Real-time observation of ligand-induced allosteric transitions in a PDZ domain
Olga Bozovic, Claudio Zanobini, Adnan Gulzar, Brankica Jankovic, David Buhrke, Matthias Post, Steffen Wolf, Gerhard Stock, Peter Hamm
RReal-time observation of ligand-induced allosteric transitions in a PDZdomain
Olga Bozovic, Claudio Zanobini, Adnan Gulzar, Brankica Jankovic, David Buhrke, Matthias Post, SteffenWolf, Gerhard Stock, a) and Peter Hamm b) Department of Chemistry, University of Zurich, Switzerland Institute of Physics, University of Freiburg, Germany (Dated: 5 August 2020)
While allostery is of paramount importance for protein regulation, the underlying dynamical process of ligand(un)binding at one site, resulting time evolution of the protein structure, and change of the binding affinity ata remote site is not well understood. Here the ligand-induced conformational transition in a widely studiedmodel system of allostery, the PDZ2 domain, is investigated by transient infrared spectroscopy accompaniedby molecular dynamics simulations. To this end, an azobenzene derived photoswitch is linked to a peptideligand in a way that its binding affinity to the PDZ2 domain changes upon switching, thus initiating anallosteric transition in the PDZ2 domain protein. The subsequent response of the protein, covering fourdecades of time ranging from ∼ ∼ µ s, can be rationalized by a remodelling of its rugged free energylandscape, with very subtle shifts in the populations of a small number of structurally well defined states. It isproposed that structurally and dynamically driven allostery, often discussed as limiting scenarios of allostericcommunication, actually go hand-in-hand, allowing the protein to adapt its free energy landscape to incomingsignals. INTRODUCTION
Allostery represents the coupling of two sites in a pro-tein or a protein complex, where the binding of a ligandto the distal site modifies the affinity at the active site. Since biological function is intimately related to proteinstructure, ligand-induced changes of the protein’s func-tion (e.g., the transition from an inactive to an activestate) are often associated with a change of the protein’smean structure. On the other hand, ligand (un)bindingmay also alter the protein’s flexibility, which changes thevariance of the structure and gives an entropic contri-bution to the free energy. Referring to the associatedchange of the structural fluctuations, the latter scenario,termed “dynamic allostery,” has been invoked to explainapparent absence of conformational change upon lig-and (un)binding.
Studying the effects of dynamic al-lostery has been mainly done by NMR spectroscopy which, however, only accounts for equilibrium dynamics.While both models, structural change vs. dynamicchange, may appear plausible, the nature of the “al-losteric signal” is not known. A stringent examinationultimately requires us to study the genesis of allostery.This includes three steps: (1) The (un)binding of a lig-and (usually initiated by a change of its concentration )causes (2) the atoms of the protein to undergo a non-equilibrium time evolution, which (3) eventually leadsto a change of the binding affinity at a remote site ofthe protein. This so-called “allosteric transition” is anon-equilibrium process and has been observed directlyonly rarely, in part because the smallness of the struc- a) Electronic mail: [email protected] b) Electronic mail: [email protected] trans cis α β N α β C β β FIG. 1. Ligand-switched PDZ2 domain. Main secondarystructural elements and C α -distances d , and d , dis-cussed below are indicated. In the trans conformation of thephotoswitch (red), the ligand (blue) fits well in the bindingpocket, while it starts to move out when switching to cis . tural changes makes the transition pathways challeng-ing to observe experimentally, and also because ofthe time-scale limitations of molecular dynamics (MD)simulations. In this work, we outline an approachto study the first two steps, i.e., the ligand-induced al-losteric transition, employing a PDZ2 domain as modelsystem.Known for their modest conformational change uponligand binding, PDZ domains are considered as prime ex-amples of dynamic allostery.
PDZ domain-mediatedinteractions play a pivotal role in many signal transduc-tion complexes.
Allosteric information flow in PDZdomains is thought to be transduced via conserved al-losteric networks in the protein.
The system con-sidered here is the PDZ2 domain from hPTP1E (hu-man tyrosine phosphatase 1E) and a RA-GEF-2 peptidederivative (Ras/Rap1 associating guanidine nucleotideexchange factor 2) with an azobenzene moiety linked as a r X i v : . [ phy s i c s . b i o - ph ] A ug photoswitch, see Fig. 1. It was recently reported for avery similar system that the phosphorylation of the ser-ine (-2) residue, a common target in regulatory processesof PDZ domains, leads to a ∼ We will see thatthe binding affinity can be perturbed to the same extent( ≈ where the photoswitch was covalently linked across thebinding pocket of the PDZ2 domain. In addition, usingthe ligand as a trigger, one can apply this strategy tovirtually any system.By photo-isomerizing the azobenzene moiety, wechange the binding affinity of the ligand at a preciselydefined point in time. We employ time-resolved vibra-tional spectroscopy in connection with a isotope labelingstrategy to monitor the structural change of the proteinin real time, and perform extensive (more than 0.5 msaggregate simulation time) all-atom non-equilibrium MDsimulations combined with Markov modeling to interpretthe experimental results in terms of the structural evo-lution of the system. We find that the mean structuralchange of the protein is rather small. Yet, in both ex-periment and MD simulations the free energy surface ofthe protein can be characterized by a small number ofmetastable conformational states. In agreement with theview of allostery as an interconversion between the rel-ative population of metastable states, we see how theligand-induced response of the PDZ2 domain is best de-scribed as remodelling of the free energy landscape, and how the response is transduced from the ligand tothe protein without introducing a significant structuralchange. RESULTSExperimental
