Protein modelling

● Protein structure is the key to understanding protein function

● Protein structure● Topics in modelling and computational methods

– Comparative/homology modelling– Fold recognition– Fold prediction– Dynamics of proteins

Motivation

● Protein structure determines protein function● For the majority of proteins the structure is not

known

structures

sequences

0 250000 500000 750000 1000000 1250000 1500000

Structural coverage

Correlation structure & sequence

● Chothia & Lesk (1986): Correlation between structural divergence and sequence similarity

Fold space

Tim

e

Fold 1 Fold 2

Evolution

Comparative/homology modelling

Template sequenceTemplate structure

Target sequence

Alignment

Model

The crucial importance of the alignment

● An alignment defines structurally equivalent positions!

Template sequence

Template structure

Target sequence

Alignment

Model

Steps in comparative modelling

● Find suitable template(s)● Build alignment between target and template(s)● Build model(s)

– Replace sidechains– Resolve conflicts in the structure– Model loops (regions without an alignment)

● Evaluate and select model(s)

State of the art in homology modelling

● Template search

– (iterative) sequence database searches (PSIBLAST)● Alignment step

– multiple alignment of close to fairly distant homologues● Modelling step

– rigid body assembly– segment matching– satisfaction of spatial constraints

Modelling by spatial restraints

● Generate many constraints:– Homology derived constraints

● Distances and angles between aligned positions should be similar

– Stereochemical constraints● Bond lengths, bond angles, dihedral angles, nonbonded

atom-atom contacts

● Model derived by minimizing restraints

Modeller: Sali & Blundell (1993)

Loop modelling

● Exposed loop regions usually more variable than protein core

● Often very important for protein function● Loops longer than 5 residues difficult to built● Mini-protein folding problem

Model evaluation

● Check of stereochemistry– bond lengths & angles, peptide bond planarity, side-

chain ring planarity, chirality, torsion angles, clashes● Check of spatial features

– hydrophobic core, solvent accessibility, distribution of charged groups, atom-atom-distances, atomic volumes, main-chain hydrogen bonding

● 3D profiles/mean force potentials– residue environment

Knowledge-based mean force potentials

Melo & Feytmanns (1997)

● Compute typical atomic/residue environments based on known protein structures

● Sequence from different species

● Is binding to ligand conserved?

Ligand

DNA

Modelling a transcription factor

Ligand binding domain

hydrogen bonds to ligand homo-serine lactone moiety binding acyl moiety binding

DNA binding domain

Linker DNA binding domain

Template

Target

Variable loops

New Loop

MODELLER output

Ligand binding pocket

Errors in comparative modelling

Marti-Renom et al. (2000)

a)Side chain packing

b)Distortions and shifts

c)Loops

d)Misalignments

e)Incorrect template

TemplateModel

True structure

Modelling accuracy

Marti-Renom et al. (2000)

Applications of homology modelling

Marti-Renom et al. (2000)

Structural genomics

● Post-genomics:– many new sequences, no function

● Aim: a structure for every protein● High-throughput structure determination

– robotics– standard protocols for

cloning/expression/crystallization

Structural coverage

Vitkup et al. (2001)

high quality models

Complete models

Total = 43 %

Target selection

Protein modelling

● Protein structure is the key to understanding protein function

● Protein structure● Topics in modelling and computational methods

– Comparative/homology modelling– Fold recognition– Fold prediction– Dynamics of proteins

Fold recognition

● Structure is more conserved than sequence

Limit of sequence similarity searches

Structural similarity

Fold space

Target

Protein structures

Fold recognition / Threading

● Is a sequence compatible with a structure?● The idea: evolutionary related proteins share

common folding motifs● Contact matrix = motif● Mean-force potentials

to score every contact● Optimize alignment to

minimize pseudo-energy

AAGGT YAAT YAAGGTYAATY

Protein modelling

● Protein structure is the key to understanding protein function

● Protein structure● Topics in modelling and computational methods

– Comparative/homology modelling– Fold recognition– Fold prediction– Dynamics of proteins

Fold prediction – Rosetta method

● Knowledge based scoring function

P(structure) * P(sequence|structure)

P(sequence)P(structure|sequence) =

P(structure) = probability of a protein-like structure(no clashes, globular shape)

P(sequence|structure) = f(residue contacts in native structures)

Simons et al. (1997)

Bayes' law:

protein-likestructures

sequence consistentlocal structure

near-native structures

Environment specific scoring function

● Environment Ei specific interactions

● Environment – defined by the number of neighbours– implicitely distinguishes between buried and exposed

residuesP žaa1, aa2,‹ , aan#structureŸ= P žaai#E iŸ

P žaa i , aa j#rij , E i , E jŸP žaai#rij , E i , E jŸ P žaa j#r ij , E i , E jŸi i<j

cf. mean force potential

Simons et al. (1997)

Collection of putative backbone conformations

Protein sequence

Library of small segments

sequences structures

... ...For each window of 9 residues:

lookup 25 closest (sequence) neighbours in library

...

Simons et al. (1997)

MC-SA optimization

Simons et al. (1997)

● for each random position– pick a random neighbour– replace backbone conformation– calculate probability of new structure

● MC: Monte-Carlo– accept up-hill moves with a certain probability

● SA: simulated annealing– first allow many changes, later less changes

Results

● Small molecules: ok● Proteins with mostly

α-helices: ok● Proteins with mostly

β-sheets: not so ok

Simons et al. (1997)

Dynamics of proteins

● Protein structure is the key to understanding protein function

● Protein structure● Topics in modelling and computational methods

– Comparative/homology modelling– Fold recognition– Fold prediction– Dynamics of proteins

Dynamics of proteins

● Local Motions (0.01 to 5 Å, 10-15 to 10-1 s)

– Atomic fluctuations

– Sidechain Motions

– Loop Motions

● Rigid Body Motions (1 to 10Å, 10-9 to 1s)

– Helix Motions

– Domain Motions (hinge bending)

– Subunit motions

● Large-Scale Motions (> 5Å, 10-7 to 104 s)

– Helix coil transitions

– Dissociation/Association

– Folding and Unfolding

Molecular dynamics/molecular modelling

● Molecular mechanics● Normal mode analysis● Quantum mechanical simulations● ...

Molecular mechanics● Atom representation

– sphere– charge– topology

● Forces– Bonded interactions– Non-bonded interactions

● Electrostatic interactions● Van-der-Waals interactions

– Forcefields: AMBER, GROMOS, ...● Newton's law of mechanics

http://cmm.info.nih.gov/modeling/guide_documents/molecular_mechanics_document.html

Molecular mechanics

● Molecular mechanics simulations take long!– because of the size of the system

● Proteins are large ● Water molecules to consider solvent effects● 10.000 to millions of atoms

– because of the number of iterations● update atom positions according to time-scale of fastest

fluctuations: bond vibrations ca. 1 fs● movements of interest frequently have long time-scale,

e.g. folding● 1s => 1015 iterations!

Benefit of simulations

● Result is an ensemble of structures– Time-averaged statistical quantities– e.g., relative free energies of different conformations

● Protein engineering– e.g., relative free energies of different mutants

● Physical accuracy of models?– chemical reactions?– cutoff and long-range interactions? – dielectric constant?

movie from: C. Letner, G. Alter Journal of Molecular Structure (Theochem) 368 (1996) 205–212

The end

Proteins are beautiful!

www.holmgroup.org