Effect of Stapling on the Thermodynamics of mdm2-p53 Binding

Protein-protein interaction (PPI) is one of the key regulatory features to drive biomolecular processes and hence is targeted for designing therapeutics against diseases. Small peptides are a new and emerging class of therapeutics owing to their high specificity and low toxicity. For achieving efficient targeting of the PPI, amino acid side chains are often stapled together resulting in the rigidification of these peptides. Exploring the scope of these peptides demands a comprehensive understanding of their working principle. In this work, two stapled p53 peptides have been considered to delineate their binding mechanism with mdm2 using computational approaches. Addition of stapling protects the secondary structure of the peptides even in the case of thermal and chemical denaturation. Although the introduction of a stapling agent increases the hydrophobicity of the peptide, the enthalpic stabilization decreases. This is overcome by the lowering of the entropic penalty and the overall binding affinity improves. The mechanistic insights into the benefit of peptide stapling can be adopted for further improvement of peptide therapeutics.


Introduction
Proteins are part of several important biomolecular processes like enzyme catalysis, signal transduction, etc. and they regulate these processes at different stages. Regulation of these processes by protein is governed by specific protein-protein interactions. 1 In the diseased condition, these sophisticated protein-protein interactions are compromised, inhibited, or dis-regulated. 2 The strategy to design ways to fight diseases involves restoring those interactions by using some chemical moieties which can mimic one of the original partners in the protein-protein interaction. 3 Different types of molecules are used as therapeutics 4 e.g. small organic molecules, 5 peptides, 6 biologics such as growth factor, antibodies 7 etc. The small molecule inhibitors (having molecular weight below 500 Da) and the biologics (having molecular weight above 5000 Da) form the two ends of the molecular inhibitors in terms of molecular weight. 8 Due to their size, the small molecule inhibitors have high oral bioavailability and permeability. However, sometimes they suffer from limited target selectivity due to their chemical nature. On the other hand, the biologics are very target specific due to their larger interaction area with their target and shows high affinity. Unfortunately because of their size, they suffer from low membrane permeability and metabolic stability.
Considering the advantages and disadvantages of these two classes, a third class of therapeutic having a molecular weight in between small molecules and biologics is emerging as a potential improvement. 9,10 These are orally bioavailable, cell-permeable and have lower manufacturing costs. 11 Members of this class are mainly peptides derived from naturally occurring proteins and their modified or engineered versions. The design of these bio-active molecules has immensely improved in the last decade to increase their efficiency by introducing chemical modifications to their conformation. One such chemical modification is known as 'cross-linking' or 'stapling' and the modified peptides are known as 'stapled peptides'. 12,13 The side chains of some suitably positioned amino acids are replaced by a variety of chemical moieties, and joined together using ring-closing metathesis. This puts a restrain to the backbone conformations of the peptide which results in a loss of its conformational flexibility and the entropic penalty during complexation is reduced. The design of a stapled peptide can be modulated by controlling two factors -(i) nature of stapling agent and (ii) stapling position. The most used stapling agent is a simple aliphatic hydrocarbon chain although several other modifications are also used like lactam, 14  There are some example of i−i+3 16 and i−i+11 17 stapled peptides also. Examples of proteins targeted by stapled peptide are mdm2/mdmx, 18 anti-apoptotic Bcl-2 family proteins, 19 estrogen receptor 20 etc. Amongst these, the ones targeting mdm2 are very important in the context of designing therapeutics.