To set the stage, we have investigated the influenceof photoswitching of the ligand on its binding affinity.By choosing the spacing between the anchoring points ofthe azobenzene moiety, the peptide ligand was designedsuch that the longer trans conformation mimics the na-tive extended β -strand conformation, while the cis con-figuration shortens the peptide and perturbs it from itsextended form. To that end, the alanine residue at posi-tion -1 (the ligand is labelled by negative numbers) waschosen as the first anchoring spot for the photoswitch,since it has been shown that a mutation at this positiondoes not significantly affect the binding, while residuesthat are crucial for binding (Val(0), Ser(-2) and Val(-3))are preserved. The second anchoring point chosenwas Asp(-6) which allows the peptide to be maximallystretched in the trans configuration of the photoswitch.Protein and peptide have been expressed/synthesized us- ing standard procedures, see Materials and Methodsfor details. The dissociation constants ( K D ) in the twoconfigurations of the photoswitchable peptide were de-termined by ITC, fluorescence and CD spectroscopy (seeSupplementary Figs. S2 and S3). The obtained val-ues averaged for all methods ( K D,trans = 2 . ± . µ M, K D,cis = 9 . ± . µ M, see Supplementary Table S1)reveal an appreciable ∼ cis state being the destabilized one, asanticipated.Considering these binding affinities and the relativelyhigh concentrations needed for the transient IR experi-ment (1.25 mM for the peptide and 1.5 mM for the pro-tein), it is clear that most of the ligands are bound inboth states to a protein of the photoswitch (97% in cis and 99% in trans ), hence we will not observe many bind-ing or unbinding events. Furthermore, as binding andunbinding in similar PDZ/ligand systems was observedto occur on 10 – 100 ms time-scales, these processesare hardly within the time window of our experiment.Nevertheless, we will be able to observe the adaptationof the protein to a perturbed peptide conformation in thebinding pocket and its transition to unspecific binding onthe protein surface.We investigate that process with the help of transientIR spectroscopy in the range of the amide I band (seeMaterials and Methods for details). This band origi-nates from mostly the C=O stretch vibration of the pep-tide/protein backbone, and is known to be strongly struc-ture dependent. While one cannot invert the problemand determine the structure of a protein from the amideI band, any change in protein structure will cause smallbut distinct changes in this band (see Fig. 2 a-c).Figure 2 shows the transient IR response in the spec-tral region of the amide I vibration after photoswitchingin either the trans -to- cis (panels d-f) or the cis -to- trans direction (panels g-i). To be directly comparable, thetwo data sets were scaled in a way that they refer tothe same amount of isomerizing molecules, and not thesame amount of excited molecules. The scaling took intoaccount the different pump-pulse energies used in the ex-periments (see Materials and Methods), cross sections(23500 cm − M − for trans at 380 nm vs 2000 cm − M − for cis at 420 nm) , and isomerization quantum yields(8% for trans -to- cis switching and 62% for cis -to- trans switching). The left panels of Fig. 2 show the results for the wildtype PDZ2 domain, and the middle panels those withthe protein C N labelled, which down-shifts the fre-quency of the amide I band by ≈
25 cm − . The transientIR responses of both isotopologues look quite similar, asthe signal is dominated by the photoswitchable peptide,which is perturbed directly by the azobenzene moiety. Toremove that contribution and to isolate the smaller pro-tein response, the two signals have been subtracted inthe right panels of Fig. 2, with some of the more promi-nent features highlighted in Fig. 3a-d. In this way, wetake advantage of the fact that only the amide I band Probe Frequency (cm -1 ) Δ A ( n o r m . ) P u m p p r o b e d e l a y ( s ) P u m p p r o b e d e l a y ( s ) Wild type PDZ2 Difference C N PDZ2 t r an s - t o - c i s c i s - t o - t r an s a b cd e fg h i *5 *1*1*2
42 µs trans -to- ciscis -to- trans
42 µsFTIR trans -to- cis (/16) *3 *4
FIG. 2. Transient IR spectra of PDZ2 in the region of the amide I band. Panels (a-c) compare transient data at long pump-probe delay times (averaged from 20 µ s to 42 µ s to increase signal-to-noise) for trans -to- cis (blue) and cis -to- trans (red)switching, together with a properly scaled trans -minus- cis FTIR difference spectrum (black). Panels (d-f) show the completetransient data for trans -to- cis switching, and panels (g-i) for cis -to- trans switching. Left panels show the data for the wild type(WT) protein, middle panels for the sample with the protein C N labelled (the peptide ligand contains naturally abundant C N), and right panels the C N-WT difference data. Red colours in panels (d-i) indicate positive absorbance changes,blue colors negative absorbance changes. The relative scaling of the data sets and the labelled features are discussed in thetext. of the protein is affected by C N-isotope labelling andnot that of the photoswitchable ligand. By doing so,we implicitly assume that the spectra of protein and lig-and are additive and that coupling between them can beneglected. Great care was taken that protein and pep-tide concentrations were exactly the same in both exper-iments. Furthermore, both experiments were performedright after each other without changing any setting of thelaser setup.Overall, the kinetics of these double-difference spec-tra are quite complex and cover many orders of magni-tudes in time. Furthermore, the responses for trans -to- cis (Figs. 2f and 3a,c) vs cis -to- trans switching (Figs. 2iand Fig. 3b,d) are not mirror-images from each other,which one might expect if the protein would take thesame pathway in the opposite direction. For example, thestrongest band at 1636 cm − (marked as *1 in Figs. 2fand 3a) reveals the biggest step at around 1 ns in the trans -to- cis data, while the complementary feature in cis -to- trans data (marked as *2 in Figs. 2i and 3b) de- velops in a very stretched manner from ≈ ≈ µ s.Worthwhile noting is also a transient band at 1579 cm − in the trans -to- cis data (marked as *3 in in Figs. 2f and3c), living up to ≈
