Method-Unifying View of Loop-Formation Kinetics ... - ACS Publications

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A Method-Unifying View on Loop Formation Kinetics in Peptide and Protein Folding Maik H. Jacob, Roy Niky D'Souza, Thomas Schwarzlose, Xiaojuan Wang, Fang Huang, Elisha Haas, and Werner M. Nau J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b00879 • Publication Date (Web): 04 Apr 2018 Downloaded from http://pubs.acs.org on April 6, 2018

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The Journal of Physical Chemistry

A Method-Unifying View on Loop Formation Kinetics in Peptide and Protein Folding Maik H. Jacob,*, † Roy N. D’Souza,† Thomas Schwarzlose,† Xiaojuan Wang,‡ Fang Huang,‡ Elisha Haas,& Werner M. Nau*, †, ‡

†

Department of Life Sciences and Chemistry, Jacobs University Bremen, Bremen, Germany

‡

Center for Biotechnology and Bioengineering, China University of Petroleum, Qingdao,

Shandong, China. &

Bar Ilan University, Department of Life Science, Ramat Gan, Israel

*Corresponding authors ! e-mail: M.H.J: [email protected] W.M.N: [email protected]

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ABSTRACT Protein folding can be described as a probabilistic succession of events, in which the peptide chain forms loops closed by specific amino acid residue contacts, herein referred to as loop nodes. To measure loop rates, several photophysical methods have been introduced, where a pair of optically active probes is incorporated at selected chain positions, and the excited probe undergoes contact quenching (CQ) upon collision with the second probe. The quenching mechanisms involved triplet-triplet energy transfer, photo-induced electron transfer, and collision-induced fluorescence quenching, where the fluorescence of Dbo, an asparagine residue conjugated to 2,3-diazabicyclo[2.2.2]octane, is quenched by tryptophan. The discrepancy between the loop rates afforded from these three CQ techniques has, however, remained unresolved. In analyzing this discrepancy, we now report two short-distance FRET methods, where Dbo acts as energy acceptor in combination with tryptophan and naphtylalanine, two donors with largely different fluorescence lifetimes of 1.3 ns and 33 ns, respectively. Despite the different quenching mechanisms, the rates from FRET and CQ methods were, surprisingly, of comparable magnitude. This combination of FRET and CQ data led to a unifying physical model and to the conclusion that the rate of loop formation in folding reactions varies not only with the kind and number of residues that constitute the chain but in particular with the size and properties of the residues that constitute the loop node.

#!


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INTRODUCTION The loop hypothesis on the refolding of large single-chain proteins assumes that the earliest productive folding events include the formation of several long loops closed by modestly stable loop nodes.1-5 Long loops at an early stage define the gross topology of the protein and prevent the chain from multiple fatal folding pathways.2,6-7 Loop formation was first studied by using FRET to detect, at different stages of refolding, distances between labeled chain positions that form a node in the native state.8 In the past, these studies were limited by the distance resolution of FRET to relatively large proteins, as traditional pairs of dyes can be used to measure distances around 20 Å but rarely below, as would be advantageous to detect the short distances that signal loop-node formation.1-3,9-10 To understand early refolding, it is decisive to know how fast a defined loop can form. Dynamic information on the chain can be obtained from FRET, namely from a global analysis of time-resolved FRET measurements.11-14 When analyzed appropriately, FRET can yield the coefficient of diffusion between two chain positions together with the probability distribution of distances between these positions. However, a robust, convenient protocol, cross-corroborated among laboratories, has yet to emerge.15-16 Not long ago, a novel group of methods were enthusiastically embraced that were seemingly able to access loop rates directly.17-20 Fundamental questions were posed and apparently answered, on the speed limit of protein folding,17,19,21-22 on how fast a loop can form in dependence of its length,21-22 of its amino-acid composition,23-25 of its sequence,

25-26

and of its

solvent environment.27-29 In these studies, by others and us, the question of which method is most accurate has moved to the foreground at the expense of the question why the methods afford different results. Outwardly, these methods are similar: Two optically active probes are incorporated at selected chain positions; one probe is optically excited, we call it the primary $!



