First-principles quantum chemistry in the life sciences

10.1098/rsta.2004.1469

First-principles quantum chemistryin the life sciences

By Tanja van Mourik

Department of Chemistry, University College London,20 Gordon Street, London WC1H 0AJ, UK ([email protected])

Published online 24 September 2004

The area of computational quantum chemistry, which applies the principles of quan-tum mechanics to molecular and condensed systems, has developed drastically overthe last decades, due to both increased computer power and the efficient implementa-tion of quantum chemical methods in readily available computer programs. Becauseof this, accurate computational techniques can now be applied to much larger systemsthan before, bringing the area of biochemistry within the scope of electronic-structurequantum chemical methods. The rapid pace of progress of quantum chemistry makesit a very exciting research field; calculations that are too computationally expensivetoday may be feasible in a few months’ time!

This article reviews the current application of ‘first-principles’ quantum chem-istry in biochemical and life sciences research, and discusses its future potential. Thecurrent capability of first-principles quantum chemistry is illustrated in a brief exam-ination of computational studies on neurotransmitters, helical peptides, and DNAcomplexes.

Keywords: quantum chemistry; ab initio calculations;density functional theory calculations; gas-phase biomolecules

1. Introduction

As a result of the rapid development of computational quantum chemistry, high-accuracy techniques can be applied to much larger systems than previously envis-aged, bringing the area of biochemistry within the reach of electronic structure quan-tum chemistry. With the ongoing advances in computer architecture and quantumchemical software development, the range of molecular systems that can be studiedcontinues to increase progressively. This paper will focus on the application of ‘first-principles’ (ab initio and density functional theory) quantum chemical methods inbiochemical and life sciences research. The recent award of the 1998 Nobel Prizein Chemistry to Walter Kohn and John Pople reflects the enormous capability andvalue of first-principles quantum chemistry in today’s chemistry research. John Poplewas honoured for the development of quantum chemical methods, whereas WalterKohn’s contribution was the development of the relatively new density functionaltheory (DFT) methodology.

One contribution of 17 to a Triennial Issue ‘Chemistry and life science’.

Phil. Trans. R. Soc. Lond. A (2004) 362, 2653–26702653

c© 2004 The Royal Society

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2654 T. van Mourik

First-principles quantum mechanical computations are traditionally not well suitedfor large molecules, because of their huge computational demand. The results ofcheaper methods (such as force-field and semi-empirical methods), however, varysignificantly depending on the specific parametrization. As first-principles methodsdo not require empirical calibration, they are applicable to all molecular systemsand properties one may be interested in, even in the absence of experimental data.As a result of this, they have the potential of yielding much more accurate resultsthan the methods traditionally used in the life sciences, thereby greatly enhancingthe reliability of computational research in this area.

A comprehensive appraisal of first-principles studies in biochemistry and the lifesciences is, if at all possible, beyond the scope of this paper. Researchers apply aplethora of different methods, implemented in a large number of quantum chemistryprograms, to calculate properties of a wide variety of biomolecular systems. In thispaper, I will therefore not attempt to be complete, but instead I will present aselection of interesting research done in this field, and hope that these case studiesillustrate the current potential of first-principles methods. I will start with a verybrief review of the theory of first-principles methods, after which calculations in threesubareas, neurotransmitters, peptides, and DNA fragments, will be discussed. Thereviewed research is focused on gas-phase studies at a temperature of 0 K. The paperconcludes with an outlook on the future potential of first-principles research in thelife sciences.

2. First-principles methods

Computational chemistry encompasses many methods, which can be divided intoquantum chemical and classical (non-quantum chemical) methods. Classical methodsconsider only the nuclei of a molecular system, while ignoring the electronic motions.These methods calculate the energy of a molecular system using a force field, whichis a parametric function of the positions of the nuclei only. Classical methods are verycomputationally efficient, and are generally applied to very large molecular systems.

In contrast, quantum chemical (or electronic structure) methods do take themotions of the electrons into account—they deal with the computation of molec-ular electronic structures, and are therefore much more computationally demandingthan their classical counterparts. Molecular quantum chemistry attempts to solve thetime-independent Schrodinger equation: HΨ = EΨ . Solving this equation yields thewavefunction of a molecular system, from which all its molecular properties can (inprinciple) be derived. The Schrodinger equation can be solved exactly only for thehydrogen atom, and therefore, all quantum chemical methods are necessarily approx-imate. In this review, I will consider two groups of quantum chemical methods: thepure ‘ab initio’ methods and DFT.