The p53 tumor suppressor is a crucial modulator of growth arrest and apoptosis in response to cellular damage and stress. 21 For example, in response to DNA damage, it controls the growth arrest to allow DNA repair or propagates apoptosis. These prevent the proliferation of damaged cells and transfer of lethal mutations to the next generation of cells. 22 In normal cellular condition, p53 is present in the cell in very low concentration and their tumor suppressor function is antagonized by mdm2. 23 Interestingly mdm2 is overexpressed in cells for different types of tumors. 24,25 The cancerous cells produce more mdm2 to inactivate p53 to ensure their growth. Designing compounds that can prevent the interaction between p53 and mdm2 is therefore an attractive strategy to restore p53 tumor-suppressor activity in tumors. There are approaches to design both small-molecule inhibitor 26,27 as well as peptide-based inhibitor, 28 'stapled peptide' in particular. Significant numbers of stapled peptides have been proposed and their mdm2-bound structures have been solved using X-ray crystallography 29 and NMR spectroscopy, 16 yet the success in the clinical trials is not very promising. For example, a stapled peptide developed by Chang et al. as a dual inhibitor of mdm2 and mdmx has passed the phase-Ib clinical trial. 30 This limitation of the designed peptides demands a detailed understanding of the binding mechanism of stapled peptides with mdm2. The structural details available from crystallographic structures are not suffi-cient as it does not capture the dynamic aspect of the protein-peptide interaction however, the structures obtained using NMR spectroscopy often provide useful information about the dynamics. 16 In this context, a computational approach combining molecular modeling and molecular dynamics simulation can provide significant insight. Significant progress has been made by several research groups in this direction which includes comparisons of stapled and unstapled peptide binding, benchmarks of stapling position on the peptide from the calculated thermodynamic properties, 31-34 comparison of performances of force fields to model stapled peptide, 35 and development of new simulation methodology which can address the kinetics of binding. 36 Most of these studies address the changes in p53 conformation inside the binding pocket upon addition of the stapling agent. Though that gives a considerable picture of the binding process, the whole picture will not be clear without considering the free state conformations. While going from its free state (having large numbers of possible conformations) to the mdm2-bound state (having effectively reduced numbers of conformations), the p53 peptide will undergo a large conformational change. This transformation from high entropy state to low entropy state will cost entropic penalty to the overall binding energy. Since stapling agents introduce positional restraint in the peptide that can be expected to influence the free sate and hence the entropic penalty value. Therefore it is equally important to compare the free-state conformation of p53 and stapled p53.
The binding of mdm2 with three peptides p53, p53 with an aliphatic hydrocarbon staple, and a biaryl aromatic staple has been studied extensively in this communication using allatom molecular dynamics simulation accumulating 27 µs simulation time. The free peptides have been simulated in the aqueous solution, at a higher temperature (330K) and in the presence of 8M urea to check their efficiency in restricting conformational flexibility. The p53 with the aliphatic staple is conformationally more restricted than wild-type p53 and for p53 with the aromatic staple, the flexibility is even less than that. The addition of stapling agents makes the peptides resistant to thermal and chemical denaturation also. Though the addition of stapling agent increases the hydrophobicity of the peptides, the enthalpy values do not improve. Instead the preferential binding of mdm2 with stapled peptides compared to the wild-type p53 is guided by lowering of entropic penalty which is proportional to the restriction in the conformational flexibility of the peptides. To the best of our knowledge, this is the first study of this kind where extensive quantification of the thermodynamics of p53-mdm2 binding in the presence of two stapling agents and the conformational sampling of the peptides in different environments have been combined to get a comprehensive understanding of the relation between conformational rigidification and binding efficacy. The finding from this investigation can be adopted further to design more efficient stapling agents with enhanced binding efficacy.

Methods and Materials
Modeling The 13-residue stretch of human tumor suppressor p53 (sequence:ETFSDLWKLLPEN) which binds with mdm2, is considered as the system of interest. This 13-residue stretch has been used in several studies and has shown to recapitulate several aspects of the p53-mdm2 interactions. Two stapling agents were used in this investigation, one is an aliphatic hydrocarbon chain and another is a biaryl linker ( Figure 1).
