How Does the Recently Discovered Peptide MIP Exhibit Much Higher

Article Cite This: J. Chem. Inf. Model. XXXX, XXX, XXX−XXX

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How Does the Recently Discovered Peptide MIP Exhibit Much Higher Binding Affinity than an Anticancer Protein p53 for an Oncoprotein MDM2? Tatsuya Yamada,† Tomohiko Hayashi,† Simon Hikiri,†,‡ Naohiro Kobayashi,§ Hiroshi Yanagawa,∥ Mitsunori Ikeguchi,⊥,# Masato Katahira,† Takashi Nagata,† and Masahiro Kinoshita*,† †

Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage, Chiba 263-8522, Japan § Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan ∥ Y-Lab. of IDAC Theranostics, Inc., 1-1-48 Suehiro-cho, Tsurumi, Yokohama 230-0045, Japan ⊥ Graduate School of Medical Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan # RIKEN Medical Sciences Innovation Hub Program, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan

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‡

S Supporting Information *

ABSTRACT: An oncoprotein MDM2 binds to the extreme Nterminal peptide region of a tumor suppressor protein p53 (p53NTD) and inhibits its anticancer activity. We recently discovered a peptide named MIP which exhibits much higher binding affinity for MDM2 than p53NTD. Experiments showed that the binding free energy (BFE) of MDM2-MIP is lower than that of MDM2-p53NTD by approximately −4 kcal/mol. Here, we develop a theoretical method which is successful in reproducing this quantitative difference and elucidating its physical origins. It enables us to decompose the BFE into a variety of energetic and entropic components, evaluate their relative magnitudes, and identify the physical factors driving or opposing the binding. It should be applicable also to the assessment of differences among ligands in the binding affinity for a particular receptor, which is a central issue in modern chemistry. In the MDM2 case, the higher affinity of MIP is ascribed to a larger gain of translational, configurational entropy of water upon binding. This result is useful to the design of a peptide possessing even higher affinity for MDM2 as a reliable drug against a cancer.

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INTRODUCTION The anticancer protein p53 plays a leading role in cell cycle arrest and cell apoptosis, which suppresses tumorigenesis and malignant progression of a cell.1−3 Therefore, p53 is called “guardian of the genome”.2,4 However, the functional expression of p53 can be invalidated due to the overexpression of the oncoprotein MDM2.5 MDM2 binds to the extreme Nterminal peptide region of p53 (p53NTD) and inhibits its anticancer activity.6,7 On the basis of structural analysis of the complex of MDM2 and p53, it was suggested that p53NTD fitted into the hydrophobic pocket of the N-terminal domain of MDM2 by forming an α-helix.6 Recently, we discovered a 12-residue peptide with higher binding affinity for MDM28,9 than any other peptide currently known.7,10−15 It was named the MDM2 Inhibitory Peptide (MIP).8 MIP and p53NTD share the same number of residues (the amino-acid sequences of p53NTD and MIP are ETFSDLWKLLPE and PRFWEYWLRLME, respectively). The dissociation constant of MDM2-MIP (1.84 × 10−8 M) is about 3 orders of magnitude smaller than that of MDM2-p53NTD (1.45 × 10−5 M).9 In general, if the affinity of a peptide for MDM2 is © XXXX American Chemical Society

sufficiently high, it strongly binds to MDM2 and prevents the interaction between p53 and MDM2, recovering the anticancer activity of p53. With a higher affinity, the administration of the drug by only a smaller amount works effectively. As a result, the drug becomes more dissoluble in aqueous solution, which enables us to consider diverse administration methods, reduces adverse drug reactions, and lowers the manufacturing cost. Thus, it is worthwhile to design a peptide binding to MDM2 even more strongly than MIP for developing a reliable anticancer drug. Unfortunately, it remains unknown how MIP exhibits much higher affinity for MDM2 over p53NTD. Comparing the binding mechanisms of MDM2-p53NTD and MDM2-MIP complexes and unraveling their differences should provide us with a clue to the design of a peptide with even higher affinity for MDM2. In general, in elucidating the mechanism of a protein−peptide binding, the experimental determination of the protein−peptide complex structure is an important first Received: March 14, 2019 Published: July 8, 2019 A

DOI: 10.1021/acs.jcim.9b00226 J. Chem. Inf. Model. XXXX, XXX, XXX−XXX

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Journal of Chemical Information and Modeling

biomolecule J. (c) XJ is obtained as the average of the values of X for all the structures generated (i.e., as the ensemble average). Hereafter, X or XJ denotes this ensemble average. We note that MDM2 and p53NTD or MDM2 and MIP undergo structural changes upon binding (Figure 1). Here, we denote the change in a thermodynamic quantity X upon binding by ΔX

step. However, a detailed analysis on the complex structure or the binding mode alone is not adequate to the elucidation. This is because not only the protein−peptide interaction but also protein and peptide hydration properties play essential roles. We note that the hydration effects can be analyzed correctly only by employing a molecular model for water and accounting for the protein and peptide polyatomic structures. The binding free energy (BFE) (i.e., the change in free energy upon binding; a negative quantity) is a pivotal quantity, but its evaluation with sufficient accuracy is an intricate subject. In this study, we calculate the BFE for the MDM2-p53NTD and MDM2-MIP complexes by employing our recently developed statistical-mechanical theory16 which has been shown to yield very accurate prediction of the hydration free energy for a variety of solutes including peptides and proteins with prescribed structures. Molecular models are adopted for water and the structures of biomolecules (the MDM2p53NTD and MDM2-MIP complexes and isolated MDM2, p53NTD, and MIP) are treated at the atomic level. In order to account for the structural fluctuation of the biomolecules in water, we employ all-atom molecular dynamics (MD) simulations, thus developing a state-of-the-art theoretical method. It is proved that the BFE is much lower for MDM2-MIP. The difference between the two complexes in the BFE is in quantitatively good agreement with the experimental value. Since the use of the statistical-mechanical theory enables us to decompose the BFE into physically insightful energetic and entropic components, we are able to identify the components driving or opposing the binding, evaluate their relative magnitudes, and clarify the physical factors controlling the binding affinity for MDM2. The results obtained are useful to the design of a peptide binding to MDM2 even more strongly as a reliable drug against a cancer. Furthermore, our theoretical method should be applicable to general receptor−ligand binding processes as long as the structures of receptor−ligand complexes are experimentally available.

