Submicrosecond real-time fluorescence sampling: application to protein folding

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Tuesday Feb 15 09:55 AM StyleTag -- Journal: JPB (J. Photochem. Photobiol. B: Biol.) Article: 7915

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J. Photochem. Photobiol. B: Biol. 54 (2000) 1–15

Submicrosecond real-time fluorescence sampling:application to protein folding

John Ervin, Jobiah Sabelko, Martin Gruebele *School of Chemical Sciences and Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, IL 61801, USA

Received 5 July 1999; accepted 7 January 2000

Abstract

Time-resolved fluorescence detection has become a central tool in the study of protein folding. This article briefly reviews modernfluorescence techniques and then focuses on recent improvements made possible by array photomultipliers, computer-controlled data gating,and long-memory multi-channel digitizers. It is now possible to detect fluorescence wavelength profiles and/or fluorescence decay transientsvery cost effectively with sub-microsecond kinetic time resolution out to long times. Folding kinetics can be analyzed by singular valuedecomposition (SVD) or x-analysis. The latter provides an objective method for detecting nonexponential kinetics in two-state systems.q2000 Elsevier Science S.A. All rights reserved.

Keywords: Tryptophan; Nonexponential kinetics; Ubiquitin; Phosphoglycerate kinase; Apomyoglobin

1. Introduction

Unimolecular and bimolecular reactions are generally dis-tinguished by their time scales. Unimolecular reactions ofsmall organic molecules involve dissociations and transition-state crossings on a time scale of femtoseconds to picosec-onds. Bimolecular reactions can be diffusion limited, andtheir kinetic study in the bulk usually involves time scalesslower than nanoseconds, even though the individual colli-sion and reaction events are still ultrafast. An interestingmiddle ground is occupied by the self-assembly and foldingof macromolecules, such as man-made homopolymers orpro-teins. These molecules are sufficiently large that backbonediffusion and self-collision must not just be jointly accountedfor, but are intrinsic to the very folding process [1,2]. Inaddition, the transition states of such systems may be broadalong any reasonable reaction coordinate [3], may have ahigh degeneracy, or may be entirely absent during folding[4–6]. Caution is therefore required when applying the no-recrossing rule, Kramer’s theory, or similar transition-stateconcepts to the folding of macromolecules.

The complexity of the folding problem has attracted sus-tained theoretical and experimental interest for several dec-ades [7–10]. The demonstration of Anfinsen that water-soluble proteins in dilute solution can be unfolded andrefolded reversibly [11] has opened the subject to physical

* Corresponding author.

experimental studies. Although many spectroscopic tools,from circular dichroism to NMR, have been successfullyapplied to the protein-folding problem, fluorescence spec-troscopy remains one of the earliest and most successful fold-ing probes.

Following the realization that the indole group of trypto-phan can be quenched by electron transfer to other residues[12,13], or by Forster transfer to chromophores such as heme¨[14,15], interest in fluorescence as a probe of protein struc-ture and structural fluctuations grew rapidly [16,17]. Extrin-sic probes such as cysteine-conjugated dyes were later addedto the repertoire. Both intrinsic and extrinsic probes havebeenused to perform distance measurements in proteins, often byintroducing quenchers via site-directed mutagenesis [18–20]. In addition, tryptophan fluorescence is highly solventsensitive, and can exhibit )20 nm shifts upon desolvationinto a protein hydrophobic core [21]. Tryptophan residuesare thus ideal tools to probe local protein structure and solventenvironment.

Protein-folding dynamics are a natural extension of time-resolved fluorescence measurements, which have been madeon proteins since the earliest days [22]. Initial studies focusedon the decays themselves as probes of conformational fluc-tuations or differences under steady-state conditions [23].This was soon supplemented by dynamic relaxation studiesin which protein populations are perturbed from equilibriumand undergo large-scale concerted structural changes. One

J. Ervin et al. / J. Photochem. Photobiol. B: Biol. 54 (2000) 1–152


can distinguish several approaches to initiating and probingrelaxation kinetics by fluorescence. In pump–probe studies,folding is initiated repetitively and probed with different timedelays at each initiation. The pump–probe technique offersthe highest time resolution (down to a few femtoseconds),but usually requires flowing samples due to the fragility ofproteins, which cannot be optically pumped repetitively. Incontinuous flow studies, which now push the 50 ms limit,folding is initiated by mixing protein and renaturant solutionsinto a continuous liquid jet [24–26]. The time axis is mappedinto a distance axis along the jet, and this distance axis canbe monitored by an array detector. In true real-time experi-ments, folding is initiated only once and then followed intime continuously or by fast repetitive sampling. Stopped-flow is a widely used technique that allows real-time kineticmeasurements down to milliseconds and resolves fluores-cence decays down to -0.1 ns. More recently temperaturejumps (T-jumps), originally developed in the 1950s withresistive heating, and in the 1970s with laser heating [27],have been applied to protein-folding dynamics [28–30].Laser T-jumps reduce the dead time into the nanosecond oreven picosecond regime and maintain the main advantage ofreal-time detection: small static sample volumes. Fast tech-niques such as continuous flow, electron transfer,photochem-ical initiation or laser T-jump are necessary to reveal theearliest events during protein folding.

The challenge of investigating the earliest stages of thefolding reaction by fluorescence is therefore to achieve rapidinitiation, and then rapid probing of the kinetics, by obtaininghighly resolved lifetime and wavelength information simul-taneously with one apparatus. After reviewing present fast-fluorescence techniques, we discuss our newest develop-ments, which provide multi-channel fluorescence decay and/or wavelength information with -20 ns dead time and sub-microsecond resolution of the kinetics, probing even the fas-test-folding proteins. We begin with the T-jump technique,which provides the fast kinetic initiation, then follow up withthe more technical details of rapid fluorescence decay andspectral profile capture used to probe the kinetics. We con-clude with a review and discussion of appropriate data-anal-ysis tools. Tryptophan fluorescence decays are complexmultiexponential functions and require careful analysis [31–34]. Several alternatives have been developed to avoid theneed for delving into these complexities. Quenching studieswith tryptophans or extrinsic donors can provide distanceinformation while avoiding detailed knowledge of the tem-poral decay profiles. Techniques such as singular valuedecomposition or x-value analysis can extract independentcomponents of the kinetics, without detailed knowledge ofthe decays. In particular, x-value analysis uses fluorescencedecays without detailed interpretation of their shape to testfor dynamical two-state versus multistate folding when ther-modynamic two-state folding has been verified. This tech-nique will be discussed in detail.

