stereoselectioninthediels–alderaseribozyme ......charmm nucleic acids force ﬁeld parameter set...

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Stereoselection in the Diels–Alderase Ribozyme:A Molecular Dynamics StudyTomasz Berezniak,[a,b] Andres Jäschke,[b] Jeremy C. Smith,[a,c] and Petra Imhof∗[a]

The Diels-Alderase ribozyme is an in vitro-evolved ribonucleicacid enzyme that catalyzes a [4 + 2] cycloaddition reactionbetween an anthracene diene and a maleimide dienophile. Theribozyme can in principle be used to selectively synthesizeonly one product enantiomer, depending on which of the twoentrances to the catalytic pocket, “front” or “back”, the substrateis permitted to use. Here, we investigate stereoselection andsubstrate recognition in the ribozyme by means of multiplemolecular dynamics simulations, performed on each of the twosubstrates individually in the pocket, on the reactant state, andon the product state. The results are consistent with a binding

mechanism in which the maleimide likely binds first followedby the anthracene, which enters preferentially through the frontdoor.The free energy profiles for anthracene binding indicate thatthe pre-(R, R)-enantiomer conformation is slightly preferred, inagreement with the experimentally observed small enantiomericexcess of the (R, R)-enantiomer of the product. The reactant stateis stabilized by the simultaneous presence of both substratesbound to their binding sites in the hydrophobic pocket as well asby stacking interactions between them. © 2012 Wiley Periodicals, Inc.

DOI: 10.1002/jcc.22993

Introduction

Ribozymes are ribonucleic acid molecules with catalytic proper-ties. This combination of catalysis with the capability of RNAto store genetic information has resulted in the hypothesisof a preprotein “RNA world” in which RNA was the prevail-ing molecule.[1–3] The chemistry of presently naturally occurringribozymes is largely restricted to cleavage and joining reactionsat internucleotide bonds. In contrast, artificial ribozymes, syn-thesized using in vitro selection and evolution techniques, havebeen shown to accelerate a broad range of chemical reactions.[4–9]

These findings suggest that in vitro evolved ribozymes may beregarded as analogs of the missing links in the transition froman RNA world to the contemporary, protein-dominated life.[10]

The Diels–Alder [4 + 2] cycloaddition is one of the most sig-nificant carbon–carbon bond formation reactions available toorganic chemists,[11] creating simultaneously two C–C bonds andup to four stereocenters.[12] The artificially evolved 49-mer Diels–Alderase ribozyme was found to accelerate C–C bond formationbetween an anthracene molecule, which is covalently tetheredto the ribozyme, and a biotinylated maleimide molecule by upto 20,000-fold.[13] It has been further shown that this ribozymeconverts a nontethered 9-hydroxymethylanthracene as the min-imum diene with N-pentylmaleimide as the dienophile into therespective cycloaddition product (Fig. 1). Hence, the ribozyme actsas a true catalyst, accelerating the reaction between two smallorganic molecules free in solution, with fast multiple turnovers ofabout six transformations per catalyst molecule per minute. Theestimate for the rate acceleration of nontethered substrates is1100-fold. A reverse reaction cannot be detected, which indicatesan irreversible chemical reaction step. Addition of the Diels–Alder product inhibits the forward reaction, suggesting that theproduct competes for the same binding site as the substrates.[14]

Previous molecular dynamics (MD) simulation work found thatthe catalytic pocket of the Diels–Alderase ribozyme is highly

dynamic, fluctuating between catalytically active open and cat-alytically inactive closed states.[17] The simulations are consistentwith a conformational selection mechanism according to whichthe unbound enzyme exists as an ensemble of conformations indynamic equilibrium. The substrate interacts preferentially withone of these conformations–the open state of the pocket–thusshifting the equilibrium in favor of the active conformation.[18]

An experimental study of the interactions of the ribozymewith a panel of 44 systematically varied substrate analogs ledto the conclusion that the RNA-diene interaction is governed bystacking, whereas hydrogen bonding and metal ion coordinationappear to be less important.[15] The stereochemistry of the Diels–Alder reaction is controlled by the RNA-diene interactions. Thediene must contain three linearly annealed rings, for example,the anthracene derivative in Figure 1. The role of the oxygenatom from the 9-hydroxymethyl group was probed by differentsubstitutions, and the data obtained indicate that this oxygenis involved neither in metal ion coordination nor hydrogen-bonding, suggesting that the substituent at the 9-position doesnot contribute significantly to the binding energy.[15]

[a] T. Berezniak, J. C. Smith, P. Imhof

Computational Molecular Biophysics, IWR,University of Heidelberg,

Im Neuenheimer Feld 368, 69120 Heidelberg,Germany

E-mail: [email protected]

[b] T. Berezniak,A. Jäschke

Institute of Pharmacy andMolecular Biotechnology,University of Heidelberg,

Im Neuenheimer Feld 364, 69120 Heidelberg,Germany

[c] J. C. Smith

University of Tennessee/Oak Ridge National Laboratory,

Center for Molecular Biophysics, P.O.Box 2008MS 6309,Oak Ridge,

Tennessee 37831-6309,USA

Contract/grant sponsor: Deutsche Forschungsgemeinschaft; Contract/grant number: IGK 710 (TB), Ja 794-3 (AJ); Contract/grant sponsor: U.S.Department of Energy, Laboratory Directed Research and Development(JCS); Contract/grant sponsor: Landesstiftung Baden-Württemberg (PI)

© 2012 Wiley Periodicals, Inc.

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Figure 1. 9-Hydroxymethylanthracene as the diene andN-pentylmaleimide asthe dienophile are converted by the Diels–Alderase ribozyme into a cycload-dition product with a rate acceleration of 1100-fold. The (R, R)-enantiomer ofthe product has been concluded to be more favorable by 16% of enantiomericexcess based on chemical studies.[15, 16] [Color figure can be viewed in the onlineissue, which is available at wileyonlinelibrary.com.]

The dienophile must be a five-membered maleimide ring sys-tem. The maleimide side chain was found to have no effect onstereoselectivity. However, increasing the size of its N-alkyl chainimproves the acceptance by the ribozyme, and the maximumrate is reached at pentyl.[15] Increasing the dienophile’s hydropho-bicity strengthens the hydrophobic interactions between themaleimide and the pocket, favoring binding.

