Kamila Re´blova´ Filip Lankas˘ Structure, Dynamics, and Filip ......Structure, Dynamics, and Elasticity of Free 16S rRNA Helix 44 Studied by Molecular Dynamics Simulations Kamila

Structure, Dynamics, andElasticity of Free 16S rRNAHelix 44 Studied byMolecular DynamicsSimulations

Kamila Reblova1

Filip Lankas2

Filip Razga1

Maryna V. Krasovska1

Jaroslav Koca3

Jirı Sponer11 Institute of Biophysics,

Academy of Sciences of theCzech Republic,

Kralovopolska 135,61265 Brno,

Czech Republic

2 Institute for Mathematics B,EPFL (Swiss Federal Institute

of Technology), Station 8,CH-1015 Lausanne,

Switzerland

3National Centre forBiomolecular Research,

Kotlarska 2,61137 Brno,

Czech Republic

Received 5 January 2005;revised 2 March 2006;accepted 2 March 2006

Published online 9 March 2006 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/bip.20503

Abstract: Molecular dynamics (MD) simulations were employed to investigate the structure, dy-namics, and local base-pair step deformability of the free 16S ribosomal helix 44 from Thermus

thermophilus and of a canonical A-RNA double helix. While helix 44 is bent in the crystal structureof the small ribosomal subunit, the simulated helix 44 is intrinsically straight. It shows, however,substantial instantaneous bends that are isotropic. The spontaneous motions seen in simulationsachieve large degrees of bending seen in the X-ray structure and would be entirely sufficient toallow the dynamics of the upper part of helix 44 evidenced by cryo-electron microscopic studies.Analysis of local base-pair step deformability reveals a patch of flexible steps in the upper part ofhelix 44 and in the area proximal to the bulge bases, suggesting that the upper part of helix 44 has

Correspondence to: Jirı Sponer; e-mail: [email protected]

Contract grant sponsor: The Wellcome Trust (WT), GrantAgency of the Czech Republic (GACR) and Ministry of Educationof the Czech Republic (MSMT CR)

Contract grant number: GR067057 (WT); GA203/05/0388,GA203/05/0009, and GA204/03/H016 (GACR); MSM0021622413,LC512 and AVOZ50040507 (MSMT CR)

This article contains supplementary material available via theInternet at http://www.interscience.wiley.com/jpages/0006-3525/suppmat

Biopolymers, Vol. 82, 504–520 (2006)

# 2006 Wiley Periodicals, Inc.

504

enhanced flexibility. The simulations identify two conformational substates of the second bulge area(bottom part of the helix) with distinct base pairing. In agreement with nuclear magnetic resonance(NMR) and X-ray studies, a flipped out conformational substate of conserved 1492A is seen in thefirst bulge area. Molecular dynamics (MD) simulations reveal a number of reversible a-g backboneflips that correspond to transitions between two known A-RNA backbone families. The flipped sub-states do not cumulate along the trajectory and lead to a modest transient reduction of helical twistwith no significant influence on the overall geometry of the duplexes. Despite their considerableflexibility, the simulated structures are very stable with no indication of substantial force field inac-curacies. # 2006 Wiley Periodicals, Inc. Biopolymers 82: 504–520, 2006

This article was originally published online as an accepted preprint. The ‘‘Published Online’’ datecorresponds to the preprint version. You can request a copy of the preprint by emailing theBiopolymers editorial office at [email protected]

Keywords: molecular dynamics simulations; helix 44; ribosome; force field; RNA deformability;nanosecond scale dynamics

INTRODUCTION

Ribosome is a large nucleoprotein machine that car-

ries out the mRNA-directed synthesis of proteins.

Structures of small and large ribosomal subunits were

determined at atomic resolution by X-ray crystallo-

graphy.1–6 Further, ribosome was arrested at nearly

every stage of the protein synthesis cycle and visual-

ized using cryo-electron microscopy (cryo-EM) with

single-particle reconstruction.7 These experimental

studies showed that the ribosome undergoes large

conformational changes during protein synthesis,

such as the ‘‘ratchet-like motion’’ of the ribosomal

subunits, where the ribosome moves exactly three nu-

cleotides along the messenger RNA.8,9 This move-

ment represents the first step in the process of translo-

cation and it is followed by elongation factor G (EF-

G)-dependent tRNA translocation.8,9 Deep insight

into the mechanism of EF-G-dependent tRNA trans-

location was provided by a study that incorporated X-

ray crystallography and nuclear magnetic resonance

data into cryo-EM maps of ribosomal complexes.10

This study indicated that helix 44 (Figure 1), running

from the decoding site to the bottom of the 30S subu-

nit and making four major intersubunit contacts with

the 50S subunit (B2a, B3, B5, and B6a) (Figure 2),

plays a significant role in the translocation of tRNA.

Particularly, the upper part of helix 44 acts as a dy-

namical domain during translocation which is, to-

gether with mRNA/tRNA complex, pushed away

from the A-site to the P-site by EF-G, following GTP

hydrolysis.10 In a recently published work, Frank’s

group showed conformational changes (shift and rota-

tion) of the upper part of helix 44 upon ribosome-

recycling factor binding.11 Another experimental

study revealed that the binding of translational initia-

tion factor IF1 on the 30S subunit induced long-range

conformational changes in helix 44.12 These experi-

mental studies clearly demonstrate the importance of

structural deformations of the helix 44 in the course

of protein synthesis. Further, the conserved bases

1492A and 1493A in the helix 44 play a key role in

the discrimination of correct tRNAs in the A-site via

formation of A-minor interactions proofreading the

codon–anticodon helix (Figure 1).13

Computational studies represent a useful tool to

complement the experimental methods in the investi-

gation of the structure, dynamics, and deformability

of RNA. For example, explicit solvent molecular dy-

namics (MD) simulations were instrumental in struc-

tural studies of RNA.14–25 MD can bring, despite the

approximations inherent to the empirical force fields

FIGURE 1 (Left) Position of the helix 44 (red) in the

30S subunit (cyan). Note the modest bend of the helix 44.

(Right) detail of the upper part of the helix 44 with bases

1492A and 1493A flipped out to recognize the codon–anti-

codon helix (formed by mRNA and tRNA) via A-minor

interactions. Structures of the 30S subunit (PDB codes:

1J5E and 1IBM) were used for preparing this figure.

Free 16S rRNA Helix 44 505

Biopolymers DOI 10.1002/bip

and limitations due to the nanosecond simulation

time-scale, unique information that cannot be ob-

tained by experiments.26,27 Simulations have been suc-

cessfully employed in studies of ribosomal RNA and

proteins14,15,17,18,21,28,29 and in our previous work

focused on the investigation of structure and dynam-

ics of ribosomal RNA secondary motifs.30–34 These

studies characterized structural dynamics, base pair-

ing, specific hydration, cation binding, electrostatic

potential distributions, effects of selected base muta-

tions, and some other RNA features.

Several recent studies demonstrated that appropri-

ate processing of the MD data can be used to study

deformability and elasticity (i.e., mechanical proper-

ties) of nucleic acids beyond the level obtained by

visual inspection of the trajectories. Analysis of the

elasticity allows us to quantify the stiffness of the

molecule with respect to the given change of shape

(deformation), including its sequence dependence.

