Restoration of the Y220C p53 Full-Length Mutant by PK11000: a Molecular Dynamics Study of an Intrinsically Disordered Protein

Abstract

The tumor suppressor protein p53 plays a key role in cellular homeostasis, with its dysfunction linked to over half of all cases of human cancer. The Y220C mutation in the DNA-binding domain (DBD) destabilizes p53, compromising its function. The most well-studied case of Y220C p53 rescue via a small molecule, PK11000, has been shown to restore stability and reinstate activity both in vitro and in vivo in rodent models. While prior in silico studies have focused on the DBD in isolation, this work explores the full-length p53 protein, incorporating its intrinsically disordered N- and C-terminal regulatory regions, which are known to be sites of extensive post-translational modifications utilized to modulate its activity. Using molecular dynamics (MD) simulations, we investigate the wild-type (WT) p53, the destabilized Y220C mutant, and the PK11000-rescued Y220C variant. Our findings illuminate a multilayered allosteric landscape: the Y220C mutation disrupts DBD stability through long-range effects while PK11000 counteracts this destabilization through its own distal interactions. Importantly, the N- and C-terminal regions mediate additional allosteric regulation, dynamically influencing both the mutation’s impact and the rescue mechanism. This triple allosteric framework underscores the regulatory regions’ critical role in restoring p53 functionality. By providing a first-order exploration into the behavior of full-length p53, this study advances our understanding of its regulatory mechanisms and sets the stage for developing targeted therapies aimed at reactivating mutant p53 in cancer.

Introduction

The mechanism underlying allosteric regulation is often referred to as the “second secret of life.” Allostery is the means by which an enormous number of biological functions occur, including but not limited to bacterial promoter control, , DNA repair, , G-coupled protein signaling, , protein kinase regulation, and transcription activation, and as such, it is hard to overstate its importance. Despite this, the exact mechanism of allostery remains elusive. Two pervasive models exist, one being the pathway model − and the other being the energy landscape model. − The pathway model supposes that a local perturbation will have a domino effect on neighboring residues, transducing a signal from the site of the perturbation to some allosterically active site. The energy landscape model posits that the local perturbation will alter the local energetic network, which will have a similar domino effect from the site of the perturbation to the allosterically active site.

While allostery is typically considered in the context of ligand binding, a more generalized definition could encompass post-translational modifications or mutations. Such allosteric interactions play a critical role in the tumor suppressor protein p53 carrying out its function, acting as the so-called "guardian of the genome", protecting against cancers. − While the disruptive effect of some common point mutations (known as "hotspot" mutantions) at the interface of p53 and its DNA binding sites can be readily rationalized, many others, like Y220C, occur distally, conferring a change across the protein allosterically. − Furthermore, post-translational modifications (PTM) known to modulate p53 activity in the core DNA binding domain concentrate almost exclusively in the disordered N- and C-terminal domains. , Similarly, the serendipitous discovery of PK11000, a restorative compound for the Y220C p53 mutant, acts from yet a third site distal from the original mutation and the active site. These observations raise the question of how the transcriptional activity of p53 via the DNA Binding Domain (DBD) is influenced by modulators acting from distal locations largely lacking secondary structure.

Furthermore, preliminary studies indicate that truncating the N- and C-terminal domains at various points, as is observed in the naturally occurring splice variants, also affects the DBD activity as a kind of hard-coded signal. While this may not be considered allostery in the traditional sense, we show in this paper that the removal of the N- or C-terminal domain causes a physical and energetic perturbation that propagates through to the DBD, categorizing it as a type of allostery. With these observations in mind, we aim to gain atomic-level structural insights into the full-length p53 protein, uncovering the mechanisms underlying its multiple layers of long-range regulation. This work represents a step toward not only de novo allosteric drug design for reactivating the Y220C mutant but also developing generalizable principles to guide the design of reactivating compounds for other p53 hotspot mutants.

p53 Structure and Function

The p53 protein, encoded by the TP53 gene, comprises 393 amino acids and plays a central role in regulating cell cycle, DNA repair, and apoptosis, making it a critical tumor suppressor. p53 is activated in response to cellular stress, particularly DNA damage, and plays a critical role in mediating cell cycle arrest, apoptosis, and senescence. − Under normal conditions, p53 is negatively regulated by MDM2, an E3 ubiquitin ligase that targets p53 for proteasomal degradation. − Upon stress induction, post-translational modifications such as phosphorylation at Ser15 and Ser20 disrupt the p53-MDM2 interaction, stabilizing p53 and allowing its accumulation and activation. Dawson et al. used NMR to show that the N-terminal domain of p53, notably including the transactivation domain, has a high chain flexibility and an absence of tertiary structure except transiently. Wells et al. use similar approaches to exhibit that the p53 transactivation domain forms a transient α-helix upon binding to MDM2. p53 has also been shown to become more rigid and compact upon binding to DNA.

At the core of p53’s activity as a transcription factor is its well-studied DNA-binding domain (DBD) spanning residues 94–292, which enables sequence-specific interactions with DNA to modulate genes involved in cell cycle arrest, DNA repair, and apoptosis. This domain adopts a β-sandwich structure, characterized by two opposing antiparallel β-sheets. The β-sandwich is stabilized by loops that engage in direct DNA interactions. Notable DNA-contacting residues within these loops include Arg248, Arg273, and Lys120, whose precise interactions with DNA’s phosphate backbone are critical for transcriptional specificity. Mutations to Arg248 in loop L3, which directly contacts DNA and provides stability to the p53-DNA complex, such as R248Q, significantly impair p53’s DNA-binding ability, contributing to the loss of tumor-suppressive function. Arg273, located within loop L1, also forms stabilizing hydrogen bonds with the DNA backbone; mutations here, including R273H, further undermine DNA-binding capacity, disrupting p53’s regulatory role. Lys120, positioned within loop L2, interacts with the minor groove of DNA, adding another layer of specificity in recognizing target promoters.

The structural integrity of the DBD is further supported by a zinc ion coordinated by Cys176, His179, Cys238, and Cys242. , This ion is crucial for maintaining the DBD’s conformation, as it stabilizes the β-sandwich structure and its associated loops. Loss of this coordination, whether due to mutations or external factors affecting zinc availability, destabilizes the DBD, leading to misfolding and reduced DNA-binding efficiency. For instance, the gain-of-function mutation Y220C introduces a destabilizing cavity in the DBD, resulting in partial unfolding that compromises p53’s DNA-binding and tumor-suppressive capabilities. Such mutations within the DBD are prevalent in p53-related cancers.

While the DBD is structurally well-defined, the N- and C-terminal domains are intrinsically disordered, resulting in poor structural characterization. Despite this, they each play critical roles in the regulation of p53. , The N-terminal domain (NTD), comprised of residues 1–95, is primarily made up of two subdomains. The transactivation domain (TAD), located at residues 1–61, facilitates the recruitment of transcriptional coactivators necessary for p53’s gene regulatory functions, and is itself made up of two subdomains, TAD1 and TAD2. A proline-rich domain (PRD) from residues 62–90 contributes to apoptotic signaling and interactions with proteins such as p300/CBP.

The C-terminal domain (CTD), extending from residues 363–393, is highly flexible and undergoes various post-translational modifications (PTMs), including acetylation, ubiquitination, and phosphorylation. These modifications play a regulatory role in modulating p53’s DNA-binding affinity and protein–protein interactions, enabling dynamic responses to cellular stress signals. For instance, acetylation at the CTD can enhance DNA affinity, whereas ubiquitination, the universal signal for degradation, targets p53 for proteasomal breakdown, regulating its intracellular concentration and activity. The disordered C-terminal domain also contains the tetramerization domain (TD), spanning residues 325–356, which is critical for the formation of p53 tetramers, which are required for high-affinity DNA binding and robust transcriptional activation. ,

While the p53 DBD has been extensively studied using techniques such as X-ray crystallography and, more recently, cryo-electron microscopy, , due to the disorder and complexity of the N- and C-terminal domains, most structural studies to date have focused primarily on the DBD, leaving the dynamics of the full-length protein largely unexplored. This raises the critical question of how the N- and C-terminal domains, almost exclusively housing all the post-translational modification sites, confer DBD specificity. At a more fundamental level, it raises the question of the structure and dynamics of the full-length protein. This lack of knowledge hinders the ability to fully grasp p53’s role in cellular decision-making and limits the development of targeted cancer therapies designed to modulate p53 activity. Given the importance of p53 function for prevention of cancer, understanding how mutations disrupt p53’s function and identifying restorative compounds that can reactivate its activity is of great importance.