2. Fluorescence-detected folding experiments

2.1. Information obtainable from protein fluorescence

Fluorescence allows a large amount of information to bederived from fluorophores present in the molecule of interest.Tryptophan residues in proteins (and to a lesser extent tyro-sine and phenylalanine) will readily fluoresce when excitedat wavelengths near 280–300 nm; tryptophan is singled outat wavelengths greater than 295 nm [35]. The properties ofthis fluorescence strongly depend on the local environmentof the fluorophore [17]. For example, certain residues (e.g.,cysteine, glutamate, methionine) quench the tryptophanexcited state through double electron transfer when placedwithin a few (-10) angstroms. This decreases the fluores-cence intensity and shortens the temporal profile [12,34].Additionally, the Stokes shift of the fluorescence spectrumgives an indication of the polarity of the protein environment.Protein unfolding is accompanied by a large red shift in thefluorescence spectrum of buried tryptophan residues. Twoexamples presented here are phosphoglycerate kinase, thefluorescence maximum of which shifts from 336 to 353 nmupon cold denaturation, and ubiquitin, for which the fluores-cence maximum shifts by more than 10 nm. Tryptophans canalso probe their less immediate environment by Forsterënergy transfer, for example to heme [36], nitrosated tyro-sine [37], or cysteine-bound organic dyes [19]. The dipole–dipole interaction provides an ry6 distance dependence,allowing distance measurements to be made in the 10–30 Arange given the 0.05–0.15 quantum yield of not specificallyquenched tryptophan residues [14]. Fluorescence depolari-zation is another powerful tool because rotational diffusiontime scales of proteins in vitro are on the order of nanosec-onds, commensurate with the 1–5 ns lifetime typically foundfor tryptophan residues in proteins.

Generally proteins contain at most a few tryptophan resi-dues. Those with none or too many can be manipulated bysite-directed mutagenesis to contain only the desired number,usually a single one. Specific quenchers can also be intro-duced through site-directed mutagenesis or through covalentmodification of the protein, allowing the distance measure-ments outlined above to be made. Similar ideas can also beapplied with extrinsic probes such as cysteine-linked dyemolecules; the disadvantage is that the dyes could perturb thefolding process. The great advantage is that the distance rangecan be greatly expanded beyond the range accessible withtryptophan because dyes usually have quantum yields muchcloser to unity.

When coupled with laser-induced relaxation experiments,another advantage of fluorescence over transmission tech-niques such as circular dichroism (CD) or absorption spec-troscopy is its relatively isotropic nature (barringpolarizationeffects). Relaxation techniques such as the temperaturejumps discussed in Section 2.2 tend to perturb the refractiveindex of the sample and can cause micro-cavitation due tonucleation at solute aggregates. This adversely affects trans-

J. Ervin et al. / J. Photochem. Photobiol. B: Biol. 54 (2000) 1–15 3


Fig. 1. Real-time fluorescence detection schemes: top, time-correlated photon counting; bottom, direct sampling of fluorescence profiles. Photon countingachieves the better Dt9, while direct sampling achieves the better Dt. At short times, both techniques are limited by the initiation of the relaxation, here shownas a T-jump heating pulse.

mission experiments on a 1–10 ms time scale. Fluorescenceis less affected by scattering and other fluctuations becauseof the large collection area and resulting averaging.

2.2. Fluorescence probing of real-time relaxation kinetics

Relaxation techniques have been continuously improvedto study protein-folding reactions. When discussing foldingkinetics and fluorescence decays, it is important to distinguishbetween the kinetic time scale(s) t and the fluorescence timescale(s) t9. Generally, a very short sampling time Dt9 andinstrument-response time Dt9 are required to resolve fluores-cence decays, while the folding kinetics can be sampled atwider intervals Dt and with a slower instrument response Dt.t can range from nanoseconds to seconds, depending on theprotein and the types of folding processes involved. Forexample, diffusional contacts in peptides occur in microse-conds, or perhaps as fast as 50 ns [2,38]. Some proteins canfold downhill (entirely or from the transition state) as a resultof a few hundreds to a thousand such diffusional events,yielding times in the microsecond range. Hydrophobic corescan be formed in just a few microseconds. Extension of ahelix can be accomplished in a few hundred nanoseconds.

Recovery from a misfolded structure due to an incorrectlyisomerized prolyl residue can take many seconds. To see thefastest elementary folding motions of the protein backbone,kinetic sampling intervals Dtf50–100 ns are thereforerequired. On the other hand, the average fluorescence lifetimeof tryptophan is on the order t9s1–10 ns. The fluorescencedecay is a complex multiexponential function with compo-nents as short as 100 ps. If the temporal profile of the decaysis to be analyzed in detail, a fluorescence sampling rate andresponse Dt9 and Dt9 less than 100 ps are therefore necessary.Even if only overall lifetimes, shape, or the slower compo-nents are of interest, an instrument response Dt9-1 ns muststill be achieved.

State-of-the-art stopped-flow experiments, which use cor-related photon counting for fluorescence decay measure-ments, typically have instrument dead times and kineticsampling intervals Dt of a few milliseconds, and a lifetimeresolution below Dt9;50 ps (Fig. 1) [39,40]. The instru-ment dead time is set by two factors: the rapidity of the mixing(ms) and the need for acquiring enough photons by single-photon correlation to build a reliable fluorescence decay(typ-ically at least 10 000 photons for 1% shot noise). With a 20ns laser pulse repetition rate from a mode-locked laser, and



keeping in mind that reliable photon counting requires a largenumber of photon-free laser shots, this translates into at least0.5 ms to sample each fluorescence decay. The fluorescenceresolution Dt9 of such experiments is excellent, and in thebest case limited only by photomultiplier jitter, typically lessthan 50 ps with good photomultiplier tubes (PMTs).

A different approach with different limitations on deadtime, sample rate, and Dt9 resolution of the fluorescencedecays is offered by real-time acquisition of both fluorescenceand folding kinetics (Fig. 1). This is one of the twoapproaches that will be discussed in detail in the followingsubsections. In such an experiment, the power of the laser isset to the highest possible value that will not photodegradethe sample during the collection time. (A typical empiricalvalue we find is 10 mW at 295 nm in a 0.03 mm2 area for1 s in degassed tryptophan-containing protein solutions; atshorter wavelengths, photodegradation speeds up consider-ably.) Folding is initiated as rapidly as possible (e.g., byT-jump), and fluorescence transients are collected by asub-nanosecond-risetime photomultiplier directlydigitizedatthe highest possible rate. As will be seen below, dead timesand sample times Dt-20 ns, Dt9s0.25 ns with an instrumentresponse Dt9-1 ns are possible, making the fastest foldingevents accessible with reasonable fidelity of the fluorescencedecays.

When sufficient signal is available, the fluorescencedecaysobtained by real-time sampling can be dispersed in a mono-chromator. By using multichannel PMTs and fast digitizers,time- and wavelength-resolved fluorescence surfaces with awavelength resolution of a few nanometers, time resolutionDt9-1 ns, and kinetic sampling rate Dt-20 ns can beobtained to study kinetics from nanoseconds to seconds, pro-viding the maximum amount of simultaneous information.The drawback is that the combination of time and spectralresolution requires many fast digitization channels, repre-senting a large investment. In many situations, only the wave-length information is required, in which case the fluorescencetransients can be integrated and the necessary sampling rateis now dictated by the folding kinetics only. Sampling rateson the order of Dts50–200 ns are then adequate, and the t9information is replaced by a wavelength axis. This is thesecond real-time approach to be discussed in detail below.Both of these approaches can be combined as shown in Fig.2 so that time-resolved total fluorescence decays and wave-length-resolved fluorescence can be collected simultaneouslyin real time.

2.3. T-jump initiation

Before delving into the details of fast fluorescence detec-tion, it will be useful to discuss the mechanism whereby thefolding reaction is initiated. Resistive-heating temperaturejumps were originally developed by Eigen in the 1950s [41].This technique can achieve 10 ms time resolution at ionicstrengths compatible with proteins. Twenty years later, thiswas extended to the nanosecond and even picosecond time

scale by laser heating of the solvent, although laser heatingwas applied to protein folding only recently.

