k+1(1.9)

The important parameters from equation 1.8 for the interpretation of the results

are: the catalytic constant kcat, the equilibrium constant, KM , and the specificity

constant, kcatKM

[26].

According to equation 1.8, kcat measures the number of substrate molecules

turned over per enzyme molecule per second. Thus, kcat is sometimes called the

turnover number. This is a first order rate constant that relates the reaction rate to

the concentration of enzyme-substrate complex, [ES].The significance of KM becomes obvious if one considers the case when the rate

of reaction, v, is exactly half of the maximal reaction rate, vmax. Applying this turns

the Michaelis – Menten equation 1.8 in:

vmax

2=

vmax[S]KM + [S]

, KM = [S] (1.10)

KM of an enzyme represents thus the substrate concentration at which the re-

action occurs at half of the maximum rate. KM can be used as an indicator of

the affinity of an enzyme to substrate. Enzymes with a high KM require a higher

substrate concentration to achieve a given reaction velocity.

The ratio kcatKM

is often referred to as ”specificity constant”. It is used for com-

paring the relative rates of enzyme acting on alternative, competing substrates. The

meaning of kcatKM

becomes clear when is assumed that [S] ¿ KM . Then equation 1.8

transforms to:

v ≈ kcat

KM[E][S] (1.11)

1.4. ENZYME KINETICS 13

This is a second-order rate constant that relates the reaction rate to the concen-

tration of free enzyme and free substrate molecules, and can function as an indicator

of catalytic efficiency.

Chapter 2

Modeling of Enzymatic Reactions

Quantum chemical studies of enzymes come with many obstacles. The main problem

is that the systems are too large for a quantum mechanical treatment. As mentioned

previously, DFT methods allow us to treat ca 100 atoms, at a reasonable level of

accuracy, quite routinely with the computer power of today. Although this is a very

big progress compared to a few years ago, it allows us to treat only a very small portion

of the enzyme. How can we then study the reaction mechanism of an enzyme that

consists of thousands of atoms? Obviously, a number of approximations have to be

made. In the last 5-10 years, a quite powerful methodology has been developed that

deals with these issues [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]. The basic

idea is to use the DFT methods to treat the critical parts of the active site of the

enzyme and make much cruder approximations about the rest of the enzyme. Here,

this methodology will be briefly outlined. A more detailed discussion and evaluation

of the various aspects of this approach is offered in Paper IV, for the case of the

histone lysine methyltransferase (HKMT).

2.1 Modeling Methodology

An essential part of the theoretical study of an enzyme is the choice of the active site

model. A good model should reflect the chemistry that takes place, i.e. the essential

groups of the active site that take part in the reaction have to be properly accounted

for. However, from a computational point of view it is important to keep the size

of the model relatively small to reduce the computational cost. For every enzyme

studied, these issue have to be taken into consideration.

Figure 2.1 represents the basic steps applied in this thesis for constructing active

site models. The starting point for modeling is usually the X-ray crystal structure of

the investigated enzyme. If such a structure is not available, a homologue structure

15

16 CHAPTER 2. MODELING OF ENZYMATIC REACTIONS

can many times be useful as a starting point. These structures are deposited at

different free databases, one of the most popular being the Protein Data Bank (PDB),

http://www.rcsb.org. Figure 2.1 shows an example of X-ray crystal structure of

GNMT enzyme with highlighted active site.

Since the chemical events that take place at the active site, such as bond making

or breaking, have to be treated with some accurate quantum chemical methods, in

our case DFT, the size of the model has to be limited. Consequently, a part of

the active site is usually cut out from the crystal structure. Based on the available

knowledge about the enzyme and the importance of various parts, a number of

groups are selected and the coordinates are extracted from the pdb-file. The groups

are truncated and hydrogen atoms are added manually. In some cases it is not

obvious which protonation state a certain group holds, and several scenarios have to

be tested.

What does one miss by this procedure? Two obvious effects are missing in this

kind of models of active sites. The enzyme surrounding that is not explicitly included

in the model could provide electrostatic polarization effects that could affect the

calculated energetics, and could also impose steric restraints on the active site groups,

limiting thus their movements in during the reactions. In the methodology adopted

in this thesis, these effects are takes care of in a quite simple way, which has turned

out to be quite powerful and robust.

As for the steric effects, they have to be treated in a different way. The enzyme

matrix around the active site can prevent groups from moving in a certain direction,

or from rotating in a certain way. This could be important for the reactivity and se-

lectivity of the enzyme. The quantum chemical model has to be able to reflect this.

One simple way to mimic these features is by using a coordinate locking scheme.

Some centers, typically where the truncation from the surrounding has been made,

are kept fixed during the geometry optimizations of the model. In metalloenzymes,

this is less of a problem since the metal ions help to keep things in place. However,

groups that are not bound to a metals, or not connected somehow by bonds or hy-

drogen bonds to other groups at the active site, they can move a lot in the geometry

optimization and form thus artificial structures that lead to the wrong description of

the active site. Therefore, the coordinate locking scheme is very helpful to ensure

that the model does not deviate a lot from the experimental structures, yet allowing

for some flexibility of various groups. If the model is too small, there is a risk that

the coordinate locking scheme yields a too rigid active site model, with severe conse-

quences on the calculated energies. However, the error made by this approximation

becomes smaller as the size of the quantum model increases, because the locked

points move further away from the active site.

The combination of continuum solvation and the coordinate locking scheme has

proved to be quite powerful. It has been applied to a wide spectrum of enzymes with

quite successful outcome in elucidating the reaction mechanisms. The calculated

2.1. MODELING METHODOLOGY 17

energies are often been enough to distinguish between different reaction pathways

and to support or dismiss proposed mechanisms.

GNMT enzyme

f

f

f

f

f

f

f

Rest of the enzyme

treated as a continuum solvation model

f

f

f

f

f

ff

GNMT active site

QM active site model

Figure 2.1: Construction of enzyme active site model using GNMT enzyme as an example.First, the coordinates of the X-ray crystal structure are retrieved from databases. The importantgroups of the active site are identified, and a model is constructed. Groups are truncated andhydrogen atoms are added manually. A number of centers are kept fixed during the geometryoptimizations (indicated here by arrows), and the missing enzyme surrounding is modeled by acontinuum solvation model.

18 CHAPTER 2. MODELING OF ENZYMATIC REACTIONS

2.2 Computational Details

All the calculations discussed in this thesis were performed using the hybrid DFT func-

tional B3LYP as implemented in Gaussian03 program package [39]. Unless stated oth-

erwise, all geometry optimizations were performed in gas phase with the 6-31G(d,p)

basis set. As discussed in Section 1.2.1, this double-ζ basis set is good enough to

yield reasonable geometric structures (see Table 1.1), but the errors in the energies

could be large (see Table 1.1). Therefore, to obtain more accurate energies (see

Table 1.2), single point calculations with a large basis set, 6-311+G(2d,2p), were

done.

Zero-point vibrational effect (ZPVE) were obtained by performing frequency cal-

culations on the optimized structures at the same level of theory as used in geometry

optimization. The frequency calculations were also used to confirm the nature of the

stationary points. Minimum have no imaginary frequencies, while transition states

have only one imaginary frequency. Locking the coordinates of some atoms during

the geometry optimizations (see discussion above) can lead to a few small imag-

inary frequencies, typically on the order of 10i - 20i cm−1. These frequencies do

not contribute significantly to the ZPVE and should thus not affect the accuracy of

the energies. However, they render the evaluation of the entropy effects unreliable.

Therefore, entropy was not considered in this thesis.

The solvation effects were added by performing single-point calculations using

the polarizable continuum model (PCM) or some variation of it [40, 41, 42, 43].

Usually, a dielectric constant equal to 4 is used to model the enzyme surrounding.

This value corresponds to an average of ε = 3 for the protein itself and ε = 80 for

the water medium surrounding the protein [44].

Chapter 3

Modeling of Methyl Transfer

Reactions

Methyl transfer, or methylation, represents a simple process of adding or removing a

CH3 group. In chemistry methylation refers to the alkylation process of transferring

one alkyl group from one molecule to another. The alkyl group (methyl group)

transfers as an alkyl carbocation (CH+3 ), a free radical (•CH3), a carbanion (CH−

3 )

or a carbene (••CH2).

