On the interaction mechanisms of a p53 peptide and nutlin with the MDM2 and MDMX proteins

Abstract

The interaction of p53 with its regulators MDM2 and MDMX plays a major role in regulating the cell cycle. Inhibition of this interaction has become an important therapeutic strategy in oncology. Although MDM2 and MDMX share a very high degree of sequence/structural similarity, the small-molecule inhibitor nutlin appears to be an efficient inhibitor only of the p53-MDM2 interaction. Here, we investigate the mechanism of interaction of nutlin with these two proteins and contrast it with that of p53 using Brownian dynamics simulations. In contrast to earlier attempts to examine the bound states of the partners, here we locate initial reaction events in these interactions by identifying the regions of space around MDM2/MDMX, where p53/nutlin experience associative encounters with prolonged residence times relative to that in bulk solution. We find that the initial interaction of p53 with MDM2 is long-lived relative to nutlin, but, unlike nutlin, it takes place at the N- and C termini of the MDM2 protein, away from the binding site, suggestive of an allosteric mechanism of action. In contrast, nutlin initially interacts with MDM2 directly at the clefts of the binding site. The interaction of nutlin with MDMX, however, is very short-lived compared with MDM2 and does not show such direct initial interactions with the binding site. Comparison of the topology of the electrostatic potentials of MDM2 and MDMX and the locations of the initial encounters with p53/nutlin in tandem with structure-based sequence alignment revealed that the origin of the diminished activity of nutlin toward MDMX relative to MDM2 may stem partly from the differing topologies of the electrostatic potentials of the two proteins. Glu25 and Lys51 residues underpin these topological differences and appear to collectively play a key role in channelling nutlin directly toward the binding site on the MDM2 surface and are absent in MDMX. The results, therefore, provide new insight into the mechanism of p53/nutlin interactions with MDM2 and MDMX and could potentially have a broader impact on anticancer drug optimization strategies.

Introduction

The p53 protein is a tumor suppressor that plays a central role in maintaining genomic stability and protection against malignant cell transformation.^1,2 Upon cellular stress the p53 protein is stabilized, while in normal cells it is kept at very low levels.³ DNA damage, aberrant growth signals, interaction with chemotherapeutic drugs or protein-kinase inhibitors are among the common causes of cellular stress.⁴ Release of p53 in stressed cells shuts down multiplication of damaged cells and inhibits progression through the cell cycle and can induce programmed cell death (apoptosis).⁵ In general, the amount of p53 protein in cells is primarily determined by its rate of degradation.⁵ p53 degradation takes place through a process called ubiquitin-mediated proteolysis, where several copies of small peptides (ubiquitin) are attached to p53. These peptides act as a flag targeting p53 to the proteasomal degradation machinery.^4,5 The MDM2 protein is the ubiquitin E3 ligase centrally involved in this process.⁶ In normal cells, p53 interacts with MDM2 in a negative feedback loop^4,7 such that p53 stimulates transcription of the MDM2 protein, while p53 binding to the trans-activation N-terminal domain of the MDM2 protein (Fig. 1) triggers p53 ubiquitination and its subsequent degradation. This feedback loop maintains p53 concentrations at low levels in normal cells. More recently it has become abundantly clear that the MDMX protein, a close homolog of MDM2, also takes part in maintaining p53 at low levels in normal cells via formation of a heterodimer with MDM2.^8,9 Formation of this dimer through their RING domains^10-12 stimulates the conversion of MDM2 from a mono- to a polyubiquitination E3 ligase that is essential for the degradation of p53 via the proteasomal pathway.^10,13 p53 also binds to MDMX in a manner that is closely similar to its binding to the N-terminal of MDM2,¹⁴ i.e., masking its trans-activation domain;¹⁵ however, unlike MDM2, MDMX does not have significant E3 ligase activity.¹⁶ Upon cellular stress, posttranslational modifications of p53 and MDM2/MDMX induce the dissociation of p53 from MDM2/MDMX, blocking the ubiquitination of p53 and causing its accumulation and activation as a transcription factor.⁴ In addition to the interactions of MDM2 and MDMX with p53, they also work in close cooperation with each other to regulate p53 as well as each other’s levels in a carefully orchestrated program¹⁵.