Analysis of the ribozyme crystal structures with the Diels–Alder product bound revealed that the catalytic pocket is formedprimarily by base edges with minimal contribution of the sugar-phosphate backbone, and as such provides a highly hydrophobicenvironment for the reactants (Fig. 2a).[19] The pocket containsboth a cavity to accommodate the cycloaddition product and acanyon to hold the maleimide side chain, thus, allowing bind-ing of only one product enantiomer at a time (Fig. 2b). Thecrystal structures of the product complex, coupled with exten-sive chemical and biochemical experiments, suggest that theribozyme should bind both specifically recognized substratesin a precisely defined orientation within the catalytic pocket,thereby facilitating the reaction by reducing the translational androtational degrees of freedom (Fig. 2c).[19] Analogously, the retro-Diels–Alderase catalytic antibody 10F11, the only such antibodythat uses anthracene as the diene,[20] forms a catalytic pocketthat is also hydrophobic and with an overall shape similar to theDiels–Alderase ribozyme pocket. The anthracene ring is stackedon a tryptophan residue, similar to the position of residue A3 inthe ribozyme.[19]

It has been recently found that the Diels-Alderase ribozymecan be used to selectively synthesize both product enantiomersin one catalytic pocket by controlling access to the active sitefrom opposite directions through different “doors”.[16] Indeed, theX-ray crystal structure of the ribozyme:product complex revealedthat the catalytic center is accessible from both “front” and “back”

doors, involving openings of different sizes.[19] For the purposeof crystallization, the reaction was performed with the dienesubstrate covalently linked to the ribozyme by a short flexibletether, yielding a reaction product bound as the (S, S)-enantiomer(over 90% of enantiomeric excess), whereas the untethered cat-alytic reaction produces predominately the (R, R)-enantiomer(16% of enantiomeric excess),[15, 16] see Figure 1. It is possiblethat restriction of the translational and rotational mobility of thesubstrate arising from tethering to the RNA close to the backdoor could force the anthracene diene to enter the catalyticpocket through the narrower, disfavored back door and thusinfluence the stereochemistry of the reaction.

These experimental data are consistent with a mechanism ofstereoselection in which, in the untethered reaction the freediene enters the pocket through the wider front door resultingin the formation of the (R, R)-enantiomer, whereas tetheringthe diene to the RNA results in threading through the smallerdoor at the back of the pocket, forming the opposite productenantiomer. It was suggested that the mechanism by which thetethered anthracene passes through the narrow entrance mostlikely involves dynamic opening and closing of the ribozymetertiary base pairs, which enlarges the door and facilitates theentry.[16, 21]

In the present article, we investigate stereoselection and sub-strate recognition in the Diels–Alderase ribozyme by means ofMD and steered MD (SMD) simulations, providing insight intothe interactions of the catalytic pocket of the ribozyme con-taining each of the substrates individually, with the reactantcomplex, and with the product state. The mechanisms of sub-strate recognition and the stereoselection are analyzed, and theinteractions of the reactant and product states in the pocketdetailed. The results shed light on the mechanism by which thesubstrates enter and bind to the active site, on the stereoselec-tivity, and on the mechanism of stabilization of the catalyticallyactive geometry.

Methods

Classic MD

MD is a technique used increasingly to obtain understand-ing of RNA catalysis as well as other biological functions ofribonucleic acid molecules. The field of RNA simulations hasbeen comprehensively detailed and thoroughly reviewed inRefs. [22–24].

CHARMM nucleic acids force field parameter set 27[25, 26] isa highly versatile and widely used force field commonly usedin molecular simulation of peptides, lipids, nucleic acids, car-bohydrates, and small molecule ligands. There is a number ofpublications involving the successful use of this force field in MDsimulations of RNA. Here, only recent work related to the studypresented in this article is mentioned. Shen et al.[27] developeda computational protocol using MD simulations and bindingenergy calculation to estimate the thermodynamic propertiesfor oligonucleotide duplexes. Frank et al.[28] combined MD sim-ulations with NMR measurements to investigate dynamics ofthe binding pocket that provides support for adaptive ligand

1604 Journal of Computational Chemistry 2012, 33,1603–1614 http://WWW.CHEMISTRYVIEWS.COM


recognition via a “conformational selection” mechanism. Priyaku-mar and Mackerell[29] performed MD simulations on hybridduplexes as well as on pure RNA and DNA duplexes to under-stand the relationships between structure and energy in RNaseH binding. Sarzynska et al.[30] reported one of the most exten-sive applications of the CHARMM force field to RNA moleculesapplied to conformational transitions of HIV-1 RNA dimeriza-tion initiation site complexes. Mayaan et al.[31] obtained forcefield parameters based on density-functional calculations fora series of nonstandard residues important in RNA catalysis.Insight has been obtained into the structural role of Mg2+ ionsin hammerhead ribozyme catalysis from MD simulations usingCHARMM force field by Lee et al.[32, 33] Notably, the majority ofthese publications mention a common tendency occurring insimulations using the CHARMM27 nucleic acid force field: struc-tural distortions originating from enhanced base pairs opening(or breathing) caused by the loss of hydrogen bonding duringsimulation.[34, 35] By keeping in mind this flaw of the force field,the authors of the above publications were able to present com-prehensive and valuable results of their simulations. Being awareof the limitations in the CHARMM27 force field, the stability ofthe CHARMM27-simulations for the Diels–Alderase ribozyme wasfirst tested (see Supporting Information for more details), andthen, this force field was used as a means to study bindinginteractions between the ribozyme and the substrates.

The starting structure of the Diels–Alderase ribozyme:productcomplex was obtained from the Protein Data Bank (ID: 1YKV,resolution: 3.3 Å). The ribozyme structure was crystallized by thehanging-drop vapor diffusion technique from the solution con-sisting of 0.5% (volume/volume, v/v) ethylacetate solvent, 30%(v/v) PEG400 linker, 100 mM Na-HEPES buffering agent (pH 7.5)and 200 mM MgCl2.[19] A single ribozyme molecule was preparedand centered in a cubic primary simulation cell with a box dimen-sion of 90 Å, using the CHARMM 32b2 package.[36] In additionto the ribozyme, the reactants (9-hydroxymethylanthracene, N-pentylmaleimide) or the product, 24 Mg2+ ions with standardCHARMM27 force field parameters,[37] and 23,653 TIP3P watermolecules[38] were added, yielding electrically neutral systemscomprising 72,569 atoms.