Methylation is the most common type of alkylation undergoing in cells and it

has a huge number of effects in the body. The methylation process in cells requires

methyl donor agents. The most widely used methyl donor in the body is S-adenosyl

L-methionine (SAM). So far more than 120 different SAM-dependent methyltrans-

ferases are known to exist in the cell, and each of them catalyzes the synthesis of an

essential product. For example: creatine is important for muscle energy metabolism,

melatonine is the so called sleep hormone, acethylcholine is a neurotransmitter, car-

nitine is valuable for fat burning in mithochondria, choline is essential for fat mobi-

lization and cell membrane fluidity, etc. Hence, irregular functioning of the methyl

transferase enzymes can cause severe diseases, such as brain diseases, mental retar-

dation, epilepsy etc. Understanding the reaction mechanisms of these enzymes can

thus aid in the development of treatment for these diseases.

The present thesis is focused on studying the methyl transfer reaction mechanisms

mainly in the SAM-dependent enzymes glycine N-methyltransferase (GNMT), guani-

dinoacetate methyltransferase (GAMT), phenylethanolamine N-methyltransferase (PN-

MT), and histone lysine methyltransferase (HKMT). The HKMT enzyme has been

studied in order to test the advantages and limitations of the modeling aspects used

in this work to examine the enzyme reaction mechanism. We also did perform a

study on a DNA repair enzyme, O6-methylguanine methyltransferase (MGMT) to

shed more light on the methyl transfer reaction mechanism in this class of enzymes.

19

20 CHAPTER 3. MODELING OF METHYL TRANSFER REACTIONS

GNMT is responsible for the formation of sarcosine by methylation of glycine. So

far the product sarcosine has no known physiological role. Then why does this reaction

occur in cells? A lot of biochemical and structural studies show that the conversion

of glycine to sarcosine, and from sarcosine to glycine, play an important role in

the regulation of methyl group metabolism in the liver and pancreas, by regulating

the ratio between SAM and S-Adenosylhomocysteine (SAH). Furthermore, GNMT is

important for the folate metabolism [45].

In recent years there has been a huge interest in the product of the reaction

catalyzed by the enzyme GAMT – creatine. GAMT catalyzes the final step of the

creatine biosynthesis. Creatine is a natural energy compound used to supply en-

ergy to body muscles [46, 13]. It is produced in the liver, pancreas, and kidneys,

and then transported to the muscles through the bloodstream. Once it reaches the

muscles, it is converted into phosphocreatine (creatine phosphate), which is then

used to regenerate the muscles energy source adenosine triphosphate (ATP) [46].

GAMT deficiency may lead to creatine deficiency, which can cause different mental

diseases. Nowadays, ingesting creatine supplements has become a fashion because

it helps increasing fat-free mass and improves the anaerobic, and possibly the aer-

obic, performance. Creatine is one of the most popular and commonly used sports

supplements available today.

PNMT catalyzes the formation of adrenaline (also referred to as epinephrine)

by N-methylation of noradrenaline (also referred to as norepinephrine) [47, 48]. It

is produced in the cytosol of adrenergic neurons and cells of the adrenal medulla

(chromaffin cells). Adrenaline is a hormone and neurotransmitter that prepares the

body for action in emergency situations. Once its get into the bloodstream it increases

heart rate, blood pressure, boots the supply of oxygen and glucose to the brain and

muscles [49].

The HKMT enzymes are responsible for the regulation of chromatin structure

and control the access of a genomic DNA by transferring a single methyl group from

SAM to amino group in histone peptide [50, 51]. Breakdown this methylation process

can lead to abnormal gene regulation that usually causes cancers [52].

The MGMT enzyme repairs the alkylated DNA by directly removing the alkyl

group from the O6 position of the DNA guanine base [53, 54, 55]. These alkyl

adducts are highly mutagenic and carcinogenic because they results in transition

DNA mutations. Human MGMT is a target in cancer therapy because it repairs

damage induced by anticancer chemotherapies [56, 57].

In this chapter, the most important results of our investigations on these enzymes

will be summarized. For detailed discussions, see Papers I-V in the appendices.

3.1. SAM-DEPENDENT ENZYMES 21

3.1 SAM-dependent Enzymes

A natural methyl donor substance present in the cells and used by the methyl transfer

enzymes is SAM. The role of this compound is to donate a methyl group in a variety

of reactions catalyzed by the enzymes, Figure 3.1 [58].

S

O

CH3

SAM

HO

HO

adenine

COO

NH3+

-

S

O

SAH

HO

HO

adenine

COO

NH3+

-

R

X HB

substrate

enzy

me

R

X CH3

HB

product

enzy

me

Figure 3.1: Generic mechanism for SAM-dependent enzymes.

The substrate molecule enters the active site of the enzyme and binds there by

a number of hydrogen bonds to different protein residues. The nucleophilic entity,

having a lone pair of electrons or possessing partial negative charge, pulls the methyl

group, while the positively charged sulfur atom of SAM attracts electron density from

the methyl group. In this way the methyl transfer reaction can occur. Figure 3.1

shows a general reaction mechanism, in which a base is needed to abstract a proton

from the substrate.

3.1.1 Glycine N-methyltransferase, GNMT (Paper I)

As a SAM-dependent enzyme, GNMT follows the mechanism described in Section

3.1 to transfer a methyl group, see Figure 3.2, [59].

The reaction starts with the binding of SAM and the glycine substrates, in strict

order. In this particular case the glycine has a lone-pair of electrons and binds in such

a way that this lone-pair of the amino nitrogen is directed toward to the CE methyl

carbon of SAM. A single SN2 methyl transfer step occurs from SAM to glycine,

resulting in products SAH and sarcosine. In the case of GNMT, there is no base at

the active site that can abstract a proton, so one has to assume that the glycine

substrate is bound to the enzyme in a deprotonated amine form.

To study the reaction mechanism of GNMT described above we used the recent

X-ray crystal structure, solved in complex with SAM and an acetate molecule at a 2.0


S

O

CH3

SAM

HO

HO

adenine

COO

NH3+

-

S

O

SAH

HO

HO

adenine

COO

NH3+

-

N

H

HO

O

N

CH3

HO

O

H

glycine sarcosine

Figure 3.2: Reaction catalyzed by GNMT.

A resolution by Takata et al, Figure 3.3 [59]. As described in Chapter 2, one of the

most important parts of enzyme modeling is creating a good model for investigation.

Looking inside the GNMT enzyme it can be seen that a number of hydrogen bonds

are formed between the active site residues and the substrate molecule.

Figure 3.3: X-ray crystal structure of GNMT active site [59].


These bonds are non-covalent, elec-

trostatic interactions and they set up the

substrate molecule for the reaction that

the enzyme catalyzes. The positively char-

ged guanidino group of Arg175 forms a

pair of hydrogen bonds with the carboxy-

late group of the acetate. Other groups

that form hydrogen bonds to the sub-

strate are Tyr33, Asn138 and Gly137.

The largest model used for studying

the SN2 mechanism catalyzed by GNMT

consists of 98 atoms, Figure 3.4. This

model includes the SAM molecule – trun-

cated two carbons away in each direc-

tion from the sulfur center. The glycine

substrate, which was modeled based on

the structure of the acetate, to which an

amino group was added. The side chain

of Arg175 forms strong hydrogen bonds

to the carboxylate of glycine and is hence

essential to bind the substrate and sta-

bilize its charge. The phenol group of

Tyr21 was included to test the proposal

that this group polarizes the S −C bond

of SAM. Parts of Gly137 and Asn138, are

present as these groups are found to form

hydrogen bonds to both the amino and

the carboxylate groups of the glycine sub-

strate. The phenol group of Tyr194, was

included since this group forms hydrogen

bonds to both the glycine substrate and

to Gly137. Hydrogen atoms were added

manually.

The methyl group transfers to the gly-

cine molecule in a single SN2 reaction

that involves the displacement of the leav-

ing group (SAH), by the nucleophile (gly-

cine). The structure of the optimized

transition state is displayed in Figure 3.4B.

At the transition state the bond to the

glycine is partially formed while the bond

f

f

f

f

f

f

f

A

f

f

f

f

f

ff

B

f

f

f

f

f

f

f

C

Figure 3.4: Optimized reactant (A), transi-tion state (B), and product (C) structures ofthe largest model of GNMT active site. Ar-rows indicate atoms that are fixed during thegeometry optimizations.


to the SAM is partially broken. The critical SD−CE and CE−N bond distances

are 2.28 and 2.18 A, respectively. The barrier for the methyl transfer in GNMT is

calculated to be 15.0 kcal/mol. No experimental data for a rate constant is available,

but an energy barrier of 15.0 kcal/mol for enzyme reaction is considered energetically

feasible, see Section 1.3.