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probe, and is quenched upon collision with the secondary probe. Assuming that quenching occurs only and instantly when the probes are in contact, the measured quenching rate has been interpreted as the rate of loop formation and the associated techniques have been referred to as collision-induced (CQ) methods. However, loop rates provided by one method were compared to rates by any of the other methods merely in passing, and interpreting discrepancies as weaknesses of the other rather than the own method.22,28,30-31 Putting some of this early enthusiasm under scrutiny, we propose that none of these and neither the newly reported methods herein can provide pure dynamic chain properties, i.e., properties independent of the probes and the employed specific method. Three CQ methods lent themselves to detailed analysis because all of them have already been applied to peptide chains composed of a varying number of Gly–Ser (GS) units.19-20,22,28 The GS repeat chain was originally chosen to guarantee water solubility in the presence of large hydrophobic probes and has, by chance, evolved into a solid basis for this method comparison.17 For chain lengths from 0 (direct conjugation of the amino acid probes) to 10 GS units several data sets are already available from previous photophysical studies (Figure 1) involving collisioninduced triplet–triplet energy transfer (TTET) from xanthone to naphtylalanine (NAla),22 photoinduced electron transfer upon contact (PET) from the oxazine derivative MR121 to Tryptophan (Trp),20,28 and collision-induced fluorescence quenching (CIFQ) of Dbo by Trp.19,23 Dbo is an asparagine residue modified by 2,3-diazabicyclo[2.2.2]octene (DBO), whose unusually long fluorescence lifetime is the basis of CIFQ.32-34 With the idea to establish upper limits, beyond which, as we initially thought, rate values could not be realistic, we have applied a complementary, fluorescence-based method, namely shortdistance Förster resonance energy transfer (sdFRET),35-37 and compare herein the sdFRET quenching rates with the loop rates derived from TTET, PET, and CIFQ. Generally, FRET rates %!


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are expected to exceed loop rates in identical chains: A single energy-transfer event can already occur at a distance but becomes almost inevitable when probes can approach each other within the natural fluorescence lifetime of the donor, a phenomenon known as FRET diffusion enhancement.11,15,38 We benefited from the fact that Dbo combined with either Trp, FTrp or NAla enables not only CIFQ but also sdFRET, through which distances around 10 Å have recently become accessible to FRET detection. For the purpose of this comparison of methods and probe pairs (Figure 1), we refer to these four Dbo-based methods as Trp CIFQ, NAla CIFQ, Trp sdFRET and NAla sdFRET. The two fundamental properties of the amino acid Dbo’s fluorophore, DBO, are not found in any other probe — the long fluorescence lifetime of DBO,39 which enables CIFQ, and its small oscillator strength (extinction coefficient), which enables sdFRET.40 The comparison between CQ and FRET methods yielded surprises and novel insights. For instance, the apparent loop rates from NAla sdFRET and TTET, a FRET and a CQ method, almost coincided throughout the series of the tested peptides of varying length. Not for the first time, a more comprehensive view emerged from the combined use of FRET and CQ methods on questions on the unfolded state and the folding mechanism.29,37 Just recently, a combined FRET and CQ single-molecule study led to an improved understanding of intrachain friction in unfolded-state reconfiguration dynamics,29 despite the fact that the overall folding kinetics, the transition-state crossing into the native state, can occur in the absence of internal friction.41-43

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MATERIALS and METHODS All commercial materials were purchased from Fluka or Aldrich. The Dbo-labeled peptides were commercially synthesized in >95% purity (Biosyntan, Berlin). Details on the synthesis of Dbo and its suitability in solid-phase peptide synthesis have already been reported. The C-terminal Dbo was amidated to avoid C-terminal charge effects.37 Absorption spectra were recorded on a Cary 4000 UV-Vis spectrophotometer (Varian) and steady-state fluorescence spectra on a Cary Eclipse fluorometer (Varian). Time-resolved fluorescence decays were recorded on a time-correlated single-photon-counting instrument (FLS920, Edinburgh Instruments) by using pulsed diode lasers (Picoquant) for excitation at 280 nm in the FRET measurements, and for excitation at 373 nm for collision-induced quenching measurements. Peptide concentrations were determined by using extinction coefficients of 5.7 x 103 M!1cm–1 (FTrp), 5.4 x 103 M–1cm–1 (Trp), and 5.5 x 103 M!1cm–1 (NAla) at 280 nm; they were adjusted to about 10 µM in aerated solutions, 25°C, pH 5.0. For NAla-(Gly-Ser)n-Dbo peptides, three independent fluorescence lifetime decay traces were collected. Upon excitation of NAla (!ex = 280 nm), the emission decay of both the donor (NAla,