As an alternative to experimental studies, another promising approach to study the dynamics of the DBD is the use of molecular dynamics (MD) simulations, − which allows the focused study of allosteric disruption by the Y220C mutation and allosteric rescue by the small molecule PK11000. These studies revealed mechanistic insights into how PK11000 reinstates wild-type-like behavior in the mutant protein. Specifically, root-mean-square deviation (RMSD), root-mean-square fluctuation (RMSF), hydrogen bond analysis, sector analysis, ,, and electrostatic analyses demonstrated that, at least in the DBD of p53, the wild-type protein predominantly adopts a single conformation, the Y220C mutant favors a distinct alternative conformation, and the PK11000-bound Y220C mutant returns to the wild-type conformation.

While these observations provide compelling insights, they are limited to the DBD. Experimental evidence for the restoration of Y220C by PK11000 relies on the full-length (human) protein, raising important questions about the role of the N- and C-terminal domains. Together, these domains account for nearly half of the protein’s residues and as discussed in the context of PTMs, are critical for its regulatory functions. Furthermore, preliminary studies using short MD simulations of naturally occurring wild-type splice variants of p53 revealed distinct dynamic behaviors between the variants, though the specific contributions of the different domains to these dynamics remain unclear.

Figure shows a structural diagram of the full-length, 393 amino acid p53, generated by Phyre2, with the Y220C mutation and PK11000 small molecule added in PyMOL (see Methods section for more details).

1.

The full-length 393 amino acid p53, with Y220C mutation and with the PK11000 small molecule bound in orange. The N-terminal domain is in blue, the C-terminal domain is in red, and the DNA-binding domain is in green. DNA is shown bound to p53 in gray.

Mutations and Restoration

Mutations in the p53 gene, particularly in the DNA-binding domain, are implicated in nearly 50% of human cancers, severely disrupting its tumor-suppressive functions. , Efforts to restore wild-type p53 activity, especially through small-molecule reactivators targeting mutant p53, are of immense interest in cancer therapy. These strategies aim to reestablish p53’s conformational stability and transcriptional activity, offering significant potential for treating a wide array of cancers.

Over 25% of all of cancer can be attributed to just a dozen “hotspot” point mutations. ,, The IARC database keeps a continuous log of the most common hotspot mutations. One mutant of high interest is the Y220C mutation, which creates a cavity in the protein and lowers the melting temperature by 8.6 °K.

Another feature of the Y220C mutation of p53, is the propensity to form amyloid-like aggregates in cancer cells, caused by incorrect folding. These aggregates have pathogenic roles by limiting the function of wild-type p53, leading to oncogenic gain-of-function phenotypes such as enhanced proliferation, migration, and therapy resistance. Work by Silva et al. also indicates that mutant p53 aggregation often happens through condensate to solid transitions, along with alteration of the tumor environment, transcriptional landscapes, and response to treatments. This hypothesis is shared by Kwan et al., who state that many mutations favor amyloidogenesis, and that restoring native p53 function may not only require conformational stabilization but also intervening and directly preventing or reversing aggregation.

This idea is also supported by experimental evidence that small molecules can solubilize aggregated forms of mutant p53, restoring its function. The work by Paz et al. showed that in hepatocellular carcinoma models, Y220C mutations create cytoplasmic amyloid oligomers that can be disrupted by PRIMA-1, which lead to transcriptional reactivation of p53 targets, suppressing gain-of-function behavior. Findings by Rangel et al. are complementary, showing that PRIMA-1 prevents the formation of new aggregates and can also dissolve amyloid-looking inclusions in breast and ovarian cancer cells, converting p53 to a soluble, transcriptionally working state.

While Y220C ranks relatively low among the most common point mutations, accounting for just 1.8% of cases of cancer, it is known to be rescued by the small-molecule PK11000, which, as noted above, has been shown to eliminate Y220C-induced tumors. PK11000 stabilizes the mutant p53 by increasing the melting temperature by approximately 2.5 K, and human cancer cells see a reduction in viability when treated with PK11007, a derivative of PK11000. These compounds, however, are covalent binders to cysteine with low specificity, making them unsuitable for human use. The allosteric modulation of p53 by PK11000 limits the extent to which structure-based drug optimization can be used to optimize the drug. Nonetheless, it remains a highly interesting case study, with the expectation that any information gained studying PK11000 will be useful in studying and designing other compounds.

Recent Insights from MD Simulations of p53

Several molecular dynamics (MD) studies have contributed to our understanding of p53’s dynamics, particularly regarding the DNA binding domain (DBD) and the effects of mutations. These studies provide critical insight into how mutations like Y220C destabilize the protein and impair DNA binding. For example, an MD simulation study revealed that the Y220C mutation creates a surface crevice that destabilizes the DBD, reducing the thermal stability of p53 and leading to misfolding, which affects DNA binding and contributes to its loss of function in tumor suppression. Restoring the stability of p53 is one of the major ways p53 activity may be restored. , Another study focused on the wild-type p53 in both its DNA bound and unbound forms, examining how it interacts with DNA. The study of the unbound p53 structure helped highlight conformational flexibility, particularly in regions such as the L1 loop, which is key to DNA recognition. These simulations have also shown that mutations within the DBD, such as R248 and R273, disrupt important hydrogen bonding interactions essential for DNA binding.

Taken together, these MD studies provide valuable insight in exploring p53’s function and informing therapeutic strategies aimed at rescuing mutant forms of p53, such as Y220C, by stabilizing key regions that are critical for its DNA-binding capabilities. This growing body of MD-based research, in conjunction with our own contributions, builds a clearer picture of p53’s complex regulatory mechanisms, both for wild-type and mutant forms, and aids in understanding the structural and functional implications of cancer-related mutations. ,,

While prior studies have focused on the DBD in isolation, this work explores the full-length p53 protein, incorporating its intrinsically disordered N- and C-terminal regulatory regions. In this study, we perform MD simulations of the WT protein to gain a baseline understanding of the dynamics of p53, with a special focus on the impacts of the N- and C- terminal domains on the DBD, particularly how they may modulate its behavior. We also simulated the Y220C and PK11000-bound Y220C mutants to understand how p53 loses and regains its DNA binding affinity and specificity. Knowing that PK11000 rescues p53 in vivo, we sought to identify metrics by which this occurs. The results presented here will provide a pathway to further stimulate development in the field of small-molecule modulators of mutant p53.

For a deeper look into these topics, see references or .

Methods

Establishing the molecular dynamics system for this study required optimization of both the initial structural configurations and the force field parameters. The system comprises a partially disordered protein (full-length p53), a non-DNA-interacting zinc ion that stabilizes the DNA binding domain, DNA that interacts directly with p53, the small molecule PK11000, explicit water molecules, and counterions (Na⁺). Selecting compatible and accurate force fields to model these diverse components was particularly challenging due to the unique characteristics of the system, including the intrinsically disordered regions of p53 interspersed by the folded DBD. To ensure the validity and reproducibility of our simulations, we provide here a detailed account of the methods used to construct and parametrize the system.

Modeling Full-Length p53 Starting Structures with Phyre2 Protein Folding

To model the full-length wild-type p53 protein, including its intrinsically disordered N- and C-terminal regions, we utilized the Phyre2 protein fold recognition server. Phyre2 employs homology modeling, threading, and ab initio techniques to predict the three-dimensional structure of proteins based on their sequence. Specifically, it uses a library of experimentally determined structures to identify homologous sequences and generate models, offering accurate predictions even for disordered or unresolved regions. The resulting 393-residue model of WT p53 included the previously unresolved N- and C-terminal domains, creating a suitable starting structure for simulations. The AlphaFold3 , predicted model of the full-length human p53 was considered, however, it reports very low confidence in the N- and C-terminal regions. We thus opted for the Phyre2 version. The Phyre2 model also predicted lower confidence in the N- and C-terminal domains, but compared to the AlphaFold3 model, the Phyre2 model is more compacted. In the context of intrinsically disordered domains, this would typically give a preference then to the AlphaFold3 model, but we felt that the N- and C- terminal domains were so unfolded and extended that they did not represent the physical conditions of the cell, namely, cramped, and filled with water other large molecules which would lead to a compaction of the structure. With this in mind, we felt the slightly more compact model generated by Phyre2 to be more physical.

