Exploring the Role of Globular Domain Locations on an Intrinsically Disordered Region of p53: A Molecular Dynamics Investigation

The pre-tetramerization loop (PTL) of the human tumor suppressor protein p53 is an intrinsically disordered region (IDR) necessary for the tetramerization process, and its flexibility contributes to the essential conformational changes needed. Although the IDR can be accurately simulated in the traditional manner of molecular dynamics (MD) with the end-to-end distance (EEdist) unhindered, we sought to explore the effects of restraining the EEdist to the values predicted by electron microscopy (EM) and other distances. Simulating the PTL trajectory with a restrained EEdist , we found an increased agreement of nuclear magnetic resonance (NMR) chemical shifts with experiments. Additionally, we observed a plethora of secondary structures and contacts that only appear when the trajectory is restrained. Our findings expand the understanding of the tetramerization of p53 and provide insight into how mutations could make the protein impotent. In particular, our findings demonstrate the importance of restraining the EEdist in studying IDRs and how their conformations change under different conditions. Our results provide a better understanding of the PTL and the conformational dynamics of IDRs in general, which are useful for further studies regarding mutations and their effects on the activity of p53.


■ INTRODUCTION
−4 TP53, the gene encoding p53, is the most mutated gene in human cancers; more than 50% of cancers have mutations found within the gene. 5,6The p53 protein is a regulatory factor responsible for maintaining genome integrity and cell cycle control and preventing cancer development across all animal species, from humans to invertebrates. 7,8Research has indicated that variants and possible precursors of p53 protein have been found in organisms across the taxonomic tree. 9,10In its functional form, p53 binds to the DNA and searches for mutations, and upon finding them, it triggers apoptosis to prevent uncontrolled cell growth. 11Of major interest to the scientific community are the mutant forms of p53, as these variants have been observed to possess oncogenic characteristics. 12,13p53 is 393 amino acids long and contains several functional domains and four IDRs, all of which are depicted below (Figure 1).
The p53 protein contains a DNA binding domain (DBD), 1,2,14−16 a transactivation domain (TAD) divided into two regions responsible for activating transcription, 2,17 a proline-rich domain (PRD), 3,18 a regulatory domain (REG) containing phosphorylation sites to activate and deactivate the protein, 2,19,20 and the tetramerization domain (TET) which enables the oligomerization of the p53 monomers. 1,2,21The TET contains an α-helix and β-sheet which enable the p53 monomers to link in tandem. 22Crucially, it also contains the pre-tetramerization loop (PTL) between residues Lys 292 and Gly 325 , an intrinsically disordered region that allows the p53 monomers to link, increasing the DNA binding affinity 1000fold. 23This region provides the flexibility necessary for tetramerization; however, the exact mechanisms of this process and the specific conformations of the PTL pre/posttetramerization are unknown.
−28 This makes determining protein−protein interaction sites, structural dynamics, and conformational analysis difficult. 27,29Fortunately, advances in computational techniques, such as molecular dynamics (MD) with force fields 30,31 specifically designed to incorporate the inherent disorder, provide researchers with great insight into the inner workings of these regions. 28IDRs are typically involved in regulatory functions and require as much flexibility as possible. 32This might explain why IDRs are commonly found in proteins at the N-or Cterminal and less frequently internally. 33However, flexibility is also important for conformational changes in the protein, such as the oligomerization processes. 16,34,35The PTL region is such a sequence in p53, as noted from the degree of disorder (Figure 2).The PTL segments contain 31 amino acids generally believed to be disorder-promoting (Ala, Arg, Gly, Gln, Ser, Glu, Lys, and Pro) based on sequence analysis of IDRs and IDPs. 33In contrast, PTL only contains seven amino acids that are believed to be order-promoting, four Leu and three Asn (the residues believed to promote order are Trp, Tyr, Phe, Ile, Leu, Val, Cys, and Asn). 36erminal IDRs are found at the periphery of the sequences 33 and their movements and dynamics are minimally restricted by being attached to only one globular domain.For internal IDRs, however, both ends are attached to the globular domains.These flexible linkers and spacers can allow domains to sample a wide range of positions with respect to one another and act as flexible loops with solvent-accessible surface areas that can interact with the globular regions.However, being attached to two structural domains limits the number of conformations the IDR can adopt and restricts the region's dynamics.The increased mass at the end of the IDR hinders movement, and some conformations are forbidden due to the steric hindrance of the globular domains.In the case of some IDRs, including PTL, the structural domains have large interaction partners that lock the protein's domains in place and either severely slow or even arrest the movement of the domains with respect to each other.This locks the IDR's EE dist which restricts the conformational ensemble to only include conformations within a specific end-to-end span.The effect of such situations on the conformational ensembles remains largely unexplored.
