Download Protein Structure Prediction

Protein Structure Prediction
Ram Samudrala
University of Washington
Rationale for understanding protein structure and function
Protein sequence
-large numbers of
sequences, including
whole genomes
?
Protein function
- rational drug design and treatment of disease
- protein and genetic engineering
- build networks to model cellular pathways
- study organismal function and evolution
structure determination
structure prediction
Protein structure
- three dimensional
- complicated
- mediates function
homology
rational mutagenesis
biochemical analysis
model studies
Protein folding
…-CUA-AAA-GAA-GGU-GUU-AGC-AAG-GUU-…
DNA
protein sequence
…-L-K-E-G-V-S-K-D-…
one amino acid
unfolded protein
spontaneous self-organisation
(~1 second)
native state
not unique
mobile
inactive
expanded
irregular
Protein folding
…-CUA-AAA-GAA-GGU-GUU-AGC-AAG-GUU-…
DNA
protein sequence
…-L-K-E-G-V-S-K-D-…
one amino acid
unfolded protein
spontaneous self-organisation
(~1 second)
native state
not unique
mobile
inactive
expanded
irregular
unique shape
precisely ordered
stable/functional
globular/compact
helices and sheets
Protein folding landscape
Large multi-dimensional space of changing conformations
J=10-3 s
free energy
unfolded
molten
globule
barrier
height
DG*
native
J=10-8 s
folding reaction
Protein primary structure
twenty types of amino acids
two amino acids join by forming a peptide bond
R
R
H
H
OH
N
H
Cα
O
H
C
N
C
N
O
H
H
H
Cα
Cα
C
H
OH
O
R
each residue in the amino acid main chain has two degrees of freedom (f and y)
R
f
N
H
H
c
N
Cα
y
H
R
C
f
H
O
y
Cα
c
f
C
N
H
O
R
H
c
Cα
y
H
N
C
f
H
y
Cα
c
O
R
the amino acid side chains can have up to four degrees of freedom (c1-4)
O
C
Protein secondary structure
many f,y combinations are not possible
b sheet (anti-parallel)
+180
b
L
f0
a
-180
-180
C
0y
a helix
+180
N
b sheet (parallel)
C
N
Protein tertiary and quaternary structures
Ribonuclease inhibitor (2bnh)
Haemoglobin (1hbh)
Hemagglutinin (1hgd)
Methods for determining protein structure
Protein sequence
-large numbers of
sequences, including
whole genomes
?
Protein function
- rational drug design and treatment of disease
- protein and genetic engineering
- build networks to model cellular pathways
- study organismal function and evolution
X-ray crystallography
NMR spectroscopy
Protein structure
- three dimensional
- complicated
- mediates function
homology
rational mutagenesis
biochemical analysis
model studies
X-ray crystallography- concept
• X-rays interact with electrons in protein molecules arranged in a crystal to produce
diffraction patterns
• The diffraction patterns of the x-rays can be used to determine the three-dimensional
structure of proteins
• Provides a “static” picture
From <http://info.bio.cmu.edu/courses/03231/LecF01/Lec25/lec25.html>
X-ray crystallography- details
• Prepare protein crystals where the proteins are organised in a precise crystal lattice
• Shine x-rays on crystals which diffract off of electrons of atoms in the crystals; the
intensities of the individual reflections are measured
• Phases are usually obtained indirectly by ismorphous replacement, from the way one or
a few heavy atoms incorporated into the same isomorphous crystal lattice affect the
diffraction patern
• Intensities and phases of all reflections are combined in a Fourier transform to provide
maps of electron density
• Interpret the map by fitting the polypeptide chain to the contours
• Refine the model by minimising the distance between the observed amplitudes and the
calculated amplitudes
NMR spectroscopy - concept
• The magnetic-spin properties of atomic nuclei within a molecule are used to obtain a
list of distance constraints between atoms in the molecule, from which a
three-dimensional structure of the protein molecule can be obtained
• Provides a “dynamic” picture
NK-lysin (1nkl)
S1 RNA binding domain (1sro)
NMR spectroscopy - details
• Protein molecules placed in a strong magnetic field have their hydrogen atoms aligned