The reaction was found to be exergonic by 14.1 kcal/mol. The optimized structure

of the product is shown in Figure 3.4C.

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

A B C D

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

E F G

Figure 3.5: Optimized transition-state structures for models A-G.

We have investigated the role of the various active site residues on the energetics

by creating different active site models. The smallest model is composed of glycine,

a truncated model of SAM, and truncated residue Arg175, Figure 3.5A. The roles

of the other amino acid residues were tested by adding the residues to the small


Model A one at the time, in order to isolate the contribution of each group. The

optimized transition state structures are shown in Figure 3.5, and the energetic results

are summarized in Table 3.1.

model parts included barrier reaction energy

A SAM + Glycine + Arg175 11.2 -20.1

B A + Tyr21 13.5 -16.8

C A + Tyr21 + His 142 11.4 -21.2

D A + Gly137 9.9 -24.8

E A + Asn 138 15.1 -12.6

F A + Tyr194 17.5 -14.5

G A + Tyr194 + Gly137 10.5 -16.6

largest A + Tyr21 + Gly137 + Asn 138 + Tyr194 15.0 -14.1

Table 3.1: Calculated Barriers and Reaction Energies (kcal/mol) for the different models.

Model A has a barrier of 11.2 kcal/mol and is exothermic by 20.1 kcal/mol.

Adding the phenol group of Tyr21 to this model (Figure 3.5B) results in a slight

increase in the barrier, to 13.5 kcal/mol, and a decrease in the exothermicity, to

16.8 kcal/mol. When both Tyr21 and the imidazole ring of His142 are added, Figure

3.5C, the barrier is found to be almost identical to Model A, 11.4 kcal/mol. These

results speak against the suggestion that Tyr21 polarizes the SD−CE bond to cause

a decrease of the barrier [59]. As also seen for the largest model discussed above,

Figure 3.4, the phenolic proton of Tyr21 was found to point away from SAM, despite

attempts to make it to point toward the sulfur center.

Adding the peptide bond of Gly137, which forms a hydrogen bond to the amino

group of the substrate (Figure 3.5D), results in a decrease of the barrier by 1.2

kcal/mol to 9.9 kcal/mol. The hydrogen bond to the carbonyl moiety of Gly137

makes the nitrogen center of the substrate slightly more negative, which would make

the transfer of the positively charged methyl group slightly easier.

On the other hand, adding the side chain of Asn138 (Figure 3.5E), which forms


a hydrogen bond to the carboxylate moiety of the substrate, and hence makes the

substrate slightly less negative, leads to a higher barrier, calculated to 15.1 kcal/mol.

Also, adding the Tyr194 residue to Model A leads to a dramatic increase in the

barrier, from 11.2 to 17.5 kcal/mol (Figure 3.5F). This is easily explained if we

note that the phenolic proton forms a hydrogen bond to the nitrogen atom of the

substrate in the reactant species. This hydrogen bond will be lost when the methyl is

transferred to the nitrogen, resulting in the barrier raise. On the other hand, if both

Tyr194 and the peptide bond of Gly137 are added at the same time (Figure 3.5G),

the tyrosine will form a hydrogen bond to the carbonyl of the glycine instead and the

barrier is lowered to 10.5 kcal/mol.

Hence, the calculations on the GNMT enzyme have confirmed that the reaction

takes place in an SN2 fashion. Furthermore, by adding or eliminating various groups

at the active site, we showed that hydrogen bonds to the amino group of the sub-

strate lower the reaction barrier, whereas hydrogen bonds to carboxylate group of the

substrate raise the barrier.

3.1.2 Guanidinoacetate Methyltransferase, GAMT (Paper II)

The GAMT enzyme catalyzes the transfer of a methyl group from SAM to guani-

dinoacetate (GAA), resulting in the formation of creatine and SAH, see Figure 3.6

[60, 61, 62, 63, 64, 65]. The way how this reaction occurs is similar to the generic

mechanism described in Section 3.1.

S

O

CH3

SAM

HO

HO

adenine

COO

NH3+

-

S

O

SAH

HO

HO

adenine

COO

NH3+

-

NE

H

O

O

N

H

HH2N

OD1

O

NE

O

O

N

H

HH2N

OD1

O

CEH3

H

Asp134Asp134

guanidinoacetate creatine

Figure 3.6: Reaction mechanism of the GAMT enzyme.


Figure 3.7: X-ray crystal structure of the GAMT active site [66].

With information about the structure of GAMT, crystallized with SAH and GAA,

Figure 3.7 [66], the reaction mechanism was theoretically investigated.

The substrate and the cofactor are attached to the active site by a number of

hydrogen bonds. Glu45 and Asp134 form hydrogen bonds with the guanidino group

of GAA, while the amide groups of Leu170 and Thr171 form hydrogen bonds with the

carboxylate group of GAA. These hydrogen bonds facilitate the orientation of GAA in

GAMT. In the GAMT:(SAH+GAA) structure, the distance between the sulfur center

of SAH (SD) and the NE of GAA is found to be 3.9 A.

The model system used to reproduce the GAMT active site and to elucidate the

reaction mechanism consisted of 92 atoms. This model includes part of the cofactor

SAM built on the basis of the SAH structure by adding a methyl group to the sulfur

atom. Furthermore, SAM was truncated in both directions relative to the sulfur

center – at the adenine group on one side and three carbons away on the other

side. This is sufficient to model the properties of the SD − CE bond and to grant

flexibility to the SAM-model. The GAA substrate molecule was included in the model

without any changes. Five amino acids were furthermore included in the model –

Glu45, Asp134, Thr135, Leu170, and Thr171 (Figure 3.7). The Glu45 group forms

strong hydrogen bonds to the GAA guanidino group, and is hence essential to bind

the substrate and stabilize the positive charge of the guanidino group. Asp134 and

Thr135 are found to form hydrogen bonds to the guanidino group of GAA. Leu170

and Thr171 form hydrogen bonds with the carboxylate group of GAA.


The optimized structure of the reac-

tant (Figure 3.8A) shows high resemblance

to the crystal structure. The hydrogen

bonding network around the substrate mo-

lecule orients it in such a way that there

is nearly a straight line between the sul-

fur center of SAM (SD) and the nitrogen

atom of GAA (NE). The distance be-

tween NE(GAA) −CE(SAM) is calculated

to be 2.98 A, and the angle SD −CE −NE is found to be 167.7◦. The distance

OD1(Asp134) − HNE(GAA) is also impor-

tant, and it is calculated to be 1.86 A in

the optimized reactant structure. The

guanidino group of GAA is planar and the

positive charge is delocalized over three

nitrogen atoms.

It was previously proposed that the

reaction mechanism starts with a proton

transfer from NE of GAA to the Asp134

base upon which the methyl group is trans-

ferred from SAM to the deprotonated GAA

[66].

To check this hypothesis, a linear tran-

sit scan of moving the proton from NE(GAA)

of the substrate to Asp134 was performed.

The HGAA − OD1(Asp134) distance was

kept fixed in steps between 1.86 A and

1.00 A, while all other degrees of free-

dom were optimized. As seen from Figure

3.9A the energy increases monotonously,

and no energy minimum could be found

corresponding to an intermediate where

the proton is transferred to the Asp134.

Transferring a proton from GAA costs in

gas phase 15.9 kcal/mol, while applying

protein environment in the form of a ho-

mogeneous medium yields a slightly lower

value of 12.6 kcal/mol. This results speaks

against the stepwise mechanism, where

the proton is transferred first.

f

f

f

f

f

f

A

f

f

f

f

f

f

B

f

f

f

f

f

f

C

Figure 3.8: Optimized reactant (A), transi-tion state (B), and product (C) structures ofthe GAMT active site model.


Instead, a linear transit scan to move the methyl group from SAM to GAA was

used to find the transition state structure. The CE −NE distance was kept fixed in

steps starting from 2.98 A, which is the distance in the reactant, to 1.46 A, which is

the distance in the product, see Figure 3.9B. As the methyl approaches the nitrogen

center, the energy increases up to a distance of 2.2 - 2.0 A, after which it starts to

drop. The NE proton moves toward Asp134 and the nitrogen center becomes more

pyramidal. At a CE −NE distance of 1.8 A the proton has transferred completely.