ΔX(MDM2‐p53NTD) = XMDM2‐p53NTD − (XMDM2 + X p53NTD)

(1a)

ΔX(MDM2‐MIP) = XMDM2‐MIP − (XMDM2 + XMIP) (1b)

Figure 1. Illustration of binding of MDM2 (blue) and p53NTD or MIP (red) in water.

Method of Calculating Hydration Entropy and Energy of a Biomolecule with a Fixed Structure. Using our recently developed statistical-mechanical method,16 a new hybrid of two types of integral equation theories (this is referred to as the “hybrid method”), we calculate thermodynamic quantities of hydration of a biomolecule with a prescribed structure under the isochoric (constant volume) condition. The quantities calculated under the isochoric condition are physically more insightful than those under the isobaric (constant pressure) condition. SVH and εVH denote the hydration entropy and energy, respectively. The subscript “V” signifies that the quantity is calculated under the isochoric condition, and the subscript “H” denotes “hydration”. The calculation procedure is briefly summarized below (see our recent publication16 and Sections S1.1−S1.5 of Supporting Information (SI) for more details). The insertion of a biomolecule can be decomposed into processes 1 and 2 (Figure 2). Process 1: The creation of a cavity in water matching the geometric characteristics of the biomolecule structure at the atomic level. The cavity is modeled as a set of fused, neutral hard spheres corresponding to the biomolecule atoms. The diameter of each hard sphere is simply set at σ, one of the LJ potential parameters, assigned to it. Hereafter, the subscript “1” is used to signify a quantity in process 1. Process 2: The incorporation of biomolecule−water interaction potentials excluding the core repulsions. Process 2 can further be decomposed into processes 2-vdW and 2-ES where biomolecule−water van der Waals (vdW) and electrostatic (ES) interaction potentials are incorporated, respectively. Hereafter, the subscripts “2”, “2,vdW”, and “2,ES” are used to signify quantities in processes 2, 2-vdW, and 2-ES, respectively. SVH,1 and εVH,1, respectively, denote the changes in entropy and energy in process 1, and SVH,2 and εVH,2, respectively,

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THEORETICAL METHODS We analyze the two binding processes, MDM2 + p53NTD → MDM2-p53NTD and MDM2 + MIP → MDM2-MIP. Therefore, we need to consider a total of five biomolecules, the MDM2-p53NTD and MDM2-MIP complexes and isolated MDM2, p53NTD, and MIP. The structure of a biomolecule is represented by the following parameters assigned to all of the atoms constituting the biomolecule: (x, y, z) coordinates of centers, Lennard-Jones (LJ) potential parameters, and partial charges. The structure of a biomolecule (in particular, that of p53NTD or MIP) in aqueous solution fluctuates to a significant extent. To account for this fluctuation, we generate a sufficiently large ensemble of structures of each biomolecule using the MD simulations. Strategy of Calculating Changes in Thermodynamic Quantities upon Binding. Our statistical-mechanical theory16 enables us to calculate a thermodynamic quantity X of a biomolecule with a fixed structure. That is, X is calculated as a functional of the biomolecule structure. X of biomolecule J (J = MDM2, p53NTD, MIP, MDM2-p53NTD, or MDM2MIP) whose structure fluctuates in aqueous solution, XJ, is calculated in the following manner: (a) Sufficiently many structures of biomolecule J are generated (i.e., a sufficiently large structural ensemble is constructed) using the MD simulations. (b) X is evaluated for each structure of B


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Figure 2. Insertion of a biomolecule with a fixed structure into water. The hydration of the biomolecule is decomposed into processes 1, 2-vdW, and 2-ES.

