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Simple toy models (An experimentalist’s perspective) . Lattice Polymers. Lattice Polymers. Do they predict absolute folding rates?. Lattice Polymers. Do they predict relative folding rates?. Two-state folding rates. k f = 2 x 10 5 s -1 k f = 2 x 10 -1 s -1.
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Lattice Polymers Do they predict absolute folding rates?
Lattice Polymers Do they predict relative folding rates?
Two-state folding rates kf = 2 x105 s-1 kf = 2 x 10-1 s-1
Putative rate-defining criterion Landscape Roughness Energy Gap Collapse Cooperativity
Landscape Roughness Bryngelson & Wolynes (1987) PNAS, 84, 7524
Kinetics switch from single exponential: A(t) = A0 exp(-t·kf)1/h To stretched exponential: A(t) = A0 exp(-t·kf)1/h When Landscape Roughness Dominates Kinetics Socci, Onuchic & Wolynes (1998) Prot. Struc. Func. Gen.32, 136 Nymeyer, García & Onuchic (1998) PNAS, 95, 5921 Skorobogatiy, Guo & Zuckermann (1998) JCP,109, 2528 Onuchic (1998)PNAS, 95, 5921
The energy landscape of protein L h = 0.98 0.08 Gillespie & Plaxco (2000) PNAS, 97, 12014
The pI3K SH3 domain Gillespie & Plaxco (2004) Ann. Rev. Bioch. Biophy, In press
The Energy Gap “The necessary and sufficient condition for [rapid] folding in this model is that the native state be a pronounced global minimum [relative to other maximally compact structures].” Sali, Shakhnovich & Karplus (1994) Nature, 369, 248
Gap Size Correlates with theFolding Rates of Simple Models Dinner, Abkevich, Shakhnovich & Karplus (1999) Proteins, 35, 34
The uniqueness of the native state indicates that it is significantly more stable than any other compact state: the energy gap is generally too large to measure experimentally.
An Indirect Test For many simple models, Tm correlates with Energy Gap size 15-mers (B0 = -2.0) r = 0.73 15-mers (B0 = -0.1) r = 0.92 27-mers (B0 = -2.0) r = 0.89 27-mers (B0 = -0.1) r = 0.97 Dinner, Abkevich, Shakhnovich & Karplus (1999) Proteins, 35, 34 Dinner & Karplus (2001) NSB,7, 321
Gillespie & Plaxco (2004) Ann. Rev. Bioch. Biophy., In press
Collapse cooperativity “The key factor that determines the foldability of sequences is the single, dimensionless parameter s …folding rates are determined by s.”””” Thirumalai & Klimov (1999) Curr. Op. Struc. Biol., 9, 197
Cytochrome C
Protein Rate Reference Cytochrome C 6400 s-1Gray & Winkler, pers com. Ubiquitin 1530 s-1 Khorasanizadeh et al., 1993 Protein L 62 s-1 Scalley et al., 1997 Lysozyme 37 s-1 Townsley & Plaxco, unpublished Acylphosphatase 0.2 s-1 Chiti et al., 1997 See also: Jaby et al., (2004) JMB, in press
Millet, Townsley, Chiti, Doniach & Plaxco (2002) Biochemistry, 41, 321
All “foldability” criterion optimal Energy landscapes unmeasurably smooth Energy gaps unmeasurably large All s within error of zero
When the energy gap dominates folding kinetics, none of a long list of putatively important parameters, including the “number of short- versus long-range contacts in the native state*”, plays any measurable role in defining lattice polymers folding rates. *Sali, Shacknovich & Karplus (1994) “How does a protein fold?” Nature, 369, 248
Do subtle, topology-dependent kinetic effects appear only in the absence of confounding energy landscape issues?
Go Polymers • Native-centric energy potential • Extremely smooth energy landscape • Topologically complex
Topology-dependence of Go folding r = 0.2; p = 0.06
The topomer search model The chain is covalent Rates largely defined by native topology Local structure formation is rapid Equilibrium folding is highly two-state
Protein folding is highly two-state Fyn SH3 domain
55 residue protein ∆Gu = -3 kcal/mol Kohn, Gillespie & Plaxco, unpublished
4 residue truncation ∆Gu ~ 2 kcal/mol Kohn, Gillespie & Plaxco, unpublished
The Topomer Search Model Makarov & Plaxco (2003) Prot. Sci., 12, 17
P(QD) <K>QD kf = k QD g <K>QD
Testing the topomer search model We can test the model if we assume that all sequence- distant residues in contact in the NATIVE STATE must be in proximity in the TRANSITION STATE Sequence-distant: > 4-12 residues Native contact: Ca-Ca < 6 - 8 Å
kf QD<K>QD r = 0.88
Crowding Effects Gaussian Chains Real Polymers Persistence length Excluded volume
kf QD<K>QD/N r = 0.92 Makarov & Plaxco (2003) Prot. Sci., 12, 17
“It is also a good rule not to put overmuch confidence in observational results that are put forward until they have been confirmed by theory.”Paraphrasing Sir Arthur Eddington theoretical simulation
Minimum requirements for topology-dependent kinetics • Connectivity • Rapid local structure formation • Smooth landscapes • Cooperativity
-eQ Q(1 - s)/QN + sQ E =
s = 2 r = 0.71; p = 10-16
s = 3 r = 0.76; p = 10-18 Jewett, Pande & Plaxco(2003) JMB,326, 247 See also: Kaya & Chan (2003) Proteins,52, 524
Acknowledgements UCSB Blake Gillespie Lara Townsley Jonathan Kohn Andrew Jewett Horia Metiu UT Austin Dima Makarov Stanford Seb Doniach Ian Millet Vijay Pande Universita di Firenze Fabrizio Chiti NIH, UC BioSTAR, ONR