Folding kinetics

Folding equilibrium vs. folding kinetics

Transient intermediate!

Partially Folded States(Molten globule)

Molten globule state:An intermediate conformation assumed by many globular proteins at equilibrium under mildly denaturing conditions

R.H. Pain, Mechanisms of protein folding

Protein folding time scale

ns s ms

Randomcoils

-helix -sheetturns

Hydrophobic collapse

Annealing, Assembly

>S, min, hr..

“Proteins are characterized by:

a) High frequency small amplitude fluctuations (10-12 – 10-9 sec) of individual side chains (NOISE!)

b) Large amplitude collective fluctuations of protein domains (10-6 sec)

c) Slower conformational transitions”

Dr. Sunney Chan

How to detect folding intermediates?

Stopped-flow designed (1970s) Continuous-flow Quench-flow

Bieri and Kiefhber, Biol. Chem., 1999

N Uk1

k2

GNU= -RT lnKeq = -RT ln (k1/k2)

0

20

40

60

80

100

0.01 0.1 1 10

Fra

ctio

n u

nfo

lde

d

Time

A0

k

A Bk

[A] = [A0] * exp (-kt)

Amplitude Rate constant

Burst Phase

•instrumental dead time•(burst phase)

Start

End

Kinetics of chemical reaction

k obs=kUN*exp (-m U-TS*[urea]/RT) + kNU*exp(-m N-TS*[urea]/RT)

GUN= -RT *ln (kUN / kNU)

m U-N = m U-TS + m N-TS

k obs=Refolding rate constant + unfolding rate constant

• G• m

Chevron Plot

Log

(R

ate

con

stan

t)

Denaturant

Refolding(UN)

Unfolding(N U)

Equilibrium mid-point

• compactness of the transition state (TS)

‡

1

Stopped-flow

H1 H2 H3 H4

Most helical bundle

(CARD of RICK)

H1

H4

H3 H2

H6

H5

Stopped-flow Apparatus:Single Mixing Experiments

Stepping Motor

Stepping Motor

Photomultiplier

Computer Control

1 2 3 4

N (0 M urea) U (~4 M urea)UnfoldingRefolding N (~0 M urea)U (4 M urea)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Fra

cti

on

Fo

lde

d

Urea (M)

280295CD

N

U

Equilibrium folding

Four Kinetic Phases are Found in Unfolding and Refolding (burst, fast, medium, slow)

0

20

40

60

80

100

0.1 1 10 100

0 to 0 in %

4 to 4 in %

4 to 0 refolding in %

0 to 4 9.5.02 unfodling data in %

Frac

tion

Unf

olde

d (%

)

Time (sec)

U signal

N signal

Unfolding NU

Refolding U N

3 exponential equations[A] = [A1] * exp (-k1t)+ [A2] * exp (-k2t)+ [A3] * exp (-k3t)

0

20

40

60

80

100

0.01 0.1 1 10 100

Frac

tion

Unf

olde

d (%

)

Time (sec)

0

20

40

60

80

100

0.01 0.1 1 10 100

Frac

tion

Unf

olde

d (%

)

Time (sec)

A

B 0.001

0.01

0.1

1

10

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Rat

e C

on

stan

t (s

ec -1

)

Urea (M)

3 exponential equations[A] = [A1] * exp (-k1t)+ [A2] * exp (-k2t)+ [A3] * exp (-k3t)

RefoldingU to N

UnfoldingN to U

[urea]

Sequential Mixing Experiments

Stepping Motor

Stepping Motor

Photomultiplier

Computer Control

1 2 3 4

t(details of fast forming unfolded species)

N U(fast) U(slow)

example:

U(cis)N(cis) U(trans)

%N

Delay time

100%

1. Double jump: N U t (details in unfolding)

N U N

2. Interrupted refolding:U N

t(N formation in refolding)

1. Double jump: N U t (details in unfolding)

Figure 6 (A) Fraction of native protein versus delay time in double jump experiments. The initial (  ) and final signals (·) of the signal traces were normalized to fraction folded and plotted versus delay time. (B) Fraction of native protein versus delay time in interrupted refolding experiments. The initial signal was normalized and plotted versus delay time.

Parallel folding model

Sequential folding pathway

Slow folding kinetics

cis-trans isomerization Large arrangement Subunit assembly Complex topology

Are the intermediate on-pathway?