Ab initio calculations use no other input than the Schrodinger equation, a fewfundamental physical constants, and the atomic numbers of the atoms present inthe molecular system of interest. The simplest ab initio method is the Hartree–Fock(HF) method. In the HF method each electron only sees an average field of the otherelectrons; local distortions of the electron distribution are ignored. As a result, HFignores electron correlation, which limits the accuracy achievable with this method.There are many approaches that attempt to include this electron correlation, such as

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First-principles quantum chemistry in the life sciences 2655

configuration interaction, coupled cluster and many-body perturbation-theory meth-ods. The basic idea of perturbation theory is that the problem at hand is first solvedfor a simpler system, after which the solution is adjusted in the direction of themore complicated, true system. Møller–Plesset perturbation theory (Møller & Ples-set 1934) considers the HF Hamiltonian to be the undistorted (simpler) system,and the electron correlation is computed as a perturbation. This leads to a series inwhich each higher-order method should (in principle) be more accurate than the pre-vious one (however, the Møller–Plesset perturbation series does not always convergetowards the ‘correct’ result, as first convincingly shown by Olsen et al . (1996)). Thesecond-order method in the Møller–Plesset series, MP2, is one of the most commonelectron-correlation methods, because of its relative inexpensiveness as comparedwith other correlated ab initio methods.

Another way to include electron correlation is via DFT. DFT is based on the notionthat the total energy of a molecular system is a functional of the charge density(Hohenberg & Kohn 1964). The main idea of DFT is to describe a molecular systemdirectly via its density, without first finding the wavefunction. However, the exactform of the universal energy density functional is unknown. The general strategy istherefore to approximate it by various model functionals. One of the most widelyused functionals is B3LYP, devised by Becke (1993). The precise form of densityfunctionals is commonly determined by fitting to atomic or molecular data. DFT istherefore strictly speaking not an ab initio method (though it is often labelled as one).In principle, ‘first principles’ is a synonym for ‘ab initio’. In this paper however, I usethe term ‘first principles’ to include pure ab initio methods, as well as DFT. DFT ismore computationally efficient than correlated ab initio methods and can thereforebe applied to larger molecular systems. However, one of the major deficiencies ofcurrent density functionals is their inability to correctly account for the dispersionenergy—the intermolecular energy contribution arising from the correlation betweenfluctuations in the electron distributions of neighbouring molecules (van Mourik &Gdanitz 2002)—which makes DFT less suitable for dispersion-dominated interactions(such as stacking interactions and hydrogen bonds to π electron clouds).

Both ab initio and (Kohn–Sham) DFT methods generally use basis sets, whichare collections of basis functions representing atomic orbitals (AOs). From a linearcombination of these AOs, molecular orbitals (MOs) can be constructed. In HF-based methods, the MOs are a representation of the wavefunction, whereas in DFTthe so-called Kohn–Sham orbitals are simply a way of representing the density. Theexpansion of the MOs (or Kohn–Sham orbitals) in a set of AOs is not an approxima-tion if the basis is complete. Practically, however, finite basis sets are used, therebyintroducing an additional approximation in the calculations. Particularly for ab initiomethods it generally holds that, the larger the basis, the better the approximation,and the choice of basis set is therefore often determined by a trade-off between accu-racy and computational cost.

3. First-principles calculations on neurotransmitters

(a) Neurotransmitters

Neurotransmitters are small chemical messengers that transmit information acrossthe gap (‘synapse’) between nerve cells (‘neurons’). The neurotransmitter’s release


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NH2 NH2

NH2

NH2

NH2

NH2

OH

O

GABA

O

CH3

O

OH

OHOH

OH

OH

NHCH3

OH

OH

OH

N NOH

acetylkcholine dopamine NA

adrenaline tryptamine serotonin

Figure 1. The structures of a selection of neurotransmitters.

from one side of the synapse to the other is triggered by an electrical impulse travel-ling along a nerve towards the synapse. The neurotransmitters cross the synapse andare received by a receptor, which is a protein that binds the neurotransmitter andsuffers some conformational change as a result of it. The result is either a continuedelectrical impulse, or an inhibition of it, on the other side of the synapse.

