Computational Molecular Biology. Protein Structure and Homology Modeling

Computational Molecular Biology Protein Structure and Homology Modeling Prof. Alejandro Giorge1 Dr. Francesco Musiani

Sequence, function and structure relationships v Life is the ability to metabolize nutrients, respond to external stimuli, grow, reproduce and evolve v From a chemical point of view, proteins are linear hetero-polymers formed by amino acids (aa) v Proteins assume a 3D shape which is usually responsible for function v The consequence of the tight link between structure, function and evolutionary pressure distinguish proteins from ordinary polymers

Protein structure v v v v v The sequence of amino acids is called the primary structure Secondary structure refers to local folding Tertiary structure is the arrangement of secondary elements in 3D Quaternary structure describes the arrangement of a protein subunits The peptide bond is planar and the dihedral angle it defines is almost always 18

Protein structure v What is a dihedral angle? Is the angle between two planes. In practice, if you have four connected atoms and you want measure the dihedral angle around the central bond, you orient the system in such a way that the two central atoms are superimposed and measure the resulting angle between the first and last atom.

Protein structure v The simplest arrangements of aa is the alpha-helix, a right handed spiral conformation. v The structure repeats itself every 5.4 Å along the helix axis. v There are 3.6 aa per turn. O (n) - NH (n+4) H- bond

Protein structure v The beta sheet. v The R groups of neighboring residues in strand point in opposite directions. v There are parallel or anti-parallel beta sheets.

Protein structure Ramchandan plot: pairs of angles that do not cause the atoms of a dipeptide to collide.

Protein structure

Protein structure Right- handed α- helix

Protein structure Parallel β- sheet Right- handed α- helix

Protein structure An<- parallel β- sheet Parallel β- sheet Right- handed α- helix

Protein structure An<- parallel β- sheet Le?- handed α- helix Parallel β- sheet Right- handed α- helix

Protein structure An<- parallel β- sheet Parallel β- sheet Collagen triple helix Le?- handed α- helix Right- handed α- helix

Protein structure Loops: regions without repetitive structure that connects secondary structure elements.

Protein structure Supersecondary elements (motifs): arrangements of two or three consecutive secondary structure that are present in many different protein structures, even with completely different sequences.

Protein structure Domains: portion of the polypeptide chain that folds into a compact semi-independent unit. v Class (C) Derived from secondary structure content is assigned automa<cally v Architecture (A) Describes the gross orienta<on of secondary structures, independent of connec<vity. v Topology (T) Clusters structures according to their topological connec<ons and numbers of secondary structures v Homologous superfamily (H)

Ala: transient interac<ons Thr, Ser: phosphoryla<on target: protein kinases anack phosphate group to the side- chain. Gly: unusual ramachandran, o?en found in turns Thr: Beta- branched more o?en found in beta- sheets. Cys: Very reac<ve, coordinate metals.

The problem of protein folding What is protein fold: v Compact, globular folding arrangement of the polypeptide chain v Chain folds to optimize packing of the hydrophobic residues in the interior core of the protein Thermodynamics: ΔG = ΔH TΔS (i.e. stability of a given conformation) Enthalpy: electrostatics, dispersion, van der Waals, H-bonds. Entropy: water molecules form ordered cages around hydrophobic amino acids. The protein folding process breaks this order. The free energy of folding of a protein is of the order of few kcal/mol

The problem of protein folding v Anfinsen s dogma: (at least for small globular proteins) the native structure is determined only by the protein's amino acid sequence

The problem of protein folding v Anfinsen s dogma: (at least for small globular proteins) the native structure is determined only by the protein's amino acid sequence v Levinthal paradox: because of the very large number of degrees of freedom in an unfolded polypeptide chain, the molecule has an astronomical number of possible conformations

The problem of protein folding - + ΔH Internal interactions TΔS Conformational entropy TΔS Hydrophobic effects Result: ΔG Folding

Evolution of protein structure v What if a base-substitution event occurs in a protein-coding DNA region? A. The fine balance between the gain and loss of free energy of folding is compromised: no single energy minimun NOT FOLD B. The energy landscape of the protein change, but there is a global minimum of energy same or similar function (i.e. local perturbations without affecting the general shape or topology) FOLD