The equilibrium constant of proteins is highly temperaturedependent, making them ideal subjects for T-jump relaxation.Two general approaches can be distinguished: native proteinscan be heated above the melting point (typically 40–608C).In this process, the unfolding rate exceeds the folding rate,and an ‘unfolding’ reaction is observed. Proteins also have alower melting point, resulting from cold denaturation (typi-cally below 08C) [42,43]. T-jumps starting with unfoldedproteins and returning them to the native temperature rangetherefore have faster folding than unfolding rates and a‘refolding’ reaction is observed. For two-state folding reac-tions D°N, the actual observed rate is the sum of foldingand unfolding rates. (Of course, the kinetics of folding maybe highly temperature dependent, and so the un/refoldingrates deduced from unfolding or cold-denaturation refoldingexperiments may still differ.) For multi-step reactions, dif-ferent kinetic phases may be weighted very differently inunfolding or refolding experiments.

The experiments outlined below look at refolding fromcold-denatured proteins. By using high-power infrared laserpulses, large solvent T-jumps and hence large populationchanges may be obtained with -20 ns time resolution bydirect heating of the aqueous buffer. In order to achieve alarge cold-denatured protein population in standard biochem-ical buffers without undesirable additives, aqueous samplesare supercooled to temperatures as low as y208C. Samplescannot be flowed or mixed, and only by keeping nucleationsites to a minimum can reliable supercooling be achieved.Currently, quartz capillaries of 3 mm diameter and 300 mmpathlength are flame sealed on one side, creating a nearlydefect-free cell (Fig. 2). In solutions of methanol, D2O, orother more weakly absorbing solvents, cells up to 1 mmpathlength can be used. The capillary cells make temperatureslower than y158C routinely accessible in filtered anddegassed biological buffers. The low sample volume (-10ml) means that expensive mutant proteins need be used onlyin microgram quantities.

Our current T-jump setup uses up to 200 mJ, 1540 nm, 10ns pulses derived by Raman shifting a 800 mJ Q-switchedNd:YAG laser in CH4 to excite the OH stretching overtoneof the aqueous sample at a rate of up to 3=109 8C sy1. Jumpsof the order of 158C are routinely obtained: jumps in excessof 308C can be obtained if mild aberrations during the first10 ms of the transient can be tolerated. Due to the cell geom-etry, a 108C temperature increase relaxes exponentially witha time constant of about half a second, allowing data to becollected for )20 ms before the temperature drops by morethan 0.58. The recooling on one hand, and the width of the T-jump pulse on the other, set the experimental window to sixorders of magnitude in time between 20 ns and 20 ms. Severalother laser schemes will produce T-jumps by directly heatingwater. The output of a Nd:YAG laser has been used directlyfor fast temperature jumps of a few tenths of a degree [44].The direct output of an iodine laser at 1.32 mm may be used



Fig. 2. Experimental diagram for simultaneous integrated fluorescence lifetime and dispersed fluorescence spectra measurements. Two counter-propagatingpulses of 1.54 mm light (IR) heat a 1–2 mm diameter spot in the sample cell (SC). A UV beam focused to 200 mm diameter excites fluorescence within theheated area. A back reflection of the probe beam from the focusing lens is collected by an Si diode (PD) and used for intensity normalization. To the left thetemporal profile experiment is shown. Here the fluorescence is imaged with a 0.50 f/0.8 aspheric glass lens, which also removes any scattered probe light. Thesignal then passes through a bandpass filter onto a fast photomultiplier tube (PMT) with homebuilt conditioning and amplification. The signal is digitized at2–4 GS/s with 1 GHz bandwidth. The total measured instrument response function of the system is shown (IRF1). The fluorescence on the right is collectedwith a liquid light guide (LG), and passes through a two-lens system that images onto the slit of a monochromator. This disperses the fluorescence onto a PMTarray where each of the 16 available channels collects 3.7 nm of the fluorescence spectrum. Each of these 16 signals is then fed into a separate filter-digitizer,which averages over a 210 ns time interval with shown instrument response (IRF2).

to heat directly H2O/D2O mixtures by more than a degree[45]. A Nd:glass laser Raman shifted with liquid nitrogenproduces light at 1.41 mm where water absorbs strongly,leading to temperature jumps of several degrees [46].

The local relaxation rate of water is less than 50 ps, andeven faster vibrational relaxation rates have been measuredfor CH stretches and other high-frequency vibrational modesof organic molecules in solvents. Although the 1540 nm lightwill excite both the water and some protein OH, NH and CHovertones, all high-frequency modes equilibrate in less than50 ps. The heating time is thus limited by the pump laserpulse width.

As has been discussed in detail, care is needed to avoidcavitation and lensing artifacts with large T-jumps[47].Eventhe most carefully constructed and aligned optical heatingabout the density maximum of water (48C) will introducedensity gradients in the sample due to the fact that the laserbeam is not a perfect pillbox. The approximately Gaussiandistribution of laser energy across the width of the sample

also induces refractive-index perturbations across the heatedarea. Measurements of the change in the transmission of anincident probe beam are therefore susceptible to time-depend-ent lensing as this gradient relaxes. We minimize theseeffectsby probing only the central few percents of the area beingheated, by using counterpropagating heating pulses that resultin a very small longitudinal sample temperature gradient, andby using a nearly isotropic detection technique such as fluo-rescence spectroscopy.

2.4. Real-time fluorescence measurements: commonfeatures

Real-time measurement is required of the fluorescenceprobe in our T-jump experiments because supercooled solu-tions cannot be flowed or T-jumped at high repetition rates.Fig. 2 illustrates the experimental setup for the two types ofdata that can be simultaneously measured: the spectral pro-



files f(l) of the fluorescence at intervals Dt, and the fluores-cence decay profiles f(t9) at intervals Dt .

We use a mode-locked laser to provide a regularly spacedtrain of excitation pulses for both types of experiments. Fortotal fluorescence decay profiles measured in real time, thissource must satisfy two requirements: the pulses should beconsiderably shorter than the remaining instrument response,so as not to affect lifetime measurements; and the pulses inthe train should be spaced by at least three fluorescence life-times to avoid overlap between successive decays. For spec-tral profiles, the pulse width can be much broader becausesampling occurs only on the kinetic timescale )10 ns. Forboth experiments, a narrow spectral bandwidth (less than afew nanometers) is desirable, and a high power density isnecessary to allow collection of enough photons in a singleshot.

A commercial titanium sapphire laser producing 840–885nm pulses of f100 fs duration and 71.4 MHz repetition rateis ideally suited for these requirements. This laser is fre-quency tripled to between 280 and 295 nm with -2 nmbandwidth and )5 mW/nm power density. The pulse widthassures a ‘d-function’ contribution to the instrumentresponse. The 14 ns repetition period matches the time t9needed to acquire complete fluorescence decays, and doesnot compromise the -20 ns time resolution offered by theT-jump itself (see Section 2.5); it can also be adjusted tolonger periods by cavity dumping, should longer fluorescencedecays necessitate it. The high laser power allows the col-lected fluorescence to be divided into several simultaneouslyacquired spectral channels, each receiving enough photons togive reasonable signal to noise ratios with sub-microsecondtime resolution of the kinetics. Mode-locked double Arq

lasers have also been used in this wavelength range, althoughthey lack the advantage of tunability near 300 nm, useful fordistinguishing the contributions of tyrosine and tryptophanresidues to the total fluorescence. A CW laser would permitthe measurement of the dispersed fluorescence, but the shapeof the fluorescence decay could not be extracted.