The predicted structure was then superimposed onto the 1TUP crystal structure of the p53 DBD defined in this paper as residues 96–289, along with bound DNA and the zinc ion. Using PyMOL (“The PyMOL Molecular Graphics System, Version 2.0”), we replaced residues 100–285 of the Phyre model with the corresponding residues from 1TUP, ensuring alignment of the DBD. The N- and C-terminal regions from Phyre were retained, and small overlapping regions of the 1TUP crystal structure (residues 96–100 and 285–289) were removed to resolve conflicts at the boundaries. This resulted in a hybrid model incorporating the crystal-resolved DBD (residues 101–289, with DNA and zinc) and the Phyre-predicted N- and C-terminal regions (residues 1–100, 290–393). Particularly, Phyre2 was unable to incorporate the zinc atom in its homology model, resulting in an incorrect structure for the zinc corrdinating residues. Zinc coordination with Cys176, His179, Cys238, and Cys242 was established during parametrization of the system in in the AMBER molecular dynamics package’s tLeaP module. ,,

Using this hybrid WT structure, the Y220C mutant was generated by introducing the point mutation in PyMOL. The drug-bound systems, WT_PK11000 and Y220C_PK11000, were created by superimposing the Y220C_PK11000 DBD structure from Han et al. (denoted simply as the PK11000 structure in that paper) onto the WT and Y220C full-length structures, respectively, in PyMOL. All components from the DBD structure except PK11000 were removed, leaving the drug in its correct binding position. In tLeaP, PK11000 was covalently bonded to Cys182, as described by Han et al.

Protonation and Charge-State Preparation

Protonation states were assigned using the H++ 3.0 server, which predicts residue protonation at a target pH based on electrostatic calculations. The system was protonated to pH 7.0. For the histidine residues, residue H214 was predicted to be in the epsilon protonation state, while residues H115, H168, H178, H193, H233, H296, H297, H365, H368, and H380 were predicted to be in the delta protonation state. However, to maintain comparability with the study conducted by Han et al., we chose to revert H115, H168, H178, H193, H214, and H233 to the epsilon protonation state. Extensive testing concluded that p53 is sensitive to the protonation state of its histidine residues, and that this set of protonation states maintains folding of the DBD.

Deriving DNA-Binding Domain (DBD) Structures

To isolate the DBD structures for the different constructs for comparative simulations, residues 1–95 (the NTD) and 290–393 (the CTD) were removed from each full-length model. This ensured consistent zinc placement, protonation states, and initial structures between the full-length and DBD-only systems, facilitating direct cross-comparisons. Notably, residues 96–100 and 285–289 from the Phyre model were retained in the DBD structures for consistency.

Force Field and Parameter Selection

Accurately modeling the diverse components of the p53 system required careful evaluation and selection of compatible force fields and parameters. After extensive testing, the ff14SB force field was selected for the protein, owing to its robust performance and reliable agreement with p53 DBD simulations. For nucleic acid dynamics, the bsc1 force field was employed to model the DNA. The parameters for the PK11000 small molecule were derived using the GAFF2 force field in combination with AMBER’s Antechamber module. Zinc was parametrized using the ZAFF force field, ensuring proper coordination with its chelating residues, Cys176, His179, Cys238, and Cys242. The TIP3P water model was chosen for solvation, as it offers well-established compatibility with ff14SB. As is the default with the ff14SB force field, counterions (Na⁺) were parametrized using the Li/Merz 12–6 parameters to maintain system neutrality and ionic strength.

The selection process involved evaluating multiple protein force fields, including ff19SB, ff14SB, and ff99SB_ILDN, in combination with TIP3P and OPC water models. Variations in protonation states and parametrization schemes were also tested to optimize system performance. Although ff19SB has shown improvements for certain proteins and other niche protein/water force field combinations promise accurate simulation of IDPs, the limited experimental validation for p53 dissuaded their use in this study. Ultimately, ff14SB was chosen due to its consistency with high-confidence DBD simulations and its compatibility with other system components. Figure S1a–f shows the secondary structure of several of the tests conducted. We observed that the above-described conditions yield the most stable.

Molecular Dynamics Simulations

The prepared systems were used to conduct molecular dynamics (MD) simulations to investigate the dynamic behavior and interactions of the full-length p53 protein, its Y220C mutant, and the PK11000-rescued variants. Our protocol follows recommended practices in the field for macromolecular simulation with the AMBER simulation package, consistent with procedures used in our recent project designs. ,,,,− In brief, simulations were performed in explicit TIP3P solvent in an octahedral box with periodic boundary conditions and particle mesh Ewald (PME) electrostatics to handle long-range interactions. Each simulation began with energy minimization to relax unfavorable interactions, followed by heating to the target temperature of 300 K under constant volume conditions. Equilibration was conducted under constant pressure to stabilize the system density, after which production simulations were carried out. Example input files are included in the supplemental files. This approach ensured the stability of the systems and allowed for robust analysis of their dynamics. Simulations were set up and carried out on Wesleyan University’s High Performance Computing Cluster.

Replicates and Convergence

For each construct, FL WT, Y220C, WT_PK11000, and Y220C_PK11000, and DBD WT, Y220C, WT_PK11000, and Y220C_PK11000, four replicates were run for 1000 ns each. Additionally, for the full-length structures, all 4000 ns were concatenated together, sampling 10 frames per nanosecond, stripped to only residues 110–289, leaving just the DBD, then clustered in AMBER’s cpptraj using the kmeans command with k = 10 to seed starting structures for 10 additional 200 ns FL simulations, totaling 6000 ns for the FL constructs.

Computational Analyses

A variety of analyses were carried out to assess the conformational dynamics of the construct systems. Analyses were performed using cpptraj , from the AMBER18 suite, and Python with numpy, matplotlib, and pandas libraries. Visualizations were made in PyMOL or VMD. Methods for Root Mean Square Deviation (RMSD), Root Mean Square Fluctuation (RMSF), Secondary Structure Analysis, End-to-End Distance, Maximum Pairwise Distance, Radius of Gyration (RoG), and Solvent Accessible Surface Area (SASA) are given in Appendix A1.

Dihedral RMSD

The more disordered a protein, the less significance external coordinates, such as XYZ position, have on assessing stability of the protein, necessitating the development of internal coordinate systems that can accurately measure protein stability over time. We have chosen to use dihedral angles, specifically the φ and ψ angles formed by the intersection of the dihedral planes of residue i and residue i+1.

Dihedral angles were generated with the cpptraj command multidihed using Amber18 sampling one frame per nanosecond, then dihedral RMSD was computed using Python using the following procedure. One consideration is how to compute the distance between an angle (φ₁, ψ₁) and another angle (φ₂, ψ₂). Consider the one-dimensional case, computing the distance between θ₁ and θ₂, both angles within the range [0, 360). The one-dimensional case of the Euclidean distance formula says the distance is $d({\theta }_1,{\theta }_2)=\sqrt{{({\theta }_2-{\theta }_1)}^2}$ , but this fails in the case where, say, θ ₁ = 10 and θ ₂ = 350. Intuition says the distance should be 20 degrees, rather than 340 degrees. We want to take the distance between points in a modulus space, modulus 360 in this case. The way to solve this is by using the formula

$$d_{360}({\theta }_1,{\theta }_2)=\min \{d({\theta }_1-360,{\theta }_2),d({\theta }_1,{\theta }_2),d({\theta }_1+360,{\theta }_2)\}$$

The two-dimensional case generalizes from this. Let

$$S_1=\{{\varphi }_1-360,{\varphi }_1,{\varphi }_1+360\}$$

$$S_2=\{{\psi }_1-360,{\psi }_1,{\psi }_1+360\}$$

$$d^{\prime }(({\theta }_1,{\gamma }_1),({\theta }_2,{\gamma }_2))=\sqrt{{({\gamma }_2-{\gamma }_1)}^2+{({\theta }_2-{\theta }_1)}^2}$$

Then

$${d_{360}}^{\prime }(({\varphi }_1,{\psi }_1),({\varphi }_2,{\psi }_2))={\min }_{{\psi }^{\prime }in{S}_2}^{{\varphi }^{\prime }in{S}_1}{d}^{\prime }(({\varphi }^{\prime },{\psi }^{\prime }),({\varphi }_2,{\psi }_2))$$

Thus, we define Dihedral RMSD to be the following:

$$\mathrm{Dihedral}\mathrm{RMSD}=\sqrt{\frac{1}{N}\sum _{i=1}^N{d}_{360}^{\prime }(({\varphi }_i,{\psi }_i),({\varphi }_{ref},{\psi }_{ref}))}$$

Where ϕ _i and ψ _i represent the phi and psi dihedral angle number i and ϕ _ref and ψ _ref are the reference angles, we used the angle of the first frame of the simulation. Note that dihedral angles are defined between two residues, so there are only 391 of each φ and ψ dihedral angles in the 393 amino acids in the FL p53 chain. We number the dihedral angle between residue i and i + 1 as i + 1.

k-Means Clustering

The cpptraj command cluster is quite versatile, allowing for the clustering of frames with the k-means, hierarchical agglomerative, dbscan, or dpeaks algorithm, based on a variety of metrics: dme, rms, srmsd, qrmsd, Euclidean, and Manhattan.