It has been experimentally shown that the catalytic activityof the ribozyme is dependent on magnesium ion concentration.In this kinetic characterization and salt dependence experiment,the concentration of Mg2+ ions was varied in the range of 0–80 mM, and the highest activity of the ribozyme was determinedat the concentration of 40–80 mM Mg2+.[13] Hence, in the presentwork, the system was neutralized exclusively by 24 Mg2+ ions(equal to the concentration of 54 mM Mg2+). The crystallographicpositions of eight structural Mg2+ ions are known from the X-raymeasurements. Based on these, it was concluded that six of theseparticipate in the stabilization of the RNA architecture and theother two mediate contacts between ribozyme molecules in thecrystal lattice.[19] The non-crystallographic Mg2+ ions were posi-tioned in the simulation box by replacing the water molecules atrandomly chosen positions in the solvent bulk. It has been shownthat out of 16 such cations, only one is in principle necessary forbridging the residues forming the catalytic pocket to stabilizethe active conformation prior to ligand binding. Furthermore,

even the randomly placed, non-crystallographic Mg2+ ions mayultimately diffuse to the crystallographically identified bindingsites.[17]

In this study, the concentration of the magnesium cations was

chosen to be high enough to allow the binding pocket to be in

an open state, leading to a conformational selection mechanism

for ligand binding/unbinding through the “front door”. Hence, the

model assumes that the ligand does not cross the unfavorable,

higher energy barrier to binding/unbinding to the ribozyme

with a closed pocket via an induced fit mechanism. In case

of the “back door” access, the positions of Mg2+ ions do not

influence the mechanism of entrance and the resulting free

energies. This is because the size of the “back door” does not

significantly change upon binding of Mg2+. Hence, the entrance

must always take place via induced fit, independently of the

Mg2+ ions concentration. These conditions do not exaggerate

the ionic effects by over-stabilizing the structure, as it was shown

in previous work that the stabilization is not due to ionic effects

associated with higher ion concentration. This was made clear

from the simulation with 48 Na+ cations (i.e., the simulation

with 0 Mg2+ ions) at which the ionic strength is the same as

in the 24 Mg2+-ion simulation, but there is neither stabilization

of the overall tertiary structure, nor of the catalytically active

conformation of the pocket.[17]

The geometries of maleimide, anthracene, and the Diels–

Alder product were optimized to default tolerances at the

MP2/6-31G** level of theory using Turbomole 5.7.[39] The force

field parameters for these molecules, including the bonds,

angles, and torsional angles, were originally taken from the

CHARMM27, and subsequently refined and optimized using

AFMM (Automated Frequency Matching Method).[40, 41] The opti-

mized parameters and AFMM results are given in the Supporting

Information.

All simulations were performed using the NAMD package[42]

with the CHARMM 27 force field and periodic boundary condi-

tions. Long-range electrostatic interactions were computed every

4 fs without any truncation using the PME method,[43] which the

reciprocal sum computed on a 90 × 90 × 90 Å3 grid using sixth

order interpolation and 1.5 Å Fourier grid spacing. Short-range

electrostatics were computed at each time step without any trun-

cation, and van der Waals interactions were computed every 2

fs with a smoothing function between 8 Å and the cutoff value

of 10 Å applied.Nine sets of multiple 20–50 ns long ribozyme simulations were

performed as follows:MD1: S, S-product within the ribozyme catalytic pocket (50 ns)MD2: R,R-product within the pocket (50 ns)MD3: maleimide substrate within the pocket (20 ns)MD4: anthracene substrate as in the pre-(S, S)-enantiomer

conformation (that is, the conformation of the reactants prior toformation of the (S, S)-product) within the pocket (20 ns)

MD5: anthracene substrate as in the pre-(R, R)-enantiomerconformation (that is, the conformation of the reactants prior toformation of the (R, R)-product) within the pocket (20 ns)

MD6: reactant state: anthracene as in the pre-(S, S)-enantiomerconformation and maleimide within the pocket (50 ns)



MD7: reactant state: anthracene as in the pre-(R, R)-enantiomer conformation and maleimide within the pocket(50 ns)

MD8: anthracene entering the pocket through the back doorwith no maleimide in the pocket (20 ns)

MD9: anthracene entering the pocket through the back doorwith maleimide in the pocket (20 ns).

The systems were energy minimized for 5000 steps by useof the conjugate gradient algorithm, heated for 30 ps, and equi-librated with the number of particles, pressure (1.01325 bar)and temperature (300 K) kept constant (NPT ensemble) during3 × 50 ps equilibration time, using Langevin dynamics to main-tain constant temperature,[44] and the Nosé–Hoover Langevinpiston for constant pressure.[45] The harmonic restraints weregradually lifted (0.5, 0.25 and 0.05 kcal/mol · Å2) in the threeequilibration steps. An integration time step of 2 fs was usedand coordinates were saved with a sampling interval of 2 ps dur-ing the NPT production runs without positional restraints. TheSHAKE algorithm was applied to constrain covalent bonds withhydrogen atoms.[46] For the purpose of analysis, all coordinatesets of any given trajectory were superimposed on a crystallo-graphic reference structure to remove overall unit cell rotationand translation.

SMD

One method for modeling ligand binding and unbinding is SMDsimulation. This technique allows the free energy of binding orunbinding to be evaluated as a potential of mean force alonga chosen reaction coordinate (RC), and has been successfullyapplied to this end for several molecular systems.[47–53] In termsof accuracy of the resulting free energy profile as well as its com-putational cost, this technique shows similar performance to theumbrella sampling method.[54] Validation of the SMD techniquefor the present system of interest is discussed in the SupportingInformation.

SMD simulations were performed on the ribozyme startingfrom the equilibrated structures obtained from solution MD sim-ulations as described above. Either the reactants or product ofthe reaction were pulled out from the catalytic pocket withconstant velocity using an external force.

