ISSN 00268933, Molecular Biology, 2012, Vol. 46, No. 1, pp. 34–46. © Pleiades Publishing, Inc., 2012. Original Russian Text © E.I. Leonova, M.V. Baranov, O.V. Galzitskaya, 2012, published in Molekulyarnaya Biologiya, 2012, Vol. 46, No. 1, pp. 37–51.
REVIEWS UDC 577.322
Formation of RNA Spatial Structures E. I. Leonovaa, b, M. V. Baranova, c, and O. V. Galzitskayaa a
Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region, 142290 Russia; email:
[email protected] b Shemyakin and Ovchinnikov Institute of Bioorganic Chemistry, Russian Academy of Sciences, Pushchino, Moscow Region, 142290 Russia c Biological Department, Lomonosov Moscow State University, Moscow, 119991 Russia Received March 3, 2011; in final form, June 21, 2011
Abstract—The review considers different experimental and theoretical approaches to the investigation of RNA folding and identification of nucleotides that critically affect the folding of molecules, such as tRNA, and several classes of ribozymes. For instance, it has been shown that nucleotides of the D and Tloop regions are the last to be involved in the tRNA structure, or, rather, they are not included in the tRNA folding nucleus. A specially developed SHAPE method was used to show that the longrecognized hierarchical fold ing model does not hold true for tRNA folding. In the second part of the review, algorithms and programs used for the prediction of RNA secondary structures, as well as for modeling RNA folding, are considered. DOI: 10.1134/S0026893312010104 Keywords: RNA folding, folding nucleus, Hbonds, base stacking, hydrophobic interactions, nonhierarchical model of folding.
INTRODUCTION
repression, regulation of certain genes, and centro meric chromatin formation; RNA interference system is also crucial for embryonic development and cell dif ferentiation [8, 9]), RNA switches (able to turn on/off both mRNA transcription and translation [10, 11]), and many others [1]. However, the functions of many noncoding RNAs so far remain unknown [1]. The major difference between RNA folding and a similar process in proteins is that RNA must establish secondary structure–associated quasinative contacts before it acquires its final spatial structure [12–15]. In contrast, in proteins, some tertiary structure contacts may appear even before the secondary structure is complete. A further point to the RNA/protein comparison is that they are both subject to Levinthal’s paradox, which indicates that they attain their native structure without searching through all possible conformations of a polypeptide/nucleotide chain [16]. In the course of folding, an RNA chain, similarly to a protein glob ula, passes through a number of transition states that may play a key role in the kinetics of the process. Energy landscapes of protein and RNA molecules rep resenting the free energy of their transition states and folding intermediates contain many transitions with similar energies. Since an RNA molecule sequence is a combination of only four nucleotides, in contrast to the 20 amino acid residues of a protein, one could expect that the transition states would be much more diverse for a protein than for RNA. However, the num ber of potential RNA folding pathways is comparable to that of a similarsized protein.
The functioning of a living cell is supported by a great number of different biochemical processes, many of which crucially involve RNA. This is not sur prising, since protein synthesis depends on a large assortment of ribosomal, messenger, transport, and regulatory RNAs. In spite of the seemingly insignifi cant differences in the RNA and DNA structure, that is, substitution of ribose for deoxyribose and uracyl for thymine, their functions differ considerably. The main reason is that DNA exists in the cell in a double stranded form, making it fairly rigid, while single stranded RNA is much more flexible and can acquire a great variety of configurations. The final conforma tion of an RNA molecule determines its function, varying much wider than just the DNA–protein mes senger: only 2% of the genome encodes mRNAs, while a larger part is transcribed as noncoding RNAs [1]. Noncoding RNAs perform numerous functions ranging from transcriptional and translational regula tion to catalysis. In addition to rRNA and tRNA, this group includes telomerase RNA (a component of the telomerase complex used as a template in the synthesis of telomeric DNA repeats [2, 3]), small nuclear RNAs (regulate mRNA transcription and posttranscriptional modification of mRNA and tRNA precursors [4, 5]), ribozymes (catalytic activity [6, 7]); small interfering RNAs (participate in antiviral defense, transgene Abbreviations: FRET, fluorescent resonance energy transfer; SAXS, small angle Xray scattering; SHAPE, selective 2hydroxyl acylation analysed by primer extension; NMIA, Nmethylisatoic anhydride.
34
FORMATION OF RNA SPATIAL STRUCTURES
ORGANIZATION OF THE PRIMARY, SECONDARY, AND TERTIARY RNA STRUCTURE Both RNA and protein molecules possess three basic organization levels: primary, secondary, and ter tiary. The primary structure of biologically active RNA is attained via posttranscriptional modification and is commonly different from the primary transcript. The abovementioned modifications may involve nucle otide methylation of ribose 2'hydroxyl, base modifi cation (e.g., to pseudouridyl and hydroxyuridyl), and nucleotide excisions or insertions. Therefore, the pri mary structure of RNA should be determined by sequencing and mass spectrometry of a biologically active form [17]. The RNA secondary structure may contain such elements as hairpins, helices, symmetric and asym metric loops, junctions and connections of three or more helices, or internal loops (Fig. 1). Although RNA molecules are singlestranded, they commonly contain complementary fragments that can interact, producing double helices. The tertiary RNA structure is formed by interacting elements of the secondary structure. Little was known about this level of RNA organization until the recent advent of techniques producing crystals for Xray crys tallography and enabling nuclear magnetic resonance (NMR) analysis of large molecules. For instance, high resolution structures were obtained for such individual RNA molecules as tRNA, the P4–P6 domain of the group I intron ribozyme of Tetrahymena termophilia, and some others. Fairly common pseudoknot struc tures are worth special attention [18] (Fig. 2). In spite of their importance for RNA functional performance, nearly all existing computer algorithms of RNA struc ture prediction do not account for pseudoknots due to the problem’s complexity. It was shown that, at low Mg2+ concentrations, tRNA acquires a loose conformation with secondary structure elements different from the classic cloverleaf [13]. Therefore, the formation and stabilization of the tertiary RNA structure depends on the presence of bivalent metal ions, especially magnesium ions: natu ral RNA mainly exists as Mg2+ salt [19]. The problem of metal ion–RNA interaction is an issue of large scientific importance. A number of stud ies have proposed different, sometimes contradictory, theoretical and experimental approaches. For instance, it has been suggested that, in contrast to dou blestranded DNA, tRNA hardly induces any counte rion condensation, while negatively charged phos phate groups of tRNA induce the charging of amino acyltRNA synthetase, allowing the enzyme to recog nize its tRNA [20]. Singlestranded RNA molecules were also used for the decondensation of DNA bound to ligands, such as spermidin, since RNA–ligand complexes have higher binding constants [21]. MOLECULAR BIOLOGY
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35 Hairpin
Double helix Loop Stem Singlestranded region
Looping out
Internal loop
Junction of three (or more) helices
Fig. 1. RNA secondary structure elements.
