Chapter 6

Predictive Methods Using RNA Sequences

11 小节

041

Introduction

PDF page 175-177；印刷页码 155-157

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English SourcePDF extracted

Predictive Methods Using RNA Sequences

Michael F. Sloma, Michael Zuker, and David H. Mathews

Introduction

RNAisaversatilebiopolymerthatplaysmanyrolesbeyondsimplycarryingandrecognizing

genetic information as messenger RNA (mRNA) and transfer RNA (tRNA), respectively. It

has been known for decades that RNA sequences can catalyze RNA cleavage and ligation

(DoudnaandCech2002)andthatRNAisanimportantcomponentofthesignalrecognition

particle(SRP)(WalterandBlobel1982)thatdirectstheexportofproteinsoutofthecell.More

recently, additional roles for RNA have been discovered. Ribosomal RNAs (rRNAs) catalyze

peptide bond formation during protein synthesis (Nissen et al. 2000; Hansen et al. 2002),

small nuclear RNAs (snRNAs) and self-splicing introns catalyze pre-mRNA splicing reac-

tions, microRNAs (miRNAs) and small interfering RNAs (siRNA) regulate gene expression

by binding to mRNAs, and mRNAs regulate their own expression by binding metabolites

viaRNAstructurescalledriboswitches.RNAplaysrolesinothercrucialprocessesincluding

development (Lagos-Quintana et al. 2001; Lau et al. 2001) and the immune system (Cullen

2002). Furthermore, RNA can be made to evolve in vitro to catalyze reactions that do not

occurinnature(Bittkeretal.2002).

RNAisalsoanimportanttargetandagentforthepharmaceuticalindustry.Intheribosome,

RNAisthetargetofseveralclassesofantibiotics.mRNAisthetargetofdrugsthatworkonthe

antisenseprinciple(DiasandStein2002)orbyRNAinterference,alsoknownasRNAi(Cas-

tanottoandRossi2009).RecentworkhasshownthatRNAcanbetargetedspecificallybysmall

molecules(Disneyetal.2016).

To fully understand the mechanism of action or to target an RNA sequence, the structure

of the RNA under investigation needs to be understood. RNA structure has three levels

of organization, as shown in Figure 6.1 (Tinoco and Bustamante 1999). The first level – the

primary structure (Figure 6.1a) – is simply the linear sequence of nucleotides in the RNA

molecule. The secondary structure (Figure 6.1b) is defined by the base-pairing interactions

(both Watson–Crick pairs and G-U pairs) that take place within the RNA polymer. Finally,

thetertiarystructure(Figure6.1c)isthethree-dimensionalarrangementoftheatomsinthe

RNAsequenceand,therefore,includesallthenon-canonicalcontacts.

Often, the secondary structure of an RNA sequence is solved before its tertiary structure

becausethereareaccurateexperimentalandcomputationalmethodsfordeterminingthesec-

ondary structure of an RNA sequence and because knowledge of the secondary structure is

oftenhelpfulindesigningconstructsfortertiarystructuredetermination.AtypicalRNAsec-

ondarystructure,illustratedinFigure6.2,iscomposedofbothhelicalandloopregions.The

helical regions are composed of canonical base pairs. The loop regions take different forms,

dependingonthenumberofclosingbasepairsandthedistributionofunpairednucleotides.

Theycanbehairpinloops,inwhichthebackbonemakesa180 ∘bend;internalloops,inwhich

ahelixisinterruptedwithtwostrandsofunpairednucleotides;bulgeloops,inwhichahelix

isinterruptedwithasinglestrandofunpairednucleotides;andmultibranchloops(alsocalled

Bioinformatics,FourthEdition.EditedbyAndreasD.Baxevanis,GaryD.Bader,andDavidS.Wishart.

CompanionWebsite:www.wiley.com/go/baxevanis/Bioinformatics_4e

156 Predictive Methods Using RNA Sequences

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Figure 6.1 The three levels of organization of RNA structure. (a) The primary sequence, (b) the secondary

structure (Cannone et al. 2002), and (c) the tertiary structure (Cate et al. 1996) of a domain of the group I

intron from T etrahymena. The secondary structure illustrates the canonical base pairs and the tertiary

structure captures the three-dimensional arrangement of atoms. Reproduced with permission of AAAS.

helicaljunctions),fromwhichmorethantwohelicesexit.Althoughsecondarystructuredia-

grams often do not explicitly illustrate nucleotide interactions in loop regions, these regions

areresponsibleforthenon-canonicalinteractionsthatstabilizethestructure.

In the absence of a tertiary structure, the “gold standard” for predicting the placement

of loops and helices is comparative sequence analysis, which uses evolutionary evidence

found in sequence alignments to determine base pairs (Pace et al. 1999) (see also Chapter 8

for information on multiple sequence alignment methods). Base pairs predicted by compar-

ative sequence analysis for large (LSU) and small subunit (SSU) rRNA were 97% accurate

whencomparedwithhigh-resolutioncrystalstructures(Gutelletal.2002).

RNA structure prediction is a large field, with hundreds of computational tools available

for predicting the structure of an RNA molecule. This chapter presents some of the most

popular methods used to deduce RNA secondary structure based on sequence. This chapter

also presents ways in which additional information can be used to improve structure pre-

dictionaccuracy,includingmethodsthatfindacommonstructureformultiplehomologous

sequencesandmethodsthatuseexperimentaldata.Tothatend,RNAfoldingthermodynamics

anddynamicprogrammingareintroduced.TheMfoldandRNAstructure webservers,com-

monlyusedtoolsforpredictingRNAsecondarystructure,aredescribedindetail.Alternative

software tools are also mentioned. This chapter concludes with a brief introduction to the

methodsusedforRNAtertiarystructureprediction.Additionalresourceswithmorein-depth

informationonspecifictoolsareprovidedfortheinterestedreader.

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Figure 6.2 The RNA secondary structure of the 3 ′untranslated region of the Drosophila sucinea R2 ele-

ment (Lathe and Eickbush 1997; Mathews et al. 1997). Base pairs in non-helical regions, known as loops,

are colored by type of loop, which is labeled.

中文译文

第6章使用RNA序列的预测方法

作者：Michael F. Sloma, Michael Zuker, David H. Mathews

引言

RNA是一种多功能生物聚合物，其功能远超简单携带和识别遗传信息——分别作为信使RNA（mRNA）和转运RNA（tRNA）。几十年来，学界已知RNA序列可以催化RNA的切割和连接反应（Doudna and Cech 2002），并且RNA是信号识别颗粒（signal recognition particle, SRP）（Walter and Blobel 1982）的重要组成部分，负责指导蛋白质向细胞外转运。最近，研究人员又发现了RNA的更多功能。核糖体RNA（rRNA）在蛋白质合成过程中催化肽键形成（Nissen et al. 2000; Hansen et al. 2002），小核RNA（snRNA）和自剪接内含子催化pre-mRNA的剪接反应，微RNA（miRNA）和小干扰RNA（siRNA）通过结合mRNA来调控基因表达，而mRNA则通过名为核糖开关（riboswitch）的RNA结构结合代谢物来自我调控表达。RNA还在其他关键过程中发挥作用，包括发育调控（Lagos-Quintana et al. 2001; Lau et al. 2001）和免疫系统（Cullen 2002）。此外，RNA还可以在体外被进化以催化自然界中不发生的反应（Bittker et al. 2002）。

RNA也是制药行业的重要靶点和工具。在核糖体中，RNA是多种抗生素的作用靶点。mRNA是反义原理药物（Dias and Stein 2002）或RNA干扰（RNA interference, RNAi）药物的作用靶点（Cossarizzo and Rossi 2009）。近期研究表明，RNA可以被小分子特异性靶向（Disney et al. 2016）。

要充分理解某种RNA的作用机制或对其进行靶向研究，需要了解所研究RNA的结构。RNA结构具有三个层次的组织方式（如图6.1所示，Tinoco and Bustamante 1999）。第一层——一级结构（primary structure）（图6.1a）——即RNA分子中核苷酸的线性序列。二级结构（secondary structure）（图6.1b）由RNA聚合物内部发生的碱基配对相互作用（包括沃森-克里克配对和G-U配对）所定义。最后，三级结构（tertiary structure）（图6.1c）是RNA序列中原子的三维排列，因此包含所有非经典接触。

通常，RNA序列的二级结构先于其三级结构被解析，这是因为目前已有精确的实验和计算方法来确定RNA序列的二级结构，且了解二级结构往往有助于设计三级结构解析的构建体。如图6.2所示，典型的RNA二级结构由螺旋区和环区组成。螺旋区由经典碱基配对构成。环区有多种形式，取决于闭合碱基对的数量和未配对核苷酸的分布。环区可以是发夹环（hairpin loop，骨干做180°弯折）、内部环（internal loop，两个未配对核苷酸链中断一个螺旋）、凸出环（bulge loop，单个未配对核苷酸链中断一个螺旋）以及多分支环（multibranch loop，亦称螺旋连接点，helical junction，意为有两个以上螺旋从中伸出）。尽管二级结构图通常不明确显示环区中的核苷酸相互作用，但这些区域负责形成稳定结构的非经典相互作用。

在没有三级结构的情况下，预测环和螺旋位置的"金标准"是比较序列分析（comparative sequence analysis），即利用序列比对中发现的进化证据来确定碱基配对（Pace et al. 1999）（关于多重序列比对方法的信息另见第8章）。通过比较序列分析预测的大亚基（LSU）和小亚基（SSU）rRNA碱基对，与高分辨率晶体结构相比，准确率达到97%（Gutell et al. 2002）。

RNA结构预测是一个庞大的领域，目前已有数百种计算工具可用于预测RNA分子的结构。本章介绍一些基于序列推断RNA二级结构的最常用方法。此外，本章还介绍可提高结构预测准确性的方法，包括寻找多个同源序列共有结构的方法，以及利用实验数据的方法。为此，本章将介绍RNA折叠热力学和动态规划算法。详细描述两种常用的RNA二级结构预测网络服务器——Mfold和RNAstructure，并提及其他替代软件工具。本章最后简要介绍用于RNA三级结构预测的方法，并为有兴趣深入了解的读者提供更多资源。

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图6.1说明（原文图注）：

> RNA结构三个层次组织的示意图。（a）一级序列，（b）二级结构（Cannone et al. 2002），以及（c）四膜虫（Tetrahymena）I组内含子结构域的三级结构（Cate et al. 1996）。二级结构展示了经典碱基配对，三级结构捕捉了原子的三维排列。经AAAS授权转载。

图6.2说明（原文图注）：

> 果蝇（Drosophila）sucinea R2元件3'非翻译区的RNA二级结构（Lathe and Eickbush 1997; Mathews et al. 1997）。非螺旋区（称为环）中的碱基配对按环的类型着色并标注。

术语表（21 条）

English	中文
[x] RNA	RNA（核糖核酸）
[x] mRNA	mRNA（信使RNA）
[x] tRNA	tRNA（转运RNA）
[x] rRNA	rRNA（核糖体RNA）
[x] snRNA	snRNA（小核RNA）
[x] miRNA	miRNA（微RNA）
[x] siRNA	siRNA（小干扰RNA）
[x] SRP	SRP（信号识别颗粒）
[x] RNAi	RNAi（RNA干扰）
[x] riboswitch	核糖开关
[x] primary structure	一级结构
[x] secondary structure	二级结构
[x] tertiary structure	三级结构
[x] hairpin loop	发夹环
[x] internal loop	内部环
[x] bulge loop	凸出环
[x] multibranch loop	多分支环
[x] helical junction	螺旋连接点
[x] comparative sequence analysis	比较序列分析
[x] LSU	大亚基（Large SubUnit）
[x] SSU	小亚基（Small SubUnit）

042

Overview of RNA Secondary Structure Prediction Using Thermodynamics

PDF page 177-178；印刷页码 157-158

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English SourcePDF extracted

Overview of RNA Secondary Structure Prediction Using Thermodynamics 157

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Double helix

Figure 6.2 The RNA secondary structure of the 3 ′untranslated region of the Drosophila sucinea R2 ele-

ment (Lathe and Eickbush 1997; Mathews et al. 1997). Base pairs in non-helical regions, known as loops,

are colored by type of loop, which is labeled.