100 ns, which has no complementarycounterpart in the cis -to- trans data (Figs. 2i and 3d).The red lines in Figs. 3a-d are fits revealed from a time-scale analysis of the signals using a Maximum Entropymethod: S ( ω i , t ) = a ( ω i ) − (cid:88) k a ( ω i , τ k ) e − t/τ k . (1)Here ω i denotes the probe frequency and t the delaytime of the signal, which is represented by a multiex-ponential function with time-scales τ k . The time-scalespectra a ( ω i , τ k ) are shown in Figs. 3a-d as blue lines.Each of the kinetic processes discussed above shows upas a peak in these time-scale spectra, and the pat-tern of peaks is different for all the examples shownin Figs. 3a-d. Nevertheless, the dynamical content, D ( τ k ) = [ (cid:80) i a ( ω i , τ k ) /n ] / , which averages over the trans‐to‐cis cis‐to‐trans ‐1 (feature *1) 1636 cm ‐1 (feature *2)1579 cm ‐1 (feature *3) 1579 cm ‐1 averaged lifetime spectrum Time (s) Time (s)a bc de f averaged lifetime spectrum g h*4 E x p e r i m e n t A ( n o r m . ) D ( n o r m . ) D ( n o r m . ) A ( n o r m . ) M D averaged lifetime spectrum averaged lifetime spectrum FIG. 3. Transient C N-WT difference data at 1636 cm − (panels a,b) and 1579 cm − (panels c,d) for trans -to- cis (left)and cis -to- trans (right) switching, highlighting features la-belled as *1 to *3 in Fig. 2. Red lines are fits obtained fromthe time-scale analysis in Eq. (1), blue lines represent theresulting time-scale spectra a ( ω i , τ j ). Panels (e,f) show thecorresponding dynamical content; the heat signal labelled as*4 is discussed in the text. Panels (g,h) show the MD dynam-ical content, obtained from a time-scale analysis of the non-equilibrium time evolution of the mean C α -distances (Supple-mentary Fig. S5). complete data set shown in Supplementary Fig. S4, seemsto indicate a relatively small number of discrete timescales, see Figs. 3e,f. We attribute the first peak around100 ps (labeled as *4 in Figs. 2f and 3e) to a “heat signal”originating from the vibrational energy released by thephoto-isomerization of the azobenzene moiety, an effectthat is seen universally in this type of experiments. The transient spectra at the latest pump-probe de-lay time that is accessible to our transient experiment(i.e., 42 µ s) are shown in Figs. 2a-c in blue for trans -to- cis switching and in red for cis -to- trans switching.They are compared to a properly scaled trans -minus- cis FTIR difference spectrum (black), which represents theresponse at effectively infinite time after photoswitching.The counterpart of the negative band in the blue andblack trans -to- cis spectra at 1600 cm − (marked as *5 inFigs. 2c) has not yet evolved in the red cis -to- trans spec-trum. We conclude from this observation that the cis -to- trans transition is not completely finished after 42 µ s. MD simulations
To aid the interpretation of the above experiments,we performed all-atom explicit-solvent MD simulationsof the cis and trans equilibrium states as well as non-equilibrium MD simulations of the ligand-induced con-formational changes of PDZ2. Using the GROMACSv2016 software package and the Amber99*ILDN forcefield, we collected in total 510 µ s simulation time(see Materials and Methods). For the structural charac-terization of the protein, we determined 56 C α -distances d i,j between residues i and j that are not redundant(such as d i,j and d i,j ± ) and whose ensemble averagechanges significantly ( (cid:104) ∆ d ij (cid:105) ≥ . followed by ro-bust density-based clustering and a recently proposedmachine learning approach (see Materials and Meth-ods and Supplementary Fig. S6 for details). While weused six dimensions for the clustering, we find that two C α -distances suffice to qualitatively characterize the con-formational distribution of PDZ2: d , accounting forthe width of the binding pocket located between β and α , as well as d , representing the distance between N-terminus and α - β loop, which reflects the compactnessof the C- and N-terminus region (see Fig. 1). Employingthese coordinates, Fig. 4a shows the free energy surface∆ G = − k B T ln P ( d , , d , ), obtained from 5 × µ s-long trans equilibrium simulations describing the ligand-bound state of PDZ2. The free energy landscape revealsfour well-defined local minima indicating metastable con-formational states of the system. Density-based cluster-ing identifies state as close to the crystal structure, while state indicates an opening of the binding pocket.Both states are mirrored by states and , which areshifted to larger values of coordinate d , .Upon switching the ligand from trans to cis configura-tion, PDZ2 undergoes a non-equilibrium time evolutionuntil it relaxes within a few microseconds (see below)into its cis equilibrium state, describing the perturbedprotein-ligand complex. Performing 25 × µ s-long trans -to- cis non-equilibrium simulations, we took the last 7 µ sof each trajectory to estimate the rather heterogeneousconformational distribution of the cis equilibrium state.When we compare the resulting free energy landscapesof cis and trans , Figs. 4a,b reveal that the accessible con-formational space in cis is considerably increased, alongwith the occurrence of additional state that reports ona further opening of the binding pocket. Representingthe populations of all states in trans and cis as a his-togram, Fig. 4d demonstrates that the photoswitching ofthe ligand causes a notable ( (cid:46)
20 %) shift of the statepopulations, mostly from state to states and .To illustrate the conformational changes associatedwith these states, Fig. 4e displays an overlay of minimum-energy structures of states and as well as the cis - d , [ n m ] . . . . .