5
5'
10
15 20
30
25 35
40
45
3'
Pseudoknot Fig. 2. Simplified pseudoknot structure.
EXPERIMENTAL IDENTIFICATION OF RYBOZYMEFOLDING PATHWAYS Since RNA functions, similarly to protein func tions, depend on the conformation of the molecule, RNA folding processes are now successfully studied using approaches developed for protein research, such as Φanalysis [22], fluorescent resonance energy trans fer (FRET) [23], and smallangle Xray scattering (SAXS) [24]. Another technique developed specially for RNA research—SHAPE (Selective 2'Hydroxyl Acylation analyzed by Primer Extension)—allows for the identification of mobile nucleotides in RNA mol ecules of any size [25]. All the abovementioned approaches have been successfully applied to investigate the formation of complex RNA spatial structures. For instance, the transition states of RNA folding are investigated using Φanalysis in combination with FRET. There have not been many studies of this kind so far, since RNAs, sim ilarly to protein molecules, are characterized by mul tiple folding pathways and, therefore, a large number of transition states. Below, we will describe the avail able RNA folding studies employing the listed tech
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LEONOVA et al.
niques and comprehensively consider examples of sev eral tRNAs and the P4–P6 domain of the Tetrahy mena group I intron ribozyme. The characteristic feature of these molecules is that they either perform important cellular functions themselves (tRNA) or constitute a part of larger ribozymes (domain P4–P6). The P4–P6 domain of the Tetrahymena group I intron ribozyme is a selfsplicing intron of the riboso mal RNA precursor from T. thermophila. This ribozyme belongs to group I introns due to the pres ence of several short conserved sequence elements that determine its secondary structure [26]. The ribozyme comprises nine paired helical fragments P1–P9 [26]. The impact of the P1 domain on the tertiary struc ture formation of the full group I intron ribozyme was studied in [27]. P1 is a duplex of six base pairs. Appar ently, the docking of P1 to the preformed ribozyme core is the last and therefore represents the limiting stage in the formation of a functional molecule. The experiment involved introducing eight different chem ical modifications of P1 nucleotides and analyzing their effects on the correct docking of P1 to the ribozyme core by means of FRET. The modifications of the P1 duplex included substituting 2'hydroxyl of ribose by hydrogen (producing 2'deoxyribose) or by the methyl group OCH3 (producing 2'methoxyri bose). In the noncanonical GU pair located near the cleavage site, the amino group of G was substituted by hydrogen, producing inosine (I). In another variant, U of the same GU pair was substituted by C to generate a canonical GC pair. The P1 docking to the ribozyme core corresponded to a FRET signal level of ≥0.75, while for the disjointed duplex, the signal was approx imately 0.5. These data can be used to calculate the docking equilibrium constant Kdock as a ratio of the time intervals corresponding to the fully folded and unfolded states. The authors found that all of the abovementioned modifications decreased the equi librium constant more than 500fold, while the dock ing constants were decreased less than twofold. The Φ values for the modified nucleotides of P1 were calcu lated using the docking rate and equilibrium constants kdock and Kdock. P1 was assumed to be initially not docked to the rest of the ribozyme, i.e., in a quasifree state. In this case, the Φvalue was calculated using the following formula:
Φ=
ΔΔ G(kdock, modified →unmodified ) . ΔΔ G(K dock, modified →unmodified )
(1)
Φ ~ 1 implied that the given nucleotide had formed native contacts with its neighbors before the transition state was acquired, while Φ ~ 0 meant that native con tacts had not been formed by that moment. Using Φanalysis, it was shown that the P1 duplex was the last to dock to the catalytic core (Φ = 0). The authors concluded that large RNAs in their native state may be comprised of locally unfolded fragments.
Next we will consider in more detail the results concerning the P4–P6 domain of the Tetrahymena group I ribozyme. The available experimental data showed that its folding was highly cooperative and that, in an isolated P4–P6 domain, tertiary contacts were formed two times faster than in the same domain within a fullsize molecule [28]. This study investi gated the folding of the 160b P4–P6 domain of the Tetrahymena group I intron ribozyme. The authors provided several important reasons for choosing P4– P6 as their research object. Firstly, at that moment, the beststudied object was tRNA. Compared to tRNA, the 160b P4–P6 domain is considerably larger, and the investigation of its folding represents the next stage leading to the understanding of the selforganization of large nucleic acids. Secondly, the P4–P6 domain can be studied independently from the whole mole cule, since its folding is not controlled by the rest of the multidomain structure. The purpose of this study was to determine the free energy of the activation barrier and identify the transition state in the course of domain folding. To follow the formation of equilib rium tertiary structures, the folding kinetics of the pyrenelabeled P4–P6 domain at different Mg2+ con centrations was monitored using the stopflow tech nique. The observed folding rate constant kobs was assessed by changing the fluorescence intensity at dif ferent Mg2+ concentrations, and the free activation energy ΔG# of Mg2+ induced domain folding was cal culated using the formula kobs = (kBT/h)exp(–ΔG#/kBT).