Figure 1. The binding mode of p53 peptide (left; cyan) and Nutlin-2 (right; cyan) to the MDM2 protein (yellow). Similar general binding modes are adopted in interactions with the MDMX protein; interactions of nutlin with MDMX are however destabilized.⁶³

In many human tumors that have an intact wild type p53 gene, elevated levels of MDM2 or MDMX are thought to inhibit its tumor suppressor function. Reactivation of the p53 protein has therefore become an important therapeutic strategy in oncology.¹⁷ One route for achieving this, which has received much attention,^18-20 is via inhibition of the interaction of MDM2 or MDMX with p53, especially the interactions at their N-terminal ends. Nutlin²¹ is a small-molecule inhibitor of the MDM2-p53 interaction that is currently undergoing phase-I clinical trials²² as an anticancer lead candidate. One major setback for nutlin is that, despite efficiently inducing transient cell cycle arrest, it is inefficient in inducing significant apoptosis.^23,24 This was mechanistically ascribed to the observation that, despite MDM2 and MDMX showing almost 50% sequence identity in their p53 binding domains, nutlin does not effectively disrupt the MDMX-p53 interaction and is thus unable to activate p53 in cells overexpressing MDMX.^16,25 To achieve full reactivation of p53 in cancer cell lines, compounds that are dual inhibitors of MDM2 and MDMX are desirable.^19,26 Indeed a recent study of cutaneous melanoma²⁷ has established that MDMX is selectively expressed at high levels in these tumors, emphasizing the need for inhibitors of the MDMX-p53 interactions to complement nutlin-like molecules.¹⁵

Manipulation of MDMX to alter p53 activity was found to require careful investigation of the dynamics of the three proteins: MDMX, MDM2 and p53.²⁸ The p53 interaction with MDM2 and MDMX is essentially a dynamic process.²⁹ It is part of a large complex network with multiple spatiotemporal aspects,³⁰ such that, in stressed cells, the p53 concentration was found to follow an oscillatory pattern upon interaction with MDM2.³¹ Meanwhile, the interaction of MDMX with the p53/MDM2 system was found to have the potential to dampen this oscillatory behavior.²⁸ Contrary to this dynamical (kinetic) nature of p53 cellular regulation, current drug development strategies of p53 inhibitors mainly rely on the optimization of the equilibrium association constant (K_a), the free energy of association (ΔG_a) or the half-maximal inhibitory concentration (IC₅₀) as proxies for the drug's biological activity.³² The mechanistic behavior of the p53 interaction with MDM2 and MDMX is clearly not captured completely in these measures. A better understanding of the mechanism of the interaction of p53/nutlin with MDM2/MDMX is therefore necessary to complement current efforts for developing suitable inhibitors. Our earlier work has indicated that investigating the kinetics of associations in these systems holds promise.³³

Toward this goal, here we report an investigation of the mechanisms of the interactions of p53 and nutlin with MDM2/MDMX. We conducted Brownian dynamics simulations of the diffusion of p53 and nutlin in the electrostatic potential field of the MDM2 and MDMX proteins and monitored their preferential interactions with these proteins. Based on partitioning the interaction landscapes of p53/nutlin with the MDM2/MDMX proteins into basins of attractions, where the rate of associative events is much larger than dissociations, we investigated the basic mechanisms underlying these interactions and identified key differences in the MDM2 and MDMX proteins that could offer an explanation for the observed discrimination of nutlin in favor of the former. This becomes important, because dual inhibitors of MDM2 and MDMX are now under study,³⁴ and mechanistic differences between these molecules and those specific for MDM2 or MDMX¹⁰ will be critical in distilling out some aspects of the complex relationships that determine how MDM2, MDMX and p53 are modulated.¹⁵ The encounter complexes (defined by the basins of attraction) represent diffusively bound states that occur prior to the classical non-diffusive bound state. In these diffusive states, the protein-ligand interactions are mainly electrostatic,^33,35-39 while the dehydration and van der Waals effects associated with the bound state are negligible. Therefore, protein-ligand interactions in these states are, to a good degree of approximation, diffusion limited. There is not much information available on the kinetics of the interactions of these proteins with p53 peptides and small molecules except for one study,⁴⁰ which clearly demonstrated a strong association between electrostatics and kinetics. Hence computational approaches offer a nice complement to the limited available experimental data. These approaches assume great significance now, given recent work that is beginning to tease out the differences in the rates at which p53-stabilizing drugs appear to manifest their effects.⁴¹