As a baseline test of the cpptraj built-in clustering, we conducted the following experiment. First, we concatenated all FL frames together, from both the 1 μs and 200 ns simulations, after removing all nonprotein residues and residues 220 (site of the Y220C point mutation), 182 (site of PK11000 binding), which ensured the amino acid sequence of each construct was identical. Further, we removed the first and last 19 amino acids, leaving just residues 20–373, which removed the most dramatic tail-effects. Finally, we sampled 1 frame from each nanosecond. We used this data set to perform the clustering, using the cpptraj command cluster with algorithm kmeans and metric rms. We tested k values between 2 and 7, using the intercluster distance and Left-Shift test , to identify the optimal k value. Further, analysis was done in Python to compare the distribution of frames by construct in each cluster.

However, as shown in the comparison between Euclidean and dihedral RMSD in Figure , Euclidean metrics as less meaningful the more disordered a protein is. The DBD, while being called the "ordered subset" of the protein p53, is still more flexible than many other ordered proteins, leading the Euclidean RMSD metric to be less significant. This led to the development of the following dihedral RMSD based k-means clustering algorithm:

Frames from all constructs were concatenated at a sampling rate of 1 frame per nanosecond, resulting in a data set of 24,000 frames. Each frame included 391 (ϕ,ψ) dihedral angle pairs, yielding a 24,000 × 782 matrix. As discussed in the section on dihedral RMSD, computing the distance between two points in a modulus space requires some modification to the standard Euclidean distance algorithm. We take a slightly different approach here. Taking advantage of the fact that each angle value lies on a circle, each angle pair was transformed (ϕ,ψ) ­(cosϕ,sinϕ,cosψ,sinψ) enabling the use of Euclidean distance for comparison. This transformation expanded the data set to a 24,000 × 1564 matrix, with each frame represented as a 1564-dimensional tuple.

Clustering the raw data directly proved ineffective due to the so-called "curse of dimensionality", where high-dimensional noise overwhelms meaningful signal. Attempts to reduce dimensionality using PCA and t-SNE did not yield a clusterable data set. We began by restricting our analysis to dihedral angles within the DNA-binding domain (dihedral angles 97–289). Further, we analyzed each (cosϕ,sinϕ,cosψ,sinψ) pair individually using the DBSCAN algorithm (using epsilon = 0.25). If an angle yielded only a single cluster, it was removed from the data set. This did leave a clusterable data set, which was clustered using the k-means algorithm in SciPy.

Angles were sampled once per nanosecond, using the cpptraj command multidihedral, and run with Amber18.

Hydrogen Bond Analysis

Two metrics were used to analyze the hydrogen bonding of p53 over time: Total Residence Time (TRT) and Exhaustive Hydrogen Bonding Sums (EHBS). TRT measures the average number of H-bonds per frame, while EHBS counts the total number of unique H-bonds formed during the simulation. Specific focus was given to K120, C277, and R280, which directly interact with nucleotide bases rather than the sugar-phosphate backbone.

We used the command hbond in Amber18 with a frequency of 10 frames per nanosecond to get a summary of all hydrogen bonds that occurred in the simulation. In the resulting data set, each hydrogen bond was given a “residence time”, the fraction of the frames for which the hydrogen bond was present. To compute the TRT of a simulation, we simply summed all residence fractions for all hydrogen bonds. To compute the specific TRT, we summed the fraction of frames for which there was a hydrogen bond made to K120, C277, and R280.

EHBS is a measure of the unique hydrogen bonds made in a simulation. To compute the total EHBS, we simply counted the number of unique hydrogen bonds made.

Together, the TRT gives a measure of the strength of all hydrogen bonds made during the simulation, the specific TRT gives a measure of how strongly K120, C277, and R280 bind to the DNA, and the EHBS gives a measure of how specific p53 is with its DNA binding.

Electrostatic Analysis

We used the command pairwise to generate a matrix of atom-by-atom pairwise electrostatic connections, one from each nanosecond. Following the procedure of Cowan et al. and optimized by Abramson et al., residue-by-residue electrostatic interaction matrices were computed using Python. To normalize the data and highlight highly active interactions, raw edge weights were divided by the total outgoing edge weight at each node, creating a directed multigraph network. The directed multigraph was flattened to a simple weighted graph by choosing the maximum edge weight between nodes i and j. Thresholding was applied at 0.003 to retain only the most significant interactions.

Data Analysis

Much of the data presented here is in the form of a violin plot. Violin plots are similar to box plots in showing the range that a data set spans, but they also show the probability distribution of values in the data set.

Ramachandran plots were generated in Python using the Matplotlib visualization package, using dihedral angle data generated in cpptraj in the Amber package.

Results

In order to uncover the mechanisms underlying p53 regulation and the impact of the Y220C mutation, we conducted extensive molecular dynamics simulations of the full-length protein. This study, incorporating p53 intrinsically disordered N- and C-terminal regions, as well as the structured DBD, allowed us to explore the allosteric effects of the Y220C mutation, the restorative action of PK11000, and the interplay between these factors and p53’s regulatory regions. We simulated the following four constructs of full-length (FL; residues 1–393) p53 and the structured DNA binding domain subset of p53 (DBD; residues 96–289): wild-type (denoted WT), Y220C mutant (denoted Y220C), wild-type with PK11000 (denoted WT_PK11000), and the Y220C mutant with PK11000 (denoted Y220C_PK11000). For each of the four constructs, four independent one-microsecond (μs) replicates were run (denoted Rep1 through Rep4). In addition, for the full-length constructs, the four one-microsecond simulations were concatenated and clustered using the k-means algorithm with k = 10 to seed 40 new simulations, each run for 200 ns. This yielded a total of 6 μs simulations of each FL construct, and 4 simulated μs of each DBD construct. For the full-length proteins, we use the following notation to indicate a subset of the protein: system|_a‑b to indicate residues a-b of the system. For example, FL|_96–289 corresponds to residues 96–289 of the FL, the same residues as in the 1TUP DBD. In this special case, we may also write FL|_DBD to indicate the DBD subset of the FL system.

Analysis of FL Simulations

The first part of this study is to assess and analyze the simulations of full-length p53. We investigate whether the simulations were stable, then we move onto structural analysis of the disordered tails. Finally, we use various metrics to identify and characterize PK11000 rescue of the Y220C mutant.

Global Structural Measures

Euclidean Root-Mean-Squared Deviation (RMSD)

Root mean square deviation (RMSD) calculations were performed for each replicate of every construct, using the first frame of the respective simulation as the reference structure. For the 200 ns trajectories, RMSD was calculated relative not to their own first frame but to the first frame of the simulation from which they were seeded. RMSD values were analyzed both as time series and as histograms, the latter depicting the relative frequency of RMSD values (rounded to one decimal place).

Two subsets of the full-length (FL) p53 protein were analyzed: FL|_1–393, which includes all 393 residues, and FL|_20–373, which excludes the N-terminal residues 1–19 and C-terminal residues 374–393. The FL|_20–373 subset was chosen for detailed analysis to minimize the influence of fraying at the termini, while still encompassing the majority of the protein, including regions of interest.