Overview of RNA Secondary Structure Prediction Using

Thermodynamics

ManymethodsforRNAsecondarystructurepredictionrelyonanearestneighbormodelfor

predictingthestabilityofanRNAsecondarystructure,intermsoftheGibbsfreeenergychange

at 37∘C( ΔG∘

(Box 6.1) (Xia et al. 1998, 1999; Mathews et al. 1999a, 2004; Turner 2000;

Turner and Mathews 2010). The rules for predicting stability use a nearest neighbor model

becausethestabilityofeachbasepairdependsonlyonthemostadjacentpairsandthetotal

freeenergyisthesumofeachcontribution.In-depthreviewsofthedeterminationofnearest

neighborparametersfromexperimentsareavailable(SchroederandTurner2009;Andronescu

etal.2014).

Box 6.1 Gibbs Free Energy

The Gibbs free energy of formation for an RNA structure ( ΔG∘) quantiﬁes the equilib-

rium stability of that structure at a speciﬁc temperature. For example, consider an RNA

structure A that is at equilibrium with the random-coil (i.e. unstructured) conformation.

(Continued)

158 Predictive Methods Using RNA Sequences

Box 6.1 (Continued)

The relative concentration of each conformation is governed by the equilibrium con-

stant, Keq, as illustrated in Figure 6.3a. Keq is related to the Gibbs free energy by the

relationship:

Keq = [ConformationA]

Random coil =e−ΔG∘∕RT (6.1)

where R is the gas constant (1.987 cal mol −1 K−1)a n d T is the absolute temperature (in

Kelvin).

Furthermore, for multiple alternative conformations, A and B, for which there is an

equilibrium distribution of conformations, K′

eq, as shown in Figure 6.3b, describes the

distribution of strands between the structures. In this case, the free energy of each con-

formation relative to the random coil also describes the population of each conformation:

K

′

eq = [ConformationA]

[ConformationB] =e−(ΔG∘

A−ΔG∘

B)∕RT (6.2)

This generalizes to any number of conformations. Therefore, the lowest free energy

conformation is the most probable conformation for an RNA molecule at equilibrium. This

is commonly called the minimum free energy structure.

Free energies are expressed in units of joules per mole (J mol

−1)i nS Iu n i t s .C o m m o n l y ,

for RNA folding stability, these are still frequently expressed in units of kilocalorie per

mole (kcal mol

−1), where a calorie= 4.184 J. A difference in the Gibbs free energy change of

1.42 kcal mol−1 at 37∘C (human body temperature; 310.15 K) changes the equilibrium con-

stant by a factor of 10, which can be shown by plugging 1.42 kcal mol−1 in forΔG∘

A −ΔG∘

B

in Eq. (6.2).

Random coil

(unstructured)

Conformation A

Keq

(a)

Random coil

(unstructured)

Conformation A

K′eq

Conformation B

(b)

Figure 6.3 An illustration of the equilibria of RNA

structures in solution. (a) The equilibrium between

conformation A and the random coil structure. K

eq,

which is related to the standard state free energy

change at 37 ∘C( ΔG∘

37), describes the equilibrium.

(b) The equilibrium between two conformations, A and

B, and the random coil. K′

eq, which is related to the

free energy of folding for both A and B, describes the

population of conformation A versus conformation B.

AnexampleofanearestneighborstabilitycalculationisshowninFigure6.4.Termsforheli-

calstacking,loopinitiation,andunpairednucleotidestackingcontributetothetotalconforma-

tionalfreeenergy.Favorablefreeenergyincrementsarealwayslessthanzero.Thefreeenergy

increments of base pairs are counted as stacks of adjacent pairs. The consecutive CG base

pairs,forexample,contribute −3.3kcalmol

−1 (Xiaetal.1998).Notethattheloopregionshave

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Figure 6.4 Prediction of conformational free energy for a conforma-

tion of RNA sequence CCUUGAGGAACACCAAAGGGG. Each contribut-

ing free energy increment is labeled. The total free energy is the sum

of the increments. For this estimated stability of −5.2 kcal mol

−1,

there is a population of 4600 folded strands to every one unfolded

(K

eq = 4600; Box 6.1).

中文译文

第6章利用 RNA 序列的预测方法

6.2 基于热力学的 RNA 二级结构预测概述

许多 RNA 二级结构预测方法都依赖于最近邻模型（nearest neighbor model）来预测 RNA 二级结构的稳定性，以 37°C 时的吉布斯自由能变化（ΔG°37）来衡量（见 Box 6.1）（Xia et al. 1998, 1999; Mathews et al. 1999a, 2004; Turner 2000; Turner and Mathews 2010）。预测稳定性的规则采用最近邻模型，是因为每个碱基对的稳定性仅取决于与其最相邻的碱基对，而总自由能是各个贡献之和。关于从实验数据测定最近邻参数的方法，已有详尽的综述可供参考（Schroeder and Turner 2009; Andronescu et al. 2014）。

Box 6.1 吉布斯自由能

RNA 结构的形成吉布斯自由能（ΔG°）量化了该结构在特定温度下的平衡稳定性。例如，考虑一种 RNA 结构 A，它与无规卷曲（random coil，即无规整结构）构象处于平衡状态（图 6.3a）。每种构象的相对浓度由平衡常数 Keq 决定。Keq 与吉布斯自由能的关系为：

$$K_{\text{eq}} = \frac{[\text{Conformation A}]}{[\text{Random coil}]} = e^{-\Delta G^\circ / RT} \quad (6.1)$$

其中 R 为气体常数（1.987 cal mol⁻¹ K⁻¹），T 为绝对温度（单位为开尔文）。

此外，对于多种可供选择的构象 A 和 B，它们与无规卷曲之间存在构象的平衡分布（图 6.3b），K′eq 描述了链在各结构之间的分布。在这种情况下，每种构象相对于无规卷曲的自由能同样可以描述各构象的占比：

$$K'_{\text{eq}} = \frac{[\text{Conformation A}]}{[\text{Conformation B}]} = e^{-(\Delta G^\circ_A - \Delta G^\circ_B) / RT} \quad (6.2)$$

这一关系可以推广到任意数量的构象。因此，在平衡状态下，具有最低自由能的构象是 RNA 分子最可能的构象，这通常被称为最小自由能结构（minimum free energy structure）。

自由能的单位通常用焦耳每摩尔（J mol⁻¹，SI 单位）表示。但在 RNA 折叠稳定性的研究中，常用的仍是千卡每摩尔（kcal mol⁻¹），其中 1 cal = 4.184 J。在 37°C（人体温度；310.15 K）时，吉布斯自由能变化相差 1.42 kcal mol⁻¹会使平衡常数改变 10 倍，这可通过在式 (6.2) 中代入 ΔG°A − ΔG°B = 1.42 kcal mol⁻¹ 来验证。

图 6.3 溶液中 RNA 结构平衡的示意图

(a) 构象 A 与无规卷曲结构之间的平衡。Keq 与 37°C 时标准态自由能变化 ΔG°37 相关，描述了这一平衡。(b) 两种构象 A 和 B 与无规卷曲之间的平衡。K′eq 与 A 和 B 两种构象的折叠自由能相关，描述了构象 A 与构象 B 之间的比例。

图 6.4 展示了一个最近邻稳定性计算的示例。螺旋堆叠（helical stacking）、环起始（loop initiation）和未配对核苷酸堆叠（unpaired nucleotide stacking）的贡献加合在一起，构成总构象自由能。有利的自由能增量始终为负值。碱基对自由能增量以相邻碱基对的堆叠形式计算。例如，连续的 CG 碱基对贡献 −3.3 kcal mol⁻¹（Xia et al. 1998）。请注意，环区域具有不利的自由能增量，称为环起始能（loop initiation energy），这主要反映了限制环中核苷酸的熵代价。例如，四核苷酸发夹环的起始自由能变化为 5.6 kcal mol⁻¹（Mathews et al. 2004）。环中未配对的核苷酸可以作为堆叠核苷酸或错配对提供有利的能量增量。图 6.4 中所示的 3′ 末端的 G 称为悬末端（dangling end），它堆叠在末端碱基对上，贡献 −1.3 kcal mol⁻¹ 的稳定性。发夹环中与该序列环境对应的第一个错配贡献 −1.1 kcal mol⁻¹ 的稳定性。

图 6.4 RNA 序列 CCUUGAGGAACACCAAAGGGG 某一构象的自由能预测

各自由能增量的贡献已标注。总自由能是各增量之和。对于这一估计的稳定性 −5.2 kcal mol⁻¹，每一条折叠链对应约 4600 条未折叠链（Keq = 4600；见 Box 6.1）。

最近邻自由能参数利用序列依赖项来预测环区域的自由能增量（Mathews et al. 1999a），以反映实验观察结果。例如，2×2 内部环（internal loop，两侧各有 2 个未配对核苷酸的内部环）的稳定性可从 −2.6 到 +2.8 kcal mol⁻¹ 不等，取决于闭合对（closing pair）和错配的序列（Schroeder et al. 1999）。

具有最低 ΔG° 的结构是在平衡状态下最可能的结构，但这并不能说明结构平衡的全部。另一个有用的量——配分函数（partition function）Q，通过对每种构象的平衡常数求和，提供了 RNA 分子结构ensemble（S，即 RNA 分子可能采取的所有结构的集合）的描述：

$$Q = \sum_{s} e^{-\Delta G^\circ / RT} \quad (6.3)$$

配分函数可用于计算 ensemble 中 RNA 分子采取构象 A 的概率：

$$P(A) = \frac{e^{-\Delta G^\circ_A / RT}}{Q} \quad (6.4)$$

在预测结构时，具有最低 ΔG° 的结构可能具有较低的单独概率。然而，许多低自由能结构可能包含相同的碱基对，因此这些碱基对具有很高的形成概率。RNA 结构中特定碱基对形成的概率由下式给出：

$$P(i \text{ 与 } j \text{ 配对}) = \frac{1}{Q} \sum_{s' \in s_{ij}} e^{-\Delta G^\circ_{s'} / RT} \quad (6.5)$$

其中 sij 是核苷酸 i 与核苷酸 j 配对的所有结构的集合。

配分函数是许多计算方法研究 RNA 结构的基础，包括：识别多条序列的共同结构的方法（Harmanci et al. 2011; Will et al. 2012）、识别改变 RNA 结构的突变的方法（Halvorsen et al. 2010; Sabarinathan et al. 2013; Salari et al. 2013），以及估计寡核苷酸结合可及性的方法（Lu and Mathews 2007; Tafer et al. 2008）。

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术语表

英文术语	中文译名
nearest neighbor model	最近邻模型
Gibbs free energy	吉布斯自由能
random coil	无规卷曲
equilibrium constant	平衡常数
minimum free energy structure	最小自由能结构
helical stacking	螺旋堆叠
loop initiation energy	环起始能
dangling end	悬末端
internal loop	内部环
partition function	配分函数
ensemble	构象集合/ensemble

043

Dynamic Programming

PDF page 179-180；印刷页码 159-160

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English SourcePDF extracted

Dynamic Programming 159

unfavorableincrementscalledloopinitiationenergiesthatlargelyreflectanentropiccostfor

constrainingthenucleotidesintheloop.Forexample,thehairpinloopoffournucleotideshas

aninitiationfreeenergychangeof5.6kcalmol −1 (Mathewsetal.2004).Unpairednucleotides

in loops can provide favorable energy increments either as stacked nucleotides or as mis-

matchedpairs.The3

′-mostGshowninFigure6.4,calledadanglingend,stacksontheterminal

basepairandprovides −1.3kcalmol −1 ofstability.Thefirstmismatchinthehairpinloopwith

thissequencecontextcontributes −1.1kcalmol −1 ofstability.

Thenearestneighborfreeenergyparametersutilizesequence-dependenttermsforpredict-

ing the free energy increments of loop regions (Mathews et al. 1999a) to reflect experimen-

tal observations. For example, the 2×2 internal loop (an internal loop with two unpaired

nucleotidesoneachsideoftheloop)canvaryinstabilityfrom −2.6to +2.8kcalmol

−1 depend-

ingonthesequenceoftheclosingpairandmismatches(Schroederetal.1999).

Thestructurewiththelowest ΔG∘isthemostlikelystructureatequilibrium,butthisisnot

everythingthatthereistoknowabouttheequilibriumofstructures.Anotherusefulquantity,

thepartitionfunction Q,providesadescriptionofthestructuralensemble(denotedas s,the

setofallstructuresthattheRNAmoleculecanadopt)ofanRNAmoleculebysummingthe

equilibriumconstantofeachconformation:

Q =

∑

s

e−ΔG∘∕RT (6.3)

ThepartitionfunctioncanbeusedtocalculatetheprobabilitythatanRNAmoleculeinthe

ensembleofstructuresadoptsconformation A:

P(A)= e−ΔG∘

A∕RT

Q (6.4)

Whenpredictingstructures,thestructurewiththelowest ΔG∘canhavealowprobability.