2.0 1.8 1.6 1.4 1.2 1.0-2

0

2

4

6

8

10

12

14

16

18

Rel

ativ

e E

nerg

y [k

cal/m

ol]

H - O distance [Å]

gas phase incl. solvation

3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4-40-36-32-28-24-20-16-12-8-4048

12162024

[1.02]

[1.01]

[1.02]

[1.47][1.79]

[1.84]

[1.86][1.86]

Rel

ativ

e en

ergy

[kca

l/mol

]

C - N distance [Å]

gas phase incl. solvation

A B

Figure 3.9: Linear transit scans for: A) moving the proton from NE of the substrate to OD1

of Asp134, and B) moving the methyl group from SAM to NE of GAA substrate, the H −OD1

distance is given in brackets. Solvation is added using ε = 4.

Based on this, the fully optimized transition state for this reaction was located,

see Figure 3.8B. At the transition state the critical SD−CE and CE −NE distances

are calculated to be 2.29 A and 2.16 A, respectively. The other two important

distances NE − H and H − OD1 in the transition state structure are found to be

1.05 A and 1.73 A, respectively. The nature of the transition state was confirmed

to have one imaginary frequency of -446i cm−1. It shows that the methyl and the

proton transfer take place in one concerted asynchronous step. The activation barrier

for this process was calculated to be 14.9 kcal/mol in gas phase, and 19.7 kcal/mol

in protein environment with ε = 4. This energy barrier is in good agreement with the

measured rate constant of 3.8 ± 0.2 min−1, which corresponds to ca 19 kcal/mol.

The reaction was calculated to be exergonic by as much as 36.2 kcal/mol in gas

phase and 24.0 kcal/mol using ε = 4.

The optimized structure of the product is displayed in Figure 3.8C. The protonated

Asp134 rotates in such a way that the hydrogen bond to the guanidino group of GAA

is broken, while a hydrogen bond to acetate of GAA is formed.

We tried to optimize the intermediate structure in which the substrate is methy-

lated, but the proton is not transferred to Asp134, i.e. corresponding to a stepwise


mechanism, but this was not possible. We tried also to optimize the intermediate in

which the proton is transferred to Asp134 before the methyl transfer, but it was not

possible either.

The calculations on the GAMT enzyme show thus that the methyl transfer from

SAM to the substrate takes place in a concerted asynchronous step with the proton

transfer from the substrate to the Asp134 base.

3.1.3 Phenylethanolamine N-methyltransferase, PNMT (Paper III)

The PNMT enzyme catalyzes the transfer of a methyl group from SAM to nora-

drenaline, resulting in the formation of adrenaline and SAH (Figure 3.10) following

the generic mechanism described in Section 3.1:

S

O

CH3

SAM

HO

HO

adenine

COO

NH3+

-

S

O

SAH

HO

HO

adenine

COO

NH3+

-

N

H

HHO

OH

OH

N

CH3

HHO

OH

OH

noradrenaline adrenaline

Figure 3.10: Reaction catalyzed by PNMT.

Several X-ray crystal structures of PNMT with various substrates and inhibitors

have been solved [67, 68, 69, 70]. To investigate the reaction mechanism, several

quantum chemical models of the PNMT active site were constructed on the basis

of the X-ray crystal structure (PDB code: 2AN4, Figure 3.11), which is in complex

with SAH and a methyl acceptor substrate, p-octopamine [69].

Model A is composed only of parts of cofactor and substrate molecule, as shown

in Figure 3.12. It is assumed that the proton of the amino group of the substrate is

lost, so the substrate was modeled in its neutral form. In the optimized structure of

the reactant, Figure 3.12A, it is found that the important SD−C and C−N distances

are 1.83 A and 3.40 A, respectively. Those distances are very similar to the distances


Figure 3.11: X-ray crystal structure of PNMT active site [69].

in GNMT enzyme where the methyl group is transferred from the same cofactor to

the amino group of the glycine residue. The transition state for the methyl transfer

was located (Figure 3.12B) and the distances SD − C and C − N are 2.36 A and

2.19 A, which are also quite similar to the distances found for GNMT (2.38 A and

2.20 A). The barrier for this transfer was calculated to be 16.7 kcal/mol which is

about 2 - 4 kcal/mol too low compared to the experimental rate constant of kPEAcat =

2.6 ± 0.1 min−1, corresponding to ca 19 -20 kcal/mol (PEA - phenyletanolamine ).

The reaction is calculated to be exothermic by 5.7 kcal/mol (13.2 and 15.8 kcal/mol

including solvation with ε = 4 and ε = 80, respectively).

A somewhat larger model consisting of 48 atoms was also used, Figure 3.13.

This model includes the important Glu185 and Glu219 (represented by acetates)

and a water molecule (W), which initially was bridging the substrate and the Glu185

residue. Both glutamate residues were initially modeled in the deprotonated form, and

the substrate was modeled as a cation, i.e. in its protonated state. The total charge

of the model is thus 0. In the optimization, a proton moved spontaneously from

the amino group of the substrate to Glu185, through the bridging water molecule,


O

N

C

C

C

C

C

C

S

C

3.40

1.83

SAM

substrate

molecule

N

O

C

CC

C

C

C

S

C

2.19

2.36

SAM/SAH

substrate

molecule

C

CN

C

O

S

CC

C

C

1.50

3.82

SAH

product

molecule

A B C

Figure 3.12: Optimized reactant (A),transition state (B), and product (C) structures of ModelA of PNMT.

which subsequently moved out to bridge the two glutamate groups instead, see Figure

3.13A. Effectively, in this model the substrate is in the neutral form and one of the

glutamates protonated.

Using this reactant structure, a transition state for the methyl transfer was lo-

cated, Figure 3.13B. The transition state is characterized by an imaginary frequency

of -359i cm−1, and the SD−C and C−N distances are calculated to be 2.22 A and

2.40 A, respectively. This model has a calculated barrier of 6.0 kcal/mol without

solvation effects, which increases to 11.8 and 13.7 kcal/mol, using ε = 4 and ε = 80,

respectively. These values are significantly lower than the ones found for Model A.

It is easy to rationalize this result if one recognizes that in the reaction a methyl

cation is transferred to the substrate. In the case of Model B a charged glutamate

is present that can stabilize the product better than the substrate, lowering thus the

barrier for the reaction.

This fact is more evident from the calculated exothermicity of the reaction.

Model B yields a reaction energy of -48.3 kcal/mol, which however is considerably

decreased to -28.5 and -21.8 kcal/mol when ε = 4 and ε = 80 are used, respectively.

For this model, we also found another product structure in which a proton from

the substrate nitrogen has transferred to the Glu219 residue (Figure 3.13D). This

structure has a very similar energy compared to the other product structure (-47.9,

-27.7 and -20.9 kcal/mol, without solvation, and with ε = 4 and ε = 80 respectively).

The biggest PNMT active site model used in the investigations consists of 93

atoms. In addition to Model B, this model contains parts of the amino acids Asp267,

Arg44, and Asn39, see Figure 3.14. A second water molecule (W2) observed in the

crystal structure is also included. Also, the full phenylethanolamine substrate was

used and one more carbon was kept in the SAM to grant even more flexibility to

the model. The total charge of the model is thus 0. As in the case of Model B,


O

C

C

C

C

C

C

O

N

C

O

O

S

C O

C

C

C

2.84

1.57

2.91

1.45

1.86

1.78

SAM

Glu185

Glu219

substrate

molecule

OW

O

C

C

C

C

C

C

O

N

O

C

O

S

CO

C

C

C

2.85

1.57

2.40

1.46

2.22

1.75

SAM/SAH

Glu185

Glu219

substrate

molecule

WO

A B

C

O

C

C

C

C

CO

O

O

S

O

O

C

N

C

C

C

C

1.71

1.99 Å1.741.14

1.40

1.48

SAH

Glu185

Glu219

W

productmolecule

O

C

C

C

C

C

C

O

O

O

S

OC

C

C

C

1.65

1.821.62

1.53

1.49

SAH

Glu185

Glu219

methylated

substrate

molecule

W

N

C

O

C D

Figure 3.13: Optimized reactant (A),transition state (B), and products (C, and D) structuresof Model B of PNMT.

the substrate was initially modeled in the protonated form and the two glutamates

(Glu185 and Glu219) were anionic. Also here, during the geometry optimization of

the reactant a proton was transferred spontaneously from the amino group of the

substrate to the Glu185 residue through a water bridge (Figure 3.14A).