Natively Unfolded Proteins

Natively unfolded proteins occupy a unique niche within the protein kingdom in that they lack ordered structure under conditions of neutral pH in vitro.

A lot of them became structured while binding to their binding partners

Natively unfolded proteins Anthony L Fink  Department of Chemistry and Biochemistry, University of California, Santa Cruz, CA 95064, USA

It is now clear that a significant fraction of eukaryotic genomes encode proteins with substantial regi

ons of disordered structure. In spite of the lack of structure, these proteins nevertheless are functio

nal; many are involved in critical steps of the cell cycle and regulatory processes. In general, intrinsi

cally disordered proteins interact with a target ligand (often DNA) and undergo a structural transition

to a folded form when bound. Several features of intrinsically disordered proteins make them well su

ited to interacting with multiple targets and to cell regulation. New algorithms have been developed t

o identify disordered regions of proteins and have demonstrated their presence in cancer-associate

d proteins and proteins regulated by phosphorylation.

Current Opinion in Structural Biology Volume 15, Issue 1, February 2005, Pages 35-41

Ultra-fast foldingContinuous flow

Methods 34 (2004)15-27

Quench-flow microsecond time scale

Chem Rev. 2006 May;106(5):1769-84.                   LinksProbing protein folding and conformational transitions with fluorescence.Royer CA.Centre de Biochimie Structurale, 29, rue de Navacelles 34090 Montpellier Cedex France.

Figure 1 (a) Structure of the regulatory domains of an activated mutant of LicT (tryptophan residues are in purple); (b) intrinsic fluorescence emission spectra of the WT and activated mutant forms

Trp location

Figure 2 Intrinsic tryptophan emission of P13MTCP1 in buffer (full line) and 3 M guanidine hydrochloride (dotted line).

Figure 3 Intrinsic emission spectra of WT protein L (circles) and the Y43W mutant (squares) under native (closed symbols) and denaturing (open symbols) conditions.

Figure 4 Stereoview of ribbon model overlays of the WT* form (green) and the WT NMR-derived solution #1 model (orange). The proteins exhibit the same overall fold, although the main-chain rmsd is 1.46. Major differences occur in the loop regions as well as the N-terminus of -strand 4. The side chains for residues Y47/W47, Y34, and I60 are shown

Figure 5 Ribbon representation of the 3-D structure of nuclease.29 Note that the tryptophan residue (purple) is the last residue in the sequence that exhibits order.

Trp Repressor

Figure 7 Steady-state spectra as a function of urea concentration for (A) trpR W99F and (B) W19F mutants. Increasing numbers correspond to increasing urea concentration. Insets: Urea unfolding profiles based on the average emission wavelength.

tryptophan 19 are red, tryptophan 99 are blue.

Figure 8 DAS (decay associated spectra) as a function of urea concentration for (A) trpR W99F and (B) W19F mutants. Increasing numbers correspond to increasing urea concentration

ANS used to probe folding intermediates

Figure 9 Spectrum of ANS in the presence of beta-lactamase at (A) pH 1.7 and (B) pH 12: (1) no added salt; (2) 0.6 M salt; dotted lines correspond to the spectrum of ANS in the absence of protein.

Figure 10 Stopped-flow fluorescence of ANS and the trp repressor in a refolding experiment. IAA (indole acrylic acid)

Figure 11 Time-dependence of ANS fluorescence from stopped-flow refolding studies of DHFR as a function of increasing acrylamide concentration (higher acrylamide concentration corresponds to lower intensities).

Figure 12 Burst phase intermediate ANS intensity as a function of increasing denaturant.

FRET

Figure 14 Recovered energy transfer distance distributions from the global analysis of the time-resolved decays of D-PGK and D-PGK-A. The predicted dye-to-dye distances from MD simulations (diamonds) are shown for comparison.

Figure 15 Unfolding of PGK monitored by tryptophan emission from D-PGK and D-PGK-A (circles and squares), AF emission from D-PGK-A (inverted triangles), AEDANS emission from D-PGK (triangles), and FRET efficiency from D-PGK-A (diamonds) for all six FRET pairs.

Figure 16 Stopped-flow FRET distances for the six FRET pairs of PGK. (A, 202-412; B, 135-412; C, 412-75; D, 290-412; E, 135-290; F, 75-290).

Demonstrate unfolding of PGK is a multistep process and bending of the hinge between the two domain occurs.