2.5. Real-time fluorescence decays

The real-time fluorescence decay collection illustrated inFig. 2 is capable of sampling fluorescence decays in 0.25 nstime intervals with f1 GHz bandwidth, and follows foldingkinetics in 14 ns steps out to 20 ms. This is achieved asfollows. The fluorescence is collected at a right angle to thepump beam (Fig. 2), then passes through a f/0.8 asphericglass lens, which removes Rayleigh scattering. The fluores-cence then passes through a bandpass filter, which selects the300–400 nm region (essentially the integrated tryptophanfluorescence range). Finally, the light images onto a 650 psrisetime mini PMT (Hamamatsu R5600) using homebuiltvoltage division and amplification circuitry [47]. The outputis digitized every 0.25–0.5 ns with 1 GHz bandwidth(LeCroy9384L with CKTrig option or Tektronix TDS720A).

The overall instrument response function (measured usingRaman scattering of water and shown as IRF1 in Fig. 2) hasa full width at half maximum of 850 ps. Because of the 100fs width of the laser pulse, the excitation source itself makesa negligible contribution to the instrument response, whichis mainly due to the electron flight-time spread of the PMTand the input amplifier characteristics of the digitizing scope.The instrument response function varies very little with PMTcurrent and can therefore be accurately measured to decon-volve reproducibly the actual sample fluorescence response.The bandwidth is sufficient to reveal in detail the multiex-ponential character of tryptophan fluorescence decays downto about 700 ps. Unlike photon counting, it cannot accuratelyquantify the very fast (-700 ps) component that is some-times present.

As mentioned above, the sample temperature stays nearlyconstant for about 20 ms after the T-jump, a length of timethat presents two difficulties for sub-nanosecond resolvedfluorescence decay measurements. First, the over 1 millionfluorescence decays sampled in that time interval will showaliasing unless the digitization frequency is closely and con-tinuously matched to the mode-locking rate. Secondly, theamount of memory necessary to store 20 ms of data sampledat 0.25–0.5 ns intervals becomes prohibitive. The commercialTi:sapphire laser shows very small short time frequency drift(1–10 Hz), which does not contribute to the frequency alias-ing very much. To lock digitizers to the laser cavity, a mod-ification of our previous bandpass filters [47] selectivelyamplifies the seventh harmonic of the output of a subnano-second Si diode, which monitors the pump laser. This filteroutputs a sine wave at 500 MHz (800 mV p–p) perfectlysynchronized to the laser pulse train, and can be used in twoways. In one approach, the reference wave can be used todirectly gate the four analog to digital converters of the digitalstorage oscilloscope (DSO) at 2 ns intervals. In order toincrease the effective sampling period to 500 ps, the signal isdivided in four by branching three resistive power dividers(Mini-Circuits ZFRSC-42). These four channels are thensent into the four DSO inputs with coaxial cables whoselengths correspond to delay times of 0, 0.5, 1, and 1.5 ns. Thedata are then reconstructed with software yielding 28 pointsper 14 ns bin. Alternatively, the 500 MHz output of thebandpass amplifier may be divided by 50 using ECL countinglogic to produce a highly stable phase-locked 800 mV p–psquare wave at 10 MHz. When fed through the CKTrig optionof a LeCroy DSO, this signal references all of the instrument’sinternal timing to the laser, in which case the data may bedigitized at up to 4 GHz on a single channel. We found bothmethods highly satisfactory, although the latter allows twiceas many active collection channels.

The currently available 4 Mb of memory allow for 2 ms ofcontinuous 2 GHz sampling, covering only 10% of the poten-tially available data window. In order to increase the lengthof the experiment the memory is used selectively. The DSOis operated in a burst mode where 50 blocks of memory 40ms long are selectively acquired with increasing time gaps.



Fig. 3. Sample temporal profile measurements for a y8 to q108C T-jump on horse apomyoglobin. (A) Top: individual transients normalized to their peakintensities. The fluorescence lifetime immediately decreases following the T-jump. Following this near-instantaneous decrease a much slower increase in thefluorescence lifetime tracks protein-folding events. (B) Kinetic traces: intensity, lifetime fit, and x-analysis. The two basis functions f1 and f2 used for the x-analysis in Section 3 are 10 ms averages of raw data from 10 ms before and 500 ms after the T-jump. For the lifetime and x-fits, the goodness of fit parameterx2 is shown. The intensity plot shown was the result of box integrating the raw apomyoglobin fluorescence over t9 (14 ns) intervals. The arrows indicate abulge due to real folding kinetics, and another one due to intensity fluctuations of the mode-locked laser. The latter undesirable effect is not present in lifetimeor x fits, which are essentially immune to laser pulse-to-pulse energy fluctuations.

This allows data to be accumulated for any length of time atthe cost of gaps in the data. The latter is not a serious problemsince the 14 ns time resolution of the kinetics is needed onlyat short times. To generate the data-collection triggers for thescope, a master timing circuit synchronizes triggering and Q-switch firing [47]. In addition, this circuit sends a pulse to aprogrammable timing card (National Instrument PC TIO-10), which delivers either pulses or square waves from 10counter channels operating at up to 5 MHz. These channelsare combined using a high-speed CMOS NAND gate yieldinga single-pulse train of 50 pulses, which triggers the data-collection bursts of the DSO. The sequence is fully program-mable by the user via a LabWindows PC interface (NationalInstruments).

Sample data obtained with this method are given in Ref.[6]. Fig. 3 illustrates horse apomyoglobin fluorescencedecays and their change during folding kinetics. Solutionconditions were 400 mM in protein and 40 mM PO4

3y pH5.9 buffer. Under these conditions, cold denaturation ofapomyoglobin, which begins near 08C, is a two-state process.Following a T-jump from y8 to q108C, 280 nm pulsesexcite two tryptophans (positions 7, 14) in the A-helix, andto a lesser extent two tyrosines (positions 103, 146). Fig.3(A) shows fluorescence decays as a function of t9 at threetimes during the folding process, indicating the types of tem-poral profile changes that occur. The fluorescence lifetimebefore the T-jump (tsy14 ns) is much longer than that

immediately after (ts14 ns) due to the intrinsic temperaturedependence of tryptophan fluorescence [30]. At ts365 nsthe lifetime has increased because of folding. This is followedby a decrease in fluorescence intensity and lifetime on akinetic time scale f10 ms, shown in Fig. 3(B). A series ofcontrol experiments indicates that these are assignable pro-tein-folding events [48]. After 10 ms, a stable intermediateforms, which does not undergo further changes until a timescale ;1 s. Clearly, just because cold denaturation appearsto be two state thermodynamically does not mean that thekinetics of refolding have to be two state. A x-analysis of thekinetics in Fig. 3(B), to be discussed in more detail in Section3, also reveals non-monotonic changes in fluorescenceduringfolding.