Figure A presents the time series and histogram RMSD data for the FL|_20–373 constructs across all four replicates. RMSD data for the FL|_1–393 constructs, which closely resemble the FL|_20–373 results, are provided in Figure S2 of the Supporting Information.

2.

Initial survey on the quality and dynamics of the simulations over each of the replicates. Rep1 in maroon, Rep2 in blue, Rep3 in yellow, and Rep4 in green. (A) Time series and histogram data of FL|_20–373 Euclidean RMSD. (B) Time series and histogram data of FL|_21–373 dihedral RMSD. (C) FL RMSF data. (D) Various conformations of the highly mobile loop from residues 45–83.

The RMSD analysis of FL|_20–373 reveals that the structures deviate rapidly from their starting conformations within the first 200 ns of simulation. After this initial period, some trajectories stabilize, settling into local energy minima with RMSD values between 4 Å and 6 Å. However, other trajectories continue to deviate more gradually beyond 200 ns. For instance, the WT_PK11000 Replicate 3 simulation deviates further for an additional 300 ns before stabilizing at approximately 12 Å from the starting structure.

RMSD analysis restricted to the DNA binding domain (DBD), shown in Figure S3, highlights that the majority of the structural deviations observed in the full-length protein are attributable to the intrinsically disordered N- and C-terminal regions. Histogram analysis further supports the conclusion that many individual replicates occupy distinct conformational states, reflecting the dynamic nature of the full-length p53 protein in these simulations.

Dihedral RMSD Analysis

The chaotic behavior of the intrinsically disordered N- and C-terminal regions in the full-length p53 protein significantly obscures the structural insights typically derived from standard Euclidean RMSD. To extract more meaningful signal from the noise, we employed dihedral RMSD as an alternative metric. Dihedral RMSD was calculated for two subsets of interest: FL|_1–393, corresponding to dihedral angles for residues 2–392, and FL|_20–373, corresponding to dihedral angles for residues 21–372. Figure B presents the dihedral RMSD for residues 21–372 as both a time series and a histogram, while data for residues 2–392 are provided in Figure S4 of the Supporting Information.

Similar to the trends observed in Euclidean RMSD, the dihedral RMSD data indicate that the protein undergoes significant deviation from its starting structure during the initial approximately 200 ns of simulation. However, in contrast to Euclidean RMSD, most replicates stabilize after this period, with minimal further increase in deviation. This stabilization results in a greater convergence among the replicates, suggesting a more consistent description of the protein’s conformational landscape. The disparity between the two metrics can be attributed to the sensitivity of Euclidean RMSD to small changes in dihedral angles (ϕ, ψ), which can propagate into large deviations in Cartesian XYZ coordinates, particularly in the disordered tails.

For example, the WT_PK11000 Replicate 3 simulation is a notable outlier in Euclidean RMSD, showing significantly higher deviation from the starting structure compared to other replicates of the same construct. However, dihedral RMSD reveals that its deviation is comparable to that of Replicate 2, which has a more stable Euclidean RMSD, highlighting the robustness of dihedral RMSD in capturing meaningful conformational changes.

Furthermore, the dihedral RMSD histograms closely approximate a normal distribution, in stark contrast to the broader and more irregular distributions observed in Euclidean RMSD. This observation supports the claim that dihedral RMSD provides a more reliable and interpretable measure of structural deviation, particularly for intrinsically disordered proteins, where large-scale Cartesian deviations may not reflect significant conformational changes.

RMSF

Next, we computed the RMSF of each construct across each replicate, as shown in Figure C. Generally, each replicate has a similar distribution of values. As expected, the first and last 20 residues have a much higher RMSF due to fraying. This is the motivation that led us to our consideration of the FL|_20–373 subset. Further, we notice a large spike in values at around residues 45–83, which corresponds to a particularly flexible loop region. Figure D illustrates various conformations this loop region takes over the WT Rep4 simulation. This region is approximately the second half of the transactivation domain and the first half of the proline-rich domain. K120 appears to have the lowest RMSF in the Y220C_PK11000 construct, which agrees with the data reported by Han et al.

Secondary Structure Analysis

Building on the observation that dihedral RMSD and Euclidean RMSF indicated structural similarity across replicates, we analyzed the secondary structure dynamics of Rep1 for each construct, with the confidence that similar trends would be observed in the other replicates.

Across all constructs, the DBD predominantly exhibits antiparallel β-sheets interspersed with α-helices. Notably, a long α-helix at the C-terminal end of the DBD interacts with the DNA. In contrast, the N- and C-terminal regions display significantly less ordered structure, consistent with their classification as intrinsically disordered regions. Despite this, some residual secondary structure is observed, with the tails being relatively rich in α-helices. Exceptions include regions approximately 30 residues before and after the DBD, which lack secondary structure apart from bends. Specific regions where α-helices were detected include residues 3–6, 17–25, 51–54, 66–69, 177–180, 278–293, 342–346, 355–360, and 372–382.

The tetramerization domain (TD) of p53, encompassing residues 326–356, is reported to consist of a β-strand (residues 326–333) and an α-helix (residues 335–356) (PDBID 8UQR). In our simulations, we observed the α-helix but not the β-strand, suggesting variability in the structural stability of this region under the conditions modeled. Alternatively, the β-strand could be induced by interactions with the other tetramerization domains within the tetramer structure.

Figure S5 in the Supporting Information illustrates the secondary structure of Rep1 for each construct as a function of time. The DBD region of the FL simulations remains relatively stable across all constructs, consistent with the dihedral RMSD results. Residues involved in turns and bends transiently adopt other secondary structure conformations, reflecting dynamic but localized fluctuations. Conversely, the N- and C-terminal regions are highly variable. The alpha helices observed in these regions are less stable than those within the DBD, with disordered residues frequently alternating between turns and bends, often more dynamically than in the DBD.

No significant differences in secondary structure were observed between the constructs. This finding suggests that the mechanism of rescue by PK11000 is likely driven by more subtle factors than large-scale conformational changes, even in the vicinity of the K120 region.

Other Structural Measures

In addition to the structural analyses reported above, we also computed end-to-end distance, maximum pairwise distance, radius of gyration, and solvent accessible surface area, which we report in Figures S6–S9 respectively.

Cluster Analysis

After analyzing the structural behavior of the various constructs and replicates, we investigated clustering to better understand the conformational states sampled by the protein and the restorative effects of PK11000. Motivated by the success of dihedral RMSD in mitigating the chaotic behavior in the disordered regions, we focused on clustering dihedral angles. A traditional Euclidean RMSD-based clustering approach is detailed in Appendix A2.

Dihedral Clustering Results

Using k-means clustering, with the dihedral clustering metric as defined in the Methods section, the elbow plot method determined that two clusters provided the optimal separation. Figure A shows the distribution of constructs within each cluster. Cluster 1 contained the majority of the frames from the Y220C construct, while Cluster 2 included most frames from WT and Y220C_PK11000 constructs. Overlap between constructs in Cluster 1 likely reflects their shared starting structure.

3.

Summary of dihedral clustering results. (A) Distribution of each construct’s clustered frames between the two centroids. (B) Distance between each angle pair between the two centroids. (C) Ramachandran plots of (ϕ, Ψ) angle pairs of maximum deviation between centroid 1 and 2, as identified in subfigure (B). (D) The two centroids superimposed on one another. Residues 182, 183, 184, 242, 244 drawn in sticks, zinc in silver spheres.

To compare clusters, we calculated centroid distances for all (cos­(ϕ),sin­(ϕ),cos­(ψ),sin­(ψ)) pairs. Figure B illustrates the differences between the two centroids, highlighting significant deviations in the tail regions, with relative similarity in the DBD except for angle pairs 182–184 and 243–244. Ramachandran plots for these angles, shown in Figure C, reveal high mobility across all constructs. PK11000 appears to suppress the mobility of angle 184 and partially rescue the behavior of angle pairs 183 and 244. Angle pairs 182–184 correspond to residues near the PK11000 binding site (C182), while angle pair 244 lies near the zinc interaction region, as shown in Figure D.

Despite the observed clustering, dihedral-based clustering did not strongly differentiate mutant and rescued frames, supporting the hypothesis that PK11000’s restorative effects are subtle and not primarily driven by large-scale conformational recovery.