The comparative modeling principle

Evolutionary-based methods for protein structure prediction v Proteins evolved from a common ancestor maintain similar core 3D structures We can use protein of known structure (templates) to model protein of unknown 3D structure (targets) by starting from the sequence This can be done if the templates and the target are evolutionarily correlated

Why Protein Structure Prediction? We have an experimentally determined atomic structure for only ~1% of the known protein sequences

Why Protein Structure Prediction? Growth in the number of unique folds per year in the PDB based on the SCOP data base from 1986 to 27

Why? v We can use homology modeling to predict the structure of proteins of unknown structure but also

Why? v We can use homology modeling to predict the structure of proteins of unknown structure but also To reconstruct some missing part in an incomplete protein structure (common in low resolution structures or for large mobile loops) To calculate a mutant of a known protein structure To calculate the mean structure of an NMR ensamble

Homology modeling flowchart Query sequence

Homology modeling flowchart Query sequence Search for suitable template(s) Sequence databases

Homology modeling flowchart Query sequence Search for suitable template(s) Sequence databases Align sequence with template(s)

Homology modeling flowchart Query sequence Search for suitable template(s) Sequence databases Align sequence with template(s) Template PDB structure(s)

Homology modeling flowchart Query sequence Search for suitable template(s) Sequence databases Align sequence with template(s) Template PDB structure(s) Calculate model(s)

Homology modeling flowchart Query sequence Search for suitable template(s) Sequence databases Align sequence with template(s) Template PDB structure(s) Calculate model(s) Assess results Refinement (loops)

Homology modeling flowchart Query sequence Search for suitable template(s) Sequence databases Possible errors Align sequence with template(s) Template PDB structure(s) Calculate model(s) Model(s) Assess results Refinement (loops)

Homology modeling flowchart hnp://salilab.org/modeller/

How does it works?

1. Align sequence with structures v First, must determine the template structures Simplistically, try to align the target sequence against every known structure s sequence. In practice, this is too slow, so heuristics are used (e.g. BLAST) Profile or HMM searches are generally more sensitive in difficult cases (Modeller s profile.build method, PSI-BLAST or HHpred) Could also use threading or other web servers v Remember to look at: Sequence identity/similarity between the putative template(s) and the target Experimental method, resolution and completeness of the template(s) Other compounds bound to the template(s) Oligomerization state

1. Align sequence with structures v Alignment to templates Sequence-sequence: relies purely on a matrix of observed residue-residue mutation probabilities ( align ) Sequence-structure: gap insertion is penalized within secondary structure (helices etc.) ( align2d ) Other features, profile-profile, and/or user-defined ( salign ) or use an external program v Remember: An error in the alignment is always a fatal error for the whole modeling procedure! One amino acid sequence plays coy; a pair of homologous sequences whisper; many aligned sequences shout out loud (A.M. Lesk, Introduction to Bioinformatics, 22)

1. Align sequence with structures v Evaluation of sequence alignment quality E. Krieger, S.B. Nabuurs, G. Vriend: Homology modeling. In Structural Bioinforma<cs. P.E. Bourne and H. Weissig Eds. (23).

2. Extract spatial restraints v Spatial restraints incorporate homology information, statistical preferences, and physical knowledge Template Cα- Cα internal distances Backbone dihedrals (φ/ψ) Sidechain dihedrals given residue type of both target and template Force field stereochemistry (bond, angle, dihedral) Statistical potentials Other experimental constraints Etc.

3. Satisfy spatial restraints v Satisfaction of spatial restraints Represent system at appropriate level(s) of resolution (e.g. atoms, residues, domains, proteins) Convert each data source into spatial restraints (e.g. harmonic distance simulates using spring ) Sum all restraints into a scoring function Generate models that are consistent with all restraints by optimizing the scoring function (e.g. conjugate gradients, molecular dynamics, Monte Carlo)

3. Satisfy spatial restraints v All information is combined into a single objective function Force field (CHARMM 22) simply added in Function is optimized by conjugate gradients and simulated annealing molecular dynamics, starting from the target sequence threaded onto template structure(s) Multiple models are generally recommended best model or cluster or models chosen by simply taking the lowest objective function score, or using a model assessment method such as Modeller s own DOPE or GA341, or external programs such as PROSA or DFIRE