82 1 1 . . . . . transtranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstranstrans aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa d , [nm] . . . . . cisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscisciscis bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb . . . . . no ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligandno ligand ccccccccccccccccccccccccccccccccccccccccc . . . . . . . . . . p o pu l a t i o n trans ddddddddddddddddddddddddddddddddddddddddd state cis e state 5state 2state 1 f state 1 state 2 state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3state 3 state 4 state 5 FIG. 4. Identification of metastable conformational states. Free energy landscapes (in units of k B T ) obtained from the (a) trans , (b) cis and (c) ligand-free equilibrium simulations of PDZ2, plotted as a function of two essential inter-residue distances.The unlabeled state-like feature at the bottom right of (b) represents weakly populated ( (cid:46) and .(d) Histogram of the state populations in trans and cis equilibrium, revealing the ligand-induced population shift of PDZ2. (e)Comparison of minimum-energy structures the of states , and , revealing an increased opening of the ligand binding pocketby a downward motion of α . (f) Structures of states together with position densities of the ligand. The isosurface encloses avolume with a minimal probability of 0.4 to find a ligand atom within in all simulation snapshots belonging to a specific state.Fixed points for the comparison are the C α atoms of strands β and β . specific state . We find that the opening of the bind-ing pocket described by d , mainly reflects a shift ofthe α helix down and away from the protein core. In-terestingly, the structural rearrangement between mainstates and results in an overall root mean squared(RMS) displacement of only (cid:46) ∼
5) contacts to change (Supplementary Fig. S7). Thisis in striking contrast to the cross-linked photoswitch-able PDZ2 studied by Buchli et al. where 34 contactchanges were found for the trans -to- cis reaction, and cis and trans free energy landscapes hardly overlapped. This findings indicate that ligand-switching is consider-ably less invasive than a cross-linked photoswitch andtherefore better mimics the natural unbiased system.Is the above discussed population shift as well as thevery occurrence of states an inherent property of the pro-tein’s rugged free energy landscape, or are these fea-tures rather induced by the ligand? Figure 4c addressesthis question by showing the free energy landscape ob-tained from previously performed 6 × µ s-long simulationsof PDZ2 without a ligand . While the state separationalong coordinate d , still exists, we find that states , and merge into a single energy minimum. It is centeredat the position of state , but is wide enough to cover alarge part of states and . Similarly states and form a weakly populated (2 %) single minimum. This in- dicates that ligand-free PDZ2 provides the flexibility toassess the entire free energy landscape explored duringbinding and unbinding, while the interaction with theligand appears to stabilize conformational states and . Showing protein structures of the main states togetherwith position densities of the ligand, Fig. 4f illustratethese interactions (see also Supplementary Fig. S8). Forone, we notice that the opening and closing of the bind-ing pocket (described by d , ) is associated with theconventional binding of the ligand’s C-terminus in thispocket, which stabilizes closed state in trans . In theopen state , the probability to find the ligand in its bind-ing mode is significantly decreased, pointing to a reducedligand affinity of the protein. On the other hand, we findthat the distinct conformations of the protein’s terminidescribed by d , are a consequence of the formation ofcontacts with the ligand’s N-terminus in states and ,which are absent in states , and . In particular, state represents a situation where the hydrophobic photo-switch of the ligand forms a contact with a hydrophobicbulge at the protein surface around Ile20, which can beclassified as unspecific binding of the ligand to the pro-tein surface.Adopting our trans -to- cis non-equilibrium simulations,we can describe the overall structural evolution of PDZ2in terms of time-dependent expectation values of variousobservables. As an example, Figs. 5a,b show the timeevolution of the two C α -distances d , and d , intro-duced above. Following trans -to- cis ligand switching, ittakes about 100 ns until the sub-picosecond photoiso-merization of the photoswitch affects the protein’s bind-ing region (indicated by d , ), which becomes wideras the ligand moves out. The flexible N-terminal regionindicated by d , , on the other hand, undergoes con-formational changes already within a few nanoseconds.The weak correlation between the two inter-residue dis-tances (i.e., (cid:104) d , d , (cid:105) ( (cid:104) d , (cid:105)(cid:104) d , (cid:105) ) − / (cid:46) .