!em = 335 nm) and the acceptor (Dbo, !em = 450 nm) were monitored. In an independent set of experiments, the fluorescence decay of the acceptor (Dbo) was also measured after direct excitation (!ex = 373 nm, !em = 450 nm). The donor decay in the absence of FRET was obtained from the donor-only peptides, NAla–(Gly-Ser)6 and 5–F–Trp–(Gly–Ser)6. The emission decay of Dbo in the absence of collisional quenching was obtained from (Gly–Ser)6–Dbo.

RESULTS Methods, probes, and time scales. The arrows in Figure 1 point from the primary excited probe to the secondary probe, both appended to the (GS)n chain. The size of the primary probes (!



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increases when going from the spherical bicycle, DBO, to the tricycle, xanthone, and to the pentacycle, MR121. The secondary probes, to which the arrow heads are pointing, are all bicycles of comparable size. Pairs of probes can be utilized for different photophysical methods such as MR121/Trp for PET, Xanthone/NAla for TTET, and Dbo/Trp, Dbo/FTrp, as well as Dbo/NAla for CIFQ and sdFRET. To switch from CIFQ to sdFRET measurements merely requires changing the wavelength of the laser excitation pulse from 373 nm, at which DBO is selectively excited, to 280 nm, where the secondary probes show maximal (Trp, FTrp) or strong (NAla) absorption and DBO virtually none.19,35 This methodological reciprocity is indicated by double arrows in Figure 1. Fluorescence decays of the CIFQ/sdFRET probes in single-labeled peptides (Fig. 2, black traces) occur with lifetimes ranging from 1.3 ns (Trp) or 2.0 ns (FTrp, Fig. 2a) to 33 ns (NAla, Fig. 2b) and further to 229 ns (Dbo, Fig. 2c, d). In the presence of the secondary probe, the decays are accelerated (red traces) by FRET (Fig. 2a, b) or by CIFQ (Fig. 2c, d). Each calculation of a quenching rate requires the traces from the single-labeled and the double-labeled chain. ! !

)!


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Irel /1000 counts

4 3 FTrp(GS)6 FTrp(GS)6Dbo

2

NAla(GS)6 NAla(GS)6Dbo

1 a 0

5

b 0

15

100

200

4

Irel /1000 counts

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3 (GS)6Dbo FTrp(GS)6Dbo

2

(GS)6Dbo NAla(GS)6Dbo

1 c 0

500 Time /ns

d 1000

0

500 Time /ns

1000

Figure 2. Time courses of probe fluorescence in single-labeled and double-labeled (GS)6 peptides (black and red traces). (a) FTrp sdFRET (excitation/emission: 280 nm/350 nm): FTrp(GS)6 (" = 2.0 ns), FTrp(GS)6Dbo (1.4 ns) (b) NAla sdFRET (280 nm/350 nm): NAla(GS)6 (33.3 ns), NAla(GS)6Dbo (10.3 ns) (c) FTrp CIFQ (373 nm/420 nm): (GS)6Dbo (229 ns), FTrp(GS)6Dbo (46 ns), (d) NAla CIFQ (373 nm/420 nm): (GS)6Dbo (229 ns), NAla(GS)6Dbo (148 ns). The accuracy of time-constant determinations is better than 5%. Analysis. The basic equations of FRET and CQ rest on the decay rate constant or quenching rate, kQ. In the presence of a secondary probe (S) as quencher, the primary excited probe (P) decays with a rate kPS that is related to the decay rate kP in absence of S and the quenching rate kQ by eq 1a. For ease of comparison, we also use the respective reciprocal values, "PS = kPS–1, "P = kP–1, and

"Q = kQ–1, which are internally related by eq 1b. These equations do not distinguish between FRET and CQ but mark the beginning of the analysis in both families of methods:

kQ = kPS ! kP

(1a) *!