Computational and experimental studies of sequence-

dependent DNA deformability have focused on the

level of individual base-pair steps, i.e., estimated how

much free energy it costs to change the helical para-

meters (roll, twist, etc.) of a particular dinucleotide

step.35–40 However, computational studies also exist

on the deformability of base pairs41–43 and on global

DNA deformability, i.e., the free energy cost of

deforming a longer DNA fragment considered as a

piece of an extensible, twistable, and bendable an-

isotropic elastic rod.44 Sequence-specific elasticity of

B-DNA plays an important role, for example, in

nucleosome positioning. While DNA deformability

has been studied quite intensely, much less has been

done for RNA. Orozco and co-workers19,45 compared

the deformability of RNA and DNA duplex using X-

ray database analysis and MD simulations. They were

FIGURE 2 Two-dimensional (2D) and three-dimensional (3D) structures of the 16S ribosomal

helix 44 simulated in this study. (Left) 2D structure. The marks between pairs indicate the type of

base pairing according to the Leontis74 classification. The base-pair stacks are indicated in the gray

areas. Stacks (in circles) marked as A (bottom left) and B represent two substates seen in the simu-

lation NA. Substate A is close to the starting X-ray structure. Marks B2–B6 and dashed lines indi-

cate intersubunit bridges.46 (Right) Stereo view of the starting X-ray structure of the helix 44. The

two essential bases 1492A and 1493A are highlighted by red transparent surface. The base-pair

stacks are highlighted by light grey transparent surface.

506 Reblova et al.


interested in basic differences between the two types

of molecule, but they studied neither sequence-

dependence of elasticity nor effects of non-Watson–

Crick (non-WC) base pairs.

The present MD study investigates the structure,

dynamics, and sequence-dependent elasticity of a free

16S ribosomal helix 44 (Thermus thermophilus).Helix 44 is the longest helical structure of the small

ribosomal subunit and, besides Watson–Crick base

pairs, it contains a number of non-WC base pairs and

bulged bases (Figure 2). Although molecular contacts

of helix 44 in ribosome, such as the intersubunit

bridges with 50S subunit (Figure 2),46 inevitably

modulate the dynamics of helix 44, its intrinsic prop-

erties are certainly important for its interactions and

concerted motions involving other parts of the ribo-

some. Thus, unrestrained MD simulations combined

with Essential Dynamics Analysis (EDA) provide an

informative complementary view of the intrinsicproperties of this system that is relevant for its con-

sideration in the context of the whole ribosome. Fur-

ther, base-pair step deformabilities were calculated to

obtain insights into the flexibility of the helix 44.

These calculations provide deformability profiles

along the sequence and represent to our knowledge

the first description of the deformability of non-WC

pairs in RNA. We also compared the flexibility of

helix 44 with a canonical RNA duplex of the same

length (37 base pairs). In addition, the dynamics of

conserved bases 1492A and 1493A in the helix 44

is analyzed in detail. Simultaneously, our three 30–

40 ns MD simulations of long RNA duplexes (longest

studied so far) represent a useful test of the quality of

the molecular mechanical force field.

RESULTS

Starting Structure

The 16S ribosomal helix 44 (residues: 1404–1497)

(Figure 2) was taken from the X-ray structure of a

free 30S subunit (Thermus thermophilus) with resolu-

tion 3.05 A [Protein Data Bank (PDB) code: 1J5E]4

and was solvated and neutralized by a standard proce-

dure (see Materials and Methods). The X-ray helix 44

is bent like a longbow (Figures 1–3). Terminal parts

of the helix 44 make contacts with the rest of this sub-

unit while the middle part is not directly in contact

with 30S.

The X-ray structure shows several undefined ions

bound in the lower part of the major groove of the

helix 44 (Figure S1). The crystallization procedure

was done in the presence of KCl and Mg2þ ions, so

these ions might be bound in the major groove of

helix 44. Furthermore, there is another structure of the

30S subunit (PDB code 1IBM), which shows Mg2þ

ions bound in the upper part of the major groove of

the helix 44 (Figure S1). Nevertheless, the experimen-

tal information about ion binding is quite limited, con-

sidering the known ambiguities of X-ray studies of

cation binding to RNA.47,48 Thus, we carried out two

MD simulations of the helix 44 under different ion

conditions. The first simulation was carried out only

with Naþ ions (simulation NA, 30 ns) while the sec-

ond one was run with both Mg2þ and Naþ ions (simu-

lation MG, 30 ns) (see Materials and Methods). Mg2þ

ions were equally distributed along the helix 44 (man-

ually placed along the duplex at a distance of 5 A

from the X-ray structure) to allow them find conven-

ient binding positions. See method section and supple-

mentary material for a comment regarding the inclu-

sion of divalent cations into simulations.

Helix 44 Simulation in the Presenceof Na+

Thirty nanosecond MD simulation of the ribosomal he-

lix 44 (Figures 2 and S2) was carried out in the pres-

ence of 72 Naþ ions (see Materials and Methods, simu-

lation NA). The root mean square deviation (RMSD)

value with respect to the crystal structure was 6.2 61.1 A. Although we started from the X-ray geometry,

which is modestly bent, after 1 ns of the simulation we

obtained a straight duplex (Figure 3). Further, helix 44

appeared considerably dynamical in the course of the

simulation (see below); however, the average structure

over the trajectory was straight (Figure 3).

Base Pairing

The X-ray structure consists of twenty-four Watson–

Crick base pairs, eight non-WC base pairs, four G/U

wobble pairs, and two bulge bases 1492A and 1434A.

It contains three base-pair stacks (1414U/1486G//

1415G/1485U, 1417G/1483A//1418A/1482G, and

1432A/1468A//1433A/1467G) (Figure 2) (‘‘/’’ stands

for base pairing and ‘‘//’’ for stacking). In the course

of the simulation, we monitored all base pairs. Open-

ing events were observed for the first three base pairs

in the upper part of the duplex (Table I). Further, the

base pairs forming the U/G//G/U and G/A//A/G

stacks showed fluctuations of H-bonds (Table I). The

most significant changes of the base pairing were

observed in both bulge areas.

First Bulge Area. 1493A forms weak contacts to

the opposite 1408A in the X-ray structure. The

1493A(C2)–1408A(N1) distance is 3.0 A and the



1493A(N1)–1408A(N6) distance is 3.5 A. The base

1492A is not paired and has no other contacts

with the rest of the duplex. After equilibration, the

1493(N6)–1408(N1) H-bond was formed, which per-

sisted for the first two nanoseconds of the simula-

tion. Then it was irreversibly broken. The 1492A was

not paired and appeared considerably dynamic (see

below).

Second Bulge Area. In the X-ray structure, the base

1467G forms weak contact to the opposite bases

1433A and 1434A. The 1467G(N2)–1433A(N7) dis-

tance is 2.7 A, and the 1467G(N2)–1434A(N7) dis-

tance is 3.4 A. After equilibration, 1467G formed a

planar base pair with 1433A. This geometry was

denoted substate A and it was often seen in the simu-

lation NA (Figure 2 and Table II). After five ns of the

simulation NA the bases 1466C and 1465C moved

up, so that the base 1434A formed two H-bonds to

1466C and the adjacent guanine 1435G formed three

H-bonds to 1465C (Figure 2 and Table II). This sub-state B was observed in periods 5.8–18.8 and 20–28.7

ns (Figure 2, Table II, Figure 4) while substate A took

place for the rest of the simulation.