The transition state for the methyl transfer in Model C was located and is also

shown in Figure 3.14B. The SD − C and C − N distances are calculated to be

2.11 Aand 2.35 A, respectively. We find that the transition state now is even earlier

than in Model B, and the calculated reaction barrier is 4.8 kcal/mol, which increases

to 8.8 and 9.9 kcal/mol when ε = 4 and ε = 80 are used, respectively.


CC

C

O

C

C

CC

O

C

O

C

C

CC

N

O

C

C

N

N

O

O

O

O

O

C

N

C

C

C

C

C

O

C

N

C

S

C

C

1.47

1.61

2.02

1.53

1.80

1.70

2.93

SAM

Glu185

Glu219

Asp267

Arg44

W1

W2

phenylethanolamine

Asn39

A

CC

O

CC

C

CC

O

C

O

C

C

C

C

C

O

NC

O

N

O

O

N

C

N

C

O

O

CC

C

C

C

O

N

C

SC

C

1.63

1.46

2.01

1.82

1.50

2.35

1.69

2.11

SAM/SAH

phenylethanolamineGlu185

Glu219

Asp267

Arg44

W1W2

Asn39

B

CC

C

O

C

C

C

CC

O

C

O

O

C

C

C

O

O

C

N

N

N

C

O

N

O

O

O

C

C

C

C

C

N

C

C

C

S

C

C

1.92

1.84

1.75

1.00

1.66

1.56

1.74

SAH

methylated

phenylethanolamine

Glu185

Glu219

Asp267

Arg44

W1

W2

Asn39

C

Figure 3.14: Optimized reactant(A),transition state (B), and product(C) structures of Model C of PNMT.

C

C

C

C

O

C

CC

C

C

N

C

O

N

N

O

C

C

C C

O

O

C

C

C

O

O

O

O

C

C

N

C

O

N

C

C

S

C

C

2.75

1.71

1.70

1.841.70

1.56

1.59

1.83

3.18

2.19

SAM

phenylethanolamine

Glu185

Glu219

Asp267

Arg44

Asn39

W1 W2

A

C

C

C

O

C

C

C

C

C

O

C

C

C

NO

C C

C

N

O

N

O

O

OO

O

O

C

N

C

C

N

C

C

C

CC

SC

C

2.51

1.73

1.71

1.65 1.86

1.60

1.54

2.24

2.20

2.22

SAM/SAH

phenylethanolamine

Glu185

Glu219

Asp267

Arg44

Asn39

W1

W2

B

C

C

C

C

O

C

CC

C

C

C

O

N

C

C

O

C

N

N

C

O

O

O

O

O

O

C

O

N

C

C

N

C

C

C

CC

SC

C

2.39

1.64

1.93

1.65 1.621.92

1.55

1.82

1.49

SAH

methylated

phenylethanolamine

Glu185

Glu219

Asp267

Arg44

Asn39

W1

W2

C

Figure 3.15: Optimized reactant(A),transition state (B), and product(C) structures of Model C(H+) of PNMT.


The reaction is exothermic by 47.9 kcal/mol, which, as in the case of Model B,

is considerably decreased to -29.5 and -28.3 kcal/mol, when ε = 4 and ε = 80 are

used, respectively. We find that simultaneously with the methyl transfer, a proton is

transferred from the substrate to Glu219, Figure 3.14C.

Since inclusion of the negatively-charged Glu185 and Glu219 lowered the barrier

in both Model B (Figure 3.13) and Model C (Figure 3.14), we tried the possibility

of protonating one with them and added thus one proton to Glu219. The model,

called Model C(H+), now has a total charge of +1. The optimized geometries of the

reactant, transition state, and product are shown in Figure 3.15. The substrate was

also here modeled on its protonated state but a proton was spontaneously moved to

the Glu185 during the geometry optimization. The reaction barrier was calculated to

be 13.6 kcal/mol (15.8 and 16.4 kcal/mol including ε = 4 and ε = 80 respectively).

These values are in much better agreement with the experimental rate compared to

the Model B and Model C, in which only one of the glutamates is protonated.

These results suggest thus that either the two active site glutamates are in the

protonated form prior to the binding of a neutral substrate, or that one of them is

protonated and the other receives a proton from a charged substrate.

3.1.4 Histone Lysine Methyltransferase, HKMT (Paper IV)

HKMT catalyzes the transfer of a methyl group from SAM to the amino group

of the lysine of the histone peptide (Figure 3.16) [50, 51, 52]. By doing this it

is responsible for the regulation of chromatin structure and control the access of a

genomic DNA. The reaction mechanism of this enzyme is well-understood and follows

the same pattern as for the precious cases discussed in this thesis (GNMT, GAMT,

and PNMT). In particular, there has been a QM/MM study by Hu and Zhang that has

addressed the details of the mechanism HKMT [71, 72]. Instead, we chose to study

it as a test case to evaluate the quantum chemical methodology used throughout the

thesis.

Several models of HKMT were constructed based on the X-ray crystal structure

(PDB code: 1O9S), which is in complex with SAH and a methylated histone peptide

[73]. First we designed a very small model of the enzyme active site, consisting of

the truncated SAM and substrate molecules as shown in Figure 3.17A. This model,

called Model A, consists of 29 atoms and has a total charge of +1. The next

model, called Model B consists of 46 atoms and includes larger parts of SAM and

substrate molecules as shown in Figure 3.17B. Model C consists of 72 atoms and

includes two tyrosine molecules, Tyr245 and Tyr305, forming hydrogen bonds with

the amino group of the substrate, Figure 3.17C, while the largest model, Model D,

consists of 132 atoms and includes additional parts of the active site, such as Tyr335,

Asn265, Thr266, Lys294, Ala295, and an active site water molecule, Figure 3.17D.

For everyone of these models, several dielectric constants were used to investigate

the influence of the choice of this parameter on the calculated energies. The results


S

O

CH3

SAM

HO

HO

adenine

COO

NH3+

-

S

O

SAH

HO

HO

adenine

COO

NH3+

-

N

H

H

CH3

NH

H

Lys4(Histone Peptide)

Methylated Lys4(Histone Peptide)

Figure 3.16: Reaction catalyzed by HKMT.

are listed in Table 3.2.

Let us first look at some geometrical parameters. For Model A (Figure 3.17A), at

the transition state the critical distances Sδ−CE , CE−Nζ , and the angle Sδ−CE−Nζ

of this SN2 reaction are 2.44 A, 2.18 A, and 175.3◦ respectively. In the slightly

larger Model B those parameters are 2.41, 2.16, and 177.1◦ respectively, Figure

3.17B. The transition state for Model C is characterized by Sδ −CE , CE −Nζ , and

Sδ−CE−Nζ parameters of 2.31 A, 2.26 A, and 173.8◦, respectively (Figure 3.17C).

Very similar distances and angle are obtained for the largest model, Model D (Figure

3.17D), 2.37 A, 2.23 A, and 175.6◦, respectively. The transition state geometries are

thus internally consistent among the various models. Also, quite importantly, those

parameters agree quite well with the available QM/MM geometrical data for HKMT

enzymes [71, 72], which are 2.32 ± 0.02 A, 2.30 ± 0.02 A, and 173.3◦± 1.4◦

respectively for the Sδ − CE , CE −Nζ , and Sδ − CE −Nζ .

The solvation corrections (i.e. the effects of the applied dielectric medium on the

barrier and reaction energy) are quite different for the different models, see Table 3.2.

For the calculated barriers, the solvation effects of all models are quite small, less

than 3 kcal/mol in going from gas phase to the largest dielectric constant (ε = 80).

However, for the reaction energies, the solvation effects are quite large for Models A

and B, while for Models C and D they are much smaller. When the model size

increases, and more and more groups are added, it is thus seen that the effects of

the solvation model are diminished. In this case, more groups are added around

the substrate, which in the reactant is neutral, but in the product is methylated


C

C

C

CS

C

C

N

C

2.44

2.18

ii

i

C

C

C

OC

N

C

C

C

C

C

C

S

C

C

C

2.16

2.41

i

i

i

A B

C

C

C

C

O

C

C

C

C

C

CO

C

N

C

C

C

C

S

C

C

C

C

C

C

C

C

C

O

C

2.23

2.26

2.31

2.06

i

i

i

i

i

CC

C

C

C

C

CC

C

C

O

C

C

O

C

C

C

CC

O

C

C

C

C

C

O

N

C

C

O

NC

O

C

O

O

C

S

C

C

C

C

C

C

O

C

O

C C

N

N

C

CN

C

C

C

C

O

O

C

C

2.44 2.02

2.23

2.37

2.29

2.12

2.29

1.75

Tyr335

Asn265

Thr266

Ty305

H2O

Lys294

Ala295

Tyr245

i

i

i

i

i

i

i

i

i

i

C D

Figure 3.17: Optimized transition states for methyl transfer reaction in the different HKMTactive site models. A) ModelA, B) ModelB, C) ModelC, and D) ModelD.

