Judgment day.
Chapter 14 & 15, Du and Bourne “Structural Bioinformatics”
Topic 6
Beautiful Structures, Aren’t They?
For high profile structures, they are not merely contaminations in PDB if
serious errors occur. In this case, a software bug “flipped” two columns
of data, inverting the electron density map.
ABC transporter
Science, 314:1856, 2006
Experimental Methods for Structure Determination
Steps in Structure Determination using X-ray Crystallography
Steps in Structure Determination using NMR
Models!
Image from “Protein Structure and Function” by Gregory A Petsko and Dagmar Ringe
Structure Assessment and Validation, Why?
 The process involves instrumentation, methodology, software,
experimental procedures....., so random and systematic error scan occur.
 Experimental errors vs. interpretation errors.
 Limitation of data vs. subjectivity
“Given the same data, no two crystallographers will ever produce
identical final models” –Kleywegt GL
 Local errors vs. global errors
Global Quality Parameters for X-ray Structures
Rules of Thump for high quality X-ray structures:
resolution 2.0 Å or better and R-factor: 0.2 or less
R-factor for X-ray Structures
The agreement between the diffraction data and the model is measured by R-factor:
F: structural factor
 R-free: about 10% of the observations are removed from the data set before
refinement. Then, refinement is performed using the remaining 90%. The R-free value is
calculated to see how well the model predicts the 10% that were not used in refinement,
leading to a less biased quantity.
Serious Structural Errors
Blue: N-terminal
Red: C-terminal
1PHY
2PHY
PHOTOACTIVE YELLOW PROTEIN
1PHY was solved in 1989, the entire backbone trace is incorrect.
2PHY was solved in 1995.
RMSD between 1PHY and 2PHY ~15 Å.
Kleywegt GJ., “Validation of protein crystal structures”, Acta Cryst, 2000, D56, 249-265
Obsolete Structures in PDB
Obsolete Structures in PDB
Serious Structural Errors
Blue: N-terminal
Red: C-terminal
1PTE
3PTE
 Secondary structure assignments are correct
 Topology is incorrect
Kleywegt GJ., “Validation of protein crystal structures”, Acta Cryst, 2000, D56, 249-265
Major Errors from NMR Spectroscopy
Sequence and Structure Ensembles of Two DLC2A Structures
96% identity
A, D: human
(1TGQ)
B, C: Mouse
(1Y4O)
Intermolecular contacts vs. intramolecular contacts
Nabuurs, et al Plos Computational Biology 2(2), 2006
Major Errors from NMR Spectroscopy
Intermolecular contacts vs. intramolecular contacts
From Nabuurs, et al Plos Computational Biology 2(2), 2006…
The observed pattern of dispersed signals, ideally one for each amino
acid, provides a “fingerprint” of the protein.
However, the formation of a symmetric dimer, as shown in Figure 1A,
does not result in a doubling of the number of observed NMR signals.
Consequently, it is not straightforward to determine the oligomeric state
of a protein from its 15N-HSQC NMR spectra alone, and typically
assessments have to be made from estimates of the protein's relaxation
rates [26].
Therefore, if the oligomeric state of a protein is not known or is
incorrectly known, the NMR spectra of a dimeric protein could be easily
interpreted as originating from a monomer.
Other common errors, which tend to be less severe
Flipped residues -- Asn, Gln, and His.
SEVERITY
Missing sidechain atoms -- especially in longer-chain, solventexposed residues (i.e., lysine and arginine).
Missing backbone atoms -- especially in loop regions.
Truncated or incomplete chains -- the “PDB sequence” rarely
matches perfectly with the sequence encoded by structure. The
truncation is generally at the termini ends.
Flipping: Problems with Gln/Asn/His
Acta Cryst. (2010). D66, 12-21
The What of Validation/Assessment
 It should be independent of experimental data
 Many criteria that are based on straightforward chemical ideals and physics
can be used to validate protein structure quality.
 For example, Ramachandran plots, side-chain torsion angles, and contacts
are widely used.
 Other order parameters that can also be used: H-bonding, chirality, bond
angles and distances etc.
 Physics-based energy values, calculated using energy potentials.
