C
E
N
T
R
E
F
O
R
I
N
T
E
G
R
A
T
I
V
E
B
I
O
I
N
F
O
R
M
A
T
I
C
S
V
U
Experimentally solving protein
structures, protein-protein
interactions and simulating
protein dynamics
Lecture 15
Introduction to Bioinformatics
2007
Today’s lecture
1. Experimental techniques for determining
protein tertiary structure
2. Protein interaction and docking
i.
Zdock method
3. Molecular motion simulated by molecular
mechanics
Experimentally solving protein
structures
Two basic techniques:
1. X-ray crystallography
2. Nuclear Magnetic Resonance (NMR)
tchniques
1. X-ray crystallography
Crystallization
Purified
protein
Phase problem
Crystal
X-ray
Diffraction
Electron
density
Biological interpretation
3D structure
Protein crystals
• Regular arrays of protein molecules
• ‘Wet’: 20-80% solvent
• Few crystal contacts
• Protein crystals contain active protein
• Enzyme turnover
• Ligand binding
Example of crystal packing
Examples of crystal packing
Acetylcholinesterase
~68% solvent
2 Glycoprotein I
~90% solvent
(extremely high!)
Problematic proteins (no crystallisation)
• Multiple domains
Flexible
• Similarly, floppy ends may
hamper crystallization:
change construct
• Membrane proteins
• Glycoproteins
hydrophilic
Lipid
bilayer
hydrophobic
hydrophilic
Flexible and heterogeneous!!
Experimental set-up
• Options for wavelength:
– monochromatic, polychromatic
– variable wavelength
Liq.N2 gas stream
X-ray source
beam stop
detector
goniometer
Diffraction image
Diffuse scattering
(from the fibre loop)
Water ring
Direct beam
Beam stop
reciprocal lattice
(this case hexagonal)
Reflections (h,k,l) with I(h,k,l)
Increasing resolution
The rules for diffraction: Bragg’s law
• Scattered X-rays reinforce each other
only when Bragg’s law holds:
Bragg’s law: 2dhkl sin q = nl
Building a protein model
• Find structural elements:
– -helices, -strands
• Fit amino-acid sequence
Building a protein model
• Find structural elements:
– -helices, -strands
• Fit amino-acid sequence
Effects of resolution on electron density
d=4Å
Note: map calculated with perfect phases
Effects of resolution on electron density
d=3Å
Note: map calculated with perfect phases
Effects of resolution on electron density
d=2Å
Note: map calculated with perfect phases
Effects of resolution on electron density
d=1Å
Note: map calculated with perfect phases
Validation
• Free R-factor (cross validation)
– This has to do with the number of
parameters / observations
• Ramachandran plot showing phi-psi
angle distribution
• Chemically likely (WhatCheck)
– Hydrophobic inside,
hydrophilic outside
– Binding sites of ligands,
metals, ions
– Hydrogen-bonds satisfied
– Chemistry in order
• Final B-factor (temperature) values
(colour coded in structure in the
right)
2. Nuclear Magnetic Resonance (NMR)
800 MHz NMR spectrometer
2. NMR
Purified
protein
Interpret map
Distance
geometry:
resolve
constraints
Measure NOEs, etc.
Distance
constraints
Biological interpretation
Ensemble of
3D structures
Nuclear Magnetic Resonance (NMR)
• Pioneered by Richard R. Ernst, who won a Nobel Prize in chemistry in
1991.
• FT-NMR works by irradiating the sample, held in a static external magnetic
field, with a short square pulse of radio-frequency energy containing all the
frequencies in a given range of interest.
• The polarized magnets of the nuclei begin to spin together, creating a radio
frequency (RF) that is observable. Because the signals decays over time,
this time-dependent pattern can be converted into a frequency-dependent
pattern of nuclear resonances using a mathematical function known as a
Fourier transformation, revealing the nuclear magnetic resonance
spectrum.
• The use of pulses of different shapes, frequencies and durations in
specifically-designed patterns or pulse sequences allows the
spectroscopist to extract many different types of information about the
molecule.
Nuclear Magnetic Resonance (NMR)
• Time intervals between pulses allow—among other things—
magnetization transfer between nuclei and, therefore, the detection of
the kinds of nuclear-nuclear interactions that allowed for the
magnetization transfer.
