Identifying Conformational-Selection and Induced-Fit Aspects in the

Subscriber access provided by - Access paid by the | UCSB Libraries

Identifying Conformational-Selection and Induced-Fit Aspects in the BindingInduced Folding of PMI from Markov State Modeling of Atomistic Simulations Fabian Paul, Frank Noé, and Thomas R. Weikl J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b12146 • Publication Date (Web): 09 Mar 2018 Downloaded from http://pubs.acs.org on March 10, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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

The Journal of Physical Chemistry

Identifying Conformational-Selection and Induced-Fit Aspects in the Binding-Induced Folding of PMI from Markov State Modeling of Atomistic Simulations Fabian Paul,†,‡ Frank Noé,‡ and Thomas R. Weikl∗,† Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems, Science Park Golm, 14424 Potsdam, Germany, and Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany E-mail: [email protected],[email protected]

∗

To whom correspondence should be addressed Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems, Science Park Golm, 14424 Potsdam, Germany ‡ Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany †

1

ACS Paragon Plus Environment

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

Page 2 of 25

Abstract Unstructured proteins and peptides typically fold during binding to ligand proteins. A challenging problem is to identify the mechanism and kinetics of these bindinginduced folding processes in experiments and atomistic simulations. In this article, we present a detailed picture for the folding of the inhibitor peptide PMI into a helix during binding to the oncoprotein fragment

25−109 Mdm2

obtained from atomistic,

explicit-water simulations and Markov state modeling. We find that binding-induced folding of PMI is highly parallel and can occur along a multitude of pathways. Some pathways are induced-fit-like with binding occurring prior to PMI helix formation, while other pathways are conformational-selection like with binding after helix formation. On the majority of pathways, however, binding is intricately coupled to folding, without clear temporal ordering. A central feature of these pathways is PMI motion on the Mdm2 surface, along the binding groove of Mdm2 or over the rim of this groove. The native binding groove of Mdm2 thus appears as an asymmetric funnel for PMI binding. Overall, binding-induced folding of PMI does not fit into the classical picture of induced fit or conformational selection that implies a clear temporal ordering of binding and folding events. We argue that this holds in general for binding-induced folding processes because binding and folding events in these processes likely occur on similar timescales and do the exhibit the time-scale separation required for temporal ordering.

INTRODUCTION The binding of proteins often involves conformational changes. 1 A central question is how these binding processes are coupled to the conformational dynamics of the proteins. 2–8 Two mechanisms for this coupling are conformational selection’ 9 and ‘induced fit’. 10 In conformational-selection binding, a conformational change occurs prior to binding: the binding partners seem to ‘select’ a conformation for binding. In induced-fit binding, the conformational change occurs after binding and is apparently ‘induced’ by the binding process. These two mechanisms are plausible for the binding of proteins to small ligand molecules 2


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


that can enter and exit a protein binding pocket within transition times that are much smaller than the dwell times of the proteins in the different conformations. 11 However, such a time-scale separation between binding transition times and conformational dwell times is not obvious for protein-protein and protein-peptide binding, in particular not for large conformational changes such as folding. In binding-induced folding, a peptide or protein folds during binding to another protein. 12,13 For several protein-protein and protein-peptide systems, the coupling kinetics of folding and binding has been investigated with relaxation dispersion NMR spectroscopy 14–17 or mutational analysis. 18–21 Relaxation dispersion NMR experiments for the folding of pKID (phosphorylated kinase inducible activation domain of the transcription factor CREB) during binding to the KIX domain of the CREB-binding protein indicate an intermediate state in which pKID is partially folded. 14 This intermediate emerges from an ensemble of transient encounter complexes that are stabilized primarily by non-specific hydrophobic contacts. 14 For a different intrinsically disordered ligand of the KIX domain, the transactivation domain of the transcription factor c-Myb, NMR relaxation dispersion experiments indicate that the N-terminal region of the c-Myb ligand binds in a predominantly helically folded conformation, whereas the helical structure in the C-terminal region emerges after binding. 17 A mutational analysis for the folding of a shorter variant of the c-Myb ligand during binding to the KIX domain points towards a high content of native-like structure in the transition state. 19 For the folding of the S-peptide into an α-helix during binding to the the protein ribonuclease S, a mutational analysis that includes both backbone thioxylation and sidechain modifications shows that the folded, helical structure of the S-peptide is still absent in the transition state of binding. 18 Similarly, a mutational analysis for the folding of the the small disordered protein PUMA (p53 upregulated modulator of apoptosis) into an α-helix during binding to the protein MCL-1 (induced myeloid leukemia cell differentiation protein) indicates that the majority of folding occurs after the transition state of binding. 20 For the folding of the intrinsically disordered transactivation domain of STAT2 during binding to the

3



Page 4 of 25

TAZ1 domain of the CREB-binding protein, a mutational analysis suggests that the native protein-protein binding interface is not formed at the transition state for binding. 21 Overall, these experiments demonstrate a rather diverse spectrum of binding-and-folding scenarios. In this article, we present an analysis of the folding of the inhibitor peptide PMI (potent Mdm2/MdmX inhibitor) 22 during binding to the oncoprotein fragment

