Intrinsic Dynamics of Protein-Peptide Unbinding
IIntrinsic Dynamics of Protein-Peptide Unbinding
Brankica Jankovic, Olga Bozovic, Peter Hamm
Department of Chemistry, University of Zurich,Winterthurerstr. 190, CH-8057 Z¨urich, [email protected] (Dated: February 26, 2021)The dynamics of peptide-protein binding and unbinding of a variant of the RNase S system hasbeen investigated. To initiate the process, a photoswitchable azobenzene moiety has been covalentlylinked to the S-peptide, thereby switching its binding affinity to the S-protein. Transient fluorescencequenching was measured with the help of a time-resolved fluorometer, which has been specificallydesigned for these experiments and is based on inexpensive LED’s and laser diodes only. One mutantshows on-off behaviour with no specific binding detectable in one of the states of the photoswitch.Unbinding is barrier-less in that case, revealing the intrinsic dynamics of the unbinding event, whichoccurs on a few 100 µ s timescale in a strongly stretched-exponential manner. I. INTRODUCTION
Proteins employ sophisticated binding mechanismsduring their interplay with other physiological partnersto fulfill crucial biological processes. Starting from therecognition of small rigid molecules by proteins all theway to complex rearrangements of protein-protein inter-actions, many different models of protein binding havebeen suggested.
The important transient conforma-tional changes associated with binding can be hidden inequilibrium structures, and capturing them is the onlyway to provide comprehensive mechanistic insights. Oneexample of a challenging question related to protein in-teractions is related to intrinsically disordered proteins.These proteins interact by coupling binding and fold-ing and a lot of effort has been directed towards under-standing the temporal ordering of the underlying events. Therefore, clarifying the detailed binding mechanisms ofprotein interactions necessitates a kinetic perspective. NMR-based techniques revealed invaluable insightsinto the complicated binding mechanisms of proteins,such as the “fly-casting” interaction mechanism of the in-trinsically disordered pKID transcription factor with theKIX domain, i.e., a hydrophobic loose encounter com-plex is followed by the second (folding) phase. How-ever, approaches that allow for a direct observation ofevents related to binding in a time-resolved manner arevery scarce. They are commonly based on the stopped-flow methods, where rapid mixing of two interactingspecies is used as a trigger to initiate binding (or un-binding in competition experiments).
These meth-ods are limited by the mixing time, leaving the accessibletime window in the millisecond regime. On the otherhand, there are ultrafast laser-based approaches that relyon a temperature jump as a trigger for conformationalchanges, and fluorescence as a way of detection. Thedifferent phases in the binding process of a yeast proteaseand its intrinsically disordered inhibitor have been re-solved in this way. However, temperature jumps, whichare typically small, are limited by the size of the per-turbation that can be induced. Single molecule fluo-rescence revealed the electrostatically driven encounter + cis trans FIG. 1. Molecular construct. The S-protein (yellow) withhighlighted tyrosine residues (magenta) binds the S-peptide(blue) in the cis -state of the azobenzene moiety (orange),while it unbinds in the trans -state. The picture was adaptedfrom pdb-entry 2e3w. complex formation, followed by folding into the final3D conformation. A recent MD simulation revealed anatomistic support for the induced fit binding mechanismof an intrinsically disordered system . Key contacts be-tween the disordered peptide and the protein formed be-fore or in parallel with the secondary structure formation.However, MD simulations are limited to very fast binders,and it is still very difficult to approach the relevant rangeof milliseconds.The emerging strategy of designing photoswitch-able proteins and peptides proved fruitful for di-verse studies, where a precise control of certain as-pects of protein structure and/or function is necessaryto control for instance protein folding, allostericcommunication, or biological activity. Here weemploy the previously designed photoswitchable RNaseS to explore the kinetics and dynamics of (un)bindingof this non-covalent complex. This model system hasbeen previously used to study the mechanism of coupledbinding and folding, as the S-peptide fragment is un-folded in isolation, while it adopts the helical structureonce bound to the S-protein part.