02 forall data), however, indicates that this early motion ofthe terminal region may be not directly related to thefunctional dynamics of PDZ2. Interestingly, the associ-ated root mean squared deviations (RMSD) of the twodistances show quite similar behavior. Moreover, Sup-plementary Fig. S9 displays various ligand-protein dis-tances and contact changes, which illustrate that the lig-and leaves the binding pocket on time-scales of 0.1 – 1 µ s.When we calculate the dynamical content of all consid-ered intraprotein C α -distances, we obtain a time-scaledistribution that roughly resembles the experimental re-sult (Fig. 3g,h).It is instructive to consider the resulting time-dependent populations of the protein’s metastablestates. Choosing initial conditions close to the crystalstructure, Fig. 5c exhibits the trans -to- cis time evolu-tion of the state populations. The system starts at time t = 0 almost completely in state and converts to theother states within microseconds. To rationalize thesefindings, we construct a Markov state model (MSM)which describes the conformational dynamics of PDZ2via memory-less jumps between metastable states. Tothis end, we calculate a transition matrix T containingthe probabilities T ij , that the system jumps from state i to j within lag time τ lag , and determine its eigenvectors ψ k and eigenvalues λ k (see Materials and Methods andSupplementary Fig. S10 for technical details). As a firstimpression, Figs. 5c,d compares the state populations ob-tained from the non-equilibrium MD simulations and thecorresponding MSM predictions (using τ lag = 1 ns). Wefind excellent agreement for the first three decades oftime, but only qualitative agreement in the last decade,which reflects the bias of our non-equilibrium MD sim-ulations towards shorter time-scales (75 × µ s-long and25 × µ s-long data). Showing a network representationof the MSM, Fig. 5e illustrates the connectivity and tran-sition times of the system. We see that the open-closetransition of the binding pocket occurs on a time-scale of ∼ µ s, whereas transitions from states and to states and are a factor 4 faster with a back-rate that is evena factor 10 faster.Assuming a time-scale separation between fast in-trastate fluctuations and rarely occurring interstate tran-sitions, MSM theory states that the time-dependent ex-pectation value of any dynamical observable can be writ-ten as a sum over exponential functions e − t/t k weighted − − − − − − − − − − d i s t a n ce ( n m ) time (s) RMSD d ( t ) − d (0) aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa d , time (s) bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb d , − − − − − − − − − − p o pu l a t i o n time (s)123 45 ccccccccccccccccccccccccccccccccccccccccc time (s) ddddddddddddddddddddddddddddddddddddddddd − − − − −
54 321 eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee p o pu l a t i o n time (s) fffffffffffffffffffffffffffffffffffffffff FIG. 5. Time evolution of various structural descriptors,following trans -to- cis ligand-switching of PDZ2. Shown aremeans (blue) and RMSD (orange) of C α -distances (a) d , and (b) d , , as well as (c,d,f) populations of conformationalstates. For easier representation, all MD data were smoothed.Starting at time t = 0 almost completely in state , we com-pare results from (c) the non-equilibrium MD simulations to(d) the corresponding predictions of a Markov state model(MSM). (e) Network representation of the MSM. The size ofthe states indicate their population, the thickness of the ar-rows and numbers indicate the transition times (in µ s). Forclarity, we discard transitions that take longer than 2 . µ s. (f)MSM simulations of the trans -to- cis transition, using trans equilibrium initial conditions. by the projection of the observable onto the k th eigen-vector of transition matrix T . The implied time-scales t k = − τ lag / ln λ k of the MSM therefore govern the timeevolution of such different observables as vibrationalspectra and state populations. To facilitate a compar-ison of experimental and simulated time evolutions, werun a MSM simulation using trans equilibrium initial con-ditions, which is also the starting point of the trans -to- cis experiments. Comparing the simulation results (Fig.5f) to the experimental time traces (Fig. 3), we findthat both spectral and population evolutions appear tobe completed on microsecond time-scale. Moreover, theMSM populations exhibits various transient features ontime-scales of 10 – 100 ns, which are also present in theexperimental time signals.
DISCUSSION AND CONCLUSIONS
Combining transient IR spectroscopy and non-equilibrium MD simulations, we have described theligand-induced conformational transition in the PDZ2domain, which is thought to be responsible for proteinallosteric communication. We have found that the freeenergy landscape of PDZ2 can be described in termsof a few metastable states with well-defined structure(Fig. 4), although the mean structural changes upon lig-and switching are rather small. That is, the secondaryand tertiary structure of the protein are quite similar( (cid:46) ∼
20 %) shifts of the state’s population arefound (Fig. 4b). On average, the measurable structuralchange is therefore only in the order of 0.2 ˚A. In lightof this result, it is remarkable that we can observe suchminor structural changes by transient IR spectroscopy(Fig. 2), unpinning the extraordinary structural sensitiv-ity of the method.Using isotope labeling to discriminate the dynamics ofprotein and ligand, the resulting time-resolved double-difference IR spectra have revealed complex kinetics ofthe protein that cover many time-scales (Fig. 2). Thespectra for trans -to- cis and cis -to- trans ligand-switchingare not mirror-images from each other, and the trans -to- cis signals exhibit short-time transients that are notfound for cis -to- trans . Moreover, the cis -to- trans transi-tion does not seem to be finished within 42 µ s (Fig. 2c).The overall slower response of the cis -to- trans transitionreflects the general observation that enforced leaving of awell-defined (low entropy) ligand binding structure (here trans ) occurs faster than starting in a conformationallydisordered (high-entropy) state (here cis ) and trying tofind stabilizing interactions to end in a more organizedstructure. More specifically, the trans -to- cis non-equilibrium sim-ulations reveal that the ligand remains bound with itsC-terminus to the protein binding site between β and α up to about 1 µ s. In this way, it stabilizes the mainbound protein conformation (state ). At longer times, itstarts to move out from the