The structure of wild-type p53 is taken from its crystal structure with mdm2 (Pbd Id: 1YCR). 37 The p53 with aliphatic stapling agent attached to residues S4 and P11 is obtained from crystal structure 3V3B 29 and is labeled as p53 Al . The other stapled peptide is modeled based on p53 Al where the aliphatic stapling agent is replaced by a biaryl system connected to positions 4 and 11 via sulfur linkage. The motivation for the design is to consider a stapling agent that is different from an aliphatic staple in terms of stiffness and bulkiness.
This stapling agent is termed as aromatic staple and it is termed as p53 Ar (Figure 1). The N-and C-terminal of the peptides were capped using Acetyl and amide group respectively to avoid interaction of the terminal charges with the rest of the system. The same capping moieties have been used in previous studies as well. 38,39 The detailed system compositions and simulation environments have been listed in Table 1. The system identifiers defined in the table will be followed throughout the rest of the manuscript. Several simulations are performed where the wild type p53 and its stapled variations were considered in free state in different environments and also in complex with mdm2. Equilibrium molecular dynamics simulations often sample conformations that are around the global minima and thus are restricted in terms of sampling other regions of the conformational energy landscape. To overcome this and to sample conformations which differ from the native helical peptide, two unfolding inducing conditions were used -(i) Simulation at a higher temperature 330K and (ii) Simulation in the presence of 8M urea which is known to be standard and used for studying denaturation of several proteins 40,41 and also for shorter peptides like the 13-residue stretch of p53. 42,43 All the three peptides were simulated in these two conditions. The high temperature simulation was carried out at a slightly higher temperature than the melting temperature of p53 which is reported to be around 320K. 44,45 To model the binding of the peptides with mdm2, three complex structures are generated -mdm2+p53, mdm2+p53 Al and mdm2+p53 Ar . The first two structures are modeled according to their crystal structure 1YCR and 3V3B respectively. The mdm2+p53 Ar is modeled by

Simulation details
CHARMM36 parameters 46 for protein is used to model the peptides and the protein-peptide complexes except for the stapling agents. The stapling agents are modeled using a combination of CHARMM parameter for proteins and small molecules (CGENFF). 47 For p53 Al , first the side chains of S4 and P11 are replaced by that of lysine. Then the −NH 2 groups are replaced by an aliphatic chain of suitable length and the end of the two side chains are joined. The carbon atoms up to δ carbon are parameterized using CHARMM36 protein force-field whereas the parameter for the rest is from CGENFF of CHARMM. CHARMM force field has been successfully used earlier for studying mdm2-p53 interaction. 48 This strategy has been successfully used to model stapled peptide in several studies. 20,49 Each of the systems is solvated in a waterbox made of TIP3P water 50 where the size of the waterbox was determined by maintaining a distance of at least 1 nm between the water box edge and protein/peptide atoms. For the removal of initial steric clashes, a 5000-steps energy minimization was performed for each system using the steepest descent method. 51 Subsequently, a 500 ps equilibration in the NVT ensemble was performed to equilibrate each system at 310K to avoid void formation in the box followed by a 5 ns equilibration at isothermalisobaric (NPT) ensemble to attain a steady pressure of 1 atm. The temperature was kept constant at 310 K by applying the V-rescale thermostat 52

Binding energy calculation
The standard free energy of binding (∆G) is calculated using the MM-GBSA (Molecular Mechanics with Generalized Born and Surface Area) protocol. 59,60 In practice, the simulations of the free and the complexed states are performed using explicit water to get the conformational microstates of the solute, and then the free energy of solvation of these conformations are estimated using an implicit environment after removal of explicit water molecules. The total free energy (G) is calculated using the following equation - The first three terms represent the components of energy arising from the motion within the molecule (e.g., bond vibration, angle bending, dihedral rotation, etc.), van der Waals interactions, and electrostatic interactions, respectively. The fourth and fifth terms represent the solvation free energy calculated considering implicit environments in two separate parts, i.e., polar and non-polar components. The last term is solute entropy, where T represents the absolute temperature and S is the entropy of the solute, whereas the solvation entropy is already incorporated in solvation energy terms. 59 The sum of the first five terms is considered as enthalpy, H although it includes the solvation entropy term. The values are averaged over the total simulation time and the free energy change is quantified as - Different components of binding free energy are averaged over the last 600ns (400ns-1000ns) simulation of each system. Three independent simulations of all the systems are used for the calculation to ensure statistically significant results. Instead of using a single trajectory approach where the conformations of the components of the complex (e.g. p53 and mdm2) are derived from a single simulation of the complex (i.e. p53+mdm2) 61 we have used a threetrajectory approach where both the components of the complex were simulated separately.
