Local thermodynamic stability scores are well represented by a non-central student's t distribution.

Local folding in mRNAs is closely associated w ith biological functions. In this study, we reveal the whole distribution of local thermodynamic stability in the complete genome of the poliovirus P3/Leon/37 and the single-stranded RNA sequences that corresponds to the nucleotide sequence of the complete genome sequence (1 667 867 bp) of Helicobacter pylori (H. pylori) strain 26695. Local thermodynamic stability in the RNA sequences is measured by two standard z -scores, significance score and stability score. To estimate the distribution of thermodynamic stability, a model based on the non-central Student's t distribution has been developed. Significant patterns of extremes that are either much more stable or unstable than expected by chance are detected. Our results indicate that the highly stable and statistically more significant folding regions are predominantly in non-coding sequences in the two genome sequences. Moreover, the highly unstable folding regions, on the contrary, are predominantly in the protein coding sequences of H. pylori. The observed differences across the complete genomic sequences are statistically very significant by a chi2-test. These extreme patterns may be useful in searching for target sequences for long-chain antisense RNA and for locating potential RNA functional elements involved in the regulation of gene expression including translation, mRNA localization and metabolism.

Thermo-debonding mechanisms in dentin bonding systems using finite element analysis.

The finite element method (FEM) has been extensively used in evaluating the interfacial status of biomaterials. We used FEM to explore the microscopic debonding mechanism of the dentin/hybrid layer/resin adhesive interface. The stress status of the local material was used as an index to judge whether the adhesive interface would develop a debonding mechanism. To generate the local stress concentration, the thermal boundary condition was applied to the model which has the phenomenon of the coefficient of thermal expansion (CTE) mismatch. The thermal boundary condition was used to emulute a previous study conducted with a laser thermoacoustic technique (LTAT). The materials, Scotchbond MP, Optibond, and Tenure bonding systems, used in the previous experiment were also tested in this study. The results show that interfacial debonding in the finite element model occurred through the hybrid layer for both the Scotchbond MP and Tenure systems, as well as within the adhesive layer itself for the Optibond system. These findings are compatible with observations by SEM obtained by LTAT. Another transformed model was created to test the "elastic cavity wall" concept. The result also confirms the importance of the elastic cavity wall concept. These compatible results between FEM and LTAT indicate that FEM can be a very useful supplement to thermoacoustic testing.

The human endogenous retrovirus K Rev response element coincides with a predicted RNA folding region.

Human endogenous retrovirus K (HERV-K) is the name given to an approximately 30-million-year-old family of endogenous retroviruses present at >50 copies per haploid human genome. Previously, the HERV-K were shown to encode a nuclear RNA export factor, termed K-Rev, that is the functional equivalent of the H-Rev protein encoded by human immunodeficiency virus type 1. HERV-K was also shown to contain a cis-acting target element, the HERV-K Rev response element (K-RRE), that allowed the nuclear export of linked RNA transcripts in the presence of either K-Rev or H-Rev. Here, we demonstrate that the functionally defined K-RRE coincides with a statistically highly significant unusual RNA folding region and present a potential RNA secondary structure for the approximately 416-nt K-RRE. Both in vitro and in vivo assays of sequence specific RNA binding were used to map two primary binding sites for K-Rev, and one primary binding site for H-Rev, within the K-RRE. Of note, all three binding sites map to discrete predicted RNA stem-loop subdomains within the larger K-RRE structure. Although almost the entire 416-nt K-RRE was required for the activation of nuclear RNA export in cells expressing K-Rev, mutational inactivation of the binding sites for K-Rev resulted in the selective loss of the K-RRE response to K-Rev but not to H-Rev. Together, these data strongly suggest that the K-RRE, like the H-RRE, coincides with an extensive RNA secondary structure and identify specific sites within the K-RRE that can recruit either K-Rev or H-Rev to HERV-K RNA transcripts.

A gender-specific mRNA encoding a cytotoxic ribonuclease contains a 3' UTR of unusual length and structure.

