RNA structure analysis Jurgen Mourik & Richard Vogelaars Utrecht University.

RNA structure analysis

Jurgen Mourik &

Richard VogelaarsUtrecht University

RNA structure analysis2

Overview

• Introduction to RNA

• RNA secondary structure prediction– Nussinov folding algorithm– Zuker folding algorithm

• Demonstration

• Questions


Introduction to RNA (1)

• Ribonucleic acid

• To many people:– “RNA is the passive intermediary messenger

between DNA genes and the protein translation machinery”

• But:– Many non-coding RNAs exist

• Adopt sophisticated 3D structures• Catalyse biochemical reactions


Introduction to RNA (2)

• Three major types of RNA

• Messenger RNA (mRNA)– Serving as a temporary copy of genes that is used

as a template for protein synthesis.

• Transfer RNA (tRNA)– Functioning as adaptor molecules that decode the

genetic code.

• Ribosomal RNA (rRNA)– Catalyzing the synthesis of proteins.


RNA world hypothesis

• RNA is the only biological polymer that serves as both a catalyst (like proteins) and as information storage (like DNA).

• For this reason some people think that a RNA-like molecule was the basis of life early in evolution.


Terminology of RNA (1)

• Four nucleotides: – Adenine– Cytosine– Guanine– Uracil

• Canonical base pairs:– G-C– A-U

• Non-canonical base pairs– G-U


Terminology of RNA (2)

• Base pairs are approximately coplanar and almost always stacked onto other base pairs in a RNA structure– Contiguous stacked base pairs are called stems– In 3D, RNA stems generally form a regular double

helix


RNA secondary structure

• Unlike DNA, RNA is typically produced as a single stranded molecule which then folds intramolecularly to form a number of short base-paired stems. This base-paired structure is called the secondary structure of the RNA.


Elements of a RNA secondary structure (1)

• Loop: single stranded subsequence bounded by base pairs

• Hairpin loop: a loop at the end of a stem

• Bulge (loop): single stranded bases occurring within a stem

• Interior loop: single stranded bases interrupting both sides of a stem

• Multi-branched loop: a loop from which three or more stems radiate


Elements of a RNA secondary structure (2)

G ● C G ● C U ● A A ● U C ● G

G G 3’

G A 5’

CCC

etc.

UGU


Pseudoknots (1)

• Base pairs almost always occur in a nested fashion in RNA secondary structure

• A base pair between position i and j and a base pair between i’ and j’ are nested if and only if:

• Non-nested base pairs are called pseudoknots

''or '' jjiijjii


Pseudoknots (2)

• None of the dynamic programming algorithms can deal with pseudoknots, including the Zuker and Nussinov RNA folding algorithms.

• Pseudoknots occur in many important RNA’s:– The algorithms ignore biologically important

information.

• For database searching for RNA homologues, it is acceptable to sacrifice the information in pseudoknots.


RNA sequence evolution

• The sequence evolution of RNA is constrained by the structure.

• It is possible to have two different RNA sequences with the same secondary structure.

• Drastic changes in sequence can often be tolerated as long as compensatory mutations maintain base-pairing complementarity.


RNA sequence evolution (2)

• Suppose we want to search for a nucleotide sequence for occurrences of consensus R17 coat protein:– It is useless to use standard

sequence alignment

• R17 coat protein binds and represses translation of its replicase:– It blinds most of the primary

sequence positions

{A, C, G, U}

{A,G}

{C,U}

Complement of base N


RNA sequence evolution (3)

• How to solve this problem?– RNA pattern-matching program

(RNAMOT).

• Searches for deterministic (non-stochastic) motifs but with secondary structure constraints as extra terms.

• Works fine for small, well-defined patterns but is somewhat insensitive and problematic for finding matches to less well conserved structures.


Inferring structure by comparative sequence analysis

• In a structurally correct multiple alignment of RNAs, conserved base pairs are often revealed by the presence of frequent correlated compensatory mutations

• RNA secondary prediction method: comparative sequence analysis

• The accepted consensus structures of most well-studied RNAs have been derived by comparative analysis.


How does comparative sequence analysis work? (1)

• Inferring the correct structure by comparative analysis requires knowing a structurally correct alignment

• Inferring a structurally correct multiple alignment requires knowing the correct structure

Problem!


How does comparative sequence analysis work? (2)

• Solution: make use of an iterative refinement process of:– Guessing the structure based on the current best

guess of the alignment– Realigning based on the new guess at the

structure• The sequences to be compared must be:

– Sufficiently similar to start the process– Sufficiently dissimilar that a number of co-varying

substitutions can be detected


Mutual information (1)

• A quantitative measure of pairwise sequence covariation

• Given two aligned columns i, j, the mutual information is given by:

ji ji

ji

jixx xx

xx

xxij ff

ffM

,2log

The frequency of one of the four bases

observed in column i.

The joint (pairwise) frequency of one of the sixteen possible base pairs observed in

columns i, j.