signify those in process 2. The following equations hold: SVH = SVH,1 + SVH,2, SVH,2 = SVH,2,vdW + SVH,2,ES, εVH = εVH,1 + εVH,2, and εVH,2 = εVH,2,vdW + εVH,2,ES. SVH,1 and εVH,1, which are attributable to hydrophobic hydration, are negative. SVH,2, and εVH,2 are also negative. |SVH,2| is considerably smaller than |SVH,1| irrespective of the strength of biomolecule−water attractive interaction potentials. On the other hand, |εVH,2| is considerably larger than |εVH,1| depending on the effect of biomolecule−water attractive interaction potentials. εVH,2,ES or εVH,2,vdW consists of the biomolecule−water ES or vdW interaction energy and the change in ES or vdW energy ascribed to the reorganization of the water structure near the biomolecule. In this study, two types of statistical mechanical theories, angle-dependent integral equation (ADIE) theory17−22 and three-dimensional reference interaction site model (3D-RISM) theory,22−26 are adopted for analyses on the hydration properties of biomolecules. Our morphometric approach (MA)27,28 is a powerful tool enabling us to take account of a complexly shaped cavity created in water when the ADIE is applied to process 1. The ADIE combined with the MA is employed for calculating SVH,1 and εVH,1. εVH,2,vdW and εVH,2,ES are calculated using the 3D-RISM. SVH,2,ES is also calculated by the 3D-RISM. |SVH,2,ES| is considerably smaller than |SVH,1| and |SVH,2,vdW| is even smaller than |SVH,2,ES|. Hence, SVH,2,vdW can be neglected. Thus, SVH = SVH,1 + SVH,2,ES (SVH,2,vdW ∼ 0) and εVH = εVH,1 + εVH,2,ES + εVH,2,vdW. The molecular models best suited to the ADIE and the 3DRISM are adopted for water: They are a multipolar model17,18 and a modified version of SPC/E,29 respectively. It has been demonstrated for a variety of solutes that the hydration free energy obtained by this hybrid method is in very good agreement with that calculated using the energy-representation (ER) method30−32 developed by Matubayasi and co-workers. The ER method is an all-atom MD simulation combined with a new solution theory, which has been shown to yield very accurate values of the hydration free energy of solutes. We note, however, that it is much more time consuming than the hybrid method.16 In the previous hybrid method used in our earlier works on the binding of two biomolecules,33−36 εVH,1 was neglected. This was justifiable because the change in εVH,1 upon binding, ΔεVH,1, was much smaller than ΔεVH,2, which was attributed to the sufficiently high hydrophilicity of the portions of biomolecules within the binding interface. For MDM2p53NTD and MDM2-MIP, especially for the latter, however,

the portions are rather hydrophobic, and the effect of hydrophobic hydration becomes essential (see Roles of Hydrophobic Effects for a detailed discussion). This is why the new hybrid method is necessitated. Definition of Free-Energy Function. Our free-energy function (FEF) Gwater is defined for each biomolecule with a prescribed structure, which is immersed in water at the infinite dilution limit. It comprises the conformational (biomolecule intramolecular) energy EC and the hydration free energy (i.e., excess chemical potential of the biomolecule) μH Gwater = EC + μH

(2)

Since μH takes the same value under the isochoric and isobaric conditions, the subscript “V” is not added to μH. μH can be expressed as μH = εVH − TS VH

(3)

S VH = S VH,1 + S VH,2

(4a)

S VH,2 = S VH,2,ES(S VH,2,vdW ∼ 0)

(4b)

εVH = εVH,1 + εVH,2

(5a)

εVH,2 = εVH,2,ES + εVH,2,vdW

(5b)

T is the absolute temperature (T = 298 K). The calculation procedures for SVH,1 and εVH,1 are described in Section S1.3 of the SI, and those for SVH,2,ES, εVH,2,ES, and εVH,2,vdW are described in Section S1.4 of the SI. Substituting eqs 3−5b into eq 2 yields Gwater = EC + εVH,1 + εVH,2,ES + εVH,2,vdW − T (S VH,1 + S VH,2,ES)

(6)

EC can readily be calculated once a force field for a biomolecule is given. It is decomposed into the three terms, bonded energy EB consisting of bond-stretching, anglebending, and torsion terms, vdW interaction energy EvdW, and ES interaction energy EES EC = E B + EvdW + E ES

(7)

EvdW originates from the attractive part of the LJ potential. The decomposition of εVH,2 into εVH,2,ES and εVH,2,vdW is carried out in the following manner. First, the partial charges of all the atoms constituting a biomolecule are set at zero, and εVH,2,vdW of the resultant hypothetical biomolecule is calculated. Second, C


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Journal of Chemical Information and Modeling we obtain εVH,2,ES from εVH,2,ES = εVH,2 − εVH,2,vdW (Figure 2). Substituting eq 7 into eq 6 yields

a short length of time is reasonable because the initial structure is an experimentally determined one. Each simulation consists of the equilibration run for 50 ns and the production run for 150 ns. Snapshot structures, which are stored every 100 ps during the production run, are used in the calculation of thermodynamic quantities. We thus generate a structural ensemble of MDM2-p53NTD or MDM2-MIP comprising 9000 structures. Preparation of Structural Ensembles of Isolated MDM2, p53NTD, and MIP. The MD simulations are independently carried out for isolated MDM2, p53NTD, and MIP. The initial structures of MDM2 and p53NTD are prepared simply by separating the two biomolecules forming MDM2-p53NTD with no structural changes. MIP is simply separated from MDM2-MIP, and its structure is used as the initial structure of MIP. The methodology of MD simulations for each of the three isolated biomolecules is the same as that for the complexes. The initial structures of the isolated biomolecules are not experimentally determined ones unlike in cases of the complexes. Hence, the times required for the equilibration should be longer. Six 400 ns simulations are conducted with different initializations for each of the isolated biomolecules, and it is considered that the equilibration is reached in 250 ns (see Figures S3−S5 in SI). The time length 250 ns should be sufficiently long for the following reasons: The structural change of MDM2 upon isolation is rather small; neither p53NTD nor MIP takes a well-defined structure; and p53NTD and MIP are small molecules. Each simulation consists of the equilibration run for 250 ns and the production run for 150 ns. Snapshot structures are stored every 100 ps in a 150 ns production run, yielding a structural ensemble of each of isolated MDM2, p53NTD, and MIP comprising 9000 structures. We have verified that the equilibration and production runs are sufficiently long, and the number of simulations (i.e., six) is sufficiently large (Tables S1−S3, SI). Definition of Binding Free Energy. The binding free energy (BFE) ΔF for MDM2 + p53NTD → MDM2-p53NTD is defined as the change in system free energy after 1 M of p53NTD binds to 1 M of MDM2, forming 1 M of MDM2p53NTD. ΔF for MDM2 + MIP → MDM2-MIP is defined in the same fashion. Let SC be the conformational entropy of a biomolecule. ΔF is expressed as