Results and Discussion

The radial profiles of p53/nutlin residence times around MDM2/MDMX

Ligand residence times are increasingly being recognized as an important kinetic parameter that is directly related to biological activity in vivo.^58-62 The radial distribution profiles of the residence times of p53/nutlin around MDM2 and MDMX are markedly different in terms of intensity and modality (Fig. 2A and C). While the interaction of p53 with MDM2 and MDMX is essentially bimodal, the interaction of nutlin exhibits unimodal profiles with a sharp intense peak characterizing its interactions with MDM2 (Fig. 2C, left) and a weak broad peak characterizing its interactions with MDMX (Fig. 2C, right). Comparison of the intensities of the p53/nutlin peaks that are closest to MDM2/MDMX reveals some of the characteristics that underpin the preferential interactions of p53/nultin. The higher residence time of nutlin compared with p53 upon interaction with MDM2 is indicative of the higher local concentrations that it appears to achieve in the vicinity of MDM2. In addition to the energetics of short-range interactions that are established upon complexation,⁶³ the current finding further suggests additional mechanisms that potentially underpin the higher affinity of nutlin for MDM2.⁶³ Again, the much smaller residence time of nutlin around MDMX relative to its residence time around MDM2 is also in agreement with the known diminished affinity of nutlin towards MDMX.²⁶ However, comparison of the residence times of nutlin and p53 upon interaction with MDMX reveals that nutlin and p53 exhibit similar residence time radial profiles, which is suggestive of similar affinities towards MDMX. This, apparently, is not in accord with the available data.²⁶ In order to resolve this issue, understand the origin of the bimodal residence time profiles of p53 around MDM2/MDMX (Fig. 2A) and to gain a deeper insight into the mechanism underlying these interactions, a more detailed picture of p53/nutlin interactions with the MDM2/MDMX proteins is required; these details are usually smeared out in the radial distribution profiles.

Figure 2. The radial profile of the residence times (A and C) and 2D-representations of the density landscapes (B and D) of the p53/nutlin-2 interaction with the MDM2/MDMX protein (yellow). In (A and C), the residence time profiles were spatially normalized by dividing the total residence time at a radius r by the spherical volume slab 4πr² and then were averaged over the number of trajectories (N). In (B and D), the density landscape corresponds to a slab that passes through the centers of the highest occupied basins of attractions as determined from analysis of the 3D density around the MDM2 and MDMX proteins. The basins of attraction are shown as solid contour lines while connecting superbasins are shown as dashed contours. The basins are labeled in ascending order with respect to their residence time.

The interaction landscapes of p53/nutlin with MDM2/MDMX

The landscapes of the interactions of p53/nutlin with MDM2/MDMX show topological features that are distinctly different (Fig. 2B and D). Comparison of the location, breadth and connectivity of the basins of attraction in these landscapes provides a means for a detailed understanding of these topological features. The basins of attraction correspond to regions of space where the ligand-receptor encounter complex is formed. The ligand receptor encounter complex characterizes a state prior to the formation of the bound complex,^35,64 therefore providing clues about the mechanism underlying the ligand-protein interaction. Unlike the bound complex, the encounter complex is stabilized mainly by electrostatic interactions with the receptor⁶⁵ that dominate over other short-range interactions, such as van der Waals interactions and desolvation effects. Preferential stability of the encounter complex in certain regions of space, viz. the basins of attractions, arises from the higher rate of ligand association to the receptor in these regions of space relative to the rate of its dissociation, thus resulting in prolonged residence times of the ligand in these regions.

p53 interaction with MDM2/MDMX

The interaction landscapes of p53 with MDM2/MDMX (Fig. 2B) are well-characterized by the presence of broad basins of attraction. However, the locations of these basins are markedly different in the two landscapes. The highest occupied p53/MDM2 basins of attraction (Fig. 2B, left) lie close to the C- and N- terminal regions of the MDM2 protein surface, ~4.0 Å away from Lys75 and Lys22. Notably, these basins of attraction are quite far from the p53 crystallographic binding site on the MDM2 surface. This is consistent with recent suggestions of possible allosteric interaction mechanisms as a prerequisite for p53 binding to MDM2.⁴² In contrast, the interaction of p53 with MDMX (Fig. 2B, right) shows a drastically different landscape. In fact, two of the three dominant basins of attraction observed with MDM2 (Fig. 2B, left) have disappeared, with the third basin being dominant (Fig. 2B, right). This basin does not interact directly with either the C- or N- terminal regions of MDMX and is localized relatively close to the binding site on the MDMX surface.