Mij varies between 0 and 2 bits


Mutual information (2)

• Mij tells us how much information we get about the identity of the residue in one position if we are told the identity of the residue in the other position– If you know that i is a G, the uncertainty about j

collapses from four different possibilities to just one (C) 2 bits of information

– If i and j are uncorrelated, the mutual information is zero


RNA secondary structure prediction (1)

• Many plausible secondary structures can be drawn for a sequence

• But: the number of secondary structures increases exponentially with sequence length– An RNA of 200 bases has over 1050 possible

base-paired structures

• Goal: distinguish the biologically correct structure from all the incorrect structures.


RNA secondary structure prediction (2)

• We need:– A function that assigns the correct structure the

highest score– An algorithm for evaluating the scores of all

possible structures

• Two methods:– Nussinov folding algorithm– Zuker folding algorithm

Need a break?

Well here it is!


Nussinov folding algorithm (1)

• Goal: Find the structure with the most base pairs

• Nussinov introduced an efficient dynamic programming algorithm for this problem

• A recursive algorithm that calculates – the best structure for small subsequences and– works its way outwards to larger and larger

subsequences



• Key idea of recursion:– There are only four possible ways of getting the

best structure for i,j from the best structure of the smaller subsequences

• Two stages:– Fill stage of the algorithm– Trace back stage of the algorithm



• The four possible ways:1. Add unpaired position i onto the best structure for subsequence i+1,j

2. Add unpaired position j onto the best structure for subsequence i,j-1

3. Add i,j pair onto best structure found for subsequence i+1,j-1

4. Combine two optimal substructures i,k and k+1,j



• Formal description of the algorithm:– Given a sequence x of length L with symbols xi,…,xL

– Let if xi and xj are complementary base pairs else

– Recursively calculate scores which are the maximum number of base pairs that can be formed for subsequence xi,…,xL

1),( ji0),( ji

),( ji


Nussinov algorithm: fill stage

– Initialisation:

– Recursion: starting with all sub sequences of length 2, to length L:

Liii

Liii

to1for 0),(

to2for 0)1,(

)].,1(),([max

),,()1,1(

),1,(

),,1(

max),(

jkki

jiji

ji

ji

ji

jki


Example sequence: GGGAAAUCC

j

i

1 2 3 4 5 6 7 8 9

G G G A A A U C C

1 G 0

2 G 0 0

3 G 0 0

4 A 0 0

5 A 0 0

6 A 0 0

7 U 0 0

8 C 0 0

9 C 0 0



j

i

1 2 3 4 5 6 7 8 9

G G G A A A U C C

1 G 0 0

2 G 0 0 0

3 G 0 0 0

4 A 0 0 0

5 A 0 0 0

6 A 0 0 1

7 U 0 0 0

8 C 0 0 0

9 C 0 0

A*U= base pair

110

)7,6()6,7(

),()1,1(

jiji



j

i

1 2 3 4 5 6 7 8 9

G G G A A A U C C

1 G 0 0 0 0 0 0 1 2 3

2 G 0 0 0 0 0 0 1 2 3

3 G 0 0 0 0 0 1 2 2

4 A 0 0 0 0 1 1 1

5 A 0 0 0 1 1 1

6 A 0 0 1 1 1

7 U 0 0 0 0

8 C 0 0 0

9 C 0 0

This value gives the

maximum nr. of base pairs


Nussinov algorithm: traceback stage

• Initialisation: Push (1,L) onto the stack.

• Recursion: Repeat until stack is empty:

break

),(push

),1(push

);,( ),1(),( if :1 to1for else

)1,1(push

pair base , record

:),()1,1( if else

);1,(push ),()1,( if else

);,1(push ),(),1( if else

continue if

),(pop

,

ki

jk

jijkkijik

ji

ji

jiji

jijiji

jijiji

ji

ji

ji



j

i

1 2 3 4 5 6 7 8 9

G G G A A A U C C

1 G 0 0 0 0 0 0 1 2 3

2 G 0 0 0 0 0 0 1 2 3

3 G 0 0 0 0 0 1 2 2

4 A 0 0 0 0 1 1 1

5 A 0 0 0 1 1 1

6 A 0 0 1 1 1

7 U 0 0 0 0

8 C 0 0 0

9 C 0 0

Initialisation:Push (1,L)



j

i

1 2 3 4 5 6 7 8 9

G G G A A A U C C

1 G 0 0 0 0 0 0 1 2 3

2 G 0 0 0 0 0 0 1 2 3

3 G 0 0 0 0 0 1 2 2

4 A 0 0 0 0 1 1 1

5 A 0 0 0 1 1 1

6 A 0 0 1 1 1

7 U 0 0 0 0

8 C 0 0 0

9 C 0 0

Recursion:

)9,1()9,2(

),1(push ),(),1( if else

jijiji



j

i

1 2 3 4 5 6 7 8 9

G G G A A A U C C

1 G 0 0 0 0 0 0 1 2 3

2 G 0 0 0 0 0 0 1 2 3

3 G 0 0 0 0 0 1 2 2

4 A 0 0 0 0 1 1 1

5 A 0 0 0 1 1 1

6 A 0 0 1 1 1

7 U 0 0 0 0

8 C 0 0 0

9 C 0 0



j

i

6 7 8 9

A U C C

1 G 0 1 2 3

2 G 0 1 2 3

3 G 0 1 2 2

4 A 0 1 1 1

5 A 0 1 1 1

6 A 0 1 1 1

7 U 0 0 0 0

GG ● CG ● CA

AA

● U


SCFG version of the Nussinov algorithm

• Stochastic Context-Free Grammars– Will be discussed next Wednesday

• Makes use of production rules:– S aS | cS | gS | uS (i unpaired)

• Every production rule has a associated probability parameter.