 There are programs available for assessment of protein structure quality:
ProCheck (stereochemistry, Ramachandran plots); ProsaII (energy check);
MolProbity (bumps and contacts); WhatIF (all of the above)
There is no one correct way to measure quality!
Empirical vs. first principles
In both cases, we establish what are the structural parameters of importance (i.e.,
bond lengths and steric clashes, phi/psi angles, etc.).
In empirical methods, we use observed values to establish normal ranges and look for
exceptions (which are considered poor quality).
In first principles methods, we start from the fundamental physics and write out an
energy function to quantify the energy of the structure.
Geometry and Stereochemistry: Ramachandran plots
retinoic acid binding protein II
Kleywegt GJ., “Validation of protein crystal structures”, Acta Cryst, 2000, D56, 249-265
More About Ramachandran Plots
Left: Ramachandran plot of a wrong structure
Right: Ramachandran values for D-amino acids will look different from L-amino acids.
For example, Gramicidin A (1GRM), a prokaryotic antibiotic compound, is composed of
alternating L/D amino acids.
Left: Kleywegt GJ., Acta Cryst, 2000, D56, 249-265
Geometry and Stereochemistry: PROCHECK
 Checks the stereochemical quality of a protein
structure
 Produces a number of PostScript plots analyzing its
overall and residue-by-residue geometry
Geometry and Stereochemistry: PROCHECK
http://services.mbi.ucla.edu/SAVES/
Geometry and Stereochemistry: PROCHECK
G-factors mapped to structure, in this
case, red = unusual phi/psi angles
http://molprobity.biochem.duke.edu/index.php
Davis, IW et al.
Energy Plot: ProSA Analysis
ProSA is based on a potential of mean force (aka, knowledge-based potential) that uses
observed residue-residue pairwise distances to establish energy values.
From the ProSA webserver site:
ProSA-web provides an easy-to-use
interface to the program ProSA (Sippl
1993), which is frequently employed in
protein structure validation.
ProSA calculates an overall quality score
for a specific input structure.
If this score is outside a range
characteristic for native proteins the
structure probably contains errors.
A plot of local quality scores points to
problematic parts of the model which are
also highlighted in a 3D molecule viewer
to facilitate their detection.
Pr(x) =
e
-E ( x )/kT
Z
Radial Distribution Fxn (aka Pair Correlation Fxn)
Radial Distribution Fxn (aka Pair Correlation Fxn)
Cys-SG:SG-Cys
Cys-SG:CB-Ala
Energy Plot: ProSA Analysis
From the ProSA webserver site:
The z-score indicates overall model
quality.
Its value is displayed in a plot that
contains the z-scores of all
experimentally determined protein
chains in current PDB.
In this plot, groups of structures from
different sources (X-ray, NMR) are
distinguished by different colors.
It can be used to check whether the zscore of the input structure is within
the range of scores typically found for
native proteins of similar size.
Z = -5.65
What is a z-score (aka, standard score)?
z=
x-x
s
Energy Plot: ProSA Analysis of ABC transporter
1JSQA (retracted)
2HYDA
Anomalous bond angles:
http://swift.cmbi.ru.nl/servers/html/index.html
z-score
Structure Validation Menu:
Name check: Checks the nomenclature of torsion
angles.
Coarse Packing Quality: Checks the normality of the
local environment of amino acids
Anomalous bond lengths: Lists bond lengths that
deviate more than 4 sigma from normal.
Planarity: Checks if planar groups are planar enough.
Fine Packing Quality Control: Checks the normality of
the local environment of amino acids
Collisions with symmetry axes: Lists atoms that are too
close to symmetry axes.
Hand check: Lists atoms with a chirality that deviates
more than 4 sigma from normal.
Ramachandran plot evaluation: Determines the quality
of a Ramachandran plot.
Omega: Checks if the distribution of omega angles is
normal.
Proline puckering: Checks if proline pucker falls in a
normal range.
Anomalous bond angles: Lists bond angles that deviate
more than 4 sigma from normal.
Checking water & ion: Lists ions that might be waters
(and vice versa), or other ions.