A cDNA (2855 nt) encoding a putative cytotoxic ribonuclease (rapLR1) related to the antitumor protein onconase was cloned from a library derived from the liver of gravid female amphibian Rana pipiens. The cDNA was mainly comprised (83%) of 3' untranslated region (UTR). Secondary structure analysis predicted two unusual folding regions (UFRs) in the RNA 3' UTR. Two of these regions (711-1442 and 1877-2130 nt) contained remarkable, stalk-like, stem-loop structures greater than 38 and 12 standard deviations more stable than by chance, respectively. Secondary structure modeling demonstrated similar structures in the 3' UTRs of other species at low frequencies (0.01-0.3%). The size of the rapLR1 cDNA corresponded to the major hybridizing RNA cross-reactive with a genomic clone encoding onconase (3.6 kb). The transcript was found only in liver mRNA from female frogs. In contrast, immunoreactive onconase protein was detected only in oocytes. Deletion of the 3' UTR facilitated the in vitro translation of the rapLR1 cDNA. Taken together these results suggest that these unusual UFRs may affect mRNA metabolism and/or translation.

Transcription-coupled translation control of AML1/RUNX1 is mediated by cap- and internal ribosome entry site-dependent mechanisms.

AML1/RUNX1 belongs to the runt domain transcription factors that are important regulators of hematopoiesis and osteogenesis. Expression of AML1 is regulated at the level of transcription by two promoters, distal (D) and proximal (P), that give rise to mRNAs bearing two distinct 5' untranslated regions (5'UTRs) (D-UTR and P-UTR). Here we show that these 5'UTRs act as translation regulators in vivo. AML1 mRNAs bearing the uncommonly long (1,631-bp) P-UTR are poorly translated, whereas those with the shorter (452-bp) D-UTR are readily translated. The low translational efficiency of the P-UTR is attributed to its length and the cis-acting elements along it. Transfections and in vitro assays with bicistronic constructs demonstrate that the D-UTR mediates cap-dependent translation whereas the P-UTR mediates cap-independent translation and contains a functional internal ribosome entry site (IRES). The IRES-containing bicistronic constructs are more active in hematopoietic cell lines that normally express the P-UTR-containing mRNAs. Furthermore, we show that the IRES-dependent translation increases during megakaryocytic differentiation but not during erythroid differentiation, of K562 cells. These results strongly suggest that the function of the P-UTR IRES-dependent translation in vivo is to tightly regulate the translation of AML1 mRNAs. The data show that AML1 expression is regulated through usage of alternative promoters coupled with IRES-mediated translation control. This IRES-mediated translation regulation adds an important new dimension to the fine-tuned control of AML1 expression.

Prediction of common secondary structures of RNAs: a genetic algorithm approach.

In this study we apply a genetic algorithm to a set of RNA sequences to find common RNA secondary structures. Our method is a three-step procedure. At the first stage of the procedure for each sequence, a genetic algorithm is used to optimize the structures in a population to a certain degree of stability. In this step, the free energy of a structure is the fitness criterion for the algorithm. Next, for each structure, we define a measure of structural conservation with respect to those in other sequences. We use this measure in a genetic algorithm to improve the structural similarity among sequences for the structures in the population of a sequence. Finally, we select those structures satisfying certain conditions of structural stability and similarity as predicted common structures for a set of RNA sequences. We have obtained satisfactory results from a set of tRNA, 5S rRNA, rev response elements (RRE) of HIV-1 and RRE of HIV-2/SIV, respectively.

Differentiation-induced internal translation of c-sis mRNA: analysis of the cis elements and their differentiation-linked binding to the hnRNP C protein.

In previous reports we showed that the long 5' untranslated region (5' UTR) of c-sis, the gene encoding the B chain of platelet-derived growth factor, has translational modulating activity due to its differentiation-activated internal ribosomal entry site (D-IRES). Here we show that the 5' UTR contains three regions with a computer-predicted Y-shaped structure upstream of an AUG codon, each of which can confer some degree of internal translation by itself. In nondifferentiated cells, the entire 5' UTR is required for maximal basal IRES activity. The elements required for the differentiation-sensing ability (i.e., D-IRES) were mapped to a 630-nucleotide fragment within the central portion of the 5' UTR. Even though the region responsible for IRES activation is smaller, the full-length 5' UTR is capable of mediating the maximal translation efficiency in differentiated cells, since only the entire 5' UTR is able to confer the maximal basal IRES activity. Interestingly, a 43-kDa protein, identified as hnRNP C, binds in a differentiation-induced manner to the differentiation-sensing region. Using UV cross-linking experiments, we show that while hnRNP C is mainly a nuclear protein, its binding activity to the D-IRES is mostly nuclear in nondifferentiated cells, whereas in differentiated cells such binding activity is associated with the ribosomal fraction. Since the c-sis 5' UTR is a translational modulator in response to cellular changes, it seems that the large number of cross-talking structural entities and the interactions with regulated trans-acting factors are important for the strength of modulation in response to cellular changes. These characteristics may constitute the major difference between strong IRESs, such as those seen in some viruses, and IRESs that serve as translational modulators in response to developmental signals, such as that of c-sis.