In IDRs, it is often observed that specific conformations permit the existence of small transient secondary structures that facilitate the conformational changes in the protein. 37nderstanding the influence of end-to-end span on the IDR's structure, behavior, and interactions is therefore vital to uncovering the impact of conformational changes in the protein on secondary structure in IDRs, and vice versa.By studying the PTL with MD simulations as a free IDP and as an IDR with different restrained EE dist , we see how the restriction on the movement of the terminals of the IDR affects the conformations it can take and what secondary structure it can assume.We compare the data with previously obtained electron microscopy structure 24 of the p53 monomeric form (PDB: 8f2i) to understand how the region settles when the protein is inactive.The local interactions were evaluated by comparing predicted chemical shifts (CSs) to solution NMR data 38 to assess the fidelity of the models.(top) for the monomeric form of this region with the TET region highlighted in yellow and the PTL in red and the predicted disorder (bottom) for the p53 protein displaying the intrinsically disordered PTL and REG regions connected by the TET domain based on IUPRED. 25−49 The starting structure for the unrestrained trajectory was generated using Avogadro, 50 thereafter allowing the structures to relax.The termini were simulated in their zwitterionic state, and the charges of the side chains were set to physiological pH, giving the PTL a net charge of +3.The zwitterionic state was chosen to replicate a number of investigations into similar internal regions of IDRs.In the future, investigations into the influence of the charged termini would be fruitful, although for this investigation, this variable was not tested.In terms of NMR, however, if there is an influence on the CSs, then it is most likely localized, particularly in trajectories whose end termini are positionally restrained.The periodic boundary conditions were simulated with a rhombic box with a minimum distance of ten nm from the PTL residues, in all directions.All trajectories were solvated with ions sufficiently to neutralize the charged residues only (minimum of three chlorine atoms).
A "pool" of several thousand randomized structures was generated using Flexible-Meccano 51 to simulate hindered termini trajectories and then sorted by their EE dist .One structure was chosen (EE dist = 0.5 nm) to represent the fully contracted state, and another structure was chosen (EE dist = 7.0 nm) for the expanded state to understand the region under extreme conditions.Two other structures were chosen, one at EE dist = 3.0 nm to reflect the electron microscope structure and SAXS rigid body model prediction in the monomeric form (3.02/3.27nm), and one at EE dist = 5.0 nm as seen in the EM/ SAXS structure when p53 is DNA bound (4.10/5.33 nm).
Each simulation was implemented using the leapfrog integrator with a time step of two fs.Neighbor searching was conducted through the Verlet scheme by a grid algorithm using a cutoff of 12 Å, and the electrostatic potential was implemented through the particle mesh Ewald (PME) method.Temperature coupling was achieved by the Parrinello− Rahman barostat, and the Nose−Hoover thermostat was used to maintain a temperature of 298 K.The LINCS algorithm was employed with hydrogen bond constraints.The simulations were minimized by using the steepest descent algorithm.The system was then equilibrated at constant pressure (NVT) for 500 ps and at constant volume (NPT) for one ns.An additional 100 ns of relaxation time was given to ensure the system was not oversampling high-energy states before trajectory collection began.Each trajectory was then given time to explore its corresponding free energy landscape, generating frames at each ten ps for analysis.For the restrained trajectories, an additional command was included in the MDP file, freeze_grps, to lock the x,y,z positions of the start and end residues (Glu 281 and Gly 325 ).The trajectories were simulated in replicates of one μs, as seen in Table 1 with total varying lengths of five μs for the unrestrained trajectory, and four μs for each of the restrained trajectories.The only exception is EE dist = 7.0 nm, as it was quickly deemed to contain very little conformational variation.
Analysis of the simulations was performed using a variety of tools and packages.We computed the autocorrelation of the radius of gyration (R g ) of each atom in the molecule for each time step of the MD trajectory (see the Supporting Information).We used this autocorrelation analysis to observe how the radius of gyration changes over time in the system.The R g was computed using the MDTraj Python packages. 52heoretical scattering intensities were generated by CRYSOL, version 3.0.3. 53The scattering intensities were investigated in order to provide a visualization of the conformational properties of our system, even when not directly compared to the experimental SAXS data.Secondary structures were determined by the DSSP-PPII program, which permitted the determination of left-handed polyproline II and other traditional secondary structures defined by DSSP. 54NMR Chemical shift predictions were generated by the neuralnetwork-trained Sparta+ suite of codes. 55Free energy plots were generated using the PyEMMA python scripts 56 and the Campos and Baptista approach, 57 and dimensionality reduction (DR) such a principle component analysis (PCA) and clustering (K-means) were done by the python packages included in SciPy/Sklearn. 58PRIMUS was used to generate pairwise distribution plots, 59 and PyMol 60 and Chimera 61 were utilized for visualizations of the protein.
■ RESULTS AND DISCUSSION p53 PTL Treated as an IDP.A structural ensemble was generated at a time step of ten ps from the PTL unrestrained trajectory using the gmx trjconv tool.The theoretical scattering curves from the CRYSOL predictions of the simulation show a strongly disordered region (Figure 3a).The dimensionless Kratky plot (Figure 3b) indicates that the trajectory, in its unhindered state, is highly flexible and disordered.The pair distance distribution function (Figure 3c) is a statistical measure used to analyze the distribution of distances between pairs of atoms within a system.The distances for the unrestrained PTL region are distributed from 0 to 80 nm, with a singular peak value of around 25 nm.The shape of the curve suggests a disordered structure that is not trapped in specific conformational wells, sampling a sufficient amount of the phase space available.The R g plot (Figure 3d) suggests that the trajectory settles comfortably at about 1.8 nm.However, it can expand up to 3.4 nm and naturally contract to around one nm in its unrestrained form.Additionally, the trajectory was assessed using autocorrelation calculations, as seen in the Supporting Information.