(2)
For instance, at a Mg2+ concentration of approxi mately 10 mM, P4–P6 folded within milliseconds with kobs of 15 to 31 s–1. For the given folding rate con stant, ΔG# lies within the range of 8 to 16 kcal/mol. The relatively wide range obtained for free energy may be due to the uncertainty regarding the preexponential factor used in the formulas for kobs and ΔG#. In the Eyring equation used in this case, the preexponential factor was suggested for small molecule reactions in the gas phase. However, the P4–P6 molecule is fairly large, and the use of the kBT/h factor may be question able. In spite of this problem, the activation energy values obtained in the study look fairly reasonable, as they agree with the limit of the known free energy bar rier of tertiary folding of protein and RNA molecules (typically, a few kcal/mol). To identify the nucleotides included in the folding nucleus and affecting the folding of P4–P6, several mutations were introduced into the domain (Fig. 3). The Φvalues were determined based on the changes in the free energies of folding and the stable state. In spite of some thermodynamic differences, the folding rates of wildtype and mutated P4–P6 were similar. At the same time, the fact that Φ = ΔΔ G # ΔΔ G o ~ 0 indicated that, in the transition state, these nucle otides had not yet formed their native contacts. MOLECULAR BIOLOGY
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FORMATION OF RNA SPATIAL STRUCTURES
It was shown that the observed folding rate constant kobs depended on the Mg2+ concentration and was sig nificant at 1 mM Mg2+. It increased with growing magnesium ion concentration and reached the plateau at 30 mM Mg2+. The reason for this is that the transi tion state of the molecule is largely unfolded; accord ingly, the transition state can be attained with no more than one magnesium ion per molecule, while remote interactions require more ions for formation. How ever, a further increase in the magnesium concentra tion does not affect the folding rate due to the confor mational rearrangement of the magnesiumbound structure elements. In general, the authors admit that their singlestep description of ribozyme folding probably does not rep resent the full picture, since it does not account for folding intermediates; the reason is that the available data are insufficient to visualize all stages of the pro cess. It is still unknown what the structure of an unfolded molecule is and what interactions must be disrupted to initiate folding and attain the transition state. Most likely, in the absence of Mg2+, these inter actions are nonnative. The very high activation barrier disagrees with the nearly unfolded transition state, which probably means that there exist denatured mol ecules with residual nonnative structures that must be unfolded to achieve a unique native structure. The hairpin ribozyme of the tobacco ringspot virus catalyzes the cleavage and ligation of viral RNA in the course of rollingcircle replication. This ribozyme (studied in [29]) comprises two helical (helix–loop– helix) domains A and B existing in the stretched (unfolded) or active compact (folded) conformation (Fig. 4). FRET analysis showed that the catalytic cen ter is formed through the juxtaposition of the two domains and interaction between their A and B loops. It was also applied to evaluate the folding and unfolding rates. The folding rate constant was equal to 0.018 s–1 for all 760 folding pathways. The unfolding rate con stants fell into four groups: k1 = 0.001 s–1, k2 = 0.1 s–1, k3 = 0.8 s–1, and k4 = 6 s–1. In some cases, the molecule unfolding took several hours, and, in several cases, it did not unfold at all. To identify the contacts formed in the transition state of the hairpin ribozyme, the authors used Φanal ysis [22] to study the nucleotides of the ribose zipper. Under standard conditions, the dG11 mutation resulted in a 12.3fold increase in the unfolding con stant kU and in an only 2.9fold increase in the folding constant kN. The Φvalues were low, indicating that the ribose zipper among G11, A10 (domain A) and А24, and C25 (domain B) was formed partially (Fig. 4). The U42 mutation (dC12) resulted in a 4.4fold increase in kU and a 1.7fold increase in kN. In this case, the Φ values were also low, so the contacts between U42 (domain B) and C12 (domain A) were also partial. Finally, the g + 1 : C25 pair was substituted by a weaker one—a + 1 : U25—increasing kU 34fold and leaving kN unchanged. The Φvalues were equal to zero, mean MOLECULAR BIOLOGY
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37
200
P5a
G174A
120
P5
180
dC109:dG110
ΔC209
U168C:U177G
P4 U167C
140
P5c
P6
160
P5b 220
P6a
P6b 240
Fig. 3. Secondary structure of the P4–P6 domain and the sites of mutations introduced.
50 Helix 3 20
45
–5 Helix 2
42
12 11
24
5
+1 25 +5 30
Loop B
Loop А
Helix 1
5' Cy5
35 Helix 4
3' 3' Cy3
Domain А
5' Biotin Domain B
Fig. 4. Folded fluorophorelabeled fragment of the hairpin ribozyme. Solid lines represent the tertiary contacts within the pairs g+1–C25, G11–A and A11–C25 (ribose zipper), and C12–U42.
ing that the respective contacts were lacking in the transition state. These experiments identified those native contacts that already exist in the folding nucleus of the hairpin ribozyme. Although the Watson–Crick g +1 : C25 pair is not yet formed in the transition state,
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LEONOVA et al.
the contacts of the ribose zipper are already being formed. It should be noted that no tertiary contacts were formed in the transition folding state of the P4–P6 domain of the Tetrahymena group I intron ribozyme [28]. The folding of this fragment was studied at differ ent magnesium ion concentrations, and it was shown that, with growing Mg2+ concentration, the activation energy of the transition state decreased considerably. It was concluded that electrostatic interactions serve to make the transition state of the molecule more com pact and more similar to the native structure. Under standard conditions, the Mg2+ concentration was taken 12 mM. However, the Φvalues hardly changed with growing magnesium ion levels. RNase P RNA is a catalytic RNA molecule responsible for tRNA processing. Rnase P RNAs from Bacillus subtilis and Escherichia coli differ in their ter minal sequences and represent different RNase P classes (Fig. 5). The formation of their Sdomain intermediates was investigated using SAXS and Lan gevin dynamics simulation (LD) [14]. Two intermedi ate models were analyzed. The extended molecule structure was modeled based on either electrostatic interactions (first model) or on specific interactions between nucleotides (second model). Accordingly, the models were used to study how the folding process is affected by electrostatic interactions and special con tacts within the RNA structure, respectively. Earlier it was shown that the equilibrium intermediates of the 154b Sdomain of B. subtilis RNase P RNA typically have a more extended form than the native structure [14]. The most recent study was aimed at identifying the factors affecting the form of intermediates. A SAXSbased analysis showed that intermediate struc tures comprised three helical domains joined at the center. The angle between the first and second domains was approximately ~180°, in contrast to approximately ~60° observed in the native structure. The third domain was positioned perpendicularly to the first two both in intermediates and in the native structure. An experiment was performed at different concentrations of monovalent cations, but their effect on the intermediate conformation was insignificant, while domains 1 and 2 were extended. On the other hand, the effect of Mg2+ on the molecule conforma tion was also studied, considering that RNA interac tion with bivalent ions is much stronger [14]. However, magnesium ions had little effect on the intermediate conformation. Only when the Mg2+ level surpassed 10 mM did the RNA molecules acquire their native structure. A similar experiment was performed with the P4–P6 domain of Tetrahymena group I intron ribozyme and produced similar results: at Mg2+ con centrations below 10 mM, the intermediate structures remained extended. It was concluded that this confor mation cannot be explained by purely electrostatic effects. When five different LD trajectories were con sidered, most interactions between nucleotides