Gwater = EB + (EvdW + εVH,2,vdW ) + (EES + εVH,2,ES) + εVH,1 − TS VH,1 − TS VH,2,ES

(8)

We emphasize that the conformational entropy of a biomolecule is not included in eq 8 because the biomolecule structure is fixed. It is separately estimated and discussed. Equation 8 is rewritten as Gwater = E Total − TS VH

(9a)

E Total = E B + (EvdW + εVH,2,vdW ) + (EES + εVH,2,ES) + εVH,1 −TS VH = −TS VH,1 −TS VH,2,ES

(9b) (9c)

We add that the FEF of a biomolecule in vacuum is Gvacuum = EB + EvdW + EES which is substantially different from Gwater. Decomposition of Hydration Energy and Entropy in Process 1. As described in Section S1.3 of the SI, the MA allows us to decompose εVH,1 or SVH,1 into EV- and WASdependent terms. “EV” and “WAS” denote “excluded volume” and “water-accessible surface” generated by the cavity, respectively. The EV signifies the volume which is inaccessible to the centers of water molecules in the system.37 The WAS represents the surface area and curvature. The EV- and WASdependent terms originate from the change in water properties in the bulk and from the structural reorganization of water near the cavity upon cavity creation, respectively. Hereafter, the subscripts “EV” and “WAS” denote “EV-dependent term” and “WAS-dependent term”, respectively. The cavity creation reduces the total volume available to the translational displacement of water molecules, causing an entropic loss: SVH,1,EV < 0. For water whose molecules interact through attractive potential, εVH,1,EV < 0. On the other hand, SVH,1,WAS > 0 and εVH,1,WAS > 0 except at low temperatures (see Physical Origins of Behavior of Energetic and Entropic Components Related to Process 1 and Physical Origins of Behavior of Energetic and Entropic Components Related to Process 2) . Preparation of Structural Ensembles of MDM2p53NTD and MDM2-MIP Complexes. The simulation procedures, which are detailed in Sections S2.1−S2.4 of the SI, are briefly summarized here. Starting from a structure of the MDM2-p53NTD (Protein Data Bank (PDB) Code: 1YCR6) or MDM2-MIP (PDB Code: 2RUH9) complex, we perform MD simulations based on the NPT ensemble at 298 K using the AMBER16 program38 with the AMBER99SB force field.39 (The LJ parameter σ used for modeling the cavity in process 1, which is mentioned in Method of Calculating Hydration Entropy and Energy of a Biomolecule with a Fixed Structure, is also taken from AMBER99SB.) The aqueous solution of the SPC/E water40 containing NaCl (its concentration is 0.15 mol/L) is accommodated in a simulation box. The complex is hydrated in this aqueous solution. The minimum distance between the solute surface (the solute is MDM2-p53NTD or MDM2-MIP) and box edge is initially set at ∼20 Å that is sufficiently larger than the molecular diameter of water 2.8 Å. We conduct a total of six 200 ns simulations with different initializations for each of the two complexes. As discussed with the help of Figures S1 and S2 in the SI, we can conclude that the equilibration is reached in 50 ns. The equilibration in such

ΔF(MDM2‐p53NTD) = ΔGwater(MDM2‐p53NTD) − T{ΔSC(MDM2‐p53NTD)}

(10a)

ΔF(MDM2‐MIP) = ΔGwater(MDM2‐MIP) − T{ΔSC(MDM2‐MIP)} (10b)

ΔSC(MDM2-p53NTD), for example, signifies the total conformational-entropy loss upon binding for MDM2 + p53NTD → MDM2-p53NTD. Estimation of Total Conformational-Entropy Loss upon Binding. It is difficult to evaluate ΔSC with high accuracy. However, its approximate value can be estimated using the Boltzmann-quasi-harmonic (BQH) method41−43 combined with all-atom MD simulations. In the BQH method, the biomolecule conformation is represented by a set of bond lengths, angles, and torsion angles forming the internal D


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Table 1. Energetic and Entropic Components of Difference between MDM2-MIP and MDM2-p53NTD in Binding Free Energya Energetic Components ΔΔETotal ΔΔεVH,1 ΔΔ(EvdW + εVH,2,vdW) ΔΔ(EES + εVH,2,ES) ΔΔEB

Values

Entropic Components

Values

± ± ± ± ±

−TΔΔSVH −TΔΔSVH,1 −TΔΔSVH,2,ES

−16.28 ± 0.47 −16.80 ± 0.46 0.52 ± 0.07

11.48 12.30 −6.48 1.79 3.87

0.67b,c 0.31 0.34 0.35 0.62

a Values of −TΔΔSC = −T{ΔSC(MDM2-MIP) − ΔSC(MDM2-p53NTD)} estimated by the BQH method via two routes are approximately −2 and 2 kcal/mol, respectively. Our simplified method gives −TΔΔSC ∼ 1 kcal/mol. In this table, −TΔΔSC is approximated by zero: ΔΔF = −4.80 ± 0.69 kcal/mol. bUnit is kcal/mol. cStandard error is also given.

coordinates. For a more accurate calculation of SC of each biomolecule, we classify the torsions as harmonic improper and anharmonic proper torsions.43 The BQH method based on this classification43 has recently been shown to outperform the other quasi-harmonic and related calculation methods which are currently available.41,43−47 The total number of snapshot conformations of a biomolecule used for calculating SC is 90,000 that is an order of magnitude larger than that for calculating the other thermodynamic quantities. More details of the calculation procedure are described in Section S3.1 of the SI. ΔSC can also be estimated by our simplified method which has been quite successful in studies on the binding of two biomolecules33−36 (Section S3.2, SI).

