Protein Tertiary Protein Tertiary Structure PredictionStructure Prediction
Protein Structure Prediction & Alignment
Protein structure Secondary structure Tertiary structure
Structure prediction Secondary structure 3D structure
Ab initio Comparative modeling Threading
Structure alignment 3D structure alignment Protein docking
Predicting Protein 3D Structure
Goal: Find the best fit of a sequence to a 3D structure
Ab initio methods Attempt to calculate 3D structure “from scratch”
Lattice models off-lattice models Energy minimization Molecular dynamics
Comparative (homology) modeling Construct 3D model from alignment to protein
sequences with known structure Threading (fold recognition/reverse folding)
Pick best fit to sequences of known 2D/3D structures (folds)
How proteins interact?How proteins interact? It is believed that It is believed that hydrophobic collapsehydrophobic collapse is is
a key driving force for protein foldinga key driving force for protein folding Hydrophobic core!Hydrophobic core! Analog: water and oil separationAnalog: water and oil separation
Model: A chain of twenty kinds of beatsModel: A chain of twenty kinds of beats
““Elementary school kid Elementary school kid model”model”
Different assembles (shapes) Different assembles (shapes) Frustrated systemFrustrated system Lots of local minimumsLots of local minimums
Jose Onuchic, UCSD
Classes of Classes of Amino AcidsAmino Acids
Cubic lattice modelCubic lattice model
Hydrophobic packing Hydrophobic packing modelsmodels
Dill's HP modelDill's HP model Two classes of amino acids, hydrophobic (H) and polar Two classes of amino acids, hydrophobic (H) and polar
(P)(P) Lattice model for position of amino acids. Lattice model for position of amino acids. Thread chain of H's and P's through lattice to maximize Thread chain of H's and P's through lattice to maximize
number of H-H contactsnumber of H-H contacts
2D 3D
HydrophoHydrophobic Zipperbic Zipper
Most Designable Most Designable StructuresStructures
All the chains here are All the chains here are 21 beads21 beads long. The upper panel long. The upper panel shows some of the 107 exceptionally stable foldings of 80 shows some of the 107 exceptionally stable foldings of 80 sequences that maximize the number of sequences that maximize the number of H-HH-H contacts. In contacts. In the lower panel are a few of the other 117,676,504,514,560 the lower panel are a few of the other 117,676,504,514,560 combinations of sequences and foldings, selected at combinations of sequences and foldings, selected at random. (Brian Hayes, American Scientists,1998) random. (Brian Hayes, American Scientists,1998)
HP Lattice ModelHP Lattice Model Simplifications in the model:Simplifications in the model:
All amino acids are classified as hydrophobic All amino acids are classified as hydrophobic (H) or polar (P). A protein is represented as a (H) or polar (P). A protein is represented as a string of H’s and P’s. string of H’s and P’s. HHHHHPPPHHHPPHHHHHPPPHHHPP
Space is discretized. Each amino acid is Space is discretized. Each amino acid is embedded to a single lattice point. A protein embedded to a single lattice point. A protein fold corresponds to a fold corresponds to a self-avoiding walkself-avoiding walk over over the lattice.the lattice.
The The energy functionenergy function is defined as is defined as E = E = (# of H-H contacts not including covalent (# of H-H contacts not including covalent
interaction).interaction).
Example of HP lattice Example of HP lattice modelmodel
Hydrophobic amino acidPolar amino acidPeptide bondH-H contacts
E = Number of H-H contacts (except for peptide bonds) = -7
HP Lattice ModelHP Lattice Model Other latticesOther lattices
2D triangular lattice, 3D-diamond lattice2D triangular lattice, 3D-diamond lattice Other energy functions Other energy functions
HP=0, HH=-1, PP=1HP=0, HH=-1, PP=1 Lattice model can be usedLattice model can be used
Study qualitative features of protein foldingStudy qualitative features of protein folding Reduce search space in structure prediction Reduce search space in structure prediction
methodsmethods Study potential effectiveness of the methods for Study potential effectiveness of the methods for
structure prediction (inverse folding problem)structure prediction (inverse folding problem)
Inverse Folding Inverse Folding ProblemProblem
Example:Example:Can we find all protein sequences in Can we find all protein sequences in GenBank with the GenBank with the globinglobin fold fold??