The neurotransmitters are a diverse group of chemical compounds rangingfrom simple monoamines such as glycine, γ-aminobutyrate (GABA) and acetyl-choline, compounds containing single aromatic rings (dopamine, noradrenaline andadrenaline) or double (fused) rings (tryptamine and serotonin), to polypeptides suchas the enkephalins (see figure 1). A common characteristic of these molecules is theirflexibility, leading to a large number of possible conformations. A knowledge of thefavoured shape of these molecules is of vital importance, as the shape influences theirtransport properties and plays an important role in the binding of these biomoleculesto their receptor sites. In recent years, much effort has been devoted to illuminatethe conformational preferences of neurotransmitters.

(b) Studies on neurotransmitters in the gas phase

A recent computational study provided a prediction for the structure and functionof the β-adrenergic receptor, one of the receptors that bind the neurotransmitteradrenaline (Vaidehi et al . 2002). The novel aspect of this research was that the newset of methods used correctly predicted the structure and binding characteristics ofthe receptor, starting with nothing but a knowledge of its sequence of amino acids.However, such studies are still out of reach for first-principles quantum chemistrymethods. The neurotransmitter-in-receptor study was feasible because it used newlydeveloped computer programs for the prediction of protein structure and ligand-


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binding conformations, in which the interaction between atoms is calculated usingforce fields. Force fields methods apply a parametric function of the nuclear coordin-ates to calculate the atom–atom interactions and are much cheaper computationallythan first-principles quantum chemistry methods.

Even though first-principles studies of neurotransmitters in genuine physiologi-cal environments are not yet feasible, the area is not wholly out of reach of first-principles quantum chemistry. The strategy of physical chemists has traditionallybeen to reduce and simplify the molecular problem at hand. True to this approach,researchers have started to study neurotransmitters ‘in the gas phase’. Even thoughenvironmental effects play a very important role in modelling biological processes,an understanding of the intrinsic energetics of flexible biomolecules is essential. Bystudying the biomolecules and their hydrated clusters in the gas phase, the environ-mental effects are effectively eliminated, allowing the molecule–solvent interactionto be studied in a controlled environment. Comparison with studies in solution canthen provide information about the relative importance of the intrinsic and environ-mental effects. The study of biomolecules in the gas phase can also be considered afirst step in a progressive investigation from isolated (gas-phase) molecules, via smallhydrated clusters, to completely solvated molecules, to molecules in truly physiolog-ical systems, such as the neurotransmitter in its binding site.

There are several reasons for the recent upsurge in gas-phase studies of moleculesof biological interest. Firstly, the structures of flexible molecules depend on subtleintramolecular interactions. A study on the conformational landscape of serotoninshowed that semi-empirical methods, which are computationally much less demand-ing than first-principles methods, are incapable of accurately predicting the struc-tures and relative stabilities of the different serotonin conformers (van Mourik &Emson 2002), indicating the need for higher-level quantum chemical methods tostudy flexible biomolecules. Due to ongoing software and hardware developments, itis nowadays feasible to perform accurate first-principles calculations on a large num-ber of possible conformations of molecules of the size of those in figure 1. A secondreason for the renewed interest in gas-phase biomolecules is due to developmentsin electronic, vibrational and microwave spectroscopy techniques, using free-jet gas-phase expansions (Levy 1980; Smalley et al . 1974), which allow flexible moleculesand their hydrated clusters to be studied in the gas phase at very low rotational andvibrational temperatures (Robertson & Simons 2001; Zwier 2001).

The experimental and theoretical studies demonstrate a unique synergic relation-ship, thereby encouraging collaborative research: assignment of the experimentalspectra is crucially dependent on comparison with spectra computed using quantumchemical techniques, whereas the experimental results are indispensable for valida-tion of the theoretical results. As a result, a large number of combined experimen-tal/theoretical papers on biomolecules in the gas phase, including the neurotrans-mitters tryptamine and serotonin (Carney & Zwier 2000, 2001; van Mourik & Emson2002), the ephedra (Butz et al . 2001b, 2002), the adrenergic neurotransmitters andtheir analogues (Alagona & Ghio 2002; Butz et al . 2001a; Graham et al . 1999; Nagyet al . 2003; Snoek et al . 2003a, b) have appeared in the literature over recent years.

