Analysis of protein structures

Eran Eyal2011April

Indication to the quality of the structure ResolutionR-factor

Additional information regarding position of individual atoms B-factor Occupancy

Quality of the structure

related to the distance between sets of equivalent parallel planes of atoms in the unit cell that affects on collected diffraction data

The smaller this number is, the higher the resolution and the greater the amount of detail that can be seen:

~5Å (low resolution)one can obtain the shape of the molecule

~3Å (medium resolution)it is usually possible to trace the path of polypeptide chain

~2Å (high resolution)one can distinguish side chains

At 1Å resolution one sees atoms as a discrete balls of density

Resolution (Å)

Resolution

Diffraction pattern Brag Planes separation

Poor Resolution

Good Resolution

3Å resolution

2Å resolution

R-factor

Original diffraction patern

Model

Calculated diffraction pattern based on the modelR factor די פרקציהמודד עד כמה שו נה

מהדיפר קציה על סמך המודל תאור ט י תהמקור י ת שש ימשה לב נ י ית ו

Quality of the structure

a measure of how much an atom oscillates or vibrates around the position specified in the structure

For well refined, correct structures B-values are of the order 20 or less.

High B-values, 40 or above, in a local region can be due to flexibility or slight disorder, but also serve as a warning that the structure of this region may be incorrect.

Temperature factor

Quality of Macromolecular Modelshttp://www.usm.maine.edu/~rhodes/ModQual/

228 xB π=

In order to have an initial idea about the mean square displacement of an atom, simply divide it’s B-factor by 80

Usually (especially when comparing different structures) it is good idea to Normalize the B-factor values

)( BBBB

σ><−

=′

TYROSINE-PROTEIN KINASE

Occupancy

Sometimes it is possible to distinguish between 2 several alternative conformations of the structure in the electron density map. In this case the PDB file includes information about all ofthem.

Does crystal packing alter the protein 3D structure ?

Compatibility between crystallographic models and chemical studies

X-ray structures are compatible with other structural evidences

Compatibility between crystallographic models and NMR studies

Proteins can retain their function in the crystal

Crystalline enzymes are usually active

Analysis of molecular interactions

3D coordinates of 2 (or more) molecules How good are the interactions ?

What are the interactions ?

Different ways to score interactions in the atomic level

Pseudo energy terms aim to simulate the real forces act between and within the molecules

Use of geometrical features of the spheres representing the atoms, such as contact surface area and overlapping volumes

Using probabilistic approaches based on existing knowledge regarding atomic interactions

Contact surface areas are correlated with several energetic components which determine the structure and stability of proteins.

Contact surfaces are correlated with short range forces such as the attractive van der Waals forces. Considering the chemical types of the atoms they can also partially account for short range electrostatic interactions such as hydrogen bonds.

Most important, by considering contact surfaces with the solvent (solvent accessible surface) we might account for some affects which play important role in protein folding and stability such as internal packing and solvation affects.

Properties of molecular surfaces

• Hard to calculate• Slow to calculate• Non pair-wise function

1.89Cl1.80S1.80P1.47F1.52O1.55N1.70C1.20H

van-der-Waals radius / Åelement

Many other set of values for VDW radii can be found in the literature

Accepted values for VDW radii

Types of surfaces

• Van der Waals

• Connolly surface

Van der Waals

• Solvent accessible surface• Connolly surface

solvent accessible surface Solvent accessible surface (SAS) is determined as the free surface for interaction with solvent molecules

Buried atoms have often zero solvent accessible surface

Chotia, 1974

(j )A =ia

i=1

jn

∑

maxjA

Ajmax is the maximum possible SAS for amino acid of type j

Often it is necessary to normalize SAS so it will indicate the relative fraction of the surface which is free to interacts withsolvent molecules. This normalized value is the accessibility of the residue

GG

GGJ

buriedPartially buried

exposed

Distribution of amino acids in proteinsHow to calculate SAS ?

• The original method (Lee & Richards, 1971) – slice the molecule

• Shrake & Rupley, (1973) – count dots distributed on the surface

• Analytical methods using sophisticated 3D geometry

Popular approach is to distribute (many) points on the surface of the atoms and than count how many points are within the radius of other atoms.

SASi =4ΠR2 * (1-nred points/nall points)

Voronoi procedure for derivation of contact surfaces and volumes

Voronoi method

Original method: given a set of points in a plane, the plane is divided into polygonal regions with one region per point (Voronoi, 1908).

This may be applied to protein structures in three dimensions, and can quantify atom volumes and packing efficiencies for internal atoms (Richards et al, 1974; Tsai et al, 1999).