Ion-RNA interactions in the RNA pseudoknot of a ribosomal frameshifting site: molecular modeling studies.

The three-dimensional (3-D) structure of a RNA pseudoknot that causes the efficient ribosomal frameshifting in the gag-pro region of mouse mammary tumor virus (MMTV) has been determined recently by nuclear magnetic resonance (NMR) studies. But since the structure refinement in the studies did not use metal ions and waters, it is not clear how metal ions participate in the stabilization of the pseudoknot, and what kind of ion-RNA interactions dominate in the tertiary contacts for the RNA pseudoknotting. Based on the reported structure data of the pseudoknot VPK of MMTV, we gradually refined the structure by restrained molecular dynamics (MD) using NMR distance restraints. Restrained MD simulation of the RNA pseudoknot was performed with sodium ions and water molecules. Our results are in good agreement with known NMR data and delineate the importance of the metal ion coordination in the stability of the pseudoknot. In the non-coaxially stacking pseudoknot, stem 1 (S1), stem 2 (S2), and the intervening A14 involves unconventional stacking of base pairs coordinated by Na+ and/or bridging water molecules. A6 and G7 of loop L1 make a perfect base stacking in the major groove and are further stabilized by coordinated Na+ ions and water molecules. The first 4-nucleotide (nt) ACUC of loop L2 form a sharp turn and the following 4-nt AAAA cross the minor groove of S1 and are steadied by interactions with the nucleotides of S , bridging water molecules and coordinated Na+ ions. Our studies suggest that the metal ion plays a crucial role in the RNA pseudoknotting of VPK. In the stacking interior of S1 and S2, the Na+ ion is positioned in the major groove and interacts directly with the carbonyl group O6 of G28 and carbonyl group O4 of U13 in the wobble base pair U13:G28. The ion-RNA interactions in MMTV VPK not only stabilize the RNA pseudoknot but also modify the electrostatic properties of the nucleotides at the critical parts of the pseudoknot VPK.

Regulation of vascular endothelial growth factor (VEGF) expression is mediated by internal initiation of translation and alternative initiation of transcription.

Vascular Endothelial Growth Factor (VEGF) is a very potent angiogenic agent that has a central role in normal physiological angiogenesis as well as in tumor angiogenesis. VEGF expression is induced by hypoxia and hypoglycemia, and thus was suggested to promote neovascularization during tumor outgrowth. Yet, the molecular mechanism that governs VEGF expression is not fully characterized. VEGF induction is attributed in part to increased levels of transcription and RNA stability. Previously, we demonstrated that the 5' Untranslated Region (5' UTR) of VEGF has an important regulatory role in its expression. VEGF has an exceptionally long 5' UTR (1038 bp) which is highly rich in G+C nucleotides. This suggests that secondary structures in the 5' UTR might be essential for VEGF expression through transcriptional and post-transcriptional control mechanisms, as demonstrated for other growth factors. In this communication, we provide evidence that a computer predicted Internal Ribosome Entry Site (IRES) structure is biologically active and is located at the 3' end of the UTR. In addition, the results demonstrate that an alternative transcriptional initiation site for VEGF exists in the 5' UTR of VEGF. This alternative initiation site is 633 bp downstream of the main transcription start site and the resulting 5' UTR includes mainly the IRES structure. Therefore, our results suggest that VEGF is subjected to regulation at either translational level through a mechanism of ribosome internal initiation and/or transcriptional level through alternative initiation.

Evolution of a common structural core in the internal ribosome entry sites of picornavirus.