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Table 1. Quenching time constants, "Q/ns in double-labeled GS peptides (L1(GS)nL2) from CQ and sdFRET methods by using the optical labels L1 and L2. Trp CIFQ

NAla CIFQ

PET

Trp sdFRET

NAla sdFRET

"#! "$! n=0

Trpa Dbo 24.4

NAlab Dbo 140.2

Thioxanthonec NAla -

Xanthoned NAla -

MR121e Trp -

Trpf Dbo 0.6

NAlab Dbo 4.2

n=1

14.7

212.8

20.0

6.5

-

1.0

4.5

n=2

20.4

277.8

40.0

7.9

4.7

1.8

7.7

n=4

32.3

370.4

90.9

12.0

6.0

3.4

14.9

n=6

50.0

434.8

-

17.9

8.2

4.7

16.9

n = 10

90.9

678.6

-

33.3

15.6

11.1

50.0

L1(GS)nL2

a

TTET

Ref.19. b This work. c Ref.17. d Ref.22. e Ref.28. f Ref.35.

! ! Previous studies, including our own, have focused much on the absolute values and on arguments why which values are better than others, frequently transpiring that the faster ones are the better ones, see Introduction. The present study is not aimed on deciding which method or probe/quencher pair is best, but rather on why the quenching rates differ from method to method and that they, in fact, are expected to differ as the probes are changed. Towards this end, it proved to be more valuable to first carefully inspect the ratio of rate constants between any two methods applied to the same chain in an effort to find underlying systematic variations. The results are shown in Table 2, which compares the quenching rate ratios between two different methods I and II for peptide chains of different lengths. Remarkably, when we inspect Table 2, we notice that the ratios do not converge to unity as the chain becomes longer. It would be natural to assume that some of the probes’ impact on chain dynamics would decrease with increasing chain length, and that, therefore, the rate difference of any two CQ methods would decrease and would ideally converge when the two probe pairs are of comparable size. In fact, this was the "#!


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expressed belief in the original articles that introduced the respective methods, ourselves included,19-20,22,28 and we will follow up on the observation that, with the exception of the peptide Trp!Dbo, i.e., the (GS)0 chain, the rate constant ratios are virtually constant. We compiled Table 2 to arrive at average values, to which we will repeatedly refer.

Table 2. Quenching rate ratios, kQ(method I)/kQ(method II), among CQ and sdFRET methods applied to (GS)n chains. Entry

Method I : Method II

(GS)0

(GS)1

(GS)2 (GS)4 (GS)6

1 2 3 4 5

Trp sdFRET : NAla sdFRET Trp sdFRET : Trp CIFQ PET : TTET TTET : Trp CIFQ TTET : NAla sdFRET

(7.0) (40.7) -

4.5 14.7 2.3 1.4

4.3 11.3 1.7 2.6 1.0

a

4.4 9.5 2.0 2.7 0.8

3.6 10.6 2.2 2.8 1.1

(GS)10

Avg.a

4.5 8.2 2.1 2.5 0.7

4.3 10.9 2.0 2.6 1.0

Average value, with the value for direct probe-quencher attachment (n = 0) excluded.

The ratio between the two sdFRET methods stays robustly at an average of 4.3 (entry 1). The shortest tested peptides, Trp!Dbo and NAla!Dbo (Table 2) show an aberrant ratio of 7.0, which is taken as an outlier.47 Rates from Trp sdFRET are about an order of magnitude larger than those from Trp CIFQ (Fig. 2a,b, and Table 2, entry 2). This is in line with common sense: Quenching that can already occur when the ends are still apart leads to a larger apparent loop rate than quenching that occurs exclusively when chain ends meet. Note that the value for the (GS)0 chain (Table 2, entry 2), ratio 40.7, lies out. The ratio of the Trp sdFRET over the Trp CIFQ rate is large because the Trp CIFQ quenching rate in the Trp-Dbo peptide is very small (1/24 ns–1). 48 In this short peptide, which is clearly a special case due to the direct probe conjugation, collisions between Trp and the DBO chromophore are sterically constrained.19 PET rates are on average two-fold higher than TTET rates (Table 2, entry 3). This ratio is again independent of the chain "$!