Dynamics of the Base 1492A

The bulge 1492A reveals considerable dynamics. The

starting X-ray structure shows the base 1492A

stacked in the stem. However, in the course of the

simulation the base often flips out of the stem towards

the minor groove (Figure 5a,b) by about 1808 com-

pared to the X-ray structure. The flipped-out structure

is seen in time periods 4–11 and 20–30 ns while in

periods 0–4 and 11–20 ns it resembles the crystal ge-

ometry. The flip is associated with anti to syn � angle

oscillation (Figure 5c) and C20-endo conformation

while 1492A stacked in the stem adopts C30-endopuckering (Figure 5d). Base 1493A was not flipped

out; however, the torsion angle � fluctuated in the

range from 108 to 608. Other residues did not reveal

any changes of the � angle and their geometries were

stable in the stem during the whole simulation.

Local Conformational Variations andPhosphate Backbone Substates

Base-pair step parameters rise, roll, tilt, twist, slide,

and shift were calculated using 3DNA code.49 First

three terminal base pairs at the 50 end were omitted

due to opening events (see above). Considering two

variants of base pairing (substates A and B, see

above) seen in the second bulge area, helical parame-

ters were calculated for structures averaged in time

periods 0–5.8, 5.8–18.8 ns (see supplementary mate-

rial Table S1), and several other time windows.

Note that the numerical values of helical twist dif-

fer significantly from the common value of ca. 338 inmany steps of the present RNA molecule, since the

standard definition of the base-pair axis valid for WC

base pairs is not applicable for non-WC base pairs.

Relative comparison of X-ray and computed values is

still relevant. Note also that, for a given step, the calcu-

lated value of helical twist is sensitive to the shape of

the non-WC base pairs forming the base-pair step.

Both averaged structures showed increase or re-

duction of helical twist of several steps compared to

the starting X-ray values. These differences are mostly

caused by evidently deformed initial X-ray geo-

metries of non-WC base pairs, which can easily be

explained by the medium resolution of the X-ray

structure and the overall dynamical nature of helix 44.

This is the case of G/U wobble pairs that have nonop-

timal X-ray geometry (see supplementary material

Figure S3 and Table S1 for details) and base pairs

1423G/1477C, 1432G/1468A, and 1411C/1489G that

have incomplete H-bonding in the X-ray structure.

Immediately after equilibration, these pairs formed

complete H-bonding, which was stable until the end

FIGURE 3 Stereo view of the superposition of the starting

X-ray structure of helix 44 (red) and the averaged structure

over 30 ns of the simulation NA (blue). The superposition was

done over the lower portion of the duplex (residues 1421–

1440/1479–1461). The dashed line and the number indicate the

displacement of the terminal phosphorus atom 1497G(P).

508 Reblova et al.


of the simulation. This initial relaxation of some base

pairs resulted into new (and stable) values of helical

twist (as calculated by 3DNA code) in the base-pair

steps involving these base pairs. We suggest that all

these differences of the calculated helical twist can be

fully explained considering by imperfectness of the

H-bonding of several base pairs in the X-ray structure

and do not indicate any real structural changes in the

simulated molecule. This likely is also the case of

GA/GA step 29 having calculated helical twist of ca.

�218 throughout the simulation, while the X-ray

structure gives twist of 3.38 for this step (see supple-

mentary material Table S1). The X-ray structure con-

tains two GA/GA steps (14 and 29) with considerably

different values of twist (�21.98 and 3.38). The sec-

ond GA/GA step 29 is actually visibly deformed in

the X-ray structure. Most changes of the calculated

twist values thus reflect modest structural relaxations

of the non-WC base pairs. Further, base-pair steps

that include the temporarily formed dynamical base

pair 1493A/1408A in the first bulge area and base

pairs from the very dynamical second bulge area (see

above) showed different values of calculated helical

twist compared to the X-ray values. We also observed

that reversible transitions of �–� torsions (see below)

can cause modest temporary reduction of the helical

twist. This issue will be described in detail for the

simulation of the canonical RNA duplex.

The starting values of backbone torsions for all

residues were � ¼ 2908, � ¼ 1758, � ¼ 508–608,� ¼ 75–808, e ¼ 2008–2108, and � ¼ 2908, i.e., thecanonical A-RNA family 20 according to the

Schneider’s classification.50 In the course of the sim-

ulation, alternative ‘‘switched’’ conformations charac-

terized by concerted � (2908 ? 1458) and � (508–608 ? 1808) transitions were observed (Figure 6).

These compensatory backbone switches were reversi-

ble (obviously except for those that occurred close to

the end of the simulation). The switched geometry rep-

resents another well-established A-RNA family 24 (or

19) often seen in A-RNA duplexes.50 The number of

�–� torsions in the switched conformation at 10, 20,

and 30 ns was 8, 12, and 11, respectively. Thus, the

switched geometries do not cumulate along the trajec-

tory and have population ca. 10–15%. Several alter-

native conformations of �, �, e, and � torsions were

rarely observed (not shown).

All bases excluding 1492A (see above) adopted

puckering C30-endo throughout the simulation.

Essential Dynamics Analysis

Essential Dynamics Analysis (EDA)51 (see Materials

and Methods) was carried out to obtain deeper insight

into the flexibility of the helix 44. The first two eigen-

vectors represent 60% of the overall motion of the he-

Table I Changes in Base Pairing in the Helix 44 Observed in the Course of the Simulations

NA and MGa

Base Pair Simulation NA Simulation MG

1404C(N3)–1497G(N1) 8.5–9.3 ns OE 15–30 ns OE

1404C(N4)–1497G(O6) 8.5–9.3 ns OE 15–30 ns OE

1404C(O2)–1497G(N2) 8.5–9.3 ns OE 15–30 ns OE

1405G(N1)–1496C(N3) 0.8–4.5 ns OE 4–6.3 ns OE

1405G(N2)–1496C(O2) 0.8–4.5 ns OE 4–6.3 ns OE

1405G(O6)–1496C(N4) 0.8–4.5 ns OE 4–6.3 ns OE

1406U(N3)–1495U(O2) 16.5–17.3 ns OE Stable

1406U(O4)–1495U(N3) 16.5–17.3 ns OE Stable

1408A(N1)–1493A(N6) 0–2 ns stable 6–30 ns stable

1414U(N3)–1486G(O6) Stable Stable

1414U(O2)–1486G(N1) 3.2 A, 0–30 ns F 3.5 A, 0–30 ns F

1415G(N1)–1485U(O2) 3.7 A, 6.7–10 ns F Stable

1415G(O6)–1485U(N3) 3.7 A, 6.7–10 ns F Stable

1417G(N2)–1483A(N7) Stable Stable

1417G(N3)–1483A(N6) 3.5 A, 0–30 ns F 3.2 A, 0–30 ns F

1418A(N6)–1482G(N3) 3.2 A, 0–30 ns F 3.2 A, 0–30 ns F

1418A(N7)–1482G(N2) Stable Stable

1432G(N2)–1468A(N7) Stable Stable

1432G(N3)–1468A(N6) 3.2 A, 0–30 ns F 3.6 A, 0–30 ns F

a OE indicates an opening event of the H-bond in the specified time period and F denotes a fluctuation of the H-bond

around the averaged value in the specified time period. The gray field specifies the base pairs involved in base-pair stacks.



lix 44 on the nanosecond time scale. These eigenvec-

tors correspond to bending of the helix 44 (Figure 7)

in mutually orthogonal planes. Combination of the

first two eigenvectors results in bending motion of

the duplex in all directions during the simulation.