25−109

Mdm2

(Mouse double minute 2 homolog) that is based on a Markov state model (MSM) 23–25 of all-atom, explicit-solvent molecular dynamics (MD) simulations. Only recently, advances in both simulation technology, in particular regarding GPUs, and in MSM analysis made it possible to investigate the protein-protein and protein-peptide binding kinetics with allatom, explicit-solvent MD. 26–29 Previous simulation studies of the binding-induced folding kinetics are based on coarse-grained Go potentials that include non-physical interactions to stabilize natively bound states. 20,30–37 The MSM analysis presented here takes advantage of the recently developed multi-ensemble Markov model framework 28,38 that allows to estimate unbiased kinetics by combining unbiased and biased MD data via transition-based reweighting analysis methods 28,38,39 , which is essential to capture the long residence time of bound PMI in the seconds range. 28 The unbiased MD data consist of 481 trajectories with individual lengths between 0.95 µs and 1.21 µs and a total length of 503.6 µs. These simulations were conducted with the Amber99SB-ILDN force field 40 at the temperature 300 K on graphics processing units (GPUs). 28 A majority of 301 trajectories start from non-natively and natively bound conformations, while the remaining 107 trajectories start from the fully unbound state. The biased MD data are from Hamiltonian replica exchange simulations with a total length of about 100 µs. All MD data are available online. 41 The MSM considered here is a reanalysis of these MD data along the lines of our previously published MSM analysis. 28 In Ref. [28], our main goals were a quantitative prediction of the residence time and the description of PMI-Mdm2 kinetics in terms if a relatively small number of metastable states. The MSM in Ref. [28] therefore was optimized to accurately model the slow processes. In this article, in contrast, we aim to investigate the binding mech-

4


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


anism, which is characterized by the order of events along the binding pathways, irrespective of the duration of these events. To achieve a higher time resolution, the MSM here includes a relatively large number of states. We construct these states with the novel hierarchical TICA (hTICA) method, 42 which allows to resolve the conformational state space in higher detail than the previously used TICA method. The parameters computed with hTICA show a significantly clearer separation between conformational space regions of high density than the TICA parameters used in Ref. [28].1 Our MD simulations and MSM analysis indicate that binding-induced folding of PMI occurs along multiple parallel pathways and is funnelled by the Mdm2 binding cleft. Our MSM can be understood as a discrete energy landscape derived from atomistic simulations. The necessity of an energy landscape perspective for protein folding has been laid out in pioneering work about three decades ago. 43–46 The MSM shows that binding-induced folding of PMI cannot be described with the simple four-state model of figure 1(a) that implies rather sharp distinctions between bound and unbound, and folded and unfolded. Instead, partially folded and non-native partially bound conformations play a central role along the folding pathways of the MSM.

RESULTS Full binding trajectories support neither conformational selection nor induced fit Unbiased MD trajectories that contain the full transition from unbound to native-like bound provide a first glimpse of binding-induced folding of PMI. On 5 out of the 481 unbiased MD trajectories, a transition from the fully unbound state to native-like bound states with root1

With hTICA, it is possible to use all heavy-atom contacts between PMI and Mdm2 as input features for the computation of parameters. The hTICA analysis produces roughly 200 independent components that show separable conformational states. In contrast, the TICA projections from Ref. [28] show no separation beyond the 20th component.

5



mean-square deviation (RMSD) smaller than 0.4 nm to the crystal structure 22 occurs (see movies S1 to S5 in the Supporting Information). On trajectory 1, PMI glides rather quickly into the Mdm2 binding groove in an extended, unfolded conformation and binds with its C-terminal end. The helix then emerges at the N-terminal end and eventually settles into the binding groove. On trajectory 2, PMI is first intermediately bound at the shallow end of the binding groove in an unfolded, coiled conformation, and then ‘stands up’ into an upright conformation that is nearly perpendicular to the native bound conformation. The helix flickers and forms in this upright position, and finally rotates into the binding groove. On trajectory 3, PMI binds at the shallow end of the binding groove in a folded helical, upright conformation. After quick unbinding and rebinding at the shallow end of the groove, the helix eventually moves along the binding groove into the native state. On trajectory 4, the folded PMI helix first binds at the the rim of the binding groove, in nearly perpendicular orientation to the groove, then turns and glides into the groove. On trajectory 5, PMI binds in unfolded, extended conformation at the rim of the binding groove, glides over the top of the rim into the groove in still extended conformation, and finally adopts the folded helical conformation in the binding groove. Figure 1(b) illustrates the number of helical residues versus the number of contacts in the native binding groove of Mdm2 along these five trajectories. Along the trajectories 1 and 5, about 40 to 50 contacts in the native binding groove form before a stable helix with more than two helical residues emerges, which is reminiscent of induced fit. However, PMI first binds at different locations around the binding groove on these trajectories (see trajectory descriptions above), and the transition from 40 or 50 contacts to the roughly 60 contacts of the native-bound state occurs after helix formation on trajectory 1 and together with helix formation on trajectory 5. The fully native-like number of 6 helical residues is not reached along these trajectories, in contrast to trajectories 2, 3, and 4. On trajectories 3 and 4, PMI binds in helical conformations, which is reminiscent of conformational selection. However, the PMI helix first binds at different locations around the binding groove also on