4. Assess results

4. Assess results v How do we know if the model is a good one? Check log file for restraint violations and Modeller score (molpdf) (not reliable since the scoring function is not perfect!) Use another assessment score on the final model Ø Statistical Potential: GA341, DOPE, QMEAN Ø Other programs (e.g. Prosa, Verify3D..) Use structure assessment programs (e.g. ProCheck) Fit the model to some other experimental data not used in the modeling procedure

Typical assessments DOPE profile

Typical assessments DOPE profile Ramachandran plot (ProCheck)

Typical assessments DOPE profile Ramachandran plot (ProCheck) PROSA profile

Structural alignment Root-mean square deviation (RMSD) 2 Structural alignment of thioredoxins from humans (red) and the fly Drosophila melanogaster (yellow) Where x i and x j are the coordinate vectors of the structure i and j, respectively, and N is the number of atoms of the two strucures

Typical errors in comparative models

Model Accuracy as a Function of Target-Template Sequence Identity

Model accuracy

Applications of protein structure models Topology recogni<on Famili assignment Overall fold Mutagenesis design Func<onal rela<onship Drug design Virtual screening Docking Binding site detec<on

Model refining v Loop optimization Often, there are parts of the sequence which have no detectable templates Mini folding problem these loops must be sampled to get improved conformations Database searches only complete for 4-6 residue loops Modeller uses conformational search with a custom energy function optimized for loop modeling (statistical potential derived from PDB) Ø Fiser/Melo protocol ( loopmodel ) Ø Newer DOPE + GB/SA protocol ( dope_loopmodel )

Model refining v Accuracy of loop models as a function of amount of optimization

Model refining v Fraction of loops modeled with medium accuracy (<2Å)

Advanced topics v Modeller can also Perform more sensitive searches for templates (sequence-profile, profile-profile, similar to PSI-BLAST) Incorporate ligands, RNA/DNA and water molecules into built models Build structures of multi-chain proteins (homo or hetero) Add extra restraints to the modeling process (such as known distances, e.g. from FRET) Use multiple templates to build a model v Remember: You don t have to use Modeller for template search, alignment, assessment or refinement. If you know your template (e.g. from BLAST) just format the alignment for Modeller and skip straight to the model building step!

Hidden Markov Models A dishonest croupier could use a dice that has a higher probability of landing on a 6, (e.g., 5%). To avoid being caught, the croupier can switch from a fair die to a loaded die with a certain frequency. For example, he can change the die from fair to loaded after 2 rolls and from loaded to fair after 1 rolls. v Likelihood evaluation Given a series of emissions X1, X2, X3 Which is the probability that our model had emitted the observed sequence? v Alignment. Given the sequence of observed emissions: which is the sequence of hidden states that generated it? v Training: How can we optimize the statistical parameters in order to maximize probabilities 1 and 2? 42

Hidden Markov Models: Protein Structural Bioinformatics In structure prediction, models can best be thought of as sequence generators (e.g., Hidden Markov Models) or sequence classifiers (e.g., Neural Networks) v Likelihood evaluation Performed using dynamic programming algorithms (similar to the ones used in sequence alignments) v Alignment Thus, given a model and a sequence we want to determine the probability of any specific (query) sequence having been generated by the model in any of each possible paths. v Training The model is trained by aligning protein families. 43

Hidden Markov Models v Described by ü A set of possible states: match, insert, deletion. ü A set of possible observations: frequencies of aa in each position. ü A transition probability matrix ü An emission probability matrix (frequencies of aa occurring in a particular state). ü Initial state probabilities. 44

Sequence profiles are a condensed representation of alignments master sequence HBA_human W G K V G A - - H A G E HBB_human W G K V - - - - N V D E MYG_phyca W G K V E A - - D V A G LGB2_luplu W K D F N A - - N I P K GLB1_glydi W E E I A G A D N G A G Each column of the profile p j (a) contains the amino acid frequencies in the multiple sequence alignment A C D E F G H I K L M N P Q R S T V W Y 1..2.6.2.2.2.6.25.75.2.4.2.2.25.4.2.25.25.2.2.4.2.2.2.2.25.6.2.6.4