Although MDM2 and MDMX share more than 50% sequence identity,⁶³ their electrostatic potentials are distinctly different (Fig. 3A). The electrostatic potential of the MDMX protein partitions the space nearby the protein surface into two regions of positive and negative potential, with the positive potential being more dominant and enveloping a significant part of the structure (Fig. 3A, right). Interestingly, the dominant basin of attraction in the p53/MDMX landscape (Fig. 2B, right) lies within this region, which indicates that the p53 peptide, being negatively charged, seeks favorable electrostatic interactions by following the positive electrostatic potential of MDMX in this region of space. These two factors, i.e., continuity of the potential and favorable electrostatic interactions, collectively provide an explanation for the presence of a single dominant basin in the p53/MDMX landscape. The exact location of this basin is rather dictated by the gradient of the interaction potential between the p53 peptide and the MDMX protein. In contrast, MDM2 is characterized by two regions of positive potential spanning the N- and C termini (Fig. 3A, left), away from the p53 binding site. The locations of these two regions coincide with those of the two dominant basins of attraction observed for the p53/MDM2 interaction (Fig. 2B, left).

Figure 3. (A) The electrostatic potential of the MDM2 and MDMX proteins. Positive and negative potentials are contoured in blue and red respectively. Negatively charged residues are shown in magenta, positively charged residues in light blue, while neutral residues are shown in yellow. Residues are labeled by the corresponding residue ids of the MDM2 and MDMX proteins (PDBIDs: 1YCR and 3DAB). Structure-based sequence alignment of the two proteins is shown in (B) with a similar color code.

Nutlin interaction with MDM2/MDMX

Unlike p53, the interaction landscapes of nutlin with the MDM2/MDMX proteins lack the broad basins of attraction observed for the p53 MDM2/MDMX interactions (Fig. 2D). The nutlin/MDM2 landscape (Fig. 2D, left) is quite distinct from the nutlin/MDMX landscape (Fig. 2D, right), being less rugged, almost flat, with two basins of attraction that lie very close to the crystallographic binding site. In contrast, the number of basins of attraction in the MDMX landscape is quite high. The MDMX basins are far from the binding site, scattered and not connected, leading to the observed ruggedness of the nutlin/MDMX landscape. Connectivity between basins is essential for secure channelling of the ligand towards the protein surface.³³ Isolated basins could potentially lead to ligand entrapment and possibly to depletion of its local concentration around the receptor. Clearly, the locations of the basins of interaction in the rugged nutlin/MDMX interaction landscape are also different from those of the p53/MDMX interaction. Whereas p53 is being channeled to a single broad basin that is relatively close to the binding site on the MDMX surface (Fig. 2B, right), nutlin is scattered into small basins of attraction (Fig. 2D, right). This provides a partial explanation for the observed diminished affinity of nutlin towards MDMX.²⁶

Since nutlin is electrically neutral, the locations of the basins of attraction cannot directly be accounted for in terms of the nature of individual regions of the electrostatic potential around the MDM2/MDMX proteins. However, interaction of a neutral ligand, like nutlin, with a receptor would involve interactions of its different individual atomic charges (positive and negative) with the electrostatic potential of the receptor. Favorable modes of ligand interaction are therefore expected to optimize interactions of all of its individual charges with the electrostatic potential of the receptor. This can only be achieved if the ligand interacts with the electrostatic potential of the receptor in regions of space that span both positive and negative potentials. In fact, comparison of the locations of the two most occupied basins in the nutlin MDM2/MDMX interaction landscapes (Fig. 2D) with the MDM2/MDMX electrostatic potentials (Fig. 3A) reveals that the basins are indeed located at the clefts between the positive and negative electrostatic potential regions in both cases. Interestingly, the location of one of these electrostatic clefts relative to the MDM2 surface coincides with the location of the crystallographic nutlin binding site. In contrast, these electrostatic clefts lie far from the binding site for the MDMX protein. This leads to a higher residence time of nutlin near the MDM2 binding site compared with MDMX, thereby providing a partial explanation for the observed higher affinity of nutlin towards MDM2 compared with MDMX.