In constant velocity pulling, the molecule to be pulled isattached to a dummy atom (an atom having neither mass norcharge) via a virtual spring.[52, 53, 55] As this dummy atom movesat constant velocity along a prespecified vector the tension inthe spring increases and the pulled molecule experiences a forcethat depends linearly on the distance between the dummy atomand the pulled molecule. Here, the external force acting on eitherthe substrates or product was calculated. The pulling force wasapplied along the z-axis, defined as a vector pointing from thecenter of the catalytic pocket to the center of mass of the product,the maleimide, or the anthracene substrate, in the direction ofthe pocket egress. The pulling force was applied along the z-axis, defined as a vector pointing from the geometrical centerof the catalytic pocket to the center of mass of either the prod-uct, the maleimide, or the anthracene substrate, in the directionof the pocket egress. Hence, the RC z is the distance between

the pocket and the particular ligand, or between the pocket andthe product, respectively. The work performed along each of thepulling directions, W(t), is defined as a contour integral alongthe force-extension profile,

W(t) =∫ z(t)

z(0)

Fdz, (1)

where F = F(t) is the force and z = z(t) is the distance betweenthe two force centers. The PMF along the RC z can then beobtained from repeated SMD simulations:[56–58]

e−�(z)/kBT = 〈e−W(t)/kBT 〉. (2)

Equation (2) is an extension of Jarzynski’s identity,[59] whichestablished a connection between nonequilibrium (irreversible)work and equilibrium free energy differences, where kB isBoltzmann’s constant, and T the absolute temperature.

The second law of thermodynamics states that the averagework recorded over many realizations of the process cannot besmaller than the difference of free energies between the initialand the final states. This equality holds only if the process isquasistatic or reversible, in which case the work is independentof the path. The Jarzynski identity is a more general result thatholds regardless of the speed of the process.[59] In the presentsimulations, the work was calculated from different trajectorieswith independent canonically distributed initial velocities. Theresulting PMF was estimated using the second order cumulantexpansion.[54]

A strong requirement is to have a sufficiently large collectionof trajectories to allow an accurate estimation of the expo-nential average in eq. (2). It has been demonstrated that thePMF is more accurate when derived from fewer, slower-pullingtrajectories.[53, 54] Hence, a pulling speed of v = 0.001 Å/ps waschosen as a tradeoff between staying as close as possible toequilibrium and keeping the computing time within manage-able limits. Furthermore, a low pulling speed permits detailedinsight into the structural substrate recognition to be obtained.Nevertheless, full equilibrium is not expected to be reached andthe resulting PMFs are therefore not expected to accurately rep-resent the binding free energies. Rather, they give an indicationas to relative resistance to substrate or product release. Thespring constant k was selected to be 7.2 kcal/mol · Å2 so as toallow the pulled ligands to relax in the z-direction in additionto being totally free in the (x, y) plane.

Eight sets of SMD simulations were prepared as follows:SMD1: (S, S)-product release through the front doorSMD2: (R, R)-product release through the front doorSMD3: maleimide release through the front door with

anthracene as in the pre-(S, S)-enantiomer conformationSMD4: maleimide release through the front door with

anthracene as in the pre-(R, R)-enantiomer conformationSMD5: anthracene release as in the pre-(S, S)-enantiomer

conformation through the front door with maleimideSMD6: anthracene release as in the pre-(S, S)-enantiomer

conformation through the back door with maleimideSMD7: anthracene release as in the pre-(R, R)-enantiomer

conformation through the front door with maleimide



SMD8: anthracene release as in the pre-(R, R)-enantiomerconformation through the back door with maleimide

For each setup 10 independent simulations were performed,each 11 ns long for the front door, and 15 ns long in the caseof back door release.

Error analysis

The statistical error in the PMF profile from the SMD simulationswas estimated as the standard error of the mean,σmean, calculatedover n subsets of the trajectories:

σ mean = σ√n

(3)

σ =√∑n

i=1(ai − a2)

n − 1(4)

a =∑n

i=1 ai

n(5)

where ai is the mean of the PMF evaluated in the ith subset,and a and σ are the mean value over the n samples and thestandard deviation, respectively. In the present case, 10 indepen-dent subsets of the trajectories were used (n = 10) which wasfound to be a good compromise between the statistical quantitywithin each subset and the sample size, n. Assuming a normaldistribution of the mean value, a, the expected value of a is with95% confidence inside the a ± 2σmean interval.

All molecular images were prepared with the molecularvisualization program VMD, version 1.8.6.[60]

Results

The MD simulations described below allow a detailed charac-terization of the interactions between each of the substratesindividually and the catalytic pocket, reactant state, and prod-uct state. The SMD simulations provide qualitative insight intothe energetics of substrate binding and product dissociationpathways. Particular attention is given to factors providing anoptimal reaction environment within the hydrophobic pocket ofthe Diels–Alderase ribozyme.

Diels–Alder product state

MD simulations were performed of the Diels–Alderase ribozymewith the cycloaddition product inside the catalytic pocket as the(S, S)-enantiomer (MD1), as found in the X-ray structure,[19] and asthe (R, R)-enantiomer (MD2), which chemical studies have indi-cated is favorable by 16% of enantiomeric excess,[15, 16] Figure 1.In the R,R-product simulations, the maleimide ring moiety isstacked on the C25 residue, while the anthracene rings I andIII are stacked on the A43 and U45, and G2 and A3 residues,respectively (cf., Figs. 1 and 2a and 2b). The most flexible partof the product is the N-pentyl chain that in the course of thesimulation frequently leaves the hydrophobic canyon formedby the C25, A43, and G24 residues. The product state is stable

inside the pocket, and structural changes of the product aresimilarly small for both the (S, S)- and (R, R)-enantiomers, withroot-mean-square deviation values of 0.9 ± 0.4 and 0.8 ± 0.3 Å,respectively.

Table 1. Hydrogen bond network between the residues forming thecatalytic pocket and the reactant state as in pre-(S, S)- orpre-(R, R)-enantiomer conformation, and the product state as (S, S)- or(R, R)-enantiomer.

Donor Acceptor Avg occ (%)[a]

Pre-(S,S)-enantiomerANT; O16 A3; N7 16A3; N6 ANT; O16 61ANT; O16 U45; O4 59G24, N2 MAL; OE2 93C25; N4 MAL; OE2 23MAL; OE2 C25; N3 27MAL; OE2 U42; O2’ 11

Pre-(R,R)-enantiomerANT; O16 A3; N1 10ANT; O16 A3; N3 81G24, N2 MAL; OE2 90MAL; OE2 G24, N3 12MAL; OE2 U42; O2 11

S,S-enantiomerDAI; O16 A3; N1 24A3; N6 DAI; O16 52DAI; O16 U45; O2’ 17U45; N3 DAI; O16 19DAI; O16 U45; O4 63G24; N2 DAI; OE2 98C25; N4 DAI; OE2 44DAI; OE2 U42; O2 22DAI; OE2 U42; O2’ 11

R,R-enantiomerDAI; O16 A3; N1 24A3; N6 DAI; O16 11G24; N2 DAI; OE2 83DAI; OE2 C25; N3 28

For atom numbering conventions, see Supporting Information Figure 1.[a] avg occ = average occupancy.