6


Page 6 of 25

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


these trajectories, and the native-like bound state is only reached after rotation and motion of the PMI helix into the binding groove. Trajectory 3 also includes quick unbinding and rebinding and at least partial unfolding prior to the native-like bound state. On trajectory 2, native-like numbers of contacts and helical residues emerge jointly. Together, these five trajectories already show that the binding-induced folding of PMI cannot be described with the simple four-state picture of figure 1(a). The clear temporal sequence of binding and folding in this four-state picture does not occur on MD trajectories, also not on trajectories that are reminiscent of induced-fit and conformational-selection scenarios. The trajectories illustrate that helix formation and funneling of PMI from sites of first encounter with Mdm2 to native-like binding positions occur on rather similar timescales and, thus, do not exhibit the time scale separation that is required for a temporal ordering of binding and folding. 11

Markov-state model (MSM) analysis quantifies the flux along multiple parallel pathways To systematically analyse all unbiased and biased MD data for the folding of PMI during binding to Mdm2, we have constructed an MSM with the software package PyEMMA 47,48 using the recently developed TRAMMBAR method 28 (see Supporting Information for details). Figure 2 illustrates the reactive flux from unbound microstates (blue disks) to native-like bound micostates (yellow disks) for the full MSM with 771 microstates. In the two diagrams of figure 2, the microstates are positioned along a degree of folding and a degree of binding. We use different measures for the degree of folding and binding in these diagrams to show that the overall picture for the kinetics of binding-induced folding of PMI obtained from the MSM does not depend on specific definitions. The area of the disks is proportional to the overall reactive flux of the microstates calculated with transition-path theory (TPT). 49,50 For the non-native bound microstates (black disks), the reactive flux can be understood as either the sum of all incoming or the sum of all outgoing fluxes because these two sums are equal. 7



For unbound microstates (blue disks), the reactive flux per microstate is defined as the sum of all outgoing fluxes. For native-like bound microstates (yellow disks), the reactive flux is the sum of the incoming fluxes. The grey ellipses around the microstates with the highest reactive fluxes represent the standard deviations in the degrees of folding and binding for these microstates and, thus, illustrate the ‘size’ of these microstates in the two-dimensional diagrams. The black lines represent the flux between microstates with direct connections in MD trajectories. For clarity, only connections with fluxes larger than 1% of the maximum flux between pairs of microstates are shown. The structural representations of eight selected microstates with high flux in figure 2 illustrate the PMI conformations in these microstates. For each of these microstates, a ‘main representant’ of PMI is shown in color. This main representant is the PMI conformation closest to the average PMI coordinates for the microstate among 1000 randomly chosen conformations. In the non-natively bound microstates C and D, the main PMI representants are bound at the shallow end of the binding groove. In A, B, E, F, G, the main representants are located in the binding groove but still deviate from the native-like bound conformation in N. Besides the main representants, 50 random PMI conformations for each cluster are shown as grey thin curves with semi-transparent spheres at the termini. The random PMI conformations of microstate D, for example, illustrate that PMI is mostly bound at the shallow end of the binding groove in this microstate, but can also be bound to the rim of the groove. Figure 2 shows that binding-induced folding of PMI in our MD simulations occurs along multiple parallel pathways and, thus, confirms the impression obtained from the five bindingand-folding trajectories of figure 2. The rather dense accumulation of microstates and flux lines in the center of the diagrams of figure 2 indicates a close coupling of binding and folding rather than a clear ordering of binding and folding as in the simple four-state picture of figure 1(a). This close coupling of folding and binding is quantified in figure 1(c), which is obtained from coarse-graining the flux in the left diagram of 2 into rectangular grid cells

8


Page 8 of 25

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


(see Supporting Information for details). According to figure 2, induced-fit-like binding and folding can occur from the blue unbound and unfolded microstate with zero helical residues via microstates E and F to the native state N. These microstates indeed are populated prominently on the induced-fit like trajectories 1 and 5 of figure 1(b). On both trajectory 1 and 5, first binding involves exchange between the microstates E and A, and microstate F is visited on route to the native state. On the conformational-selection-like trajectories 3 and 4, in contrast, the microstate D is most prominent in first binding. In figure 2, the microstate D provides a conformationalselection-like connection from unbound but folded microstates to the native state. Figure 3 complements the fluxes along degrees of folding and binding represented in figure 2 and figure 1(c) by illustrating the spatial positioning and overall reactive flux of PMI binding on the Mdm2 surface. The figures 3(a) and (b) show the average PMI centerof-mass positions in the microstates in side and top view, while figures 3(c) and (d) visualize the coarse-grained reactive flux along Mdm2. Two spatial pathways emerging from figure 3 are a main pathway from the shallow end of the binding groove into the groove, and minor pathway across the rim of the binding groove. Trajectories 2 and 3 follow the main pathway from the shallow end into the groove and illustrate that PMI helix formation can occur early or late on this pathway (see movies S2 and S3). The trajectories 4 and 5 are along the minor pathway and show that the crossing of the rim of the groove along this pathway is possible both for unfolded extended and helically folded PMI conformations. Insight into the interactions that stabilize the different bound states in and around the native binding groove can be gained from the average numbers of intermolecular salt bridges and hydrogen bonds in these states (see Figure 4). Intermolecular salt bridges and hydrogen bonds are prominent at the shallow end of the binding groove. The salt bridges are formed by the glutamic acid residue and charged ends of the peptide, which bind to protein surface charges at the shallow end of the binding groove. The two charged protein ends are located at this shallow end. In the native binding groove and at the rim of this groove, in contrast,

9



intermolecular salt bridges and hydrogen bonds are largely absent. The native-like bound state is clearly dominated by hydrophobic interactions.