(cation). Proper description of the active site around this area is quite important to

obtain stable results. As seen for Model D the barrier is essentiallt unaffected by the

solvation, while the reaction energy changes by up to 3 kcal/mol. As a consequence

of this, one can conclude that the particular choice of the dielectric constant becomes

less critical as the model size increases. This is a very important result to realize for

future quantum chemical studies of enzyme active sites.

In this study (Paper IV), we also investigated the validity of some other technical


Model A Model B Model C Model D29 atoms 46 atoms 72 atoms 132 atoms

barrier reaction barrier reaction barrier reaction barrier reaction

energy energy energy energy

no solvation 18.8 -2.9 21.7 +0.5 15.4 -16.7 18.9 -9.2

ε = 2 18.2 -9.3 20.6 -7.2 16.7 -17.5 19.0 -10.6

ε = 4 17.8 -12.7 19.9 -11.4 17.3 -18.0 19.1 -11.5

ε = 8 17.6 -14.5 19.5 -13.6 17.6 -18.3 19.1 -12.0

ε = 16 17.4 -15.4 19.3 -14.8 17.8 -18.5 19.1 -12.2

ε = 80 17.3 -16.1 19.1 -15.7 17.9 -18.6 19.1 -12.4

Table 3.2: Calculated energetics for the various active site models of HKMT enzyme.

assumptions. For example, it is a very common procedure to first optimize the

geometries in the gas phase and then perform a single-point solvation correction.

To check the validity of this strategy, we performed the geometry optimization for

Model A in PCM with ε = 4 and ε = 80 with two different basis sets (6-31G(d,p),

and 6-311+G(2d,2p)). As seen from Table 3.3, optimization in PCM gives barriers

and reaction energies that are almost the same as the ones calculated with the above-

mentioned methodology. The differences are smaller than 1 kilocalory/mol. It can

thus be concluded that it is a safe procedure, at least for this kind of reactions, to

first optimize the geometry in the gas phase and then apply solvation.

6-311+G(2d,2p) 6-31G(d,p)gas phase PCM gas phase PCM

barrier reaction barrier reaction barrier reaction barrier reaction


no solvation 18.8 -2.9 16.3 -6.0

ε = 4 17.8 -12.7 18.4 -12.5 15.4 -15.8 15.9 -15.8

ε = 80 17.3 -16.1 18.2 -16.0 14.8 -19.2 15.6 -19.6

Table 3.3: Calculated energetics for ModelA using different geometry optimization schemes.

It is commonly argued that the B3LYP functional underestimates reaction barriers

[71, 72]. Therefore, we decided to study the reaction of Models A using different

methods, such as BLYP, MPW1K [74, 75], and MP2, following the same strategy

described above. The results are presented in Table 3.4. For BLYP, which has

no Hartree-Fock exchange, the barrier lowered by around 5 kcal/mol compared to

3.2. OTHER METHYL TRANSFER ENZYMES 39

the B3LYP, while using MPW1K, which includes more Hartree-Fock exchange than

B3LYP, the barrier is raised by 7-8 kcal/mol. MP2 gives barriers that are around 10

kcal/mol higher compared to B3LYP. Clearly, the BLYP barrier is too low compared

to experiments (ca 13 vs. 20.9 kcal/mol), and the MPW1K and MP2 are too high

(ca 26 and 27 vs. 20.9 kcal/mol). B3LYP seems to yield the good agreement with

the experimental data, which is also consistent with the results of our previous studies

on the other SAM-dependent methyl transfer enzymes.

B3LYP BLYP MPW1K MP2barrier reaction barrier reaction barrier reaction barrier reaction


no solvation 18.8 -2.9 13.5 -1.7 26.4 -3.3 28.3 -6.4

ε = 4 17.8 -12.7 12.8 -11.5 25.7 -13.2 27.0 -16.3

ε = 80 17.3 -16.1 12.4 -14.9 25.3 -16.6 26.4 -19.7

Table 3.4: Calculated energetics for ModelA using different methods. Experimental barrier is20.9kcal/mol. Barriers calculated by Zhang et al with QM/MM are: 14.6±1.7 (B3LYP/6-31G*/ MM), 21.9± 1.9 (MP2/6-31G* / MM), and 21.5± 1.9 (MP2/6-31+G* / MM) [71, 72].

In conclusion, the results of Paper IV, provide confidence in the methodology

used in this thesis for studying enzyme reactions. Both the size of the model, and

the adopted technical details seem reliable enough to provide useful information about

the reaction mechanism of the considered enzymes.

3.2 Other Methyl Transfer Enzymes

3.2.1 O6-Methylguanine Methyltransferase, MGMT (Paper V)

MGMT, also called alkylguanine alkyltransferase (AGT) repairs the alkylated DNA

by directly removing the alkyl group from the O6 position of the guanine. It works

by transferring the alkyl lesion to an active site cysteine residue (Cys145 in human

MGMT) in an irreversible stoichiometric suicide reaction, Figure 3.18.

To study the repair reaction mechanism of MGMT we have used a recent X-ray

crystal structure (PDB code: 1T38) of the protein in complex with DNA [76], Figure

3.19, in which the critical Cys145 is mutated into a serine residue. The hydroxyl group

of the Cys145Ser moiety is hydrogen bonded to a Water-His146-Glu172 triad that

is believed to be a charge-relay system to shuttle the proton of the thiol. Several

interactions help binding the flipped-out O6-methylguanine base. Tyr114 forms a

hydrogen bond to the N3 atom and the peptide bond of Ser159 forms a hydrogen

bond to the O6 atom.

Based on the information from X-ray crystal structure we have created an active


CO

O

Cys145

S

His146

N

N

N

N N

N

O

H2N

DNA

H3C

H

O

H

H

H

O6-methylguanine

Cys145

S

His146

N

N

N

N N

N

O

H2N

DNA

H3C

H

O

H

H

H

O6-methylguanine

Glu172

Cys145

S

His146

N

N

N

NN

N

O

H2N

DNA

CH3

H

O

H

H

H

guanine

CO

O

Glu172

CO

O

Glu172

Figure 3.18: Reaction mechanism of the MGMT enzyme.

Figure 3.19: X-ray crystal structure of the MGMT active site.


site model consisting of 74 atoms, see Figure 3.20. In the model, the Ser145 residue

was modified to cysteine by changing the oxygen atom from hydroxyl group of serine

to a sulfur atom. The methylated guanine base, which in the crystal structure is

already flipped out from the DNA strand and positioned in the enzyme active site, is

cut on the place where the ribose start. The glycosidic bond is kept in the chemical

model as an N − CH3 bond. Glu172 from the H2O −His146−Glu172 hydrogen

bonding network is modeled as an acetate molecule. Tyr114 (modeled as a phenol

group) was also included in the model. This residue makes a hydrogen bond with

N3 of the guanine base and it is proposed to assist the reaction by stabilizing the

negative charge developing at the guanine.

The optimized structure of the reactant species shows high resemblance to the

crystal structure, Figure 3.20. The hydrogen bonding network connecting the thiol

group of Cys145, the ordered water molecule, His146, and Glu172 is well reproduced.

Because Glu172 is in the deprotonated form, the hydrogen bond to the histidine is

rather short, with O −H and H −N distances of 1.41 A and 1.14 A, respectively.

The substrate NH2 is forming a hydrogen bond to the carbonyl oxygen of the peptide

bond connecting Cys145 and His146. The methyl lesion is pointing toward the sulfur

atom of the Cys145 residue, with a C − S distance of 4.07 A.

C

C

C

C

C

S

C

C

O

C

O

C

N

C

C

O

C

C

N

N

N

C

O

C

C

C

N

O

C

NC

C

O

C

C

N

C

N

C

4.072.37

1.411.85

1.81

1.77

Glu172

His146

Cys145

Tyr114

Methylguanine

f

f

f

f

Figure 3.20: Optimized reactant structure of the MGMT active site model.