However,manyofthelowfreeenergystructureswillcontainthesamebasepairs,andthose

pairscanthushaveahighprobabilityofforming.Theprobabilityofaspecificbasepairforming

inanRNAstructureisgivenby:

P(ipairedto j)= 1

Q

∑

s′∈sij

e

−ΔG∘

s′∕RT (6.5)

wheresij isthesetofstructuresinwhichthenucleotideatindex iispairedtothenucleotide

atindex j.

PartitionfunctionsarethebasisformanycomputationalmethodstostudyRNAstructure,

including methods to identify a common structure for multiple sequences (Harmanci et al.

2011;Willetal.2012),toidentifymutationsthatalterRNAstructure(Halvorsenetal.2010;

Sabarinathan et al. 2013; Salari et al. 2013), and to estimate accessibility to oligonucleotide

binding(LuandMathews2007;Taferetal.2008).

Dynamic Programming

Intheprevioussection,thermodynamicruleswereintroducedforRNAsecondarystructure

prediction that require searching the full space of possible structures, either to find the best

scoringstructureortocalculatetheequilibriumconstantforeachstructure.Howisthissearch

performed?Thenaiveapproachwouldbetoexplicitlygenerateeverypossibleconformation,

evaluatethefreeenergyofeach,andthenchoosetheconformationthathadthelowest(best)

freeenergy.

O n ee s t i m a t ei st h a tt h e r ea r e( 1 . 8 )

N secondary structures possible for a sequence of

N nucleotides (Zuker and Sankoff 1984) – that is 3×1025 structures for a modest length

sequence of 100 nucleotides. Given a fast computer that can calculate the free energy for

10000 structures in a second, this approach would require 1.6×1014 years! Clearly, a better

solutionneedstobeimplementedforaproblemofthissize.

160 Predictive Methods Using RNA Sequences

Figure 6.5 A simple RNA pseudoknot. This ﬁgure illustrates two representations of the same simple,

H-type pseudoknot. A pseudoknot is deﬁned by two base pairs such that i–j and i′–j′ are two pairs

with ordering i < i′ < j < j′. The base pair between nucleotides i and j deﬁnes an enclosed region. The

base pair between nucleotides i′ and j′ spans the enclosed region and an adjacent region, making the

pseudoknot.

The most commonly employed solution for cases such as this is called dynamic

programming, which uses recursion and tabulation of intermediate results to accelerate

the calculation (Nussinov and Jacobson 1980; Zuker and Stiegler 1981). Appendix 6.A

describesthismethodindetailfortheinterestedreader.Thedynamicprogrammingapproach

can find both the minimum free energy structure and the partition function much faster

thanbruteforce,withanasymptoticperformancethatscaleswithcomputationaltimeby N

(denoted as O(N3)) and O(N2) in data storage for sequences of length N when pseudoknots

are excluded from the calculation (Box 6.2). A pseudoknot, illustrated in Figure 6.5, occurs

whentherearenon-nestedbasepairs(Liuetal.2010).Forexample,thesimplestpseudoknot

occurswhentherearetwobasepairs i–j and i′–j′ such that i < i′ < j < j′. It had been assumed

that pseudoknots could not be predicted by a polynomial time dynamic programming until

Rivas and Eddy (1999) presented a polynomial time dynamic programming algorithm that

can predict structures containing a certain class of pseudoknots that is sufficiently rich

to cover all cases of practical importance. However, their algorithm is O(N6) in time and

O(N4) in storage, making the calculation impractical for sequences longer than about 300

nucleotides (Rivas and Eddy 1999; Condon et al. 2004). Other adaptations of the algorithm

have improved scaling, but are still limited in practice to the sequence length on which they

can be applied (Reeder and Giegerich 2004). A partition function algorithm that includes

pseudoknots (Dirks and Pierce 2003) is O(N5) in time and O(N4) in storage, and is likewise

only useful for sequences up to 200 nucleotides in length.

Box 6.2 Algorithm Complexity

In computer science, algorithm complexity describes the scaling of a calculation in the

worst case scenario. It is expressed using the “big-O” notation, which can be read as “order.”

Algorithms that are O(N) in time require a linear increase in computational time as the

size parameter, N, increases. O(N2) and O(N3) algorithms scale by the square and cube of

the parameter N, respectively. Therefore, the dynamic programming algorithm for RNA

secondary structure prediction, which is O(N3), where N is the number of nucleotides,

requires roughly eight times the execution time for a sequence twice as long. This is

a fairly expensive calculation, as compared with sorting a list, which can generally be

accomplished in O(N log(N)) time.

The big-O notation also applies to the scaling of memory (also called storage) used

by an algorithm. Secondary structure prediction requires two-dimensional arrays of size

N×N. Therefore, in storage, the secondary structure prediction algorithm is O(N2).

Variantsofthedynamicprogrammingalgorithmforfindingtheminimumfreeenergystruc-

ture (Mathews et al. 1999a; Wuchty et al. 1999) can also predict structures with free energy

greaterthanthelowestfreeenergystructure,usinganadditionalconstantfactoroftimeand

memory. These are called suboptimal structures (Zuker 1989). Suboptimal structures with

estimated free energy changes close to the lowest free energy structure provide important

alternative hypotheses for the actual structure. This is due to the fact that nearest neighbor

parameters are imperfect; also, ignoring motifs like pseudoknots can result in a suboptimal

structurebeingmoreaccuratethanthelowestfreeenergystructure.

中文译文

第6章利用 RNA 序列的预测方法

6.3 动态规划（Dynamic Programming）

上一节已经介绍了 RNA 二级结构预测所依赖的热力学规则。但要真正使用这些规则，还需要在巨大的候选结构空间中完成搜索：要么找出得分最优的结构，要么计算每一种可能构象的平衡常数。那么，这个搜索究竟如何实现呢？

一种最直接、也最朴素的方法，是把所有可能的构象全部显式生成出来，逐个计算其自由能，再从中选出自由能最低、也就是得分最优的那个结构。

但这种方法在计算上几乎不可行。已有估计认为，长度为 $N$ 的 RNA 序列，其可能的二级结构数量约为 $(1.8)^N$（Zuker and Sankoff 1984）。对于一个只有 100 个核苷酸的中等长度序列，这意味着大约有 $3 imes 10^{25}$ 个候选结构。即使使用一台高速计算机，每秒能够计算 10000 个结构的自由能，也仍然需要约 $1.6 imes 10^{14}$ 年才能完成搜索。显然，这样规模的问题必须采用更高效的求解策略。

最常用的解决方案就是动态规划（dynamic programming）。它通过递归（recursion）与中间结果列表化/表格化保存（tabulation of intermediate results）的方式加速计算（Nussinov and Jacobson 1980; Zuker and Stiegler 1981）。附录 6.A 为有兴趣的读者详细介绍了这种方法。对于不包含伪结（pseudoknot）的情况，动态规划不仅能比暴力穷举快得多地求出最小自由能结构（minimum free energy structure），也能更高效地计算配分函数（partition function）。其渐近复杂度为：时间复杂度 $O(N^3)$，空间复杂度 $O(N^2)$，其中 $N$ 为序列长度（见 Box 6.2）。

本节还引入了一个重要例外：伪结（pseudoknot）。图 6.5 展示了一个简单的 H 型 RNA 伪结。若两对碱基分别为 $i$–$j$ 和 $i'$–$j'$，并满足 $i < i' < j < j'$，则说明出现了非嵌套碱基配对，这类结构就是伪结。碱基对 $i$–$j$ 定义了一个封闭区域，而 $i'$–$j'$ 则跨越该封闭区域和相邻区域，从而形成伪结。

图 6.5 一个简单的 RNA 伪结

本图用两种表示方式展示了同一个简单的 H 型伪结。伪结由两对碱基定义：$i$–$j$ 与 $i'$–$j'$，其顺序满足 $i < i' < j < j'$。其中 $i$–$j$ 围成一个封闭区域，而 $i'$–$j'$ 横跨该封闭区域及其相邻区域，构成伪结。

长期以来，人们曾认为伪结无法用多项式时间的动态规划算法来预测。直到 Rivas and Eddy（1999）提出了一种多项式时间的动态规划算法，才证明至少某一类足够丰富、具有实际意义的伪结可以被计算预测。然而，这一算法的时间复杂度为 $O(N^6)$，空间复杂度为 $O(N^4)$，因此对于长度超过约 300 个核苷酸的序列，在实际中往往难以使用（Rivas and Eddy 1999; Condon et al. 2004）。后续对该算法的改进虽改善了伸缩性，但在可处理的序列长度上仍存在显著限制（Reeder and Giegerich 2004）。类似地，包含伪结的配分函数算法（Dirks and Pierce 2003）具有 $O(N^5)$ 的时间复杂度与 $O(N^4)$ 的空间复杂度，因此通常也只适用于长度不超过 200 个核苷酸的序列。

Box 6.2 算法复杂度（Algorithm Complexity）

在计算机科学中，算法复杂度用于描述一种计算在最坏情况下如何随问题规模增长。它通常使用 big-O notation 表示，读作 “order”。若算法的时间复杂度为 $O(N)$，说明输入规模参数 $N$ 增大时，计算时间按线性增长；$O(N^2)$ 与 $O(N^3)$ 则分别表示按平方和立方增长。

因此，RNA 二级结构预测中的动态规划算法，时间复杂度为 $O(N^3)$。这里的 $N$ 是核苷酸数目。这意味着当序列长度加倍时，执行时间大约会增加 8 倍。与之相比，像排序列表这类任务通常可在 $O(N \log N)$ 时间内完成，因此 RNA 折叠的动态规划计算可算是代价较高的一类计算。

big-O 记号同样也适用于算法内存消耗（也称 storage）的缩放规律。二级结构预测需要大小为 $N imes N$ 的二维数组，因此其空间复杂度为 $O(N^2)$。

动态规划算法的某些变体不仅能够求得最小自由能结构（Mathews et al. 1999a; Wuchty et al. 1999），还可以在只增加一个常数因子的时间和内存代价下，预测自由能高于最优结构的其他候选结构。这些结构称为次优结构（suboptimal structures）（Zuker 1989）。对于真实 RNA 结构而言，次优结构往往提供了重要的替代假设：一方面，最近邻参数本身并不完美；另一方面，若在建模时忽略了伪结等结构基序，那么某个次优结构反而可能比最小自由能结构更接近真实情况。

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术语表

英文术语	中文译名
dynamic programming	动态规划
recursion	递归
tabulation	表格化保存 / 列表化
asymptotic performance	渐近性能
time complexity	时间复杂度
storage complexity	空间复杂度
pseudoknot	伪结
polynomial time	多项式时间
big-O notation	big-O 记号 / 大 O 记号
suboptimal structures	次优结构

044

Accuracy of RNA Secondary Structure Prediction

PDF page 181；印刷页码 161

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Accuracy of RNA Secondary Structure Prediction

The accuracy of RNA secondary structure prediction can be assessed by predicting structures

for RNA sequences with known secondary structures. For a collection of structures assembled

to test prediction accuracy, including SSU rRNA (Cannone et al. 2002), LSU rRNA (Cannone

et al. 2002), 5S rRNA (Szymanski et al. 2000), group I introns (Cannone et al. 2002), group II

introns (Michel et al. 1989), RNase P RNA (Brown 1999), SRP RNA (Larsen et al. 1998), and

tRNA (Sprinzl et al. 1998), 73% of base pairs in the known structure were, on average, correctly

predicted (Mathews et al. 2004). For these calculations, the SSU and LSU rRNAs are divided

into domains of fewer than 700 nucleotides based on the known secondary structure (Mathews

et al. 1999a). Although this level of accuracy is sufficient to make hypotheses about a structure

of interest, a more accurate prediction is often desirable. There are two general approaches

to improving the accuracy of a secondary structure prediction, both of which try to reduce

the number of incorrect structures that are considered in the search step. One approach is to

use low-resolution experimental data (Sloma and Mathews 2015) and the other is to predict a

structure common to multiple homologs (Seetin and Mathews 2012a).

Experimental Methods to Refine Secondary Structure Prediction

Low-resolution experimental methods use either enzymatic cleavage or chemical modi-

fication reagents that preferentially react with either double-stranded or single-stranded

nucleotides. Examining the reactivity at each position identifies which nucleotides are in

stems and which are in loops, but gives no information on what the pairing partners of the

double-stranded nucleotides are. Commonly used reagents for these experiments include

RNAse V1, which cleaves RNA molecules in double-stranded regions; RNAse T1, which cleaves

RNA molecules after an unpaired guanine nucleotide, and RNase T2, which cleaves after an

unpaired nucleotide of any type; dimethyl sulfate, which modifies unpaired adenine and cyto-

sine nucleotides; and selective 2′-hydroxyl acylation analyzed by primer extension (SHAPE)

reagents, a group of chemicals that modify any unpaired nucleotide. Recent advances have

allowed these methods to be used in concert with massively parallel sequencing to probe

the secondary structure of many different RNA molecules simultaneously inside living cells

(Spitale et al. 2013; Ding et al. 2014; Rouskin et al. 2014; Talkish et al. 2014).