ClaimClaim::There exist two native sequence SThere exist two native sequence Sii, S, Sjj such that such that
E(S(SE(S(Sii), S), Sii) ) E(S(S E(S(Sii), S), Sjj))where S(Swhere S(Sii) and S(S) and S(Sjj) be the native structures of S) be the native structures of Sii & & SSjj..
i.e. the sequence Si.e. the sequence Sj j “scores” better on S“scores” better on Sii’s native ’s native structure than Sstructure than Sii itself. itself.
NO.
ExerciseExercise Find native structures of SFind native structures of S11 and S and S22
SS11 = HHPPPPHPPPH = HHPPPPHPPPH SS22 = HHPHPPHPHPH = HHPHPPHPHPH
Thread SThread S2 2 on to the structure of Son to the structure of S1 1 and and find the energy associated with that fold find the energy associated with that fold
ExerciseExercise Find native structures of SFind native structures of S11 and S and S22
SS11 = HHPPPPHPPPH = HHPPPPHPPPH SS22 = HHPHPPHPHPH = HHPHPPHPHPH
Thread SThread S2 2 on to the structure of Son to the structure of S1 1 and find the and find the energy associated with that fold energy associated with that fold
SS11
E(S(SE(S(S11), S), S11) = -2; E(S(S) = -2; E(S(S11), S), S22) = -3; E(S(S) = -3; E(S(S22), S), S22) ) = -4.= -4.
H
P P
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SummarySummary Approach
Reduce computation by limiting degrees of freedom
Limit α-carbon (Cα) atoms to positions on 2D or 3D lattice
Protein sequence → represented as path through lattice points
H-P (hydrophobic-polar) cost model Each residue → hydrophobic (H) or hydrophilic (P) Score position of sequence → maximize H-H contacts
Problem Still NP-hard Greatly simplified problem Emphasis on forming
hydrophobic core Need more accurate cost models
Off-Lattice Models Approach
Compromise between lattice model and molecular dynamics
Backbone placement → allowed by Ramachandran plot
Represent as phi & psi angles of α-carbon atoms Degree of precision
α-carbon only All backbone atoms All backbone atoms + side chains (residues) Common conformation (positions) of side chain = rotamer
Problem Still simplified problem Increased computation cost
Molecular Dynamics GoalGoal
Provides a way to observe the motion of large Provides a way to observe the motion of large molecules such as proteins at the atomic level – molecules such as proteins at the atomic level – dynamic simulationdynamic simulation
Approach Model all interatomic forces acting on atoms in protein
Potential energy function (Potential energy function (Newtonian mechanics)Newtonian mechanics) Perform numerical simulations to predict fold
Repeat for each atom at each time step Calculate & add up all (pairwise) forces
bonds:bonds: non-bonded: electrostatic and non-bonded: electrostatic and van der Waals’
Apply force, move atom to new position (Newton’s 2nd law ? Newton’s 2nd law ? ) )
Obtain trajectories of motion of moleculeObtain trajectories of motion of molecule
F = maF = ma
MDMD Problem with MD
Smaller time step → more accurate simulation Modeling folding is computationally intensive Current models require tiny (10-15 second) time
steps Simulations reported for at most 10-6 seconds Folding requires 1 second or more
Demo (12 nanosecond MD simulation)
Types of Inter-atomic Forces
Molecular Dynamics Molecular Dynamics
Potential EnergyPotential Energy ComponentsComponents
(1) bond length (1) bond length Bonds behave like spring with equilibrium bond Bonds behave like spring with equilibrium bond length depending on bond type. Increase or length depending on bond type. Increase or decrease from equilibrium length requires decrease from equilibrium length requires higher energy. higher energy.