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The distances between primary and secondary probe in these flexible peptides can be considered to be random in the confluence sphere: When distances become short in comparison to the average distance, the Gaussian and the random distribution begin to coincide, as the latter is simply the first term in the Taylor expansion of the former. Thus, according to the model, the measured ratio of quenching rates from the two sdFRET methods will equal the ratio of their confluence volumes (eq 10). kQW C W = kQN C N

(10)

The simple condition, namely that kC, the quenching rate for probes within the contact volume, is the same for any two methods, turns indeed out to be sufficient to determine the ratio of the confluence volume radii of Trp sdFRET and NAla sdFRET. For that, we realize that the quenching rates within these volumes can only be identical, when the local FRET rates at a specific distance, r, kTW (r) and kTN (r) , are identical at the respective radii of the confluence spheres, rW, and rN (eq 11). Although this conclusion might appear to be trivial, we treat it in additional detail in the Supporting Information.

kTW ( r W ) = kTN ( r N )

(11)

6

Inserting Förster’s equation, kT (r) = kD ( R0 / r ) (eq 2), into both sides of the confluence–radius condition (eq 11), we obtain eq 12. This equation can be solved for the ratio of confluence radii rW / rN (eq 13).

(

kDW R0W / r W

)

6

(

= kDN R0N / r N

)

6

(12)

1

r W R0W " kDW % 6 = ! r N R0N $# kDN '&

(13)

#+!


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When we now use C = 4/3"r3 (spherical approximation), we finally obtain the ratio of the confluence volumes. 3

C W ! rW $ ! R0W $ = = C N #" rN &% #" R0N &%

3

! kDW $ #" k N &% D

(14)

The Förster radii of the Trp/Dbo and NAla/Dbo pair are close; R0W = 9.2 Å and R0N = 9.8 Å. The main photophysical difference between Trp and NAla sdFRET is the larger intrinsic decay rate, !1

i.e., the shorter natural lifetime of Trp, where ( kDW ) = ! DW = 1.3 ns, compared to NAla, where N !1 D

(k )

= " DN = 33.3 ns.15,35 With these values used in eq 14, the confluence volume ratio becomes

4.2. This ratio is almost identical to the experimentally observed ratio of about 4.3 (Table 2, entry 1). Thus, indeed, we found experimental corroboration for the model’s prediction that W N kFRET / kFRET ! C W / C N (eq 10) and, by that, for the validity of the underlying assumptions.

When eq 14 is inserted back into eq 10, eq 15 is obtained. In this text, we address it as the confluence sphere approximation (CSA) of diffusion-enhanced FRET. W ! R0W $ kFRET =# N& N kFRET " R0 %

3

! kDW $ #" k N &% D

(15)

6

In the absence of diffusion, Förster’s law, kT (r) = kD ( R0 / r ) would imply that the observed FRET rate increases with kD, the inverse natural fluorescence lifetime of the donor, and not with the square root of kD, as in eq 15. In the presence of strong diffusion, the expression 6

kFRET = kD ! ( R0 / r ) " p(r)dr (compare eq 7) is valid, and states again that the FRET rate grows in r

direct proportion to kD. However, the experimental results and the suggested model imply a much weaker, square root, dependence of the FRET rate on the inverse donor lifetime. It is therefore important to estimate the value range of diffusion coefficients, at which the CSA applies. #"!




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N = qN / ! DN = 0.13 / (33.3 ns) = 256 !1 ns !1 ). The radiative Förster radii were RFW = 14.3 Å and krad

1/6

and RFN = 13.8 Å , as obtained from RF = ( R06 / q ) . The result of the HSE simulations is summarized in Figure 6. The ratio of the FRET rate constants is close to 16 in the near absence of diffusion, with diffusion coefficients between 10–3 and 10–2 Å2/ns, and also in the presence of vigorous diffusion, with coefficients between 103 and 105 Å2/ns, as expected from eq 7. However, with coefficients between 1-100 Å2/ns, we find a minimum with values close or virtually identical to the value of 4.2 predicted by the CSA (eq 15), and close to the experimentally observed ratio of 4.3 (see above). The experimental rate ratios are therefore a manifestation of the square-root dependence of the FRET rates within the CSA.