to the field; the alignment can be excited by applying radio frequency (RF) pulses
• Possible to obtain unique signal (chemical shift) for each hydrogen atom in a protein
molecule
• Structural information arises primarily from the Nuclear Overhauser Effect (NOE),
which gives information about distances between atoms in a molecule
• A pair of protons give a detectable NOE cross-peak if they are within 5.0 Å of each
other in space
• After obtaining NOE data for protons througout the structure, a number of independent
structures can be generated that are consistent with the distance constraints
Computer representation of protein structure
• Structures are stored in the protein data bank (PDB), a repository of mostly
experimental models based on X-ray crystallographic and NMR studies
• <http://www.rcsb.org>
• Atoms are defined by their Cartesian coordinates:
ATOM
ATOM
ATOM
ATOM
ATOM
ATOM
ATOM
ATOM
ATOM
ATOM
ATOM
1
2
3
4
5
6
7
8
9
10
11
N
CA
C
O
CB
CG
CD
OE1
OE2
N
CA
GLU
GLU
GLU
GLU
GLU
GLU
GLU
GLU
GLU
PHE
PHE
1
1
1
1
1
1
1
1
1
2
2
18.222
17.706
17.368
16.780
16.552
16.952
15.881
16.012
14.701
17.762
17.509
18.496
17.982
16.466
16.073
18.744
20.118
21.145
22.316
20.768
15.746
14.262
-16.203
-14.905
-15.121
-16.175
-14.351
-13.803
-13.597
-13.292
-13.799
-14.052
-14.184
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
21.95
16.74
15.45
18.81
17.35
24.48
31.51
29.12
35.19
15.83
13.24
• These structures provide the basis for most of theoretical work in protein folding and
protein structure prediction
Comparison of protein structures
• Need ways to determine if two protein structures are related and to compare predicted
models to experimental structures
• Commonly used measure is the root mean square deviation (RMSD) of the Cartesian
atoms between two structures after optimal superposition (McLachlan, 1979):

N
2
2
2
dx

dy

dz
i
i
i
i 1
N
• Usually use Ca atoms
3.6 Å
NK-lysin (1nkl)
2.9 Å
Bacteriocin T102/as48 (1e68)
• Other measures include contact maps and torsion angle RMSDs
T102 best model
Methods for predicting protein structure
Protein sequence
-large numbers of
sequences, including
whole genomes
?
Protein function
- rational drug design and treatment of disease
- protein and genetic engineering
- build networks to model cellular pathways
- study organismal function and evolution
comparative modelling
fold recognition
ab initio prediction
Protein structure
- three dimensional
- complicated
- mediates function
homology
rational mutagenesis
biochemical analysis
model studies
Comparative modelling of protein structure
• Proteins that have similar sequences (i.e., related by evolution) have similar
three-dimensional structures
• A model of a protein whose structure is not known can be constructed if the structure of
a related protein has been determined by experimental methods
• Similarity must be obvious and significant for good models to be built
• Need ways to build regions that are not similar between the two related proteins
• Need ways to move model closer to the native structure
Comparative modelling of protein structure
scan
align
…
KDHPFGFAVPTKNPDGTMNLMNWECAIP
KDPPAGIGAPQDN----QNIMLWNAVIP
** * *
* *
* * *
**
build initial model
refine
…
construct non-conserved
side chains and main chains
Fold recognition
• The number of possible protein structures/folds is limited (large number of sequences
but few folds)
• Proteins that do not have similar sequences sometimes have similar three-dimensional
structures
3.6 Å
5% ID
NK-lysin (1nkl)
Bacteriocin T102/as48 (1e68)
• A sequence whose structure is not known is fitted directly (or “threaded”) onto a known
structure and the “goodness of fit” is evaluated using a discriminatory function
• Need ways to move model closer to the native structure
Fold recognition
evaluate
fit
…
KDHPFGFAVPTKNPDGTMNLMNWECAIP
KDPPAGIGAPQDN----QNIMLWNAVIP
** * *
* *
* * *
**
build initial model
refine
…
construct non-conserved
side chains and main chains
Ab initio prediction of protein structure – concept
