Lecture 12. DNA/RNA Structure Prediction. Epigenectics Epigenomics: Gene Expression

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1 C N F O N G A V B O N F O M A C S V U Master Course DNA/Protein Structurefunction Analysis and Prediction Lecture 12 DNA/NA Structure Prediction pigenectics pigenomics: Gene xpression ranscription factors (F) are essential for transcription initialisation ranscription is done by polymerase type (eukaryotes) mna must then move from nucleus to ribosomes (extranuclear) for translation n eukaryotes there can be many F-binding sites upstream of an OF that together regulate transcription Nucleosomes (chromatin structures composed of histones) are structures round of which DNA coils. his blocks access of Fs Nucleosome pigenectics pigenomics: Gene xpression (closed) (open) AA mna transcription xpression Because DNA has flexibility, bound Fs can move in order to interact with pol, which is necessary for transcription initiation (see next slide) ecent F-based initialisation theory includes a wave function (Carlsberg) of F-binding, which is supposed to go from left to right. n this way the F-binding site nearest to the AA box would be bound by a F which will then in turn bind Pol. t has been suggested that Speckles have something to do with this (speckels are observed protein plaques in the nucleus) Current prediction methods for gene co-expression, e.g. finding a single shared, do not take this F cooperativity into account ( parking lot optimisation ) xpression.. Speckel mna F Pol AA mna transcription his is still a hypothetical model DNA/NA Structure-Function relationships Apart from coding for proteins via genes, DNA is now known to code for many more NA-based cell components (snna, rna,..) he importance of structural features of DNA (e.g. bendability, binding histones, methylation) is becoming ever more important. For the many different classes of NA molecules, structure is directly causing function t is therefore important to analyse and predict DNA structure, but particularly, NA structure 1

2 Canonical base pairs he complementary bases, C-G and A-U form stable base pairs with each other through the creation of hydrogen bonds between donor and acceptor sites on the bases. hese are called Watson-Crick base pairs and are also referred to as canonical base pairs. n addition, we consider the weaker G-U wobble pair, where the bases bond in a skewed fashion. Other base pairs also occur, some of which are stable. hese are all called noncanonical base pairs. NA secondary structure he secondary structure of an NA molecule is the collection of base pairs that occur in its 3-dimensional structure. An NA sequence will be represented as = r 1, r 1, r 2, r 3,, r n, where r i is called the i th (ribo)nucleotide. ach r i belongs to the set {a,c,g,u}.. Secondary Structure and Pseudoknots A secondary structure, or folding, on is a set S of ordered pairs, written as i-j, satisfying: 1.j - i > 4 2.f i-j and i -j are 2 base pairs, (assuming without loss in generality that i i ), then either: 1. i = i and j = j (they are the same base pair), 2. i j i j (i-j precedes i -j ), or 3. i i j j (i-j includes i -j ) he last condition excludes pseudoknots. hese occur when 2 base pairs, i-j and i -j, satisfy i i j j. Pseudoknots Pseudoknots are not taken into account in secondary structure prediction because energy minimizing methods cannot deal with them. t is not known how to assign energies to the loops created by pseudoknots and dynamic programming methods that compute minimum energy structures break down. For this reason, pseudoknots are often considered as belonging to tertiary structure. However, pseudoknots are real and important structural features. However, covariance methods (next slide) are able to predict them from aligned, homologous NA sequences. he Figure on the next slide represents a small pseudoknot model. A 3D model of a pseudoknot A 3D model of a pseudoknot he 2 helices in the structure (preceding slide) are stacked coaxially. NA structure can be predicted from sequence data. here are two basic routes. 1. he first attempts structure prediction of single sequences based on minimizing the free energy of folding. 2. he second computes common foldings for a family of aligned, homologous NAs. Usually, the alignment and secondary structure inference must be performed simultaneously, or at least iteratively (see next slide) 2