changed, but not the spatial positioning of the tree helical domains. It was shown that intermediate struc tures contained a nonnative C134–G176 pair, which determined the extended form of these molecules. In the native conformation, these nucleotides are located far from each other. Next, C134–G176 was substi tuted by C–U. In the absence of monovalent ions, the folding patterns of the mutant and wildtype mole cules were very similar, as shown by measuring the gyration radius Rg and the pair distribution function Рr. However, in the presence of 0.2 M NaCl, the mutant molecule had a significantly smaller Rg and, consequently, a more compact intermediate confor mation. Similar results were obtained for the Sdomain of RNase P of E. coli. It was concluded that the extended conformation of Sdomain intermedi ates is due to specific nucleotide contacts in the struc ture and not to electrostatic repulsion [14]. EXPERIMENTAL ANALYSIS OF THE NATIVE tRNA FOLDING PATHWAYS Nucleotide sequences of tRNA molecules are fairly similar, and their length varies from 74 to 95 b (50 to 60 b for mitochondrial tRNAs) [19]. A comparison of tRNA sequences representing all life domains identi fied the conserved elements of tRNA molecules, that is, U8, A14, the GG motif in loop D, U33, several res idues of the Tloop, and the 3'terminal CCA sequence. Thus, conserved residues in tRNAs of dif ferent species are preserved to interact with proteins and rRNAs. At some positions, only purines or only pyrimidines are found; these are termed semicon served bases. Another prominent feature of tRNA is the presence of several modified (minor) bases. They appear at certain positions due to posttranscriptional modifications by specific enzymes. The most common ones are ribothymidine (T); pseudouridine (Ψ); 5,6dihydrouridine (D); and inosine (I). The cloverleaf secondary structure of all tRNAs includes the following elements [19]: 1. A dihydrouridine (D) hairpin containing dihy drouridine nucleotides; its length varies among differ ent tRNAs; 2. Thymidyl–pseudouridyl (TΨ) hairpin, contain ing a constant GTΨCGA or GTΨCAA sequence in the loop; 3. Anticodon (AC) hairpin, with a loop of seven nucleotides in all tRNAs; 4. An acceptor stem (AA) with a constant CCA sequence at the 3' end; 5. A variable (V) loop, which strongly varies in length among different tRNAs. All hairpin stems are Atype double helices; the Lform tertiary structure is produced by interactions between secondary structure elements (Fig. 6a). One of the first experimental works determining the RNA folding cores employed Φanalysis for inves MOLECULAR BIOLOGY
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FORMATION OF RNA SPATIAL STRUCTURES I
A A G
P12
39
A A U U *G C G A U
200 C
G U A C G U A
G A A G
J11/12
U
G
G
G A
G 220
G A A
U G A
C
G
C A
P11
C C G C G G* U A U A A 180 G C
P10
A
C C
A
G
P7
C
A
P10.1
II
G C U U A C G C G U A A *A U*A A *A G G *A U A C G G C U G C A*U C A U *G A U G C G U C U
5'
gC G
3'
cG C U C
*
G
A G U C
A
* *
A G C G
U C C
*
C GU C GG A G
*
A U A A G
P8
A
C
U
A
G G
A U
*
G C A G U CUU
120
P9
III
Fig. 5. Secondary structure of the S domain of B. subtilis RNase P RNA.
tigating the transition state in the course of tRNA unfolding [30]. The study was performed with syn thetic tRNAPhe with unmodified bases. The technique used was based on the approach suggested by Klarke and Fersht for protein investigation and involving intromission of additional disulfide bonds [22]. Depending on the position of the introduced bonds, the transition state may be destabilized and the unfold ing rate decreased or the transition and native states may be stabilized while the unfolding rate remains unchanged. Consequently, if a disulphide bridge binds two residues that are disconnected before or during the transition state is attained during denaturation, the unfolding rate decreases. A disulfide bond within a pair unfolded after the transition state does not affect the unfolding rate. Thus, several denaturation experi ments were performed with tRNAPhe to identify the MOLECULAR BIOLOGY
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native contacts that are the last to appear in the course of folding [30]. In the first experiment, a disulfide bond joined nucleotides U1 and U72 of the AA stem (Fig. 6b, site 1); in the second one, it joined C11 and C25 of the hairpin D folding onto the interposed V loop (Fig. 6b, site 2). Finally, a disulfide bridge con nected loops D (U16) and ТΨ (C60). Each time, the free energy difference ΔGF# was calculated for the folded tRNA molecule and the transition state. Next, the ΔGF# values were compared for molecules with and without disulfide bonds (wildtype). The unfold ing process occurred at 20−35°С, i.e., below the RNA melting temperature. It was found that the disulfide bonds introduced in the AA stem and D loop did not affect the ΔGF# value. The disulfide bond between the D and ТΨ loops changed ΔGF# by approximately 0.80 kcal/mol. At the same, the unfolding of the tRNA
40
LEONOVA et al. (a)
(b)
Site 1
O S S
N
SS
3'end
Site 1
O
HO
5'end
U1 TΨloop
N
O
O
Site 2
O
OH OH
N
Site 2
NH2 N OH
N
O
O
O
O
OH O
SS
U72
OH OH
N HO
C11
Site 3
OH
N
O
NH2
SS
N
S
C25
OH OH
S
Dloop Site 3
O
NH2 N
NH HO
АСloop
U16
N
O
O
O OH O
OH
N O
S
S
C60
OH OH
Fig. 6. (a) tRNAPhe and introduced disulfide bonds. Site 1 shows a bridge between U1 and U72; site 2, a bridge between C11 and C25; site 3, a bridge between U16 and C60. (b) Detailed structure of disulfide bonds.
with a disulfide bond occurred in two steps: the first one was temperaturedependent and corresponded to the tertiary structure melting, and the second one was temperatureindependent and reflected the subse quent minor configuration changes. The results obtained suggested that native contacts between the D and ТΨ loops are the last to be formed in the course of tRNAPhe folding, which is probably related to the strong repulsion between negatively charged phos phate groups. Moreover, the authors suppose that the described order of tertiary structure formation may be a common feature of other tRNA molecules.
HIV nucleocapside protein + viral genome
HIV nucleocapside protein R1
R2 5'
3'
Fig. 7. Fluorophorelabeled tRNA. R1 and R2 are dis tances between fluorophores. On the lefthand side, the AA stem is not unwound. On the righthand side, the AA stem is unwound simultaneously with viral RNA hybrid ization.