all of the biomolecule structures in the six simulations are simultaneously treated, the result is −TΔΔSC ∼ 2 kcal/mol. On the other hand, −TΔΔSC estimated by our simplified method, which was shown to be reliable in our earlier works33−36 on the binding of biomolecules, is ∼1 kcal/mol. Hence, it is reasonable to assume that −TΔΔSC can be approximated by zero: We obtain ΔΔF ∼ −4.80 ± 0.69 kcal/ mol. It should be noted that we take the difference between two large quantities in calculating ΔX and ΔΔX with the occurrence of cancellation of significant digits. Moreover, the force field employed is more or less uncertain. Considering these matters, we can conclude that ΔΔF is in quantitatively good accord with ΔΔFexpt.. We decided to employ AMBER99SB because we were quite successful in elucidating the mechanism of protein-RNA recognition in our earlier work.36 AMBER99SB-ILDN was proposed as an improved version of AMBER99SB,49 and it was reported that the former was further improved as AMBER14SB.50 We test AMBER14SB: Assuming that −TΔΔSC can be approximated by zero, we obtain ΔΔF ∼ −8.38 ± 0.68 kcal/mol. The value from AMBER14SB deviates more from the experimental value, but the result that MIP exhibits a higher binding affinity for MDM2 than p53NTD is robust. Further, we find that the qualitative aspects of our conclusions on the physical factors driving or opposing the binding and their relative magnitudes, which are explained in the later sections, are not altered at all by the replacement of AMBER99SB by AMBER14SB (Sections S4.1 and S4.2, SI). The theoretical calculations of thermodynamic quantities of hydration are performed under the isochoric condition while the experiments are conducted under the isobaric condition. The values of ΔY (Y is an entropic, energetic, or enthalpic component of the hydration free energy of a biomolecule) calculated under the two conditions might be significantly different. As argued in Section S1.5 of the SI, however, those of ΔΔY calculated under the two conditions should be almost the same. For this reason, a comparison between theoretical and experimental values should be made for ΔΔX as well as ΔΔY. A discussion on ΔY and ΔX provides us with physical insights into the binding mechanism. Energetic and Entropic Components of Difference between MDM2-MIP and MDM2-p53NTD in Binding Free Energy. Table 1 presents the energetic and entropic components of ΔΔF. The ES contribution ΔΔ(EES + εVH,2,ES) is 1.79, and the nonelectrostatic one ΔΔεVH,1 + ΔΔ(EvdW + εVH,2,vdW) is 5.82 kcal/mol: They are both positive, but the vdW component ΔΔ(EvdW + εVH,2,vdW) is negative and rather large. ΔΔETotal is positive and significantly large, for which ΔΔεVH,1 is primarily responsible. Energetically, the binding affinity of MIP is lower than that of p53NTD for MDM2.

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RESULTS AND DISCUSSION Agreement between Theoretical and Experimental Values for Binding Free Energy. Our major concern is ΔΔX defined for a thermodynamic quantity X as ΔΔX = ΔX(MDM2‐MIP) − ΔX(MDM2‐p53NTD) (11)

We first compare ΔΔF theoretically calculated with the experimental value. The dissociation constant, KD, was experimentally measured to be 1.45 × 10−5 M for MDM2p53NTD and 1.84 × 10−8 M for MDM2-MIP.9 Using the relation ΔFexpt.=RT ln(KD) which holds for both MDM2p53NTD and MDM2-MIP (the subscript “expt.” denotes “experimental”, and R is the gas constant), we obtain ΔΔFexpt. ∼ −3.95 kcal/mol. In a strict sense, ΔF is not equivalent to ΔFexpt. for the following reasons:48 KD possesses a dimension of mol/L, but it must be dimensionless from a theoretical point of view. On the experimental side, the standard state for KD and ΔFexpt. is set at 1 mol/L, and the activity coefficients are assumed to be 1.0. On the theoretical side, however, ΔF is calculated for two biomolecules, and their complex is immersed in water at the infinite dilution limit. As a consequence, the following relation holds48 ΔFexpt. = ΔF + ΔΛ(ΔΛ > 0)

(12)

ΔΛ is significantly large. However, since the numbers of residues of p53NTD and MIP are the same and they possess some sequence similarity, it is possible that MDM2-p53NTD and MDM2-MIP share almost the same value of ΔΛ, with the result that ΔΔF can reasonably be compared with ΔΔFexpt.. As described in Sections S3.1 and S3.2 of the SI, −TΔΔSC = −T{ΔSC(MDM2-MIP) − ΔSC(MDM2-p53NTD)} calculated by the BQH method43 is significantly small. Calculating the values of −TΔΔSC for the six independent simulations and taking an average, we obtain −TΔΔSC ∼ −2 kcal/mol. When E