Fig. 4 shows another example of real-time fluorescencechanges during folding. The data shown are from a singlekinetic trace of the refolding of a human ubiquitin mutant,under conditions where the laser pulse-to-pulse amplitudestability was optimized. The Ub*G mutant (Phe 45™Trp,Val 26™Gly) [6] was studied at 50 mM concentration in40 mM pH 5.9 phosphate buffer. Following a T-jump fromy8 to q88C, fluorescence was detected every 14 ns by excit-ing the single tryptophan residue at 295 nm. The foldingkinetics contains two phases: a sub-10 ms phase is assignedto re-equilibration of some of the protein in the denaturedfree-energy well; a slower subsequent phase can be fitted toa stretched exponential function exp[y(t/t)b], and is



Fig. 4. A single set of temporal profile data for Ub* G was analyzed in twoways, first by integrating the fluorescence intensity (A) and secondly by ax1-fit with basis functions picked 10 ms after and 2 ms after the y8 to q88

T-jump (B). The integrated curve shows data obtainable with a fairly ampli-tude-stable excitation laser. Under these circumstances its signal-to-noiseratio is comparable to that of the x1-fit. The solid lines are the results of non-linear least-squares fitting a stretched exponential to the data with amplitudeand offset constrained to one and zero. For the case of the intensity datats170(54) ms and bs0.44(8). For the x1-fit these values where 105(46)ms and 0.42(4), which proves that there are population changes not explain-able by two-state activated kinetics, despite the fact that Ub* G is thermo-dynamically a two-state folder by cold denaturation.

assigned to downhill folding from the transition state. Thetransition-state region of the protein can be accessed becausethe cold-denatured state at the initial low temperature(y88C) has a structure resembling the transition state at thehigher folding temperature (88C). Fig. 4 shows both an inten-sity analysis and a x-analysis. Only the latter, discussed indetail in Section 3, can be related to population changesduring folding. It yields ts105(46) ms and bs0.42(4)(uncertainties two standard deviations). Recent measure-ments of diffusional contact times in peptides have yieldedvalues between 0.1 and 1 ms for chain lengths of 10 to 100residues. This would indicate that the downhill folding ofUb*G requires 100–1000 such transient diffusional contactsto be made for folding to be completed.

The data in Figs. 3 and 4 were obtained without normal-izing for pulse-to-pulse intensity fluctuations of the laser

(typically f"6% for the tripled light, "4% for the doubledTi:sapphire output). These fluctuations dominate the ampli-tude fluctuations among individual fluorescence decays. Fig.2 illustrates that the probe pulse train can be monitored by a1 ns response small-area UV-sensitive Si photodiode, whichcan be acquired on a separate channel and used for laterintensity normalization on the computer. However, the stan-dard singular value decomposition (SVD)or the x-analysismethod described in Section 3 obviates the need for suchnormalization.

2.6. Real-time fluorescence spectra

The spectral shape of tryptophan fluorescence changeswhen the side chain moves from a solvent-exposed state toone in which its side chain is buried in the hydrophobic coreof the protein. Here the temporal resolution need only be onthe order of the fastest protein-folding event to be resolved(no shorter than f50–100 ns), unless one wishes to collectspectrally resolved decay information. The spectral resolu-tion must be at least comparable to the spectral shifts under-gone by the protein. Although the spectral sampling shouldhave higher resolution than the protein spectral shift, sam-pling wavelength intervals about two to three times largercan be tolerated for tryptophan because the fluorescence pro-file is essentially smooth. Spectral shifts with respect to thecold-denatured state can vary from 1 to 2 nm for intermediatestages of folding to 20 nm or more for fully folded proteins.Thus commercially available small spectrometers suffice forwavelength dispersion. The f2 nm bandwidth of the tripledTi:sapphire excitation source is also not an issue for wave-length shifts on the order of a nanometer or more.

To match these requirements, we have constructed aDts200 ns time-resolved dispersed fluorescence detector,shown on the right side of Fig. 2. The fluorescence signal iscollected by a f/0.85 liquid light guide (Oriel 77554) with)80% average throughput from 300 to 500 nm. Two fused-silica lenses then image the light into the input slit of a com-puter controlled f/3.9 imaging monochromator (ISATriax-180). A 16-element linear PMT array (Hamamatsu,R5900U-L16) is attached the to output of the monochromatorto collect 16 wavelength slices with 200 ns time resolution.Using a holographic grating blazed at 330 nm with 1200grooves/mm ()60% throughput at 330 nm), this systemoffers a resolution of 3.7 nm/channel for almost 60 nm ofspectral coverage, an excellent match for tryptophanfluorescence.

The PMT uses a single bialkali cathode with 16 discreteexposure areas of 0.8 mm=16 mm at a 1 mm pitch. Thephotoelectrons from the 16 channels pass through a single10-stage dynode chain ending in 16 separate anodes, eachwith less than 3% cross talk between neighbors. This smallcrosstalk is achieved by an electron guide design that imagesthe electrons from the 16 photocathodes onto the 16 anodes,with the intermediate common dynodes acting as lensing andamplification elements.



Fig. 5. Block diagram of the filter-digitizer used to collect sub-microsecond spectrally resolved fluorescence together with timing circuitry. One of the 16 PMTchannels is shown. Two additional channels are present, one of which may be used to measure laser intensity for normalization. The computer is attached tothe experiment through its parallel port.

The digitization rate can be reduced from more than 1 GHzto less than 50 MHz because Dt rather than Dt9 now sets theshortest time scale. Because of the mode-locked source, thisrequires integration of the signal by filtering, if full use is tobe made of the available photoelectrons at the lower samplingrate. To this end we have designed and built a filtered 18-channel digitizer with a computer interface. Fig. 5 shows ablock diagram of the instrument. The 16 PMT anode signalsare first transduced to 16 separate filters, the measured aver-age instrument response of which is shown in Fig. 2 (IRF2).These are three-stage active filters in a multiple-feedbackconfiguration having four poles with values chosen for aBessel response with a full width at half maximum of about200 ns. A FET-input operational amplifier for the first stage(OPA637) is followed by two low-noise high-speed capac-itively compensated ones (AD829). The setup has a totalgain of 38 dB, and with an input resistance of 7.5 kV thesefilters have a signal to noise ratio greater than 700 when thePMT is operated at 2 mA per channel. The 16 channels (aswell as two auxiliary channels for amplitude calibration, ifdesired) are digitized at 5 MHz by AD9200 (AnalogDevices) A/D converters. The digitized signals are fed into4.5 Mb (256 kb/channel) of onboard memory. After real-time data collection, memory output is multiplexed to theparallel interface of a PC, where the data can be analyzedwith LabWindows. As in the case of decay-profile detection,the probe can be monitored by a Si photodiode and normal-ized on one of the two auxiliary channels. For the occasionswhen the f200 ns response is not quite fast enough, decon-volution is possible to 50 ns (the individual filter responsescan be measured very precisely). As configured, the presentset of filters removes all oscillations due to the 71.4 MHzlaser repetition rate, while maintaining the advantage of highexcitation power of the mode-locked source.