This approach is proven to be more accurate in predicting binding energy. 59,62 The values calculated for the three simulations are summarized in Supporting Information Tables (Table   S1-S10) and an average of the three simulations is provided in Table 2. The implicit solvent model GBSW 63 is used for the calculation and the dielectric constants values of the solvent and the protein interior are 80 and 1 respectively

Stapling agent reduces conformation flexibility
The conformations of the 13-residue p53 peptide in the presence and the absence of the stapling agents obtained from the micro-second long simulation will provide an idea of the effect of the stapling agent on the behavior of the free peptide. To compare the effect of stapling agents on the conformations, a conformational energy landscape is constructed considering two important structural parameters of the peptide, backbone RMSD (root mean square deviation) and R g (radius of gyration). The probability of occurrence of the points within 0.1 nm × 0.1 nm grid is calculated from the RMSD vs R g plots as follows - Where n ij is the number of conformations within an area confined between RMSD values i and i+∆i and R g values j and j+∆j. N ij is the total number of conformations. Free energy change is then calculated using the formula - Although several other collective variables can be used to form this kind of conformational energy surface 64-66 RMSD and R g has been found useful in understanding the conformational transition in many cases. [67][68][69] The major energy minimum points in the energy landscape have been labeled with the uppercase alphabet and the conformation of the corresponding structure has been shown in Figure 2. The plot clearly shows that the wild-type p53 has wider distribution in all the three conditions compared to p53 Al and p53 Ar systems. The distribution of the plot is restricted more along the R g axis compared to RMSD. This can be The peptide binds to mdm2 to occupy its binding pocket in a conformation which is a helix. The helical conformation is crucial for the orientation of the binding pocket anchoring residues of p53 e.g F3, W7, and L10. Thus it will be interesting to look into the helical propensity of the peptide in the presence of thermal and chemical denaturing agents and how that is altered when a stapling agent is introduced.

Stapling enhances backbone rigidity to restrict unfolding
The helical propensity of the peptide is quantified as fraction helicity. First the number of six residue alpha−helical stretch (S) in the peptide is calculated using PLUMED 70 according to the following formulae as introduced by Pietrucci et al. 71 - where {R i } i∈Ωα are the coordinates of the set Ω α describing a six residue protein-stretch and The time evolution of f H is calculated for the peptides in different system and presented in Figure 3. In Figure 3a, the helical fractions of p53, p53 Al , and p53 Ar in aqueous solution were plotted together.
It can be seen that the helical fraction of p53 gradually decreases to zero at 350ns and rest of the simulation, the peptide was in a coiled conformation. Upon addition of stapling agents the helical fraction was maintained and it was more effective for p53 Ar compared to p53 Al .