• The maximum probability parse is equivalent to the maximum probability secondary structure.


Needed terminology

• The inside-outside (recursive dynamic programming) algorithm for SCTGs in Chomsky normal form is the natural counterpart of the forward-backward algorithm for HMM.

• Best path variant of the inside-outside algorithm is the Cocke-Younger-Kasami (CYK) algorithm. It finds the maximum probabilistic alignment of the SCFG to the sequence.

Just as the viterbi algorithm for

HMMs

Chomsky normal form:All context free grammar production rules are of the form:

S SS orS a


CYK for Nussinov-style RNA SCFG (2)

• Initialisation:

• Recursion:

LiSxp

Sxpii

Liii

i

i to1for )(log

)(logmax),(

to2for )1,(

).(log),1(),(max

);(log)1,1(

);(log)1,(

);(log),1(

max),(

SSpjkki

Sxxpji

Sxpji

Sxpji

ji

jki

ji

j

i

Addition to the fill stage of the Nussinov

algorithm.The principal difference

is that the SCFG description is a

probabilistic model.



• The is the log likelihood of the optimal structure given the SCFG model

• The traceback to find the secondary structure corresponding to the best score is performed analogously to the traceback in the Nussinov algorithm

),1( L )|ˆ,(log xP̂



• Good starting example (10.2), but it is too simple to be an accurate RNA folder

• The algorithm does not consider important structural features like preferences for certain:– Loop lengths– Nearest neighbours in the structure caused by

stacking interactions between neighbouring base pairs in a stem.


Zuker folding algorithm (1)

• Most sophisticated secondary structure prediction method for single RNAs– An energy minimisation algorithm which assumes

that the correct structure is the one with the lowest equilibrium free energy

• The of an RNA secondary structure is approximated as the sum of individual contributions from loops, base pairs and other secondary structure elements.

G

G



• Difference with the Nussinov folding algorithm:– Energies of stems are calculated by adding

stacking contributions for the interface between neighbouring base pairs instead of individual contributions for each pair.

• Advantage:– Better fit to experimentally observed values for

RNA structures, but it complicates the dynamic programming algorithm

G


Zuker folding algorithm (3)Freier energy rules

• The energies in the tables are from the older ‘Freier rules’ at 37ºC.

• For more information see the article ”Improved free-energy parameters for predictions of RNA duplex stability” by Freier et al.



• The minimum energy structure can be calculated recursively by a dynamic programming algorithm very similar to how the maximum base-paired structure was calculated like the Nussinov algorithm.

• Now we keep two matrices– W(i,j) is the energy of the best structure on i,j– V(i,j) is the energy of the best structure on i,j given

that i,j are paired.


Suboptimal RNA folding(CYK algorithm will be explained next Wednesday)

• The original Zuker algorithm finds only the optimal structure.

• The biologically correct structure is often not the calculated optimal structure.

• Zuker introduced a suboptimal folding algorithm.– Is similar to running the CYK algorithm in both inside and

outside directions.

• The algorithm samples one base pair sub optimally.

• The rest of the structure is the optimal structure given that base pair.

Demonstration

RNAstructureBy David H. Mathews

Michael Zuker

Doulas H. Turner


Demo: RNAstructure (1)

• The core of RNAstructure is a dynamic programming algorithm to predict RNA or DNA secondary structures from sequence based on the principle of minimizing free energy.



• The prediction of a secondary structure is based on the Zuker algorithm for free energy minimization using the nearest neighbour parameters of Doug Turner and co-workers.

• A recursive algorithm is used that generates an optimal structure and a series of structures that are called sub-optimal structures (structures with free energy similar to the lowest free energy structure).



• The number of sub-optimal structures generated is controlled by two parameters entered by the user:– Max % Energy Difference: Sets the percent difference

from the lowest free energy allowed for the structures output. For example if the lowest-free energy structure is -100 kcal/mol, and the Max % Energy Difference is 10, any structures with an energy of -90 kcal/mol or higher is rejected (higher means less negative).

– Max number of structures: Sets an absolute upper limit on the number of structures that can be generated. A maximum of 1000 structures can be generated.



• A third parameter entered is Window Size. This controls how different the sub-optimal structures must be from each other. A small window size allows very similar structures to be generated while a larger window size requires them to be more different

Demonstration

Questions?

RNA structure analysis Jurgen Mourik & Richard Vogelaars Utrecht University.

Documents

Transcript of RNA structure analysis Jurgen Mourik & Richard Vogelaars Utrecht University.