binding pocket, but remainsnon-specifically bound to the protein surface. While dif-fusion on the surface may continue for long times after trans -to- cis switching, it only little affects the protein in-ternal structure. Nevertheless, this diffusion will be thefirst rate-limiting step after cis -to- trans switching, whichmight be the reason that the ligand does not completelylocalize in the binding pocket within 42 µ s.The existence of well-defined metastable conforma-tional states implies a time-scale separation between fastintrastate fluctuations and rarely occurring interstatetransitions. This allowed us to construct a Markov statemodel (MSM), which illustrates the connectivity andtransition times between the metastable states (Fig. 5d).In particular, the discrete time-scales predicted by theMSM are directly reflected in the dynamical content cal-culated for experiments and MD simulations (Fig. 3e-h), which both cover time-scales from ∼ µ s. Re-flecting different observables (transition dipole vs. C α -distances, respectively), the weights of the various peaksare different.While ligand switching was shown to cause a confor-mational transition of PDZ2 in terms of the mean struc-ture, at the same time it may also effect a change of theprotein’s fluctuations. Comparing the time evolution ofthe means of the distances and their RMSD, Figs. 5a,breveal that the two quantities correlate closely, a behav-ior that is found for all considered C α -distances (Sup-plementary Fig. S5). This finding reflects the fact thatthe C α -distance distributions pertaining to the individualstates are in most cases well separated (SupplementaryFig. S11), such that a transition between two states af-fects both mean and variance. Accounting for an entropiccontribution of the conformational transition, the lattereffect is often referred to as “dynamic allostery”. Theabove findings indicate that allosteric transitions may in-volve both, conformational and dynamic changes in thecase of the PDZ2 domain. The answer to what is thedominant effect will greatly depend on the system underconsideration and on the applied experimental method.While the overall structural change ( (cid:46) . but dephasing dueto fast fluctuation might also affect the IR lineshape.In conclusion, we have characterized the non-equilibrium allosteric transition in a joint experimental-theoretical approach. The protein per se was kept un-modified, hence ligand-switching mimics very closely thenaturally occurring allosteric perturbation caused by lig-and (un)binding events. We employed a widely stud-ied model system for this purpose, the PDZ2 domain,which is small enough to allow for a characterizationof the process in atomistic detail by MD simulations,but we believe that the findings are of more general na-ture. That is, while the ligand-induced allosteric transi-tion originates from a population shift between variousmetastable conformational states, the measurable meanstructural change of the protein may be tiny and there-fore difficult to observe . Moreover, we suggest that theseparation between purely dynamically driven allosteryand allostery upon a conformational change may not beas clear-cut as previously thought, but rather that theremay be an interplay between both that allows proteinsto adapt their free energy landscape to incoming signals.The photo-switching approach presented here is very ver-satile, and allows us to shed light on the aspects of “time”and “speed” in allosteric communication. MATERIALS & METHODSA. Protein and Peptide Preparation
Expression of the wild type PDZ2 domain from hu-man phosphatase 1E, isotope labelled ( C N) pro-tein variant and synthesis of the photoswitchable peptideligand was performed as described earlier.
The wildtype RA-GEF-2 sequence was modified in order to enablecross-linking the photoswitch, while preserving residuesthat are important for regulation and binding. That is,amino acids at positions (-1) and (-6) were chosen as an-choring points for the photoswitch and mutated into cys-teine residues. Four N-terminal residues (RWAK) wereadded to the sequence in order to improve the water sol-ubility and facilitate the concentration determination ofthe construct. Final sequence of the peptide was RWAK-SEAKECEQVSCV. The purity of all samples was con-firmed by mass spectrometry analysis (Fig. S1). All sam-ples were dialyzed against 50 mM borate, 150 mM NaClbuffer, pH = 8.5. For transient infrared measurements,samples were lyophilized and resuspended in D O. Incu-bation of the samples in D O overnight at room tempera-ture before the measurements eliminated H/D exchangeduring experiments. The concentration of the sampleswas determined via the tyrosine absorption at 280 nm forthe protein and 310 nm for the peptide and confirmed byamino-acid analysis.
B. Determining the Binding Affinity
Isothermal titration calorimetry (ITC) measurementswere performed on a MicroCal ITC200 (Malvern, UK).In order to ensure the obtained values for the cis and trans measurement were mutually comparable, the ex-periments were performed using the same stock solutionof the peptide and protein for both measurements, andunder exactly the same experimental conditions. Theexperiment was performed in triplicate in order to en-sure the reproducibility of the data. The sample cell wasloaded with 250 µ l of 80 µ M PDZ2 domain solution andthe syringe was loaded with 40 µ l of 800 µ M photoswitch-able peptide solution. For the trans measurement, thesystem was kept in the dark for the duration of the ex-periment, while for the cis measurement the syringe wasconstantly illuminated with a 370 nm cw laser (Crys-taLaser, power ≈
90 mW). The results are shown inFig. S2.As alternative method to determine the binding affin-ity, we also used circular dichroism (CD) spectroscopyas well as fluorescence quenching. Both spectroscopicsignals change upon the formation of a protein-ligandcomplex, hence, when measuring them in dependenceof peptide and protein concentration, the binding affin-ity can be fitted assuming a bimolecular equilibrium.CD measurements were done on Jasco (Easton, MD)model J810 spectropolarimeter in a 0.1 cm quartz cuvette as described previously. . Intrinsic tryptophan fluores-cence quenching experiment was done on PelkinElmerspectrofluorimeter as described previously. In eithercase, the protein concentration was kept constant at5 µ M, respectively, while the peptide concentrations werevaried. Fig. S3 shows the results for the CD spec-troscopy and trypthophan fluorescence quenching, whileTable S1 compares the binding affinities obtained fromall different methods.