Our molecular construct is illustrated in Fig. 1. Theazobenzene moiety (orange) is covalently linked to theS-peptide (blue) via two cysteines (see Methods for de- a r X i v : . [ phy s i c s . b i o - ph ] F e b tails). By choosing the distance between these anchoringpoints, the α -helicity of the S-peptide in the two states( cis or trans ) of the photoswitch is either stabilized ordestabilized, which in turn determines its binding affin-ity to the S-protein (yellow). One can selectively switchbetween both states with light of the proper wavelength.In Ref. 33, we designed five different mutants with vary-ing anchoring points, and in one case with an additionalmutation. The binding affinities of the S-peptide to theS-protein in the cis and the trans -states of the photo-switch have been measured by a combination of ITC, CDspectroscopy and intrinsic tyrosine fluorescence quench-ing. As anticipated by our design, the binding affinityis larger in the cis -state for all mutants we investigated.However, the values for the binding affinities, and in par-ticular the factors by which the binding affinity changesupon switching, vary significantly. S-pep(6,13), with thephotoswitch linked at positions 6 and 13, sticks out inthis regard, as it binds with reasonable affinity in the cis -state, but no specific binding could be detected byCD spectroscopy in the trans -state (fluorescence quench-ing indicated some degree of unspecific binding). Thismutant will be the focus of the present kinetic study,as it approaches the “speed limit” of ligand unbindingand thus reveals its intrinsic dynamics, analogous to theconcept of downhill protein folding.
As a control, wewill also consider S-pep(6,10), which has a large (20 fold)change in binding affinity, but stays specifically bound tothe protein in both states. In either case, the photoswitchable S-peptide does nothave any fluorophore, while the S-protein has six tyrosineresidues, one of which is located in the binding groove(Fig. 1). The amount of fluorescence will be sensitive topeptide binding, as the peptide (presumably mostly itsazobenzene moiety) quenches the tyrosine fluorescence;this is the effect that enables one to determine bind-ing affinities from the concentration dependent fluores-cence yield. Here, we measure fluorescence in a tran-sient manner in order to follow the kinetics and/or dy-namics of ligand binding and unbinding.
II. METHODSA. Experimental Setup
Fig. 2a shows the experimental setup, which has beenspecifically designed for this study. A UV-LED at 265 nmwith active area 1 mm (M265D2, Thorlabs) was usedto excite the fluorescence of the tyrosine residues of theprotein sample. It was operated by a pulsed laser diodedriver (LDP-V 10-10, PicoLAS), producing 15 ns pulsesat a repetition rate of 200 kHz. The light was collectedwith a 50 mm lens, spatially filtered with an aperturewith dia=5 mm, and focused with a 15 mm lens intothe sample with a spot size of ≈ µ m. We estimatedthat the time-averaged power in the sample was ≈ µ W.A low power was anticipated to minimize the number of
PM LEDAPD
Stepper ab L E D n m LaserPump SampleExchange c Aperture 5mm
LaserPump SampleExchange
FIG. 2. Time-resolved fluorometer. (a) Experimental setupused in this study; the various components are discussed inthe text. Test experiments demonstrating the performance ofthe system are shown in panel (b) for a high frequency (33 Hz)and in panel (c) for a low frequency (1.1 Hz) of the syringepushes. Source data are provided as a Source Data file. molecules that photo-isomerize induced by that measure-ment light (we estimated that it takes about a minute un-til every molecule in the measurement volume would haveseen a 265 nm photon). The transmitted light was mea-sured by an avalanche photo diode (APD, APD120A2/M,Thorlabs). The fluorescence light was collected in a 90 ◦ geometry by an large-aperture aspherical lens ( f =40 mm,dia 50 mm), spectrally filtered with an interference filtertransmitting ≈ µ s lengthat typical repetition frequencies of 1-33 Hz. While themaximum power of laser diode is specified at 3.5 W in cw-operation, we found that one can go up to 10 W in pulsedoperation, revealing 20 µ J of pulse energy in the 2 µ slong pulses. The laser diode beam was pre-collimated(LTN330-C, Thorlabs), its elliptical shape corrected withtwo cylindrical lenses (50 mm and 150 mm), and thenfocused into the sample with a 150 