The origin behind the topological differences in the electrostatic potentials of the MDM2 and MDMX proteins can be traced back to the differences in their residual compositions. Inspection of the structure-based sequence alignment of MDMX relative to MDM2 (Fig. 3B) reveals that the distribution of charged residues is markedly altered in MDMX relative to MDM2. The I24E25, Q68E69 and E70Q71 differences clearly contribute significantly to the differences in the electrostatic potentials of the two proteins (Fig. 3A). Clearly, the presence of Glu25 on the surface of MDM2 leads to the generation of a region of negative electrostatic potential that is otherwise positive around MDMX. In MDM2, the presence of negatively charged Glu25 in the vicinity of positively charged Lys51 (which is conserved across the MDM2 and MDMX), leads to the presence of the cleft regions of positive and negative electrostatic potentials that were shown to localize nutlin in the vicinity of the MDM2 binding site. This suggests that mutation of Glu25 and/or Ly51 will likely lead to a significant reduction in the affinity of nutlin for MDM2 while that of Lys50 (in MDMX) will likely impact the binding to MDMX; indeed the removal of the negative charge at Glu25 (by a virtual Ala mutation, Fig. S1) does change the potential landscape and makes it quite similar to that of MDMX. In contrast, the Q68E69 and E70Q71 differences seem only to fine-tune the location of the clefts between the positive and negative regions of the electrostatic potentials of MDM2 and MDMX; indeed the 68-69-70 region in MDM2 has been demonstrated to be linked to phosphorylation-controlled association between p53 and MDM2 mediated via electrostatics.^66,67

Interestingly, the I24E25, Q68E69 and E70Q71 differences relate to residues that do not line the nutlin binding site of MDM2. The picture that emerges is of a set of events orchestrated by MDM2, such that it deals efficiently with two consecutive interaction stages. The first stage is kinetically controlled, where nutlin is securely driven and “hovers” in the vicinity of the MDM2 binding site for a sufficiently large residence time, with Glu25 and Lys51 residues collectively playing a key role. The second stage is the formation of the nutlin-MDM2 complex, where another set of residues, previously identified as Leu54, His96 and Ile99,^26,63,68-71 is key for stabilizing the nutlin-MDM2 bound complex; indeed, a similar set of events characterize the binding of p53. Such insight is clearly not attainable from the standard analyses of the structure of the p53/nutlin MDM2 bound complex since they are largely based on thermodynamic considerations of only the bound state of the complex. Consideration of the kinetics underlying ligand-receptor interactions prior to reaching the bound state is clearly an important avenue that could unveil many of the aspects of the mechanisms underpinning these interactions.

The kinetics of p53/nutlin interactions with MDM2/MDMX

In bulk solution, the p53 peptide and nutlin are diffusively transported, while in the vicinity of the MDM2/MDMX proteins, their transport is biased by the topology of the underlying interaction landscape. The rate of such transport is enhanced in the regions of space that correspond to the basins of attraction and diminished elsewhere. These localized interactions appear to be quite important for their global effects; for example a study combining computational and experimental approaches suggested how local electrostatics modulate the phosphorylation-dependent interactions between p53 and MDM2.⁶³ Both the p53 and nutlin exhibit association rates k_on, that are largely diffusion-limited (k_on > 1.0 × 10⁸) (Fig. 4, top). However, p53 experiences a much higher on-rate and residence time (1/k_off) relative to nutlin (Fig. 4). The higher on-rate of p53 is due to its net negative charge that enhances its electrostatic-steering by the electrostatic potentials of MDM2 and MDMX. However, its higher residence time compared with nutlin is attributed to the different topology of the basins of attraction in their interaction landscapes, being much broader than those of nutlin (Fig. 2). It is interesting to note the coincidence between such high kinetic precedence of p53 in terms of its high residence time with the location of its basins of interaction being far from the binding site, therefore suggestive of an allosteric mechanism. In fact, such high residence times confirms this suggestion, as it allows p53 to exert a prolonged effect on the receptor in order to induce conformational changes that allow for its subsequent binding. This is clearly not the case for nutlin, which does not need such prolonged residence times, since it interacts directly with the binding site. Atomistically detailed simulations of ligand binding events performed recently have demonstrated the complex trajectories that characterize the binding of ligands to the active sites.⁷² It has been demonstrated that nutlin acts quite rapidly in increasing the synthesis of MDM2 mRNA.⁴¹ However, it appears to reside long enough within the binding site of MDM2 to conformationally stabilize it against degradation.⁴¹ Availability of models of structural coupling between the N-terminal and the acidic and RING domains of MDM2 and its interactions with MDMX will undoubtedly reveal the allosteric nature of interactions that modulate the stability of MDM2.^73,74