An analysis of the hydrogen bond network between theribozyme catalytic pocket and the product state is summarized inTable 1. For the (S, S)-enantiomer moderately populated hydro-gen bonds are formed mostly between the oxygen (O16) of theanthracene moiety and the A3 or U45 residues. A further hydro-gen bond is formed between the maleimide part of the productwith G24 residue of the ribozyme, with an occupancy of 98%,and another, partially populated (44%) hydrogen bond is formedwith C25. The above two hydrogen bonds are in good agreementwith those expected based on the X-ray structure.[19] In contrast,when the product is simulated as the (R, R)-enantiomer, theform not observed crystallographically, no hydrogen bonds werefound between the anthracene moiety and the ribozyme, andthe maleimide part forms a single highly occupied (83%) hydro-gen bond with G24. Although there are fewer hydrogen bondsformed by the (R, R)-enantiomer than by the (S, S)-enantiomer,the (R, R)-enantiomer is the preferred product (in the absence



Figure 2. Catalytic pocket of the Diels–Alderase ribozyme. a) The A3–U45 andU23•A43 base pairs and U42•(C25–G2) base triplet together with the unpairedG24 base constitute a hydrophobic pocket.The hydrophobic Diels–Alder prod-uct is shown as the more favorable (R, R)-enantiomer. b) The pocket is preciselycomplementary to the product.The lower part of the R,R-product is positionedwith ring I (cf., Fig. 1) wedged between the base and sugar components ofA43 and U45, and ring III stacked between purines G2 and A3. The upperpart is stacked on the C25 residue. c) Complementarity of the pocket to thereactant state suggested by the X-ray structure of the product complex. Themaleimide ring is stacked on C25, the maleimide side chain runs inside ahydrophobic canyon created by bases C25 (top), A43 (bottom), and G24 (back).The anthracene is stacked on A43 and U45 as well as G2 and A3.

of tethering, i.e., for free substrates), suggesting that hydrogenbonding is not the major factor governing stereoselection.

The SMD simulations SMD1 and SMD2 examine the departureof the product from the hydrophobic catalytic pocket of theribozyme into the polar solvent. The corresponding potentialsof mean force (PMFs) are presented in Figure 3.

Figure 3. PMF upon releasing the product as the (R, R)- (blue) and (S, S)-enantiomer (red) through the front door. RC = 0 Å is the bound state.

In the PMF profiles, there is only ∼1 kcal/mol differencebetween dissociation of the product as the (S, S)- and (R, R)-enantiomers. The difference between the PMF at the start andend states (∼11 kcal/mol) indicates that in the simulations thebound state is highly favored. The PMF profiles show a steepincrease in the first 6 Å of the RC, after which full dissociation ofthe (S, S)- or (R, R)-enantiomers takes place. Analyzing the modeof dissociation structurally showed that the N-pentyl chain isthe first moiety of the product to leave the pocket, followed bydeparture of the anthracene ring I that is initially stacked on theA43 and U45 residues, and finally ring III.

Maleimide

MD simulations (MD3) were performed with only maleimide inthe catalytic pocket, starting from its crystallographic orientation.During the course of the simulation the maleimide moleculefrequently changes its position and orientation, probing differenthydrophobic sites within the pocket, and was also found to bindat the anthracene binding site at the bottom of the pocket,stacked between the rings of the G2 and A3 residues (Fig. 4a).Although the maleimide changes its position in the catalyticpocket frequently, it never leaves the pocket, due most likely tostrong hydrophobic interactions, and occasionally returns to theoriginal X-ray position (Fig. 4b).

In the reactant state (simulations MD6 and MD7), the posi-tion of the maleimide molecule is stabilized by the presence ofanthracene at its binding site, and the maleimide ring system isstacked between the anthracene rings and the C25 residue (Fig.2c). As was found for the product, the maleimide N-pentyl chainis the most flexible part of the molecule, and occasionally leavesthe hydrophobic canyon defined by residues C25, A43, and G24.

There is a considerable difference between the maleimidedynamics when the molecule is present within the pocket aloneor as a part of the reactant state, that is, stacked on the anthracene.Although in both cases the alkyl chain is the most flexible partof the maleimide molecule, only in the reactant state do stack-ing interactions between maleimide and anthracene inside the



Figure 4. Selected orientations of maleimide within the pocket from MD simu-lations.a) Maleimide at the anthracene binding site.b) Maleimide at the bindingsite proposed from the X-ray structure of the product complex.[19] The struc-tures are colored the same as in Figure 2. [Color figure can be viewed in theonline issue, which is available at wileyonlinelibrary.com.]

pocket prevent the maleimide ring from leaving its binding site.The hydrogen bond analysis (Table 1) reveals that maleimideforms a highly populated hydrogen bond with the G24 residue(>90%), as was found in the crystal structure.[19]

To obtain insight into the substrate recognition, and theinteractions between the substrate and the ribozyme, SMD sim-ulations were performed of the substrate release, which is thereverse of the binding process. The corresponding PMF profilefor maleimide release from the catalytic pocket (SMD3, SMD4)is shown in Figure 5.

The positive overall free energy change for maleimide unbind-ing indicates that the aromatic molecule prefers to be inthe bound state inside the hydrophobic pocket than in thehydrophilic solvent. The PMF profiles for release of the maleimidefrom the pocket through the front door with anthracene presentin the binding site show no energy barrier. The interactionsbetween both substrates and between the maleimide and thepocket lead to the free energy difference being ∼6.5 kcal/mol.Release of the maleimide through the wider front door doesnot lead to any structural rearrangements in the catalyticpocket geometry, and is thus consistent with the conformationalselection mechanism previously proposed for the ribozyme.[17]

Figure 5. PMF upon releasing maleimide substrate through the front dooras in the pre-(R, R)- (blue) and pre-(S, S)-enantiomer conformation (red) withanthracene present at its binding site. [Color figure can be viewed in the onlineissue, which is available at wileyonlinelibrary.com.]