DISCUSSION AND CONCLUSIONS We have analyzed the coupling of binding of folding for the inhibitor peptide PMI with a MSM based on atomistic simulations. Central elements of this analysis are the quantification and visualization of the reactive flux of the MSM from unbound to native-like bound (i) along degrees of folding and binding (see figure 2), and (ii) along the surface of protein Mdm2 (see figure 3). Our analysis shows that binding-induced folding of PMI does not fit into the four-state picture of figure 1(a) that implies a clear ordering of binding and folding events. In general, such an ordering is not to be expected for binding-induced folding because it requires a time-scale separation between binding transition times and conformational dwell times, which is implausible for the coupling of binding and folding. 11 For PMI, the transitions from sites of first encounter with Mdm2 to native-like binding positions and the changes from unfolded to helically folded conformations can occur on rather similar timescales. The complete picture of binding-induced folding of PMI that emerges from the MSM includes a multitude of parallel pathways that are funneled by the Mdm2 binding cleft. The reactive fluxes along these pathways are quantified by the MSM. An investigation of protein-protein binding and binding-induced folding with atomistic simulations and MSM analysis as in this article is made possible by recent advances in computational resources and MSM methods. In contrast to coarse-grained simulations, which typically require non-physical interactions in Go potentials to stabilize natively bound states, atomistic simulations of protein-protein binding provide a physical balance of native and nonnative interactions.

Caveats are that structural properties of disordered peptides can be

misrepresented in atomistic MD simulations, 51,52 and that protein-protein binding affinities appear to be systematically overestimated. 53,54 Also kinetic properties like the precise values

10


Page 10 of 25

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


of autocorrelation times 55 or the order of events in a folding mechanism 56 can depend on the choice of force field. Our MSM leads to values for the binding equilibrium constant and off-rate constant that agree well with experimental values within expected force field errors. 28 A misrepresentation of partially bound disordered states in our simulations may affect the fluxes along different binding pathways. MSM analysis of atomistic simulations quantifies the parallel, multiple pathways of individual conformational changes 57,58 and binding-induced folded processes observed in atomistic simulations and can, thus, complement data from NMR relaxation dispersion or mutational experiments for protein ensembles. For example, φ values of 0 and 1 for single-residue mutations are classically interpreted to indicate the absence or presence, respectively, of native-like structure in the transition state at the site of the mutations. However, φ values are often ‘fractional’ between 0 and 1, also for binding-induced folding processes. 19–21 Such fractional φ values can arise from parallel pathways or from different degrees of secondary and tertiary structure formation in transition states, 59–62 which can be distinguished based on atomistic simulations 63 and MSM analysis.

Acknowledgement This research has been partially funded by Deutsche Forschungsgemeinschaft (DFG) through grant CRC 1114 "Scaling Cascades in Complex Systems", Project A4 "Efficient calculation of slow and stationary scales in molecular dynamics".

Supporting Information Available The following files are available free of charge. • Supporting text • S1.mp4: movie of binding trajectory 1 • S2.mp4: movie of binding trajectory 2 11



• S3.mp4: movie of binding trajectory 3 • S4.mp4: movie of binding trajectory 4 • S5.mp4: movie of binding trajectory 5 This material is available free of charge via the Internet at http://pubs.acs.org/.

12


Page 12 of 25

Page 13 of 25

folding

40

1

(b)

4

3

2

20

0

(a)

5

60

0

2

4

6

number of helical residues of PMI

(c)

2(1)

4(1)

9(3)

60 2(1) 2(1) 17(7) 22(7) 29(8) 47(8) 99(1) 50 3(1)

7(2)

23(5) 33(4) 54(6) 73(8) 71(8)

40 7(2) 11(3) 27(5) 40(4) 42(4) 25(3) 10(2) 30 9(3) 15(3) 27(3) 48(4) 29(3) 14(2) 9(2) 20 19(4) 27(3) 35(3) 52(3) 15(2) 12(2) 10(3) 10 28(5) 36(5) 37(3) 51(4) 35(4) 22(3) 19(3) 0 49(6) 29(5) 28(8) 41(8) 31(5) 13(4) 9(3) 0

8

degree of folding

contacts in native groove of Mdm2

F

U

4(2)

70

degree of binding

FL


UL

degree of binding

80

binding

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


1

2

3

4

5

6


6(2)