Hydrogen Bond Analysis

To further investigate the restorative effects of PK11000, we analyzed hydrogen bonding (H-bonding) profiles using the cpptraj contacts command. This analysis focused on protein–DNA interactions and identified key binding interactions that were stabilized or disrupted in different constructs. Specific interactions were defined based on Cho et al.’s study of the p53-DNA complex, which highlighted residues R283, R280, R273, R248, A276, C277, K120, and S241 as core DNA-binding residues.

Total and Specific H-Bond Analysis

Total H-bond residence time (TRT) and exhaustive hydrogen bond sums (EHBS) were calculated to quantify the number and duration of H-bonds. TRT measures the cumulative residence time of all H-bonds, while EHBS counts the total number of unique H-bonds formed during the simulation. Specific focus was given to K120, C277, and R280, which directly interact with nucleotide bases rather than the sugar–phosphate backbone.

Figure A shows TRT values for all constructs, while Figure B compares average specific and exhaustive H-bond counts. The WT construct established a baseline TRT of 14.9. The Y220C mutant exhibited a lower TRT of 13.9, indicating disrupted H-bond interactions. The Y220C_PK11000 construct displayed a higher TRT (15.3) than WT, suggesting that PK11000 even enhances WT H-bond stabilization. Specific binding scores followed a similar trend, with Y220C forming fewer specific H-bonds and Y220C_PK11000 forming more than the WT.

4.

Hydrogen bonding analysis of the FL constructs. (A) The total residence time (TRT) of the four FL constructs, a measure of the strength of hydrogen bonds made over the simulation. (B) The specific and total exhaustive hydrogen bonding sums (EHBS), a measure the number and specificity of hydrogen bonds made throughout the simulations.

The EHBS reveals an opposing pattern. The WT forms an average of 748.3 unique hydrogen bonds per microsecond. The Y220C forms a total of 873.3 unique bonds, much higher than the WT. PK11000 lowers the total number of unique bonds, with the Y220C_PK11000 simulation making only 827.3 H-bonds per microsecond, signaling an increased DNA binding specificity. Interestingly, the WT_PK11000 simulations form the highest number of unique hydrogen bonds at 966.8 per microsecond, despite having a nearly identical total and specific TRT score compared to the WT.

Notably, we do observe H-bonding in the C-terminal domain with the DNA, defined as any residue after 289. Very little H-bonding is seen in the N-terminal domain. While the DBD is known for making the most DNA interactions, we show here that the C-terminal domain also makes noninsignificant interactions with DNA, potentially leading to yet another level of DNA specificity.

Electrostatic Network Analysis

Finally, we examined the electrostatic networks of the p53 constructs to compare their residue-level interactions. Following the procedure of Cowan et al. and optimized by Abramson et al., residue-by-residue electrostatic interaction matrices were computed using cpptraj. To normalize the data and highlight highly active interactions, raw edge weights were divided by the total outgoing edge weight at each node, creating a directed multigraph network. The directed multigraph was flattened to a simple weighted graph by choosing the maximum edge weight between nodes i and j. Thresholding was applied at 0.003 to retain only the most significant interactions. For more details, see ref .

We analyzed network connectivity using a heat kernel-based diffusion model with a smoothing factor of 5. PCA was used to reduce the dimensionality of the network data to three components, and the Wasserstein metric quantified differences between constructs. Figure A shows the residue-wise embedding error (EE) relative to the WT network, which is a measure of how similar the local energetic network is compared to the WT electrostatic network.

5.

Electrostatic network analysis of the FL constructs. (A) FL Embedding Error (EE) value, measuring the deviation in local electrostatic network from the WT. (B) Average EE score per construct and the percent of maximum EE values per construct. (C) The difference between the Y220C_PK11000 and Y220C EE scores, more negative values indicate the network is more similar to the WT.

The Y220C construct exhibited the highest EE values, with over 60% of residues showing the most deviation from the WT, as shown in Figure B. In contrast, the Y220C_PK11000 construct demonstrated the lowest EE values, indicating that PK11000 effectively restores WT-like electrostatic networks.

Figure C shows the difference between the Y220C and Y220C_PK11000 embedding error scores (themselves relative to the WT). More negative values indicate the Y220C_PK11000 is closer to the WT than the Y220C. Regions showing significant rescue included residues E68, A84, P85, S166, K305, and K382, several of which are known sites of post-translational modification critical to p53 function. This difference plot emphasizes a large restorative effect by PK11000 in the N-terminal domain and in the N-terminal residues 50–85, corresponding to the proline-rich domain. Residues between 275 and 325 generally show rescue by PK11000, though there are some residues of the Y220C_PK11000 whose energetic network seems to be drastically farther from the WT compared to the Y220C. The tetramerization domain encompassing residues 326–356 exhibits a heterogeneous pattern, with some residues of the Y220C_PK11000 construct favoring a WT-like electrostatic network and others quite similar between the Y220C and the Y220C_PK11000.

Comparison between FL|_DBD And DBD

The second half of our study consists of a comparison between the DBD subset of the simulated FL, denoted FL|_DBD, and the simulated DBD. Until now, virtually all computational work done on p53 has been on the DBD. We investigate if a simulation of the DBD is sufficient to understand the true dynamics of the FL|_DBD, or if the tails have significant effects on the FL|_DBD that the DBD alone inaccurately depicts. If the characterization of PK11000 rescue on the DBD differs from the FL|_DBD, we will know that a simple simulation of the DBD may be insufficient to truly understand if an unknown compound has restorative capabilities.

Global Structural Measures

Similar motivation that led us to our choice of two FL subsets (FL|_1–393 and FL|_20–373) led us to consider two DBD subsets: DBD and DBD|_111–289 (and the corresponding FL|_DBD and FL|_111–289), which consist of the whole DBD (residues 96–289) and the DBD without some of its N-terminal residues (residues 111–289). The C-terminal region of the DBD is an ordered, DNA-interfacing α-helix, so very little fraying was observed over the simulations.

Euclidean and Dihedral RMSD, RoG

Figure A–C show violin plots of Euclidean RMSD, dihedral RMSD, and radius of gyration for the FL|_DBD and the DBD constructs. Violin plots are similar to box plots in showing the range that a data set spans, but they also show the probability distribution of values in the data set. Quartile 1 and 3, median, and standard deviation for the three analyses are given in Tables T1–T3, respectively.

6.

Structural comparisons between the FL|_DBD and DBD. (A) Alpha-carbon RMSD, referencing each simulation’s first frame, shown as a violin plot. (B) Dihedral RMSD, referencing each simulation’s first frame, shown as a violin plot. (C) Radius of gyration, shown as a violin plot. (D) RMSF comparison between the FL|_DBD and DBD, shown as a function of residue number. (E) Average RMSF value for the FL|_111–285 and DBD|_111–285 constructs.

The RMSD data reveal that the WT, both FL|_DBD and DBD, has a wide distribution of values, between roughly 1.5 Å and 3.0 Å, indicating a baseline value of flexibility. The mean value is approximately 2.0 Å. The Y220C FL|_DBD and DBD show a much narrower distribution in data, but the mean value of FL|_DBD RMSD is about 2.0 Å, while the mean RMSD value of the DBD is closer to 2.25 Å. The FL|_DBD and DBD Y220C_PK11000 structures have a narrower distribution in the RMSD data compared to the WT. The mean RMSD value of the FL|_DBD is about 2.0 Å, similar to the WT and Y220C FL|_DBD, but the mean RMSD value of the DBD shows knockdown, closer to 2.0 Å. While the FL|_DBD mean RMSD value is relatively constant between constructs, the mean RMSD value of the DBD demonstrates the same pattern reported by Han et al.

While RMSD values are more meaningful for structured proteins like the DBD subset of the FL, we also investigated the dihedral RMSD, as with the FL. The pattern observed in this data is similar, but more subtle. We observe that the WT simulations have a baseline distribution, the Y220C has a wider distribution, then finally the Y220C_PK11000 has a tighter distribution, more similar to the WT. Again in the DBD, we observe the rescue pattern in the median dihedral RMSD values, but none in the FL|_DBD; the Y220C_PK11000 has the same mean as the Y220C.