• Interactions that can be detected are usually classified into two kinds.
There are through-bond interactions and through-space interactions.
The latter is a consequence of the so-called nuclear Overhauser effect
(NOE). Measured NOEs lead to a set of distances between atoms.
• These distances are subjected to a technique called Distance
Geometry which normally results in an ensemble of possible structures
that are all relatively consistent with the observed distance restraints
(NOEs).
• Richard Ernst and Kurt Wüthrich —in addition to many others—
developed 2-dimensional and multidimensional FT-NMR into a powerful
technique for the determination of the structure of biopolymers such as
proteins or even small nucleic acids.
• This is used in protein nuclear magnetic resonance spectroscopy.
Wüthrich shared the 2002 Nobel Prize in Chemistry for this work.
2D NOESY spectrum
Gly
Val
Gly
Leu
Ser
Thr
Phe
Asp
Asn
Asp
• Peptide sequence (N-terminal NH not observed)
• Arg-Gly-Asp-Val-Asn-Ser-Leu-Phe-Asp-Thr-Gly
NMR structure determination:
hen lysozyme
• 129 residues
– ~1000 heavy atoms
– ~800 protons
1.2 104
• NMR data set
• 80 structures calculated
• 30 low energy
structures used
4
8000
Total energy
– 1632 distance restraints
– 110 torsion restraints
– 60 H-bond restraints
1 10
6000
4000
2000
0
10
20
30
40
50
Structure number
60
70
Solution Structure Ensemble
• Disorder in NMR ensemble
– lack of data ?
– or protein dynamics ?
Problems with NMR
• Protein concentration in sample needs to
be high (multimilligram samples)
• Restricted to smaller sized proteins
(although magnets get stronger, 800 MHz,
900 MHz, even 1100 MHz).
• Uncertainties in NOEs introduced by
internal motions in molecules (preceding
slide)
X-ray and NMR
summary
• Are experimental techniques to solve
protein structures (although they both
need a lot of computation)
• Nowadays typically contain many
refinement and energy-minimisation steps
to optimise the structure (next topic)
X-ray and NMR
summary (Cntd.)
• X-ray diffraction
– From crystallised protein sample to electron
density map
• Structure descriptors: resolution, R-factor, B-factor
• Nuclear magnetic resonance (NMR)
– Based on atomic nuclear spin
– Produces set of distances between residues
(distance restraints)
– Distances are used to build protein model using
Distance Geometry (a technique to build a
protein structure using a set of inter-residue
distances)
Protein binding and protein-protein
interactions
• Complexity:
– Multibody interaction
• Diversity:
– Various interaction types
• Specificity:
– Complementarity in shape and binding
properties
Protein-protein interactions
• Many proteins interact through
hydrophobic patches
• Hydrophobic patches often have a
hydrophilic rim
• The patch-rim combination is believed to
be important in providing binding
specificity
hydrophilic
hydrophobic
very
hydrophilic
PPI Characteristics
• Universal
– Cell functionality based on protein-protein interactions
• Cyto-skeleton
• Ribosome
• RNA polymerase
• Numerous
– Yeast:
• ~6.000 proteins
• at least 3 interactions each
~18.000 interactions
– Human:
• estimated ~100.000 interactions
• Network
– simplest: homodimer (two identical domains interact)
– common: hetero-oligomer (more)
– holistic: protein network (all)
• Contact area
Interface Area
– usually >1100 Å2
– each partner >550 Å2
• each partner loses ~800 Å2 of solvent accessible surface
area
– ~20 amino acids lose ~40 Å2
– ~100-200 J per Å2
• Average buried accessible surface area:
– 12% for dimers
– 17% for trimers
– 21% for tetramers
• 83-84% of all interfaces are flat
• Secondary structure:
–
–
–
–
50% -helix
20% -sheet
20% coil
10% mixed
• Less hydrophobic than core, more hydrophobic than exterior
Complexation Reaction
• A + B  AB
– Ka = [AB]/[A]•[B]
 association
– Kd = [A]•[B]/[AB]
 dissociation
Experimental Methods for determining PPI
• 2D (poly-acrylamide) gel electrophoresis  mass spectrometry
• Liquid chromatography
– e.g. gel permeation chromatography
• Binding study with one immobilized partner