7

degree of folding

Figure 1: (a) Simple four-state picture of binding-induced folding. In this picture, a protein or peptide adopts an unfolded state U and folded state F both in its unbound state and when bound to a ligand protein L. Along the induced-fit pathway U → UL → FL, the protein or peptide folds after binding. Along the conformational-selection pathway U → F → FL, the protein or peptide folds prior to binding. (b) Number of helical residues against the number of non-hydrogen atom contacts in the native binding groove of Mdm2 along five trajectories that contain a full transition from fully unbound to native-like bound conformations of PMI (see movies S1 to S5 in the Supporting Information). The number of helical residues is a measure for the degree of folding of PMI and is determined here according to the standard DSSP criteria. 64 This number varies between 0 and the maximal number of 8 helical residues for the 12-residue peptide PMI. In the native bound state, the number of helical residues is 6, i.e. the helix is nearly fully formed. The number of contacts in the native binding groove of Mdm2 is a measure for the degree of native-like binding. We count here all contacts of non-hydrogen atoms within a cutoff distance of 0.4 nm and define the native binding groove as the set of Mdm2 residues that have contacts with PMI in the crystal structure. The number of helical residues and number of contacts are averaged over 100 frames of the trajectories. The frames are taken at intervals of 0.1 ns. (c) Coarse-grained reactive flux in the MSM from the unbound state to the natively bound state. The numbers represent the reactive flux for the rectangular cells in percent of the total reactive flux from unbound to natively bound, with errors given in brackets (see Supporting Information for details). The coloring of the rectangular cells reflects the reactive flux.

13



F

E

N

G

N F

60

N

F G 40

20 E

A

G

1

RMSD of PMI for aligned Mdm2

number of contacts in native binding groove of Mdm2

0

degree of binding

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

Page 14 of 25

B

2

E

A

C

B

D

3

D

C

4

0 0

2

4

6

8


0.5

0.4

0.3

0.1

degree of folding

degree of folding

A

0.2

least backbone RMSD of PMI

B

C

D

Figure 2: Two-dimensional representations of the reactive flux from unbound microstates (blue disks) to native-like bound microstates (yellow disks) in the MSM. Each of the 771 microstates of the MSM is represented by a disk with an area that is proportional to the reactive flux through the microstate. These disks are positioned according to average degrees of folding and binding for the microstates. In the left diagram, the degree of folding is quantified by the number of helical residues, and the degree of binding is the number of non-hydrogen atom contacts of PMI with residues in the native Mdm2 binding groove, as in Figure 1(b) and (c). In the right diagram, the degree of folding is measured by the least RMSD of the PMI backbone atoms to the crystal-structure conformation of PMI (PDB code 3eqs), and the degree of binding is the RMSD of all PMI atoms to the crystal structure after alignment of Mdm2. The grey ellipses represent the standard deviations of these degree of folding and binding for the 25 (left) and 30 (right) microstates with the largest reactive flux. The width of the lines that connect microstates are proportional to the reactive flux between the states. Only connections with a flux larger than 1% of the maximum flux between states are shown. In this MSM, microstates are only connected if a direct transition in unbiased MD simulations has been observed. In the structural representations of the selected 8 microstates A, B, C, D, E, F, G, N with high reactive flux, a ‘main representant’ that is closest to the average PMI coordinates of the microstates is shown with residue coloring TSFAEYWNLLSP. The shown side chains are involved in binding, with intermolecular contact probabilities of at least 0.5 for the microstate. In addition to the main representant, a cloud of 50 random PMI conformations is represented as grey thin curves with semi-transparent spheres at the termini. The structural images were generated with VMD. 65 14 ACS Paragon Plus Environment

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


side view

top view

(a)

(b)

(c)

(d)

Figure 3: (a) and (b) Average location of PMI in bound microstates (blue spheres) on the Mdm2 surface (grey). Every microstate is represented here by a sphere located at the average center of mass of PMI for the microstate with a volume proportional to the reactive flux through the microstate. The natively bound PMI helix is represented in yellow. – (c) and (d) Reactive flux along the Mdm2 surface obtained from a discretization into grid cells and the summation of fluxes between microstates that are located in different cells (see Supporting Information for details). The thickness of the arrows indicate the magnitude of the flux.

15



side view

top view

3 2

salt bridges

1 0

(a)

(b)

(c)

(d)

8 6 4 2 0

hydrogen bonds

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

Figure 4: (a) and (b) Numbers of intermolecular salt bridges and (c) and (d) numbers of intermolecular hydrogen bonds in the microstates of the MSM. As in Figure 3, every microstate is represented by a sphere with a volume proportional to the reactive flux through the microstate. Numbers of salt bridges and hydrogen bonds are represented by the coloring of the states (see color bar). The natively bound PMI helix is represented in yellow. A salt bridge here is defined as a charged oxygen atom and a charged nitrogen atom within a distance of 0.35 nm. Hydrogen bonds are determined by Baker-Hubbard criteria 66 as implemented in the MDTraj software. 67