• Go from sequence to structure by sampling the conformational space in a reasonable
manner and select a native-like conformation using a good discrimination function
• Problems: conformational space is astronomical, and it is hard to design functions that
are not fooled by non-native conformations (or “decoys”)
Ab initio prediction of protein structure
sample conformational space such that
native-like conformations are found
select
hard to design functions
that are not fooled by
non-native conformations
(“decoys”)
astronomically large number of conformations
5 states/100 residues = 5100 = 1070
Sampling conformational space – continuous approaches
• Most work in the field
- Molecular dynamics
- Continuous energy minimisation (follow a valley)
- Monte Carlo simulation
- Genetic Algorithms
• Like real polypeptide folding process
• Cannot be sure if native-like conformations are sampled
energy
Molecular dynamics
• Force = -dU/dx (slope of potential U); acceleration, m a(t) = force
• All atoms are moving so forces between atoms are complicated functions of time
• Analytical solution for x(t) and v(t) is impossible; numerical solution is trivial
• Atoms move for very short times of 10-15 seconds or 0.001 picoseconds (ps)
old position
new position
acceleration
x(t+Dt) = x(t) + v(t)Dt + [4a(t) – a(t-Dt)] Dt2/6
old velocity
new velocity
old velocity
acceleration
v(t+Dt) = v(t) + [2a(t+Dt)+5a(t)-a(t-Dt)] Dt/6
Ukinetic = ½ Σ mivi(t)2 = ½ n KBT
• Total energy (Upotential + Ukinetic) must not change with time
n is number of coordinates (not atoms)
Energy minimisation
• For a given protein, the energy depends on thousands of x,y,z Cartesian atomic
coordinates; reaching a deep minimum is not trivial
starting conformation
energy
deep minimum
number of steps
• With convergence, we have an accurate equilibrium conformation and a well-defined
energy value
energy
steepest descent
give up
conjugate gradient
number of steps
converge
RMSD
Monte Carlo simulation
• Discrete moves in torsion or cartesian conformational space
• Evaluate energy after every move and compare to previous energy (DE)
• Accept conformation based on Boltzmann probability:
  ΔE 
P  exp 

kT


• Many variations, including simulated annealing (starting with a high temperature so
more moves are accepted initially and then cooling)
• If run for infinite time, simulation will produce a Boltzmman distribution
Genetic Algorithms
• Generate an initial pool of conformations
• Perform crossover and mutation operations on this set to generate a much larger pool of
conformations
• Select a subset of the fittest conformations from this large pool
• Repeat above two steps until convergence
Sampling conformational space – exhaustive approaches
enumerate all possible conformations
view entire space (perfect partition function)
select
must use discrete state
models to minimise
number of conformations
explored
computationally intractable:
5 states/100 residues = 5100 = 1070 possible conformations
Scoring/energy functions
• Need a way to select native-like conformations from non-native ones
• Physics-based functions: electrostatics, van der Waals, solvation, bond/angle terms
• Knowledge-based scoring functions: derive information about atomic properties from a
database of experimentally determined conformations; common parametres include
pairwise atomic distances and amino acid burial/exposure.
Requirements for sampling methods and scoring functions
• Sampling methods must produce good decoy sets that are comprehensive and include
several native-like structures
• Scoring function scores must correlate well with RMSD of conformations (the better
the score/energy, the lower the RMSD)
Overview of CASP experiment
• Three categories: comparative/homology modelling, fold recognition/threading, and
ab initio prediction
• Goal is to assess structure prediction methods in a blind and rigourous manner; blind
prediction is necessary for accurate assessment of methods
• Ask modellers to build models of structures as they are in the process of being solved