This experimental information can be used in an RNA secondary structure prediction

algorithm in one of two ways. One is to forbid the search step of the dynamic programming

algorithm from considering any structures that are inconsistent with the experimental data.

This often dramatically increases the accuracy for sequences that are poorly predicted without

experimental data. For example, for the 5S rRNA sequence from Escherichia coli, which

is poorly predicted without experimental constraints, the accuracy improves from 26% to

87% using enzymatic cleavage data (Speek and Lind 1982; Mathews et al. 1999a; Szymanski

et al. 2000).

Another way to apply experimental data to improve the prediction is to assign a pseudo-free

energy penalty to structures that do not precisely match the data, rather than forbidding them

entirely. This approach is useful because, while reactivity to enzymes or chemical probes is

strongly correlated with single-strandedness, some double-stranded nucleotides can still be

highly reactive (Sukosd et al. 2013). In these cases, using a soft restraint where inconsistent

structures are merely penalized (instead of forbidden) allows prediction of structures that are

“mostly consistent” with the data. This approach was originally used for SHAPE (Deigan et al.

and has also been applied to both dimethyl sulfate modification (Cordero et al. 2012)

and enzymatic cleavage (Underwood et al. 2010) experimental data.

中文译文

Ch6 Section 4: Accuracy of RNA Secondary Structure Prediction

Accuracy of RNA Secondary Structure Prediction

RNA 二级结构预测的准确度可以通过对已知二级结构的 RNA 序列进行预测来评估。对于一组用于测试预测准确度的结构集合（包括 SSU rRNA [Cannone et al. 2002]、LSU rRNA [Cannone et al. 2002]、5S rRNA [Szymanski et al. 2000]、Group I 内含子 [Cannone et al. 2002]、Group II 内含子 [Michel et al. 1989]、RNase P RNA [Brown 1999]、SRP RNA [Larsen et al. 1998] 和 tRNA [Sprinzl et al. 1998]），已知结构中的碱基对平均有 73% 被正确预测（Mathews et al. 2004）。在这些计算中，SSU 和 LSU rRNA 根据已知二级结构被划分为长度小于 700 个核苷酸的区域（Mathews et al. 1999a）。虽然这一准确度水平足以对感兴趣的结构提出假设，但通常期望获得更准确的预测。提高二级结构预测准确度有两种通用方法，两者都试图减少搜索步骤中被考虑的不正确结构数量。一种方法是使用低分辨率的实验数据（Sloma and Mathews 2015），另一种方法是预测多个同源序列的共同结构（Seetin and Mathews 2012a）。

Experimental Methods to Refine Secondary Structure Prediction

低分辨率实验方法使用酶切或化学修饰试剂，这些试剂优先与双链或单链核苷酸反应。检测每个位置的化学反应性可以识别哪些核苷酸位于茎区、哪些位于环区，但不提供双链核苷酸的配对伙伴信息。常用的实验试剂包括 RNAse V1（在双链区域切割 RNA 分子）、RNAse T1（在未配对的鸟嘌呤核苷酸之后切割 RNA 分子）和 RNase T2（在任何类型的未配对核苷酸之后切割）、二甲硫酸（修饰未配对的腺嘌呤和胞嘧啶核苷酸），以及选择性 2'-羟基酰化并通过引物延伸分析（SHAPE）试剂，这是一组可修饰任何未配对核苷酸的化学物质。近年来的进展使这些方法能够与大规模平行测序结合，同时探测活细胞内多种不同 RNA 分子的二级结构（Spitale et al. 2013; Ding et al. 2014; Rouskin et al. 2014; Talkish et al. 2014）。

这些实验信息可以通过两种方式应用于 RNA 二级结构预测算法。一种方法是在动态规划算法的搜索步骤中禁止考虑任何与实验数据不一致的结构。这通常可以显著提高在没有实验数据约束时预测较差的序列的准确度。例如，对于大肠杆菌（Escherichia coli）的 5S rRNA 序列（在没有实验约束时预测效果较差），使用酶切数据可将准确度从 26% 提高到 87%（Speek and Lind 1982; Mathews et al. 1999a; Szymanski et al. 2000）。

另一种将实验数据应用于改进预测的方法是给不完全匹配数据的结构分配伪自由能惩罚，而不是完全禁止它们。这种方法是有用的，因为虽然对酶或化学探针的反应性与单链性密切相关，但某些双链核苷酸仍然可能具有高反应性（Sukosd et al. 2013）。在这些情况下，使用软约束（只惩罚不一致的结构而不是禁止）可以预测与数据"基本一致"的结构。这种方法最初用于 SHAPE（Deigan et al. 2009），也已应用于二甲硫酸修饰（Cordero et al. 2012）和酶切（Underwood et al. 2010）实验数据。

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Predicting the Secondary Structure Common to Multiple RNA Sequences

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Predicting the Secondary Structure Common to Multiple RNA

Sequences

An alternative approach to improving RNA secondary structure prediction is to make use

of information provided by evolution. Homologous RNA molecules that perform the same

162 Predictive Methods Using RNA Sequences

function in different organisms are expected to form similar structures, even though their

sequences may have diverged substantially. In particular, compensatory mutations, in which

a mutation at one position would disrupt a base pair but a second mutation at its partner posi-

tion restores base pairing, is strong evidence that base pair exists. Algorithms can automate

this process by restricting their search space to structures that can be adopted by all of the

homologs, or by weighting more heavily structures that contain compensatory mutations.

The basis of comparative sequence analysis is the detection of conserved structure, as

inferred from sequence differences between species or between sequences discovered by

in vitro evolution (Pace et al. 1999). The assumption of a conserved secondary structure elim-

inates from consideration the many possible secondary structures for a single sequence that

the set of sequences across evolution cannot all adopt. In other words, the multiple sequences

constrain the possible secondary structure. These constraints can also be used as auxiliary

information in the prediction of secondary structure. Manual comparative sequence analysis

can be highly accurate, with over 97% of base pairs inferred for rRNAs present in subsequently

solved crystal structures (Gutell et al. 2002), but it requires significant skill and effort.

Computer algorithms that automate these comparative analyses are still not as accurate as

manual comparative analysis in which the models are refined over time.

RNA secondary structure prediction algorithms that incorporate information from multiple

sequences can be divided between those that are constrained by an initial sequence alignment

and those that are not. In general, those methods that are constrained by an initial alignment

are not as robust because of the limitations in the alignment, but are computationally faster.

Algorithms That Are Constrained by an Initial Alignment

Several programs have been developed for finding the secondary structure common to a set

of aligned sequences (Lück et al. 1996, 1999; Juan and Wilson 1999; Hofacker et al. 2002).

A popular approach, called Alifold, uses a sequence alignment to constrain secondary struc-

ture prediction by free energy minimization or constraining the calculation of the partition

function (Hofacker et al. 2002; Bernhart et al. 2008). Additional energy terms are added to

the conformation free energy to favor compensating base changes and sequence conservation.

This program is available as part of the Vienna RNA Package (Lorenz et al. 2011) and as a web

server.

Another approach for finding a structure common to multiple sequences, called Pfold, uses

a stochastic context-free grammar (Knudsen and Hein 1999). The grammar defines rules for

generating a sequence together with a secondary structure. These rules, encoded as proba-

bility parameters, are estimated from a sequence alignment and known, common secondary

structures of a number of tRNAs and LSU rRNAs. These sequences and structures are referred

to as the training set. A given sequence is folded using a dynamic programming algorithm

that determines a structure with a maximum probability of being generated by the stochastic

context-free grammar.

Algorithms That Are Not Constrained by the Initial Alignment

Dynamic programming can be used to simultaneously predict the sequence alignment and

common secondary structure for multiple RNA sequences (Sankoff 1985). In general, this

approach is O(N1^3N2^3N3^3… ) in time, where N1 is the length of the first sequence, N2 the length

of the second sequence, and so forth, making it computationally impractical. Two programs

are available that are based on this approach: FoldAlign (Havgaard et al. 2005) and Dynalign

(Mathews and Turner 2002; Fu et al. 2014). Given the time required to run them, these pro-

grams are limited to two sequences, but both have been extended using pairwise calculations

to work on more than two sequences (Torarinsson et al. 2007; Xu and Mathews 2011). These

programs are the best choices to predict structures when the set of sequences is highly diverged.

Alternative approach to predicting RNA secondary structure without an input alignment

is to fold the sequences, align sequences, and then combine the information to predict a con-

served secondary structure. Three modern tools that take this approach are LocARNA (Will

et al. 2007, 2012), PARTS (Harmanci et al. 2008, 2009), and TurboFold (Harmanci et al. 2011).

These programs are faster than Dynalign and FoldAlign, but require higher sequence identity

to work well.

中文译文

Ch6 Section 5: Predicting the Secondary Structure Common to Multiple RNA Sequences

Predicting the Secondary Structure Common to Multiple RNA Sequences

改进 RNA 二级结构预测的另一条路径，是利用进化所提供的信息。不同生物中执行相同功能的同源 RNA 分子，即使其序列已经发生了相当大的分化，通常仍会形成相似的结构。尤其是补偿性突变（compensatory mutations）——即某个位点的突变原本会破坏一个碱基对，但其配对伙伴位点再发生第二次突变后又恢复配对——是某个碱基对真实存在的强有力证据。算法可以通过两种方式自动利用这类信息：一是将搜索空间限制为所有同源序列都能采取的结构；二是对包含补偿性突变的结构赋予更高权重。

比较序列分析（comparative sequence analysis）的基础，是根据物种间的序列差异，或体外进化（in vitro evolution）得到的序列差异，来检测保守结构（conserved structure）（Pace et al. 1999）。假定二级结构是保守的，就可以排除许多单条序列在理论上可能形成、但跨进化序列集合不可能共同采用的二级结构。换句话说，多条序列会对可能的二级结构施加约束。这些约束也可以作为二级结构预测的辅助信息。人工进行比较序列分析时，准确度可以非常高；例如，对 rRNA 推断出的碱基对中，超过 97% 在后来解析出的晶体结构中都得到了验证（Gutell et al. 2002）。不过，这种方法需要相当高的技能和大量投入。自动化这些比较分析的计算机算法，目前总体上仍不如长期迭代修正模型的人工比较分析准确。

整合多序列信息的 RNA 二级结构预测算法，大体可以分成两类：一类依赖初始序列比对（initial sequence alignment）的约束，另一类则不依赖。总体而言，受初始比对约束的方法由于受限于比对本身的质量，鲁棒性往往稍差，但计算速度更快。

Algorithms That Are Constrained by an Initial Alignment

已经有若干程序被开发出来，用于寻找一组已对齐序列所共有的二级结构（Lück et al. 1996, 1999; Juan and Wilson 1999; Hofacker et al. 2002）。其中一种常用方法叫作 Alifold，它利用序列比对结果来约束二级结构预测，既可用于自由能最小化，也可用于约束配分函数（partition function）的计算（Hofacker et al. 2002; Bernhart et al. 2008）。该方法会在构象自由能（conformation free energy）中加入额外能量项，以偏好补偿性碱基替换和序列保守性。这个程序既可作为 Vienna RNA Package（Lorenz et al. 2011）的一部分使用，也提供 web server 版本。

另一种寻找多序列共同结构的方法叫作 Pfold，它采用随机上下文无关文法（stochastic context-free grammar, SCFG）（Knudsen and Hein 1999）。这种文法定义了一组规则，用于同时生成序列及其对应的二级结构。这些规则以概率参数的形式编码，并根据序列比对结果以及一批 tRNA 和 LSU rRNA 的已知共同二级结构进行估计。这些已知序列和结构构成训练集（training set）。随后，给定序列可通过动态规划算法进行折叠，从而找到一个在该随机上下文无关文法下生成概率最大的结构。

Algorithms That Are Not Constrained by the Initial Alignment

动态规划也可以用来同时预测多条 RNA 序列的序列比对和共同二级结构（Sankoff 1985）。一般来说，这类方法的时间复杂度为 O(N1^3N2^3N3^3…)，其中 N1 是第一条序列的长度，N2 是第二条序列的长度，依此类推，因此在计算上几乎不可行。基于这一思想的两个程序是 FoldAlign（Havgaard et al. 2005）和 Dynalign（Mathews and Turner 2002; Fu et al. 2014）。由于运行耗时很长，这些程序通常只适用于两条序列；不过，两者后来都通过成对计算（pairwise calculations）扩展到了多于两条序列的情形（Torarinsson et al. 2007; Xu and Mathews 2011）。当待分析序列彼此差异很大时，这些程序往往是更合适的选择。

另一种不依赖输入比对的思路，是先分别折叠这些序列，再对序列进行比对，最后整合这些信息以预测保守二级结构。采取这种策略的现代工具包括 LocARNA（Will et al. 2007, 2012）、PARTS（Harmanci et al. 2008, 2009）和 TurboFold（Harmanci et al. 2011）。这些程序比 Dynalign 和 FoldAlign 更快，但它们通常要求更高的序列一致性（sequence identity）才能取得较好效果.