3 Predicting NA Secondary Structure By hermodynamics Method Minimize Gibbs Free nergy By Phylogenetic Comparison Method (Covariance method) Compare NA Sequences of dentical Function From Different Organisms By Combination of the Above wo Methods n principle, this could be the most powerful method hermodynamics Gibbs Free nergy, G Describes the energetics of biomolecules in aqueous solution. he change in free energy, G, for a chemical process, such as nucleic acid folding, can be used to determine the direction of the process: G=0: equilibrium G>0: unfavorable process G<0: favorable process hus the natural tendency for biomolecules in solution is to minimize free energy of the entire system (biomolecules + solvent). hermodynamics G = H - S H is enthalpy, S is entropy, and is the temperature in Kelvin. Molecular interactions, such as hydrogen bonds, van der Waals and electrostatic interactions contribute to the H term. S describes the change of order of the system. hus, both molecular interactions as well as the order of the system determine the direction of a chemical process. For any nucleic acid solution, it is extremely difficult to calculate the free energy from first principle Biophysical methods can be used to measure free energy changes hermodynamics he quilibrium Partition Function For a population of structures S, a partition function Q and the probability for a particular folding, s can be calculated: G s Q = e s S Gs e he heat capacity for the NA can be obtained: 2 G G = ln Q and Cp = Heat capacity Cp (heat required to change temperature by 1 degree) can be measured experimentally, and can then be used to get information on G Q 2 is probability Zuker s nergy Minimization Method (mfold) An NA Sequence is called = {r 1,r 2,r 3 r n }, where r i is the i th ribonucleotide and it belongs to a set of {A, U, G, C} A secondary structure of is a set S of base pairs, i.j, which satisfies: 1=<i<j=<n; j-i>4 (can t have loop containing less than 4 nucleotides); f i,j and i.j are two basepairs, (assume i =< i ), then either» i = i and j = j (same base pair)» i < j < i < j (i.j proceeds i.j ) or» i < i < j < j (i.j includes i. j ) (this excludes pseudoknots which is i<i <j<j ) 5 3 f e(i,j) is the energy for the base pair i.j, the total energy for is ( S ) = e( i, j) he objective is to minimize (S). 3 5 i, j S Zuker s nergy Minimization Method (mfold) Free nergy Parameters xtensive database of free energies for the following NA units has been obtained (so called inoco ules and urner ules ): Single Strand Stacking energy Canonical (AU GC) and non-canonical (GU) basepairs in duplexes Still lacking accurate free energy parameters for Loops Mismatches (AA, CA etc) Using these energy parameters, the current version of mfold can predict ~73% phylogenetically deduced secondary structures. 3

4 Dynamic Programming (mfold) An xample of W(i,j) A matrix W(i,j) is computed that is dependent on the experimentally measured basepair energy e(i,j) ecursion begins with i=1, j=n 1. f W(i+1,j)=W(i,j), then i is not paired. Set i=i+1 and start the recursion again. 2. f W(i,j-1)=W(i,j), then j is not paired. Set j=j-1 and start the recursion again. 3. f W(i,j)=W(i,k)+W(k+1,j), the fragment k+1,j gets put on a stack and the fragment i k is analyzed by setting j = k and going back to the recursion beginning. 4. f W(i,j)=e(i,j)+W(i+1,j-1), a basepair is identified and is added to the list by setting i=i+1 and j=j-1 Suboptimal Folding (mfold) For any sequence of N nucleotides, the expected number of structures is greater than 1.8 N A sequence of 100 nucleotides has 3x10 25 foldings. f a computer can calculate 1000 strs./s -1, it would take years! mfold generates suboptimal foldings whose free energy fall within a certain range of values. Many of these structures are different in trivial ways. hese suboptimal foldings can still be useful for designing experiments. A computer predicted folding of Bacillus subtilis Nase P NA hese three representations are equivalent.. Secondary Structure Prediction for Aligned NA Sequences Both energy as well as NA sequence covariation can be combined to predict NA secondary structures o quantify sequence covariation, let f i (X) be the frequency of base X at aligned position and f ij (XY) be the frequency of finding X in i and Y in j, the mutual information score is (Chiu & Kolodziejczak and Gutell & Woese) fij ( XY ) M ij= fij ( XY )log X, Y fi ( X ) f j ( Y ) if for instance only GC and GU pairs at positions i and j then M ij =0. he total energy for NA is set to a linear combination of measured free energy plus the covariance contribution Other Secondary Prediction Methods Nusinov algorithm (historically important), Hogeweg and Hesper (1984) Vienna: uses the same recursive method in searching the folding space Added the option of computing the population of NA secondary structures by the equilibrium partition function Specific heat of an NA can be calculated by numerical differentiation from the equilibrium partition function NACAD: An effort in improving multiple NA sequence alignment by taking into account both primary as well secondary structure information Use Stochastic Context-Free Grammars (SCFGs), an extension of hidden Markov models (HMMs) method Bundschuh,., and Hwa,. (1999) NA secondary structure formation: A solvable model of heteropolymer folding. PHYSCAL VW LS 83, his work treats NA as heteropolymer and uses a simplified Go-like model to provide an exact solution for NA transition between its native and molten phases. unning mfold Constraints can be entered 1. force bases i,i+1,...,i+k-1 to be double stranded by entering: F i 0 k on 1 line in the constraint box. 2. force consecutive base pairs i.j,i+1.j-1,...,i+k-1.j-k+1 by entering: F i j k on 1 line in the constraint box. 3. force bases i,i+1,...,i+k-1 to be single stranded by entering: P i 0 k on 1 line in the constraint box. 4. prohibit the consecutive base pairs i.j,i+1.j-1,...,i+k-1.j-k+1 by entering: P i j k on 1 line in the constraint box. 5. prohibit bases i to j from pairing with bases k to l by entering: P i-j k-l on 1 line in the constraint box. 4