mm lens, roughlymatching the diameter of the probe light.The experiment required the exchange of sample be-tween subsequent excitations from the 447 nm laser,which was achieved with a pulsed syringe pump pushedby a stepper motor (DRV014, Thorlabs). The steppermotor controller (KST101, Thorlabs) has an externaltrigger input, moving the stepper motor at desired timepoints with steps whose size can be pre-programmed.The syringe was connected to the sample cuvette viarigid Teflon tubings. The channel in the sample cuvettewas about 1 mm wide and 200 µ m thick. The ratio ofthe dimension of the syringe vs that of the channel in thesample cuvette translated the 4 µ m steps of the steppermotor into the desired ≈ µ m steps of the excited spotin the sample cuvette. The stepper motor controller hadto be programmed in Labview, allowing one to overwritethe default settings for the maximal velocity and accel-eration, which was needed for stepping frequencies up to33 Hz. A total sample volume of about 1 ml was needed.The timings of all components have been controlled witha programable delay generator (T560, Highland Technol-ogy).Figs. 2b,c demonstrate the performance of the pulsedsyringe pump, using only the azobenzene-photoswitch(without protein, the part colored in orange in Fig. 1) astest sample. To this end, the sample was first preparedin its cis -state with an excess of 370 nm light from acw-LED, which illuminated the fused silica syringe. The trans -absorption is significantly larger at this wavelength(see Fig. 3), thereby shifting the photo-equilibrium to the cis -state with typically 85%. The 447 nm laser pulse theninduced a cis -to- trans isomerization at time-zero.Fig. 2b shows that photo-isomerization is instanta-neous on the timescale of this experiment, revealing astep-like increase in transmission of the 265 nm lightfrom the UV-LED at time-zero, since the absorption ofthe photoswitch changes upon photo-isomerization (seeFig. 3). The signal stays roughly constant for ≈
15 ms af-ter laser excitation, which will be the usable time windowfor measuring transient fluorescence, followed by a periodof ≈
10 ms for sample exchange upon pushing the syringepump. The overall data are periodic, and we shifted thesubsequent 5 ms, which are used to determine an offset,to negative times in Fig. 2b. The dead time of the exper-iment is thus ≈
15 ms. When a lower repetition rate ischosen, the dead time remains the same, while the usable time window increases accordingly, see Fig. 2c (some ofthe protein samples were “sticky”, hampering a smoothmotion of the piston in the syringe, in which case it wasnecessary to increase the time between the syringe pushesand the 447 nm laser pulses to 100-250 ms). This plotalso shows that the sample does not move and/or diffuseon a 1 s timescale between the syringe pushes. For a quickand complete exchange of the sample, it turned out to bevery critical that absolutely no bubbles were present inthe syringe, teflon tubings or the sample cuvette, andthat the spatial overlap between the 265 nm probe lightand the 447 nm laser pulses was carefully aligned.
B. Sample Preparation
The S-protein was prepared by cleaving the com-mercial ribonuclease A from bovine pancreas (Sigma-Aldrich) with subtilisin (Sigma-Aldrich), as described inRefs. 33 and 38 (with small modifications). To limit theproteolysis to a single peptide bond (between residues20 and 21), we performed the cleavage reaction on iceovernight. The reaction was stopped by adjusting thepH value to 2. The S-protein was purified by C5 reverse-phase chromatography.Photoswitchable peptides were prepared by crosslink-ing the cysteine-containing peptides with the water-soluble azobenzene-based photoswitch. The peptideswere first synthesized by standard Fmoc-based solid-phase peptide-synthesis using a Liberty 1 peptide syn-thesizer (CEM Corporation, Matthews, NC, USA). Allamino acids were purchased from Novabiochem (La Jolla,CA, USA). The photoswitch (3,3’-bis(sulfonato)-4,4’bis(chloroacetamido)azobenzene) was added to a peptidereduced by tris(2-carboxyethyl)phosphine (TCEP) in 5xmolar excess and incubated overnight. The linked pep-tides were purified by C18 reverse-phase chromatography.The purity of all protein and peptide sampleswas analyzed by mass spectrometry. Concentrationswere determined by amino acid analysis. All solutionswere prepared in 50 mM sodium phosphate buffer pH 7.0.