– e.g. surface plasmon resonance
• In vivo by two-hybrid systems (yeast two-hybrid or Y2H), FRET or
tanden affinity purification (TAP)
• Binding constants by ultra-centrifugation, micro-calorimetry or
competition
• Experiments with labelled ligand
– e.g. fluorescence, radioactivity
• Role of individual amino acids by site directed mutagenesis
• Structural studies
– e.g. NMR or X-ray
PPI Network
http://www.phy.auckland.ac.nz/staff/prw/biocomplexity/protein_network.htm
Some terminology
• Transient interactions:
– Associate and dissociate in vivo
• Weak transient:
– dynamic oligomeric equilibrium
• Strong transient:
– require a molecular trigger to shift the equilibrium
• Obligate PPI:
– protomers no stable structures on their own (i.e. they
need to interact in complexes)
– (functionally obligate)
Analysis of 122 Homodimers
• 70 interfaces
single patched
• 35 have two
patches
• 17 have three
or more
Interfaces
• ~30% polar
• ~70% non-polar
Interface
• Rim is water accessible
rim
interface
Some amino acid preferences
prefer
avoid
Ribosomal 70S structure at 5.5 Å
(Noller et al. Science 2001)
Calculating interface areas
Given a complex AB:
1. Calculate Solvent Accesible Surface Area
(ASA) of A, of B, and of AB
1. ASA lost upon complex formation is
ASA(A)+ASA(B)-ASA(AB)
3. Interface area of A and of B is
(ASA(A)+ASA(B)-ASA(AB))/2
Docking:
predicting binding sites with ZDOCK
• Protein-protein docking
– 3-dimensional (3D) structure of protein complex
– starting from 3D structures of receptor and ligand
• Rigid-body docking algorithm (ZDOCK)
– pairwise shape complementarity function
– all possible binding modes
– using Fast Fourier Transform algorithm
• Refinement algorithm (RDOCK)
– Take top 2000 predicted structures from ZDOCK (RDOCK is too
computer intensive to refine very many possible dockings)
– three-stage energy minimization
– electrostatic and desolvation energies
• molecular mechanical software (CHARMM)
• statistical energy method (Atomic Contact Energy)
• Example: 49 non-redundant unbound test cases:
– near-native structure (<2.5Å) on top for 37% test cases
• for 49% within top 4
Protein-protein docking
• Finding correct surface
match
• Systematic search:
– 2 times 3D space!
• Define functions:
– ‘1’ on surface
– ‘r’ or ‘d’ inside
– ‘0’ outside
d
r
Docking Programs
•
•
•
•
•
•
•
•
•
•
•
•
•
•
ZDOCK, RDOCK
AutoDock
Bielefeld Protein Docking
DOCK
DOT
FTDock, RPScore and MultiDock
GRAMM
Hex 3.0
ICM Protein-Protein docking (Abagyan group,
currently the best)
KORDO
MolFit
MPI Protein Docking
Nussinov-Wolfson Structural Bioinformatics Group
…
Docking Programs
Issues:
• Rigid structures or made flexible?
– Side-chains
– Main-chains
• Full atomic detail or simplified models?
• Docking energy functions (purpose built
force fields)
Summary protein(-protein)
interactions
• Different binding modes (transient,
obligate, also depending on
(co)localisation, etc.)
• Hydrophobic patch/hydrophilic rim
conferring binding specificity
• Interfaces are physico-chemically
positioned in between surface and protein
core (amino acid composition, etc.)
• Many approaches exist to computationally
predict binding sites and therefore PPI
Protein motion
1. For protein function, architecture and
dynamics are both essential
2. Protein are very mobile and flexible
objects
3. Energy measurements upon protein
folding show that most proteins are
marginally stable
Molecular motions
Proteins are very dynamic systems
• Protein folding
• Protein structure
• Protein function (e.g. opening and closing
of oxygen binding site in hemoglobin)
Protein motion
• Principles
• Simulation
– MD
– MC
The Ramachandran plot
Allowed phi-psi angles
Red areas are preferred, yellow areas are
allowed, and white is avoided
Molecular mechanics techniques
Two basic techniques:
• Molecular Dynamics (MD) simulations
• Monte Carlo (MC) techniques
Molecular Dynamics (MD)
simulation
• MD simulation can be used to study protein motions. It is
often used to refine experimentally determined protein
structures.