Starting from this structure a transition state for proton transfer from Cys145

through the Glu172-His146-water network was located, Figure 3.21A. At the transi-

tion state, the critical SCys145−H and H−Owater distances are 1.57 A and 1.32 A,

respectively, and the Owater−H and H−NHis146 distances are 1.22 A and 1.28 A, re-

spectively. We noticed also that a proton has transferred from His146 to the Glu172,

in a charge relay fashion. This could be an artefact of the model used in the current

study, since in our calculations, we have completely neglected the surrounding of

the Glu172 residue, which makes the ion pair (protonated His146 and deprotonated


Glu172) relatively unfavored, leading therefore to the proton transfer. Whether the

proton transfers to Glu172 or not, it does not affect the energetics of the reaction

significantly.

The activation barrier for the first step is calculated to be 9.3 kcal/mol, and the

product of this step, i.e. the thiolate intermediate, is found to have an energy of

+5.9 kcal/mol above the reactant structure. The optimized structure is shown in

Figure 3.21B.

The barrier is not affected when the surrounding is included as a homogenous

dielectric medium with ε = 4. The energy of the intermediate, however, is lowered

somewhat, from +5.9 to +2.0 kcal/mol, relative to the reactant. This is a result

of the fact that the Cys145 its charge state from neutral to anionic it is located at

the edge of the quantum chemical model. Solvation will thus stabilize the charged

species more than the neutral one.

At the first step a thiolate ion is generated and Cys145 and can act as a nuclephile

in the dealkylation reaction. In the second step the methyl group is transferred from

O6-methylguanine to Cys145 residue of the enzyme active site.

The unconstrained transition state of methyl group transfer was located and the

optimized structure is shown on the Figure 3.21C. At the TS, the critical bond dis-

tance for methyl group transfer Omethylguanine−Cmethylguanine and Cmethylguanine−SCys145 are 1.97 A and 2.44 A, respectively. We note that the hydrogen bond to the

Tyr114 is tightened somewhat in this step, from 1.73 A to 1.62 A. This is a result

of the negative charge created at the guanine ring and delocalized to the N3 center.

The accumulated activation barrier for the methyl transfer (i.e. the barrier for this

step added to the endothermicity of the previous step) was calculated to be 24.1

kcal/mol in the cluster model and 23.2 kcal/mol using ε = 4.

Once the methyl is transferred a guanine base is repaired and a negative charge

is delocalized between the N1 and N3 atoms of a substrate molecule, Figure 3.21D.

The overall reaction is found to be exothermic by 0.3 kcal/mol in the cluster model

and 6.4 kcal/mol using ε = 4.

In conclusion, the calculations on the MGMT enzyme give support to the sug-

gested reaction mechanism and provide detailed characterization of the structures

and energies of the various stationary points along the reaction path.


A

Glu172

His146

Cys145

Tyr114

Methylguanine

f

f

f

f

C

C

S

O

C

C

C

CNN

C

N

C

O

O

C

O

CC

C

C

N

C

C

N

C

C

O

C

C

C

N

O

C

C

N

N

C

C

1.57

3.79

1.05 1.55

1.32

1.28

1.22

1.85

1.75

B

Glu172

His146

Cys145

Tyr114

Methylguanine

f

f

f

f

C

C

S

O

C

C

C

C

N

C

N

C

O

N

O

C

O

CC

C

C

N

C

N

C

C

C

O

C

C

C

N

C

O

C

N

N

C

C

2.053.61

1.03

1.621.86

1.05

1.64

1.45

1.36

1.33

1.36

1.33

1.73

C

Glu172

His146

Cys145

Tyr114

Guanine

f

f

f

f

C

C

S

C

O

C

C

NO

C

C

N

C

N

O

C

O

C

CC N

C

C

N

C

C

C

O

C

C

N

C

C

C

O

N

N

C

C

2.16 2.44

1.02

1.662.01

1.04

1.71

1.97

1.34

1.36

1.36

1.28

1.67

D

Glu172

His146

Cys145

Tyr114

Guanine

f

f

f

f

C

C

S

C

O

C

N

O

C

C

C

C

N

C

O

N

CNC

C

C

C

O

N

C

C

O

C

C

N

C

C

C

C

O

N

N

C

C

1.83

2.25

1.71

2.00

1.83

1.33

1.39

1.36

1.25

1.62

Figure 3.21: Optimized stationary points along the reaction path of MGMT.

Chapter 4

Conclusions

This thesis has dealt with the quantum chemical modeling of enzyme reactions.

More specifically, five methyl transfer enzymes were considered, namely glycine N-

methyltransferase (GNMT), guanidinoacetate methyltransferase (GAMT), phenyl-

ethanolamine N-methyltransferase (PNMT), histone lysine methyltransferase (HKMT),

and O6-methylguanine methyltransferase (MGMT). The four first enzymes use the

S-adenosyl L-methionine (SAM) cofactor to a transfer methyl group to their specific

substrates, while the last one is a suicide enzyme that repairs methylated DNA by

abstracting a methyl group from a guanine base.

Active site model of these enzymes were developed systematically in order to

develop detailed understanding of the reactions under consideration and also to eval-

uate the methodology used in the investigations. Points along the reaction paths

were optimized and characterized, and potential energy surfaces for the reactions

were calculated. By comparing the results of the calculations with available exper-

imental data, the plausibility of the suggested reaction mechanisms was judged. In

most cases, the presented calculations give support to the reaction mechanisms that

are proposed based on experiments. The calculations help working out the details

of the reactions, and similarities and differences among the various enzymes are dis-

cussed.

Apart from the conclusions concerning the specific enzymes, the overall results

of this thesis prove that the DFT methods, in particular the B3LYP functional, are

a very useful tool in the study of enzyme reactions. The effectiveness of the use of

relatively small active site models in the elucidation of reaction mechanisms is clearly

demonstrated.

45

Bibliography

[1] Szabo A.; Ostlund N.;. Modern Quantum Chemistry. McGraw - Hill, 1982.

[cited at p. 5]

[2] Cramer C.;. Essentials of Computational Chemistry. Theories and Models. John

Wiley & Sons Ltd, England, 2002. [cited at p. 5, 7]

[3] Jensen F.;. Introduction to Computational Chemistry. John Wiley & Sons Ltd,

England, 1999. [cited at p. 5, 7]

[4] Parr R.; Yang W.;. Density Functiona Theory of Atoms and Molecules. Oxford

University Press, 1989. [cited at p. 6, 7]

[5] Koch W.; Holthausen M.;. A Chemist’s Guide to Density Functiona Theory.

Wiley - VCH Verlag GmbH, 2001. [cited at p. 6, 7]

[6] Hohenberg P.; Kohn W.;. Phys. Rev., 136(3B):B864, 1964. [cited at p. 6]

[7] Kohn W.; Sham L.;. Phys. Rev., 140(4A):A1133, 1965. [cited at p. 6]

[8] Becke A.;. Phys. Rev. A, 38:3098, 1988. [cited at p. 7]

[9] Becke A.;. J. Chem. Phys., 96:2155, 1992. [cited at p. 7]

[10] Becke A.;. J. Chem. Phys., 97:9173, 1992. [cited at p. 7]

[11] Becke A.;. J. Chem. Phys., 98:5648–5652, 1993. [cited at p. 7]

[12] Vosko S.; Wilk L.; Nusair M.;. Can. J. Phys., 58:1200, 1980. [cited at p. 7]

[13] Lee C.; Yang W.; Parr R.;. Phys. Rev. B, 37:785, 1988. [cited at p. 7, 20]

[14] Miehlich B.; Savin A.; Stoll H.; Preuss H.;. Chem. Phys. Lett., 157:200, 1989.

[cited at p. 7]

[15] Curtiss L.; Raghavachari K.; Trucks G.; Pople J.;. J. Chem. Phys., 94:7221,

1991. [cited at p. 8]

47

48 BIBLIOGRAPHY

[16] Bauschlicher C.;. Chem. Phys. Lett., 246:40, 1995. [cited at p. 8]

[17] Bauschlicher C.; Partridge H.;. Chem. Phys. Lett., 240:533, 1995. [cited at p. 8, 9]

[18] Curtiss L.; Raghavachari K.; Redfern P.; Pople J.;. J. Chem. Phys., 109:7764,

1998. [cited at p. 9]

[19] Curtiss L.; Redfern P.; Raghavachari K.;. J. Chem. Phys., 123:124107, 2005.