experimentally
• After prediction season is over, compare predicted models to the experimental
structures
• Discuss what went right, what went wrong, and why
• Compare progress from CASP1 to CASP4
• Results published in special issues of Proteins: Structure, Function, Genetics 1995,
1997, 1999, 2002
Comparative modelling at CASP - methods
• Alignment: PSI-BLAST, FASTA, CLUSTALW - multiple sequence alignments
carefully hand-edited using secondary structure information
• More successful side chain prediction methods include:
backbone-dependent rotamer libraries (Bower & Dunbrack)
segment matching followed by energy minimisation (Levitt)
self-consistent mean field optimisation (Bates et al)
graph-theory + knowledge-based functions (Samudrala et al)
• More successful loop building methods include:
satisfaction of spatial restraints (Sali)
internal coordinate mechanics energy optimisation (Abagyan et al)
graph-theory + knowledge-based functions (Samudrala et al)
• Overall model building: there is no substitute for careful hand-constructed models
(Sternberg et al, Venclovas)
A graph theoretic representation of protein structure
-0.6 (V1)
represent
residues
as nodes
-0.5 (I)
-0.9 (V2)
weigh
nodes
-0.7 (K)
-1.0 (F)
construct
graph
-0.6 (V1)
-0.5 (I)
W = -4.5
-0.1
-0.3
-1.0 (F)
-0.9 (V2)
-0.1
-0.2
-0.7 (K)
find cliques
-0.5 (I)
-0.1
-0.3
-1.0 (F)
-0.9 (V2)
-0.1
-0.2
-0.7 (K)
-0.2
Historical perspective on comparative modelling
BC
alignment
side chain
short loops
longer loops
excellent
~ 80%
1.0 Å
2.0 Å
Historical perspective on comparative modelling
alignment
side chain
short loops
longer loops
BC
CASP1
excellent
~ 80%
1.0 Å
2.0 Å
poor
~ 50%
~ 3.0 Å
> 5.0 Å
Prediction for CASP4 target T128/sodm
Ca RMSD of 1.0 Å for 198 residues (PID 50%)
Prediction for CASP4 target T111/eno
Ca RMSD of 1.7 Å for 430 residues (PID 51%)
Prediction for CASP4 target T122/trpa
Ca RMSD of 2.9 Å for 241 residues (PID 33%)
Prediction for CASP4 target T125/sp18
Ca RMSD of 4.4 Å for 137 residues (PID 24%)
Prediction for CASP4 target T112/dhso
Ca RMSD of 4.9 Å for 348 residues (PID 24%)
Prediction for CASP4 target T92/yeco
Ca RMSD of 5.6 Å for 104 residues (PID 12%)
Comparative modelling at CASP - conclusions
alignment
side chain
short loops
longer loops
BC
CASP1
CASP2
CASP3
CASP4
excellent
~ 80%
1.0 Å
2.0 Å
poor
~ 50%
~ 3.0 Å
> 5.0 Å
fair
~ 75%
~ 1.0 Å
~ 3.0 Å
fair
~75%
~ 1.0 Å
~ 2.5 Å
fair
~75%
~ 1.0 Å
~ 2.0 Å
CASP4: overall model accuracy ranging from 1 Å to 6 Å for 50-10% sequence identity
**T128/sodm – 1.0 Å (198 residues; 50%)
**T111/eno – 1.7 Å (430 residues; 51%)
**T122/trpa – 2.9 Å (241 residues; 33%)
**T125/sp18 – 4.4 Å (137 residues; 24%)
**T112/dhso – 4.9 Å (348 residues; 24%)
**T92/yeco – 5.6 Å (104 residues; 12%)
Fold recognition at CASP - methods
• Visual inspection with sequence comparison (Murzin group)
• Procyon - potential of mean force based on pairwise interactions and global dynamic
programming (Sippl group)
• Threader - potential of mean force and double dynamic programming (Jones group)
• Environmental 3D Profiles (Eisenberg group)
• NCBI Threading Program using contact potentials and models of sequence-structure
conservation (Bryant group)
• Hidden Markov Models (Karplus group)
• Combination of threading with ab initio approaches (Friesner group)
• Environment-specific substitution tables and structure-dependent gap penalties
(Blundell group)
Fold recognition at CASP - conclusions
• Fold recognition is one of the more successful approaches at predicting structure at all
four CASPs
• At CASP2 and CASP4, one of the best methods was simple sequence searching with
careful manual inspection (Murzin group)
• At CASP3 and CASP4, none of the threading targets could have been recognised by the
best standard sequence comparison methods such as PSI-BLAST
• For the most difficult targets, the methods were able to predict  60 residues to 6.0 Å
Ca RMSD, approaching comparative modelling accuracies as the similarity between
proteins increased.