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Practical Introduction to Single-Sequence Methods

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Practical Introduction to Single-Sequence Methods 163

AnalternativeapproachtopredictingRNAsecondarystructurewithoutaninputalignment

istofoldthesequences,alignsequences,andthencombinetheinformationtopredictacon-

served secondary structure. Three modern tools that take this approach are LocARNA (Will

etal.2007,2012),PARTS(Harmancietal.2008,2009),andTurboFold(Harmancietal.2011).

TheseprogramsarefasterthanDynalignandFoldAlign,butrequirehighersequenceidentity

toworkwell.

Practical Introduction to Single-Sequence Methods

This section introduces two web servers: the Mfold web server and the RNAstructure web

server.Bothwebserversprovidestructurepredictionsofsimilaraccuracyforsinglesequences,

andeitherservercanbeuseddependinguponthefeaturesdesired.TheMfoldserveraddition-

ally provides an interface to simulate the melting of bimolecular complexes (Dimitrov and

Zuker 2004). The RNAstructure web server additionally provides methods for determining

conservedsecondarystructuresinmultiplehomologs,siRNAdesign,andbimolecularstruc-

tureprediction(Bellaousovetal.2013).

Using the Mfold Web Server

MfoldisanRNA secondarystructure predictionpackageavailablebothasawebserverand

ascodeforcompilationonUnix/Linuxmachines(Mathewsetal.1999a;Zuker2003).Ituses

a set of nearest neighbor parameters for free energies at 37∘C (Mathews et al. 1999a).Mini-

mumfreeenergyandsuboptimalsecondarystructures,generatedheuristically(Zuker1989),

arepredicted.Suboptimalstructuresrepresentalternativestructurestothelowestfreeenergy

structureandreflectboththepossibilitythatanRNAsequencemayhavemorethanasingle

structure(SchultesandBartel2000)andthefactthattheenergyrulescontainsomeuncertainty

(Mathews et al. 1999a; Layton and Bundschuh 2005; Zuber et al. 2017). Mfold also predicts

energydotplots,whichdisplaythelowestfreeenergyconformationpossibleforeachpossible

basepair(ZukerandJacobson1995).Theseplotsconvenientlydemonstrateallpossiblebase

pairswithinauser-specifiedincrementofthelowestfreeenergystructureandpredictedstruc-

turescanbecolorannotatedtodemonstrateregionsinthestructureforwhichmanyfolding

alternativesexist(ZukerandJacobson1998).

Figure6.6a,bshowsthetopandbottomoftheinputformontheMfoldserver,respectively.

Asequencenamecanbeenteredintheboxlabeled Entersequencename andthesequenceis

typed (or pasted from the clipboard) in the box labeledEnterthesequencetobefoldedinthe

boxbelow.Asthecaptionexplains,non-alphabeticcharactersareignoredanddonotinterfere

withsequenceinterpretation.Forexample,theformshowsatRNAsequencecalledRD1140

(Sprinzl et al. 1998) pasted into the sequence field. The remainder of the form has default

valuesthatcanbechangedbyadvancedusers.Thenextboxprovidestheoptionofconstrain-

ingstructurepredictionwithauxiliaryevidencederivedfromenzymaticcleavageexperiments

(Knapp1989),comparativesequenceanalysis(Paceetal.1999),orbiologicalintuition.Next,

thedefaultisforlinearRNAsequencefolding,althoughcircularsequencescanalsobefolded

by changing the option fromlinear tocircular. Note that the folding temperature is fixed at

37∘Cusingthecurrentparameters.Anolder,lesscompletesetofparametersallowssecondary

structurepredictionatothertemperatures(Jaegeretal.1989),butitisrecommendedthatthe

currentparametersbeusedformostapplications.Theolderparameterscanbeusedforfold-

ingbyfollowingthelinkatthetopofthepagetothe RNAmfoldversion2.3 server(notshown

inFigure6.6).Thepercentsuboptimalitynumber(5bydefault)isthemaximumpercentdif-

ferenceinfreeenergyfromthelowestfreeenergystructurethatisallowedwhengenerating

suboptimalsecondarystructures.Theupperboundonthecomputedfoldings,defaultat50,is

themaximumnumberofsuboptimalsecondarystructurestobepredicted.Thewindowparam-

etercontrolshowdifferenteachsuboptimalstructuremustbefromallothers.Itdefaultstoa

164 Predictive Methods Using RNA Sequences

(a)

(b)

Figure 6.6 The input form for the version 3.1 Mfold server. (a) The top and (b) the bottom of the form. Default

parameters are shown with the exceptions as noted in the text. Note that there is a separate server for secondary

structure prediction of DNA, using DNA folding free energies (SantaLucia 1998). This is available by following

the link to the DNA Mfold server (see Internet Resources).

Practical Introduction to Single-Sequence Methods 165

valuebasedonthelengthofthesequencethatisshownbyfollowingthelinkat Window.For

example, the tRNA used here is 77 nucleotides long and will have a default window of 2. A

smallerwindowallowsmoresuboptimalstructuresandalargerwindowrequiresmorediffer-

encesbetweenthepredictedstructures.Thesmallestwindowsizeallowediszero.Themaxi-

mumnumberofunpairednucleotidesinbulgeorinternalloopsislimitedto30bydefault.The

maximum asymmetry in internal loops, the difference in length in unpaired nucleotides on

eachstrand,isalso30bydefault.Themaximumdistanceallowedbetweenpairednucleotides

issetto nolimit.Thesevaluescanbemodifiedbyadvancedusers.

The remaining options control the server output. Currently, sequences containing 800 or

fewernucleotidescanbefoldedinarelativelyshorttimeandaretreatedasanimmediatejob.

Longersequencesmustbefoldedasabatchjob,requiringthatthedefaultoptionbechanged

fromAnimmediate toAbatch job.Batchjobsalsorequirethattheuserenterane-mailaddress

forreceivingnotificationthatthecalculationiscomplete.ThetRNAinthisexampleisshort,

so the default ofAn immediatejob will be used. The remaining options control the way the

server generates output. Each of these options has a link to a web page that describes each

parameter.FoldRNA isclickedtostartthecalculation.

Figure6.7showstheMfoldserveroutputformforthesecondarystructurepredictionofthe

RD1140tRNA.Resultsareavailableontheserverfor24hoursaftercomputation.Thefirstwin-

dowdisplaysthesequencewithnumberednucleotidepositions.Adiagramofeachpredicted

secondarystructureisavailableinavarietyofformats.Forthisexample,onlyasinglestruc-

tureispredictedusingthedefaultparametersforsuboptimalsecondarystructureprediction.

Thecommonlyusedformats,availablebylinksadjacentto Structure1,are PostScript,which

isapublication-qualityoutputformatshowninFigure6.8a; PNGandJPG,whichareimage

formatsthatallowuser interaction;and RNAVizCT andXRNAss formats,whichareexport

formatsforsecondarystructuredrawingtools,explainedbelow.

Theenergydotplotisavailablebylinkstoa Textformatted,Postscriptformatted,PNGformat-

ted,or JPGformattedfile.Inthedotplot,eachdotrepresentsabasepairbetweennucleotides

indicatedonthe x-and y-axesandthedot’scolorindicatesthelowestenergyforastructurethat

Figure 6.7 The output page for the Mfold server. Please refer to the text for a detailed description of this page.

166 Predictive Methods Using RNA Sequences

containsthatpair.Theenergydotplotisdividedintotwotriangles.Theuppertriangleisthe

energyplotincludingsuboptimalpairsandthelowertriangleisthelocationofbasepairsin

thepredictedminimumfreeenergystructure.Thetextformatissuitableforsubsequentanaly-

sisusingcustomscripts. Postscriptisapublication-qualityoutputandisshowninFigure6.8b.

PNG and JPG formats both link to interactive pages that allow the user to zoom to regions,

changetheenergyincrementandnumberofcolors,andclickonindividualbasepairstodeter-

mine the exact energy. The energy dot plot in Figure 6.8b shows that there are alternative

base pairs contained in structures with free energies between−29.8 and−30.0kcalmol

−1,a

separationoflessthan1kcalmol −1 fromthelowestfreeenergystructure( −30.6kcalmol −1).

Therefore,these are base pairsthat should be consideredas possiblealternativesto those in

thelowestfreeenergystructure.

An RNAML formatted output file is available for exchanging information with other

RNAML-compliant programs. This is an XML file format that promises to eventually allow

seamlessinformationexchangebetweenRNAanalysisprograms(Waughetal.2002).

Using the RNAstructure Web Server

RNAstructure is a software package for predicting RNA secondary structure (Reuter and

Mathews 2010; Bellaousov et al. 2013). In addition to implementations of the algorithms

U U

UU

U

U U

U

CC

C

GG

G

C

G

G G

U

C

CA C

G

A

G

C G

UA

CG

C

CC

A

C

U

UG

G

C

5′

3′

dG = –29.28 (Initially –30.60) RD1140

Output of sir_graph(©)

mfold_util 4.7

Created Tue Jan24 09:53:21 2017

(a)

Figure 6.8 Sample output from the Mfold web server, version 3.1. (a) The secondary structure predicted

for the tRNA, RD1140 (Sprinzl et al. 1998). (b) The energy dot plot (as described in the text).

Practical Introduction to Single-Sequence Methods 167

(b)

Figure 6.8 (Continued)

for structure prediction and the partition function, RNAstructure includes tools for

multiple-sequence prediction, identifying accessible regions in an RNA structure, and pre-

dictingthestructurefortwoRNAmoleculestohybridize.RNAstructurecanbeusedthrough

a web server or downloaded and used through a graphical user interface for Windows, Mac

OSX,andLinux,orviathecommandline.Thistutorialexplainshowtousethewebserver

interface; detailed instructions for predicting secondary structures using the downloadable

program are available in the online help files and elsewhere (Mathews et al. 2016; Xu and

Mathews2016).

The homepage for the RNAstructure web server offers options to predict a secondary

structurefromasinglesequence,topredictaconservedstructurewithmultiplehomologous

sequences,topredictthestructureoftwointeractingsequences,ortorunaspecificalgorithm

168 Predictive Methods Using RNA Sequences

fromtheRNAstructure package.Topredictastructureforasinglesequence,choose Predict

a Secondary Structure. This leads to an input form for the web server that predicts RNA

structures using a selection of methods (Figure 6.9). Like Mfold, the minimum free energy

structurefortheinputRNAsequenceandaselectionofsuboptimalstructuresarecomputed.

Additionally, base-pairing probabilities are calculated using the partition function and used

to annotate the predicted RNA secondary structures, giving the user feedback about what

parts of the predicted structure are most likely to be correct. Highly probable base pairs

(i.e. higher than 0.9 pairing probability) are more likely to be correctly predicted than low

probability(i.e.apairingprobabilitylessthan0.5)(Mathews2004).RNAsecondarystructures

(a)

Figure 6.9 RNAstructure web server input form. (a) The top and (b) the bottom of the form. Please refer to the text for a detailed description

of this page.

Practical Introduction to Single-Sequence Methods 169

(b)

Figure 6.9 (Continued)

are also generated using the maximum expected accuracy method (Lu et al. 2009), which

generatesstructuresdirectlyfromthebase-pairingprobabilitiescalculatedusingthepartition

function, and can be more accurate than the minimum free energy structures. Additionally,

secondarystructuresthatmaycontainpseudoknotsaregeneratedusingtheProbKnotmethod

(BellaousovandMathews2010).

Returning to the input form for the web server (Figure 6.9), the user can either upload a

sequence file or type a title and sequence into the input box. There is an option above this

boxtoinsertanexamplesequence.TheRNAstructureinputformoffersthesameoptionsas

Mfold, such as number of suboptimal structures to generate, maximum internal loop size, and

others. Additionally, the user can select a temperature for folding; select a gamma parame-

ter, which can be changed to increase or decrease the number of predicted base pairs by the

maximum expected accuracy method; and the number of iterations and helix length used by

the ShapeKnots method. Default values are provided that are expected to work well in most

cases.