HMM include position specific gap penalties Deletions Insertions Probabilities for Insert Open Insert Extend Delete Open Delete Extend M/D M/D M/D I I M/D M/D M/D M/D M/D HBA_human V G A.. H A G E Y HBB_human V - -.. N V D E V MYG_phyca V E A.. D V A G H LGB2_luplu F N A.. N I P K H GLB1_glydi I A G a d N G A G V A C D E F G H I K L M N P W Y M I I I M D D D.25.75.2.4.2.2.25.4.2.25.25.2.2.4.2.4.2.2.2.25.6.2.2.25.5.2 1. Match or Delete

Profile HMM can be represented as states connected by transitions Probability that a sequence is emitted by an HMM rather than by a random model? M/D M/D M/D I I M/D M/D M/D M/D M/D HBA_human V G A.. H A G E Y HBB_human V - -.. N V D E V MYG_phyca V E A.. D V A G H LGB2_luplu F N A.. N I P K H GLB1_glydi I A G a d N G - G V I I I I I I I I HMM p M M M M M M M M D D D D D D D D The probability for emitting the sequence x1,.., xl along the path through an HMM is: P(x1,..., x1 emission on path). This probability is a product of the amino acid emission probabilities for each state on the path and the transition probabilities between states.

Profile HMM can be represented as states connected by transitions M/D M/D M/D I I M/D M/D M/D M/D M/D HBA_human V G A.. H A G E Y HBB_human V - -.. N V D E V MYG_phyca V E A.. D V A G H LGB2_luplu F N A.. N I P K H GLB1_glydi I A G a d N G - G V HMM p I M I M I M I I I I I M M M M M Matrix: p i (a) p i (X Y) A C W Y M I I I M D D D D D D D D D D D.25.75.2.4.2.25.5.2 1.

State q State p M D I M D I M D I M D I M D I M D I M D I HMM q M M M M M I M M M M D M M M D I M D I M D I M D I M D I HMM p x 1 x 2 x 3 x 4 x 5 x 6 Söding, J. (25) Bioinformatics 21, 951-96. Include Null model maximize log-sum-of-odds score Co-emitted sequence Find path through two HMM that maximizes co-emission probability

Excercise v Target: human thioesterase 8 : interacts with HIV-1 Nef protein. v Procedure: Search for templates using HHpred Prepare Modeller input files Build the models Evaluate the model structure v Materials and Methods: UniProt Modeller (http://salilab.org/modeller/) Modeller manual ProCheck web server (http://www.ebi.ac.uk/thornton-srv/ databases/pdbsum/generate.html) Prosa web server (https://prosa.services.came.sbg.ac.at/ prosa.php)

Fold recognition Principle: Find a compatible fold >Target Sequence XY MSTLYEKLGGTTAVDLAVAAVA GAPAHKRDVLNQ Profile method For each aa we can calculate the frequency in Secondary elements Surface of the protein Hydrophobic environment Each aa is substituted by a letter (property) From the structure we can analyze positions in terms of: Build model of target protein based on each template structure Rank models according to SCORE or ENERGY - Presence in secondary structure element - Percentage of solvent exposition - Hydrophobic or polar environment? Thus each structure is converted into property sequencesnot aa PDB becomes a property sequence DB. Thus we have to just align property sequences

Fold recognition v Threading methods Ø Statistical Potentials Ø Programs: Threader, mgenthreader. M A T E A F T Q S G Several approximations: Frozen approximation used for accelerate calculations In the past used for remote homology assessment Now used in automatic projects for the structural prediction of the entire human genome.

New folds

New folds v Ab inito modeling or de novo prediction Ø Folding by statistical approaches: very coarse-grained Ø Force Fields Ø Fragment Assemblies. Ø Ø Structure with common structural motifs or supersecondary structures The relationship between local sequence and local structure is highly degenerated Ø Programs: Fragfold and Rosetta Ø These approaches were a real breakthrough in the field Ø New folds, difficult crustal structures, difficult modeling, protein design: see articles by David Baker.

Fragment Assembly MSSPQAPEDGQGCGDRGDPPGDLRSVLVTTV ROSETTA 9 aa fragments Choose the 25 closest sequences FRAGFOLD Supersecondary structure elements tri, tetra and penta peptides Each fragment is energetically evaluated (Statistical potential) ROSETTA Simulated Annealing of dihedral angles Optimization and Assembly (statistical potential) FRAGFOLD Random combination of fragments Simulated annealing