Figure 17 Positions of the four inserted tryptophan residues and the seven inserted cysteine residues in the RNase A structure.

Figure 18 FRET distance distributions at different GuHCl concentrations for doubly labeled RNase A mutants in the reduced native (Rn) and (U) unfolded states. The distances were also determined in the unfolded, oxidized state (Oxi 6M GdnHCl).

How fast can folding be

Figure 19 Transient from the folding of horse apomyoglobin after a laser T-jump. The inset (B) shows the response of free tryptophan.

Figure 21 Ultrafast fluorescence intensity kinetic traces after laser T-jumps of (a) 265-275 K, (b) 273-293 K, and 303-319 K. Relaxation times obtained from fits of the data to single exponential decays were on the order of tens of nanoseconds.

Designed small helical peptide labeled with extrinsic probe

Figure 23 Autocorrelation function and residuals of the simple diffusion model and an additional dynamics model for V60Flu FABP (Fatty acid binding protein).

Single molecule study

FRETfluorescence resonant energy transfer

thio

Case in a helix bundle(B) Unmodified ACBP (sharp decrease due to FL quenching)(C) AEDANS-labeled ACBP.Ex the Trp, Em at AEDANSLarge increase at first 80usec (due to major decrease of distance) following by decay phase from 10-100msec

First 80us forms loosely packed and highly dynamic ensembles of statesThe dimension is similar to the native state

New Technology for protein folding

Direct Observation of the Three-State Folding of a Single Protein Molecule Ciro Cecconi,1,2* Elizabeth A. Shank,1* Carlos Bustamante,1,2,3   Susan Marqusee  UC Berkeley

Science 23 September 2005:Vol. 309. no. 5743, pp. 2057 - 2060

We used force-measuring optical tweezers to induce complete mechanical unfolding and refolding of individual Escherichia coli ribonuclease H (RNase H) molecules. The protein unfolds in a two-state manner and refolds through an intermediate that correlates with the transient molten globule–like intermediate observed in bulk studies. This intermediate displays unusual mechanical compliance and unfolds at substantially lower forces than the native state. In

a narrow range of forces, the molecule hops between the unfolded and intermediate states in real time. Occasionally, hopping was observed to stop as the molecule crossed the folding barrier directly from the intermediate, demonstrating that the intermediate is on-pathway. These studies allow us to map the energy landsc

ape of RNase H.

Mechanical Unfolding

Membrane protein folding

Nature 438, 581-589 (1 December 2005) Solving the membrane protein folding problem

Membrane protein foldingStephen White

laboratory UC Irvine

General Principles of Membrane Protein

Folding and Stability

Constitutive Membrane Protein Assembly

Inconstitutive Membrane Protein Assembly

WHY IS PROTEIN FOLDING SO DIFFICULT TO UNDERSTAND?

It's amazing that not only do proteins self-assemble -- fold -- but they do so amazingly quickly: some as fast as a millionth of a second. While this time is very fast on a person's timescale, it's remarkably long for computers to simulate.

In fact, it takes about a day to simulate a nanosecond (1/1,000,000,000 of a second). Unfortunately, proteins fold on the tens of microsecond timescale (10,000 nanoseconds). Thus, it would take 10,000 CPU days to simulate folding -- i.e. it would take 30 CPU years! That's a long time to wait for one result!

Computation

Molecular Dynamicsab initio protocol: Ignore sequence homology and atte

mpts to predict the folded state from fundamental energetic or physicochemical properties associated with the constituents residues. (Finding a single structure of low energy)

secondary structure predictionbased on the preference of a.a. for certain conformational states (50%) In combination of homologous sequences (70%)

(computational prediction of folding is not yet reliable)

http://www.stanford.edu/group/pandegroup/folding/villin/index.html

Simulations of the villin headpiece  The villin headpiece is a small, 36-residue alpha helical protein. It has been heavily studied experimentally and by simulation since is perhaps one of the smallest, fastest folding proteins. It has a hydrophobic core made of 3 phenylalanines, but also has two groups (a tryptophan and another phenylalanine) which are hydrophobic, but are solvent exposed (for functional reasons). Duan and Kollman simulated 1 microsecond of MD time, in a ground breaking simulation. However, since the folding time is on the order of 10 microseconds, it is not surprising that they did not see it fold. Our simulations contain hundred of microseconds of MD time, and we have seen 35 simulations which have folded.

http://folding.stanford.edu/