The FRET technique was used to investigate the initiation of the reverse transcription of the HIV genome [31]. One of the tRNALys acceptor chains acts as a primer for DNA synthesis. Consequently, its hybridization to the primer site of viral RNA requires the AA stem to be unwound. Using fluorescent labels at the 3' and 5'ends of tRNALys, it was shown that the viral nucleocapside protein accelerates the acceptor chain denaturation considerably. However, the pres ence of viral genetic material is indispensable; other wise, the nucleocapside protein cannot perform its function (Fig. 7). Therefore, the AAstem denatur ation occurs simultaneously with the viral RNA hybridization. Until recently, it has been assumed that RNA fold ing is a strictly hierarchical process: energetically sta ble elements of the secondary structure, including nucleotide pairs, are formed first, followed by tertiary RNA structure formation [32, 33]. However, Wilkin son et al. [15] dispute this model, since their newly developed SHAPE technique showed that, in syn thetic tRNAAsp lacking modified bases, the loss of ter tiary contacts commonly coincides with base unpair ing of the secondary structure elements. SHAPE is a technique delivering information on the local molecular environment of a particular nucle otide as a function of temperature. For this purpose, NMIA (Nmethylisatoic anhydride), which is a struc turesensitive reagent capable of acylating the 2' hydroxyl of a nucleotide and not involved in second ary or tertiary structure formation, is used. The MOLECULAR BIOLOGY
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B O
O
O
O−
O−
P O
B O
O
O
O−
OH
O
O N
NMIA
P O
O
41
Immobile conformation and low activity
CO2
B O O
O
O P O
O−
O−
O P
B
O
O−
O O O N H
Mobile conformation and high activity Fig. 8. NMIA–2' hydroxyl reaction [15]. Ribose can exist in different conformations: it does not react with NMIA when the 3'phosphodiester group is close to the 2'hydroxyl group, but a reaction is possible when these two groups are further apart.
2' hydroxyl reactivity can also be inhibited by a neigh boring 3'phosphodiester anion (Fig. 8). For instance, free nucleotides are involved in the reaction more readily than those, the conformational mobility of which is restricted due to the pairing to other nucle otides. Higher temperatures result in an increasing conformation mobility of tRNA; some nucleotides get unpaired and can react with NMIA. SHAPE analysis involves RNA treatment with NMIA and initiation of cDNA synthesis with reverse transcriptase (Fig. 9). Transcription will be interrupted at RNA nucleotides containing NMIAmodified ribose. A study was performed for temperatures ranging from 35 to 75°С with a step of ≤3.5°С. At each tem perature, tRNAAsp was treated with NMIA, and the mobile nucleotides were identified using primer extension. Altogether, five groups were recognized: 1. Ten positions, including all bases of the ТΨ loop, that remained unbound to NMIA at all temperatures; 2. Ten tRNAAsp nucleotides (G18, U19, C20, U33, G34, U35, G37, C38, C75, and A76) that, in contrast, react with NMIA at all temperatures. They are mainly located in the Dloop and at the 3'end of the acceptor stem; 3. Nucleotides, the activity of which was gradually growing with increasing temperature; MOLECULAR BIOLOGY
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4. Some nucleotides of the D and ТΨloops that were reactive at 35°С and the reaction capacity of which grew dramatically with increasing temperature; 5. Three positions that were capable of reaction with NMIA from the beginning, but the reaction capacity of which changed uniquely. For instance, the reaction capacity of G73 was first growing with increasing temperature, but then declined. To employ these results for the description of tRNAAsp folding intermediates, the nucleotides were divided into eight groups by the reaction capacity at different melting temperatures; each group contained nucleotides located in adjacent tRNAAsp regions. Initially, for a temperature of 35°С, the SHAPE data were in agreement with the canonical structure of tRNAAsp: nucleotides within all loops and at the 3'end of the acceptor stem, as well as one G–U pair of the anticodon hairpin, reacted with NMIA, whereas nucleotides involved in the secondary and tertiary structure levels did not react with NMIA. At the second stage, at 51°С, tertiary interactions between the D and ТΨloops and the A9–U13 bond were disrupted, retaining the secondary structure and interactions between pyrimidine rich regions G10– U13. At the third step, at 53°С, the D stem was fully unwound and the stacking interactions between G6, A7, and C49 of ТΨ and the acceptor stem were dis
42
LEONOVA et al. Forward primer 5'linker
5'
3'
Promoter
tRNA gene
5'
3'
Reverse transcription primer binding site
3'
5' 3'linker Reverse primer
PCR transcription in vitro
tRNA
UC U G UC C G U G G U G C G C C 3'linker G G C C G C G C G U G U A A U A U U C G CC A A U C
AA C G C G G C G C G U CU
Reverse transcription primer binding site 3'
5' 5'linker
Fig. 9. RNA transcript and the structural cassette linked to RNA by transcription from a PCRgenerated template.
rupted. The tertiary interactions of purinerich frag ments (G22–U25) also disappeared. The results obtained for different temperatures using the SHAPE approach demonstrated the com plexity of internucleotide interactions in balanced conformation states of tRNAAsp and their incomplete agreement with the hierarchical folding model. It was shown that hairpins can melt by fragments, asymmet rically, and, at the same time, singlestranded frag ments can shift and form new pairs. In other words, at higher temperatures, the whole tRNA molecule can acquire alternative conformations. The authors con cluded that the hierarchical tRNA folding model was insufficient to predict the conformational equilibrium states of tRNAAsp. Hopefully, further studies involving SHAPE analy sis will accumulate sufficient information to deter mine the internucleotide interactions in the folding of other RNA molecules. RNA STRUCTURE PREDICTION Theoretical studies are commonly focused on pre dicting the secondary and tertiary RNA structure or on describing the RNA folding kinetics presented as a free energy landscape. In this section, we will consider the existing algorithms used for the first task. RNA folding and secondary structure formation are crucial for correct RNA functioning. The investi gation of the secondary RNA structure began immedi ately after Watson and Crick’s discovery of base pairing in 1953. In the last decades, the problems of molecular
biology, including RNA folding, have increasingly been addressed using computerbased approaches. The knowledge concerning RNA structures is growing rapidly. However, the number of possible sec ondary RNA structures also increases greatly with growing RNA molecule length. For instance, 16S rRNA comprises approximately 1500 nucleotides and can potentially form over 15000 helices, but only less than 100 are actually included in the final structure. For instance, the maximal number of all possible per mutations of helix combinations that would finally produce utterly different structural models of 16S rRNA was estimated at 4.3 × 10393 [34]. The above mentioned estimate illustrates Levinthal’s paradox [16]: it takes a fraction of a second for an unfolded polymer (protein or RNA) to attain its native structure choosing from an enormous number of possible con formations, while, theoretically, the search would require more than the Universe’s lifetime. Levinthal proposed that the native protein structure is specified by kinetics rather than stability or thermodynamics; i.e., it corresponds not to the global but to the rapidly attainable free energy minimum [35]. The problem of RNA folding pathways, as well as of protein folding, is still a highly controversial issue. Experiments investigating large polymer molecules are mainly performed in vitro, i.e., under conditions that cannot fully represent a living cell’s environment. It is still unclear whether similar processes occur in vivo. Computer simulation experiments seek to take into account all of the factors affecting RNA folding in a solution; however, the simulation conditions are also strongly simplified and only account for a few thermo dynamic parameters. Nevertheless, in many cases, such simplifications do not affect the outcome of an experiment and can be used for the sake of optimizing and accelerating computations. All currently existing algorithms can predict either the structure of a single RNA molecule or the structure of the RNA–DNA or ribozyme–ribozyme com plexes. The algorithms described below predict the sec ondary structure of a single RNA molecule without pseudoknots. Zuker and Stiegler’s algorithm of free energy mini mization [36] employs the RNA sequence as input data and searches for the structure with the minimal free energy using the dynamic programming approach. The method is based on the nearest neighbor model. Lyngsö et al. reduced the time complexity and improved the optimization technique of the algorithm [37]. Mathews et al. suggested considering up to 750 structures in the neighborhood of the energy min imum to improve the accuracy [38]. Zuker and Stie gler’s program mfold [39] is available at http:// mfold.rna.albany.edu/?q=mfold. The partition function algorithm is another dynamic programming algorithm suggested by McCa MOLECULAR BIOLOGY