C. Model
For a quantitative determination of the on and off-rates, we considered the following coupled equilibria, inwhich two molecular species, the S-peptide in its cis and trans -states, compete for the same binding site on theS-protein P : P L cis k off,cis −−−−− (cid:42)(cid:41) −−−−− k on,cis P + L cis P L trans k off,trans −−−−−− (cid:42)(cid:41) −−−−−− k on,trans P + L trans (1)The corresponding differential equations were solved nu-merically with the help of Mathematica. For the initial
300 400 5000.00.10.2 A b s o r ban c e ( O D ) Wavelength (nm)
LaserpumpLEDswitchFluorescencepump + probe transcis
FIG. 3. Absorption spectra. Absorption spectra exempli-fied for S-pep(6,13) (dashed lines) and S-pep(6,13)+S-protein(solid lines) in their cis (red) and trans (blue) states. The ar-rows indicate the wavelengths of the various light sources usedin the experimental setup, as well as that of the fluorescenceemission. Source data are provided as a Source Data file. conditions, we first determined the equilibrium condi-tions in either the cis or the trans -state, assuming theS-peptide is 100% in this state, and then switched 10%or 5% of the molecules for the cis -to- trans or trans -to- cis isomerization, respectively (accounting for the smallerisomerization quantum yields of the latter). Despite thefact that the solutions of these differential equations arenot strictly exponential, the deviation from exponentialis very small and the data from the model were fit tosingle-exponential functions. The model is too simple toexpect a quantitative fit of the experimental data; forexample it ignores the possibility of unspecific binding,while we have evidence from comparing CD and fluores-cence binding curves that unspecific binding does existto a certain extent. We therefore concentrated on thetime constants; in the case of trans -to- cis switching onlyon those at lower S-protein concentration, when the ef-fect of unspecific binding is expected to be less. Bindingaffinities known from Ref. 33 were taken over, and theother parameters of the model ( k on,cis and k on,trans forS-pep(6,10), and k on and K d,trans for S-pep(6,13)) werevaried until similar time constants as in experiment wereobtained. III. RESULTS
The experimental setup, which has been specificallydesigned for this study, is discussed in detail in Methods.It allows for the investigation of both binding and unbind-ing events with high, 5 µ s time resolution. Unbindingupon cis -to- trans switching of the S-peptide is measured by pre-illuminating the sample in excess with a high-power 370 nm LED, in which case the photo-equilibriumis shifted to the cis -state with typically 85% popula-tion, since the trans -absorption is significantly larger at370 nm (see Fig. 3). A subsequent 447 nm laser pulseinduces cis -to- trans isomerization with a quatum yieldof ≈ Binding upon trans -to- cis switching is mea-sured by keeping the sample in the dark, in which casethe sample will eventually relax into the lower-energy trans -state. Illumination with the 447 nm laser theninduces trans -to- cis isomerization, since in essence no cis -peptides are present and since the trans -state alsoabsorbs at this wavelength (see Fig. 3). The quan-tum yield is however significantly lower in this case. Photo-isomerisation competes with thermal cis -to- trans back relaxation, but since the time-averaged power of the447 nm laser is very small (40 µ W at 2 Hz), the photo-equilibrium of the sample as a whole will almost exclu-sively be on the trans -side. Tyrosine is excited at 265 nmwith low power in order to minimize additional isomeri-sation reaction induced by that light, and its fluorescenceis detected between 300 nm and 360 nm (Fig. 3).