Figure 4. The association rate constant; k_on, (top) and the residence times; τ~1/k_off, (bottom) of the two most occupied basins of attraction (white and gray) in the interaction landscapes of p53/nutlin with the MDM2 and MDMX proteins.

Material and Methods

Modeling the ligand protein diffusional association

Detailed Brownian dynamics simulations cannot account for the flexibility of the whole molecular system, and so we decided to use representative structures of the p53 and nutlin bound complexes with the MDM2 and MDMX proteins from molecular dynamics simulations that have previously been used to understand the differences in the equilibrium behavior of the complexes.⁴² As noted in our previous study,³³ at least 50,000 BD trajectories are needed in order to reach convergence of the overall residence time. Carrying out such a large number of trajectories with full account of protein/ligand flexibility will be prohibitively costly in term of computing power and time. So using conformational snapshots of the protein/ligand complexes generated from simulations is a trade off between the two extremes of using fully rigid protein/ligand complexes (neglecting flexibility) and fully flexible protein/ligand complexes (prohibitively costly). We note that such an approximation is the basis of the successfully used relaxed complex scheme of McCammon and coworkers,⁴³ which incorporates receptor flexibility into computational drug design through the explicit inclusion of multiple receptor conformations that are extracted from molecular dynamics simulations.

Fifteen snapshots of the ligand-protein complexes in different conformations were therefore extracted from molecular dynamics trajectories⁴² and used as the starting structures for the Brownian dynamics (BD) simulations. BD simulations of the diffusional association of p53 and nutlin-2 to the MDM2 and MDMX proteins were performed for the association schemes (1) and (2) using the SDA package (Table 1).^36,37

Table 1.The association schemes of p53 and nutlin-2 to the MDM2 and MDMX proteins.

Protein		Ligand		Complex	Scheme
		p53	→	MDM2:p53
MDM2 +					(1)
		Nutlin	→	MDM2:Nutlin
		p53	→	MDMX:p53
MDMX +					(2)
		Nutlin	→	MDMX:Nutlin

The details of the BD simulations along with the algorithm for the identification of the basins of attraction were described in a previous work,³³ and we only describe it briefly here. The BD trajectories were propagated by solving the translational and rotational diffusion equations, using the Ermak-McCammon algorithm⁴⁴ as implemented in the SDA package version 4.23b. The translational and rotational diffusion coefficients were calculated using the HYDROPRO software.⁴⁵ Initially, the center of mass (COM) of the protein was placed at the origin, and that of the ligand was placed at b = 150.0 Å COM-COM separation relative to the protein COM. At this separation, there is no preferential orientation of the ligands, since the electrostatic potential of the protein is nearly isotropic at distances of about 80 Å from its center of mass. A time step of 0.1 ps was used when the COM-COM separation of the protein-ligand was less than 90 Å. At larger separations, the time step was increased linearly with a slope of 0.5 ps Å^-1. A total of 50,000 trajectories were run for each simulation; the simulations were terminated if the ligand-protein COM-COM separation exceeded c = 3b Å.