(c) The adrenergic neurotransmitters

As figure 1 shows, the neurotransmitters noradrenaline (NA) and adrenaline (A)have a very similar structure; the only difference is that a methyl group in adrenaline


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R

OH

O

H

R

O

O

H

H

… …

Figure 2. The two hydrogen-bonding configurations of the catechol hydroxyl groups.

replaces one of the amino hydrogens in NA. Noradrenaline has one chiral centre (theside chain carbon atom bearing four different groups), and thus, every conformer hasa corresponding non-superimposable mirror image. The two mirror images (the chiralforms R and S) are spectroscopically indistinguishable, and therefore only one formneeds to be considered. The substitution of one of the amino hydrogens by a methylgroup to form adrenaline introduces a second chiral centre (the nitrogen), resultingin the existence of two ‘diastereoisomers’, structures that are not mirror images ofeach other: one of these (1R2S/1S2R) is adrenaline, and the other (1S2S/1R2R) ispseudoadrenaline (PA). Thus, for A/PA, twice as many structures will need to beconsidered than for NA.

The two molecules do not only have a similar structure, they also have a similarfunction in the body. Both are released as a response to mental or physical stress,and prepare the body for strenuous activity: the so-called ‘fight-or-flight’ syndrome,causing the familiar ‘adrenaline rush’. They also act as hormones and are secreted inresponse to a low blood-glucose level. They increase the amount of glucose releasedinto the blood by the liver and decrease the use of glucose by muscle.

Most of the flexibility of NA and adrenaline is located in the ethanolamine sidechain. The orientation of the side chain is determined by four torsion angles. Inaddition, the catecholic OH groups have two different orientations supporting anintramolecular hydrogen bond (see figure 2). If one only considers side-chain confor-mations in which atomic groups on adjacent atoms are in a staggered position withrespect to each other, and not those that are eclipsed, then one needs to take intoaccount only three different orientations of each of the four side-chain torsion angles.With these restrictions, there are

34 (four flexible bonds, each having three different values for the torsion angle)× 2 (two different orientations of the catechol groups)

= 162 possible conformations.

Considering that a B3LYP/6-31+G∗ geometry optimization of one structure maytake 1–2 days of computer time on a reasonably fast PC (1.7 GHz Pentium 4), itmay be obvious that the full characterization of these molecules takes a fair amountof computer time.

A theoretical search for the most stable NA, A, and PA conformer reveals a closecompetition between two structures: AG1a, which has an extended side chain, and


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PA (AG1a) PA (GG1a)

A (AG1a) A (GG1a)

NA (AG1a) NA (GG1a)

Figure 3. The two most stable conformers of the neurotransmitters NA, A and PA.

GG1a, in which the side chain is folded back towards the catechol ring (Snoek et al .2003b; van Mourik 2004) (see figure 3). The AG1a and GG1a structures are nearlyisoenergetic, and which of the two is the most stable is dependent on the level oftheory used. The narrow energy gap between the AG-type and GG-type conformerswas also observed in 2-amino-1-phenylethanol (APE), the benzene analogue of NA(Graham et al . 1999; Macleod et al . 2003). However, whereas both AG1 and GG1APE conformers were observed experimentally, almost the entire NA population wasfound to adopt the global-minimum structure (Snoek et al . 2003b). The reasons for


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2660 T. van Mourik

the absence of a larger spread of populated conformers in jet-cooled NA are notwell understood. In the experiments, NA was created by laser ablation into a super-sonic argon expansion. The relatively large barriers (of the order of 10–20 kJ mol−1

(van Mourik & Fruchtl 2005)) between different NA conformers indicate that it isunlikely that conformational relaxation occurs during cooling in the supersonic jet.Hence, it seems likely that laser-ablated NA is generated predominantly in the global-minimum conformation. Thus far there have been no jet-cooled experimental dataavailable for A/PA. It would be very interesting to see which A and PA conformersare formed experimentally.

(d) Protonated neurotransmitters

Under aqueous physiological conditions, biomolecules containing basic aminogroups will exist predominately in their protonated form. Though some theoret-ical studies on protonated neurotransmitters have appeared in the literature (Alag-ona & Ghio 2002; Nagy et al . 2003), corresponding spectroscopic work has beenlacking behind. This is partly due to the fact that it is notoriously difficult to pro-duce reasonable quantities of protonated biomolecules at sufficiently low vibrationaland rotational temperatures to allow their structural analysis. However, a recentspectroscopic study on protonated ethanolamine (Macleod & Simons 2004) intro-duces a potentially very promising approach to generate protonated molecules inhigh concentration in the gas phase. The method is based upon the photo-excitationof hydrogen-bonded complexes with phenol. It is found that the infrared spectrum ofthe [phenoxy-protonated-ethanolamine] complex is almost identical to the computedspectrum of free protonated ethanolamine. I expect that this new approach will pavethe way for an upsurge in experimental and theoretical studies probing the structuralpreferences of protonated biomolecules.