A. S-pep(6,10)
To set the stage, we start with S-pep(6,10), whosebinding affinities change by a large factor (20 fold) upon cis -to- trans switching, but with specific binding in bothstates (see Table I). Fig. 4a shows the transient fluo-rescence measurement for cis -to- trans switching. Flu-orescence increases, as expected since the tyrosines arequenched less upon unbinding of the S-peptide. An ex-ponential fit to the data reveals a time-constant of 74 ms.Upon trans -to- cis switching (Fig. 4b), the sign of the sig-nal inverts, representing stronger quenching of the tyro-sine fluorescence upon ligand binding. The kinetics isconcentration dependent with time constants of 42 msfor 100 µ M S-protein (red) and 16 ms for 400 µ M S-protein (blue, the concentration of the S-peptide has been200 µ M in both cases), as anticipated for second-orderkinetics. The ratio of time constants closely resemblesthat of the S-protein concentrations. Furthermore, theamplitude of the 400 µ M data (blue) is smaller, since weplot relative fluorescence change. In absolute numbers,the isomerized S-peptide is the same in both experiments(i.e., about 5% of the S-peptide or 10 µ M). In a relativesense, this is less for the large S-protein concentration.In its simplest form, ligand binding/unbinding is dis-cussed in terms of the following chemical equilibrium:
P L k off −−− (cid:42)(cid:41) −−− k on P + L (2)where P L is the ligand-bound state, and P and L de-note protein and ligand, respectively. The dissociationconstant K d is related to the rate constants k on and k off trans ‐to‐ cis S‐pep(6,10)
Time (ms)Time (ms) cis ‐to‐ trans F l u o r e s c e n c e C h a n g e ( r e l . ) F l u o r e s c e n c e C h a n g e ( r e l . ) ab S‐pep(6,13)
Time (ms)Time (ms) cd =0.25 ms, =0.5 or =0.29 ms FIG. 4. Time-resolved fluorescence. Relative fluorescence change for (a) cis -to- trans switching of S-pep(6,10) with 200 µ MS-pep(6,10) and 200 µ M S-protein, and (b) trans -to- cis switching with S-pep(6,10) concentration 200 µ M, and S-proteinconcentration 100 µ M (red) as well as 400 µ M (blue). The same for (c) cis -to- trans switching of S-pep(6,13) with 400 µ MS-pep(6,13) and 200 µ M S-protein, and (d) trans -to- cis switching with S-pep(6,13) concentration 400 µ M, and S-proteinconcentration 100 µ M (red) as well as 400 µ M (blue). In panels (a,b,d), the solid lines are exponential fits with the timeconstants indicated. In panel (c), the solid red line shows a stretched exponential fit ( τ =0.25 ms, stretching factor β =0.5), andthe dashed line a single exponential fit ( τ =0.29 ms). The data in panel (c) are shown without any smoothing, those in panel(a,b,d) with a Gaussian filter with width 2.5 ms. Source data are provided as a Source Data file. by: K d = k off k on . (3)The equilibrium experiments of Ref. 33 can only deter-mine the dissociation constant K d , while the present ki-netic experiments can also determine the on- and off-rates. Trends can be read off directly from Fig. 4a,b,but a more quantitative modelling is needed to extractthese rates, taking into account the fact that both statesof the photoswitch bind to the protein to a certain ex-tent, and competitive binding of the S-peptide in its cis and trans -states, both of which exist after photoswitch-ing (see Fig. 5, for details of that model, see Meth-ods). The resulting kinetics are not strictly exponen-tial owing to the coupled and nonlinear character of thecorresponding differential equations, however, they devi-ate from exponential by less than what the experimen-tal noise would allow one to see (Fig. 5). We thereforealso fit the simulated data to exponential functions, andcompare the extracted time-constants with the experi-mental ones. We obtain good qualitative agreement forboth cis -to- trans and trans -to- cis switching when as- suming on-rate constants k on,cis = 3 · M − s − and k on,trans = 1 · M − s − , see Table I.The extracted on-rate constants are in the same rangeas what has been observed in Refs. 34 and 35 for a se-ries mutants of the RNase S system without photoswitch.Two factors determine binding rates. The first is thediffusion controlled formation of an encounter complex,taking into account the fact that the two partners needto approach each other with a specific orientation, whichresults in typical on-rate constants in the range between10 M − s − to 10 M − s − . The second factor con-cerns the fraction of molecules that leave the encountercomplex before a stable protein-ligand complex is formed
TABLE I. Thermodynamic and kinetic constants for the twosamples considered in this study. K d,cis k on,cis K d,trans k on,trans S-pep(6,10) 2.3 µ M a · M − s − µ M a · M − s − S-pep(6,13) 70 µ M a · M − s −