Ratio of FRET rates

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


16

16

12

12

8

8

4 0 10–3

4

CSA 10–1

101

103

105

0 100

D /(Å2/ns)

CSA 101

102

D /(Å2/ns)

Figure 6. HSE simulations as described in ref.15 were used to project FRET rates for Trp sdFRET (!!"#"18.6 ns, RF = 14.3 Å) and NAla sdFRET (!!"#"256 ns, RF = 13.8 Å) at diffusion coefficients ranging from 103 to 105 Å2/ns. Between 1 and 100 Å2/ns (left), the rate ratio approaches the CSA prediction (dashed line). The minimal value is 4.3 at a diffusion coefficient of 8.3 Å2/ns. The equilibrium probability density distribution, p(r), of donor–acceptor distances, r, was set to p(r) = "r2cexp(–a(r–b)2) with a = 0.0123 Å–1, b = 10 Å, and c was calculated from

#$!



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the normalization condition, #p(r)dr = 1. Note that the individual FRET rates (not their ratio, which is shown here) always increase with diffusion in a sigmoidal fashion (not shown).

To estimate whether the end-to-end diffusion coefficients in the investigated peptides fall into this range, we performed a global analysis based on the HSE. The experimental donor and acceptor fluorescence kinetics from Nala!(GS)n!Dbo peptides were simultaneously analyzed. The diffusion coefficients increased with chain length from 1 to 15 Å2/ns when going from the (GS)0 peptide, NAla!Dbo, to the (GS)4 chain as further detailed in the Supporting Information. In summary, theory (the confluence sphere model), simulations (Fig. 6), and experiments (Table 2, entry 1) corroborate each other.

DISCUSSION In the Introduction, we emphasized the importance of loop and loop-node formation. We should also mention that a loop in the native structure of a protein typically contains about 20-30 residues.1,3,54-55 In consequence, it is critically important to apply the handful of methods that are tailored to the investigation of loop formation to experimental chains composed of up to 20 amino acid residues, and to contrast the results obtained by the different approaches (Tables 1 and 2). As a basis for interpretation, we propose the confluence sphere model. It states that the loop rate is proportional to the confluence product, the volume of the confluence sphere times the concentration of secondary probes within this sphere (Eq. (6)). The confluence sphere is defined to be sufficiently large such that any quenching outside of it has no measurable impact. At the same time it is sufficiently small such that a random distance distribution within the sphere can be assumed as well as that the number of chains with probes outside the sphere is almost equal #%!


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among the methods. The most important condition, however, is that quenching within the sphere follows a monoexponential time law, which is equivalent to a probability density distance distribution of chains with optically excited probe that does not change with time (Supporting Information). Not only in our newly included measurements but also in the reported TTET and PET measurements, the measured nanosecond kinetics were monoexponential, and the conclusion of a stable distribution of chains with excited primary probe was reached by all authors.15,17,22,28 Only the Trp sdFRET rates had to be calculated from amplitude-weighted lifetimes because of the well known lifetime heterogeneity of the tryptophan residue, which is why 5-fluoro-L-tryptophan (Fig. 1) is an analytically favorable alternative to Trp.15,56-57 The concept of the confluence sphere has almost naturally arisen from the analysis. The confluence volume defined herein differs from the so-called sphere of effective quenching/action (used in the analysis of static quenching)44 in that the quenching does not need to be instantaneous. The confluence sphere model could be compared to the fluorescence blob model (FBM), which indeed inspired us.58 The FBM is, however, a far more intricate concept, which has found a wide variety of applications in the analysis of polymer dynamics based on pyrene excimer formation. A blob is the volume that an excited pyrene probe can explore during its fluorescence lifetime.59-63 The significance of the confluence sphere model is that it leads naturally to the CSA, the confluence sphere approximation (eq 15, eq 17). What also distinguishes both models is the possibility to add an external quencher to reduce the quantum yield and lifetime of the pyrene probe and the size of the blob volume it can explore.62 The CSA, however, is independent of the quantum yield (eq 17). It is certainly also a novelty that such a simple model can be used to explain FRET and CQ data simultaneously. It is, however, not only fortunate that the confluence sphere model can be applied to the peptides of our study. In FRET, a global analysis based on the HSE could yield both the distance #&!