Potential EnergyPotential Energy(2) bond angle (2) bond angle
Bond angles have equilibrium value eg 108 for Bond angles have equilibrium value eg 108 for H-C-HH-C-H
Behave as if sprung. Behave as if sprung.
Increase or decrease in angle requires Increase or decrease in angle requires higher energy. higher energy.
Potential EnergyPotential Energy(3) torsion angle(3) torsion angle
Rotation can occur about single bond in A-Rotation can occur about single bond in A-B-C-D but energy depends on torsion B-C-D but energy depends on torsion angle (angle between CD & AB viewed angle (angle between CD & AB viewed along BC). Staggered conformations along BC). Staggered conformations (angle +60, -60 or 180 are preferred). (angle +60, -60 or 180 are preferred).
Potential EnergyPotential Energy(4) van der Waals interactions(4) van der Waals interactions
Interactions between atoms not near Interactions between atoms not near neighbours expressed by Lennard-Jones neighbours expressed by Lennard-Jones potential. Very high repulsive force if potential. Very high repulsive force if atoms closer than sum of van der Waals atoms closer than sum of van der Waals radii. Attractive force if distance greater. radii. Attractive force if distance greater. Because of strong distance dependence, Because of strong distance dependence, van der Waals interactions become van der Waals interactions become negligible at distances over 15 negligible at distances over 15 ÅÅ..
Potential EnergyPotential Energy(5) Electrostatic interactions(5) Electrostatic interactions
All atoms have partial charge eg in C=O, C has All atoms have partial charge eg in C=O, C has partial positive charge, O atom partial negative partial positive charge, O atom partial negative charge. Two atoms that have the same charge charge. Two atoms that have the same charge repel one another, those with unlike charge repel one another, those with unlike charge attract. attract.
Electrostatic energy falls off much less quickly Electrostatic energy falls off much less quickly than for van der Waals interactions and may not than for van der Waals interactions and may not be negligible even at 30 be negligible even at 30 ÅÅ. .
Potential EnergyPotential Energy Potential Energy is given by the sum of Potential Energy is given by the sum of
these contributions:these contributions:
Hydrogen bonds are usually supposed to Hydrogen bonds are usually supposed to arise by electrostatic interactions but arise by electrostatic interactions but occasionally a small extra term is added.occasionally a small extra term is added.
Force fieldsForce fields A force field is the description of how potential A force field is the description of how potential
energy depends on parametersenergy depends on parameters Several force fields are availableSeveral force fields are available
AMBER used for proteins and nucleic acids AMBER used for proteins and nucleic acids (UCSF)(UCSF)
CHARMM (Harvard)CHARMM (Harvard) ……
Force fields differ: Force fields differ: in the precise form of the equations in the precise form of the equations in values of the constants for each atom typein values of the constants for each atom type
Obtain TrajectoryObtain Trajectory Start with a initial structure (Ex. Structure from Start with a initial structure (Ex. Structure from
PDB)PDB) Assign random starting velocities to the atomsAssign random starting velocities to the atoms Calculating the forces acting on each atomCalculating the forces acting on each atom
Bonds, non-bonded (electrostatic and van der Val’s)Bonds, non-bonded (electrostatic and van der Val’s) Numerically integrate Numerically integrate Newton’s equations of Newton’s equations of
motionmotion Verlet method Verlet method Leapfrog method Leapfrog method
After equilibrating the system, record the positions After equilibrating the system, record the positions and momentum of the atoms as a function of timeand momentum of the atoms as a function of time
Molecular DynamicsMolecular Dynamics Energy minimization gives local minimum, not Energy minimization gives local minimum, not
necessarily global minimum.necessarily global minimum.
Give molecule thermal energy so can explore Give molecule thermal energy so can explore conformational space & overcome energy barriers.conformational space & overcome energy barriers.
Give atoms initial velocity random value + direction. Give atoms initial velocity random value + direction. Scale velocities so total kinetic energy =3/2kT * number Scale velocities so total kinetic energy =3/2kT * number atomsatoms
Solve equation of motion to work out position of atoms at Solve equation of motion to work out position of atoms at 1 fs.1 fs.