The translational control involving internal ribosome binding occurs in poliovirus (PV), human rhinoviruses (HRV), encephalomyocarditis virus (EMCV), foot-and-mouth disease virus (FMDV), and hepatitis A virus (HAV). Internal ribosome binding utilizes cis-acting genetic elements of approximately 450 nucleotides (nt) termed the internal ribosome entry sites (IRES) found in these picornaviral 5'-untranslated region (5'UTR). Although these IRES elements are quite different in their primary sequence, a similar folding structure with a conserved 3' structural core exists in the IRES. Phylogenetic analysis and RNA folding of the 5' UTR of picornaviruses, including PV types 1-3, coxsackievirus types A and B, swine vesicular disease virus, echoviruses, enteroviruses (human and bovine), HRV, HAV, EMCV, mengovirus, Theiler's murine encephalomyelitis viruses, FMDV, and equine rhinoviruses, indicates that the predicted conserved structural core is indeed a general structural feature for all members of the picornavirus family. The evolution of a common structural core likely occurred by the gradual addition or deletion of structural domains and elements to preserve a similar tertiary structure that facilitates the utilization of the IRES in specific host-cell environments.

Phylogenetic evidence for the improved RNA higher-order structure in internal ribosome entry sequences of HCV and pestiviruses.

The strong requirement for a small segment of the 5'-proximal coding sequence of hepatitis C virus (HCV) is one of the most remarkable features in the internal initiation of HCV mRNA translation. Phylogenetic analysis and RNA folding indicate a common RNA structure of the 5' untranslated region (UTR) of HCV and the animal pestiviruses, including HCV types 1-11, bovine viral diarrhea (BVDV), border disease virus (BDV) and hog cholera (HoCV). Although the common RNA structure shares similar features to that proposed for the internal ribosome entry sequence (IRES) of picornavirus, phylogenetic evidence suggests four new tertiary interactions between conserved terminal hairpin loops and between the terminal hairpin loop of F2b and the short coding sequence for HCV and pestiviruses. We suggest that the higher-order structures of IRES cis-acting elements for HCV and animal pestivirus are composed of stem-loop structures B-C, domains E-H, stem-loop structure J and four additional tertiary interactions. The common structure of IRES elements for these viruses forms a compact structure by these tertiary interactions and stem stacking. The active structural core is centered in the junction domain of E-H that is also conserved in all members of picornaviruses. Our model suggests that the requirement for a small segment of the 5' coding sequence is to form the distinct tertiary structure that facilitates the cis-acting function of the HCV IRES in the internal initiation of the translational control.

PDGF2/c-sis mRNA leader contains a differentiation-linked internal ribosomal entry site (D-IRES).

It has become clear that a given cell type can qualitatively and quantitatively affect the expression of the platelet-derived growth factor B (PDGF2/c-sis) gene at multiple levels. In a previous report, we showed that PDGF2/c-sis 5'-untranslated region has a translational modulating activity during megakaryocytic differentiation of K562 cells. This study points to the mechanism used for this translational modulation. The unusual mRNA leader, which imposes a major barrier to conventional ribosomal scanning, was found to contain an internal ribosomal entry site that becomes more potent in differentiating cells and was termed differentiation-linked internal ribosomal entry site (D-IRES). The D-IRES element defines a functional role for the cumbersome 1022-nucleotide-long mRNA leader and accounts for its uncommon, evolutionary conserved architecture. The differentiation-linked enhancement of internal translation, which provides an additional step to the fine tuning of PDGF2/c-sis gene expression, might be employed by numerous critical regulatory genes with unusual mRNA leaders and might have widespread implications for cellular growth and development.

A common RNA structural motif involved in the internal initiation of translation of cellular mRNAs.

The 5'-non-translated regions (5'NTR) of human immunoglobulin heavy chain binding protein (BiP), Antennapedia (Antp) ofDrosophilaand human fibroblast growth factor 2 (FGF-2) mRNAs are reported to mediate translation initiation by an internal ribosome binding mechanism. In this study, we investigate predicted features of the higher order structures folded in these 5'NTR sequences. Statistical analyses of RNA folding detected a 92 nt unusual folding region (UFR) from 129 to 220, close to the initiator AUG in the BiP mRNA. Details of the structural analyses show that the UFR forms a Y-type stem-loop structure with an additional stem-loop in the 3'-end resembling the common structure core found in the internal ribosome entry site (IRES) elements of picornavirus. The Y-type structural motif is also conserved among a number of divergent BiP mRNAs. We also find two RNA elements in the 5'-leader sequence of human FGF-2. The first RNA element (96 nt) is 2 nt upstream of the first CUG start codon located in the reported IRES element of human FGF-2. The second (107 nt) is immediately upstream of the authentic initiator AUG of the main open reading frame. Intriguingly, the folded RNA structural motif in the two RNA elements is conserved in other members of FGF family and shares the same structural features as that found in the 5'NTR of divergent BiP mRNAs. We suggest that the common RNA structural motif conserved in the diverse BiP and FGF-2 mRNAs has a general function in the internal ribosome binding mechanism of cellular mRNAs.