This observation is confirmed by the calculation of

projections of the trajectory onto the eigenvectors

(Figure 8). The diagram in Figure 8 shows approxi-

mately isotropic distribution of projections around

the point 0.0. In summary, the averaged helix is

straight (Figure 3) but it can easily achieve substan-

tial bends on the 10 ns scale.

The upper part of the helix 44 in ribosome is flexi-

ble while the bottom part is fixed.10 During the EF-G-

dependent tRNA translocation, the A-site region of

the helix 44 moves toward the P-site by approxi-

mately 8 A.10 We thus superimposed the straight ge-

ometry (averaged MD structure) and the most bent

geometry (an MD snapshot) over the lower portion

of the helix 44 (over residues 1421–1440/1479–1461)

to estimate the range of spontaneous bending. This

superposition revealed maximal displacement of the

upper terminal phosphorus atom 1497G(P) by 25 A

and of the essential base 1493A by 23 A (Figure 9).

The average displacement of 1497G(P) was 9 A.

Although it is obvious that the flexibility of helix 44

in the ribosome may be affected by, for example, the

intersubunit bridges, helix 44 is capable of easily

achieving the range of motions seen in the ribosome.

Also note that spontaneous bending in the course of

the simulation reaches values almost identical to

those seen in the starting X-ray structure (Figures 3

and 9). The temporary bending seen in the simulation

is smooth, i.e., uniformly distributed along the double

helix, with no local kinks.

FIGURE 4 Formation of H-bonds between bases 1435G

and 1466C (substate A, 0–5.8, 18.8–20, and 28.7–30 ns)

and between bases 1435G and 1465C (substate B, 5.8–18.8

and 20–28.7 ns), simulation NA.

Table II Base Pairing of the Helix 44 in the Area of the Second Bulgea

Substate A

Base Pair Simulation NA Simulation MG

1433A(N7)–1467G(N2) Stable Stable

1433A(N6)–1467G(N3) 3.4 A, 0–30 ns F 3.3 A, 0–30 ns F

1435G(N1)–1466C(N3) 5.8–18.8 ns and 20–28.7 ns OE Stable

1435G(N2)–1466C(O2) 5.8–18.8 ns and 20–28.7 ns OE Stable

1435G(O6)–1466C(N4) 5.8–18.8 ns and 20–28.7 ns OE Stable

1436U(N3)–1465C(N3) 5.8–18.8 ns and 20–28.7 ns OE Stable

1436U(O4)–1465C(N4) 3.5 A, 5–19 ns and 20–28.7 ns F No H-bond

Substate B

Base Pair Simulation NA

1434A(N6)–1466C(O2) 3.5 A, 0–30 ns F

1434A(N3)–1466C(O2) 0–5.8 ns, 18.8–20 ns and 28.7–30 ns OE

1435G(N2)–1465C(O2) 0–5.8 ns, 18.8–20 ns and 28.7–30 ns OE

1435G(N1)–1465C(N3) 0–5.8 ns, 18.8–20 ns and 28.7–30 ns OE

1435G(O6)–1465C(N4) 0–5.8 ns, 18.8–20 ns and 28.7–30 ns OE

a Substate A represents crystal base pairing and was observed in both simulations NA and MG, while sub-

state B was identified only in the simulation NA. OE indicates an opening event of the H-bond in the specified

time period and F indicates a fluctuation of the H-bond around the averaged value in the specified time period.

510 Reblova et al.


Simulation in the Presence of Mg2+

A thirty nanoseconds long MD simulation of the helix

44 (Figures 2 and S2) was also carried out in the pres-

ence of 24 Mg2þ ions (simulation MG, see Materials

and Methods and supplementary material) and 24

Naþ ions, which were added to complete the neutrali-

zation (ion concentration and the binding positions

are specified in supplementary material). Similar to

the simulation NA, after the first nanosecond of the

simulation we obtained a straight duplex with RMSD

value with respect to the crystal structure 5.0 6 1.2 A

(Figure S2). The simulation MG revealed base pair-

ing of the helix 44 identical to the simulation NA and

identical transient changes of base pairing (e.g., open-

ing events in terminal base pairs and fluctuations of

pairs forming stacks) (see Table I). However, in con-

trast to the simulation NA, the simulation MG did not

show the B substate in the second bulge area and the

initial X-ray geometry with planar base-pair 1467G/

1433A was stable (Figure 2, Table II). Further, we

observed once again the H-bond 1493(N6)–1408(N1)

in the first bulge area, which was formed in the time

period 6–30 ns. The spontaneous flipping of 1492A

was limited; it flipped out modestly towards the

minor groove (approximately by 308) and towards the

major groove (approximately by 608) while keeping

the stable C30-endo sugar conformation. Essential dy-

namics analysis revealed two main eigenvectors iden-

tical to those in the simulation NA. More details can

be found in supplementary material, including analy-

sis of helical parameters and backbone dynamics.

The simulation MG provides an essentially identical

picture of the dynamics as simulation NA. Thus even

such a high concentration of Mg2þ exerts surprisingly

little effect on the dynamics of the long duplex on the

30-ns scale. In contrast to the widespread opinion that

Mg2þ ions may substantially improve RNA MD sim-

ulations, we suggest that inclusion of Mg2þ is mostly

unnecessary. Inclusion of divalent cations such as

FIGURE 5 (Left) Stereo views of the upper part of the helix 44 with 1492A and 1493A high-

lighted in black. (A) 1492A is stacked in the stem; (B) 1492A is flipped out. (C) Time development

of the torsion angle � of 1492A. (D) Time development of the pseudorotation phase angle (P) of

the sugar ring of 1492A. Changes of both angles correspond to the flipping of the 1492A.

FIGURE 6 Time development of torsions � and � for

residue 1411C. The graphs show typical reversible back-

bone flip between canonical A-RNA and family 24.50



Mg2þ ions may cause local RNA structure distortions

due to force field and sampling limitations.30

Simulation of the Canonical Duplex

Forty nanosecond long control MD simulation of a 37

base-pair (bp) canonical RNA duplex (50CGCGGC-AGCCCAUCCCGGGCGCGGGCCCCGCUUCAGC30,simulation CAN) was carried out (Figure S2). The

starting structure is a standard straight duplex. The

averaged structure over the trajectory is also a

straight duplex; however, similar to helix 44, it exhib-

its considerable dynamics with the RMSD value with

respect to the starting structure 5.9 6 1.3 A.

All canonical base pairs were stable except for one

terminal pair at the 50 end and two terminal pairs at

the 30 end with opening events (data not shown). Hel-

ical parameters were calculated for a structure aver-

aged over the time period 20–30 ns while omitting

two terminal steps at either end (supplementary mate-

rial Table S1). The average MD value of helical twist

was 29.28 with a standard deviation of 2.68. The

base-pair steps have quite uniform distribution of hel-

ical twists; however, twist is slightly underestimated,

as usual with AMBER.52 All steps were within a nar-

row range of helical twist values except of a CC/GG

step 10 (Table S1). Its helical twist averaged over the

time periods of 1–10, 10–20, and 20–30 ns was 30.38,24.08, and 21.58, respectively. This twist reduction

was actually associated with presence of two long-

living alternative �/� backbone substates in this step.