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skill for RNA molecules without pseudoknots [40]. It involves the calculation of a number of molecule structures and their partition function:
Q=
∑e
−ΔG(S )
RT
,
(3)
S
where the summation is performed over all potential RNA folding structures. Based on the partition func tion Q, the probability of a particular structure S can be calculated as follows: −ΔG(S ) RT P(S) = 1 e . Q
(4)
However, biologically, RNA is rather characterized by a set of constantly interchanging similar structures [40] (also termed as a kinetic group of objects [41]). For this reason, this algorithm is focused on calculat ing the probabilities of RNA structures of the same group or class of similar structures. These substruc tural classes are important, because they represent the major features of the structure set. Eventually, the equilibrium probability of each possible base pair can be calculated, and the relationship between the pairing probability and the optimal structure can be visual ized. The author tested his method using four natural RNA sequences with known structures and showed that the actual base pairs were predicted with a high, although not the highest possible, probability. The partition function algorithm is included in the Vienna software package [42]. Thus, both the minimal free energy algorithm and the partition function algorithm share two important shortcomings: (1) they cannot predict structures with pseudoknots; (2) they largely employ simplified ther modynamic models. In addition, there are several further approaches to RNA structure prediction. For instance, a large group of comparative analysis algorithms was developed by Gutell et al [34]. A comparative analysis algorithm is based on two simple, but efficient, principles : (1) dif ferent RNA molecules may acquire the same second ary structure, and (2) the unique RNA structure and function are a product of mutations and selection in the course of evolution. The prediction results are usu ally compared with the available crystal structures. The comparative analysis group includes several methods; one of them is based on the identification of structural motifs and predicts 70% of base pairs. There are also algorithms combining thermody namic models with comparative analysis. A method suggested by Hofacker [43] for secondary structure calculation for a set of aligned RNA sequences simul taneously employs the thermodynamic stability and sequence correlation. The RNAalifold program is also included in the Vienna package. MOLECULAR BIOLOGY
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RNA FOLDING MODELING Although the primary structure of RNA is simple, these molecules are involved in a large number of bio logical processes. The spatial structure and folding of large RNA molecules have recently been a subject of extensive research [44]. The RNA secondary structure, in comparison to proteins, contains fewer contacts between remote chain fragments [45]. However, it is their behavior that specifies the nature of the helix–globule transition in large RNA molecules: helices formed through the pairing of remote fragments melt simultaneously by secondorder phase transition, while those formed by neighboring chain fragments melt nearly indepen dently [46]. Kinetic studies of the heteropolymer chain self organization have shown that the folding rate depends strongly on both the external conditions [47–50] and the sequence itself [51]. For protein models, it was shown that the geometric properties of the native state affect both the folding rate and the native state stability [51–53]. For instance, on the one hand, nonlocal contacts are essential for restoring the native structure [53], and, on the other hand, protein model structures containing a large number of nonlocal contacts acquire their stable structure by two orders of magni tude faster than models with many local contacts [51]. It would be natural to suppose that the folding of large RNA molecules implying a search through an enor mous number of possible structures also employs cer tain facilitating geometric factors. In our previous studies [54, 55], it was shown that, for an RNA secondary structure model, such a factor was the presence of highenergy contacts between remote chain fragments in the native structure: sequences, which were “geometrically edited” to adjust native contact energies so that the contacts between the most remote fragments were the stron gest, acquired their native state in optimized external conditions (temperature and efficient component interaction) by an order of magnitude faster than ran dom sequences. When a discrete molecular dynamics algorithm previously used in protein modeling was applied to RNA, it predicted well both 3D structures and the folding kinetics [56]. For calculations based on this algorithm, the molecule structure was simplified and considered. The essence of the model is that the exper imentally obtained full atomic structure is approxi mated by a coarsegrained model in such a manner that each nucleotide corresponds to three points: P is the center of mass of the phosphate group nearly coin ciding with the phosphorus of PO4, S is the center of mass of the ribose, and B is a point representing the base, i.e., the center of mass of the sixmember purine or pyrimidine ring. The model was tested using 153 RNA sequences available from the nucleic acid database (NDB). The selected molecules were 10 to
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100 nucleotides long (shorter RNA molecules do not possess a recognizable tertiary structure) and repre sented the major types of tertiary structure: Lform RNA, a hairpin, and a pseudoknot structure. First, for each RNA, the unfolded state was modeled, and then the replica exchange algorithm was run for different temperatures. The major algorithm for calculating the RNA fold ing pathway kinetics employed the discrete molecular dynamics approach [56]. The replica exchange algo rithm was used to present the energy landscape of fold ing pathways. The energy landscape is very rough: it consists of ripples and slopes leading to energy wells that correspond to the stable states of a molecule or its free energy minima. A global minimum is achieved more rapidly at higher temperatures. The replica exchange algorithm is used to surmount the energy barriers in the landscape. The idea is that the folding of numerous identical molecule models is simulated simultaneously for different temperatures, and the data obtained by modeling individual molecules’ fold ing are combined using a Monte–Carlo algorithm. The latter serves to exchange temperatures Ti and Tj between replicas i and j (with energies Ei and Ej) during preassigned time intervals. The temperature exchange is performed using the Metropolis Monte Carlo method with an exchange probability of p = 1 if Δ = (1/kBTi – 1/kBTj)(Ej – Ei) ≤ 0 and p = exp(–Δ) if Δ > 0 [57]. The replica exchange algorithm is used to rapidly fill in accessible RNA conformation spaces. For the sake of simplicity, the algorithm employs eight tem peratures: 0.200, 0.208, 0.214, 0.220, 0.225, 0.230, 0.235, and 0.240 (in conventional units). The abovementioned model was successfully applied for predicting tRNA folding cores. The algo rithm designed for studying protein folding/unfolding processes [58] was also efficient for tRNA [59]. For four tRNA molecules with available free state struc tures (tRNAPhe, tRNAAsp, tRNAfMet, and tRNALys), the Φvalue profiles were calculated. These profiles agreed with experimental data, indicating that the nucle otides of the D and Tloops are the last to be involved in the tRNA structure or, more precisely, they are not included in the tRNA folding core. The high Φvalues obtained for the anticodon loop nucleotides indicate that this is where the tRNA folding core is located. The great diversity of RNA biological functions implies that different molecules may employ different folding pathways. It is still unclear what structural ele ments determine the folding of different RNA types and how a molecule chooses the kinetic folding path ways. Both theoretical and experimental approaches must be developed to identify the respective structures and to describe the kinetic folding pathways. Studies concerning RNA folding modeling should take into account the available data discussed in this review.