Two sample experiments that illustrate the sensitivity ofthe technique are shown in Fig. 6. Here a 100 mM solutionof a point mutant of PGK (Trp 308™Phe, buffer: 20 mMPO4

3y, pH 6.2, 100 mM GuHCl, 1 mM EDTA, and 1 mMDTT) was jumped from y8 to q48C (Fig. 6(A)) and from

y9 to q88C (Fig. 6(B)) and probed with excitation cen-tered at 280 and 287 nm, respectively. In the former case 16channels of spectral data were simultaneously digitized at 5MHz. After averaging 50 data sets, the spectra were thenfurther averaged into 2 ms bins. Fig. 6(A) shows two of thosebins taken from 1 ms and 2 ms after the T-jump. The visibleblue shift in the 2 ms trace shows that the protein has under-gone some conformational changes. However, the shape ofthis spectrum is far closer to the 1 ms spectrum than it is tothe steady-state spectrum because the tryptophan has notbecome hydrophobically protected, although PGK has con-tracted appreciably in size [49]. The x1 parameter describedin depth below shows that the transition between the ts1 msfluorescence and ts2 ms spectra is continuous and mono-tonic. This result illustrates that the multichannel sub-micro-second detector is clearly capable of monitoring very smallsignal changes, of only a few percent of the denaturated/native difference. The somewhat larger T-jump shown in Fig.6(B) is the result of averaging seven traces, again with 2 msbinning. Here the data were analyzed with SVD and will bediscussed in some detail below.

2.7. Multiparameter detection, noise, and otherconsiderations

Wavelength-resolved decay profiles can be measured bycombining the PMT array detector with up to 16 channels ofGHz digitization, in analogy to Section 2.5. Due to the mas-sive storage requirements, this is mainly useful for signals inthe 20 ns to 100 ms range, where multidimensional discrim-ination of subtle changes is desired. Usually, it is more con-venient to collect wavelength-integrated fluorescence decaysand spectral profiles simultaneously. Fig. 2 shows how thishas been achieved concurrently by detecting from both sidesof the sample cell, one side measuring the decay of the overallfluorescence, while the other side measures the spectrallyresolved fluorescence. This does not reduce the collectionefficiency of either measurement.



Fig. 6. Time-resolved dispersed fluorescence measurements under two conditions. (A) 128C T-jump from the single-shot real-time folding kinetics at 48C ofa PGK mutant (Trp 308™Phe) with 2 ms binning times. The 1 ms spectrum represents the spectrum for the initial ensemble containing a large percentage ofunfolded PGK molecules and is therefore shifted to the red. After 2 ms this spectrum has moved slightly to the blue but does not show the extensive blue shiftof the Ts58C trace, indicating that the molten globule intermediate is still far from the native conformation. The x1 parameter together with the goodness offit is shown. (B) 178C T-jump with fluorescence excitation at 287 nm. Here the data were taken with a particularly noisy laser as evident in the fluctuations ofthe SVD 1 component, which follows the overall fluorescence intensity. Nevertheless the SVD 2 component tracks the chages in fluorescence spectrum as theprotein folds toward the molten globule intermediate. SVD basis functions for the same kinetic data are shown in the inset (singular values 1 and 0.015; theother basis functions account for -0.1% of the signal).

The intrinsic noise of the electronic data-processing anddigitization circuitry for both decay and wavelength meas-urements is about "1 in the least significant bit. It generallymakes only a small contribution to the overall noise figure.Absolute amplitude measurements are limited by the typi-cally 6% shot-to-shot fluctuations of the UV pulse trainobtained by tripling the Ti:sapphire laser, but can be elimi-nated by ratioing with a photodiode signal. In any case, ampli-tude fluctuations do not affect most of the data-analysistechniques described in Section 3. The main source of noise,which cannot be eliminated by amplitude normalization, isthe shot noise due to the finite number of photons reachingthe detector. The mode-locked Ti:sapphire oscillator operat-ing at a repetition rate of 71.4 MHz irradiates a 200 mmdiameter spot with 2.4=105 W/m2 incident intensity. Typi-cally a 50 mM solution of single tryptophan protein will beused in a 300 mm thick quartz capillary for a total of 3=1011

molecules in the probe area. Taking the absorbance of tryp-tophan to be on average 5000 My1 cmy1, about 1 in 25 000

molecules absorbs a photon in any one laser pulse. With aquantum yield of 10%, about one million photons are emittedfrom the sample per shot. With a total collection efficiencyof 10% for the fluorescence decay measurement, about12 000 photons can be collected in the first 500 ps Dt9 intervalfor a peak signal-to-noise ratio of 1%. The signal-to-noiseratio decrease at longer times due to the smaller number ofphotons per channel. The dispersed fluorescence collectionefficiency is about a factor of 10 lower. After dividing theavailable fluorescence into 16 3.7 nm channels, about 325photons/laser pulse are detected. After filtering, the 4500photons available in any 200 ns point result in measuredf1.5% fluctuations.

Finally, it should be mentioned that in the present experi-ments, fluorescence is excited with a polarized laser pulse,but detected without polarization preference. The polariza-tion reorientation times following alignment lie in the pico-second to nanosecond regime for the proteins studied here,below the kinetic time scale Dts20–200 ns. As expected,



experiments conducted with depolarized or circularly polar-ized laser pulses yield similar results to the ones reported inFigs. 3 and 6. However, polarization anisotropy measure-ments may be useful in other contexts and can be added bysimply replacing the wavelength-dispersed detector at theright of Fig. 2 by another single channel detected such asshown on the left, and inserting perpendicular polarizers ineach of the two simultaneously operating detection paths.

3. Data analysis

The fluorescence detection schemes outlined above pro-duce very large amounts of data (currently up to 8 Mb/shot)that require efficient analysis methods. The simplest dataanalysis involves integrating either the wavelength- or decay-resolved data to obtain total fluorescence as a function oftime, as shown in the top panel of Fig. 3(B) for apomyoglo-bin and in Fig. 4(A) for ubiquitin. This yields overall quench-ing information that can be useful for approximate distancemeasurements. The drawback of amplitude analysis lies inthe loss of information (Stokes shift, lifetime, populations offolded and unfolded states).

More information can be extracted if complete fluores-cence decay transients are fitted as a function of t9 to eachkinetic data point at tsnDt. In order to do this, single- totriple-exponential models of the tryptophan fluorescencedecay are convolved with the measured instrument responsefunction. A fit of this type to a single exponential is illustratedin the middle panel of Fig. 3(B) together with a goodness offit (x2). As the folding reaction progresses, an increase andsubsequent decrease in lifetime that tracks the intensitychange can be seen. Note that the fluorescence lifetime is lessnoise sensitive than absolute amplitudes because it is insen-sitive to laser amplitude fluctuations. Unfortunately the rel-ative lifetime variation itself is also smaller. Thesingle-exponential fit ignores the multiexponential nature ofthe tryptophan decays. It also neglects the fact that even the‘single-exponential’ reactants and products yield a biexpo-nential signal when both are present in appreciable concen-trations. Indeed, the x2 fit of the lifetime in Fig. 3(B) has amaximum near 8 ms, where the transition between a rapidlyformed intermediate state and a more highly quenchedlonger-lived intermediate occurs.

Similar analyses could be performed in the spectraldomain; a model of the fluorescence as a function of wave-length l would replace the (multi)exponential as a functionof t9. The drawbacks of lifetime or spectral fits are modeldependence and sensitivity to parameter correlation and fitinstabilities when the obtainable signal-to-noise ratio is rel-atively low. To cope with these problems, the shape of thefluorescence decays/spectra can be analyzed by the powerfulmethods of singular value decomposition or x-analysis.These are described below, the former only briefly since it iswell represented in the literature. Either method can be

applied to fluorescence decay profiles or spectral profiles, and‘profile’ is used interchangeably for both below.