By compiling the dihedral angles into an "integrated Ramachandran plot," we understand the possible secondary structures sampled in the trajectory.The distribution of dihedral angles is expressed (Figure 4a), with four regions of interest, as described in a similar investigation. 62These regions are commonly associated with the formation of specific secondary structures, including β-strands (I), polyproline type II (PPII) helices (II), 3 10 -and right-handed α-helices (III), and left-handed α-helices (IV).The relative distribution of these dihedrals in the unrestrained trajectory shows the prospective secondary structures available (Figure 4b).The majority of the trajectory is purportedly in the PPII region (∼45%) with very little to no (<3%) left-handed α-helices.In addition to the dihedral angles, a DSSP-PPII analysis of the MD simulations was performed to obtain an estimated secondary structure (Figure 4c).From this analysis, most of the trajectory seems to be unstructured, with some instances of helices, bends, and turns.While the integrated Ramachandran suggests the presence of β-strands or α-helices that are not detected in such quantities in the DSSP-PPII predictions, there is agreement for PPII helices.The integrated Ramachandran plot shows that ∼45% of the replicates exist in a region associated with PPII helices, and the DSSP-PPII analysis detected ∼19% of the unrestrained trajectory present structures that have been identified as such.This is expected, as PPII helices have been observed frequently in disordered regions of proteins.As opposed to the common helical structures, the PPII helices have little to no hydrogen bonding capacity and have been observed to play a role in interactions between the domains of the proteins.
In addition to the transient secondary structure in the largely disordered regions, the intramolecular contact between the residues is of note for loop dynamics.The minimum distances observed between any given residue pair were plotted for analysis (Figure 5).Regions shaded in blue or purple represent residues that are permitted to contact.By contrast, regions shaded orange or red are residues that are not capable of interacting.These regions are significant because, in regions where the residues are in contact and interacting (e.g., hydrogen bonding), there are typically adjacent regions that make contact conformationally unobtainable or extremely unlikely.Figure 5a is also overlaid with a second black/white contour plot, demonstrating the probability that the two residues are in contact as a significant portion of the total trajectories.Dotted lines are drawn between the residues to discern these high-probability interaction sites.
Several residues share significant contact in the unrestrained trajectory (Figure 5a).The maximum number of contacts per residue is plotted (Figure 5b), with several contacts spread across multiple residues.In contrast, others are concentrated between specific points (Figure 5c).Nearly all of these residue interactions occur between residue pairs containing either one (blue) or two (purple) proline residues.Only one significant site of interaction was observed between nonproline residues, GLY 302 and ARG 306 (red), highlighting the oftentimes overlooked importance of the proline residues' contribution to the overall structure in IDPs/IDRs.p53 TET Treated as an IDR.So far, analysis has been concentrated on the PTL region simulated as an independent free-moving IDP.We now seek to compare with the terminally restrained trajectories to gain an understanding of the IDR as its energy landscape diverges.The shape factor analysis for the restrained trajectories can be seen in the Supporting Information, although since the trajectories were artificially restrained, the results are negligible.DR techniques such as PCA allow us to compress large data sets, identifying meaningful patterns.Figure 6a shows a PCA DR on the ϕ and ψ dihedrals in the unrestrained trajectory, with the free energy estimated using PyEMMA's plot_f ree_energy tool. 56he reduction splits the trajectory into six distinct clusters clustered using k-means clustering (Figure 6b).Evaluating the clusters by R g (Figure 6c) and EE dist (Figure 6d) we see that the clusters follow specific patterns corresponding to collective variables.Clust Applying this machine learning technique to the restrained trajectories shows that the conformational landscape is greatly altered by restricting the end terminals (Figure 6e−h).Comparing these landscapes, we can interpret a bifurcation in the available conformations present when the end terminals are hindered by globular regions, as in internal IDRs.In the contracted state (EE dist = 0.5 nm), the trajectory exhibits a significant region of the phase space at lower energy states, with few to no restrictions on the conformations sampled.As the trajectory is simulated at a more expanded state (EE dist = 3.0 nm), we see the development of restricted regions and energetically unfavorable states.At an EE dist of 5.0 nm (Figure 6g), the landscape begins to resemble the unrestrained PTL trajectory, with noticeably reduced regions akin to Clust 5 /  Clust 6 (Figure 6b).When the simulation is extended (EE dist = 7.0 nm), the landscape presents strong separations between the conformations and rarely settles in energetically favorable conformations (Figure 6h).
Evaluating the observed secondary structure (Figure 7a), several notable trends emerged.As the EE dist increases, random coils are increased, while all other instances of secondary structure (bends, turns, α-helices, and β-sheets/strands) decrease.The one exception to this trend is the PPII helices, which noticeably increase from ∼10% at 0.5 nm to ∼21% at 7.0 nm.The integrated Ramachandran plot (Figure 7b) also shows a similar trend, with the regions associated with PPII helices increasing upon expansion, while those about α-helices decrease.This interchange in structure between more globularrelated moieties to intrinsically disordered structures upon expansion is a significant clue to interpret how the p53 tetramerization process is implemented.In simpler terms, stabilization at extended states appears to depend more on the formation of PPII helices than those that stabilize globular regions.
