Doug Raiford Lesson 19

 Framework model  Secondary structure first  Assemble secondary structure segments  Hydrophobic collapse  Molten: compact but denatured  Formation of secondary structure after: settles in  van der Waals forces and hydrogen bonds require close proximity 10/26/20152Protein Conformation Prediction (Part III)

 Two main approaches  Focus this lesson: De novo 10/26/2015Protein Conformation Prediction (Part III)3 Structure prediction methods De novo Ab initio Molecular Dynamics Knowledge based Lattice Off-lattice Local structure Comparative / Homology modeling

 Did a quick look at threading (homology based)  Chou-Fasman (frequency of occurrence of aa’s at specific locations in structure)  Looked at HMM’s (HMMR and Protein Families—PFAM)  Looked at ROSETTA (De Novo, knowledge based) 10/26/20154Protein Conformation Prediction (Part III) Name P(a) P(b) P(turn) Alanine Arginine Aspartic Acid Valine

 Lattice Approach  Abstraction: take a problem of extreme complexity and simplify  Levinthal’s paradox (Physicist, Berkely, MIT, Columbia)  Protein with 100 amino acids => possible structures  Even if really fast ( seconds to sample each structure)  1.6*10 27 years to go through all structures 10/26/20155Protein Conformation Prediction (Part III)

 Premise: proteins fold into lowest energy conformation  Reduce complexity by restricting amino acid locations to evenly spaced lattice points  Generate all possible conformations (within certain constraints)  Lowest energy models should be representative 10/26/20156Protein Conformation Prediction (Part III)

 Only occupy nodes of a lattice  Globular  limit number of nodes to 50  Ellipsoidal bounding volume  No nodes without at least 2 connecting edges (no dead- ends)  Fewer nodes than aa’s in sequence (n/2)  Must align after the fact  From 0 to 3 residues between nodes 10/26/20157Protein Conformation Prediction (Part III)

 Limit to sequence length of 100 (n)  Energy function statistically derived (verses computationally expensive energy calculations)  Minimal edge lattice – diamond lattice  Between 10 5 and 10 7 enumerated conformations 10/26/2015Protein Conformation Prediction (Part III)8

 “We are able to do exhaustive searches of compact, bounded lattice structures with up to approximately 40 vertices. These searches take on the order of a few hours on a fast workstation, and can easily be executed in parallel over several machines.” 10/26/20159Protein Conformation Prediction (Part III)

 At most 3 choices at each node  Self avoiding therefore much pruning  Constrained to small volume (ellipse)  Probably recursive enumeration with self avoidance  Filter  Symmetry check: remove conformations that differ only in their orientation  26 already  Remember, total of 50 10/26/201510Protein Conformation Prediction (Part III)

 How to align sequence  Remember there are more aa’s than nodes (from 0 to 3 residues between nodes)  How to score overall energy of a conformation  How to judge similarity to known protein (native) conformation 10/26/201511Protein Conformation Prediction (Part III)

 Iterative/Dynamic  Start out evenly spaced  For each node determine the seven possible residues  Choose lowest energy not taken previously  Rinse and repeat  Converges in 3 to 5 iterations 10/26/201512Protein Conformation Prediction (Part III) Sequence Position Nodal Position

mm+1m-1 nn+1n-1  Energy associated with m,n contact average of 5 adjacent energies  m and n given double weight  Rest given single weight  Average of all energies (divide by 6) 10/26/201513Protein Conformation Prediction (Part III)

 But from where did e rm,rn come  Statistically derived 10/26/201514Protein Conformation Prediction (Part III)

 Given a database of proteins the energy of any given combination of two amino acids is given by: How contacty is a given protein Expected number of u,v contacts Across all proteins, number of v’s next to u’s If 1 then across all proteins there are about as many u,v’s as expected. If >1 then more If <1 then fewer 10/26/201515Protein Conformation Prediction (Part III)

 Instead of limiting residues to regularly spaced lattice nodes in space…  Limit phi and psi angles to a reduced set of discrete angles 10/26/2015Protein Conformation Prediction (Part III)16

 Off lattice models often attempt to minimize total energy 10/26/2015Protein Conformation Prediction (Part III)17 G : Free energy H : Enthalpy S : Entropy G : Free energy H : Enthalpy S : Entropy ΔE=q-w ΔH=ΔE+Δ(PV) S=klnΩ ΔG = ΔG van der Waals + ΔG H-bonds + ΔG solvent + ΔG Coulomb

 Backbone RMSD  Root mean square deviation  Usually choose top 100 or so predictions and show that actual resides in the set 10/26/2015Protein Conformation Prediction (Part III)18 Top 100 conformations !!Actual!! Top 100 conformations !!Actual!!

10/26/201519Protein Conformation Prediction (Part III)

10/26/201520Protein Conformation Prediction (Part III) X Y Z Occu Temp Element ATOM 1 N THR A N ATOM 2 CA THR A C ATOM 3 C THR A C ATOM 4 O THR A O ATOM 5 CB THR A C ATOM 6 OG1 THR A O ATOM 7 CG2 THR A C

10/26/2015Protein Conformation Prediction (Part III)21 Name P(a) P(b) P(turn) f(i) f(i+1) f(i+2) f(i+3) Alanine Arginine Aspartic Acid Asparagine Cysteine Glutamic Acid Glutamine Glycine Histidine Isoleucine Leucine Lysine Methionine Phenylalanine Proline Serine Threonine Tryptophan Tyrosine Valine