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Direction dependent mechanical unfoldingand Green Fluorescent Protein as a force
sensor
Alessandro Pelizzola
Physics DepartmentPolitecnico di Torino
Bari, Sep 21, 2011
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Single molecule manipulation: Atomic ForceMicroscopy
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Single molecule manipulation: Laser Optical Tweezers
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Single molecule manipulation: protocols
I Constant velocity:I the moving end of the molecule is pulled through an elastic
forceI the center of the corresponding harmonic potential moves
at v = constI the force on the molecule can be measured as a function of
the elongation
I Constant force:I the force on the molecule is kept constant using a feedback
apparatusI elongation is measured as a function of time
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Pulling Poly–Titin (I27): AFM, v = const
Worm Like Chain fits⇒ contour length (and variations)
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Pulling an RNA hairpin, f = const
2–state behaviour is clearly observed at f ' fu
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A recent theoretical review
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Mechanical unfolding: a simple theory
Elongation is a natural reaction coordinate⇒ Bell’s model
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Theory: f = const
Assuming TS is not moved by f :
∆G‡u(f ) = ∆G‡u(0)− fxu
ku(f ) = ku(0) exp(
fxu
kBT
)(1)
Similarly,
kf (f ) = kf (0) exp(− fxf
kBT
)
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Theory: f = rt , r = const
Unfolding rate at time t , force f = rt
ku(rt) = ku(f ) = ku(0) exp(
fxu
kBT
)
Probability of unfolding at force f
P(f ) =ku(f )
rexp
{kBTrxu
[ku(0)− ku(f )]
}
Most probable unfolding force fM = argmaxP(f )
fM =kBTxu
ln[
xu
ku(0)kBTr]
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More complex phenomena
I Intermediates: metastable states which retain only part ofthe native structure
I Pathway diversity: the unfolding of a protein with manyintermediates can proceed through pathways whichdepend on the details of the pulling protocol
I Direction dependence: when the force is not appliedend–to–end, but only a portion of the chain is pulled, theunfolding phenomenon depends on the application pointsof the force
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Modeling approaches
Degrees of freedom:I atomistic (all or heavy atoms)I coarse–grained (Cα, one or a few beads per aminoacid)I lattice polymersI Ising–like (e.g. a binary variable per aminoacid or peptide
bond)
Interactions:I native (Go) vs. non–native interactionsI explicit vs. implicit solvent
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Ising–like models
I Galzitskaya and Finkelstein, PNAS 96, 11299 (1999)I Alm and Baker, PNAS 96, 11305 (1999)I Muñoz and Eaton, PNAS 96, 11311 (1999)
A binary degree of freedom mk , taking valuesnative/non–native (resp. 1, 0) is associated to each aminoacidor to each peptide bond ⇒ 2N microstates
Can be thought of as an extremely crude discretization of a pairof dihedral angles ((φi , ψi) for an aminoacid, (ψi , φi+1) for apeptide bond)
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Ising–like models (cont’d)
Many more non–native conformations ⇒ excessentropy q (∼ kB) associated to non–native value (or entropycost associated to native)
Different (native only) contact interaction energies: contact map∆ read from the PDB putting some threshold on interatomicdistances (typically 0.4–0.5 nm between nonhydrogen atoms,or 0.65–0.7 nm between Cα’s)
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(Wako–Saitô–)Muñoz–Eaton (or ISLAND) model
A microstate (1 = native, 0 = non–native):
00000001111111111000000000011111110111000110
ISLANDS of 1’s can be identified
Only aminoacids in the same island can interact: a non–nativepeptide bond (or aminoacid) breaks the chain into twonon–interacting parts.