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In this study we combined published data as well as new experimental data from CIFQ and sdFRET.19,22,28,35 As can be seen from Table 1 and Figure 7, an expanded portion of Figure 3, we are now in the fortunate position to have a portfolio of methods in our hand which afford both, the fastest (Trp sdFRET) and the slowest (NAla CIFQ) available kinetics of loop formation in GS repeat peptides. Our range of data, which bracket those of previous studies,19,22,28,35 suggest that all photophysical methods report on the same event but through different readouts. Our combined results demonstrate that all photophysical techniques report reliably on relative rates of loop formation in peptides and that the individual absolute data sets differ mainly by a constant factor. A unified kinetic view therefore emerges. As can be seen, all original data sets (Fig. 7a) can be brought into accord by applying confluence sphere-specific correction factors (Fig. 7b), normalized to the TTET data set. We have entered arrows (i-iv) in Fig. 7a, corresponding to the method-specific offsets. This harmonic behavior resolves controversies (see Introduction), on which method or probe quencher pair is “the best”, and reduces discussions to why the confluence products differ. The exception is the Dbo/NAla CIFQ data set; it is by far the slowest, and the peptide length dependence differs in slope and curvature from the other ones, suggesting that a contrasting quenching mechanism or a change in quenching mechanism in dependence on chain length is at work. We also need to accept minor variations at short peptide chain length (Fig. 7b, n < 4), at which effects related to steric constraints and probe/chain size ratio are largest (see also ref.19) . At large chain length all methods afford overlapping results, which are also close to or in conformity with the Gaussian-chain limiting slope of –3/2.19,64. The experimental factor that distinguishes Trp sdFRET and NAla sdFRET loop rate constants is 4.3 (Figure 7, arrow i; Table 2, entry 1) and the CSA (eqs 15 and 17) predicts it correctly (4.2). Within a range of diffusion coefficients (1-100 Å2/ns ), this prediction is also supported by #(!



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simulations based on the HSE partial differential equation (Fig. 6), a correspondence, which, in turn, corroborates the validity of the HSE. This range is indeed the relevant range for peptide chains studied in aqueous solution, not only according to the diffusion coefficients we have obtained in our own global analysis (Supporting Information) but also according to those obtained by other groups. Haas and coworkers found a diffusion coefficient of 14.2 (10.7-15.2) Å2/ns for the (GS)7 peptide Dansyl-Ala-(Gly-Ser)7- Ala-NAla-Ser-Arg-Gly-NH2,65 and Kiefhaber 2

16

and coworkers found an end-to-end diffusion coefficient of about 50 Å /ns for a (GS)16 peptide.

This range guarantees that a stationary distribution is quickly attained after excitation. When this stationary distribution differs little from the equilibrium distribution in short-distance FRET measurements, it will differ even less in CQ measurements, where quenching occurs at even shorter distances. Of course, there is always a small very fast kinetic decay expected instantly after excitation from probes which are already in contact or extremely close. This kinetics is, however, invisible to time-resolved fluorescence measurements with nanosecond resolution but it has been detected in TTET measurements with picosecond resolution.66 In Trp sdFRET and Trp CIFQ ( Figure 7, arrow ii), the same pair of probes is used, Trp and Dbo, and any hydrophobic or hydrophilic interactions between the probes are identical in both methods. Nevertheless, the former method affords faster absolute loop rates. The associated larger confluence volume is due to the fact that FRET quenching is, in contrast to CIFQ, also effective at larger probe-probe distances. The loop rates from NAla sdFRET and TTET are, on the other hand, virtually identical (tiny arrow iii), although the latter involves shorter-distance quenching. As discussed below, the concentration of probes in the TTET confluence sphere is enhanced by hydrophobic probe-probe interactions, which increases the product of concentration and confluence volume to the same value as for the NAla sdFRET method (compare eq 9).