However, at 37 ns we evidenced a reversal of one of

the backbone flips and the average helical twist in a

time period 37–40 ns increased to ca 268. This indi-cates that the step is returning to a common range of

helical parameters.

Dynamics of backbone torsion angles is very simi-

lar to the simulations NA and MG, i.e., there are re-

versible �–� flips between two established A-RNA

families 20 and 24. The number of nucleotides in

conformation family 24 found at 10, 20, 30, and 40

ns was 3, 10, 7, and 9, respectively, i.e., ca. 10–12%

population. Temporary reduction of twist to 258–268

FIGURE 8 Projections of the trajectory onto eigenvec-

tors 1 and 2 in the course of the simulation NA (point 0.0

corresponds to the straight duplex).

FIGURE 7 The first eigenvector showing bending

motion of helix 44 in the course of the simulation NA. The

duplex oscillates (left and right) around the averaged geom-

etry (in the middle) in one plane.

FIGURE 9 Stereo view of two MD structures of helix 44

superimposed over the lower portion of the duplex (residues

1421–1440/1479–1461). Straight (averaged) geometry is in

black, bent (snapshot) geometry is in gray; base 1493A is in

van der Waals representation. The dashed lines and the

numbers indicate the displacement of terminal phosphorus

atom 1497G(P) and base 1493A.

512 Reblova et al.


seen in some steps correlates with such �/� family 24

backbone substates.

EDA again identifies two main eigenvectors, which

represent a symmetrical bending of the standard duplex

in two mutually orthogonal planes. However, superim-

posing bottom parts of the straight and most bent struc-

tures we found the displacement of the terminal phos-

phorus atom 74G(P) to be 45 A, which is almost twice

as much as for the helix 44. The average displacement

of the phosphorus atom 74G(P) was 15 A. This means

that globally the canonical helix is more bendable than

the native helix 44.

Base-Pair Step (Local) Deformabilityof Helix 44 and Canonical Duplex

Base-pair step deformabilities (elastic or force con-

stants) were calculated with respect to the six helical

variables (rise, roll, tilt, twist, shift, and slide, see Mate-

rials and Methods) for all steps in the noncanonical he-

lix 44 and in the standard RNA canonical duplex. The

calculations were carried out only over stable parts of

the trajectories where no opening events occurred. All

the coupling terms in the harmonic energy function

have been considered, so that the stiffness of each

base-pair step is described by a 6 by 6 symmetric ma-

trix of elastic constants, the stiffness matrix. The diago-

nal force constants that reflect free energy changes

upon deforming just one conformational parameter (the

others are kept at equilibrium values) are plotted along

the sequence in Figure 10 (see also supplementary ma-

terial Table S2). To estimate the error on the calculated

stiffness constants, diagonal force constants were calcu-

lated over nonoverlapping 1-ns long time intervals

along the trajectories (only over stable parts of the tra-

jectories) from 1 to 30 ns, providing both averages and

standard deviations (see Figure 10 and Tables S2a–c)

(in the case of the simulation NA, we used only time

periods corresponding to substate A). For the sake of

clarity, error bars in Figure 10 are shown only for the

NA simulation. The complete set of values is provided

in the supplementary material (Tables S2a–c). The

error bars of force constants represent approximately

10–20% of the mean values for both helix 44 and ca-

nonical duplex.

Deformability profiles of the native helix 44 in the

simulations NA (calculated for substate A) and MG

are rather similar (Figure 10). Thus even this quanti-

tative analysis does not reveal any substantial rigidifi-

cation of the long helix by the high Mg2þ concentra-

tion. Both the NA and MG elasticity profiles suggest

lowered force constants in the upper part of the helix

44 (first four steps) and in both bulge areas (steps 5,

6, and 30–33). This indicates larger flexibility of

these regions compared to the rest of the duplex.

Superposition of the deformability profiles of the ca-

nonical duplex over the profiles of the native helix 44

duplex (Figure 10) shows that the force constants of

the standard RNA duplex fall into the range of force

constants of the native helix 44. Note that, when com-

paring the helix 44 with the canonical duplex, the

central part of the helix 44 shows increased stiffness,

specifically for rise and roll. It might result in de-

creased global flexibility of the helix 44 and reduced

overall amplitude of bending motion at the ends. We

suggest that the enhanced rigidity of the helix 44 in

the central region explains the twice as large ampli-

tude of the global fluctuations (bend angles) seen for

the canonical helix. Note again that the upper part of

helix 44 has locally enhanced flexibility. RNA per-

sistence lengths for helix 44 and duplex RNA have

been also calculated and compared with experimental

values. The dynamic bending persistence length has

been found to be ca 120 nm. (For more details, in-

cluding discussion of the estimated total persistence

length, see supplementary material.)

We further compared elasticity of canonical py-

rimidine–purine (YR/YR), pyrimidine–pyrimidine

(YY/RR), and purine–pyrimidine (RY/RY) steps. We

did not consider steps with non-WC base pairs pres-

ent in helix 44, because there are only very few

examples of each of the different types (RY/RR, YR/

RR, RY/YY, and RR/RR). For rise, roll, and tilt, the

YR/YR steps were by far the most flexible (Figure

S4), whereas steps in other two groups were stiffer.

Particularly, RY/RY steps exhibited increased stiff-

ness for rise and roll while YY/RR steps were of in-

termediate flexibility. In the case of tilt, YY/RR steps

were the stiffest and RY/RY steps were of intermedi-

ate flexibility. This was observed consistently in all

three simulations.

DISCUSSION AND CONCLUSIONS

Atomistic, explicit-solvent MD simulations were

employed to investigate structure, dynamics, and

local base-pair step deformability of free 16S ribo-

somal helix 44 from Thermus thermophilus. The helix44 (residues: 1404–1497) was taken from the crystal

structure of a free 30S subunit (PDB code: 1J5E) and

simulated in the presence of explicit Naþ and Mg2þ

ions (simulations NA and MG, both 30 ns) and

explicit water molecules, assuming the X-ray struc-

ture as the starting geometry. Comparison with a

standard RNA duplex of the same length (37 bp) was

carried out (simulation CAN, 40 ns).