40 mM b · M − s − taken from Ref. 33 b nominal dissociation constant; see text for discussion. trans ‐to‐ cis S‐pep(6,10)
Time (ms)Time (ms) cis ‐to‐ trans F r ee P r o t e i n C h a n g e ( r e l . ) F r ee P r o t e i n C h a n g e ( r e l . ) ab S‐pep(6,13)
Time (ms)Time (ms) cd FIG. 5. Model calculations. Change of free S-protein upon (a) cis -to- trans and (b) trans -to- cis switching of S-pep(6,10), andupon (c) cis -to- trans and (d) trans -to- cis switching of S-pep(6,13), as deduced from the model described in Methods. Theconcentrations are the same as in the experiment (Fig. 4). The points are the result from the model, the solid lines exponentialfits to it, with the fitted time constants indicated. (in an induced fit scenario). Since the diffusion controlledstep is often rate-limiting, k on typically varies only in asmall range, in the case of the mutants of the RNase Ssystem between 1 . · M − s − and 5 . · M − s − ,see Ref. 35. In our case, the cis -state is more tightlybound, and correspondingly, k on,cis is ≈ k on,trans , however, this factor 3 is small in com-parison to the overall factor 20, by which the bindingaffinities differ. B. S-pep(6,13)
With that, we turn to S-pep(6,13), which is char-acterized as on-off system, for which no specific bind-ing could be detected in the trans -state. At a firstsight, the results in Fig. 4c,d look similar to those ofS-pep(6,10) (Fig. 4a,b), however, binding and unbind-ing happens on completely different timescales (to thatend note the different time ranges in Figs. 4c,d). Bindingupon trans -to- cis switching, which is again concentrationdependent, reveals 60 ms for 100 µ M S-protein concen-tration and 40 ms for 400 µ M S-protein concentration,with the S-peptide concentration being 400 µ M in bothcases (Fig. 4d). These are similar timescales as for S-pep(6,10). However, the ratio of time constants deviatessignificantly from that of the S-protein concentrations, for two reasons: First, the observed rate is the sum ofthe effective (i.e., concentration dependent) on-rate andthe off-rate, and the off-rate contributes more in a rel-ative sense at lower protein concentrations. This effectis taken care of in the model of Fig. 5d, where a ra-tio of time constant smaller than 4 is indeed observed.In addition, by comparing CD with fluorescence quench-ing data, we concluded in Ref. 33 that some amount ofnon-specific binding also occurs in the trans -state of S-pep(6,13). Binding of this fraction of molecules will be aunimolecular process, and thus not concentration depen-dent.Unbinding upon cis -to- trans switching is faster by twoorders of magnitudes, see Fig. 4c. Furthermore, the datareveal stretched-exponential kinetics exp[ − ( t/τ ) β ] withtime-constant τ =0.25 ms and a significant stretching fac-tor β =0.5. Despite the noise of the data, it is clear thatthe stretched exponential fit is better than the single-exponential fit with time-constant 0.29 ms (Fig. 4c, com-pare solid red line vs dashed line). The binding affinity ofthe trans -state could not be measured in Ref. 33, since itis too small. For a modelling similar to the one used for S-pep(6,10), we therefore had to assume k on,cis = k on,trans (which is justified by the fact that on-rate constants varyonly by small amounts), revealing k on ≈ · M − s − and a nominal dissociation constant of K d = 40 mM, seeFig. 5c,d. F ( R ) RV b R R R a b k on k off barrier‐lessunbinding cis trans -TS -TS FIG. 6. Free energy model: (a) Free energy of the ligand asa function of the distance R of the ligand from the protein,where R is the interaction range of the protein (in essenceits size), V b the binding energy, and S an activation entropy.Panel (b) shows the same for barrier-less unbinding with V b =0. The two scenarios resemble the situations in the cis - and trans -states of the photoswitch. IV. DISCUSSION AND CONCLUSION
A dissociation constant of K d = 40 mM is no longera meaningful number; for example, with the molecularweight of protein plus peptide (14 kDa), one would con-clude that a 50% binding equilibrium is reached only at aprotein density of 560 g/l, i.e., in a sample that containsabout the same amount of water as it contains protein.This density is beyond a regime, in which Eq. 2 is valid.In other words, the peptide does not bind at all to theprotein in the trans -state, and unbinding is a barrier-less process. To illustrate this concept, Fig. 6a shows avery simple model for the free energy of ligand bindingas a function of the distance R of the ligand from theprotein. The protein-ligand complex is stabilized by abinding energy V b . Beyond the interaction range of theprotein ( R ), the free energy decreases due to an entropiccontribution, which accounts for the larger space avail-able to the ligand with increasing distance. The bindingenergy V b determines an energetic