ACKNOWLEDGMENTS The authors are grateful to the referee, A.K. Surin, and O.M. Selivanova for their valuable critical com ments and helpful advice given regarding the text of this paper. This work was supported by the Russian Founda tion for Basic Research (project no. 110400763), Russian Academy of Sciences (programs “Molecular and Cell Biology” (project no. 01200959110) and Basic Research for Medicine), and the Federal Agency for Science and Innovations (project no. 16.512.11.2204). REFERENCES 1. Makarova Yu.A., Kramerov D.A. 2007. Noncoding RNAs. Biochemistry (Moscow). 72, 1161–1178. 2. Koziel J.E., Fox M.J., Steding C.E., Sprouse A.A., Herbert B.S. 2011. Medical genetics and epigenetics of telomerase. J. Cell Mol. Med. 15, 457–467. 3. Caslini C. 2010. Transcriptional regulation of telomeric noncoding RNA: Implications on telomere biology, replicative senescence and cancer. RNA Biol. 7, 18–22. 4. Makarova Yu.A., Kramerov D.A. 2007. Noncoding RNAs. Mol. Biol. (Moscow). 41, 214–227. 5. Taft R.J., Pang K.C., Mercer T.R., Dinger M., Mattick J.S. 2010. Noncoding RNAs: Regulators of disease. J. Pathol. 220, 126–139. 6. Zhang J., Lau M.W., FerréD’Amaré A.R. 2010. Ribozymes and riboswitches: Modulation of RNA function by small molecules. Biochemistry. 49, 9123– 9131. 7. FerréD’Amaré A.R., Scott W.G. 2010. Small self cleaving ribozymes. Cold Spring Harb. Perspect. Biol. 2, a003574. 8. PeraltaZaragoza O., BermúdezMorales V.H., MadridMarina V. 2010. RNA interference: Biogenesis molecular mechanisms and its applications in cervical cancer. Rev. Invest. Clin. 62, 63−80. 9. Ketting R.F. 2011. The many faces of RNAi. Dev. Cell. 20, 148−161. 10. Mulhbacher J., StPierre P., Lafontaine D.A. 2010. Therapeutic applications of ribozymes and riboswitches. Curr. Opin. Pharmacol. 10, 551−556. 11. Baird N.J., Kulshina N., FerréD’Amaré A.R. 2010. Riboswitch function: Flipping the switch or tuning the dimmer? RNA Biol. 7, 328−332. 12. Thirumalai D., Hyeon C. 2005. RNA and protein fold ing: Common and variations. Biochemistry. 44, 13, 4957–4970. 13. Draper D. 1996. Parallel worlds. Nature Struct. Biol. 3, 397−400. 14. Baird N.J., Gong H., Zaheer S.S., Freed K.F., Pan T., Sosnick T.R. 2010. Extended structures in RNA folding intermediates are due to nonnative interactions rather than electrostatic repulsion. J. Mol. Biol. 397, 1298− 1306. 15. Wilkinson K.A., Merino E.J., Weeks K.M. 2005. RNA SHAPE chemistry reveals nonhierarchical interactions MOLECULAR BIOLOGY
Vol. 46
No. 1
2012
FORMATION OF RNA SPATIAL STRUCTURES
16. 17.
18.
19.
20.
21. 22. 23. 24.
25.
26.
27.
28.
29.
30.
31.
32.
dominate equilibrium structural transitions in tRNAAsp transcripts. J. Am. Chem. Soc. 127, 4659–4667. Levinthal C. 1968. Are there pathways for protein fold ing? J. Chem. Phys. 65, 44–45. Batey R.T., Rambo R.P., Doudna J.A. 1999. Tertiary motifs in RNA structure and folding. Angew. Chem. Int. 38, 2326–2343. Dost B., Han B., Zhang S., Bafna V. 2006. Structural alignment of pseudoknotted RNA. Proc. Int. Conf. on Research in Computational Molecular Biology (RECOMB), LNBI 3909. Berlin: Springer, pp. 143–158. Spirin A.S. 2011. Molekulyarnaya biologiya. Ribosomy i biosintez belka (Molecular Biology: Ribosomes and Protein Biosynthesis). Moscow: Akademiya. Ivanov V.V., Stepanenko V.A., Zrelov P.V., Zhel tukhin E.I., Chirgadze Yu.N., Sivozhelezov V.S., Polo zov R.V. 2009. Toward protein–DNA stereochemical recognition codes. In: Mathematical Modeling and Computational Physics (MMC’2009): Book of Abstracts of the International Conference, Dubna, July 7–11. Gubna: OIYaI, 2009, p. 152. Tsumuto K., Yoshikawa K. 1999. RNA switches the higherorder structure of DNA. Biophys. Chem. 82, 1–8. Fersht A. 1999. Structure and Mechanism in Protein Sci ence. N.Y.: Freeman. Förster T. 1948. Zwischenmolekulare Energiewan derung und Fluoreszenz. Ann. Physik. 437, 55–75. Svergun D.I., Feigin L.A. 1985. Rentgenovskoe i neitronnoe malouglovoe rasseyanie (SmallAngle Xray and Neutron Scattering). Moscow: Nauka. Merino E.J., Wilkinson K.A., Coughlan J.L., Weeks K.M. 2005. RNA structure analysis at single nucleotide reso lution by selective 2'hydroxyl acylation and primer extension (SHAPE). J. Am. Chem. Soc. 127, 4223– 4231. Fedorenko E.C., Irodov D.M., Kordyum V.A. 1995. Properties of ribozyme from Tetrahymena thermophilia. Biopolim. Kletka. 11, 20–29. Bartley L.E., Zhuang X., Das R., Chu S., Herschlag D. 2003. Exploration of the transition state for tertiary structure formation between an RNA helix and a large structured RNA. J. Mol. Biol. 328, 1011–1026. Silverman S.K., Cech T.R. 2001. An early transition state for folding of the RNA P4–P6 RNA domain. RNA Soc. 7, 161–166. Bokinsky G., Rueda D., Misra K., Rhodes M.M., Gor dus A., Babcock H.P., Walter N.G., Zhuang X. 2003. Singlemolecule transitionstate analysis of RNA fold ing. Proc. Natl. Acad. Sci. U.S.A. 100, 9302–9307. Maglott E.J., Goodwin J.T., Glick G.D. 1999. Probing the structure of an RNA tertiary unfolding transition state. J. Am. Chem. Soc. 121, 7461–7462. Chan B., Weidemaier K., Yip W.T., Barbara P.F., MusierForsyth K.M. 1999. IntratRNA distance mea surements for nucleocapsid proteindependent tRNA unwinding during priming of HIV reverse transcription. Proc. Natl. Acad. Sci. U.S.A. 96, 459–464. Tinoco I.J., Bustamante C. 1999. How RNA folds. J. Mol. Biol. 293, 271–281. MOLECULAR BIOLOGY