Base Pairing Is Stable, Except for TwoSubstates in the Bottom Bulge Area

Geometries of many base pairs were substantially

relaxed (improved) at the very beginning of the simu-

lation, compared with the starting X-ray structure.The largest deviations in base pairing compared tothe starting X-ray structure were observed in the areaof the bulge base 1434A in the simulation NA. In thisarea, two bases 1466C and 1467C moved temporarily

FIGURE 10 Deformability profiles for helix 44 in simulations NA (calculated for substate A,

red), MG (green), and for the canonical duplex CAN (black). Error bars (standard deviations) are

shown for the simulation NA. The horizontal axis shows the base-pair step number while the

sequence of each base-pair step is also specified (helix 44—bottom and red; canonical helix—top

and black). The color dots (‘‘contact steps’’—see the inset top left) mark those steps of helix 44 that

are involved in the intersubunit bridges (B2a, B3, B5 and B6a).46

514 Reblova et al.


one step up (Figure 2) and formed a new base-pairing

and stacking pattern not seen in the starting X-ray

structure (Table II, Figure 4). This conformational

switch was spontaneous and reversible, occurring

twice during the simulation (Table II, Figure 4). This

suggests that there might be two substates of this

non-WC region with similar free energies. Note that,

assuming the standard Arrhenius kinetics, 10-ns scale

simulations are capable of regularly overcoming free

energy barriers that are on a scale of ca. 5–7 kcal/

mol, which likely is the barrier separating the above

two substates. This region thus could act as a flexible

structural switch. To the best of our knowledge, simi-

lar duplex pairing bistability was not observed in any

RNA simulation study published so far. Further, the

simulation suggested transient formation of a H-bond

between 1408A and 1493A (Table I), which was not

present in the starting X-ray structure but was

observed in previous solution NMR study.53 MD sim-

ulations reveal several opening events and fluctua-

tions of 1–3 terminal base pairs of the duplex (Table I),

that, however, can be considered as a common end

effect. Internal WC base pairs are firmly paired (we

assume that this is correct behavior on the ns time

scale) with no breathing or opening. This contrasts

recent RNA duplex simulations with the CHARMM

force field, showing very frequent ns-scale base-pair

breathing in RNA duplexes.41

1492A Flips Out Spontaneously

Both NA and MG simulations revealed considerable

dynamics of the essential base 1492A (Figure 5). In

the simulation NA, the 1492A flipped out repeatedly

by about 1808 towards the minor groove while the dy-

namics of 1492A was modestly restricted in the simu-

lation MG. Such conformational substates (stacking

inside the stem and flipped-out substate) of both key

residues 1492A and 1493A during the process of dis-

crimination of cognate and near-cognate tRNA have

been proposed by experiments.13 Our simulations on

the nanosecond time scale showed spontaneous

dynamic behavior of the 1492A in the free helix 44

with Naþ ions. The reduced dynamics of 1492A in

the simulation MG might be caused by closing of the

upper part of the helix 44 by an interstrand contact

via one specific Mg2þ ion (outer shell binding). Note

that this result can be incidental due to poor sampling

of divalent cations in ns-scale simulations. The

observed dynamical behavior of 1492A is in agree-

ment with a previous NMR study53 that indicated dy-

namics of both 1492A and 1493A and revealed their

sugar conformations to be a mixture of C20-endo and

C30-endo. Exactly this is seen in our study for 1492A

in the simulation NA. Moreover, conformational sub-

states of 1492A and 1493A have been also seen in the

experimental study that combined X-ray crystallogra-

phy and fluorescence measurements.54 Thus, we

assume that these bases might flip out quite freely in

the ribosome. Regarding 1493A, we suggest that a

longer simulation time scale would be needed to evi-

dence its flipping. Note, however, that the confor-

mational plasticity of the A1492/A1493 bases is quite

remarkable. This region adopts multiple distinct

substates in the available experiments and both bases

can be bulge out and bulge in. Thus, much longer

simulations would be needed to obtain statistically

significant sampling of the A1492/A1493 dynamics,

and it is not guaranteed that the force field would

fully capture the tiny balance of all the substates.55

Phosphate Backbone and HelicalParameters Indicate a GoodPerformance of the Force Field

Recent AMBER MD studies of B-DNA duplexes56–58

reported long-lived �–� ‘‘switched’’ conformations in

DNA sugar–phosphate backbone. These alternative

conformations appeared irreversible, and caused a

reduction of helical twist and some other structural

effects. Related backbone flips occurred in locally en-

hanced sampling MD simulations of G-DNA loops and

led to incorrect loop topology of the d(GGGGTTTTG-

GGG)2 quadruplex.59 In contrast, recent analysis of

RNA backbone behavior in simulations of the hepatitis

delta virus ribozyme and sarcin–ricin loop suggested

that the force field performs well across a wide range

of A-RNA and noncanonical RNA backbone topolo-

gies.20,34 Obviously, the long 37-bp double helices

studied here represent an optimal system to compare

with B-DNA simulations. For both the native helix 44

and the canonical RNA duplex, we evidenced a number

of �–� ‘‘switched’’ conformations. These compensa-

tory backbone switches, however, were reversible (Fig-

ure 6), and did not cumulate during the simulations.

The population of flipped backbones in the 40-ns simu-

lation of the canonical helix was ca. 10–12% since

10 ns into the simulation while the helix 44 simulations

gave the same picture. The second substate was associ-

ated with modest helical twist reduction, which, how-

ever, did not affect the outcome of the simulation

because the flips were temporary. The present A-RNA

flips correspond to a switch between the canonical A-

RNA family 20 and one of the three other most fre-

quently occurring RNA backbone families, namely,

family 19/24.50 Such RNA backbone flips seen in the

simulations are basically in agreement with the X-ray

data, although their population may be somewhat exag-



gerated.50 Sugar puckering remained consistently in the

C30-endo range. Thus, no indication of a force field

imbalance for the RNA backbone was detected on the

present time scale.

There appear to be substantial changes of calcu-

lated values of helical twist for some steps of the

simulated helix 44 compared to the starting X-ray

values. These differences are, however, primarily

caused by nonoptimized geometries of some base

pairs in the initial X-ray structure. These base pairs

relax immediately after the simulation start, changing

the numerical value of helical twist. Thus, these

changes do not indicate any structural transition. Fur-

ther, some inherently flexible elements of helix 44

show substantial variations of calculated helical twist.

Perhaps the largest deviation of twist with respect to

the X-ray value was indicated in both simulations NA

and MG for non-WC GA/GA step 29 (supplementary

material Table S1). The X-ray structure gives a twist

of 38 while MD leads to a twist around �218. (Notethat numerical values of helical twist are affected by

the presence of non-WC base pairs.) The latter value,

however, is in agreement with another GA/GA step

14 in the crystal structure. Actually, step 29 is visibly

deformed in the X-ray structure. In the case of the ca-

nonical RNA duplex, a single CC/GG step 10 shows

considerably lower helical twist of ca. 228 in the pe-

riod of 20–30 ns, which is well below the common

A-RNA twist ranges. This substate develops in the

first 10–15 ns of the simulation and is associated with

the presence of two �/� alternative backbone sub-

states in this step. However, at 37 ns, one of the

switched phosphates flips back to the canonical ge-

ometry and the whole step starts to return to the ca-

nonical helical geometry— it is thus not a permanent

substate. Anyway, the total population of low-twist

steps in this simulation is 1 out of 36. Such substates,

if randomly formed, could evade detection by experi-

mental techniques.

The simulations also reveal a systematic differ-

ence of base-pair roll between YR (18–68) and RY

(58–138) steps (Y and R stand for pyrimidine and pu-

rine). This is another indication of a meaningful per-

formance of the force field, because the roll redistrib-

ution between YR and RY steps in A-type duplexes

is known from X-ray data.60–62

EDA Shows Large-Scale BendingFluctuations of the Long Duplex

The 16S ribosomal helix 44 is conformationally re-

strained inside the ribosome. First, the 30S subunit

X-ray structure shows bent helix 44 (Figures 1–3).