C. Transient IR Spectroscopy
Transient VIS-pump-IR-probe spectra were recordedusing two electronically synchronized Ti:Sapphire lasersystems running at 2.5 kHz. The wavelength of thepump-laser was tuned as to obtain 380 nm pump pulses(2.1 µ J) for the trans -to- cis experiment, and 420 nm(1.3 µ J) for the cis -to- trans experiment, respectively, via second harmonic generation in a BBO crystal. The beamdiameter of the pump pulse at the sample position was ≈ µ m, employing a pulse duration of ≈
200 ps (byextracting the light directly after the regenerative am-plifier and before the compressor) to minimize the sam-ple degradation during the measurements. Mid-IR probepulses centered at ≈ − (pulse duration ≈
100 fs,beam diameter on the sample ≈ µ m) were obtained ina optical parametric amplifier (OPA), passed througha spectrograph and detected in a 2 ×
64 MCT array detec-tor with a spectral resolution of ≈ − /pixel. Pump-probe spectra were acquired up to the maximum delayvalue of ≈ µ s with a time resolution of ≈
200 ps. Nor-malisation for noise suppression was performed as de-scribed in Ref. .The samples ( ≈ µ l) were pumped through a closedflow-cell system purged with N . The system consistedof a sample cell with two CaF windows separated by a50 µ m Teflon spacer and a reservoir. The flow speed inthe sample cell was optimized in order to minimize lossof sample at the largest pump-probe delay time ( ≈ µ s)on the one hand, but to have the sample exchanged es-sentially completely for the subsequent laser shot after400 µ s on the other hand. The concentrations of thesamples were set at 1.25 mM for the peptide and 1.5 mMfor the protein. A slight excess of protein was neededto ensure that the peptide was fully saturated with theprotein; in order to eliminate the response of free, pho-toswitchable peptide. As a reference, FTIR differencespectra have been taken in a Bruker Tensor 27 FTIRspectrometer, using the same sample conditions.For the experiment with trans -to- cis switching, we re-lied on thermal cis -to- trans back reaction. By comparingits rate with the isomerization probability induced by the380 nm pump light (determined by pump light power,total sample volume, absorption cross sections, andisomerization quantum yield ), we estimated that thephoto-equilibrium in the total sample volume is 70%/30% trans / cis during measurement. It furthermore helps thatthe absorption cross section at 380 nm of the azobenzenemoiety in the trans -state is ≈
20 times larger than thatof the cis -state, which leads us to conclude that > trans -to- cis experiment undergothe desired isomerisation direction.For the experiment with cis -to- trans switching, thesample could be actively switched back by illuminatingthe reservoir with an excess of light at 370 nm from a cwlaser (CrystaLaser, 150 mW). D. MD Simulations
All MD simulations of PDZ2 were performed usingthe GROMACS v2016 software package and the Am-ber99*ILDN force field. Force field parameters of theazobenzene photoswitch were taken from Ref. . Protein-ligand structures were solvated with ca. 8000 TIP3P wa-ter molecules in a dodecahedron box with a minimalimage distance of 7 nm. 16 Na + and 16 Cl - were addedto yield a charge-neutral system with a salt concentra-tion of 0.1 M. All bonds involving hydrogen atoms wereconstrained using the LINCS algorithm, allowing for atime step of 2 fs. Long-range electrostatic interactionswere computed by the Particle Mesh Ewald method, whereas the short-range electrostatic interactions weretreated explicitly with the Verlet cutoff scheme. Theminimum cutoff distance for electrostatic and van derWaals interactions was set to 1.4 nm. A temperatureof 300 K was maintained via the Bussi thermostat (akavelocity-rescale algorithm) with a coupling time constantof τ T = 0.1 ps. A pressure P =1 bar was controlled us-ing the pressure coupling method of Berendsen with acoupling time constant of τ P = 0.1 ps.The starting structure of the photoswitched ligandbound to PDZ2 was prepared previously (see Ref. )based on the crystal structure (PDB ID 3LNX ). Here,the azobenzene photoswitch was attached in trans con-formation to the ligand at positions (-6) and (-1), whichhad been mutated to cysteins as in experiment to providecovalent connection points. Residues missing at the N-terminus of the ligand were added (see Sec. A). FollowingNPT equilibration of the system in trans conformationfor 10 ns, 4 statistically independent (i.e., with differentinitial velocity distributions) NVT runs of 100 ns eachwere performed. For one, we selected 5 randomly chosensnapshots from the end of these trajectories to perform5 × µ s-long trans equilibrium simulations. Moreover,we selected 25 randomly chosen snapshots from each ofthe last 50 ns of these four NVT trajectories to per-form trans -to- cis nonequilibrium simulations, yielding atotal of 100 starting structures which consists mostlyof metastable state 1 (for state definition, see Sec. E).Employing these initial conditions, trans -to- cis photo-switching was performed using a previously developedpotential-energy surface switching approach . All 100 trans -to- cis nonequilibrium simulations were run for1 µ s; 25 of them were extended to a length of 10 µ s. Upon switching the ligand from trans to cis config-uration, PDZ2 undergoes a nonequilibrium time evolu-tion until it relaxes within a few microseconds (see be-low) into its cis equilibrium state, describing the un-bound protein-ligand complex. Performing 25 × µ s-long trans -to- cis nonequilibrium simulations, we took thelast 7 µ s of each trajectory to estimate the rather het-erogeneous conformational distribution of the cis equi-librium state. To generate initial structures for cis -to- trans photoswitching, we took from the 25 trans -to- cis trajectories 100 randomly chosen snapshot at a simula-tion time around 3.0 µ s. Following photoswitching, 100 cis -to- trans nonequilibrium trajectories were simu-lated for a trajectory length of 1 µ s; 10 simulations wereextended to a length of 8 µ s.Gromacs tools gmx angle and gmx mindist were em-ployed to compute backbone dihedral angles, interresidue C α -distances, and the number of contacts between var-ious segments of PDZ2. Time-dependent distributionsand mean values of these observables were calculated viaan ensemble average over 100 nonequilibrium trajecto-ries. E. Dimensionality reduction and clustering
To choose suitable internal coordinates that accountfor the conformational transitions of the system, wedetermined 56 C α -distances d i,j between residues i and j that are not redundant (such as d i,j and d i,j ± ) andwhose ensemble average changes significantly ( (cid:104) d ij (cid:105) ≥ . trans -to- cis nonequi-librium simulations, see Fig. S5. Moreover, we consideredall backbone dihedral angles that show a change of (cid:38) ◦ from their initial value during the trans -to- cis nonequi-librium simulations.Since the interresidue C α -distances appear to pro-vide more information, these coordinate are chosen forthe subsequent principal component analysis (PCA),which was performed on all data. For adequate rela-tive weighting of short and long distances, the data wasnormalized. Diagonalizing the resulting covariance ma-trix, we obtain its eigenvectors (yielding the PCs) andeigenvalues (reflecting the fluctuations of the PCs). Thefirst two PCs cover 43 % of the overall fluctuations, whilesix PCs yield about 65 %. Calculating the free energyprofiles pertaining to the PCs, we find that in particu-lar PC 1–4, 6 and 7 show multistate behavior reflectingmetastable states.Including these 6 PCs, we performed robust density-based clustering, which first computes a local free en-ergy estimate for every structure in the trajectory bycounting all other structures inside a 6-dimensional hy-persphere of fixed radius R . Normalization of these pop-ulation counts yields densities or sampling probabilities P , which give the free energy estimate ∆ G = − k B T ln P .Thus, the more structures are close to the given one, thelower the free energy estimate. By reordering all struc-0tures from low to high free energy, finally the minimaof the free energy landscape can be identified. By iter-atively increasing a threshold energy, all structures witha free energy below that threshold that are closer thana certain lumping radius will be assigned to the samecluster, until all clusters meet at their energy barriers.In this way, all data points are assigned to a cluster asone branch of the iteratively created tree. For PDZ2, weused a hypersphere R = 0 .