(e) Hydrated neurotransmitters

Gas-phase biomolecule-(H2O)n clusters bridge the gap between isolated and fullyhydrated biomolecules. Their study allows the relative importance of individual watermolecules to be investigated. To find the most stable hydrates, it is not sufficient toconsider the water complexes of just the most stable isolated-biomolecule conformer,as the interaction with water may change the relative stability of the conformers(Butz et al . 2002). Indeed, the interaction with water may even change the biomolec-ular conformation to one that is non-existent in the absence of water, as found incalculations on adrenaline–(H2O)2 (van Mourik 2004). Thus, as a minimum, one hasto study hydrates involving several of the most stable isolated-biomolecule conform-ers. The functional groups of the adrenergic neurotransmitters provide many possiblewater-binding sites: calculations on 1:1 hydrates of NA and A (Snoek et al . 2003a;van Mourik 2004) show that there are about 10 different ways for a single watermolecule to bind to these neurotransmitters. In addition, the number of local min-ima increases steeply with the number of constituents in the cluster, and thus, a fullstudy of the hydrates is a formidable task. Structural data from spectroscopy exper-iments may help to reduce the conformational space that needs to be investigated,further stressing the importance of collaborative research in this field.


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H

C C

R1 R2 R3 R4

O H

N

O

H

H

N

O

HO−

H

N

O

H

peptide bond

+H3N C C C C C C

amino-terminal residue carboxyl-terminal residueamino acid residue amino acid residue

amino acids are linked by peptide bonds to form polypeptide chains:

Figure 4. The basic structure of a peptide.

(f ) Anharmonic vibrational frequencies

The interpretation of the experimental IR vibrational spectra in the studies dis-cussed above crucially depends on comparison with reliable theoretical vibrationalfrequencies. Most standard algorithms to calculate vibrational frequencies employ theharmonic approximation, yielding harmonic vibrational frequencies. As the anhar-monicity contribution to the vibrational frequencies can be rather large in hydrogen-bonded systems, this complicates the comparison between computed and experimen-tal infrared spectroscopic data. The application of scaling factors (Scott & Radom1996) can remedy this to some extent, but it is very difficult to account for varyingdegrees of anharmonicity in the frequency modes using scaling factors. To over-come these deficiencies, techniques have been developed to compute anharmonicvibrational frequencies. One of the principal methods for calculating anharmonicfrequencies is the vibrational self-consistent field (VSCF) method, of which thebasic structure was first introduced in 1978 (Bowman 1978). Because VSCF and itscorrelation-corrected form, CC-VSCF (Jung & Gerber 1996), require the calculationof many points on the ab initio potential energy surface, they are very computa-tionally demanding, restricting their application to only small molecules. However,promising new implementations of the CC-VSCF method, employing cost-reducingtechniques such as the use of ab initio-improved semi-empirical potentials (Gerberet al . 2003), or the use of pseudo-potential basis sets for heavy atoms coupled withan algorithm to reduce the number of pair-coupling elements (Benoit 2004), showpotential for widening the application field of the CC-VSCF method.

4. First-principles calculations on peptides

(a) Peptide terminology

Amino acids are the building blocks of peptides and proteins. An amino acid consistsof a central α carbon, an amino (NH2) group, a carboxyl (COOH) group, and adistinctive R group, often called the side chain (for reasons mentioned below). Insolution, and at neutral pH, amino acids predominantly occur in their zwitterionicforms, containing a protonated amino group (NH+

3 ) and a deprotonated carboxylgroup (COO−). In peptides and proteins, amino acids are commonly called ‘residues’.They are linked by peptide bonds: the carboxyl group of one amino acid is joinedto the amino group of another amino acid under elimination of a water molecule(see figure 4). The amino group of the first amino acid in a polypeptide chain,


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2662 T. van Mourik

and the carboxyl group of the last amino acid, remain intact. By convention, thechain extends from the ‘amino (or N) terminus’ to the ‘carboxyl (or C) terminus’.The successive peptide bonds generate the ‘main chain’ or ‘backbone’ of the peptide,which consists of repeating NH–CαH–C=O units. Thus, an n-residue peptide consistsof a main chain and n side chains.