Second, in the complete ribosome, the helix 44 makes

several intersubunit bridges (Figure 2) with 50S, rep-

resenting fixed nodes likely serving as anchoring

patches for large-scale motions.46 Nevertheless, we

were interested in understanding how could these

interactions be interrelated with intrinsic properties of

the helix 44 and what are the differences between he-

lix 44 composed of 30% of non-WC base pairs

(including wobble pairs) and the standard RNA du-

plex. The simulations reveal that the helix 44 is in-

trinsically straight—it is thus not pre–deformed to-

ward its bent geometry seen in the 30S subunit (Fig-

ure 3). However, fluctuational bending represents

60% of the overall motion of both the helix 44 (Fig-

ure 7) and the canonical RNA duplex. Both duplexes

bend isotropically around a straight geometry (Figure

8). Further, the bending is not caused by the presence

of any kink in the structure, which was, for instance,

seen in study of ribosomal kink–turn motifs.32,33 The

range of statistical bends is significant and on the 30-

ns time scale it exceeds the range of deformations

seen in ribosomal structures.

Based on cryo-EM, Frank and coworkers10 ob-

served a bending of the upper part of the helix 44 dur-

ing translocation. They showed that after the binding

of EF-G, this factor pushed the upper part of helix 44

using energy from GTP hydrolysis, shifting (by ap-

proximately 8 A) the mRNA/tRNA complex from the

A-site to the P-site. The experiments suggest that the

upper part of the helix 44 represents a moveable do-

main while the lower portion is motionless and acts

as an anchor. Although the helix 44 is partly fixed by

intersubunit bridges with 50S and its contacts with

30S, which certainly affect its dynamics, MD simula-

tions provide a surprisingly similar type of motion.

The superimposition of the straight averaged MD

structure and a bent MD structure over the lower por-

tion of the helix 44 reveals that the maximal displace-

ment of the upper part of the helix 44 in simulations

is ca. 25 A, with the average value ca. 9 A (Figure 9).

The simulations indicate that helix 44 can spontane-

ously reach ranges of bends that are evidenced by

cryo-EM studies. Note also that our MD average

structure is straight compared to the starting X-ray

structure that is modestly bent (Figure 3). This indi-

cates that helix 44 in the ribosome (before transloca-

tion) is strained.

Structure and Dynamics of theIntersubunit Bridge Areas

Let us now briefly summarize key results regarding

the contact areas of helix 44 involved in the intersu-

bunit bridges. As noted above, fluctuations and num-

516 Reblova et al.


ber of opening events were observed for base pairs

involved in intermolecular bridge B2a in the course

of the simulations NA and MG. Other instabilities in

base pairing were seen in U/G//G/U and G/A//A/G

stacks, which are involved in bridge B3 and partially

B6a.

To obtain further insight into the elasticity of helix

44, we calculated the local deformability along the

duplex.35 Analysis of deformability profiles (derived

from fluctuations seen in MD) along the sequence

enables us to identify flexible and stiff regions in the

duplex. The profile reveals very flexible steps in the

upper part of helix 44 and in the areas of bulge bases

of helix 44 (Figure 10). On the other hand, base-pair

steps in the central portion of helix 44 are rather rigid

(Figure 10 and supplementary material Table S2).

Comparison with the canonical duplex shows that

force constants of the steps formed by non-WC pairs

have much larger sequence variability, i.e., there exist

stiffer and more flexible regions of helix 44 (Figure

10). We assume that non-WC pairs in helix 44 not

only stabilize interactions with 50S (intersubunit

bridges, see Figure 2) but they also modulate (en-

hance) the local flexibility of the helix to promote

motions localized in the upper part of helix 44.10–12 It

is evident that the area of the key bridge B2a is

unusually flexible. Analysis of force constants shows

that steps 2–5 involved in B2a bridge have enhanced

flexibility compared to steps 11–13, 15, 18, 20–22,

24–26, and 28 involved in the bridges B3, B5, and

B6a that are more rigid. Range of force constants of

all the later steps is close to range of canonical duplex

(i.e., these steps are medium-rigid, see Figure 10).

As noted above, base pairs 1423G/1477C, 1425U/

1475G, 1432G/1468A, and 1411C/1489G have in-

complete base pairing in the X-ray structure, which is

swiftly repaired in the simulation. It is likely that the

disturbed base pairing in the refined X-ray structure

results from some kind of a dynamical disorder. Note

that the first three perturbed pairs actually belong to

bridges B5 and B6a. Thus, it may happen that these

pairs are fully stabilized only upon formation of the

bridges or offer energetically accessible substates to

optimize formation of the bridges.

Finally, we have noted before that the bottom

bulge area (its upper part is adjacent to intersubunit

bridge B6a) reveals dynamical switching between

two substates A and B while the X-ray structure is

not optimally paired. We speculate that this structural

switch may regulate the position of the RNA above

the bulge (including the bridge) with respect to the

very bottom of helix 44. More specifically, when

using the sandwiching WC base pairs 1431C/1469G

and 1438G/1463C as reference base pairs, the helical

twist and rise between them are 1578 and 18.2 A, and

1378 and 17.0 A for the substates B and A, respec-

tively. The X-ray values are 1328 and 19.7 A (note

that the X-ray structure is bent and this area contacts

30S).

It is also notable that both bulge regions and sev-

eral pairs sandwiching them are contacting the 30S

subunit. Thus, the areas seen as soft in the simulation

contribute to the interaction between 30S and helix

44. Two of the four initially distorted pairs, 1432G/

1468A and 1411C/1489G, interact with the rest of

30S. On the other hand, the dynamical bases A1492

and A1493 appear to be free of any contact with 30S

that could impair their mobility. All these data indi-

cate that noncanonical segments of helix 44 are opti-

mally designed to mediate contacts with both sub-

units and to facilitate motions of the upper part of

helix 44.

Comparison of Sequence-DependentElasticity of A-RNA and B-DNA

A recent B-DNA elasticity study35 focused on sequence-

dependent B-DNA deformability at the base-pair step

level and revealed distinct trends for YR/YR, RR/

YY, and RY/RY steps. YR/YR B-DNA steps were

flexible for roll and rise, RR/YY were intermediate,

and RY/RY were stiff. For tilt and partially twist,

YR/YR steps were also flexible whereas shift and

slide lacked simple trends. The present A-RNA study

identifies similar trends of these three distinct groups

of steps for rise, roll, and tilt for both helix 44 and the

canonical duplex (Figure S4). Like in B-DNA, A-

RNA YR/YR steps are the most flexible for roll, tilt,

and rise, while RY/RY and YY/RR steps show

increased stiffness (Figure S4). Particularly for rise, a

trend similar to that for B-DNA is observed. In the

case of roll, A-RNA RY/RY steps show on average

increased stiffness compared to YY/RR. Considering

tilt, A-RNA YY/RR steps have increased stiffness

while RY/RY steps are intermediate, which is

reversed compared to B-DNA. Further, similar to

DNA steps, no simple trends of RNA steps were iden-

tified for shift and slide. In summary, the A-RNA

results for YR/YR, RR/YY, and RY/RY steps reveal

some simple trends similar to B-DNA.35

Concluding Remarks

Helix 44 is intrinsically straight, with a substantial

flexibility towards isotropic bending. The spontane-

ous motions seen in simulations would be, e.g.,

entirely sufficient to allow the dynamics of the upper

part of helix 44 evidenced by cryo-EM studies. Anal-



ysis of local base-pair step deformability suggests

that the upper part of helix 44 has markedly enhanced

flexibility while its central region is stiffer. The simu-

lation data indicate that noncanonical segments of he-

lix 44 are optimally designed to mediate contacts

with both subunits and to allow large-scale dynamics

of the upper part of helix 44. The structural dynamics

of the conserved adenines 1492A and 1493A in simu-

lations is basically in agreement with NMR and

X-ray data. The analysis of dynamics and substates

occurring in the RNA sugar–phosphate backbone is

more careful than in any RNA MD study published

until now and parallels similar studies recently done

for B-DNA. The simulations reveal a number of tem-

porary backbone flips, but they are always reversible.