In the reactant state, maleimide is intercalated betweenC25 and anthracene as in either the pre-(S, S)- or pre-(R, R)-enantiomer conformation (cf., Figs. 1 and 2c). When theanthracene is as in the pre-(S, S)-enantiomer, there are steric inter-actions between the maleimide ring and the 9-hydroxymethylgroup of the anthracene at the beginning of the release sim-ulation. Upon maleimide release with anthracene present asin the pre-(S, S)-enantiomer this steric clash is quickly relievedwhile optimizing stacking interactions between the substrates,resulting in a free energy minimum at the RC value of 1 Å.In contrast, in the reactant state with the anthracene as inthe pre-(R, R)-enantiomer there are no initial steric interactionsin the beginning of departure simulation, as the anthracene9-hydroxymethyl group and the maleimide ring are already opti-mally adjusted. However, a steep increase of the PMF profilealong the RC is found, corresponding to increased steric repul-sions between the anthracene 9-hydroxymethyl group and themaleimide ring upon maleimide departure.The free energy differ-ence between maleimide being bound within the pocket in thereactant state and free in solution is ∼6.5 kcal/mol, independentlyof the anthracene orientation.

Anthracene

The simulations with anthracene alone in the pocket show thatit has significant rotational freedom. This finding is in goodagreement with experimental work demonstrating that in thepocket there is enough space for substituents in front and back,but tight fit occurs on the sides.[15] In the simulations, this freevolume is used by the anthracene to rotate in such a way thatit stays within the hydrophobic pocket while rearranging thepositions of its aromatic rings. In both the pre-(S, S)- (MD4) andpre-(R, R)-enantiomers (MD5) the anthracene rotates by ∼180◦

in multiple simulations. Moreover, in the pre-(R, R)-enantiomerthe anthracene makes a full rotation of 360◦ back to the originalcrystallographic position.



Figure 6. Rotation of anthracene within the catalytic pocket during MD simu-lations. a) Rearrangement of anthracene position due to absence of maleimideresulting in disrupted stacking interactions between anthracene ring I and U45residue.Anthracene moves to the maleimide binding site,where it interacts withG2,C25,and A43 residues.b) Further movements inside the pocket at 0.5 ns sim-ulation time combined with rotation of around 90◦ lead to anthracene bindingto G2 and A3.c) Rotation of anthracene by another 90◦ takes place after ∼2.5 nssimulation time, and leads to anthracene as in the pre-(S, S)-enantiomer. d)Rotation by another 90◦ after 4.5 ns. e) Anthracene is stacked on A43 and U45,with its 9-hydroxymethyl group positioned towards G2 and A3 before rotationby another 90◦ . f ) Partially disturbed geometry of the pocket upon comple-tion of the rotation. g) The pocket geometry is rebuilt at the end of the 10 nssimulation, and the anthracene orientation is as in the pre-(R, R)-enantiomer.

The rotational freedom of the anthracene leads frequently tothe molecule adapting a position at which the stacking betweenanthracene ring I and the U45 residue is disrupted. However,this rearrangement is possible only when maleimide is absent(Fig. 6a), and involves the anthracene moving to the maleimidebinding site, where it interacts with G2, C25, and A43 residuesinstead of A3 and U45 as observed in the crystal structure.At 0.5 ns simulation time, after further motion in the pocketcombined with a rotation of ∼90◦ (Fig. 6b), the anthracene isagain found to bind to G2 and A3 at the bottom of the pocket. At2.5 ns simulation time (Fig. 6c), the anthracene rotates by another90◦ such that the 9-hydroxymethyl group points toward theback door of the pocket resulting in the pre-(S, S)-enantiomer

Figure 7. PMF upon releasing anthracene substrate through the front dooras in the pre-(R, R)- (blue) and pre-(S, S)-enantiomer conformation (red) withmaleimide present at its binding site.

conformation. After 4.5 ns (Fig. 6d), and rotation by a total of∼270◦, the anthracene is stacked between A43 and U45, and the9-hydroxymethyl group is positioned toward G2 and A3 residues(Fig. 6e). In the last 5 ns, the full rotation is completed to the pre-(R, R)-enantiomer. Upon completion of the rotation the pocketgeometry is partially disturbed by the bulky 9-hydroxymethylgroup which breaks hydrogen bonds bridging residues G2 andC25 (Fig. 6f ). However, at the end of the 10 ns simulation theoriginal pocket geometry is restored, and the anthracene is asin the pre-(R, R)-enantiomer as in the crystal structure (Fig. 6g).

The simulations with both substrates (MD6 and MD7) providefurther useful insight into the anthracene dynamics. As soon asthe anthracene rings stack between G2 and A3 residues on oneside and A43 and U45 on the other, with the five-memberedmaleimide ring system on top (Fig. 2c), rotation is no longerobserved. Hence, the interactions between the reactants signif-icantly decrease their translational and rotational mobility, thusfurther stabilizing the reactant state for the reaction.

Finally, the hydrogen bond network of the anthracene in thereactant state was analyzed (Table 1). The oxygen O16 fromthe 9-hydroxymethyl group forms hydrogen bonds with A3and U45 in the pre-(S, S)-enantiomer (MD6), and with A3 inthe pre-(R, R)-enantiomer (MD7), respectively. For the pre-(S, S)-enantiomer, these occupancies are very similar to those in thecorresponding product state (MD1). Although the occupancies ofthe above mentioned hydrogen bonds are relatively high, that is,61 and 59%, respectively, when anthracene is alone in the pocket,these hydrogen bonds seem to not play an important role inanthracene binding, as evidenced by its high rotational freedom.The major binding stabilization would thus appear to arise fromhydrophobic and stacking interactions with the catalytic pocketand with the maleimide substrate.

Two sets of SMD simulations were performed with maleimidepresent, in both of which the anthracene was pulled out ofthe pocket through the front door as in either the pre-(S, S)-enantiomer (SMD5) or in the pre-(R, R)-enantiomer (SMD7). Thefree energy profiles presented as PMFs are shown in Figure 7.



The change of the environment of the aromatic anthracenegoing from the hydrophobic pocket to the polar solvent resultsin a free energy change of ∼9 kcal/mol for both the pre-(S, S)-and pre-(R, R)-enantiomer. The profiles again show no barrierto anthracene release, again in agreement with the model ofconformational selection in which there is no need for struc-tural rearrangement of the ribozyme upon substrate binding.[17]

Interestingly, for pre-(R, R) conformation the free energy min-imum is found at RC ∼0.75 Å, indicating that anthracene inthe pre-(R, R)-enantiomer can, to a certain extent, optimize itsorientation with respect to both the maleimide substrate andthe catalytic pocket at the beginning of the release simula-tion. In case of pre-(S, S) conformation only a constant steepincrease of the free energy along the RC is found, reflect-ing steric interactions between the anthracene 9-hydroxymethylgroup and the maleimide ring rising upon anthracenerelease.