The peptide group, (C=O)–N–H, is planar and rigid, but the peptide main chainhas flexibility through the two bonds that flank the peptide bond, the Cα–C andN–Cα bonds. The dihedral angles that define the orientation of these bonds, δNCαCNand δCNCαC (ψ and φ), can be plotted against each other to produce a so-called‘Ramachandran plot’ (Ramachandran et al . 1963). It turns out that many anglecombinations almost never occur because they would produce collisions betweendifferent parts of the peptide (the exception is glycine, which, with only a hydrogenas its side chain, can adopt conformations that are forbidden for other residues).

(b) The dimensionality problem

One of the major problems of computational studies of peptides is their flexibility,resulting in large number of possible conformations. Even if one would ignore theflexibility of the side chains (which is reasonable only for glycine and alanine residues,which contain as their side chain just a hydrogen or methyl group, respectively), andwould only take into account three different positions of the Ramachandran anglesφ and ψ, then for an octapeptide one still needs to consider 314 = 4 782 969 differ-ent conformations. This dimensionality problem can be overcome to some extent byrealizing that most polypeptide chains fold into regular periodic structures. Theserecurring structural motifs are called secondary structures. Some common secondarystructure elements include the α helix, β pleated sheets and the β turn. Proteinfolding can be regarded as a process in which first secondary structure elementsare formed before the protein assembles into its complete three-dimensional struc-ture (Karplus & Weaver 1994). A detailed understanding of the properties of thesesecondary structures is therefore paramount to understanding protein folding.

(c) Studies on helical peptides

Until just a few years ago, first-principles calculations on peptides have focusedmainly on elucidating conformational preferences of small peptides (dipeptides andtripeptides), as reviewed by Csaszar & Perczel (1999). However, researchers havestarted to do calculations on unprecedentedly large systems, thereby advancing theboundaries of first-principles quantum chemistry. With HF, calculations on completeproteins are becoming feasible. In 1998, van Alsenoy et al . (1998) performed a HFgeometry optimization of crambin, a 64-residue protein containing 642 atoms. Veryrecently, Zhang et al . (2003) computed the interaction energy of the streptavidin–biotin complex, containing 1775 atoms, at the HF level of theory. This calculationwas made possible by using a new computational technique, MFCC (molecular frag-mentation with conjugate caps). Other researchers have used the (more expensive)DFT method to study helical peptides containing 10 (Elstner et al . 2000; Topol etal . 2001) or 17 (Wieczorek & Dannenberg 2003) alanine residues. In addition to tra-ditional DFT, the study by Elstner et al . (2000) also used the self-consistent chargetight binding scheme (SCC-DFTB), which can be viewed as an approximation to


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DFT, which enabled them to study 20-residue alanine-based peptides with inclusionof as many as 38 water molecules.

Many studies have focused on α helical peptides because the α helix is themost common secondary structure motif in peptides. Most of these studies con-centrate on alanine-rich peptides, as alanine has one of the highest helix propensities(Chakrabartty & Baldwin 1995; Marqusee et al . 1989; O’Neil & DeGrado 1990). Ala-nine peptides also have a slight advantage for theoretical studies, because alanine,with a methyl group as its side chain, is one of the simplest amino acids. Studies onalanine-based peptides are nevertheless computationally demanding. α-helices formhydrogen bonds between the C=O group of the nth residue and the NH group of the(n + 4)th residue, and thus, at least five residues are needed to form one α helicalturn. Studies on α helical peptides therefore need to consider peptides containing atleast five amino acid residues. However, calculations on alanine-based peptides showthat, in vacuum, short peptides adopt the more tightly coiled 310 helical structure.310-helices form hydrogen bonds between the nth and (n+3)th amino acid residues.Longer peptide chains, and inclusion of solvent effects, are needed to stabilize theα helix (Elstner et al . 2000), increasing the complexity of the problem.