579 that equaled the lumpingradius employed in the last step.Figure S6(top) shows the resulting total number ofstates obtained as a function of the minimal populations P min a state must contain. Here we chose P min = 50 000,resulting in a clustering into 12 states. According to vi-sual inspection of the resulting free energy landscapes(Fig. S6(middle)), these states separate accurately alldensity maxima of the system. Since the 5 lowest pop-ulated states cover less than 5 % of the total popula-tion, we lumped them to main states to as follows:(
1, 9 ) → , (
2, 10 ) → , (
4, 12 ) → , (
5, 8, 11 ) → . This isjustified due to their geometric vicinity in the free energylandscape (Fig. S6(middle)), as well as due to their ki-netic vicinity in the transition matrix. Following the cal-culation of the time-dependent states populations, in alast step we lumped states (
4, 7 ) → and states (
5, 6 ) → for the sake of easy interpretability.Finally we employed a recently proposed machinelearning approach to identify the internal coordinatesthat allow to discuss the 5 main states of PDZ2 in atwo-dimensional free energy landscape. On the basis ofthe decision-tree based program XGBoost, we traineda model that determines the features of the molecular co-ordinates that are most important to discriminate givenmetastable states. Using a new algorithm that exploitsthis feature importance via an iterative exclusion princi-ple, we identified the essential internal coordinates, thatis, the most important C α -distances of PDZ2. FigureS6(bottom) shows that three distances, d , , d , and d , suffice to qualitatively distinguish the 5 main statesof PDZ2. The XGBoost parameters are chosen as inRef. , including learning rate η = 0 .
3, maximum treedepth of 6, 10 training rounds, and 70% and 30% of thedata used for training and validation, respectively.
F. Markov state model
On the basis of the above defined 7 metastable states,we constructed a Markov state model of the trans -to- cis transition of PDZ2, using all (75 × µ s and 25 × µ s) trans -to- cis nonequilibrium trajectories. A general prob-lem with the definition of metastable states is that, dueto the inevitable restriction to a low-dimensional spacecombined with insufficient sampling, we often obtain amisclassification of sampled points in the transition re-gions, which causes intrastate fluctuations to be mistakenas interstate transitions. As a simple but effective rem-edy, we use dynamical coring which requires that a tran- sition must a minimum time τ cor in the new state for thetransition to be counted. A suitable quantity that re-flects these spurious crossings is the probability W i ( t ) tostay in state i for duration t (without considering backtransitions). As shown in Fig. S10, without coring weobserve a strong initial decay of W i ( t ) for all states, in-stead of a simple exponential decay we would expect forMarkovian states. Applying coring with increasing cor-ing times, this initial drop vanishes because fluctuationson timescales t (cid:46) τ cor are removed. Here we determined τ cor = 1 ns as shortest coring time, which removes thespurious interstate transitions.Figure S10shows the resulting implied timescales andeigenvectors of the model. Using a lag time of 1 ns, wemoreover show the time evolution of the state popula-tions, assuming that we start completely in a specificstate. ACKNOWLEDGEMENTS
We thank Rolf Pfister for the synthesis of the pep-tides and the Functional Genomics Center Zurich, espe-cially Serge Chesnov and Birgit Roth, for their help withthe mass spectrometry and amino-acid analysis. We alsothank Benjamin Lickert, Daniel Nagel and Georg Diez formany enlightening discussions concerning the MD dataanalysis. The work has been supported by the SwissNational Science Foundation (SNF) through the NCCRMUST and Grant 200020B 188694/1, as well as by theDeutsche Forschungsgemeinschaft through Grant STO247/10-2. We acknowledge support by the High Per-formance and Cloud Computing Group at the Zentrumf¨ur Datenverarbeitung of the University of T¨ubingen andthe Rechenzentrum of the University of Freiburg, thestate of Baden-W¨urttemberg through bwHPC and theDFG through Grant Nos. INST 37/935-1 FUGG (RVbw16I016) and INST 39/963-1 FUGG (RV bw18A004),the Black Forest Grid Initiative, and the Freiburg In-stitute for Advanced Studies (FRIAS) of the Albert-Ludwigs-University Freiburg.
AUTHOR CONTRIBUTIONS
O.B., C.Z. and A.G. contributed equally to this work.O.B, S.W., G.S., and P.H. designed research, O.B andB.J prepared samples, all authors provided data and/oranalyzed them, O.B, C.Z., S.W., G.S., and P.H con-tributed to the writing of the paper.
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