A common structural core in the internal ribosome entry sites of picornavirus, hepatitis C virus, and pestivirus.

Cap-independent translations of viral RNAs of enteroviruses and rhinoviruses, cardioviruses and aphthoviruses, hepatitis A and C viruses (HAV and HCV), and pestivirus are initiated by the direct binding of 40S ribosomal subunits to a cis-acting genetic element termed the internal ribosome entry site (IRES) or ribosome landing pad (RLP) in the 5' noncoding region (5'NCR). RNA higher ordered structure models for these IRES elements were derived by a combined approach using thermodynamic RNA folding, Monte Carlo simulation, and phylogenetic comparative analysis. The structural differences among the three groups of picornaviruses arise not only from point mutations, but also from the addition or deletion of structural domains. However, a common core can be identified in the proposed structural models of these IRES elements from enteroviruses and rhinoviruses, cardioviruses and aphthoviruses, and HAV. The common structural core identified within the picornavirus IRES is also conserved in the 5'NCR of the divergent viruses, HCV, and pestiviruses. Furthermore, the proposed structural motif shares a structural feature similar to that observed in the catalytic core of the group 1 intron. The conserved structural motif from these divergent sequences that looks like the common core region of group 1 introns is probably a crucial element involved in the IRES-dependent translation.

An RNA pseudoknot is an essential structural element of the internal ribosome entry site located within the hepatitis C virus 5' noncoding region.

Translation of the human hepatitis C virus (HCV) RNA genome occurs by a mechanism known as "internal ribosome entry." This unusual strategy of translation is employed by naturally uncapped picornaviral genomic RNAs and several cellular mRNAs. A common feature of these RNAs is a relatively long 5' noncoding region (NCR) that folds into a complex secondary structure harboring an internal ribosome entry site (IRES). Evidence derived from the use of dicistronic expression systems, combined with an extensive mutational analysis, demonstrated the presence of an IRES within the HCV 5'NCR. The results of our continued mutational analysis to map the critical structural elements of the HCV IRES has led to the identification of a pseudoknot structure upstream of the initiator AUG. The evidence presented in this study is based upon the mutational analysis of the putative pseudoknot structure. This is further substantiated by biochemical and enzymatic probing of the wild-type and mutant 5'NCR. Further, the thermodynamic calculations, based upon a modified RNAKNOT program, are consistent with the presence of a pseudoknot structure located upstream of the initiator AUG. Maintenance of this structural element is critical for internal initiation of translation. The pseudoknot structure in the 5'NCR represents a highly conserved feature of all HCV subtypes and members of the pestivirus family, including hog cholera virus and bovine viral diarrhea virus.

Unusual folding regions and ribosome landing pad within hepatitis C virus and pestivirus RNAs.

A statistically significant folding region is identified in the 5' untranslated region (5'-UTR) of hepatitis C virus (HCV), bovine viral diarrhea virus and hog cholera virus. This unusual folding region (UFR) detected in HCV encompasses 199 nucleotides (nt) and coincides with the reported internal ribosome entry site or ribosome landing pad (RLP), as determined by the 5' and 3' deletions [Tsukiyama-Kohara et al., J. Virol. 66 (1992) 1476-1483]. The RNA structure predicted in the UFR of HCV consists of a large stem-loop and a pseudoknot. The proposed structural model is consistent with RNase sensitivity studies [Brown et al., Nucleic Acids Res. 20 (1992) 5041-5045]. Moreover, the structure is highly conserved among these divergent HCV and pestivirus RNAs. The covariation of paired bases in the helical regions offers support for the proposed structural models. The pseudoknot predicted in these UFR shares a similar structural feature to those proposed in the RLP of cardioviruses, aphthoviruses and hepatitis A virus. Based on the common structural motif, a putative base-pairing model between HCV RNA and 18S rRNA, as well as pestiviral RNAs and 18S rRNA are suggested. Intriguingly, the proposed base-pairing models in this study are comparable to those proposed in picornaviruses in terms of their folded shape and location of the predicted complementary sequences between viral RNAs and 18S rRNA. Taken together, we suggest that the common base-pairing model between the UFR detected in the 5'-UTR of pestivirus and HCV and 18S rRNA have a general function in the internal initiation of cap-independent translation.

