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)

Hespenheide, et al. JMGM (2002)

Rigid Cluster Decomposition

Reduced Representation

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

Thanks to …

FundingIUPUI Dept. of Physics and Center for Mathematical Biology

http://flexweb.asu.edu

FIRSTMichael F. Thorpe (Ariz St U)Leslie A. Kuhn (Mich St U)Don Jacobs (UNC-Charlotte)Brandon Hespenheide

RhodopsinIvet Bahar (Pittsburgh)Judith Klein-Seetharaman (Pittsburgh)Basak IsinOznur Tastan