16


Page 16 of 25

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


References (1) Gerstein, M.; Krebs, W. A database of macromolecular motions. Nucleic Acids Res. 1998, 26, 4280–4290. (2) Henzler-Wildman, K.; Kern, D. Dynamic personalities of proteins. Nature 2007, 450, 964–972. (3) Boehr, D. D.; Nussinov, R.; Wright, P. E. The role of dynamic conformational ensembles in biomolecular recognition. Nat. Chem. Biol. 2009, 5, 789–796. (4) Changeux, J.-P. 50th anniversary of the word “allosteric". Protein Sci. 2011, 20, 1119– 1124. (5) Lange, O. F.; Lakomek, N.-A.; Fares, C.; Schröder, G. F.; Walter, K. F. A.; Becker, S.; Meiler, J.; Grubmüller, H.; Griesinger, C.; de Groot, B. L. Recognition dynamics up to microseconds revealed from an RDC-derived ubiquitin ensemble in solution. Science 2008, 320, 1471–1475. (6) Plattner, N.; Noe, F. Protein conformational plasticity and complex ligand-binding kinetics explored by atomistic simulations and Markov models. Nat. Commun. 2015, 6, 7653. (7) Chakrabarti, K. S.; Agafonov, R. V.; Pontiggia, F.; Otten, R.; Higgins, M. K.; Schertler, G. F. X.; Oprian, D. D.; Kern, D. Conformational selection in a proteinprotein interaction revealed by dynamic pathway analysis. Cell Reports 2016, 14, 32– 42. (8) Paul, F.; Weikl, T. R. How to distinguish conformational selection and induced fit based on chemical relaxation rates. PLoS Comput. Biol. 2016, 12, e1005067. (9) Ma, B.; Kumar, S.; Tsai, C. J.; Nussinov, R. Folding funnels and binding mechanisms. Protein Eng. 1999, 12, 713–720. 17



(10) Koshland, D. E. Application of a theory of enzyme specificity to protein synthesis. Proc. Natl. Acad. Sci. USA 1958, 44, 98–104. (11) Weikl, T. R.; Paul, F. Conformational selection in protein binding and function. Protein Sci. 2014, 23, 1508–1518. (12) Wright, P. E.; Dyson, H. J. Linking folding and binding. Curr. Opin. Struct. Biol. 2009, 19, 31–38. (13) Kiefhaber, T.; Bachmann, A.; Jensen, K. S. Dynamics and mechanisms of coupled protein folding and binding reactions. Curr. Opion. Struct. Biol. 2012, 22, 21–29. (14) Sugase, K.; Dyson, H. J.; Wright, P. E. Mechanism of coupled folding and binding of an intrinsically disordered protein. Nature 2007, 447, 1021–1025. (15) Brüschweiler, S.; Schanda, P.; Kloiber, K.; Brutscher, B.; Kontaxis, G.; Konrat, R.; Tollinger, M. Direct observation of the dynamic process underlying allosteric signal transmission. J. Am. Chem. Soc. 2009, 131, 3063–3068. (16) Schneider, R.; Maurin, D.; Communie, G.; Kragelj, J.; Hansen, D. F.; Ruigrok, R. W. H.; Jensen, M. R.; Blackledge, M. Visualizing the molecular recognition trajectory of an intrinsically disordered protein using multinuclear relaxation dispersion NMR. J. Am. Chem. Soc. 2015, 137, 1220–1229. (17) Arai, M.; Sugase, K.; Dyson, H. J.; Wright, P. E. Conformational propensities of intrinsically disordered proteins influence the mechanism of binding and folding. Proc. Natl. Acad. Sci. USA 2015, 112, 9614–9619. (18) Bachmann, A.; Wildemann, D.; Praetorius, F.; Fischer, G.; Kiefhaber, T. Mapping backbone and side-chain interactions in the transition state of a coupled protein folding and binding reaction. Proc. Natl. Acad. Sci. USA 2011, 108, 3952–3957.

18


Page 18 of 25

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


(19) Giri, R.; Morrone, A.; Toto, A.; Brunori, M.; Gianni, S. Structure of the transition state for the binding of c-Myb and KIX highlights an unexpected order for a disordered system. Proc. Natl. Acad. Sci. USA 2013, 110, 14942–14947. (20) Rogers, J. M.; Oleinikovas, V.; Shammas, S. L.; Wong, C. T.; De Sancho, D.; Baker, C. M.; Clarke, J. Interplay between partner and ligand facilitates the folding and binding of an intrinsically disordered protein. Proc. Natl. Acad. Sci. USA 2014, 111, 15420–15425. (21) Lindstrom, I.; Dogan, J. Native hydrophobic binding interactions at the transition state for association between the TAZ1 domain of CBP and the disordered TAD-STAT2 are not a requirement. Biochemistry 2017, 56, 4145–4153. (22) Pazgier, M.; Liu, M.; Zou, G.; Yuan, W.; Li, C.; Li, C.; Li, J.; Monbo, J.; Zella, D.; Tarasov, S. G.; Lu, W. Structural basis for high-affinity peptide inhibition of p53 interactions with MDM2 and MDMX. Proc. Natl. Acad. Sci. USA 2009, 106, 4665–4670. (23) Chodera, J. D.; Noe, F. Markov state models of biomolecular conformational dynamics. Curr. Opin. Struct. Biol. 2014, 25, 135–144. (24) Husic, B. E.; Pande, V. S. Markov state models: From an art to a science. J Am Chem Soc 2018, 140, 2386–2396. (25) Schütte, C.; Sarich, M. Metastability and Markov State Models in Molecular Dynamics: Modeling, Analysis, Algorithmic Approaches; American Mathematical Society, 2014. (26) Kashif Sadiq, S.; Noe, F.; De Fabritiis, G. Kinetic characterization of the critical step in HIV-1 protease maturation. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 20449–20454. (27) Plattner, N.; Doerr, S.; De Fabritiis, G.; Noe, F. Complete protein-protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling. Nat. Chem. 2017, 9, 1005–1011. 19