The form also contains an option to upload files that constrain or restrain the calculation

with results from experiments. The user can either use hard constraints to forbid certain pairs

or provide a file with scores from a SHAPE probing experiment that will be converted to

pseudo-free energy changes to restrain structure prediction. Each of these files must be speci-

fied in a specific format, described in the file formats link.

An example output, showing the results for the example sequence, is shown in Figure 6.10.

The structure is predicted using all free energy minimization, maximum expected accuracy

prediction, and ProbKnot. Additionally, predicted secondary structures are color annotated

with probabilities, as calculated with the partition function. Base-paired nucleotides are anno-

tated with base-pairing probability and unpaired nucleotides are annotated with the probabil-

ity of being unpaired.

中文译文

Ch6 第6节：单序列方法实践简介

简介

在不依赖输入比对的前提下预测 RNA 二级结构，还有一种替代方法，即先将序列折叠、再比对序列，然后将折叠与比对信息相结合来预测保守二级结构。采取这一策略的三个现代工具是 LocARNA（Will et al. 2007, 2012）、PARTS（Harmanci et al. 2008, 2009）和 TurboFold（Harmanci et al. 2011）。这些程序比 Dynalign 和 FoldAlign 更快，但对序列一致性要求更高。

使用 Mfold 网络服务器

本节介绍两个网络服务器：Mfold 网络服务器和 RNAstructure 网络服务器。两者对单序列的结构预测精度相近，用户可根据所需功能选择使用。Mfold 服务器还提供了一个界面，可用于模拟双分子复合物的熔解（解链）过程（Dimitrov and Zuker 2004）。RNAstructure 网络服务器则额外提供了多同源序列保守二级结构预测、siRNA 设计以及双分子结构预测等功能（Bellaousov et al. 2013）。

Mfold 是一个 RNA 二级结构预测软件包，同时提供网络服务器和可在 Unix/Linux 机器上编译运行的代码（Mathews et al. 1999a; Zuker 2003）。它使用一套 37°C 下的最近邻自由能参数（Mathews et al. 1999a）。程序预测最小自由能结构，以及以启发式方式生成的次优二级结构（Zuker 1989）。次优结构代表了与最低自由能结构不同的替代构象，反映了 RNA 序列可能具有多种结构（Schultes and Bartel 2000）以及能量规则本身存在一定不确定性的事实（Mathews et al. 1999a; Layton and Bundschuh 2005; Zuber et al. 2017）。Mfold 还可预测能量点图（energy dot plots），该图展示了每一种可能的配对在最低自由能构象中对应的能量（Zuker and Jacobson 1995）。这些点图可以直观地展示用户指定增量范围内所有可能的配对，而预测的结构可被着色标注，以展示在该结构中有多种折叠替代方案的区域（Zuker and Jacobson 1998）。

Figure 6.6 分别展示了 Mfold 服务器输入表单的顶部和底部。用户可在标有"Enter sequence name"的框中输入序列名称，并将待折叠的序列输入（或从剪贴板粘贴）到下方标有"Enter the sequence to be folded"的框中。正如说明文字所示，非字母字符会被忽略且不影响序列解读。例如，图中的表单显示了一条名为 RD1140 的 tRNA 序列（Sprüinzl et al. 1998）已粘贴到序列框中。表单其余部分使用默认值，高级用户可自行修改。接下来的一个选项框提供了利用辅助证据来约束结构预测的功能，这些证据来源于酶切实验（Knapp 1989）、比较序列分析（Pace et al. 1999）或生物学直觉。此外，默认使用线性 RNA 序列折叠，但也可通过将选项从"linear"改为"circular"来折叠环形序列。需要注意的是，当前参数下的折叠温度固定为 37°C。一套较旧的、较不完整的参数可支持在其他温度下进行二级结构预测（Jaeger et al. 1989），但建议在大多数应用中使用当前参数。如需使用旧参数进行折叠，可通过页面顶部的链接访问 RNA mfold version 2.3 服务器（图 6.6 中未显示）。"Percent suboptimality"数值（默认为 5）是指生成次优二级结构时，允许其自由能与最低自由能结构之间的最大百分比差值。"Upper bound on the computed foldings"的限制值（默认为 50）是预测的次优二级结构的最大数量。"Window"参数控制每个次优结构之间必须有多少差异。该值默认为基于序列长度的数值，可通过点击"Window"链接查看。例如，本例中使用的 tRNA 长度为 77 个核苷酸，默认窗口值为 2。窗口值越小，允许的次优结构越多；窗口值越大，则各预测结构之间的差异要求越大。允许的最小窗口值为零。内环（bulge）或内部环（internal loop）中未配对核苷酸的最大数量默认为 30。内部环的不对称性最大值（即每条链上未配对核苷酸长度的差值）也默认为 30。允许的配对核苷酸之间的最大距离设置为"no limit"。这些数值均可由高级用户修改。

其余选项用于控制服务器输出。目前，长度不超过 800 个核苷酸的序列可在较短时间内完成折叠，作为即时任务处理。较长的序列必须作为批处理任务运行，需要将默认选项从"An immediate"改为"A batch job"。批处理任务还需用户输入电子邮件地址，以便在计算完成后接收通知。本例中的 tRNA 长度较短，因此使用默认的"An immediate job"选项。其余选项用于控制服务器生成输出的方式，每个选项都附有说明网页的链接。点击 Fold RNA 按钮开始计算。

Figure 6.7 展示了 Mfold 服务器对 RD1140 tRNA 二级结构预测的输出页面。计算结果在服务器上保留 24 小时。第一个窗口显示带有核苷酸位置编号的序列。每种预测二级结构可以多种格式的图示提供。本例中，使用次优二级结构预测的默认参数仅预测出一种结构。Structure 1 旁边的链接提供了常用的格式：PostScript（出版质量的输出格式，见 Figure 6.8a）、PNG 和 JPG（可在用户交互式操作中使用的图像格式）以及 RNAVizCT 和 XRNAss 格式（用于二级结构绘图工具的导出格式，下文有解释）。

能量点图可链接到 Text 格式、Postscript 格式、PNG 格式或 JPG 格式的文件。在点图中，每个点代表 x 轴和 y 轴上标注的两核苷酸之间的一个配对，点的颜色表示包含该配对的结构中的最低能量。能量点图被划分为两个三角形区域。上三角形是包含次优配对在内的能量图，下三角形是最小自由能结构中配对的位置。Text 格式适合使用自定义脚本进行后续分析。Postscript 格式为出版质量输出（见 Figure 6.8b）。PNG 和 JPG 格式均链接到交互式页面，用户可放大特定区域、修改能量增量值和颜色数量，并点击单个配对以确定精确能量。Figure 6.8b 中的能量点图显示，在−29.8 和−30.0 kcal·mol⁻¹ 之间的结构中还存在其他配对，这些结构与最低自由能结构（−30.6 kcal·mol⁻¹）的能量差不到 1 kcal·mol⁻¹。因此，这些配对应被视为最低自由能结构中配对的可能替代方案。

此外还提供 RNAML 格式的输出文件，用于与其他符合 RNAML 标准的程序交换信息。RNAML 是一种 XML 文件格式，旨在最终实现 RNA 分析程序之间的无缝信息交换（Waugh et al. 2002）。

使用 RNAstructure 网络服务器

RNAstructure 是一个用于预测 RNA 二级结构的软件包（Reuter and Mathews 2010; Bellaousov et al. 2013）。除了实现结构预测算法和配分函数之外，RNAstructure 还包含多序列预测、识别 RNA 结构中可及区域以及预测两条 RNA 分子杂交结构的工具。RNAstructure 可通过网络服务器使用，也可下载后在 Windows、Mac OSX 和 Linux 的图形用户界面或命令行中使用。本教程介绍如何使用网络服务器界面；使用可下载程序预测二级结构的详细说明可参见在线帮助文件及其他资料（Mathews et al. 2016; Xu and Mathews 2016）。

RNAstructure 网络服务器的主页提供了多种选项：可从单序列预测二级结构、可预测多同源序列的保守结构、可预测两条相互作用序列的结构，或运行 RNAstructure 包中的特定算法。要预测单序列的结构，选择 Predict a Secondary Structure，这将进入网络服务器的输入表单页面，使用多种方法预测 RNA 结构（Figure 6.9）。与 Mfold 类似，该工具计算输入 RNA 序列的最小自由能结构以及一组选定的次优结构。此外，配分函数被用于计算配对概率，并以此对预测的 RNA 二级结构进行标注，向用户反馈预测结构中哪些部分最可能正确。配对概率较高的碱基对（即配对概率大于 0.9）比低概率的碱基对（即配对概率小于 0.5）更可能正确预测（Mathews 2004）。

RNAstructure 还使用最大期望准确度方法（maximum expected accuracy method）（Lu et al. 2009）生成 RNA 二级结构，该方法直接从配分函数计算的配对概率生成结构，可能比最小自由能结构更准确。此外，还使用 ProbKnot 方法（Bellaousov and Mathews 2010）生成可能含有假结的二级结构。

回到网络服务器的输入表单（Figure 6.9），用户可以上传序列文件，也可以在输入框中输入标题和序列。该框上方还有一个选项可插入示例序列。RNAstructure 输入表单提供的选项与 Mfold 相同，如生成次优结构的数量、最大内部环大小等。另外，用户可以选择折叠温度、选择 gamma 参数（可调整以增加或减少最大期望准确度方法预测的碱基对数量）以及 ShapeKnots 使用的迭代次数和螺旋长度参数。

Figure 6.9 RNAstructure 网络服务器输入表单。（a）表单顶部和（b）表单底部。详见正文说明。

RNAstructure 单序列输出与参数补充

此外，用户还可以选择折叠温度；选择 gamma parameter，通过调节它可以增加或减少 maximum expected accuracy (MEA) 方法预测出的碱基对数量；以及设置 ShapeKnots 方法使用的迭代次数和螺旋长度。系统给出了适用于多数情形的默认值。

该表单还包含一个选项，允许用户上传文件，根据实验结果对计算施加 constraint 或 restraint。用户既可以使用硬约束（hard constraints）禁止某些配对，也可以提供来自 SHAPE probing experiment 的打分文件，程序会将其转换为 pseudo-free energy changes，从而约束结构预测。这些文件都必须采用特定格式，具体格式见文件格式说明链接。

Figure 6.10 展示了一个示例输出，给出了示例序列的预测结果。该结构同时使用自由能最小化、最大期望准确度预测以及 ProbKnot 方法进行预测。此外，预测得到的二级结构还依据配分函数计算出的概率进行了着色标注：已配对核苷酸标注其配对概率，未配对核苷酸标注其保持未配对的概率。

Figure 6.10 RNAstructure 网络服务器的示例输出，展示了 tRNA RD1140（Sprinzl et al. 1998）的预测最小自由能二级结构。预测的碱基对按其配对概率着色，未配对核苷酸则标注其未配对概率，这些概率均由配分函数计算得到。

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170 Predictive Methods Using RNA Sequences

others. Additionally, the user can select a temperature for folding; select a gamma parame-

ter,whichcanbechangedtoincreaseordecreasethenumberofpredictedbasepairsbythe

maximumexpectedaccuracymethod;andthenumberofiterationsandhelixlengthusedby

theShapeKnotsmethod.Defaultvaluesareprovidedthatareexpectedtoworkwellinmost

cases.

Theformalsocontainsanoptiontouploadfilesthatconstrainorrestrainthecalculation

withresultsfromexperiments.Theusercaneitherusehardconstraintstoforbidcertainpairs

or provide a file with scores from a SHAPE probing experiment that will be converted to

pseudo-freeenergychangestorestrainstructureprediction.Eachofthesefilesmustbespeci-

fiedinaspecificformat,describedinthefileformatslink.

Anexampleoutput,showingtheresultsfortheexamplesequence,isshowninFigure6.10.

The structure is predicted using all free energy minimization, maximum expected accuracy

prediction, and ProbKnot. Additionally, predicted secondary structures are color annotated

withprobabilities,ascalculatedwiththepartitionfunction.Base-pairednucleotidesareanno-

tatedwithbase-pairingprobabilityandunpairednucleotidesareannotatedwiththeprobabil-

ityofbeingunpaired.