The helicity measured using experimental techniques by Zondlo et al. 72 and Xiong et al. 73 show the wildtype p53 to have considerable extent of helical structure which is in agreement with the initial part of our simulation but not with the unfolded ensemble. On the other hand, Bernal et al. 18 reported the helicity of the wild type p53 to be 11% which corresponds to an unfolded peptide and it matches well with the conformations from our simulated en- semble. An introduction of an aliphatic staple has improved the helicity to 60% in the same study and the enhancement in helicity for p53 Al in the present study agrees with that result.  Overall the structural changes of p53 and its stapled variants in water and in the presence of thermal and chemical denaturant show that there is a significant reduction of the conformational flexibility when the S4 and P11 side chains were modified and joined together like a stapled residue. This restriction in the conformations and modification of the amino acid side chain of p53 will influence the binding to its partner mdm2. Although the effect can influence the binding in many ways it could be categorized into two major types -(i) The In all cases, p53 has highest value of rdf because of the higher accessibility of the backbone atoms due to unfolding (magenta lines). Rdfs for p53 Al and p53 Ar appear below that of p53 ensuring the lower solvent exposure of backbone atoms and hence maintaining the helical conformation (green and cyan lines respectively). The number of hydrogen bonds between water molecules and backbone atoms of different peptides throughout the simulation in a-ii) aqueous solution, b-ii) at 330K, and c-ii) in the presence of urea are shown. The hydrogen bonds between peptide backbone and urea molecules for three systems during the simulation are presented in d-ii). In each case, addition of stapling agent reduces the number of hydrogen bonds representing more folded conformation.
interaction of the polar S4 and P11 with mdm2 binding pocket residue will be compromised and instead there will be additional interaction of hydrophobic stapling agent with the binding pocket. A resultant of these will be reflected in the protein-peptide interaction. (ii) The energetic cost to bring the peptide from a free state to a mdm2-bound state will be different when the conformation in the free state itself is modified. To understand these in detail, the free enegry of mdm2-p53 binding has been calculated using MM-GBSA protocol. Although there are other methods for binding energy calculation, 36,76 they are computationally more expensive and are not extensively used to study protein-peptide binidng. Whereas, MM-GBSA is a well standardized protocol for calculating binding free energy and it is widely used.

Entropy determines the binding affinity
The binding free energy was estimated considering one microsecond long simulation of mdm2+p53, mdm2, and p53 systems. The average binding free energy was quantified considering both enthalpy and entropy. The enthalpy was calculated using the MMGBSA protocol, a formalism used to find the solvation energy using a continuum model for solvent.
The conformational entropy is estimated considering quasi harmonic approximation on the ensemble of conformations. These values are further averaged over the three simulations of the protein+peptide systems. The results for the three systems are summarized in Table 2.  resenting the change in van der Waals energy and total polar interaction energy respectively.
There is a loss of ∼2 and ∼4 kcal/mol in the van der Waals interaction energy for p53 Al is negative here i.e. going from the 'free' state to the 'mdm2-bound' state the peptide loses entropy. Interestingly the amount of entropy loss has been significantly reduced when the stapling agents were added. This reduction in entropic penalty has significantly contributed to the overall free energy. Overall the binding of stapled p53 peptides is thermodynamically more favorable than the wild-type peptide.
The experimentally determined binding energy values for p53 with mdm2 lie in the range of -6.8 to -9.1 kcal/mol [80][81][82][83] and the value obtained from the present study (-8.46 kcal/mol) are in good agreement with that. On the other hand, binding energy values obtained from some previous computational studies are -6.4 kcal/mol 32 , -7.4 kcal/mol 84 and -12.9 kcal/mol. 85 The difference between the predicted and experimental binding energy values arises from a number of reasons such as force field parameters, binding energy calculation method, simulation length etc. For example, Zhou et al. 84 and Paul et al. 85 have used extensively long simulations and other statistical means. Whereas, we have used relatively simpler and computationally less expensive techniques yet the binding energy value is in good agreement with the experiment. However, the deviation of computationally predicted values from experimental values by an amount of 1-2 kcal/mol has also been argued to be in the limit of force field inaccuracies. 85,86 Moreover the effectiveness of the stapling agents to enhance the binding affinity, found here is in agreement with experiments and previous computational studies.
Since both the free state of p53 and its mdm2-bound conformation have roles to play in determining the binding efficiency, a comparison of the important features of mdm2 binding in the two states will be insightful to rationalize the binding free energy values. In the next section, two such key features will be discussed in detail.