Effective free energy (“Hamiltonian”)
H = −∑i<j
εij∆ij
j∏k=i
mk − T∑
i
qi(1−mi)
εij ∝ number of close–by atom pairs
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(Wako–Saitô–)Muñoz–Eaton (or ISLAND) model(cont’d)
Several choices for the kinetics:
I Monte Carlo simulations
I diffusion on a 1D free energy profile
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Mechanical unfolding: generalizing the island model
I To each island we associate an orientational degree offreedom, which in the simplest case is still Ising–like(parallel/antiparallel to the force)
I We do not need any more the introduction by hand of anexcess entropy for non–native bonds
I The equilibrium thermodynamics is still exactly solvableI Summing over orientational variables we get back the
island model with an excess entropy q = kB ln 2
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Mechanical unfolding: generalizing the island model(cont’d)
PROTEIN ≡ sequence of rigid (native) stretches
For each stretch: native length lij , orientation σij = ±1
H(m, σ) = H0(m)− fL(m, σ)
H0(m) = −∑i<j
εij∆ij
j∏k=i
mk
L(m, σ) =∑
0≤i<j≤N+1
lijσij(1−mi)(1−mj)
j−1∏k=i+1
mk
[A. Imparato, A. P. and M. Zamparo, Phys. Rev. Lett. 98, 148102 (2007)]
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Summary of previous results
I 2–state behaviour in agreement with theory andexperiments (PRL ’07, JCP ’07)
I Ubiquitin 3–state behaviour: intermediate has samestructure as in all–atom models. Multi–stage refolding as inexperiments (PRL ’08)
I Multi(5)–state behaviour in an RNA fragment: pathwaysconsistent with experiments and coarse–grained models(PRL ’09)
I Pathway diversity in a fibronectin domain (JCP ’10)
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Green Fluorescent Protein (GFP)
11–strands β–barrel + small helices
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Green Fluorescent Protein (GFP)
I Large protein: 238 aminoacids
I Bright green fluorescence when exposed to light of asuitable wavelength (395 nm, blue) AND native structure isintact
I Applications in biotechnology
I localization of proteins in living cells
I metal ion or pH sensors
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Experiments: pulling GFP end–to–end (Reif et al, PNAS ’07)
Major unfolding pathway
Minor unfolding pathway
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Pulling a protein from different directions
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Experiments: pulling GFP from different directions (Reif
et al, PNAS ’06)
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Model: landscape (at equilibrium unfolding f )
Intermediates: β1 and β11 (∼ 110 Å), β10β11 (∼ 180 Å), β1β2β3(∼ 250 Å)[A. Imparato, A. P. and M. Zamparo, Phys. Rev. E 84, 021918 (2011)]
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Model: pulling end–to–end
Major unfolding pathwayOrder of unfolding events
I N–terminal α–helix(small signal)
I β1
I β2β3
I β10β11
I all the rest
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Model: pulling end–to–end
Minor unfolding pathway
Order of unfolding events
I N–terminal α–helix(small signal)
I β11
I . . .
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Model: pulling from different directions
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GFP as a force sensor
http://pre.aps.org/kaleidoscope/pre/84/2/021918
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GFP as a force sensor
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Coworkers:I Marco Zamparo (Padova University)I Alberto Imparato (Aarhus University, Denmark)I Michele Caraglio (PoliTO)
Main Refs for our work:I A. Imparato, A. P. and M. Zamparo, Phys. Rev. Lett. 98, 148102
(2007).I P. Bruscolini, A. P. and M. Zamparo, Phys. Rev. Lett. 99, 038103
(2007).I A. Imparato, A. P. and M. Zamparo, J. Chem. Phys. 127, 145105
(2007).I A. Imparato and A. P., Phys. Rev. Lett. 100, 158104 (2008).I A. Imparato, A. P. and M. Zamparo, Phys. Rev. Lett. 103,
188102 (2009).I M. Caraglio, A. Imparato and A. P., J. Chem. Phys. 133, 065101
(2010).I M. Caraglio, A. Imparato and A. P., Phys. Rev. E 84, 021918
(2011).
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Thanks for your attention