3.1. SVD analysis

Singular value decomposition minimizes assumptionsabout the nature of the fluorescence spectrum or fluorescencedecays. Both fluorescence decay transients and fluorescencespectra may be thought of as m=n matrices whose n columnstrack the fluorescence profile (as a function of l or t9), andwhose m rows track the kinetics (as a function of t). SVDreduces this matrix to a set of n basis functions that describethe fluorescence profile, n singular values that describe theimportance of each profile to the total signal, and n vectorsof length m that describe how each of the basis functionscontributes to the kinetic signal as a function of time t[50,51].

Fig. 6(B) shows the 88C PGK folding data analyzed bySVD. Unlike the ubiquitin data in Fig. 4(A), this data sethad particularly large pulse-to-pulse laser amplitude fluctu-ations. (To illustrate the power of SVD, the laser cavity wasnot fine-tuned to minimize the quasi-periodic output intensityfluctuations characteristic of mode-locked lasers.) The firstSVD component shown in Fig. 6(B) tracks all signal ampli-tude fluctuations. The fluorescence intensity decreases rap-idly after ts0 due to the temperature jump. This is the‘instantaneous’ response of the tryptophan residue and hasno relation to folding kinetics. Subsequently, the intensitydecreases over 2 ms, but the trend is barely discerniblebecause of the shot-to-shot laser intensity fluctuations. Thesecond SVD component shown at the bottom tracks only thechange in shape of the signal. It does not have a large initialdecrease because the shape of the spectrum does not changeat the temperature jump. The signal dynamic range isenhanced from about 2:1 to 50:1, allowing kinetics to befollowed over three orders of magnitude in time. The formof the kinetics is seen to be highly nonexponential on a log–log plot [6].

Pronounced singular values up to n9Fn indicate that atleast an n9-state kinetic model is required to account for thedata. n9 sets a lower limit on the complexity of the kineticsbecause some intermediates may have spectral signaturessimilar to reactant or product. Furthermore, one should keepin mind that the Gn9 intermediates need not correspond todistinct (separated by )3kT barriers) free-energy minimaalong the reaction coordinate(s). In fact, the PGK foldingkinetics in Fig. 6(B), although nonexponential, cannot beaccounted for by intermediates with a spectral signature dif-ferent from the initial state (the x2 for the x1 is independentof t), nor by long-lived intermediates with a spectral signatureidentical to the initial state (there is no lag phase in thekinetics), as discussed in Ref. [6]).

3.2. x-Analysis

When the thermodynamic data for a folding reaction as afunction of temperature (or some other variable) can be rep-



resented by a cooperative two-state folding model, the fol-lowing question becomes relevant: are the folding kineticsthose of an activated two-state system, and hence single expo-nential? In that case the reaction proceeds as

D°N, [D](t)s([D] y[D] , exp(ykt)q[D] (1)0 ` `

A similar question can be asked if a long-lived intermediateI is formed from D because the reaction D°I is then a quasi-two-state reaction. The x-fit is a powerful tool to test thesequestions without making any assumptions about the func-tional form of the fluorescence decays or spectra of D, N (orI).

The practical implementation of the procedure for time-resolved fluorescence decays requires two steps. (In the fol-lowing discussion, l may replace t9 in any formula, if spectraare analyzed instead of decays.) First, two fluorescence pro-files f1 and f2 are constructed. f1 represents the fluorescencejust after (or just before) initiation of the kinetics. f2 repre-sents the fluorescence long after initiation of the kinetics. Forexample, in Fig. 3(B) f1(t9) for apomyoglobin was obtainedby binning about 700 fluorescence decays from before the T-jump, and f2(t9) is the average of 700 fluorescence decays at500 ms after the T-jump (when apomyoglobin has formed anintermediate with a 1 s lifetime).

The sampled data matrix f(t,t9) has m rows indexed by tand n columns indexed by t9. Each row of f is fitted by linearleast-squares to a combination of the two basis spectra f1 andf2, which themselves are functions of t9:

f(t,t9)sa (t)f (t9)qa (t)f (t9) (2)1 1 2 2

The function x1 is then defined as

a (t)1x (t)s (3)1 a (t)qa (t)1 2

It describes how the shape of the fluorescence profileevolves from a more unfolded signature towards a morefolded signature, independent of the signal amplitude. Thisfunction has three important properties, which make it anexcellent choice for representing folding kinetics. Itapproaches a signal-to-noise ratio limited only by the Poissonstatistics of photon numbers in each temporal (spectral)channel (like ideal fluorescence intensity analysis); it isimmune to laser intensity fluctuations (like fluorescence life-time analysis); it allows one to extract species populationsfor two-state folders, and distinguishes two-state from multi-state folding (unlike amplitude or lifetime analysis). Wediscuss these three properties in turn.

If the laser has no pulse-to-pulse energy fluctuations, inte-grated fluorescence yields the smallest noise, simply becauseit maximizes the number of photons per data point, therebyreducing Poisson fluctuations. Fig. 3(B) for apomyoglobinillustrates the result obtained with a carefully stabilized laser,which approaches this ideal case: the top trace reveals thefluorescence change due to folding with a much better signal-to-noise ratio than the lifetime fit, and somewhat better thanthe x-analysis. The slightly smaller signal-to-noise ratio of

the latter is due to the fact that the intensity data depend onthe total number of photons, whereas the x-analysis is mostsensitive to the smaller number of photons in those t9 channelswhere the fluorescence is changing rapidly. Fig. 4 for ubi-quitin illustrates the more typical case where the noise figuresare comparable due to residual pulse-to-pulse energy fluctu-ations. Fig. 6(B) for PGK illustrates a worst-case scenario,when the laser is not highly stable from pulse to pulse.

The shape of the fluorescence decay is independent of thepulse energy. Therefore lifetime fits and x-analysis are essen-tially immune to shot-to-shot laser intensity fluctuations. Fig.3(B) (arrows) indicates that even in the best cases, inte-grated intensity data are more susceptible to occasional slow(few microsecond) laser energy fluctuations, which are sup-pressed in x-analysis by the normalization property of Eq.(3). The x-analysis is therefore more reliable than the ampli-tude fit under any circumstances, even though its rms signal-to-noise ratio may be somewhat less.

x1 essentially tracks the ‘mole fraction’ of the initial andfinal spectroscopic signatures f1 and f2 as the protein folds.For two-state folding, these signatures are in turn linear com-binations of the unfolded and folded fluorescence profiles.The functions xi are then linearly related to the concentrationsof folded and unfolded species. The precise scaling dependson the pre-jump equilibrium constant K0 and the final equi-librium constant K`, as derived in more detail below. Inte-grated intensity plots such as Fig. 4(A) or lifetime plots suchas Fig. 3(B) are not necessarily linearly related to two-statespecies concentrations. This represents the most importantadvantage of x -analysis over integrated fluorescence inten-sities or fluorescence lifetimes.

The x-analysis can be used with wavelength-resolved dataas well. Fig. 6(A) shows a logarithmically smoothed x1 plotof the PGK dispersed fluorescence data. Here f1 was chosenimmediately after the temperature jump. The f2 function wastaken at the end of the data set, 2 ms after the T-jump, whenPGK has collapsed to form a long-lived intermediate I.Although the spectrum of PGK has only slightly evolvedtowards the native state (the small spectral shift shown at thetop) the x-fit extracts kinetic data with a 15:1 dynamic rangeover three orders of magnitude in time.