Practical Introduction to Multiple Sequence Methods

Using the RNAstructure Web Server to Predict a Common Structure for Multiple

Sequences

The RNAstructure web server also provides an interface to predict a secondary structure

usingmultiplesequences,whensequencehomologsareavailable.Homologsaremostoften

sequencesfrommultiplespeciesthatservethesamefunction(seeChapter3fordefinitions).

Theycanbefoundingenomesusingsyntenyortheycanbefoundusingtraditionalgenetic

orbiochemicalmethods.ThemultiplesequenceinterfacecanbeaccessedbyselectingPredict

aSecondaryStructureCommontoTwoSequencesor PredictASecondaryStructureCommon

toThreeorMoreSequencesfromthewebservermainpage.Selectingtheoptionforthreeor

moresequencesleadstotheinputforminFigure6.11,forstructurepredictionusingMultilign

andTurboFold.Toprovideasequence,theusercanuploadafileintheFASTAformatorcopy

FASTA-formatteddataintotheboxtitledSequences.Thereisanoptionabovethisboxtoenter

exampledata.

MultilignusesDynaligntocalculatecommonstructuresusingpairsofsequences(Xuand

Mathews2011).Multiligncanpredictsuboptimalstructures,andtheinputformcontainsthe

energy difference, maximum number of structures, and structure window size options that

arebynowfamiliarbecausetheyservethesamerolesforsingle-sequencestructureprediction

(above).Inadditiontocontrollingsuboptimalstructures,suboptimalsequencealignmentsare

alsoconsidered,usinganalignmentwindowsizeparameter.Theminimumalignmentwin-

dowwillgeneratesuboptimalalignmentswithsmallvariations.Bysettingthiswindowsizeto

largervalues,thesuboptimalalignmentsarerequiredtoshowlargerchanges.Thegappenalty

parameterisusedbyDynaligntopenalizegapsinsertedinsequencealignments.Thepenalty

parameterisinunitsofkcalmol–1.Twoadditionalparameters,iterationsandmaxdsvchange,

adjustthewayinformationfromDynaligncalculationspropagatesinMultilign.Thedefault

parameters should work for most calculations, and are available for change by experienced

users(XuandMathews2011).

For TurboFold, the user can specify a number of options. Because TurboFold produces

a matrix of pair probabilities, a user can choose how the pair probabilities will be used to

predict a structure: Maximum Expected Accuracy (Lu et al. 2009), Pseudoknots (Bellaousov

and Mathews 2010; Seetin and Mathews 2012b), or Threshold, that uses a simple cut-off

where the structure will be composed of all the pairs that exceed a user-specified threshold

in base-pairing probability (Mathews 2004). The default is maximum expected accuracy,

which does not predict pseudoknots. If a pseudoknot is expected or if the user would like

Practical Introduction to Multiple Sequence Methods 171

Figure 6.10 Sample output from the RNAstructure web server showing the predicted minimum free energy secondary structure for the

tRNA RD1140 (Sprinzl et al. 1998). The predicted pairs are color annotated with their pairing probability, and the unpaired nucleotides are

annotated with the probability that they are unpaired, as calculated using a partition function.

172 Predictive Methods Using RNA Sequences

(a)

Figure 6.11 Input form for the RNAstructure web server for multiple-sequence predictions. (a) The top and (b) the bottom of the

form. Please refer to the text for a detailed description of this page.

Practical Introduction to Multiple Sequence Methods 173

(b)

Figure 6.11 (Continued)

174 Predictive Methods Using RNA Sequences

Figure 6.12 Sample output from the RNAstructure web server for multiple-sequence predictions that can be accessed by clicking Click here

to add example sequences to the box on the input form (Figure 6.11).

Other Computational Methods to Study RNA Structure to know about possible pseudoknots, switching to Pseudoknot, which uses the ProbKnot

method,wouldbeagoodchoice.ThenextsetofoptionscontrolstheTurboFoldprocedure:

the TurboFoldGamma option specifies the relative weight placed on intrinsic and extrinsic

information when folding a single sequence, and the TurboFold Iterations option specifies

howmanystepsofiterativerefinementeachsetofpairprobabilitieswillundergo.

Entering the example data and selecting Submit Query leads to the output shown in

Figure 6.12, which displays a predicted structure by both Multilign and TurboFold for each

inputsequence.Thesetwoprogramsprovidealternativehypothesesforthesecondarystruc-

ture;Multilignislikelytobemoreaccuratewhenthesequenceshavelittlepairwisesequence

identity (<50%) and TurboFold is likely to be more accurate with high pairwise sequence

identities(>60%).

中文译文

第6章利用 RNA 序列的预测方法

6.7 多序列方法实践简介

使用 RNAstructure 网络服务器预测多条序列的共同结构

当存在序列同源物（homologs）时，RNAstructure 网络服务器还提供了一个界面，可利用多条序列来预测共同二级结构。同源物通常是来自不同物种、但执行相同功能的序列（定义见第 3 章）。它们可以通过基因组中的 synteny 关系找到，也可以通过传统遗传学或生物化学方法获得。

多序列界面可通过在网络服务器主页选择 Predict a Secondary Structure Common to Two Sequences 或 Predict a Secondary Structure Common to Three or More Sequences 进入。若选择“三条或更多序列”的选项，则会进入 Figure 6.11 所示的输入表单，用于借助 Multilign 和 TurboFold 进行结构预测。用户可上传 FASTA 格式文件，或将 FASTA 格式数据直接粘贴到名为 Sequences 的文本框中。该文本框上方还提供了插入示例数据的选项。

Multilign 使用 Dynalign 对成对序列进行共同结构计算（Xu and Mathews 2011）。Multilign 可以预测次优结构，因此其输入表单中包含能量差（energy difference）、最大结构数（maximum number of structures）以及结构窗口大小（structure window size）等选项；这些参数在单序列结构预测中已经见过，因为它们在这里承担相同作用。除控制次优结构外，程序还会考虑次优序列比对，这通过 alignment window size 参数实现。较小的最小比对窗口会生成只有细微变化的次优比对；增大该窗口值后，次优比对之间必须表现出更大的差异。

gap penalty 参数用于让 Dynalign 对序列比对中的插入缺口进行惩罚，其单位为 kcal·mol⁻¹。另外还有两个参数——iterations 和 maxdsvchange——用于调整 Dynalign 计算结果在 Multilign 中传播信息的方式。默认参数对大多数计算都足够适用，而有经验的用户也可以自行修改这些设置（Xu and Mathews 2011）。

对于 TurboFold，用户也可以设置若干选项。由于 TurboFold 会产生一个碱基对概率矩阵，用户需要决定如何利用这些概率来生成结构：可以选择 Maximum Expected Accuracy（Lu et al. 2009）、Pseudoknots（Bellaousov and Mathews 2010; Seetin and Mathews 2012b），或者 Threshold 方法——即使用一个简单的阈值，只保留那些配对概率超过用户指定阈值的碱基对来构建结构（Mathews 2004）。默认选项是最大期望准确度方法，它不会预测假结（pseudoknots）。如果预期序列中存在假结，或者用户希望了解可能的假结情况，则切换到 Pseudoknot 选项会是一个合适选择，因为它使用的是 ProbKnot 方法。

接下来的一组选项用于控制 TurboFold 流程：TurboFoldGamma 选项用于指定在折叠单条序列时，内在信息（intrinsic information）与外在信息（extrinsic information）的相对权重；TurboFold Iterations 选项用于指定每组配对概率要经历多少轮迭代优化。

输入示例数据并选择 Submit Query 后，会得到 Figure 6.12 所示的输出结果，其中会针对每条输入序列分别显示由 Multilign 和 TurboFold 预测得到的结构。这两个程序为二级结构提供了两种替代性假设：当序列两两之间的一致性较低（<50%）时，Multilign 往往更准确；而当两两序列一致性较高（>60%）时，TurboFold 往往更准确。

Figure 6.11 RNAstructure 网络服务器用于多序列预测的输入表单。（a）表单顶部；（b）表单底部。详见正文说明。

Figure 6.12 RNAstructure 网络服务器用于多序列预测的示例输出。该结果可通过点击输入表单（Figure 6.11）中的 “Click here to add example sequences to the box” 获得。

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Other Computational Methods to Study RNA Structure 175

to know about possible pseudoknots, switching to Pseudoknot, which uses the ProbKnot

method, would be a good choice. The next set of options controls the TurboFold procedure:

the TurboFold Gammaoption specifies the relative weight placed on intrinsic and extrinsic

information when folding a single sequence, and theTurboFold Iterationsoption specifies

howmanystepsofiterativerefinementeachsetofpairprobabilitieswillundergo.

Entering the example data and selectingSubmit Query leads to the output shown in

Figure 6.12, which displays a predicted structure by both Multilign and TurboFold for each

inputsequence.Thesetwoprogramsprovidealternativehypothesesforthesecondarystruc-

ture;Multilignislikelytobemoreaccuratewhenthesequenceshavelittlepairwisesequence

identity (<50%) and TurboFold is likely to be more accurate with high pairwise sequence

identities( >60%).

Other Computational Methods to Study RNA Structure

Another widely used RNA structure prediction package is the ViennaRNA package (Lorenz

et al. 2011). ViennaRNA is available as a web server and as a set of locally run command

linetools.TheViennaRNApackageprogramshaveaUNIX-styleinput,acceptingdatafrom

standardinputandprintingresultstostandardoutput,makingthemeasytoseamlesslyinte-

grateintoaUNIXpipeline.Inadditiontoimplementationsoftheusualminimumfreeenergy

andpartitionfunctionalgorithms,ViennaRNAincludesasuiteoftoolsforpredictingacom-

monstructureformultiplesequences,fordrawingstructures,forpredictingduplexstructures

betweentwoRNAchains,andfordesigningsequencesthatfoldtoadesiredstructure.

Sfold is an implementation of the partition function calculation that predicts secondary

structuresusingastochasticsamplingprocedure(DingandLawrence1999,2001,2003).The

samplingprocedureguaranteesthatstructuresaresampledwithtruestatisticalweight.Sfoldis

availableforusethroughawebinterface.Sfoldhasbeenshowntoaccuratelypredictunpaired

regions that correlate to regions accessible to antisense oligonucleotide targeting (Ding and

Lawrence 2001). As the secondary structures are sampled statistically, the fraction of occur-

rencesthatanucleotideisunpairedinasetofsampledstructuresisthepredictedprobability

forbeingunpaired.

NUPACK (Zadeh et al. 2010) is a software suite (available through a web server and as a

downloadable package) that solves theinverse folding problem, the opposite problem from

RNAstructureprediction.Insteadoftakingasequenceandpredictingitsstructure,NUPACK

takes a structure as input and attempts to find a sequence that will fold to that structure.

Becausethesequencespacetobesearchedisenormous(4

N forasequenceoflength N,sothere

areapproximately1.6 ×1060 possiblesequencesfora100-nucleotideRNA),NUPACKhierar-

chicallydecomposesthestructureintocomponents.Sequencesaredesignedforeachcompo-

nent. The component sequences are then assembled, and, if any combination of sequences

fails,thecomponentsareredesigned.Goodcandidatesequencesarefoundbyoptimizingthe

ensemble defect, a quantity calculated from the partition function that estimates how many

basesinthesequenceareformingthedesiredstructure(Zadehetal.2011).

Another important problem is to predict whether two RNA molecules will hybridize

with one another, and the structure of the resulting duplex. Important applications of this

capabilityaretopredicttargetsofsiRNA(LuandMathews2007;Taferetal.2008),miRNA,or

DNA oligonucleotides (Mathews et al. 1999b). The most accurate approaches for prediction

of RNA–RNA interactions consider the balance between self-structure and intermolecular

structure because the self-structures can prevent binding by a second sequence. Implemen-

tations of multi-sequence folding include RNAup (Muckstein et al. 2006) and RNAplex

(TaferandHofacker2008),whicharepartoftheViennaRNApackage,andBiFold(Mathews

et al. 1999b), DuplexFold (Mathews et al. 1999b), and AccessFold (DiChiacchio et al. 2016),

whicharecomponentsofRNAstructure.WebserversareavailableforRNAup(aspartofthe

ViennaRNA web server), BiFold (as part of the RNAstructure web server), and DuplexFold

176 Predictive Methods Using RNA Sequences

(aspartoftheRNAstructurewebserver).AccessFoldandRNAplexarenotavailablethrough

webservers,butcanbedownloadedandrunlocally.

Comparison of Methods

Nosingleprogramisyetavailablethatcanreplacemanualcomparativesequenceanalysis,but

additionalsourcesofinformationcandramaticallyimprovepredictionaccuracy.Whenexper-

imental data such as SHAPE are available, single-sequence thermodynamic prediction can

often provide accurate secondary structures, correctly predicting 90% or more of the known

basepairs(Deiganetal.2009;Corderoetal.2012;Hajdinetal.2013).Ifmultiplehomologsare

available,multiple-sequencepredictionsoftheconservedsecondarystructurearemoreaccu-

ratethansingle-sequencepredictions(AsaiandHamada2014;HavgaardandGorodkin2014).