Intramolecular interactions are crucial to understanding the influence of expansion on the disordered regions and how these regions operate differently between internal IDRs and IDPs. Figure 8a−d shows the contact probability for each restrained trajectory.The contacts between the end terminals are excluded from analysis, as they are in forcibly close proximity to each other.As expected, the number of interactions decreases as the trajectory is extended (Figure 8e).Comparing the contact map from the contracted PTL trajectory (Figure 8a) to the contact map from the unrestrained trajectory (Figure 5a), there is a region that indicates that intramolecular interactions are prohibited, whether the trajectory is restrained at any length or unrestrained, between Gly 298 and Glu 302 .Interactions between these regions are discouraged by the structure, whether the simulation is restrained or freely moving.A possible explanation for this is binding in local adjacent residues, which "pinches" the sequence, prohibiting the residues from interacting.In the contracted trajectory, contacts are generally between distant residues, while more extended trajectories show favoritism for  local residue interaction.This shift in the localization of the contacts may contribute to the transition in secondary structure from traditional α-helices and β-sheets to the more typically disordered associated PPII helices, which have been recorded to play a significant role in IDRs. 63The percent instances of PPII helices (Figure 9a) and more traditional 3 10 -/ α-/π-helices (Figure 9b), as determined by DSSP-PPII, are plotted for analysis.
The presence of PP-II helices is observed most when the segment is extended and the least when contracted.Still, the change in the secondary structures is not found unilaterally across all residues.The helices forming between Glu 298 −Gly 302 and Lys 320 −Leu 323 are less impacted by the span of the region.In sharp contrast, the PP-II helices found between Lys 291 − Glu 298 , Arg 306 −Gln 310 , and Pro 316 −Lys 320 seem diminished at smaller EE dist .For other helices, three regions present such structure; Arg 283 −Asn 288 , Gly 302 −Asn 305 , and Lys 310 −Ser 314 .Toward the N-terminus, this is most likely due to a partial secondary structure extending from the DBD, which, while not predicted in the IUPred (Figure 2), is observed in the EM structure and several rigid body models.The existence of these helices is favored at 3.0 and 5.0 nm and hindered at extreme EE dist .The other two regions seem transiently in the unrestrained and restrained simulations, with a significant preference (∼25%) when extended.These transient structures at which restraints are observed paint a picture of a dynamic region that is stabilized differently in different conformations.
In terms of the structures formed, there is great difficulty in expressing the conformations available in an ensemble due to the tremendous number of degrees of freedom.Generating clusters requires a focus on preserving the relationship of data as it is expressed in lower dimensional space.Since PCA primarily preserves the variance in the data, a more complex DR technique is required for representative sampling, in this case, t-distributed Stochastic Neighbor Embedding (tSNE).For the unrestrained trajectory, tSNE DR was implemented using the ϕ and ψ dihedral angles as features, generating a reduced landscape (Figure 10).The different states in the landscape were clustered using density-based OPTICS clustering algorithms and plotted with colors according to the averaged propensity for PPII helices.Nine clusters were determined to describe the trajectory well (>95% of all total structures) with a silhouette score of ∼0.83.The comparison of the other cluster sizes, as well as the individual PPII propensities (Figure S10) based on a previous investigation into the importance of such structures for similar systems. 63he nine clusters from the unrestrained trajectory all contain some residues with PPII helices, as demonstrated by the DR and clustering (Figure 10) ranging from four to 12 residues on average.The distribution of the PPII helices varies, although there is a strong preference for the C-terminal and central residues.In three clusters, 2/4/8, some α-helices are also visible at the central residue.This structure has partially been observed in the electron microscopy 24 of the monomeric form at this region.Experimental Assays and Models Assessment.The CS predictions from the various atoms in the residues were predicted using Sparta+ and compared (Figure 11) to the experimental NMR data 38 for their correlation coefficient (R 2 ) and RMSE.The experimental results errors are 0.015 ppm for 1 H and 0.15 ppm for 13 C and 15 N.The C β all produce such an excellent agreement (>0.99) that comparison between the models is ineffectual.The H N CSs were not considered due to such a low correlation between experimental data and predicted CSs (<0.1), although the trend is the same as observed for other atoms (Figure 11).Additionally, the 15 N CSs were also removed due to the nature by which Sparta+ derives its predictions.Since proline residues are particularly difficult to obtain experimentally, and Sparta+ is a neural network trained on experimental data, the program omits proline residues for 15 N CSs. 55The PTL contains numerous proline residues; therefore, the 15 N CSs were excluded.
The backbone carbons, however, strongly prefer the trajectory simulated with EE dist = 3.0 nm, improving the RMSE by 0.22 nm from the unrestrained trajectory with C α atoms and the R 2 value from 0.33 to 0.56 for the C′ atoms.These results also agree with the EM structure observed (Figure 2) as the distance between the end terminals in the observed monomeric structure was 3.02 nm.The least agreement is found in the trajectories fully extended or fully contracted (0.5 and 7.0 nm), with the unrestrained trajectory somewhere in between.This tells us that sampling the trajectories with restrained terminals has a higher agreement regarding sampling local interactions and environments, drastically improving the model's agreement with the experimental data.
Several rigid body models were generated/tested based on SAXS data collected of the protein in different bound states and compared to those generated from EM, 24,64,65 as well as a predicted p53 monomeric form generated by AlphaFold. 66As seen in Table 2 the p53 protein can adopt multiple conformers depending on the bound state, and due to the limitations in the resolution of the experimental methods, these EE dist values differ slightly.The observed general trend, however, is that p53 in its monomeric form expands upon tetramerization and DNA binding from ∼3 nm to ∼4.5 nm and contrasts upon binding to RNAPII to ∼2.4 nm.The AlphaFold prediction seems to underestimate the EE dist by about 0.6 nm.The overall EE dist distribution from the unrestrained trajectory can be seen as a box plot (Figure 12), with the restrained trajectories displayed as black lines and the experimental regions for the different bound states overlaid.Noticeably, the unrestrained trajectory explores conformations that are not observed in any experimentally derived methods (EE dist > 6 nm), and this is reflected by the agreements seen between the NMR CSs (Figure 11).