5 unning mfold 5 -CUUGGAUGGGUGACCACCUGGG-3 No constraint F entered Predicting NA 3D Structures Currently available NA 3D structure prediction programs make use the fact that a tertiary structure is built upon preformed secondary structures So once a solid secondary structure can be predicted, it is possible to predict its 3D structure he chances of obtaining a valid 3D structure can be increased by known space constraints among the different secondary segments (e.g. cross-linking, NM results). However, there are far less thermodynamic data on 3- D NA structures which makes 3-D structure prediction challenging. Mc-Sym Mc-Sym uses backtracking method to solve a general problem in computer science called the constraint satisfaction problem (CSP) Backtracking algorithm organizes the search space as a tree where each node corresponds to the application of an operator At each application, if the partially folded NA structure is consistent with its NA conformational database, the next operator is applied, otherwise the entire attached branch is pruned and the algorithm backtracks to the previous node. Mc-Sym (Continued) he selection of a spanning tree for a particular NA is left to the user, but it is suggested that the nucleotides imposing the most constraints are introduced first Users also supply a particular Mc-Sym conformation for each nucleotide. hese conformers are derived from currently available 3D databases Sample script: SQUNC 1 A r GAAUGCCUGCGAGCAUC CC DCLA 1 helixa * 2 helixa * 3 helixa * 4 helixa * 5 helixa * 6 helixa * 19 helixa * Mc-Sym (Continued) LAONS 18 helix * helix * helix * helix * 6 4 helix * 5 3 helix * 4 2 helix * 3 1 helix * 2 BULD ; CONSANS (enter experimental constraints) NA-protein nteractions here is currently no computational method that can predict the NA-protein interaction interfaces; Statistical methods have been applied to identify structure features at the protein-na interface. For instance, NANCL finds that most atoms contributed from a protein to recogonizing an NA are from main chains (C, O, N, H), not from side chains! But much remains to be done; lectrostatic potential has primary importance in protein-na recognition due to the negatively charged phosphate backbones. fforts are made to quantify electrostatic potential at the molecular surface of a protein and NA in order to predict the site of NA interaction. his often provides good prediction at least for the site on the protein. 5

6 eferences Predicting NA secondary structures: good reviews 1. urner, D. H., and Sugimoto, N. (1988) NA structure prediction. Annu ev Biophys Biophys Chem 17, Zuker, M. (2000) Calculating nucleic acid secondary structure. Curr Opin Struct Biol 10, Obtaining experimental thermodynamics parameters: 3. Xia,., SantaLucia, J., Jr., Burkard, M.., Kierzek,., Schroeder, S. J., Jiao, X., Cox, C., and urner, D. H. (1998) hermodynamic parameters for an expanded nearest-neighbor model for formation of NA duplexes with Watson- Crick base pairs. Biochemistry 37, Borer, P. N., Dengler, B., inoco,., Jr., and Uhlenbeck, O. C. (1974) Stability of ribonucleic acid double-stranded helices. J Mol Biol 86, hermodynamics heory for NA structure prediction: 5. Bundschuh,., and Hwa,. (1999) NA secondary structure formation: A solvable model of heteropolymer folding. PHYSCAL VW LS 83, McCaskill, J. S. (1990) he equilibrium partition function and base pair binding probabilities for NA secondary structure. Biopolymers 29,