This indicates a good performance of the AMBER

MD method for the studied RNA system.

MATERIALS AND METHODS

The simulations were carried out using the AMBER-6.0

program63 with the Cornell et al. force field.64 The 16S ri-

bosomal helix 44 (residues: 1404–1497) was taken from the

X-ray structure of a free 30S subunit (Thermus thermophi-lus) with a resolution of 3.05 A (PDB code: 1J5E).4 Two

simulations of the helix 44 were carried out under different

ion conditions. The first simulation (NA) was run only with

neutralizing Naþ ions. They were initially placed by the

Xleap module of AMBER at positions of the lowest electro-

static potential. The second simulation (MG) was run with

24 Mg2þ ions, which were manually placed along the

duplex at a distance of 5 A from the structure (see supple-

mentary material). As explained in the Results section, even

such excessive concentration of divalent cations did not

affect the outcome of the simulation; thus, simulations with

lower concentration of divalent cations were not attempted.

Twenty-four Naþ ions were then added by the Xleap to

complete the neutralization. The following van der Waals

parameters for cations were used in the simulations: Naþ

radius 1.868 A and well depth 0.00277 kcal/mol, Mg2þ ra-

dius 0.7926 A and well depth 0.8947 kcal/mol.65 It is fair to

admit that the use of minimal counterions and the simula-

tion time scale do not guarantee that a Boltzmann distribu-

tion is fully established. On the other side, approximations

stemming from the simple force field indicate that it is not

advisable to increase the number of ions in the simulation

and especially to try mimic highly polarizable anions such

as Cl� and divalent cations associated with huge polariza-

tion/charge transfer effects. Such particles are fairly outside

the applicability of the force field. Several recent studies in

addition indicate good performance of the simulations with

minimal salt. Based on simulations of Kastenholz and

Hunenberger,66 periodicity effects tend to be minimized in

simulations with minimal, net-neutralizing salt (in contrast

to zero or excess salt). Simulations by Varnai and Zakrzew-

ska56 have also demonstrated surprisingly good sampling of

monovalent ions (in minimal salt), which is fully in agree-

ment with more than 2 �s of our own RNA data.16,30–34

Specifically, we have shown that even molecules that in so-

lution experiments require excess ions for folding (kink–

turn and hepatitis delta virus ribozyme) do not experience

any structural destabilization (unfolding) on the present

simulation time scale. In addition, simulations with differ-

ent initial monovalent ion placements or multiple simula-

tions reproducibly predict highly occupied monovalent cat-

ion binding sites around RNA molecules once the simula-

tions exceed ca 10 ns.

Both systems were solvated by a box of TIP3P water mol-

ecules to a distance of 12 A on each side of the solute. The

last studied system was a standard RNA duplex with the

sequence 50CGCGGCAGCCCAUCCCGGGCGCGGGCCC-CGCUUCAGC30. This structure was built in the program

Insight II (Biosym/MSI, San Diego, CA). We used a random

GC-rich sequence. (A shorter 10 ns control simulation of an

AU-rich sequence indicated overlapping results and is not

discussed in this article.) It was neutralized by 72 Naþ ions

and solvated by explicit water molecules, using the same pro-

tocol as for the helix 44. Due to the width/length proportions

of our box (ca. 1:2.5), we systematically monitored the posi-

tion of the solute in the box. The solute molecule in all three

simulations showed only limited rotation and remained

entirely inside the box for most of the simulation time. Occa-

sionally, ends of the solute molecule temporarily crossed the

box borders, but not significantly. No mutual approach of sol-

ute molecules from different boxes occurred. Thus, it was not

necessary to increase the width of the box. Simulations were

carried out using the particle mesh Ewald technique67 with 9

A nonbonded cutoff and 2-fs integration time step. Equilibra-

tion started by 5000 steps of minimization followed by 200

ps of MD, with the atomic positions of the solute molecule

fixed. Then, two series of minimization (1000 steps) and MD

simulation (20 ps) were carried out with restraints of 50 and

25 kcal/(mol � A2), which were applied to all solute atoms. In

the next stage, the system was minimized in five 1000-step

rounds with restraints [20, 15, 10, 5, and 0 kcal/(mol � A2)]

applied only to solute atoms. During the following 100 ps of

unrestrained MD, the system was heated from 50 to 300 K.

The production MD runs were carried out with constant pres-

sure boundary conditions (relaxation time of 1.0 ps). A con-

stant temperature of 300 K using the Berendsen weak-cou-

pling algorithm was applied with a time constant of 1.0 ps.

SHAKE68 constraints with a tolerance of 10�8 A were

applied to all hydrogens to eliminate the fastest X—H vibra-

tions and allow a longer simulation time step. Translational

and rotational center-of-mass motion was removed every 5 ps.

The Sander module of AMBER 6.0 was used for all

minimization and equilibration MD runs, the PMEMD

code69 was then used for production. Trajectories were ana-

lyzed using the Ptraj and the Carnal modules of AMBER

and structures were visualized using the VMD molecular

visualization program, http://www.ks.uiuc.edu/Research/

vmd/.70 The figures were prepared using VMD. The EDA51

of RNA duplexes was performed using the onv, g_covar,

and g_anaeig modules of the GROMACS package71 and

visualized using the Interactive Essential Dynamics code72

518 Reblova et al.


in VMD. Only phosphorus atoms (P) were included in this

analysis because they contain all the information needed for

the description of global motions. The overall motion was

decomposed into individual essential modes, which were

represented by the corresponding eigenvectors and eigen-

values. Helical parameters (rise, roll, tilt, twist, slide, and

shift) were calculated using the 3DNA code.49 The time se-

ries of these parameters were then used for the calculations

of local base-pair step deformability (force constants). The

methodology is described in detail and applied for DNA

steps in previous studies.35,73 We calculated the full 6 � 6

stiffness matrices related to the helical parameters for indi-

vidual base-pair steps along a sequence to obtain deform-

ability profiles of the duplex. In the present study we con-

sider only diagonal force constants that reflect free energy

changes upon deforming only one conformational parame-

ter while the others were kept at equilibrium values. The

calculations were carried out only over stable parts of the

trajectories where no opening events occur.

This work was supported by Wellcome Trust International

Senior Research Fellowship in Biomedical Science in Cen-

tral Europe GR067507 (JS), grants from the Grant Agency

of the Czech Republic GA203/05/0388 and GA203/05/

0009 (KR, FR, JS) as well as GA204/03/H016 (FR, MVK),

grants from the Ministry of Education of the Czech Repub-

lic MSM0021622413 (KR, FR, JS) and LC512 (JS), and the

research project AVOZ50040507 by Ministry of Education

of the Czech Republic (IBP). FL acknowledges the support

provided by the Swiss National Science Foundation.

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