barrier for unbinding,while the barrier for binding is in essence of entropic na-ture. When the binding energy becomes zero, V b = 0,unbinding is barrier-less, see Fig. 6b. Upon cis -to- trans -isomerisation, we switch from the free energy of Fig. 6ato that of Fig. 6b. The ensemble, which has been equili-brated on the free energy surface Fig. 6a, all of the sud-den finds itself in a non-equilbrium situation, and startsto evolve on the free energy surface Fig. 6b.In the realm of femtochemistry, it is important todistinguish “kinetics” from “dynamics”. The on- and off-rates in Eq. 2 determine the probability of ligand bindingand unbinding per time unit, and completely mask thecomplexity of the process. This approach is valid whenthe barriers are high enough so that their crossing be-comes rate-limiting. In that limit, one can describe the kinetics by single numbers, k on and k off . On the otherhand, it is clear from MD simulations that ligand bindingor unbinding, when looked at on an atomistic level, is avery complex and very heterogenous process, with differ-ent pathways consisting of many small steps. Thatis what we call the “intrinsic dynamics” of the process.When removing the unfolding barrier in S-pep(6,13), wetake a glance at the intrinsic dynamics. Upon switch-ing into the trans -state, the S-peptide transiently adoptsvery heterogenous structures at the protein surface be-fore unbinding, and the stretched-exponential dynamicsreflect a broad distribution of unbinding pathways.The situation strongly resembles that of “down-hill”protein folding. When the folding barrier of a proteinis removed, e.g., by mutations, one observes the intrin-sic dynamics of the protein, sometimes also called the“speed limit” of protein folding.
At the same time,the dynamics becomes pronouncedly non-exponential, just like barrier-less unbinding in Fig. 4c. Similar tothe protein folding problem, it is expected that otherprobes, e.g., transient IR instead of transient fluorescencespectroscopy, will reveal different dynamical componentsof the process.One of the scenarios discussed in the context of ligandbinding is that of an induced fit, which is described bythe following reaction scheme: P + L k on −−− (cid:42)(cid:41) −−− k off P L k r − (cid:42)(cid:41) − k (cid:48) r P L (4)Here,
P L is a high-energy bound state that relaxes into
P L upon “fitting” the ligand into the binding site of aprotein. Since the binding rate is concentration depen-dent, the diffusive step will not be rate-limiting at highenough concentrations, while the second step remainsconcentration independent. Observing an effective rateof binding that saturates with increasing concentration isconsidered an indicator for an induced fit.
However,if the rate k r of the induced fit is too fast, this approachmight miss it, as it is not possible to increase the con-centrations sufficiently. For typical on-rate constants of10 − M − s − , and typical maximal protein con-centrations of 1 mM, that regime is already reached for k r > − s − . In addition to this inherent limita-tion, the time resolution of typical stop-flow instrumentsis in the range of 1 ms. The experiment we perform here is closely related, asit can also be described by Eq. 4 (where
P L would bethe transition state in Fig. 6), just that we consider herethe unfolding direction. The forward and backward rates k r and k (cid:48) r are connected to each other by the equilibriumconstant of the second step. In the barrierless case of-Fig. 6b, the equilibrium constant is 1, and k r = k (cid:48) r . Weobserve k (cid:48) r = 4 · s − , which is fast in light of thediscussion above, but slow in terms of the structural re-arrangements that are needed to fit the S-peptide intothe binding site of the S-protein. That is, the folding ofsmall α -helices in solution occurs on a typically 3-4 or-ders of magnitude faster timescale (10 − s − ), evenunder constraints. In conclusion, due to the slow diffusive step inherentto any binding experiments, many induced fit scenariosmight be missed in such experiments. In connectionwith a fast trigger, much quicker structural processescan be observed in the unbinding direction, revealing theintrinsic dynamics of the ligand during the unbindingevent. That “speed limit” is in the range of few 100 µ sfor the RNase S system. Acknowledgement:
We thank Claudio Zanobini andKarl Hamm for technical contributions at an early stageof this project. We also thank Rolf Pfister for thesynthesis of the photoswitch (BSBCA), the FunctionalGenomics Center Zurich, especially Serge Chesnov,for his work on the mass spectrometry. The workhas been supported by the Swiss National ScienceFoundation (SNF) through the NCCR MUST and Grant200020B 188694/1.
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