The forces between the ligand and the protein derive from steric, desolvation and electrostatic interactions. Steric interactions were implicitly taken into account by preventing the ligand and the protein from overlapping during the simulations using an exclusion grid centered at each of them with a grid spacing of 1 Å. The electrostatic force on any atom of the ligand was calculated by multiplying its charge by the electrostatic potential generated by the protein at that atom. The electrostatic potential around each protein was calculated by numerically solving the nonlinear Poisson-Boltzmann equation^46,47 on a grid with dimensions 161 × 161 × 161 Å, 1 Å spacing and centered at the ligand/protein using the APBS program.⁴⁸ The solvent dielectric constant was set to 78.5, the protein interior dielectric constant was set to 4, and the salt concentration was set to 0.15 M. Atomic charges and radii of the ligand and the protein at neutral pH (pH = 7) were set using the PDB2PQR program.^49,50 At this pH, the MDM2 protein is positively charged, while the p53 ligand is negatively charged. The solute-solvent boundary was defined at the van der Waals surface as the molecular surface definition was found to result in significant underestimation of the association rates in some cases.³⁹ Electrostatic desolvation was accounted for empirically by calculation of a desolvation penalty grid⁵¹ around the ligand and the protein using the desolvation grid module in the SDA package. Consistent with the use of a van der Waals surface definition for the solute-solvent boundary, a scaling factor of 1.67, according to Gabdoulline and Wade,³⁹ was used for the desolvation energy computed by the grid module in the SDA package in order to ensure reproducibility of experimental rate values. For the sake of computational efficiency, the full set of atomic charges of the ligand and the protein was replaced during the BD simulations by a smaller set of effective charges that accurately reproduce their calculated electrostatic potential.⁵² The effective charges were derived by the ECM module in the SDA package so as to reproduce the electrostatic potential at the accessible surface (defined by a probe of 4 Å) in a 3 Å thick layer extending outwards from each structure.

Analysis of the BD simulations

From the BD trajectory data, the radial profiles of the ligand protein residence times were computed in spherical concentric radial slabs of 1 Å thickness that are centered at the center of mass of the protein. In order to get a detailed picture of the ligand protein interaction landscape, a 200 × 200 × 200 Å 3D spatial probability density grid with a spacing of 1 Å was constructed around the protein by computing the average frequency of the ligand COM visiting individual spatial grid cells. The rate of association, k_a, corresponding to each grid cell was calculated by combining the probability β of visiting that grid cell with the steady-state rate constant k(b); k(b) = 4πbD, of the ligand protein system at the initial separation b ⁵³:

The denominator in the expression for k_a accounts for the fact that we terminate the BD trajectory at separation c = 3b rather than at infinity.

The basins of attraction within the 3D grid were detected by the contour following algorithm described previously.^33,54 For the sake of completeness, we briefly describe the algorithm as follows. The 3D ligand spatial density grid is contoured at equally spaced contour intervals that extend from the highest density (strongly interacting with the receptor: diffusively bound regime) to the lowest density (weak/non-interacting: diffusive regime). Closed contours at the highest level of density represent interaction “hot spots.” Closed contour surfaces at successively lower density levels that encompass each individual hot spot are then accumulated. As a consequence of following the density gradient in this manner, the ligand flux in these regions is such that the average rate of inward ligand association (i.e., towards the hot spot) is higher than its average outward dissociation rate. As the contour surfaces are “closed,” the process therefore ensures that the direction of the ligand density gradient is maintained inward from all directions. These characteristics, which result from restriction (or channeling) of the ligand motion in the diffusional trajectories, result in these regions acting as basins of attraction. The connectivity between different basins of attraction is determined by detecting closed contour surfaces that encompass multiple hot spots: such regions represent super-basins of attraction within a global disconnectivity tree.⁵⁵

This scheme, based on ligand-receptor binding dynamics, yields a partitioning of the ligand spatial density around the receptor into kinetically distinct, spatially resolved encounter complex basins of attraction that correspond to putative binding sites in the diffusively-bound regime. The identification of these sites does not require prior knowledge of a (conventional non-diffusive) binding site on the receptor, or the use of other ad hoc criteria.^35,37,56 This is notable in view of the increasing importance of the role of allosteric sites in modulating activity⁵⁷ which are difficult to infer from static methods such as X-ray crystallography.