Asp

Gln

His Voronoi cells are mathematically equivalent to the Delaunay triangulation

http://sts.bioengr.uic.edu/castp/background.php

Connolly surface

Connolly surface

Connolly surface

Tricolor representation of Connolly surface

Convex regions

Concave regions

Saddle regions

Surface descriptions is an important tool to find compatibility between molecules

Characterization of the protein surface Perpendicular vectors might improve further the

ASP (Atomic Solvation Parameters)

Eisenberg et al., were the first to consider different types of surfaces.If we want to use the surface as a measure of free energy, it isbetter to give different weights to the solvent accessible surface according to the atoms that create these surfaces

iii AG σΔ=Δ

iiatoms

R AG ∑Δ=Δ

iσ

Nature, 319, 1986

Δσ(C)= 16calǺ-2mol-1

Δσ(N/O)= -6calǺ-2mol-1

Δσ(O-)=-24calǺ-2mol-1

Δσ(N+)=-50calǺ-2mol-1

Δσ(S)=21calǺ-2mol-1

Eisenberg et al., divided all protein atoms to 5 groups,

The values were obtained by fitting the experimental ΔGobs with the calculated ΔGcal

−−++ ++++=Δ oonnoonnoncccal AAAcAAG σσσσ //

Later works divided protein in different ways:

Ooi et al. (1987) divided protein atoms to 7 groups, including 3 types of carbons.

Usually, SAS of carbon and sulfate atoms have positive contribution to the free energy difference, while polar atoms have negative contribution.

Many works which ASP sets based on different procedures found very different values.

Since the model is empirical and not stands on solid theory, it is recommended to derive set of ASP ad hoc to defined purposes

ASP’s

ASP’s

∑∑=sc

a

all

bababcomp SWE

ad

b

ca-c contact (Sac)a-d contact (Sad)a-b contact (Sab)a-solvent

Contact surfaces serve to analyze atom-atom contacts

The CSU program for analysis of Contacting Structural Units within proteins, is a free software available also threw web server for analysis of SAS and atom-atom contact surface areas. The program was developed in the Weizmann Institute by Vladimir Sobolev. The LPC program for analysis of Ligand Protein Contacts uses the same procedure for intermolecular interactions

“Surfaces” for the residues level

Attempts were done to estimate molecular surfaces in a pair-wise manner

Tools for structural analysis based on contact surface areas Does crystal packing alter the protein 3D structure ?

Compatibility between crystallographic models and chemical studies

X-ray structures are compatible with other structural evidences

Compatibility between crystallographic models and NMR studies

Proteins can retain their function in the crystal

Crystalline enzymes are usually active

X-ray

(pdb 1ert)

NMR

(pdb 3trx)

Human thioredoxin structure determined by X-ray and NMR

superimposition

Differences in protein structure due to the crystal

loop difference

Malate dehydrogenase (pdb 4mdh)

Position of ligands associated with the protein is not affected by the crystal environment

http://ligin.weizmann.ac.il/cryco

How local perturbations affect the structure?

• Very context dependent

• In many cases the effect is minor and local

• Point mutations can change structure and functionPr

obab

ility

for c

onfo

rmat

iona

l cha

nge

ARG ASN ASP CYS GLN GLU HIS ILE LEU LYS MET PHE SER THR TRP TYR VAL

0

0.1

0.2

0.3

0.4

0.5

Prob

abili

ty fo

r con

form

atio

nal c

hang

e

Probability of conformational change of different amino acids

Natural flexibility

Mutation sites

Ligand binding

0

0.1

0.2

Total Hydrophobic Hydrophilic Aromatic

The influence of the position of the side chain on its flexibility

Buried

Exposed

http://sts.bioengr.uic.edu/castp/ http://sts.bioengr.uic.edu/castp/

Structural validation

• There is a constant need to check validity of structures and sub-structures:

Validation of theoretical modelsCheck for errors in structure determination using experimental procedures

MolProbity

http://molprobity.biochem.duke.edu/

Add hydrogens: Explicit hydrogens are needed for many of MolProbity'sanalyses to function correctly, and structures determined by crystallography almost never include them.

flip Asn, Gln, and His residues: to give the most reliable view of H-bonding and steric interactions. Options exist to review and override flip .

Analyze sterics & geometry: MolProbity automatically selects appropriate settings for PDB structure and examine relevant features

MolProbity

MolProbity is a tool for structural analysis and validation

Histidine& Asn flip

HistidineTautomerization:The Hydrogen can be on either Nitrogens, thus affecting the H-bond pattern

http://swift.cmbi.ru.nl/servers/html/index.html

PDBsum:

http://www.ebi.ac.uk/pdbsum/

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http//:www.ebi.ac.uk/pdbsum/