[cited at p. 9]

[20] Siegbahn P.;. Inorg. Chem., 39(13):2923, 2000. [cited at p. 9]

[21] Siegbahn P.;. Quarterly Review of Biophysics, 36:91, 2003. [cited at p. 9]

[22] Anderson J.;. Adv. Chem. Phys., 91, 1995. [cited at p. 10]

[23] Eyring H.; Stern A.;. Chem. Rev., 24(2):253, 1939. [cited at p. 10]

[24] Truhlar D.; Hase W.; Hynes J.;. J. Phys. Chem., 87(26):5523, 1983. [cited at p. 10]

[25] Truhlar D.; Garrett B.; Klippenstein S.;. J. Phys. Chem., 100(31):12771, 1996.

[cited at p. 10]

[26] Fersht A.;. Structure and Mechanism in Protein Science : A Guide to Enzyme

Catalysis and Protein Folding. W. H. Freeman and Company, New York, 1998.

[cited at p. 11, 12]

[27] Blomberg M.; Siegbahn P.;. J. Phys. Chem. B, 105:9375, 2001. [cited at p. 15]

[28] Himo F.; Siegbahn P.;. Chem. Rev., 103:2421, 2003. [cited at p. 15]

[29] Noodleman L.; Lovell T.; Han W.-G.; Li J.; Himo F.;. Chem. Rev., 104:459,

2004. [cited at p. 15]

[30] Himo F.;. Biophys. Biochim. Acta, 1707:24, 2005. [cited at p. 15]

[31] Siegbahn P.; Borowski T.;. Acc. Chem. Res., 39:729, 2006. [cited at p. 15]

[32] Ramos M.; Fernandes P.;. Acc. Chem. Res., 41:689, 2008. [cited at p. 15]

[33] Himo F.; Guo J.; Rinaldo-Matthis A.; Nordlund P.;. J. Phys. Chem. B,

109:20004, 2005. [cited at p. 15]

[34] Hopmann K.; Himo F.;. Chem. Eur. J., 12:6898, 2006. [cited at p. 15]

[35] Hopmann K.; Guo J.; Himo F.;. Inorg. Chem., 46:4850, 2007. [cited at p. 15]

[36] Chen S.; Marino Fang W.; Russo N.; Himo F.;. J. Phys. Chem. B, 112:2494,

2008. [cited at p. 15]

BIBLIOGRAPHY 49

[37] Liao R.; Yu J.; Raushel F.; Himo F.;. Chem. Eur. J., 14:4287, 2008. [cited at p. 15]

[38] Hopmann K.; Himo F.;. J. Chem. Theor. Comp., 4:1129, 2008. [cited at p. 15]

[39] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R.

Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M.

Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scal-

mani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota,

R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai,

M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo,

J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi,

C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Sal-

vador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C.

Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Fores-

man, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov,

G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith,

M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill,

B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople. Gaussian

03, Revision C.02. Gaussian, Inc., Wallingford, CT, 2004. [cited at p. 18]

[40] Cammi R.; Mennucci B.; Tomasi J.;. J. Phys. Chem. A, 103:9100, 2000.

[cited at p. 18]

[41] Cammi R.; Mennucci B.; Tomasi J.;. J. Phys. Chem. A, 104:5631, 2000.

[cited at p. 18]

[42] Cossi M.; Rega N.; Scalmani G.; Barone V.;. J. Chem. Phys., 114:5691, 2001.

[cited at p. 18]

[43] Cossi M.; Scalmani G.; Rega N.; Barone V.;. J. Chem. Phys., 117:43, 2002.

[cited at p. 18]

[44] Blomberg M.; Siegbahn P.; Babcock G.;. J. Am. Chem. Soc., 120(34):8812,

1998. [cited at p. 18]

[45] Rowling M.; Schalinske K.;. J. Nutr., 133:3392, 2003. [cited at p. 20]

[46] Wyss M.; Kaddurah-Daouk R.;. Physiological Reviews., 80:1107, 2000.

[cited at p. 20]

[47] Gee G.; Tyndall J.; Grunewald G.; Wu Q.; McLeish M.; Martin J.;. Biochemistry,

44:16875, 2005. [cited at p. 20]

[48] Martin J.; Begun J.; McLeish M.; Caine J.; Grunewald G.;. Structure, 9:977,

2001. [cited at p. 20]

[49] Pohorecky L.; Wurtman R. Pharmacological Reviews, 21(1):1, 1971. [cited at p. 20]

50 BIBLIOGRAPHY

[50] Strahl B.; Allis C.;. Nature, 403:41, 2000. [cited at p. 20, 35]

[51] Sims R.; Nishioka K.; Reinberg D.;. Trends. Genet., 19:629, 2003. [cited at p. 20,

35]

[52] Schneider R.; Bannister A.; Kouzarides T.;. Trends. Biochem. Sci., 27:396,

2002. [cited at p. 20, 35]

[53] Mitra S. DNA Repair, 6:1064, 2007. [cited at p. 20]

[54] Pegg A.; Fang Q.; Loktionova N.;. DNA Repair, 6:1071, 2007. [cited at p. 20]

[55] Tubbs J.;Pegg A.; Tainer J.;. DNA Repair, 6:1100, 2007. [cited at p. 20]

[56] Gerson S.;. J. Clin. Oncol., 20:2388, 2002. [cited at p. 20]

[57] Fang Q.; Gerson S.;. Clin. Cancer Res., 12:328, 2006. [cited at p. 20]

[58] Silverman R.;. The organic chemistry of enzyme-Catalyzed reactions. Academic

press, An Elsevier Science Imprint, 2002. [cited at p. 21]

[59] Takata Y.; Huang Y.; Komoto J.; Yamada T.; Konishi K.; Ogawa H.; Gomi T.;

Fujioka M.; Takusagawa F.;. Biochemistry, 42:8394, 2003. [cited at p. 21, 22, 25]

[60] Fujioka M.; Konishi K.; Takata Y.;. Biochemistry, 27:7658, 1988. [cited at p. 26]

[61] Fujioka M.; Konishi K.; Gomi T.;. Biochem. Biophys., 285:181, 1991.

[cited at p. 26]

[62] Takata Y.; Fujioka M.;. Int. J. Biochem., 22:1333, 1990. [cited at p. 26]

[63] Takata Y.; Date T.; Fujioka M.;. Biochem. J., 277:399, 1991. [cited at p. 26]

[64] Takata Y.; Fujioka M.;. Biochemistry, 31:4369, 1992. [cited at p. 26]

[65] Takata Y.; Konishi K.; Gomi T.; Fujioka M.;. J. Biol. Chem., 269:5537, 1994.

[cited at p. 26]

[66] Komoto J.; Yamada T.; Takata Y.; Konishi K.; Ogawa H.; Gomi T.; Fujioka

M.; Takusagawa F.;. Biochemistry, 43:14385–14394, 2004. [cited at p. 27, 28]

[67] Martin J.; Begun J.; McLeish M.; Caine J.; Grunewald G.;. Structure, 9:977,

2001. [cited at p. 30]

[68] McMillan F.; Archbold J.; McLeish M.; Caine J.; Criscione K.; Grunewald

G.; Martin J.;. J. Med. Chem., 47:37, 2004. [cited at p. 30]

[69] Gee C.; Tyndall J.; Grunewald G.; Wu Q.; McLeish M.; Martin J. Biochemistry,

44:16875, 2005. [cited at p. 30, 31]

BIBLIOGRAPHY 51

[70] Wu Q.; Gee C.; Lin F.; Tyndall J.; Martin J.; Grunewald G.; McLeish M.;. J.

Med. Chem., 48:7243, 2005. [cited at p. 30]

[71] Hu P.; Zhang Y.;. J. Am. Chem. Soc., 128:12728, 2006. [cited at p. 35, 36, 38, 39]

[72] Whang S.; Hu P.; Zhang Y.;. J. Phys. Chem. B, 111:3758, 2007. [cited at p. 35,

36, 38, 39]

[73] S.; Xiao B.; Jing C.; Wilson J.; Walker P.; Vasisht N.; Kelly G.; Howell S.;

Taylor I.; Blackburn G.; Gamblin. Nature, 421:625, 2003. [cited at p. 35]

[74] Lynch B.; Fast P.; Harris M.; Truhlar D.;. J. Phys. Chem. A, 104:4811, 2000.

[cited at p. 38]

[75] Lynch B.; Zhao Y.; Truhlar D.;. J. Phys. Chem. A, 107:1384, 2003. [cited at p. 38]

[76] Daniels D.; Woo T.; Luu K.; Noll D.; Clarke N.; Pegg A.; Tainer J.;. Nat.

Struct. & Mol. Biol., 11:714, 2004. [cited at p. 39]

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