A method for predicting common structures of homologous RNAs.

We have developed a procedure, composed of a set of computer programs, for predicting common RNA structures of homologous sequences. Given a set of homologous RNAs, these programs perform a multiple sequence alignment, generate a list of possible helical stems that are thermodynamically favored in RNA folding from a selected individual sequence, establish a conserved stem list by inspecting the equivalent base pairings and/or conserved helical stems from the derived alignment of homologous RNAs, and build common RNA secondary structures with the maximum scores (i.e., compensatory base changes and number of base pairs, etc.). The approach is a combination of phylogenetic and thermodynamic methods and has been applied to the prediction of common folding structures of the 5' untranslated regions in a number of positive RNA viruses.

RNA tertiary structure of the HIV RRE domain II containing non-Watson-Crick base pairs GG and GA: molecular modeling studies.

We have used molecular modeling techniques to model the RNA tertiary structure of the viral RNA element (referred to as domain II of Rev responsive element, RRE) bound by the Rev protein of HIV. In this study, the initial three-dimensional model was built from its established RNA secondary structure, including three non-Watson-Crick G:G, G:A and G:U base pairs. Molecular dynamics (MD) simulations were performed with hydrated or unhydrated sodium ions. Our results indicate that the non-Watson-Crick base pairs in the simulation with unhydrated sodium ions and water are more stable than those with hydrated sodium ions only. The RNA can maintain its compact double helical structure throughout the course of the MD simulations with water and unhydrated sodium ions, although the non-Watson-Crick base pairs and two bulge loops show much more flexibility and conformational distortion than the classical RNA helical region. The distinct distortion of the sugar-phosphate backbone significantly widens the RNA major groove so that the major groove is readily accessible for hydrogen bonding by specific Rev binding. This model emphasizes the importance of specific hydrogen bonding in the stabilization of the three-dimensional structure of the HIV Rev core binding element, not only between the nucleotide bases, but also among the ribose hydroxyls, phosphate anionic oxygens, base oxygens and nitrogens, and bridging water molecules. Moreover, our results suggest that sodium ions play an important role in the formation of base pairs G:G and G:A of the RRE by a manner similar to the arginine of the Rev-RRE complex.

Distinct structural elements and internal entry of ribosomes in mRNA3 encoded by infectious bronchitis virus.

Infectious bronchitis virus (IBV) mRNA3 encodes three small proteins, 3a, 3b, and 3c, at its 5' end. Recently, it was demonstrated that initiation of protein 3c is dependent on the upstream sequence. Monte Carlo simulations of RNA folding in this tricistronic mRNA3 indicate that a highly significant folding region occurs prior to the initiator AUG of 3c. The unusual folding region (UFR) of 265 nucleotides (nt) contains the coding sequences of proteins 3a and 3b. Details of the structural analyses show that five highly significant RNA stem-loops in the UFR can be modeled into a compact superstructure by the interaction of two predicted pseudoknot structures. The folded superstructure comprising nt 44 to 330, with additional 22 nt downstream from this UFR, is suggested to serve as a ribosome landing pad (or an internal ribosomal entry site) in the cap-independent translation of the 3c of IBV. Intriguingly, the proposed structural motif of this coronavirus shares structural features similar to those proposed in a number of picornavirus mRNAs. Based on the common structural features, a plausible base pairing model between mRNA3 and 18 S rRNA is suggested, which is consistent with a general mechanism for regulation of internal initiation described in many picornaviruses.

Prediction of alternative RNA secondary structures based on fluctuating thermodynamic parameters.

In this paper we present a new method for predicting a set of RNA secondary structures that are thermodynamically favored in RNA folding simulations. This method uses a large number of 'simulated energy rules' (SER) generated by perturbing the free energy parameters derived experimentally within the range of the experimental errors. The structure with the lowest free energy is computed for each SER. Structural comparisons are used to avoid multiple generation of similar structures. Computed structures are evaluated using the energy distribution of the lowest free energy structures derived in the simulation. Predicted be graphically displayed with their occurring frequencies in the simulation by dot-plot representations. On average, about 90% of phylogenetic helixes in the known models of tRNA, Group I self-splicing intron, and Escherichia coli 16 S rRNA, were predicted using the method.