■ CONCLUSIONS
The PTL region, when simulated as an IDP, is highly flexible and disordered, as shown by the predicted disorder (Figure 2) and by the Kratky plots from the simulation (Figure 3b).It is permitted to sample a wide variety of structures, predominantly PPII helices and random coils (Figure 4).Additionally, multiple likely sites of intramolecular interactions can be observed in the unrestrained trajectories (Figure 5), primarily consisting of proline residues.When the PTL was simulated with terminal restraints, the free energies were greatly shifted (Figure 6) with increased barriers and separation between the states observed at greater EE dist .The PTL also samples different secondary structures, with a preference for random coils and PPII helices at greater extended states (Figure 7).The intramolecular interactions also diverge, with a preference   for distant and internal interactions in contracted states and more local, terminal interactions as the PTL is expanded (Figure 8).Overall these changes show a greatly altered conformational ensemble generated from the restrained trajectories to the unrestrained.Further investigation would be fruitful to test for the influence of the zwitterionic or neutral state of the termini, specifically for intermolecular interactions of the IDR.Testing these conformations against experimental CSs shows a strong preference in agreement for the conformations encapsulated by the restrained trajectory at EE dist of 3.0 nm.This distance partially agrees with the structures obtained through SAXS rigid body modeling and EM (Figure 12).