The inclusion in the peptide structure of residues more complex than glycine or ala-nine may also complicate the calculations. The larger side chains of these residues addto the dimensionality problem as they exhibit flexibility, and their hydrogen-bondingcapabilities may affect the stability of the different structural motifs. HF calcula-tions on isolated AKAAA-AKAAA (A = alanine, K = lysine) peptides indicate thatlysine’s charged side chain (CH2CH2CH2CH2NH+

3 ) tends to bind to the C-terminusof the peptide, thereby distorting the α-helical structure. Figure 5a shows how theside chain of the second lysine curves to enable hydrogen bonding to the carboxyl ofthe C-terminus. Increasing the peptide length improves the stability of the α helix,as indicated by the only slightly distorted α-helical structure of AKAAA-AKAAA-AKAAA (see figure 5b). The inclusion of water molecules around the charged NH+

3group of lysine, as well as around the carboxyl group of the C-terminus, prevents thelysine chain to hydrogen-bond to the C-terminal carboxyl group, thereby reducingthe distortion from the ideal α helical structure (figure 5c).

5. First-principles calculations on DNA fragments

DNA (deoxyribonucleic acid) is one of the most important biomolecules, as it encodesthe genetic information in the nucleus of cells. The basic structural units of DNAare nucleotides, which consist of a deoxyribose sugar, a phosphate group, and abase. The most common and well-known form of DNA is the double helix, of whichthe three-dimensional structure was deduced by Watson, Crick (Watson & Crick1953), Franklin & Wilkins. This discovery, the 50th anniversary of which was widelycelebrated last year, won Watson, Crick and Wilkins the 1962 Nobel Prize in Medicineand Physiology. In the DNA double helix, two helical nucleotide chains, coiled arounda common axis, are held together by hydrogen bonding between the bases on oppositestrands (see figure 6). DNA contains four different bases: thymine, cytosine, adenineand guanine. Adenine pairs with thymine, and guanine pairs with cytosine.

Other forms of DNA are known to exist, however. For example, four-strandedDNA structures occur in telomeric DNA. Telomeres are the specialized ends of chro-mosomes that protect these ends from recombination and from being recognized as


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2664 T. van Mourik

(a) (b)

(c)

Figure 5. HF/3-21G optimized structures of (AKAAA)n peptides. (a) AKAAA. (b) AKAAA-AKAAA-AKAAA. The view down the helical spiral evidences the α-helical nature of the struc-ture. (c) AKAAA-AKAAA + 10H2O. The water molecules prevent the charged lysine chain tohydrogen-bond to the C-terminus.

Figure 6. The DNA double helix.


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Figure 7. Crystal structure of the potassium form of an Oxytricha nova Q-quadruplex.

(a) (b)

Figure 8. Guanine tetrad structures optimized with B3LYP/6-311++G∗∗.(a) Bifurcated hydrogen-bonded G-tetrad; (b) G·G hydrogen-bonded G-tetrad.

damaged DNA. Telomeric DNA contains guanine-rich segments, which can fold intofour-stranded G-quadruplex structures (see figure 7). These quadruplexes result fromstacking of guanine tetrads. Cations (NH+

4 or monovalent metal cations), locatedeither in the tetrad cavity or between successively stacked tetrads, are essential forstructural integrity of the DNA quadruplex. Recently, there has been considerableinterest in these G-quadruplexes, not least because of their potential use in the devel-opment of anti-cancer drugs (Neidle & Parkinson 2002). The DNA G-quadruplex hasalso attracted the interest of computational researchers, who have so far focused onthe guanine tetrad and the cation-tetrad complex. First-principles calculations onsystems of this size are computationally very demanding, and have only recentlybecome feasible. The first HF and DFT calculations on the stability and structureof the G-tetrad were presented in 1999 (Gu et al . 1999). As the crystal structures


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of DNA quadruplexes show near-coplanar geometries for the guanine tetrads, thesecalculations were performed for the planar, C4h-symmetric, structure of the guaninetetrad.

Gu and co-workers (Gu & Leszczynski 2000; Gu et al . 1999) found that, whereasthe cation-containing G-tetrad adopts the G·G N1-carbonyl, N7-amino hydrogen-bonded structure (in agreement with the crystal structures of the DNA quadru-plexes), in the optimized geometry of the bare G-tetrad the guanine monomers areheld together by bifurcated hydrogen bonds. Calculations performed in my groupshow that both the G·G hydrogen-bonded and bifurcated hydrogen-bonded C4h-symmetric tetrad (see figure 8) can be located (van Mourik & Dingley 2005); how-ever, these structures are transition states, not true minima, on the DFT/B3LYPpotential energy surface (the true minimum is a twisted S4-symmetric structure).Meyer et al . (2001) have shown that ions with a small radius (Li+, Be2+, Cu+ andZn2+) cause non-planarity of the complex, which may prevent stacking of the G-tetrads. K+ is too large to fit in the central cavity and this ion therefore prefers tobe located between successive tetrads in the Q-quadruplex.