Empirical energy potentials (force fields)
Theoretical basis of molecular mechanical force fields
The validity of molecular mechanics is based on two key assumptions:
(1) The Born-Oppenheimer approximation – enables the electronic and
nuclear energy to be separated: the much smaller mass of the
electrons means that they can rapidly adjust to any change in nuclear
positions. Consequently, the energy of the molecule (in its ground
state!) can be considered a function of the nuclear coordinates only.
(2) Transferability – enables a set of parameters developed and tested on
a relatively small dataset to be applied to a much wider range of
chemical problems.
Molecular mechanics
Molecular Mechanics (MM) is a computational technique used to model the
conformational behavior and energetic properties of molecules.
The molecule is treated at the atomic level, i.e. the electrons are not treated
explicitly.
MM uses an Energy Function, defined so that given a particular conformation, (i.e.
given a set of spatial coordinates for
all the atoms) the energy of the molecule can be calculated.
Most MM models cannot describe dissociation of covalent bonds.
The energy function is empirical, i.e. it is not entirely derived from rigorous
theories. Usually, a combination of quantum mechanical calculations and
experimental data are used to construct the energy function.
A simple force field
Many of the MM force fields in use today can be interpolated in terms of a
relatively simple four-component picture of the intra- and inter- molecular forces
within the system.
Energetic penalties are associated with the deviation of bond lengths (aka,
central forces) and angles away from their “reference” values, there is a function
that describes how the energy changes as bonds (torsions) are rotated, and
finally the force field contains terms that describe interaction between nonbonded parts of the system.
V (r N ) =
ki
ki
Vn
2
2
(l
l
)
+
(
q
q
)
+
å 2 i i,o å 2 i i,o å 2 (1+ cos(nw - g )) +
bonds
angles
torsions
æ éæ ö12 æ ö6 ù
ö
ç 4e êç s ij ÷ - ç s ij ÷ ú + qi q j ÷
å å ç ij êç r ÷ ç r ÷ ú 4pe r ÷
o ij
i=1 j=i+1
è ëè ij ø è ij ø û
ø
More sophisticated force fields
More sophisticated force fields may have additional terms (such as polarizability,
improper torsions, etc.), but invariably contain these four components.
An attractive feature of this representation is that the various terms can be
ascribed to changes in specific internal coordinates (i.e., bond lengths, angles,
torsion angles, or movements of atoms relative to each other).
Polarizability
Improper Torsion
Dissecting the force field
ki
ki
2
V (r ) = å (li - li,o ) + å (q i - q i,o )2 +
bonds 2
angles 2
N
Vn
å 2 (1+ cos(nw - g )) +
torsions
æ éæ ö12 æ ö6 ù
ö
q
q
s
s
i
j ÷
ij
ij
ç 4e êç ÷ - ç ÷ ú +
å å ç ij êç r ÷ ç r ÷ ú 4pe r ÷
i=1 j=i+1
o ij ø
è ëè ij ø è ij ø û
Dissecting the force field
V(r ) =
N
q1q2
q1q2
Coulomb’s
F=k 2 =
Law:
r
4peor 2
Force-Potential
Relationship:
Meaning:
q1q2
V=
4peo r
qi q j
4pe o rij
Dissecting the force field
ki
ki
2
2
V (r ) = å (li - li,o ) + å (q i - qi,o ) +
2
2
bonds
angles
N
Vn
wq-1qg2 )) +
å 2F(1+
qcos(n
Coulomb’s
1q2
=k 2 =
2
torsions
Law:
r
4peor
æ éæ ö12 æ ö 6 ù
ö
s
s
q
q
ij
ij
i
j ÷
ç
Force-Potential 4e êç
ú
÷÷ - çç ÷÷ +
å
å
ij ç
ç êè rij ø è rij ø ú 4 peo rij ÷
Relationship:
i=1 j= i+1
û
è ë
ø
Notes
Hooke’s law, U = 1/2·k·x2
Hooke’s law, U = 1/2·k·x2
We will ignore improper torsions
Sinusoidal potential. Note the three
minima, which depending on the
local chemistry, may or may not be
equally deep.
Positive (destabilizing) values when
++ or --.
Morse curve.