■ ASSOCIATED CONTENT
* sı Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00971.RMSD plots from all the molecular dynamics trajectories, R g plots and solvent-accessible surface area (SASA) plots for the restrained trajectories, shape factor analysis for the restrained trajectories, autocorrelation plots for all trajectories, free energy plots for the unrestrained trajectory separated by individual replicates, EE dist distances and R g plots for the different replicates of the unrestrained trajectory, tSNE dimensionally reduced landscapes for the restrained trajectories, CS prediction errors for all trajectories by residue, root-mean-square fluctuation (RMSF) plots for each trajectory, and the hydrogen bonding observed by trajectory per residue (PDF) ■

Figure 1 .
Figure 1.Structural analysis of the p53 functional domains and the amino acid residues presented.Disordered regions are shaded gray with the PTL highlighted in yellow.

Figure 2 .
Figure 2. 3D representation derived by electron microscopy24 (top) for the monomeric form of this region with the TET region highlighted in yellow and the PTL in red and the predicted disorder (bottom) for the p53 protein displaying the intrinsically disordered PTL and REG regions connected by the TET domain based on IUPRED.25

Figure 3 .
Figure3.Form factor (a) comparing the scattering vector (q) to the normalized intensity (I(q)/I(0), dimensionless Kratky plot (b) incorporating the R g , pairwise distance distribution (c) of the distances between atoms (r) and the probability (P(r)) that they will be found in such state, and R g distribution (d) for the 5 μs unrestrained trajectory.Shaded regions represent the standard deviation between each replicate.