Estimation of ligand-receptor site-specific residence time (τ_LR)

The ligand site-specific residence time is computed for individual basins of attraction by numerical integration of the time-averaged ligand probability density in each basin of attraction. Using small contour intervals, in which the ligand density D is effectively constant, the integral can be approximated by:

where (V_n–V_n-1) is the volume enclosed between two consecutive contour surfaces at ligand densities D_n and D_n-1 and Δt is the time step used in the region between V_n and V_n-1 during the BD simulation. In the case of multiple basins of attraction, it may be convenient to express the fractional residence time of a given basin as a proportion to the total residence time over all basins.

Conclusion

We investigated the mechanisms underlying the interactions between p53/nutlin and MDM2 and MDMX proteins using BD simulations. In this context, BD simulations allow for the investigation of molecular states of the ligand protein interactions prior to the formation of the bound state. The study therefore complements recent studies of p53/nutlin interactions with MDM2 and MDMX proteins near the binding site^42,63,75 as it explores interaction landscapes that are not accessible to standard MD simulations. The topological features of these landscapes modulate reaching the bound states.³³

Comparison of the topological features of the underlying interaction landscapes revealed that MDM2/MDMX interactions with p53 are distinctly different from that of nutlin. The initial interaction of p53 with MDM2 takes place away from the crystallographic binding site via two broad basins of attractions that target the N- and C termini, suggestive of an allosteric mechanism. Prolonged residence times in these basins allow for a sustained interaction between p53 and MDM2 that may be necessary for inducing conformational changes in the molecular skeleton of MDM2. In contrast, the initial interaction of nutlin with MDM2 takes place directly at the cleft of its crystallographic binding site with a much smaller residence time. On the other hand, nutlin’s interaction with MDMX takes place away from the binding site with a residence time that is much smaller than for MDM2, therefore minimizing its chances of reaching the binding site and accounting at least partially for its diminished affinity.

Identification of the locations of the different basins of attractions in the ligand-protein interaction landscape is therefore essential for understanding the mechanism underpinning ligand-protein interactions. The relationship between the location of the basins of attraction around a protein and the topology of its electrostatic potential, however, is subtle and depends on the interacting molecules. For charged ligands like p53, the basins of attraction were found to be located in regions of space where the electrostatic potential stabilizes the ligand net charge. We had previously found that indeed such local interactions modulate the phosphorylation-dependent binding of Mdm2 and p53⁶⁶ as was also shown experimentally.⁶⁷ This does not appear to be the case for neutral ligands like nutlin, where the locations of the basins of attraction were found to coincide with the cleft regions between negative and positive electrostatic potential of the receptor, allowing for optimal stabilization of its individual atomic charges. In this context, the origin of the preferential binding of nutlin to MDM2 relative to MDMX was found to stem from differences in the topology of the electrostatic potentials of MDM2 and MDMX. Two residues, Glu25 and to some extent Lys51, were found to collectively play a key role in such electrostatic differentiation between the MDM2 and MDMX proteins. In fact their presence in the MDM2 protein leads to the creation of a basin of attraction in the nutlin/MDM2 interaction landscape that directly targets the crystallographic binding site on the MDM2 surface.

These results clearly show the importance of the consideration of the kinetics of drug-receptor interaction for gaining insight into the mechanism of drug-receptor binding that may not be readily attainable from traditional thermodynamic analysis of the drug-receptor bound complex. Although there are several factors that are excluded from our studies, including the turnover rates of the target proteins, which are likely to influence the differential interactions,⁴¹ nevertheless, mechanistic insights into the rates of drug binding to targets could provide valuable new avenues for the development and design of better drug candidates. An immediate avenue is that of determining the rates at which these molecules come on or off the targets and their ability to have long lasting effects. Quantitative information for the kinetics of these drugs will be a great complement to designing cyclotherapies.^41,76 In addition, these characteristics and those of the interactions in the bound state⁶³ help to begin to define parameters that can be fine-tuned towards the design of inhibitors that can target both MDM2 and MDMX¹⁵ or in combination therapies.³⁰ In addition, these networks will undoubtedly involve several other key players whose regulations and modulations⁷⁷ will also play key roles with greater understanding, providing new and novel targets in the future.

Disclosure of Potential Conflicts of Interest

No potential conflicts of interest were disclosed.