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Journal of Chemical Information and Modeling −TΔΔSVH,2,ES is quite small. Very large, negative −TΔΔSVH arises overwhelmingly from −TΔΔSVH,1. The higher binding affinity of MIP is entropic in its origin. An important point is that the hydration properties of biomolecules related to process 1 play essential roles in the determination of ΔΔF. In summary, −TΔΔS VH,1 and ΔΔ(EvdW + εVH,2,vdW ) are responsible for negative ΔΔF. Physical Origins of Behavior of Energetic and Entropic Components Related to Process 1. We display ΔεVH,1, ΔεVH,1,EV, ΔεVH,1,WAS, −TΔSVH,1, −TΔSVH,1,EV, and −TΔSVH,1,WAS in Table 2. The presence of MDM2 and the

and by the cavity overlap. As a result, the total volume available to the other water molecules increases by the overlapping volume. The entropic gain given by this increase is larger than the entropic loss caused by the contact of water molecules mentioned above. An increase in the WASA results in a larger number of water molecules in contact with the cavity, leading to higher water entropy. Hence, ΔSVH,1,WAS < 0 and −TΔSVH,1,WAS > 0. Physical Origins of Behavior of Energetic and Entropic Components Related to Process 2. ΔEvdW, ΔεVH,2,vdW, Δ(EvdW + εVH,2,vdW), ΔEES, ΔεVH,2,ES, and Δ(EES + εVH,2,ES) for MDM2-p53NTD and MDM2-MIP are collected in Table 3. The binding is accompanied by the gain of

Table 2. Changes in Thermodynamic Quantities of Hydration upon Binding Related to Process 1 for MDM2p53NTD and MDM2-MIP Components

MDM2-p53NTD

ΔεVH,1 ΔεVH,1,EV ΔεVH,1,WAS −TΔSVH,1 −TΔSVH,1,EV −TΔSVH,1,WAS −TΔSVH,2,ES

± ± ± ± ± ± ±

8.00 114.28 −106.28 −70.81 −143.01 72.20 −7.59

a ,b

0.23 0.3 0.22 0.34 0.38 0.17 0.05

Table 3. Changes in Thermodynamic Quantities upon Binding Related to Process 2 for MDM2-p53NTD and MDM2-MIPa

MDM2-MIP 20.30 123.50 −103.20 −87.60 −154.55 66.95 −7.07

± ± ± ± ± ± ±

0.21 0.28 0.21 0.31 0.35 0.16 0.05

Components ΔEvdW ΔεVH,2,vdW Δ(EvdW + εVH,2,vdW) ΔEES ΔεVH,2,ES Δ(EES + εVH,2,ES)

a

Unit is kcal/mol. bStandard error is also given.

MDM2-p53NTD −64.14 56.21 −7.92 −304.45 318.07 13.62

± ± ± ± ± ±

0.26b 0.11 0.24 1.24 1.18 0.24

MDM2-MIP −74.17 59.76 −14.40 −132.88 148.28 15.40

± ± ± ± ± ±

0.25 0.11 0.24 1.25 1.19 0.25

−TΔSVH,2,ES = −7.59 ± 0.05 kcal/mol for MDM2-p53NTD and −7.07 ± 0.05 kcal/mol for MDM2-MIP. bUnit is kcal/mol. cStandard error is also given. a

peptide (or equivalently, their cavities) generates EVs for water molecules (Figure 3). Upon binding, the two EVs overlap, and

MDM2−peptide vdW and ES attractive interactions, leading to negative ΔEvdW and ΔEES (Figure 4). However, the binding

Figure 3. Cartoon for discussing changes in thermodynamic quantities of hydration upon binding related to process 1. Figure 4. Cartoon for discussing changes in thermodynamic quantities upon binding related to process 2.

the total volume available to the translational displacement of water molecules increases by the overlapping volume, which is followed by a water-entropy gain and negative −TΔSVH,1,EV. The reduction of the total EV causes positive ΔεVH,1,EV. We remark that the water molecules in the immediate vicinity of a cavity, which possess fewer neighbors for water− water hydrogen bonds,21,51 are energetically unfavorable.21 For this reason, εVH,1,WAS takes a positive value. Since the total water-accessible surface area (WASA) of the cavities decreases upon binding, ΔεVH,1,WAS < 0. There are two factors contributing to positive SVH,1,WAS. The first factor is relevant to positive εVH,1,WAS explained above.21,51 The number of neighbors for water−water hydrogen bonds is smaller near the cavity than in the bulk. Hence, the water molecules near the cavity are entropically less restricted. The second factor can be explained as follows.52,53 SVH,1,WAS becomes more positive as the WASA of the cavity increases. Namely, larger WASA leads to higher entropy of water. When water molecules contact the cavity, the EVs generated by them

undergoes the loss of MDM2−water and peptide−water vdW and ES attractive interactions (this is referred to as the “energetic dehydration”), giving rise to positive ΔεVH,2,vdW and ΔεVH,2,ES. Oxygen and hydrogen atoms in a water molecule carry negative and positive partial charges, respectively. Positively and negatively charged groups of a biomolecule, when they are exposed to water before the binding, interact with the oxygen atoms and with the hydrogen atoms through ES attractive potentials. When they are buried within the binding interface, these ES attractive interactions are lost. Likewise, the formation of MDM2−peptide hydrogen bonds (the hydrogen bond is usually represented by ES attractive potential) is accompanied by the break of MDM2−water and peptide− water hydrogen bonds. Part of the aforementioned loss is compensated by the recovery of water−water ES attractive F