Stapling reduces the cost of conformational transition upon binding with mdm2
The crystal structures of p53-mdm2 complexes show that the binding of p53 with mdm2 is guided by anchoring of three hydrophobic residues into the binding pocket which are F3, W7, and L10 and the p53 peptide fit into the binding pocket with a helical conformation.
These two important features i.e. the helicity of the peptide and the orientation of the three residues were monitored in the free and mdm2-bound state of p53. A comparison of helicity of the free and mdm2-bound conformation is presented in Figure 5. For p53, the helical (Movie S1), mdm2+p53 Al (Movie S2), and mdm2+p53 Ar (Movie S3) respectively.
Since the peptide has gained enhanced helicity inside the mdm2-binding pocket, the interaction of the peptide with the binding pocket residue may also get modified. To quantify that, the interaction energies of each residue of the peptides are calculated with mdm2-binding pocket residues and shown in Figure 6. It is evident from the plot that the interaction of the three anchoring residues (F3, W7 and L10) has not changed much upon addition of the stapling agent. Whereas, there is a significant improvement of the interaction when interaction of S4 and P11 of p53 with mdm2 is compared with the interaction of the stapling agent of p53Al and p53Ar with mdm2. Interestingly an increase in the helicity upon addition of stapling agent enhances the interaction of C-terminal residues (E12 and N13) of p53 with mdm2.
To compare the relative orientation of the three anchoring residues, two distances among them have been monitored throughout the simulation time which are r F 3−W 7 and r W 7−L10 . A plot of r F 3−W 7 -vs-r W 7−L10 is shown in Figure 7. The magenta points in Figure 7b represent the distances for the free p53 and the points encircled in black are distances calculated from the mdm2+p53 system. An overlap of these shows that the free peptide deviates by a large distance in terms of the favorable distances for complexation. As a result, the energetic cost of reorienting the residues as suitable for complexation will be energetically costly. This overlap for the p53 Al and p53 Ar systems depicts that the points for free and mdm2-bound states are quite close to each other, specifically for p53 Ar system. This ensures an energetically favorable transition from free to complexed state. The effect of the stapling agent in maintaining this orientation is even more evident if the free peptide simulations in different conditions are considered ( Figure S4).

Discussion
The conformational dynamics of wild-type p53 and its two stapled versions p53 Al and p53 Ar have been monitored in their free states in water and in their complexes with mdm2. The peptides are more flexible in the free state than when they are bound to mdm2 binding pocket and this flexibility is also influenced by the addition of stapling agents. The conformational flexibility has been measured using two properties, RMSD and R g . The plot clearly shows that change in both RMSD and R g is significantly large and the R g -vs-RMSD plot spans over a wide area (Figure 2a(i)). This is significantly reduced when the stapling agent is added by replacing the amino acids S4 and P11 (Figure 2b peptide. This is confirmed by comparing their helicities during the simulation. The p53 loses its helicity after 350ns whereas the stapled peptides maintain the helical fraction in the range 0.4 to 0.7 throughout the simulation (Figure 3a). Since the equilibrium simulation of the peptide in water has its limitation in sampling all possible conformations, two external conditions are imposed that can accelerate the sampling of conformations distant from the stable helical conformation. This will sample the unfolded conformations of the wild-type p53 and also check the endurance of the staple peptides in these adverse environments.
The result shows that indeed they are capable of restricting the conformational sampling ( Figure 2). In the condition of thermal denaturation both p53 Al and p53 Ar are capable of preventing the unfolding (Figure 3b) whereas in the presence of urea, there is significant loss of helicity of the p53 Al after 600ns (Figure 3c).