Back door access

An analysis was performed using MD simulations of the backdoor entry mechanism of the anthracene diene (see Introduction).To this end, a series of 10 ns simulations was performed (MD8)in which the anthracene as in the pre-(S, S)-enantiomer waspositioned in close proximity to the back door, mimicking thepresence of the short tether (Fig. 8a). The resulting mechanism ofback door entry can be described as three consecutive steps:

1. It takes ∼1 ns for anthracene ring I (cf., Fig. 1) to enter thepocket, with the whole anthracene reorienting in such a way asto permit entry of its narrow edge (Fig. 8b).

2. After ∼2 ns the anthracene orients inside the pocket suchthat the stacking interactions with the pocket bottom stabilizethe anthracene position. Next, in this flat orientation the ring IIenters the pocket.

3. Finally, an induced rearrangement of the pocket geometry(Fig. 8c) takes place, permitting the ring III to enter as well.

Figure 8. Mechanism of anthracene entering through the back door of the catalytic pocket. a) Anthracene is positioned in close proximity to the back door,mimicking the presence of a short tether. b) After 1 ns anthracene ring I enters the pocket, and the whole molecule reorients in such a way that it can subsequentlyenter with its short edge. c) After 2 ns anthracene orients inside the pocket such that the stacking interactions stabilize its position. In this flat orientation ring IIenters the pocket. d) Induced rearrangement of the pocket geometry takes place and ring III enters as well. The geometry of the pocket is temporarily disturbedwhen the hydrogen bonds between residues G2 and C25 are broken upon completion of anthracene entry. [Color figure can be viewed in the online issue, whichis available at wileyonlinelibrary.com.]



In some simulations, the geometry of the pocket was tem-porarily disturbed with the hydrogen bonds between residuesG2 and C25 being broken upon completion of anthracene entry(Fig. 8d). This observation is consistent with the experimentalspeculation that dynamic opening and closing of the ribozymetertiary base pairs enlarges the door and facilitates threading.[16]

In the simulations of back door entry, the anthracene entersthe pocket using an induced fit mechanism, as described in Steps1–3 above. However, due to the absence of the maleimide, theanthracene is able to change its position so as to interact withthe hydrophobic rings of G2 and C25, instead of A3 and U45.

In another set of simulations, the maleimide reactant wasplaced in the position found in the crystal structure,[19] andthen the anthracene as in the pre-(S, S)-enantiomer positionedclose to the back door entrance (MD9), again mimicking thepresence of the tether. During the course of these simulationsthe anthracene entry follows the same induced fit mechanismas described above. Strikingly, when the maleimide is present inthe binding site, the anthracene ring I stacks between G2 andA3 as well as ring III between the U45 and the maleimide ringsupon entering, such that the position of the anthracene closelyresembles that suggested by the X-ray structure of the productcomplex, see Figure 9.

Figure 9. Final position of the anthracene within the pocket after entering withthe maleimide already present.The anthracene is stacked between G2 and A3 aswell as between the U45 and the maleimide rings in the pre-(S, S)-enantiomerconformation. [Color figure can be viewed in the online issue, which is availableat wileyonlinelibrary.com.]

The energetics of anthracene back door release were exam-ined using SMD simulations (SMD6 and SMD8). The free energydifference between the states bound to the catalytic pocket andfree in the solvent calculated from the PMF profile is ∼16 kcal/mol(Fig. 10), and this is ∼7 kcal/mol higher than the value found forthe front door entry. This difference originates from the largeramount of work required to pull the anthracene through thenarrower back door. Indeed, the back door release is accompa-nied by substantial structural rearrangements in the ribozymestructure, also in agreement with the induced fit mechanism pro-posed above involving the opening and closing of the ribozyme

Figure 10. PMF upon releasing anthracene substrate through the back dooras in pre-(R, R)- (blue) and pre-(S, S)-enantiomer conformation (red) withmaleimide present at its binding site. [Color figure can be viewed in the onlineissue, which is available at wileyonlinelibrary.com.]

base pairs, enlarging the door. For the anthracene unbinding asin the pre-(S, S)-enantiomer a free energy minimum is found atthe RC value of ∼1 Å. In contrast, for the pre-(R, R)-enantiomeronly a steep increase in the free energy profile is observed.

As free energy is a state function, the two egresses via theback and front door should, in principle, lead to the same freeenergy difference between the bound and unbound states. How-ever, in the present calculations a significant difference is seenin the end-state free energy difference calculated from the frontand back door entries. A similar pathway dependence has beenseen in several previous SMD studies of biological systems (e.g.,Refs. [52] and [48]).The origin of the difference is incomplete equi-libration of the system, and this still occurs here even thoughthe pulling speed of v = 0.001 Å/ps in the present simula-tions is low in comparison with previous SMD simulations.[48, 52]

Incomplete equilibration may arise from incomplete relaxationof the ribozyme following the removal of the anthracene, partialresidual substrate interaction with the ribozyme and solvationdifferences. The free energy difference between back and frontdoor release should thus be interpreted as a qualitative estimateof the difference in the amount of work needed to overcomesteric interactions passing through the two entrances. The dif-ference in the PMF profiles for front and back door entry clearlyindicate the preference of the front door route for anthracenebinding.

The mechanism of anthracene departure and unbindingthrough the back door in the SMD simulations is the sameas the mechanism of anthracene entry and binding through theback door that was seen in the MD simulations, described above.In the SMD simulations, the anthracene leaves the pocket with itsnarrow edge first, followed by an induced rearrangement of thepocket geometry permitting the whole molecule to fully releasefrom the ribozyme. This mechanism involving the opening andclosing of the ribozyme tertiary base pairs enlarging the doorand facilitating the entry is in agreement with a mechanism forthreading the tethered anthracene through the back door sug-gested from the experimental work.[16] The mechanism observed



in the SMD simulations is in general the reverse of that observedin the MD.