Ab initio prediction at CASP – methods
• Assembly of fragments with simulated annealing (Simons et al)
• Exhaustive sampling and pruning using knowledge-based scoring functions
(Samudrala et al)
• Constraint-based Monte Carlo optimisation (Skolnick et al)
• Thermodynamic model for secondary structure prediction with manual docking of
secondary structure elements and minimisation (Lomize et al)
• Minimisation of a physical potential energy function with a simplified representation
(Scheraga et al, Osguthorpe et al)
• Neural networks to predict secondary structure (Jones, Rost)
Semi-exhaustive segment-based folding
EFDVILKAAGANKVAVIKAVRGATGLGLKEAKDLVESAPAALKEGVSKDDAEALKKALEEAGAEVEVK
generate
…
fragments from database
14-state f,y model
…
minimise
…
monte carlo with simulated annealing
conformational space annealing, GA
…
filter
all-atom pairwise interactions, bad contacts
compactness, secondary structure
Historical perspective on ab initio prediction
Before CASP (BC):
“solved”
CASP1: worse than
random
(biased results)
CASP2: worse than
random with one
exception
CASP3: consistently predicted correct topology - ~ 6.0 Å for 60+ residues
*T56/dnab – 6.8 Å (60 residues; 67-126)
**T61/hdea – 7.4 Å (66 residues; 9-74)
**T64/sinr – 4.8 Å (68 residues; 1-68)
*T74/eps15 – 7.0 Å (60 residues; 154-213)
**T59/smd3 – 6.8 Å (46 residues; 30-75)
**T75/ets1 – 7.7 Å (77 residues; 55-131)
CASP4: ?
Prediction for CASP4 target T110/rbfa
Ca RMSD of 4.0 Å for 80 residues (1-80)
Prediction for CASP4 target T97/er29
Ca RMSD of 6.2 Å for 80 residues (18-97)
Prediction for CASP4 target T106/sfrp3
Ca RMSD of 6.2 Å for 70 residues (6-75)
Prediction for CASP4 target T98/sp0a
Ca RMSD of 6.0 Å for 60 residues (37-105)
Prediction for CASP4 target T126/omp
Ca RMSD of 6.5 Å for 60 residues (87-146)
Prediction for CASP4 target T114/afp1
Ca RMSD of 6.5 Å for 45 residues (36-80)
Postdiction for CASP4 target T102/as48
Ca RMSD of 5.3 Å for 70 residues (1-70)
Ab initio prediction at CASP - conclusions
Before CASP (BC):
“solved”
CASP1: worse than
random
(biased results)
CASP2: worse than
random with one
exception
CASP3: consistently predicted correct topology - ~ 6.0 Å for 60+ residues
CASP4: consistently predicted correct topology - ~4-6.0 A for 60-80+ residues
**T97/er29 – 6.0 Å (80 residues; 18-97)
*T98/sp0a – 6.0 Å (60 residues; 37-105)
**T102/as48 – 5.3 Å (70 residues; 1-70)
**T106/sfrp3 – 6.2 Å (70 residues; 6-75)
**T110/rbfa – 4.0 Å (80 residues; 1-80)
*T114/afp1 – 6.5 Å (45 residues; 36-80)
Computational aspects of structural genomics
A. sequence space
B. comparative modelling
*
*
C. fold recognition
*
*
*
*
*
*
*
*
E. target selection
D. ab initio prediction
F. analysis
*
*
*
*
*
*
*
*
*
*
*
*
*
*
targets
(Figure idea by Steve Brenner.)
Key points
• DNA/gene is the blueprint - proteins are the functional representatives of genes
• Protein structure can be used to understand protein function
• Large numbers of genes being sequenced - need structures
• Protein folding (from primary sequence to tertiary structure) is a fast self-organising
process where a disordered non-functional chain of amino acids becomes a stable,
compact, and functional molecule
• The free energy difference between the folded and unfolded states is not very high
• Experimental methods to determine protein structures include x-ray crystallography
and NMR spectroscopy
• Theoretical methods to predict protein structures include comparative/homology
modelling, fold recognition/threading, and ab initio prediction
• For ab initio prediction, you need a method that samples the conformational space
adequately (to find native-like conformations) and a function that can identify them
• CASP experiment shows limited progress in protein structure prediction
Acknowledgements
Michael Levitt, Stanford University
John Moult, CARB
Patrice Koehl, Stanford University
Yu Xia, Stanford Univeristy
Levitt and Moult groups
<http://compbio.washington.edu>