Flexweb and First/Froda

Flexweb
and First/Froda
http://flexweb.asu.edu
Kirill Speranskiy
Outline
1. Rigidity analysis, rigid units, flexibility
2. FRODA model, protein mobility
http://flexweb.asu.edu
Rigidity analysis
Proteins and rigidity
Rigidity analysis of proteins, based on the distribution of constraints
(covalent bonds, hydrogen bonds, hydrophobic interactions …),
shows that proteins can be divided up into rigid regions of different
sizes. These vary from a “rigid core” which may comprise most of
the atoms in the protein, through mobile rigid clusters (e.g. sections
of alpha-helix containing some tens of atoms) to single atoms (in
flexible side chains).
These rigid clusters can form the basis of a geometric simulation, as
the SiO4 tetrahedra did for the silicate minerals. While tetrahedra
have a geometrically ideal form, the clusters in proteins are defined
empirically from an X-ray crystal structure.
Protein structure
• You need a structure to start with in PDB
format.
• Preferably high-resolution (<2A if
possible) X-ray structure, with good steric
quality.
• You need to add hydrogens.
• REDUCE adds all hydrogens, flips
sidechains etc.
Rigidity analysis
• Done in FIRST using pebble game
http://flexweb.asu.edu/software/pebble_game/2D_interactive/
http://linkage.cs.umass.edu/pg/
Rigidity analysis
• You must choose which constraints
(hydrogen bonds, hydrophobic tethers) to
include in the analysis and which to leave
out, e.g. by picking an energy scale for
hbonds: “first -E -1.5”
Rigid cluster decomposition of barnase
Mobile rigid cluster (mobile
in simulations).
Rigid core (immobile
in simulations).
Flexible region (mobile in
simulations).
Hydrogen bond dilution plot
“FRODA”
The exploration of conformational space is carried out by
FRODA (Framework Rigidity Optimised Dynamic Algorithm).
The rigid core of the protein is kept frozen while all mobile
atoms undergo random motion (Monte Carlo step) followed by
geometric simulation to produce a new conformer.
No distinction is made between main and side chain, nor
between members of closed ring† structures and other atoms.
†(In Tolkein’s story, the hobbit Frodo- or Froda in the original
hobbitish- undertakes a quest to free Middle-Earth from the
dominion of the Rings of Power).
FRODA and mobility
• Mobility depends on both instantaneous
flexibility and other (e.g. steric) constraints.
• Has to be explored; there’s generally no
analytic way to obtain mobility.
• FRODA (Framework Rigidity Optimised
Dynamic Algorithm) aims to explore the
mobility of a flexible protein structure by
perturbing the atomic positions and then
re-imposing the constraints.
The original FRODA procedure
The original FRODA procedure
The original FRODA procedure
Applications
Application 1: random walks for mobility.
Application 2: direct targeting.
Application 3: expansion/contraction.
Application 1: random walks for
mobility
• Random motion based on intrinsic
flexibility.
• From a single input crystal structure,
generate a flexible ensemble.
• Bridge between crystal and NMR data.
• A crystal structure is a structure, not the
structure.
Comparison to NMR
• Comparing globally-aligned RMSD by residue for
the FRODA ensemble and the barnase protein
(1BNR) NMR ensemble.
Barnase mobility from NMR and FRODA
3
NMR
FRODA_long
RMSD (global ensemble)
2.5
2
1.5
1
0.5
0
0
20
40
60
Re sidue (barnase )
80
100
120
Barnase motion: the NMR
ensemble.
Initial state of
Adenylate Kinase
The protein closes and opens
repeatedly.
Flexibility analysis of the bovine
mitochondrial ADP-ATP carrier
Flexibility analysis of the bovine mitochondrial ADP-ATP carrier
Total number of FRODA conformation is 10000 per run
RMSD 1.2 Ǻ
The root mean square deviation between initial structure and structure of last
snapshot from FRODA run is ~3.0 Ǻ which shows that structure without ligand
have significantly larger mobility.
Standalone version of First/Froda
Application 2: getting from A to B
• Pathway between two known conformers.
• Direct targeting: we bias the perturbation
towards the target positions.
ADK morph
• The conformational change is more than 7 A RMS-D.
• Came within 0.5 Angstroms of target after 1556
conformers (176 seconds runtime).
Application 3: using the centrifuge
• If you don’t have a specific target in mind,
one simple operation is to increase or
decrease the radius of gyration of the
protein and see if any interesting domain
motions happen.
• FRODA has a centrifuge function which
biases the perturbations radially.
• A positive directed step moves out; a
negative one moves in.
ADK collapse
Comparison of collapsed and
closed forms
Conclusions
Geometric simulation is a rapid and concise method for
handling collective motions.
Geometric simulation based on rigidity analysis of proteins
allows very rapid exploration of conformation space.
This means that conformer exploration, for e.g. drug design,
may now be faster than interpretation and analysis; for
example, it took longer to produce the graphics for this
presentation than it did to produce the data.
Simulation time and CPU resources need not be the ratelimiting step in protein simulation.