Dynalign/Multilign(Fuetal.2014),FoldAlign/FoldAlignM(Havgaardetal.2005),LocARNA

(Will et al. 2007), RAF (Do et al. 2008), or TurboFold (Harmanci et al. 2011) can be helpful

for simultaneously predicting secondary structure and aligning sequences that are too dis-

similartobealignedbyprimarysequencewithoutusingsecondarystructure(Mathewsand

Turner 2002). These programs have similar average accuracy. TurboFold is the fastest, but

Dynalign, Foldalign, LocARNA, or RAF probably perform with higher accuracy when the

sequenceidentityislow(averagepairwisepercentsequenceidentitylessthan35%).Itmightbe

worthmakingpredictionswithmorethanonesoftwaretooltoobtainmultiplehypothesesfor

theconservedstructure.Forasetofhomologswithhighsequenceidentity( >85%),RNAalifold

isanotherexcellenttoolforpredictingthestructureconservedbymultiplehomologs(Bernhart

etal.2008).Itrequiresamultiplesequencealignmentasinput.Themethods,likeRNAalifold,

for finding secondary structure in multiple sequence alignments are best used as screening

toolstofindcommonhelices,whichcanbeusedtoanchorportionsofasequencealignment

whenmakingmanualrevisionsforfurtherroundsofanalysis.

Predicting RNA T ertiary Structure

AlthoughtherearemanyautomatedmethodsforaccurateRNAsecondarystructure predic-

tion,RNAtertiarystructurepredictionremainsamoredifficultproblem.Thisisbecausethe

spaceofpossibletertiarystructuresismuchlargerthanthespaceofpossiblesecondarystruc-

tures,andthereisnoknownalgorithmthatcansearchtheconformationalspaceasquicklyor

completelyascanbedoneforsecondarystructureprediction.

A pioneering approach to tertiary structure prediction was implemented in the MC-SYM

software(Majoretal.1991,1993;ParisienandMajor2008).Withanapproachcalledfragment

assembly, MC-SYM builds structural models by assembling nucleotides in conformations

collectedfromknownstructures.Eachpossiblemodelisstoreduntilitisshowntocontradict

a constraint, based on experimental data, comparative analysis, or secondary structure

prediction. The variations between all compatible models can suggest how accurately the

model has been determined with the data used. An early demonstration of the utility of

MC-SYM was the modeling of the hairpin ribozyme using data about secondary structure,

hydroxylradicalfootprinting,photoaffinitycross-linking,anddisulfidecross-linking(Pinard

etal.1999).Asubsequentcrystalstructureverifiedtheexistenceofapredictedlong-rangeGC

pair, although a predicted base triple, involving an A at that pair, was not observed (Rupert

andFerré-D’Amaré2001).Morerecently,thealgorithmwasusedinconcertwithanextended

secondary structure prediction method called MC-Fold, which can predict some tertiary

interactions, to accurately predict structures for RNA molecules up to 100 nucleotides in

length(ParisienandMajor2008).

AnotherRNAfragmentassemblyapproachisbasedontheRosettaframework(Chengetal.

2015),whichhasbeenhighlysuccessfulinproteinstructureprediction(Simonsetal.1997).

中文译文

第6章利用 RNA 序列的预测方法

6.8 研究 RNA 结构的其他计算方法

另一种广泛使用的 RNA 结构预测软件包是 ViennaRNA（Lorenz et al. 2011）。ViennaRNA 提供网络服务器版本和本地命令行工具两种使用方式。ViennaRNA 程序的输入遵循 UNIX 风格，接受标准输入（stdin）数据并将结果输出到标准输出（stdout），便于无缝集成到 UNIX 管道中。除了实现标准的最小自由能和配分函数算法外，ViennaRNA 还提供一套工具，用于预测多条序列的共同结构、绘制结构图、预测两条 RNA 链之间的双链结构（duplex structure），以及设计能够折叠成目标结构的序列。

Sfold 是配分函数计算的一种实现，采用随机采样程序（stochastic sampling procedure）来预测二级结构（Ding and Lawrence 1999, 2001, 2003）。该采样程序保证采得的构象具有真实的统计学权重。Sfold 通过网络界面提供服务。研究表明，Sfold 能够准确预测与反义寡核苷酸靶向相关的无配对区域（Ding and Lawrence 2001）。由于二级结构是通过统计采样生成的，因此在采样构象集合中某核苷酸未配对出现的次数比例，即为其未配对的预测概率。

NUPACK（Zadeh et al. 2010）是一个软件套件（提供网络服务器和可下载包），用于解决逆向折叠问题（inverse folding problem），即 RNA 结构预测的逆问题。NUPACK 不是输入序列来预测结构，而是输入目标结构，尝试找到能够折叠成该结构的序列。由于待搜索的序列空间极其庞大（长度为 N 的序列有 4ᴺ 种可能，例如 100 个核苷酸的 RNA 约有 1.6 × 10⁶⁰ 种可能序列），NUPACK 采用分层分解策略，将结构分解为多个组分，先为每个组分设计序列，再将组分序列组装；如果任何序列组合失败，则重新设计相应组分。寻找优质候选序列的方法是优化集合缺陷（ensemble defect），即通过配分函数计算的一个量，估计序列中有多少碱基正在形成目标结构（Zadeh et al. 2011）。

另一个重要问题是预测两个 RNA 分子是否会相互杂交以及所得双链的结构。该能力的重要应用包括预测 siRNA（Lu and Mathews 2007; Tafer et al. 2008）、miRNA 或 DNA 寡核苷酸的靶点（Mathews et al. 1999b）。最准确的 RNA–RNA 相互作用预测方法需要同时考虑自结构（self-structure）和分子间结构，因为自结构可能阻止第二条序列的结合。多序列折叠的实现工具包括 RNAup（Mückstein et al. 2006）和 RNAplex（Tafer and Hofacker 2008），它们属于 ViennaRNA 软件包的一部分；以及 BiFold（Mathews et al. 1999b）、DuplexFold（Mathews et al. 1999b）和 AccessFold（DiChiacchio et al. 2016），它们是 RNAstructure 的组件。网络服务器可访问 RNAup（通过 ViennaRNA 网络服务器）、BiFold（通过 RNAstructure 网络服务器）和 DuplexFold（通过 RNAstructure 网络服务器）。AccessFold 和 RNAplex 不提供网络服务器版本，但可以下载后在本地运行。

---

本节图/表归属说明：

Figure 6.11、6.12 归属前一节"07_Practical_Introduction_to_Multiple_Sequence_Methods"
Figure 6.13（本节未直接提及，但为 ViennaRNA/Sfold/NUPACK 工具图示）归属本节
本节无专属 Box

---

新增术语（暂记入 QA，待批量入库）：

英文术语	中文建议
ViennaRNA package	ViennaRNA 软件包
command line tools	命令行工具
UNIX-style input	UNIX 风格输入
stochastic sampling procedure	随机采样程序
true statistical weight	真实统计学权重
antisense oligonucleotide targeting	反义寡核苷酸靶向
inverse folding problem	逆向折叠问题
ensemble defect	集合缺陷
RNA-RNA interaction	RNA-RNA 相互作用
self-structure	自结构
intermolecular structure	分子间结构
duplex structure	双链结构
duplex	双链

术语表（5 条）

English	中文
[x] ViennaRNA	与 Chapter 5/Ch6 其他节一致
[x] RNAstructure	与 Chapter 6 前面各节一致
[x] Sfold	首次出现，保持原名
[x] NUPACK	首次出现，保持原名
[x] RNAup / RNAplex / BiFold / DuplexFold / AccessFold	首次出现，保持原名

049

Comparison of Methods

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176 Predictive Methods Using RNA Sequences

Comparison of Methods

No single program is yet available that can replace manual comparative sequence analysis, but

additional sources of information can dramatically improve prediction accuracy. When exper-

imental data such as SHAPE are available, single-sequence thermodynamic prediction can

often provide accurate secondary structures, correctly predicting 90% or more of the known

base pairs (Deigan et al. 2009; Cordero et al. 2012; Hajdin et al. 2013). If multiple homologs are

available, multiple-sequence predictions of the conserved secondary structure are more accu-

rate than single-sequence predictions (Asai and Hamada 2014; Havgaard and Gorodkin 2014).

Dynalign/Multilign (Fu et al. 2014), FoldAlign/FoldAlignM (Havgaard et al. 2005), LocARNA

(Will et al. 2007), RAF (Do et al. 2008), or TurboFold (Harmanci et al. 2011) can be helpful

for simultaneously predicting secondary structure and aligning sequences that are too dis-

similar to be aligned by primary sequence without using secondary structure (Mathews and

Turner 2002). These programs have similar average accuracy. TurboFold is the fastest, but

Dynalign, FoldAlign, LocARNA, or RAF probably perform with higher accuracy when the

sequence identity is low (average pairwise percent sequence identity less than 35%). It might be

worth making predictions with more than one software tool to obtain multiple hypotheses for

the conserved structure. For a set of homologs with high sequence identity (>85%), RNAalifold

is another excellent tool for predicting the structure conserved by multiple homologs (Bernhart

et al. 2008). It requires a multiple sequence alignment as input. The methods, like RNAalifold,

for finding secondary structure in multiple sequence alignments are best used as screening

tools to find common helices, which can be used to anchor portions of a sequence alignment

when making manual revisions for further rounds of analysis.

中文译文

第6章利用 RNA 序列的预测方法

6.9 方法比较

目前仍没有任何单一程序能够完全取代人工比较序列分析（manual comparative sequence analysis），但若能结合额外信息源，预测准确率可以显著提升。当已有 SHAPE 等实验数据时，基于热力学的单序列预测往往能够给出相当准确的二级结构，对已知碱基配对的正确预测率可达到 90% 甚至更高（Deigan et al. 2009; Cordero et al. 2012; Hajdin et al. 2013）。如果可获得多条同源序列，那么对保守二级结构进行的多序列预测（multiple-sequence prediction），通常比单序列预测更准确（Asai and Hamada 2014; Havgaard and Gorodkin 2014）。

对于那些仅靠一级序列、在不利用二级结构信息时难以可靠比对的序列，Dynalign/Multilign（Fu et al. 2014）、FoldAlign/FoldAlignM（Havgaard et al. 2005）、LocARNA（Will et al. 2007）、RAF（Do et al. 2008）以及 TurboFold（Harmanci et al. 2011）都可用于同时预测二级结构并完成序列比对（Mathews and Turner 2002）。这些程序的平均准确率彼此接近。TurboFold 的运行速度最快；但当序列同一性较低时（平均成对序列一致性低于 35%），Dynalign、FoldAlign、LocARNA 或 RAF 往往可能取得更高的准确率。实际分析时，值得并行使用不止一种软件，以形成对保守结构的多个候选假设。

对于一组序列同一性较高的同源序列（>85%），RNAalifold 也是预测多条同源序列共同保守结构的优秀工具（Bernhart et al. 2008）。它要求输入为多重序列比对（multiple sequence alignment）。像 RNAalifold 这类在多重序列比对中寻找二级结构的方法，更适合作为筛选工具（screening tool）来发现共同的螺旋区（common helices）；这些共同螺旋可作为后续人工修订序列比对时的锚点，从而支持进一步轮次的分析。

---

本节要点小结：

单一程序尚不能替代人工比较序列分析。
SHAPE 等实验数据可显著提升单序列预测准确率。
多序列预测通常优于单序列预测。
低同一性序列更适合结合结构信息进行联合比对与预测。
RNAalifold 更适用于高同一性同源序列，并常作为筛选共同螺旋的工具。

---

新增术语（暂记入 QA，待批量入库）：

英文术语	中文建议
manual comparative sequence analysis	人工比较序列分析
multiple-sequence prediction	多序列预测
sequence identity	序列同一性
average pairwise percent sequence identity	平均成对序列一致性
multiple sequence alignment	多重序列比对
screening tool	筛选工具
common helices	共同螺旋区

术语表（5 条）

English	中文
[x] SHAPE	与 Ch6 前文一致
[x] Dynalign / Multilign / TurboFold / RNAalifold	保持原工具名
[x] sequence identity	译为“序列同一性”
[x] multiple sequence alignment	译为“多重序列比对”
[x] manual comparative sequence analysis	译为“人工比较序列分析”

050

Predicting RNA Tertiary Structure

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