Finally, we analyzed the radius of gyration (RoG) data between the constructs. In all cases, except for WT_PK11000, we see that the RoG of the DBD construct is significantly lower than the FL|_DBD, almost 0.1 Å in most cases. Additionally, we observe that in the FL|_DBD and DBD constructs, the Y220C construct has a lower RoG value than WT and Y220C_PK11000, suggesting the mutation results in a less flexible protein. The FL|_DBD WT has a wider distribution of data than the FL|_DBD Y220C or FL|_DBD Y220C_PK11000, but the DBD Y220C data has a wider distribution than the DBD WT or DBD Y220C_PK11000.

RMSF

Figure D shows the per-residue RMSF of the FL|_DBD and DBD. The peaks are in approximately the same places, residues 180–190, 205–215, and 220–230, but we see the values in the FL|_DBD are much higher than the DBD. Figure E shows the average RMSD value per residue in the range 111–285. We see that in all constructs, the FL|_DBD is nearly twice that of the DBD.

Secondary Structure

The secondary structure vs time of each construct’s replicate 1 is shown in Figure S10. Even more so than the FL, the secondary structure of the DBD construct is highly stable. We did observe a transient unfolding of the α-helix between residues 177–180 in the Y220C mutant, but this phenomenon is not exclusive to the mutant protein.

Dihedral Clustering

Analyzing the secondary structure did not reveal large differences between the FL|_DBD and the DBD constructs; thus, we turned to dihedral clustering. The methodology was similar to that of clustering the FL, except this time we concatenated the FL|_DBD and the DBD (cos­(ϕ),sin­(ϕ),cos­(ψ),sin­(ψ)) pairs, then, used k-means clustering on angle pairs that had more than one cluster identified with the DBSCAN algorithm to capture data containing variation. Notably, the addition of the DBD angles created more dihedral angle pairs that had more than cluster compared to the FL alone. In an attempt to classify the protein between “rescued” and “mutant”, we chose k = 2.

Figure A shows the distribution of clustered frames separated by construct and the cluster each frame as assigned. We see that the WT construct, between the FL|_DBD and DBD subsets, occupies approximately the same number of frames in each cluster, about 60% of frames in cluster 1 and 40% of frames in cluster 2, suggesting they have a similar structure for the same amount of time. This pattern does not hold for the rest of the constructs. The FL|_DBD Y220C mutant spends 79.6% of the simulated frames in cluster 1, while the DBD construct spends only 48.3% of the simulated frames in cluster 1. The difference is even greater with the WT_PK11000 construct, where the FL spends 64.7% of the simulation in cluster 1, and the DBD version only spends 18.7% in cluster 1. This suggests that the other constructs occupy different occupations with different probabilities throughout the simulations.

7.

Dihedral clustering between FL|_DBD and DBD. (A) Results from dihedral clustering, with frames classified between cluster and construct. (B) The difference between centroids 1 and 2, shown as a function of dihedral angle pair number. (C) For the peaks revealed in plot (B), their associated Ramachandran plot.

As with the FL dihedral clustering, we see a slight clustering out of the FL|_DBD Y220C in cluster 1, with significantly more FL|_DBD Y220C frames in cluster 1 than any other construct. However, no such pattern exists with the DBD, with approximately the same number of DBD Y220C frames appearing in cluster 1 and cluster 2.

When we look at the distance between individual angle pairs, shown in Figure B, we see that only a few angle pairs contribute to a majority of the differences between the two centroids, namely residues 116, 117, 183, 187, 207, 244, and 245. Recall that the FL dihedral clustering also revealed that residues 182–184 and 243–244 have a high variation between clusters; this aligns with the results presented here. Looking at the Ramachandran plots associated with these angle pairs, (Figure C) we observe rescue in pairs 183 and 207.

Hydrogen Bonding

The DBD results offer valuable insights into the binding interactions of p53, but they also present a more complex picture compared to the FL protein constructs. The trends in hydrogen bonding observed in the DBD constructs are not as straightforward as those seen in their FL counterparts. Figure A,B show the TRT and EHBS scores of the DBD system.

8.

Hydrogen bonding analysis of the DBD constructs. (A) The total residence time (TRT) of the four DBD constructs, a measure of the strength of hydrogen bonds made over the simulation. (B) The specific and total exhaustive hydrogen bonding sums (EHBS), a measure of the number and specificity of hydrogen bonds made throughout the simulations. (C) Total residence time of the FL|_DBD constructs. (D) Total exhaustive hydrogen bond sum of the FL|_DBD constructs.

The total EHBS follows the expected trend, with the DBD Y220C mutant making many more unique hydrogen bonds than the WT or Y220C_PK11000 constructs. However, the specific EHBS follows the opposite pattern expected, whereby the Y220C mutant actually makes more unique bonds with the R283, R280, R273, R248, A276, C277, K120, and S241 residues compared to the WT or Y220C_PK11000. Furthermore, the WT has a significantly higher TRT than any other construct, indicating the WT DBD is able to make much stronger hydrogen bonds than the others. The Y220C and Y220C_PK11000 have an identical TRT score, failing to show any rescue by PK11000. Finally, unlike the FL system, we do not see that the WT_PK11000 makes significantly more unique hydrogen bonds than the WT.

Figure C,D show the TRT and total EHBS of the FL|_DBD. We see that the WT_PK11000 construct out of the FL|_DBD structures makes the strongest hydrogen bonding, followed closely by the Y220C_PK11000, Y220C, and then WT, suggesting that the three other constructs are able to make stronger hydrogen bonds than the WT. Next, we see that the WT FL|_DBD makes a baseline number of unique hydrogen bonds with the DNA throughout the simulations, then the Y220C and Y220C_PK11000 make fewer unique bonds.

Energetic Network Analysis

Using an identical methodology to our study of the FL electrostatic network, we studied the electrostatic network of the DBD. Due to the distribution of electrostatic values in this data set, we chose a cutoff of 0.005. Figure A shows the EE values of each construct with respect to the WT electrostatic network. When we compare with Figure A, we see that there is a great difference between the embedding error of the FL|_DBD and the DBD. The presence of PK11000 does not seem to rescue the WT electrostatic nature of the Y220C mutant. This is in sharp contrast to the FL protein, where even in the FL|_DBD, PK11000 is seen to clearly restore the electrostatic network of the Y220C mutant. However, it can be seen that the rescue of the FL|_DBD is less drastic than the repair of the N- and C-terminal domains.

9.

Electrostatic network analysis of the FL constructs. (A) DBD Embedding Error (EE) value, measuring the deviation in the local electrostatic network from the WT. (B) Average EE score per construct and the percent of maximum EE values per construct. (C) The difference between the Y220C_PK11000 and Y220C EE scores; more negative values indicate the network is more similar to the WT.

Figure B shows summarizes the EE values presented in Figure A and emphasizes that PK11000 is unable to rescue the electrostatic network of the Y220C mutant. Interestingly, we see that the WT_PK11000 construct has the largest deviation from the WT electrostatic network, indicating that the presence of the drug has a large impact on the electrostatic network.

Finally, Figure C shows the difference between the Y220C_PK11000 and Y220C EE values. We see that regions 145–155 and 220–230 exhibit a rescue pattern.

Discussion and Conclusions

In this paper, we have simulated the FL WT, WT_PK11000, Y220C, and Y220C_PK11000 p53 with the purpose of understanding the dynamics of the full-length protein with the intrinsically disordered N- and C-terminal regions and to identify metrics by which PK11000 rescue of the Y220C mutant may be seen. Our analyses have shown that rescue of Y220C p53 does not occur via vast structural restoration, but rather via electrostatic restoration, which manifests itself most naturally by looking at hydrogen bonding with p53’s bound DNA.

We have also conducted simulations of the DBD WT, WT_PK11000, Y220C, and Y220C_PK11000, comparing these simulations to the FL to understand the impact of the N- and C-terminal domains on the disordered subset (DBD). We found that structurally, the DBD subset of the FL, denoted the FL|_DBD, has more structural fluctuation than the DBD simulated without the N- and C-terminal domains, and that the hydrogen bonding network and electrostatic network of the DBD differ from that of the FL|_DBD.

Structure of the FL vs DBD

Over the course of each simulation, we observe that the FL protein has adopted a wide variety of conformations. This is a hallmark of intrinsically disordered proteins: their ability to sample a wide variety of states. In the context of the free-energy landscape, this can be interpreted as the energetic landscape being flat without large peaks that would guide a more ordered protein to its folded structure. Consistent with the energetic landscape model, differences in structure may occur via a conformational dynamical shift spread over the protein, rather than domino effects of just a few residues.