Figure 4 .
Figure 4. Secondary structure predictions based on the distribution of phi and psi angles in the integrated Ramachandran plot (a).Four distinct regions were highlighted for their propensity (b) to form specific secondary structures; (I) β-strands, (II) poly proline type II helices, (III) 3 10 -and right-handed α-helices, and (IV) left-handed α-helices.Propensity is also shown using DSSP-PPII (c) for comparison.
1 and Clust 3 seem to have high EE dist and R g , while clusters Clust 5 and Clust 6 are relatively low for both.It appears that clusters Clust 2 and Clust 4 contain a mixture of both high and low values.

Figure 5 .
Figure 5. Minimum distance map (a) of the unrestrained trajectory determined between each residue (colored) as well as the probability of contact (within 0.3 nm) between each residue shaded black overlaid upon each other.Sites of notable and regular contact are highlighted with dotted lines.The maximum number of contacts is projected (b), and the seven most notable contacts are plotted (c) with shading according to the presence of proline.Purple bars are proline−proline interactions; red bars contain no proline interactions; and blue bars are proline−x residue interactions.

Figure 6 .
Figure 6.Dimensionally reduced free energy surfaces of the unrestrained trajectory (a) as well as the restrained trajectories (e−h).Different regions of the unrestrained trajectory were clustered (b) using K-means clustering and evaluated for the individual frames' R g (c) and EE dist (d).

Figure 7 .
Figure 7. Relative distribution of polyproline type II helices, random coils, turns, bends, β-strands and β-sheets, and α-helices (a) at different EE dist values predicted by DSSP-PPII (solid lines).The average EE dist (vertical) and the distribution of the secondary structure from the unrestrained trajectory (horizontal) are plotted with dotted lines.The distribution of dihedral angles in specific regions of the Ramachandran plot (b).

Figure 8 .
Figure 8. Minimum distances observed between α-carbons by residues in the restrained trajectories at 0.5 (a), 3.0 (b), 5.0 (c), and 7.0 nm (d) with dotted lines representing sites of significant contact.The average contacts by EE dist (e) and by residue (f) are plotted for comparison.

Figure 10 .
Figure 10.Graphical representation of the tSNE distributed landscape of the unrestrained trajectory along the ϕ and psi dihedral angles.Nine clusters were generated using the density-based OPTICS clustering algorithm, and the average number of residues with predicted PPII helices was calculated for color comparison on the plot (color bar).Graphical representation of the nine clusters can be seen (1−9) with PPII helices highlighted in purple and α-helices in green.

Figure 11 .
Figure 11.Comparison of predicted and experimentally obtained NMR CSs for the C α and C′ atoms by root-mean-square error (RMSE) and correlation coefficient (R 2 ) for residues in the PTL trajectories at various EE dist and the unrestrained (CNT) trajectories.Error bars are generated, showing the standard deviation of the RMSE and RSQ for each frame compared to the experimental CSs.

Figure 12 .
Figure 12.Distribution of PTL EE dist from the unrestrained simulation depicted as a box plot with vertical lines representing the restrained trajectories.Dotted lines are drawn to represent the PTL's span as observed from SAXS and EM for (red) p53 monomeric form unbound, (blue) p53 monomeric form bound to RNAPII (PDB: 6XRE), and (green) p53 tetrameric form bound to DNA (PDB: 7Y00).

Table 1 .
Simulation Parameters for the PTL Trajectories a The restrained trajectories (E dist ) are given in nanometers, the number of Cl − and Na + ions, and the total simulation time (in μs). a

Table 2 .
Distribution of PTL EE dist Observed from Predicted Models and EM for Different States of the p53 Protein