Probing the diversity of unfolding pathways by simulated ... · Probing the diversity of unfolding...
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Probing the diversity of unfolding pathways by simulated thermal
denaturationA.J. Rader
Physics Dept.Indiana University-Purdue University
IndianapolisIMA Protein Folding Workshop: 01.17.08
http://www.physics.iupui.edu/~ajrader/
Extract information about unfolding from the native stateusing network models of the protein structure.Folding: hydrophobic collapse followed by hydrogen bond formationUnfolding: Simulate thermal denaturation by removing hydrogen bonds one at a time based upon strength (energy).
The Plan: Folding by Unfolding
Native State
Denatured State(s)
Folding
Unf
oldi
ngEntropy
Ene
rgy
Rigidity is determined directly from the mechanical properties a structure, referring to constraints (bonds) that are fixed in length.
The number degrees of freedom, F, or floppy modes measure the flexibility of the structure.
(Lagrange 1785, Maxwell 1864, Laman 1970, Phillips 1979, Thorpe 1983, Tay & Whitely 1985)
These floppy modes correspond to deformations which cost no energy (i.e. along the trough of a potential).
Network Model: Rigidity & Constraints
The Constraint Network (FIRST)1
Fix physically inspired constraints in proteins; count the number of floppy modes and mean coordination (<r>).
Covalent bond
α
Chemical bond angle
D
H AB
Hydrogen bond
Hydrophobic contact
1Jacobs, Rader, Kuhn & Thorpe Proteins, 44 (2001)
Always present:Covalent bondsLocked peptide bondsHydrophobic contacts
Variably present:Hydrogen bonds (temperature dependent)
Dihedral angles left free to rotate degrees of freedom (floppy modes)
Floppy modes & hydrogen bond dilution
Rader, et al. PNAS 99 (2002)
rNF6523/ −==f
Rigidity phase transition (<r>T = 2.405) similar toone in glass networks (<r>c = 2.385).
N:= Native-like state (input structure)T:= Transition state(peak of 2nd
derivative)FC:= Folding core (last line where at least two 2°structures are mutually rigid)
Dilution Representation & Folding Cores
Rader, et al. PNAS 99 (2002);Hespenheide, et.al. JMGM 21 (2002);Rader & Bahar Polymer 46 (2004)
Folding cores correspond to most protected residues from Hydrogen-Deuterium exchange experiments.
Rhodopsin unfolding pathway Rader et. al. PNAS (2004)
Folding core residues correspond to misfoldingmutations
Core diversity of rhodopsin (Rd) structures
BacterioRd VS mammalian Rd
Tastan, et. al. Photochem & Photobiol. (2007)
FC ranges from short range (full helices) to long range (helical segments)
Commentary
These results depend on the atomic details of the input protein structure
What happens when there are multiple equally valid “native states” (such as those from NMR ensembles, MD snapshots, etc)?
Can we gain insight about the funnel from such pathways?
Related question: how well do we understand the “native states”?
Average unfolding pathway
1. Condense unfolding pathway onto a vector on [0,1] where 1 rigid and 0
flexible depending on belonging to the largest rigid cluster (LRC).
2. Average over the dilution steps to yield a pathway rigidity descriptor with N (residues) components for a given “native” structure
0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
residue
Plrc
Application to an ensemble of structures
Now take an ensemble of NMR structures
1bnr has 20 “native state” solutions to the barnase structure.Repeat the analysis for each structureNotice variation in pathways taken.
Barnase HDX most protected residues: 14, 25, 74, 89, 97 have large <Plrc>
Average over the pathways
negative Φ havemany paths
Φ-values: Serrano, et.al. JMB (1992).HDX: Perrett, et.al. Biochem (1995).
Summary
1. Simulated thermal denaturation associates a rigidity phase transition in proteins with unfolding.
2. Correspondence to experimental HDX data indicates that native state contacts encode information about folding.
3. Bacteriorhodopsin & Mammalian rhodopsin have different distributions of stable (folding) cores & unfolding pathways.
4. Pathway unfolding analysis revealsSome residues can be grouped together but different pathways are takenValleys distinguishing residues that are most likely to remain rigid throughout unfolding first residues to fold