• It is generally not used to predict structure from sequence or
to model the protein folding pathway. MD simulation can fold
extended sequences to `global' potential energy minima for
very small systems (peptides of length ten, or so, in
vacuum), but it is most commonly used to simulate the
dynamics of known structures.
• Principle: an initial velocity is assigned to each atom, and
Newton's laws are applied at the atomic level to propagate
the system's motion through time
• MD simulation incorporates a notion of time
K = kinetic energy
V = potential energy
q = coordinates
p = momentum
Molecular Dynamics
Knowledge of the atomic forces and masses can be used to solve the position of
each atom along a series of extremely small time steps (on the order of
femtoseconds = 10-15 seconds). The resulting series of snapshots of structural
changes over time is called a trajectory. The use of this method to compute
trajectories can be more easily seen when Newton's equation is expressed in the
following form:
v = dri/dt
a = d2ri/d2t
The "leapfrog" method is a common numerical approach to calculating trajectories
based on Newton's equation. This method gets its name from the way in which
positions (r) and velocities (v) are calculated in an alternating sequence, `leaping'
past each other in time The steps can be summarized as follows:
Force field
The potential energy of a system can be expressed as a sum of valence (or bond),
crossterm, and nonbond interactions:
The energy of valence interactions comprises bond stretching (Ebond), valence angle
bending (Eangle), dihedral angle torsion (Etorsion), and inversion (also called out-ofplane interactions) (Einversion or Eoop) terms, which are part of nearly all force fields
for covalent systems.
A Urey-Bradley term (EUB) may be used to account for interactions between atom pairs involved in 1-3 configurations (i.e., atoms bound to
a common atom):
Evalence = Ebond + Eangle + Etorsion + Eoop + EUB
Modern (second-generation) forcefields include cross terms to account for such
factors as bond or angle distortions caused by nearby atoms. Cross terms can
include the following terms: stretch-stretch, stretch-bend-stretch, bend-bend,
torsion-stretch, torsion-bend-bend, bend-torsion-bend, stretch-torsion-stretch.
The energy of interactions between nonbonded atoms is accounted for by van der
Waals (EvdW), electrostatic (ECoulomb), and (in some older forcefields) hydrogen
bond (Ehbond) terms:
Enonbond = EvdW + ECoulomb + Ehbond
Force field
energy
f=
distance
a/r12 - b/r6
Van der Waals forces
The Lennard-Jones potential is mildly attractive as two uncharged molecules or atoms approach one
another from a distance, but strongly repulsive when they approach too close. The resulting potential is
shown (in pink). At equilibrium, the pair of atoms or molecules tend to go toward a separation
corresponding to the minimum of the Lennard--Jones potential (a separation of 0.38 nanometers for the
case shown in the Figure)
Thermal
bath
Figure: Snapshots of ubiquitin pulling with constant velocity at
three different time steps.
Docking example:
antibody HyHEL-63 (cyan) complexed with Hen Egg White Lysozyme (yellow)
Important for
binding is a salt
bridge (i.e. charge
complementary
interaction) between
Lys97 of HEL and
Asp27 of the
antibody heavy
chain, as
demonstrated by
Molecular Dynamics
(MD)
The X-ray structure of the antibody HyHEL-63 (cyan) uncomplexed and complexed with Hen Egg White Lysozyme (yellow) has shown
that there are small but significant, local conformational changes in the antibody paratope on binding. The structure also reveals that
most of the charged epitope residues face the antibody. Details are in
Li YL, Li HM, Smith-Gill SJ and Mariuzza RA (2000) The conformations of the X-ray structure Three-dimensional structures of the free
and antigen-bound Fab from monoclonal antilysozyme antibody HyHEL-63. Biochemistry 39: 6296-6309.