We now examine in more detail how the values of theequilibrium constants, and the choice of t2 (where f2 isdefined) affect the kinetic trace x1. Ideally f1 should be chosenimmediately after the temperature jump, and f2 when equilib-rium has been reached (quasi-equilibrium in the case of along-lived intermediate). The resulting x1 then decreasesfrom one to zero while exactly tracking the concentrationrelaxation in Eq. (1). The optimal choice of f2 can only beachieved if the kinetics are sufficiently fast to achieve(quasi)equilibrium within 20 ms to avoid re-cooling, or if a carefullycalibrated steady-state profile at the final condition can beobtained. The latter is impossible for a D°I reaction, andsometimes neither is possible. One would therefore like toknow how sensitive the functional form of the kinetics is tothe choice of t2, particularly if one wishes to distinguish



Fig. 7. Fit to a simulated nonexponential relaxation, with the scaling param-eter g constrained to one. As t2/t™`, the exact value of b is approached.If t2 is too small, b is overestimated.

exponential from nonexponential processes. As it turns out,within a linear scaling factor and offset, any choice of f2preserves the functional form for a two-state process. More-over, if the offset and scaling are neglected during fitting,nonexponential forms are compressed to more exponentialforms. The x-fit therefore provides a conservative way oftesting how nonexponential the kinetics are.

To show this, consider a thermodynamic two-state folderwith denatured and native signals fD and fN, and with pre-jump equilibrium constant K0 and post-jump equilibriumconstant K`. Typical values for the equilibrium constantsare K0-1 and K`)20. Let the actual functional form ofthe relaxation kinetics be given by a function g(t) scaledsuch that g(0)s1 and g(`)s0. Examples include gsexp[yt/t] (exponential), gs[1qt/nt]yn (power law),g sexp[y(t/t)b] (stretched exponential), g sSai

exp[yt/ti] (multi-exponential). At ts0, the fluorescencesignal is f0(t9)sK0 fN/(1qK0)qfD/(1qK0), and at ts`,f`(t9)sfN/(1qK`)qK` fD/(1qK`). In terms of theseideal choices for f1 and f2,

f(t,t9)sf (t9)qg(t)( f (t9)yf (t9)) x (t)sg(t) (4)` 0 ` 1

such that x1(t) directly traces the kinetic law. If instead wehad chosen our second basis function at t2-`, f(t) and x1(t)would be expressed in terms of f0 and f2sf`qg(t2)(f0yf`)as

f yg(t )f f yf2 2 0 0 2f(t)s qf(t) ´ž /1yg(t ) 1yg(t )2 2

y1 y1x (t)sg(t)(1yg(t )) yg(t )(1yg(t )) (5)1 2 2 2

Thus x1(t)s1 still holds at ts0, and x1(t) has preciselythe same functional form, except for a negative offset at longtimes and a scaling factor that approaches unity if t2 is suffi-ciently large. The offset and scaling factor g)1 are not lin-early independent, but rather

x(t)sgg(t)q(1yg) (6)

One can thus fit the functional form f(t) of the kinetics andone additional parameter g. Even more conservatively, onecan simply assume that gs1 even though t2 is finite. Forexample, let the actual kinetics be a stretched exponentialwith b-1. Letting gs1 even though t2 is finite results in astretching factor b closer to unity (Fig. 7). The x-fit thereforeprovides a conservative approach for distinguishing nonex-ponential from exponential kinetics in complex systems suchas proteins or other polymers.

At least for true two-state folding, the scaling factor g canusually be determined independently from the T-jump exper-iment by careful equilibrium measurements, eliminatingeventhis last fitting parameter. This is desirable because correla-tions between g and the functional form of g(t) are thenremoved. Usually a steady-state measurement of the fluores-cence shape can be performed on the same sample at theknown final T-jump temperature (e.g., as calibrated by an IRtransmission measurement [47]). If an intermediate reaches

a quasi-stationary state on the time scale of the T-jump exper-iment (e.g., apomyoglobin in Fig. 3), it will be more sensibleto let gs1 and choose f2 in the quasi-steady-state region.

It should be noted that none of the fast folders describedhere has simple exponential kinetics. The apomyoglobin x1

trace first increases, then decreases, due to formation of aless-quenched nanosecond-lifetime intermediate precedingformation of a long-lived more-quenched intermediate. ThePGK and ubiquitin traces are best fitted by stretched expo-nentials, even though both proteins display two-state ther-modynamics under our cold-denaturation conditions. This,and the fact that the low temperature folding behavior (wherethe native state is destabilized) becomes exponential, indi-cates that these proteins either fold downhill, or are preparedat the transition state to probe the downhill part of the foldingprocess.

4. Conclusions

Collecting folding-kinetics data as a function of a fluores-cence parameter such as wavelength or decay time greatlyenhances the information content of the data compared withintegrated fluorescence. Where both types of data can becompared, there is good agreement between the kinetic par-ameters derived. Fluorescence lifetime measurements pro-vide additional information about tryptophan quenching,while wavelength dispersion provides information abouttryptophan solvation. Similar advantages also apply whenextrinsic probes (such as cysteine-linked dyes) are used.

Fast data collection quickly becomes memory intensive,and requires efficient processing methods. Analysis methodssuch as SVD or x-analysis provide objective and rapid meansof reducing large numbers of data points. Both provide objec-tive means of distinguishing two-state and multi-state kinet-ics; the latter is also a conservative estimate of any kineticstretching that might be found in protein or polymerdynamics.



Fast (Dt-100 ns) fluorescence lifetime and quenchingtechniques can extend the utility of distance measurementswhich have been successfully applied on millisecond andlonger timescales. Dexter transfer pairs can be used to meas-ure contact formation, while Forster transfer to dyes (orämong dyes) allows distance measurements to be made inthe 15–40 A range when combined with careful anisotropy˚

measurements.Although efforts in this direction have only just now begun,

these techniques could be used to produce low-resolution 3Dmaps of the evolution of average distances among proteinresidues during folding, providing a structural interpretationof fast folding events.

The methods described above have also been applied toaggregation of organic molecules, and folding of organicpolymers. Potential applications include other systems withreasonably narrow ‘phase transition’ temperatures that canbe probed by fluorescence, such as liquid crystals (collectiveorder–disorder transition), protein–membrane interactions(e.g., membrane intercalation of peptides), and a variety ofphase transitions in polymers and surfactant solutions (e.g.,micelle–lamellae transitions). Many of these systems can beexpected to exhibit interesting kinetics governed by masterequations that will not yield simple exponential dynamics.

Acknowledgements

This project was funded by NIH grant GM057175 and aLucile and David Packard Fellowship. We thank ProfessorDoug McDonald for helpful discussions about the dispersedfluorescence detection. The ubiquitin expression system wasa gift of Professor Tracy Handel at the University of Califor-nia at Berkeley; the PGK expression system was obtainedfrom Professor Maria Mas and Genentech. M.G. was anAlfred P. Sloan Foundation Fellow and Dreyfus Teacher-Scholar while this project was carried out.

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Submicrosecond real-time fluorescence sampling: application to protein folding