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Finally, the factor that separates PET from TTET is 2 (arrow iv). What does the CSA suggest in regard to an interpretation of the factors that distinguish PET and TTET? While it was obvious that we had to focus on the volume ratio of the confluence spheres when we compared the two sdFRET methods, the corresponding model (eqs 6 and 9) allows us to now switch our focus to the concentration of secondary probes within the spheres when we compare PET and TTET. Both probes, the oxazine probe MR121 used in PET and xanthone used in TTET, are strongly hydrophobic as also acknowledged in ref.28 and ref.66, and they can interact with Trp. Concluding from ref.28, in the (GS)4 peptide (N = 4), the fraction of chains with complexed ends is about 90%, in the (GS)10 peptide still about 70%. According to molecular dynamic simulations,

67

the

complex is basically non-fluorescent (static quenching) at distances below 5.5 Å However, the mere existence of the complex influences the equilibrium distance distribution. While the peptide without probes might well be described by a single Gaussian distance distribution, the peptide with probes will display a second distribution, which extends to about 8 Å. The enhanced concentration of the secondary probes leads, according to the CSA, to an increase of the loop rate. The situation in TTET is similar to that in PET but not as extreme. In the peptide Xan-Ser6NAla, the fraction of chains with probes in contact is about 15%, again due to the hydrophobic nature of the probes, as the authors emphasize.66,68 Thus, also in the GS peptides studied here, it is reasonable to assume an elevated concentration of hydrophobic secondary probes in the confluence sphere. The difference in probe-probe interactions of the systems in PET and TTET can readily account for the factor of 2 difference in quenching rates between PET and TTET. It can also explain the ratio of about 2.6 between rates from TTET and Trp CIFQ as the Dbo/Trp pair is least prone to hydrophobic interactions, because the fluorophore DBO is hydrophilic.36

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Complex formation between hydrophobic probes can be seen as a model for the loop node. Thus, loop rates will also depend and inform on changes of the energy landscape caused by the loop-node constituting residues. We consider loop-node stability and its measurement to be vital in making progress with modeling and understanding protein folding. Loop rates depend as much on internal chain diffusion as on the equilibrium distance distributions and are highly sensitive to interactions at short distances as we previously demonstrated in a simultaneous Trp CIFQ/sdFRET study on short peptides.37 This does not diminish the merits of the methods, which have been convincingly applied in the past. Importantly, the photophysical underpinnings of PET, TTET, sdFRET, and CIFQ have been studied in detail in experiments and simulations,40,67-70 and in the case of sdFRET also by quantum-chemical calculations.40

CONCLUSIONS The relevance of the results to mechanistic protein folding research is that measured loop rates are not absolute values but depend on the probes and photophysics in play. Moreover, loop rates are not a direct measure of chain dynamics. They depend not only on internal diffusion but also on the distance equilibrium distribution. While the latter has been recognized all along, it was less clear that loop rates can be highly sensitive to energy landscape perturbations at short distances. This is what the confluence sphere model predicts. It can be applied, whenever the measured decay kinetics are monoexponential and point to a time-independent probability distance distribution of probes during the decay. The important consequence is that loop rates in peptide and protein folding will depend on the stability of the formed loop node as well as on interactions between loop node residues at short distances, which is an area of research that should now be tackled.

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ACKNOWLEDGEMENTS We would like to thank the Deutsche Forschungsgemeinschaft (DFG, NA 686/9) for financial support. We are thankful for fruitful and continuing discussions with and instrumental assistance of Indrajit Ghosh, Eitan Lerner, Eldad Ben Ishai, Tomer Orevi, and Asaf Grupi.

Supporting Information Available Symbols and Abbreviations; traditional FRET analysis of the effective distance; the confluence radius condition in sdFRET; conditions for monoexponential kinetics in FRET- and CQ-based measurements; HSE simulations of the FRET diffusion enhancement; intrachain diffusion coefficients as estimated by a global analysis of the donor and acceptor emission decays of NAla and Dbo in NAla–(GS)n-Dbo chains; )*+,-.*/.!0+!1203.41203.!)*5.26/5)0*7!)*!89:!6*;!::9:. This information is available free of charge via the Internet at http://pubs.acs.org.

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Method-Unifying View of Loop-Formation Kinetics ... - ACS Publications

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