Salt links and electrostatic interactions provide much of the free energy of binding. Most of the charged residues face in interface in the
X-ray structure. The importance of the salt link between Lys97 of HEL and Asp27 of the antibody heavy chain is revealed by molecular
dynamics simulations. After 1NSec of MD simulation at 100°C the overall conformation of the complex has changed, but the salt link
persists. Details are described in Sinha N and Smith-Gill SJ (2002) Electrostatics in protein binding and function. Current Protein &
Peptide Science 3: 601-614.
Monte Carlo (MC) simulation
• "Monte Carlo Simulation" is a term for a general class of optimization
methods that use randomization.
• The general idea is, given the current configuration and some figure of
merit, e.g., the energy of the folded configuration, to generate a new
configuration at random (or semi-random):
 If the energy of the new configuration is smaller than the old
configuration, always accept it as the next configuration;
 if it is worse than the current configuration, accept or reject it it
with some probability dependent on how much larger the new
energy is than the old energy.
E = E(new)-E(old)
If E<0 then accept
else if random[0, 1] < e-E /kT then accept
P
E
else reject
Boltzmann -- probability of conformation c: P(c) = e-E(c)/kT
Monte Carlo (MC) simulation
• The idea is that by always accepting a better configuration, on the
average the system will tend to move toward a (local) energy
minimum, while conversely, by sometimes accepting worse
configurations, the system will be able to "climb" out of a sub-optimal
local minima, and perhaps fall into the basin of attraction of the global
minimum.
Local
minimum
Global
minimum
E
Configuration space (models)
• The specific algorithms for probabilistically generating and accepting
new configurations define the type of "Monte Carlo" algorithm; some
common methods are "Metropolis," "Gibbs Sampler," "Heat Bath,"
"Simulated Annealing," "Great Deluge," etc.
• MC techniques are computationally more efficient than MD
• MC simulations do not incorporate a notion of time!
#! /usr/bin/perl
#===============================================================================
#
# $Id: mcdemo.pl,v 1.1.1.1 2003/03/12 16:13:28 jkleinj Exp $
#
# mcdemo: Demo program for MC simulation of the number pi
#
# (C) 2003 Jens Kleinjung
#
# Dr Jens Kleinjung, Room P440
| jkleinj@cs.vu.nl
# Bioinformatics Unit, Faculty of Sciences
| Tel +31-20-444-7783
# Free University Amsterdam
| Fax +31-20-444-7653
# De Boelelaan 1081A, 1081 HV Amsterdam | http://www.cs.vu.nl/~jkleinj
#
#===============================================================================
# preset parameters
$hits = 1;
$miss = 1;
for ($i=0; $i<100000; $i++)
{
# assign random x,y coordinates
$x = rand;
$y = rand;
# calculate radius
$r = sqrt(($x*$x)+($y*$y));
# sum up hits and misses
if ($r <= 1)
{ $hits++; }
else
{ $miss++; }
# calculate pi
$pi = (4*$hits)/($hits +$miss);
# print pi if ($i%100 == 0) { print("$i $pi\n"); }
}
#===============================================================================
In many conformational search methods based on Monte Carlo (MC),
after a MC move, the system is energy minimised, i.e. put in the
lowest local energy conformation, for example by gradient descent
(steepest descent).
What can be done with MD and MC
Dynamics of proteins
• Protein folding – very difficult
• Protein unfolding – done with MD
• Structure refinement – most frequent
application
– After experimental structure elucidation
– After some model building operation
• PPI – Interaction dynamics, Docking
• Hydrophobic patch dynamics
Take home messages
• Experimentally determining protein structures
– X-ray diffraction
• From crystallised protein sample to electron density map
– Structure descriptors: resolution, R-factor
– Nuclear magnetic resonance (NMR)
• Based on atomic nuclear spin
• Produces set of distances between residues (distance restraints)
• Distances are used to build protein model using Distance Geometry
• Protein dynamics simulation
– Molecular dynamics
• Follows Newton’s equations of motion
• Simulates molecular movements through time
• Very small time steps (typically 2 femtoseconds = 2*10-15 seconds)
• Protein conformational search
– Monte Carlo
• Conformations are randomly changed
• Uses Mitropolis criterion to decide between conformation i and i+1 based
on conformational internal energy and the Boltzmann equation
• Has no notion of time, is a conformational search protocol
– Normally faster than MD so more conformations can be generated