(28) Paul, F.; Wehmeyer, C.; Abualrous, E. T.; Wu, H.; Crabtree, M. D.; Schoneberg, J.; Clarke, J.; Freund, C.; Weikl, T. R.; Noe, F. Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations. Nat. Commun. 2017, 8, 1095. (29) Zhou, G.; Pantelopulos, G. A.; Mukherjee, S.; Voelz, V. A. Bridging microscopic and macroscopic mechanisms of p53-MDM2 binding with kinetic network models. Biophys. J. 2017, 113, 785–793. (30) Turjanski, A. G.; Gutkind, J. S.; Best, R. B.; Hummer, G. Binding-induced folding of a natively unstructured transcription factor. PLoS Comput Biol 2008, 4, e1000060. (31) Huang, Y.; Liu, Z. Kinetic advantage of intrinsically disordered proteins in coupled folding-binding process: a critical assessment of the "fly-casting" mechanism. J. Mol. Biol. 2009, 393, 1143–1159. (32) Ganguly, D.; Zhang, W.; Chen, J. Electrostatically accelerated encounter and folding for facile recognition of intrinsically disordered proteins. PLoS Comput. Biol. 2013, 9, e1003363. (33) Law, S. M.; Gagnon, J. K.; Mapp, A. K.; Brooks, C. L., 3rd Prepaying the entropic cost for allosteric regulation in KIX. Proc. Natl. Acad. Sci. USA 2014, 111, 12067–12072. (34) Knott, M.; Best, R. B. Discriminating binding mechanisms of an intrinsically disordered protein via a multi-state coarse-grained model. J. Chem. Phys. 2014, 140, 175102. (35) Salmon, L.; Ahlstrom, L. S.; Horowitz, S.; Dickson, A.; Brooks, I., Charles L.; Bardwell, J. C. A. Capturing a dynamic chaperone-substrate interaction using NMRinformed molecular modeling. J. Am. Chem. Soc. 2016, 138, 9826–9839. (36) Umezawa, K.; Ohnuki, J.; Higo, J.; Takano, M. Intrinsic disorder accelerates dissociation rather than association. Proteins 2016, 84, 1124–1133.

20


Page 20 of 25

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


(37) Chu, W.-T.; Clarke, J.; Shammas, S. L.; Wang, J. Role of non-native electrostatic interactions in the coupled folding and binding of PUMA with Mcl-1. PLoS Comput. Biol. 2017, 13, e1005468. (38) Wu, H.; Paul, F.; Wehmeyer, C.; Noé, F. Multiensemble Markov models of molecular thermodynamics and kinetics. Proc. Natl. Acad. Sci. USA 2016, 113, E3221–E3230. (39) Wu, H.; Mey, A. S. J. S.; Rosta, E.; Noe, F. Statistically optimal analysis of statediscretized trajectory data from multiple thermodynamic states. J. Chem. Phys. 2014, 141, 214106. (40) Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved side-chain torsion potentials for the Amber ff99SB protein force field. Proteins 2010, 78, 1950–1958. (41) Paul, F. Molecular dynamics trajectories for the 25-109-Mdm2-PMI system. 2017; Edmond Open Access Data Repository, DOI: 10.17617/3.x. (42) Pérez-Hernández, G.; Noé, F. Hierarchical time-lagged independent component analysis: Computing slow modes and reaction coordinates for large molecular systems. J. Chem. Theory Comput. 2016, 12, 6118–6129. (43) Dill, K. A. Theory for the folding and stability of globular proteins. Biochemistry 1985, 24, 1501–1509. (44) Bryngelson, J. D.; Wolynes, P. G. Spin glasses and the statistical mechanics of protein folding. Proc. Natl. Acad. Sci. USA 1987, 84, 7524–7528. (45) Dill, K. A.; Chan, H. S. From Levinthal to pathways to funnels. Nat. Struct. Biol. 1997, 4, 10–19. (46) Bryngelson, J. D.; Onuchic, J. N.; Socci, N. D.; Wolynes, P. G. Funnels, pathways, and the energy landscape of protein folding: a synthesis. Proteins 1995, 21, 167–195. 21



Page 22 of 25

(47) Scherer, M. K.; Trendelkamp-Schroer, B.; Paul, F.; Pérez-Hernández, G.; Hoffmann, M.; Plattner, N.; Wehmeyer, C.; Prinz, J.-H.; Noé, F. PyEMMA 2: A software package for estimation, validation, and analysis of Markov models. J. Chem. Theory Comput. 2015, 11, 5525–5542. (48) PyEMMA

-

Emma’s

Markov

Model

Algorithms.

http://pyemma.