To estimate the influence of these stapling agent-induced conformational changes on the binding of p53 with mdm2, two important structural factors of p53 are checked that facilitate its binding. One of them is the helical structure of the peptide and another is the relative orientation of the three anchoring residues F3, W7, and L10. The values of these two structural parameters are compared for the free peptides and their mdm2-bound states in  Figure 7c) and a significant overlap for p53 Al (Figure 7b) whereas for p53, the points for complex state overlap only with a small part of the free state distribution (Figure 7a).
The advantages of cross-linking two amino acid side chains quantified through the above structural parameters are further verified by considering the calculation of thermodynamics of mdm2-p53 binding. The binding free energy follows the trend ∆G p53 Ar < ∆G p53 Al < ∆G p53 . This justifies the idea that restraining the peptide conformation and inducing helical propensity using a stapling agent can enhance the binding affinity. The experimental binding affinity of the p53 and p53 Al are reported to be 700 nM and 55 nM respectively which follows the same order found from our calculations. 29 The origin of this enhanced free energy of binding can be understood if the enthalpy and entropy of the binding process are considered separately. Although the addition of stapling agent results in a compact conformation of the peptides inside the binding pocket, the binding enthalpy is increased (i.e. unfavorable). The hydrophobic nature of the long stapling agent spanning over seven residues induces significant van der Waals interaction with the protein but is not sufficient to compensate for the loss of electrostatic interaction. The gain in helicity of the peptide due to the introduction of the stapling agent at the 11th position induces conformation restriction to the residues E12 and N13 also. As a result it loses some of the polar interaction with mdm2 in mdm2+p53 Al as well as in mdm2+p53 Ar . This results in the increase in ∆H value (Table 2). Interestingly the change in entropy plays an important role to recover this loss. The change in conformational entropy (∆S) is defined as - Due to the large conformational freedom of the free peptide, S p53 has a very high value and that results in an overall negative ∆S. The addition of a stapling agent has reduced the conformational flexibility of the free peptide as reflected in the R g -vs-RMSD plot and in the helicity values (Figure 2 and 3a). This reduces the free state entropy value of p53 Al and p53 Ar significantly. Since the conformational fluctuations of the complex states (the first term at the right-hand side of the equation) are almost similar for the three complexes except for the difference in some of the amino acids at the binding pocket, the major changes in ∆S arise from the entropy of the free peptide (the third term at the right-hand side of the equation).
Due to the smaller values of S p53 Al and S p53 Ar the ∆S p53 Al and ∆S p53 Ar are less negative than ∆S p53 . This decrease in the entropic penalty is large enough to overcome the increase in enthalpy and the free energy of binding decreases. This type of enthalpy and entropy compensation has been observed by previous studies as well. [88][89][90] This favors the binding of stapled peptide over the wild-type p53. Thus the conformational restrictions of free peptides checked using simulations in several conditions have their influence on the entropy values.
The structure of the two stapling agents and the thermodynamic parameters justify that a restriction of the peptide conformation is fruitful in enhancing the binding affinity and that the stiffness of the stapling agent is beneficial for the binding. Like most of the binding free energy calculation methods, MM-GBSA method also has limitations. In particular, MM-GBSA method sometimes fails to produce very accurate absolute ∆G values and it depends on the internal dielectric constant of the solutes. 91 However, the method has shown remarkable accuracy in assessing the relative order of protein-peptide binding energies in different contexts. 77,92 The understanding of the chemical nature of the stapling agent and its binding efficiency can be used as a guiding principle to design more effective therapeutics against mdm2 in the future. A successful adoption of the strategy described in this work can lead to opening of new avenues towards designing therapeutics against many other diseases.

Associated Content
Supporting Information: 2D histograms of RMSD-vs-helicity and R g -vs-helicity; R g -vshelicity overlaps between free peptides and peptide-mdm2 complexes; Orientations of anchoring residues in different conditions; Detailed average energy components for all systems with standard errors; Dynamics of p53, p53 Al , and p53 Ar at the binding pocket of mdm2.

Data and Software Availability
The coordinates (.pdb files) of proteins and peptides used for the simulations of the systems listed in Table 1