6. Future prospects

Computational quantum chemistry is a rapidly developing field. This is partly dueto the development and implementation of innovative first-principles methods. Theseinclude more efficient approaches to existing methods, such as linear scaling algo-rithms (Goedecker & Scuseria 2003), as well as hybrid (QM/MM) methods based onthe combination of classical (molecular mechanics (MM)) and quantum mechanics(QM) methodologies (Morokuma 2002). Promising new techniques that treat anhar-monicity and quantum effects to calculate free energies of biomolecular systems,which are required at temperatures above 0 K, are being developed. Whereas diffu-sion quantum Monte Carlo (DQMC) techniques (Benoit & Clary 2000; Clary 2001;van Mourik et al . 2001) yield the vibrational ground state (at 0 K) of a molecu-lar system, the torsional path integral Monte Carlo (TPIMC) technique (Miller &Clary 2002) does account for temperature effects. The construction of a global abinitio potential energy surface is not yet feasible for biomolecules larger than glycine(Miller & Clary 2004), and thus, both DQMC and TPIMC currently rely on forcefields to calculate the potential energy surface of biomolecular systems. A secondcause for the increasing capability of quantum chemistry is due to advances in com-puter technology. Moore (1965) observed that the speed of computers doubles roughlyevery 18 months (this observation has been dubbed ‘Moore’s law’). Furthermore, thedawn of parallel computer architectures and ‘Grid technology’ developments (Foster& Kesselman 1999) additionally increases the available computational power. How-ever, the rapid increase in central-processing-unit speed and novel architectures alsocomes with huge challenges for scientists and engineers (Dunning et al . 2002), asalgorithms and programs need to be rewritten and parallelized to make full use ofthe computational resources.

The future potential of first-principles quantum chemistry can hardly be over-estimated. I expect a dramatic increase in the application of first-principles quan-tum chemistry in the life sciences. This may lead to improved methodologies fordrug development as well as an increased understanding of complex processes suchas protein folding. As outlined in this paper, small biomolecular systems (such as


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neurotransmitters, DNA fragments and peptides) are already being studied usingab initio and DFT methods, and papers appear in the literature reporting first-principles computational research on ever larger systems. With more powerful com-puters and more efficient computer algorithms, electronic-structure calculations oncomplete proteins and neurotransmitter–receptor systems will be feasible. I believethat research will become more interdisciplinary, with experimental and theoret-ical researchers working side by side on the same projects. In addition, despite thecomplexity of quantum chemical methods, computer programs are becoming moreand more ‘user friendly’, inviting non-theoreticians to supplement their experimentalresearch with complementary results from computer simulations.

I gratefully acknowledge The Royal Society for their support under the University ResearchFellowship scheme. I thank my collaborators in Oxford (Professor John P. Simons and Dr Lav-ina C. Snoek) and at University College London (Dr Andrew J. Dingley) for joint experimen-tal/theoretical research and stimulating discussions.

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AUTHOR PROFILE

Tanja van Mourik

Born in 1966 in Vlissingen, a small city on the Dutch coast, Tanja van Mourik studiedchemistry at the University of Utrecht, the Netherlands, with a nine-month inter-mezzo at the Ruhr University of Bochum, Germany. She returned to Utrecht in July1989, where in the same year she graduated cum laude. She obtained her PhD inthe field of theoretical chemistry from the University of Utrecht in 1994, after whichshe spent three years as a Postdoctoral Associate at the Pacific Northwest NationalLaboratory in Richland, WA, USA. In 1997 she came to the UK to take up a post-doctoral research position at University College London. She was awarded a RoyalSociety University Fellowship in 2000, and has since been working as a UniversityResearch Fellow at the Department of Chemistry, University College London. Herresearch interests include the accurate quantum chemical computation of molecularproperties in general, and more specifically the application of these methods to thestudy of small molecules of biological interest.

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Documents

First-principles quantum chemistry in the life sciences