Discussion

The present MD simulations of the Diels–Alderase ribozyme:product complex show that the geometries of both the (S, S)-and the (R, R)-enantiomers both fit well into the catalytic pocket.In addition to the highly hydrophobic environment provided bythe pocket, the aromatic rings of the product are intercalatedbetween the aromatic rings of the ribozyme residues.The analysissuggests that hydrogen bonding plays only a supplementaryrole in product stabilization. The SMD simulations show that themechanism of product release as the (S, S)- and (R,R)-enantiomeris very similar, and that the complexed state is highly preferred.

The maleimide substrate is very mobile in the pocket, yet doesnot leave it for the solvent, due most likely to strong hydropho-bic interactions. However, while still remaining in the pocketthe molecule does leave its binding site, and probes alternativehydrophobic binding sites, including that of the anthracene. Thefluctuations of the maleimide are of larger amplitude than thoseof the anthracene, consistent with the difference in size of thesubstrates.

The ribozyme not only provides a hydrophobic environmentbut also allows the substrates to structurally reposition within thepocket in order to form an optimal reactant state. The reactivemaleimide position is stabilized by the presence of anthraceneat its binding site, owing to the maleimide ring being stackedbetween the annealed rings of the anthracene and the C25residue.

The PMF profiles for maleimide departure differ dependingon the anthracene conformation in the reactant state: whenthe anthracene is as in the pre-(R, R)-enantiomer conformationthe profile is steep, while if the anthracene is as in the pre-(S, S)-enantiomer conformation a free energy minimum appears.This difference originates from steric clashes in the pre-(S, S)-enantiomer between the maleimide ring and the anthracene9-hydroxymethyl group rising upon maleimide release.

When the maleimide substrate is not present the anthraceneexhibits high translational and rotational mobility, and under-goes full rotation. In the reactant state, the PMF profiles showno barrier to anthracene release, in agreement with the modelof conformational selection. Interestingly, for the favorable pre-(R, R)-enantiomer a free energy minimum is found, indicating thatanthracene in the pre-(R, R)-enantiomer can optimize its orien-tation upon release through the front door with respect to boththe maleimide substrate and the catalytic pocket to decreasesteric interactions. In contrast, for the pre-(S, S)-enantiomer onlya steep increase of the free energy along the RC is found, reflect-ing steric interactions between the anthracene 9-hydroxymethylgroup and the maleimide ring rising upon anthracene release.

Taken together, these results indicate that the anthraceneapproaches the front door of the pocket as in either the pre-(S, S)-or pre-(R, R)-enantiomer. Of these, only if the maleimide isthe first substrate to be bound, would the (R, R)-productenantiomer be (moderately) favored, due to the aforemen-tioned steric clash between the maleimide ring and theanthracene 9-hydroxymethyl group, consistent with the small

value (16%) of the enantiomeric excess of the (R, R)-productfound experimentally.[16] This stereoselection is evidenced bythe presence of a minimum in the PMF unbinding profileof anthracene in the pre-(R, R)-enantiomer through the frontdoor, compared to a steep increase in the unbinding profile ofanthracene as in the pre-(S, S)-enantiomer for which steric inter-actions influence the free energy. The resulting reactant state isstabilized both by the simultaneous presence of both substratesbound to their binding sites in the pocket and by stackinginteractions between the substrates.

The reactant state stabilization naturally does not depend onwhether the anthracene substrate enters through the front orback door. However, while anthracene binding to the ribozymethrough the front door is via conformational selection,[17] bindingthrough the back door requires an induced fit mechanism lead-ing to substantial changes in the ribozyme structure. The SMDcalculations are consistent with a substantially higher barrier toback door binding. Presence of a free energy minimum for theanthracene unbinding as in the pre-(S, S)-enantiomer throughthe back door is in agreement with the (S, S)-enantiomer of theproduct being favorable in case of anthracene substrate entrythrough the back door.[16]

The Diels–Alderase ribozyme specifically recognizes both sub-strates and provides a favorable hydrophobic environment forthe reaction between them. Furthermore, the ribozyme also canbe used to produce two different enantiomers of the Diels–Alder product, utilizing two distinctive mechanisms of interactionbetween the catalytic pocket and substrates.

Conclusions

Recent experimental investigations have demonstrated that theDiels–Alderase ribozyme can be used for selective synthesis ofboth product enantiomers, depending on which entrance to thecatalytic pocket the substrate is permitted to use.[16] The presentMD analysis complements this finding by providing a structuralmechanism of entry. In this mechanism, the maleimide substrateis the first reaction partner to enter the hydrophobic pocket. Thesecond step is binding of anthracene for which two possibilitiescan be differentiated: (1) entrance through the narrower backdoor, via an induced fit mechanism, that requires substantiallymore work than (2) entrance through the front door, followingconformational selection of an open pocket. The energetic pref-erence for anthracene entering through the front door as in thepre-(R, R)-enantiomer conformation in the simulations is smalland in agreement with the experimentally observed small enan-tiomeric excess of the (R, R)-product. The free energy minimumfor the anthracene unbinding as in the pre-(S, S)-enantiomerconformation through the back door is consistent with the (S, S)-product being favorable. The stabilization of the product stateis achieved by an optimal fit between the hydrophobic catalyticpocket and the Diels–Alder product both possible enantiomers.Catalysis is achieved largely by the preference of both reactantsfor a hydrophobic environment together with the pocket shapethat allows binding of the reactants in a stacked, preattackconformation and stabilizes the product state.



Acknowledgments

The simulations were run on the Heidelberg Linux Cluster System

at the Interdisciplinary Center for Scientific Computing (IWR) of the

University of Heidelberg. This research was also supported by the

National Science Foundation through TeraGrid resources provided

by National Institute for Computational Sciences as well as by the

bw-GRiD (http://www.bw-grid.de), member of the German D-Grid

initiative, funded by the Ministry for Education and Research (Bun-

desministerium für Bildung und Forschung) and the Ministry for

Science, Research and Arts Baden-Wuerttemberg (Ministerium für

Wissenschaft, Forschung und Kunst Baden-Württemberg).

Keywords: RNA • enzyme catalysis • molecular dynamics •stereoselection • binding mechanism

How to cite this article: T. Berezniak, A. Jäschke, J. C. Smith,P. Imhof, J. Comput. Chem. 2012, 33, 1603–1614. DOI: 10.1002/jcc.22993

Additional Supporting Information may be found in theonline version of this article.

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Received: 6 December 2011

Revised: 5 March 2012

Accepted: 18 March 2012

Published online on 2 May 2012


stereoselectioninthediels–alderaseribozyme ......charmm nucleic acids force ﬁeld parameter set...

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