Bond stretching
Potential energy
Inreality, the bond stretching potential would be best approximated by the Morse
potential, yet is some cases a Harmonic potential (Hooke’s law) is used.
Bond length and energy deviations
from equilibrium values
•
Vb = 0.5 · Kb(r-req)2
•
Kb = 500-1200 kcal/mol/Å2
•
Bond length changes of 0.05 Å implies 1.5 kcal/mol.
Angle bending
The deviation of bond angles is modeled with the Harmonic potential (Hook’s
law).
The contribution of each angle is characterized by a force constant and a
reference value. Meaning, less energy is required to perturb the equilibrium
angle a small bit.
Additionally, the force constant here is much less than that used in the bond
stretching potentials. Meaning, bond angles deviate more frequently than bond
lengths.
Higher order terms can be included here
as well to model more pathological
systems, but they generally are not
employed.
ki
V (q ) = å (qi - q i,o ) 2
2
angles
Bond angle and energy deviations
from equilibrium values
•
Vb = 0.5 · Ka(-  eq)2
•
Kb = 80 kcal/mol/radian2
Torsional terms
The bond stretching and angle bending terms are often referred to as the hard
degrees of freedom, meaning that substantial energies are required to cause
significant deformations.
Most of the variation in chemical structure and relative energies is due to the
complex interplay between the torsional and non-bonded terms.
The existence of barriers to rotation about chemical bonds is fundamental to our
understanding the structural properties of molecules and conformational
analysis.
The three minimum energy staggered conformations (1 anti and 2 gauche) and
three maximum energy eclipsed conformations of ethane are a classic example of
this.
Torsional terms
Torsional terms
Torsion angle potentials are almost always expressed as a cosine expansion.
Vn
V (w ) = å
(1+ cos(nw - g ))
torsions 2
Vn is often referred to as the barrier height, however to do so is misleading. The
barrier is directly proportional to the sum of V’s when more than one term is
present in the expansion. Moreover, other terms contribute to the barrier height
as a bond is rotated, especially the non-bonded interactions between atoms 1 &
4. Having said this, the term does give a qualitative indication of the relative
barriers to rotation.
Torsional terms
4
Potential Energy (KJ/mol)
Note: 1 kcal = 4.184 kJ
3
2
1
0
-1
0
60
120
180
Torsion angle
240
300
360
Attractive non-bonded potentials
Attractive London dispersion (VDW) forces
• Induced dipole
• Varies as 1/r6
• Can be computed “exactly”
• Aij depends STRONGLY on chemistry
Repulsive non-bonded potentials
Repulsive forces (two particles occupying the same space)
• Exponential (Morse) or power law
• V minimum at RVDW determines B from A
• A can be set from depth of well
• Parameters thus determined from depth and position of minimum alone.
æ s ö12 æ s ö6
V (r) = çç ij ÷÷ - çç ij ÷÷
è rij ø è rij ø
where  is the depth of the potential well and  is the
(finite) distance at which the interparticle potential is
zero and r is the distance between the particles.
Attractive term
Repulsive term
In practice, a truncated potential is used to increase compute
efficiency
To reduce compute time, the LJ potential is often truncated at the cut-off
distance of rc = 2.5, because VVDW = 0!!!
Electrostatic interactions
• Partial charges are known to exist.
• In fact, peptide has a dipole moment of 3.7 D.
• Terms are small, but there are LOTS of them.
• Dielectric “constant” is a major problem.
• Constant at short range
  = r at longer distances
V (r) =
qiq j
4 peo rij
An aside: Electrostatic interactions
V (r) =
qiq j
4 peo rij
Note that the electrostatic interactions don’t die off
abruptly since they are linear with separation
distance.
Nevertheless, because the non-bonded terms are the most compute intensive
(there are N·(N-1)/2 atom pairs!), cut-off values may be frequently employed to
speed up computation time. (This is especially critical when coupled to a
minimization algorithm or dynamics simulations)
However, doing so cause the long-range (weaker) electrostatic interactions to be
ignored, which is a cause of significant model error.
As such, reaction field methods, Ewald summation, particle mesh Ewald, etc.
are used to account for the long-range effects.