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and hydrogen bonds. However, undertaking the enhancement of this energy lowering in the design of another peptide does not necessarily lead to higher binding affinity for MDM2. Crucial Importance of Shape Complementarity at Atomic Level within Binding Interface. The water-entropy gain is a principal contributor to large, negative BFE. As argued in our earlier publications,33−36 most of the gain is ascribed to an increase in translational, configurational entropy of water, which originates primarily from the mitigation of water crowing (i.e., entropic correlation among water molecules) in the system. The mitigation is brought by a decrease in the total EV. The water-entropy gain can be made sufficiently large by the achievement of shape complementarity at the atomic level (or equivalently, highly efficient packing of atoms) within the binding interface. Overall, the achievement is more complete for MDM2-MIP. The decrease in the total EV upon binding ΔVex is calculated to be −1226.7 Å3 for MDM2-p53NTD and −1325.7 Å3 for MDM2-MIP. ΔΔVex = −99.0 Å3 which is about nine times larger than the volume of a water molecule and therefore significantly large. Roles of Hydrophobic Effects. On the basis of structural analysis of the complex of MDM2 and p53, it was suggested that p53NTD fits into the hydrophobic pocket of the Nterminal domain of MDM2 by forming an α-helix, and the stacking of flat moieties (i.e., the so-called π−π stacking) takes place. The fitting and the stacking play essential roles in the binding. This suggestion can be interpreted in our own way as follows.36 The fitting and the stacking reduce the total EV and enlarge the water entropy, making a significant contribution to the negative value of −TΔSVH,1, which originates from the entropic EV effect. At the same time, they lower EvdW. This is particularly true for the stacking. Unlike in a vacuum, the stacking in water is accompanied by the loss of water-flat moiety vdW attractive interaction, giving rise to higher εVH,2,vdW. However, closer stacking leads to lower EvdW with essentially no change in εVH,vdW, which is in favor of the entropic EV effect. It follows that Δ(EvdW + εVH,2,vdW) takes a negative value. The hydrophobic effects, which are reflected in the negative values of −TΔSVH,1 and Δ(EvdW + εVH,2,vdW), are larger for MDM2-MIP than for MDM2-p53NTD because −TΔΔSVH,1 = −16.80 and ΔΔ(EvdW + εVH,2,vdW) = −6.48 kcal: Importantly, the former makes a larger contribution than the latter to the lower BFE. Analysis on Efficiency of Packing of Peptide and MDM2 Residues. More efficient packing of residues of the peptide (p53NTD or MIP) and those of MDM2 should lead to a larger gain of water entropy. We analyze this packing efficiency in each complex. From the complex, we remove all of the residues of the peptide except residue n and obtain “MDM2-residue n”. An important quantity is ΔVex,n defined as “EV of MDM2-residue n” − (“EV of MDM2” + “EV of residue n in the peptide”). We take 900 representative structures of the complex from its snapshot structures obtained by the MD simulation and calculate the average value of ΔVex,n. The results for p53NTD or MIP are compared in Figure 5 (ΔΔVex,n = ΔVex,n(MDM2-MIP) − ΔVex,n(MDM2-p53NTD)). The MDM2-p53NTD and MDM2-MIP complexes are illustrated in Figure 6. The amino-acid sequences of p53NTD and MIP are ETFSDLWKLLPE and PRFWEYWLRLME, respectively. They share the same third, seventh, tenth, and twelfth residues: F3 (Phe), W7 (Trp), L10 (Leu), and E12 (Glu). As observed in Figures 5 and 6, for both of MDM2-p53NTD

interactions and hydrogen bonds following the release of water from MDM2 and the peptide to the bulk upon binding. Most of ΔEvdW, and ΔEES are canceled out by ΔεVH,2,vdW and ΔεVH,2,ES, respectively, with the result of much smaller Δ(EvdW+εVH,2,vdW) and Δ(EES + εVH,2,ES). Interestingly, Δ(EES + εVH,2,ES) is positive, whereas Δ(EvdW + εVH,2,vdW) is negative. |ΔEES| for MDM2-p53NTD is much larger than that for MDM2-MIP. This implies that upon binding of MDM2 and p53NTD the contact or approach of oppositely charged groups occurs within or near the binding interface between the two biomolecules, leading to a gain of much stronger ES attractive interactions. However, the energetic dehydration effect is also much stronger, with the result that Δ(EES + εVH,2,ES) becomes almost equal to that for MDM2-MIP. Table 2 includes −TΔSVH,2,ES for MDM2-p53NTD and MDM2-MIP. When the biomolecule−water ES interaction is switched on, water molecules near biomolecules are rotationally and translationally more restricted, causing the entropic instability. The amount of the entropically unstable water reduces upon binding, leading to an entropic gain. However, this effect is not essential (−TΔSVH,2,ES is much smaller than −TΔSVH,1; see the next section). Major Physical Factors Leading to Higher Binding Affinity of MIP for MDM2. −TΔΔSVH,1 makes the largest contribution to negative ΔΔF (Table 1). The lower value of ΔΔF for MDM2-MIP is attributed primarily to the larger gain of water entropy upon binding. The EV term −TΔΔSVH,1,EV = −11.54 is larger than the WAS term −TΔΔSVH,1,WAS = −5.25 kcal/mol. Therefore, the higher binding affinity of MIP for MDM2 can be explained as follows. The decrease in the total EV upon binding is larger for MDM2-MIP. Within the binding interface, the biomolecule atoms are driven to become closely packed. Equivalently, the shape complementarity is intended at the atomic level, but the close packing or the shape complementarity is more complete for MDM2-MIP. ΔΔ(EvdW + εVH,2,vdW) makes a nontrivial contribution to negative ΔΔF (Table 1). When the atoms within the binding interface are more closely packed to increase the entropy of water, ΔEvdW also becomes lower. (We note that ΔEES does not necessarily become lower.) Therefore, ΔEvdW cooperates with −TΔΔSVH,1,EV. Though ΔEvdW and ΔεVH,2,vdW are compensating, ΔEvdW is larger and Δ(EvdW + εVH,2,vdW) becomes negative. The water-entropy effect is larger for MDM2-MIP than for MDM2-p53NTD with the result of negative ΔΔ(EvdW + εVH,2,vdW). Roles of Electrostatic Attractive Interaction or Hydrogen Bonding between Biomolecules. Upon binding, MDM2−peptide ES energy exhibits a significant decrease. Counterintuitively, the decrease is much larger for p53NTD than for MIP. However, the binding is unavoidably accompanied by a significant increase in the sum of MDM2−water, peptide−water, and water−water ES energies. The increase is much larger for p53NTD. The increase and the decrease are canceled out, and their sum makes only a minor contribution to the BFE. Likewise, the formation of protein− peptide hydrogen bonds upon binding is unavoidably accompanied by the break of protein−water and peptide− water hydrogen bonds, and the changes in energy due to the formation and the break are compensating. The energy lowering by the acquisition of MDM2−peptide ES attractive interaction or by MDM2−peptide hydrogen bonding plays essential roles of compensating for the loss of MDM2−water and peptide−water ES attractive interactions G