org(accessedMarch7,2018). (49) Metzner, P.; Schütte, C.; Vanden-Eijnden, E. Transition path theory for Markov jump processes. Mult. Mod. Sim. 2009, 7, 1192–1219. (50) Noé, F.; Schütte, C.; Vanden-Eijnden, E.; Reich, L.; Weikl, T. R. Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations. Proc. Natl. Acad. Sci. USA 2009, 106, 19011–19016. (51) Rauscher, S.; Gapsys, V.; Gajda, M. J.; Zweckstetter, M.; de Groot, B. L.; Grubm¨ller, H. Structural ensembles of intrinsically disordered proteins depend strongly on force field: A comparison to experiment. J. Chem. Theory Comput. 2015, 11, 5513– 5524. (52) Nerenberg, P. S.; Head-Gordon, T. Optimizing protein-solvent force fields to reproduce intrinsic conformational preferences of model peptides. J. Chem. Theory Comput. 2011, 7, 1220–1230. (53) Best, R. B.; Zheng, W.; Mittal, J. Balanced protein-water interactions improve properties of disordered proteins and non-specific protein association. J. Chem. Theory Comput. 2014, 10, 5113–5124. (54) Petrov, D.; Zagrovic, B. Are current atomistic force fields accurate enough to study proteins in crowded environments? PLoS Comput. Biol. 2014, 10, e1003638.

22


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


(55) Vitalini, F.; Mey, A. S. J. S.; Noe, F.; Keller, B. G. Dynamic properties of force fields. J. Chem. Phys. 2015, 142, 084101. (56) Piana, S.; Lindorff-Larsen, K.; Shaw, D. E. How robust are protein folding simulations with respect to force field parameterization? Biophys. J. 2011, 100, L47–L49. (57) Pontiggia, F.; Pachov, D. V.; Clarkson, M. W.; Villali, J.; Hagan, M. F.; Pande, V. S.; Kern, D. Free energy landscape of activation in a signalling protein at atomic resolution. Nat. Commun. 2015, 6, 7284. (58) Buchenberg, S.; Sittel, F.; Stock, G. Time-resolved observation of protein allosteric communication. Proc. Natl. Acad. Sci. U. S. A. 2017, 114, E6804–E6811. (59) Fersht, A. R.; Sato, S. Φ-value analysis and the nature of protein folding transition states. Proc. Natl. Acad. Sci. USA 2004, 101, 7976–7981. (60) Sosnick, T. R.; Dothager, R. S.; Krantz, B. A. Differences in the folding transition state of ubiquitin indicated by Φ and Ψ analyses. Proc. Natl. Acad. Sci. USA 2004, 101, 17377–17382. (61) Merlo, C.; Dill, K. A.; Weikl, T. R. Φ-values in protein folding kinetics have energetic and structural components. Proc. Natl. Acad. Sci. USA 2005, 102, 10171–10175. (62) Weikl, T. R.; Dill, K. A. Transition states in protein folding kinetics: The structural interpretation of Φ-values. J. Mol. Biol. 2007, 365, 1578–1586. (63) Best, R. B.; Hummer, G. Microscopic interpretation of folding φ-values using the transition path ensemble. Proc. Natl. Acad. Sci. USA 2016, 113, 3263–3268. (64) Kabsch, W.; Sander, C. Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 1983, 22, 2577–2637. (65) Humphrey, W.; Dalke, A.; Schulten, K. VMD: visual molecular dynamics. J. Mol. Graph. 1996, 14, 33–38, 27–28. 23



(66) Baker, E. N.; Hubbard, R. E. Hydrogen bonding in globular proteins. Prog. Biophys. Mol. Biol. 1984, 44, 97–179. (67) McGibbon, R. T.; Beauchamp, K. A.; Harrigan, M. P.; Klein, C.; Swails, J. M.; Hernandez, C. X.; Schwantes, C. R.; Wang, L.-P.; Lane, T. J.; Pande, V. S. MDTraj: A modern open library for the analysis of molecular dynamics trajectories. Biophys. J. 2015, 109, 1528–1532.

24


Page 24 of 25

Page 25 of 25

Graphical TOC Entry Individual trajectories

Coarse-grained reactive flux 4(2)

70

60

40

1

4

3

2

degree of binding

5

20

0

0

2

4

6



degree of binding

80


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


2(1)

4(1)

9(3)

60 2(1) 2(1) 17(7) 22(7) 29(8) 47(8) 99(1) 50 3(1)

7(2)

23(5) 33(4) 54(6) 73(8) 71(8)

40 7(2) 11(3) 27(5) 40(4) 42(4) 25(3) 10(2) 30 9(3) 15(3) 27(3) 48(4) 29(3) 14(2) 9(2) 20 19(4) 27(3) 35(3) 52(3) 15(2) 12(2) 10(3) 10 28(5) 36(5) 37(3) 51(4) 35(4) 22(3) 19(3) 0 49(6) 29(5) 28(8) 41(8) 31(5) 13(4) 9(3) 0

8

1

2

3

4

5

6


degree of folding

degree of folding

25


6(2)

7

Identifying Conformational-Selection and Induced-Fit Aspects in the

Recommend Documents