While the secondary structure (given in Figures S5 and S1b) may indicate that the FL|_DBD is similar to the DBD, dihedral clustering points to the contrary (Figure A), indicating that either the two constructs occupy different substates of the energetic landscape, or at least they occupy the same substate of the energetic landscape but at different frequencies. In either case, we have evidence saying that the FL|_DBD and DBD are structurally different, and they are therefore behaviorally different. The violin plots showing distributions of Euclidean and dihedral RMSD show that while dihedral clustering indicates it is a subtle difference.

Furthermore, RMSF (Figure D,E) and RoG data (Figure C) reveal that not just the FL, but the FL|_DBD is vastly more flexible than the DBD. This is likely due to the long and heavy N- and C-terminal regions providing the DBD with more inertia than water interactions alone would cause, leading to larger compressions and expansions of the structured subset.

Our results agree with those provided by Barros et al., who use NMR to demonstrate that the L6 loop between residues 221 and 230 is highly flexible, and Dawson et al., who showed that the N-terminal domain has high chain flexibility and only transient secondary structure. Our secondary structure analysis (Figure S5) indicates some α-helical character in this domain (primarily residues 17–25, and 51–54), but the N-terminal domain remains far more unstructured than structured. Wells et al. indicated that p53 binding to MDM2 induces α-helices in the first transactivation subdomain of p53, and Kussie et al. went on to find that residues 19–26 are the specific residues involved in the induced α-helix. , Further, when p53 binds to the nuclear receptor coactivator binding domain of the CREB binding protein, Lee et al. found, in their NMR structure, that two α-helices are induced, the α-helix from residues 19–25 and another helix from residues 47–53. These are the N-terminal helices observed during our trajectories. Our findings are in agreement with these experimentally determined structural elements of p53.

We claim here that due to the allosteric N- and C-signaling domains, a simulation of the DBD alone is insufficient to capture the wide dynamics sampled by the FL protein. Especially in the context of analyzing small-molecule recovery of p53, the FL protein is essential to capture the true dynamics of the protein.

Rescue of Y220C Mutant in FL vs DBD

In this paper, we present the most detailed simulations of full-length p53 to understand two things: the mechanism by which PK11000 can restore the WT function of the Y220C mutant, and to understand the structural and therefore functional differences between the FL|_DBD and the DBD constructs on a molecular level. Within the FL p53, we observe that the restoration of Y220C p53 by PK11000 is largely not structural in nature; rather, it is in the electrostatic network that rescue occurs most readily (Figure ). This manifests itself in the hydrogen bonding network, where we see the Y220C protein making more, but less specific hydrogen bonds with the DNA (Figure ). This was the same observation made by Han et al. and indicates that the Y220C p53 mutant may be able to bind nonspecifically and promote the transcription of genes not otherwise under the control of p53, thereby causing tumorous growth of the cell.

The restoration of the Y220C mutant by PK11000 in the DBD is much more subtle. Some rescue is observed in the violin plots of Euclidean RMSD, dihedral RMSD, RoG, and RMSF (Figure ), but we no longer observe the same electrostatic rescue of p53 (Figure ), nor do we see a restoration of the WT hydrogen bonding network (Figure ). In fact, while we expected the Y220C mutant in the DBD to be less specific, it appears that it was more specific in its DNA binding than the WT construct. Furthermore, we see that the Y220C and Y220C_PK11000 constructs make equally strong hydrogen bonds. When we compare the results between the FL and FL|_DBD, we see that the TRT is lower in the presence of PK11000, in agreement with the fact that PK11000 tightens hydrogen bonding. We see a similar effect in the EHBS, whereby PK11000 is able to reduce the number of total hydrogen bonds made by p53. However, in the FL|_DBD, we see the EHBS of the Y220C is lower than that of the WT, emphasizing the novelty and importance of the full-length p53 protein. The full-length p53 is necessary to see the whole picture. The presence of disordered terminal regions adds an additional layer of regulation and interaction complexity that cannot be captured by the DBD construct alone. These regions likely influence not only the flexibility of the protein but also its interaction specificity, especially when considering therapeutic intervention. The FL construct offers a more complete and biologically relevant model for studying p53’s behavior, particularly in the context of rescue by compounds such as PK11000.

Furthermore, we observed a curious result in the FL hydrogen bonding: the WT_PK11000 has an EHBS score much higher than any other construct, indicating that in the presence of the drug and no mutation, rather than keeping the number of unique hydrogen bonds similar to the WT, the number of unique hydrogen bonds is drastically increased. The same observation was not made in the case of the DBD, and if we look at the EHBS of the FL|_DBD we see a much lower value for WT_PK11000, so we can conclude that these extra hydrogen bonds are likely made in the disordered tails. This observation is likely the result of a transient conformation that forms an unusually high number of hydrogen bonds with the DNA, and may therefore reflect a simulation-specific artifact rather than a representative feature of the system’s typical behavior.

These results paint a far more complex picture than those presented by Han et al., who observed large conformational differences (in addition to energetic) between the WT, Y220C_PK11000, and Y220C constructs in the DBD.

However, the knowledge that PK11000 is sufficient in vivo to restore the WT function of p53 enough to eliminate tumors caused by its own malfunction, combined with the evidence of only partial rescue presented here, paints an optimistic picture for the future of p53-restorative drug design: the successor to PK11000 needs only to restore the WT function “enough.”

We propose the following condition needed for a drug to be successful at rescuing the WT behavior of p53. The Y220C mutant may be able to promote the transcription of nonspecific genes, and it may be less thermally stable than the WT, causing it to fail to halt the cell cycle or initiate apoptosis. If the PK11000 molecule, or any other molecule, can shift the proportion of time the mutant p53 spends between its “mutant” activity and “wild type” activity to the “wild type”, the p53 would be able to trigger apoptosis, and any subsequent damage done by nonspecific gene transcription would be irrelevant.

We showed that dihedral RMSD, RMSF, and especially hydrogen bonding and electrostatics are useful metrics in determining if PK11000, but in general, any ligand has restorative properties on p53. An understanding of how the allosteric signal delivered by PK11000 can be propagated through the protein can give insight into what residues should be targeted for ligand interactions and what kinds of ligands would be best suited.

The pipeline developed can be applied to variants of p53, including other hotspot mutations, splice variant isoforms, diverse small molecule-bound systems, and different DNA promoters found in the cell. While one strategy for p53 reactivation employed by the PRIMA-1 compound and the APR series mentioned in the Introduction is to solubilize mutant aggregates, another approach is to prevent the unfolding of p53 altogether, as is the approach of PK11000. Furthermore, the approaches developed herein are suitable for study of any other protein system involving mutations and long-range signaling.

This naturally raises the question, if p53 rescue really can be achieved by such partial methods, then why has no successor to PK11000 been discovered? There are a number of difficulties in the way of designing a restorative drug. For one, proposing, synthesizing, and testing molecules in an experimental setting one at a time is, by nature, an arduous process. The nature of the disease caused by mutant p53 makes this especially difficult. Second, p53, with its highly complicated binding interactions, necessitates an allosteric modulator. Researchers trying to design an allosteric drug, until now, have had to use a brute-force, “shotgun” approach to hope to find a compound that might work; in fact, this is how PK11000 was discovered. But with these data in hand and the in silico computational drug-testing pipeline presented, the speed at which compounds can be tested is only limited by the speed at which simulations can be run and data can be analyzed.

Relevant files and scripts can be found uploaded to GitHub here: https://github.com/Sean-S1225/FL-Monomer.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c05639.

• Additional methods (Euclidean RMSD, RMSF, secondary structure analysis, end-to-end distance, maximum pairwise distance, radius of gyration, solvent accessible surface area), Euclidean-RMSD based k-means clustering, secondary structure analysis of a variety of force fields, additional structural metrics (RMSD, dihedral RMSD, end-to-end distance, maximum pairwise distance, radius of gyration, solvent available surface area), and tables containing statistical measurements comparing FL|_DBD and DBD RMSD, dihedral RMSD, and radius of gyration can be found in the supplementary documents (PDF)

The authors declare no competing financial interest.