Vol. 46
No. 1
2012
45
33. Privalov P.L., Filimonov V.V. 1978. Thermodynamic analysis of transfer RNA unfolding. J. Mol. Biol. 122, 447–464. 34. Gutell R.R., Lee J.C., Cannone J.J. 2002. The accu racy of ribosomal RNA comparative structure models. Curr. Opin. Struct. Biol. 12, 301–310. 35. Finkelstein A.V. and Ptitsyn O.B. 2005. Fizika belka: Kurs lektsii s tsvetnymi i stereoskopicheskimi illyus tratsiyami i zadachami (Protein Physics: A Course of Lectures with Color and Stereoscopic Illustrations and Example Problems). Moscow: Universitet. 36. Zuker M., Stiegler P. 1981. Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 9, 133–148. 37. Lyngsø R.B., Zuker M., Pedersen C.N. 1999. Fast eval uation of internal loops in RNA secondary structure prediction. Bioinformatics. 15, 440–445. 38. Mathews D.H., Sabina J., Zuker M., Turner D.H. 1999. Expanded sequence dependence of thermody namic parameters improves prediction of RNA second ary structure. J. Mol. Biol. 288, 911–940. 39. Zuker M. 2003. Mfold web server for nucleic acid fold ing and hybridization prediction. Nucleic Acids Res. 31, 3406–3415. 40. McCaskill J.S. 1990. The equilibrium partition func tion and base pair binding probabilities for RNA sec ondary structure. Biopolymers. 29, 1105–1119. 41. Andronescu M.S. 2000. Algorithms for predicting the secondary structure of pairs and combinatorial sets of nucleic acid strands. Master Science Thesis. Bucharest, Romania: Academy of Economic Studies. 42. Schuster P., Fontana W., Stadler P.F., Hofacker I.L. 1994. From sequences to shapes and back: A case study in RNA secondary structures. Proc. Biol. Sci. 255, 279– 284. 43. Hofacker I.L., Fekete M., Stadler P.F. 2002. Secondary structure prediction for aligned RNA sequences. J. Mol. Biol. 319, 1059–1066. 44. Woodson S.A. 2010. Compact intermediates in RNA folding. Annu. Rev. Biophys. 39, 61–77. 45. De Gennes P.G. 1968. Statistics of branching and hair pin helices for the dAT copolymer. Biopolymers. 6, 715–729. 46. Gutin A.M., Galzitskaya O.V. 1993. Helix–coil transi tion in an elementary model of large natural RNA: 1. Allowance only for native helices. Biofizika. 38, 84–92. 47. Socci N.D., Onuchic J.N. 1994. Folding kinetics of proteinlike heteropolymers. J. Chem. Phys. 101, 1519–1528. 48. Galzitskaya O.V., Finkelstein A.V. 1995. Folding of chains with random and edited sequences: Similarities and differences. Protein Eng. 8, 883–892. 49. Galzitskaya O.V., Finkelstein A.V. 1996. Computer simulation of secondary structure folding of random and “edited” RNA chains. J. Chem. Phys. 105, 319– 325. 50. Sali A., Shakhnovich E., Karplus M. 1994. Kinetics of protein folding: A lattice model study of the require
46
LEONOVA et al. ments for folding to the native state. J. Mol. Biol. 235, 1614–1636.
51. Abkevich V.I., Gutin A.M., Shakhnovich E.I. 1995. Impact of local and nonlocal interactions on thermo dynamics and kinetics of protein folding. J. Mol. Biol. 252, 460–471. 52. Leopold P.E., Montal M., Onuchic J.N. 1992. Protein folding funnels: A kinetic approach to the sequence structure relationship. Proc. Natl. Acad. Sci. U.S.A. 89, 8721–8725. 53. Go N., Taketomi H. 1978. Respective roles of short and longrange interactions in protein folding. Proc. Natl. Acad. Sci. U.S.A. 75, 559–563. 54. Galzitskaya O.V. 1997. Geometrical factor and physical reasons for its influence on the kinetic and thermody namic properties of RNAlike heteropolymers. Fold Des. 2 (3), 193–201.
55. Galzitskaia O.V. 1997. Effect of the energy of distant contacts on the time of finding the native structure for RNAlike heteropolymers. Mol. Biol. (Moscow). 31, 409–412. 56. Ding F., Sharma S., Chalasani P., Demidov V.V., Broude N.E., Dokholyan N.V. 2008. Ab initio RNA folding by discrete molecular dynamics: From structure prediction to folding mechanisms. RNA Soc. 14, 1164– 1173. 57. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. 1953. Equation of state calcula tions by fast computing machines. J. Chem. Phys. 21, 1087–1092. 58. Galzitskaya O.V., Finkelstein A.V. 1999. A theoretical search for folding/unfolding nuclei in 3D protein struc tures. Proc. Natl. Acad. Sci. U.S.A. 96, 11299–11304. 59. Pereyaslavets L.B., Baranov M.V., Leonova E.I., Gal zitskaya O.V. 2011. Prediction of folding nuclei in tRNA molecules. Biochemistry (Moscow). 76, 236–244.
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