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for n = D5 and K8 of p53NTD or for E5 and L8 of MIP. This is because the side chains of these residues are directed outward and not within the binding interface. Further Examination of Robustness of Our Theoretical Method: Calculations for MDM2-DI Binding. To further examine the robustness of our theoretical method, we evaluate the binding affinity of another peptide, DI, for MDM2 using AMBER99SB as the force field. It possesses 12 residues like p53NTD and MIP. Its amino-acid sequence is LTFEHYWAQLTS. The structure of the MDM2-DI complex is experimentally available (PDB Code: 3G03).55 Just in this section, ΔΔX = ΔX(MDM2-DI) − ΔX(MDM2-p53NTD), where ΔX is the change in thermodynamic quantity X upon MDM2−peptide binding. The experimentally measured value of KD for MDM2-DI is 2.10 × 10−7 M.9 Therefore, ΔΔFexpt. ∼ −2.51 kcal/mol. We calculate ΔΔF by our theoretical method. All of the calculation procedures for MDM2-DI are the same as those for MDM2-p53NTD and MDM2-MIP, which are described in the above sections. Since the numbers of residues of p53NTD and DI are the same and they possess some sequence similarity, we assume that −TΔΔSC can be approximated by zero. We then obtain ΔΔF ∼ −2.60 ± 0.68 kcal/mol that is close to the experimental value (ΔΔFexpt. ∼ −2.51 kcal/mol). We are thus successful in reproducing the order of the binding affinity, MIP > DI > p53NTD. The energetic and entropic components of ΔΔF and the changes in the thermodynamic quantities of hydration upon binding related to processes 1 and 2 are given in Tables S7−S9 in Section S5.2 of the SI. The qualitative aspects of the conclusions on the physical factors driving or opposing the MDM2-DI binding are the same as those described above for the MDM2-p53NTD or MDM2-MIP binding. In particular, the water-entropy gain upon binding is a principal contributor to large, negative BFE for MDM2-DI as well. Interestingly, however, −TΔΔSVH is positive, and the water-entropy gain upon binding is smaller for MDM2-DI than for MDM2p53NTD. The higher binding affinity of DI, the negative value of ΔΔF, is ascribed to ΔΔ(EvdW + εVH,2,vdW) and ΔΔ(EES + εVH,2,ES), especially the latter. Toward Theoretical Design of a Peptide with Higher Affinity for MDM2. A question then arises: How can we design a peptide whose affinity for MDM2 is even higher than that of MIP? In general, a shorter peptide with a smaller number of residues is preferred. This is because it tends to present higher solubility in aqueous solution, higher cell permeability, and lower manufacturing cost. The number of residues of MIP, 12, is already considerably large. It should be emphasized that MIP currently exhibits the highest binding affinity for MDM2. A significant change in the amino-acid sequence of MIP, which is almost optimized, can substantially influence the binding mode and give a worse result. For these reasons, we choose to modify one of the residues of MIP rather than to examine another peptide. Modifying MIP should be a shorter way toward the design. A further increase in the waterentropy gain upon binding primarily through larger ΔVex is a simple but reliable approach because ΔVex is closely related to geometric properties of the binding interface. To this end, we look at the residues possessing large values of |ΔVex,n| within the binding interface rather than those with small values of |ΔVex,n| directing outward. Namely, further increases in |ΔVex,n| are to be undertaken. A paradigmatic example is discussed below.

Figure 5. Values of ΔVex,n and ΔΔVex,n for the MDM2-p53NTD and MDM2-MIP complexes. ΔVex,n is defined as “EV of MDM2-residue n” − (“EV of MDM2” + “EV of residue n in the peptide”), and ΔΔVex,n = ΔVex,n(MDM2-MIP) − ΔVex,n(MDM2-p53NTD). EV denotes the excluded volume.

Figure 6. MDM2-p53NTD (A) and MDM2-MIP (B) complexes. The initial structures in the MD simulations are shown here. F3 (Phe), W7 (Trp), L10 (Leu), and E12 (Glu) shared by p53NTD and MIP are emphasized. The molecular images are created using the Visual Molecular Dynamics (VMD).54

and MDM2-MIP, three of these residues (F3, W7, and L10) exhibit relatively large values of |ΔVex,n| and thereby play important roles in the achievement of shape complementarity. They are closely packed with the surface of the binding pocket of MDM2. In terms of the difference ΔΔVex,n, however, W4, Y6 (Tyr), and L10 of MIP make significantly large contributions to the decrease in the total EV upon binding for MDM2-MIP. In particular, W4 is the most important contributor. It is interesting to note that |ΔVex,n| of n = E12 is significantly smaller than that of F3, W7, or L10, and ΔΔVex,n of n = E12 takes a somewhat large, positive value. Especially for MDM2-MIP, the role of E12 is probably to enlarge not the binding affinity but the solubility in water. ΔVex,n is almost zero H


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the input data for the MD simulations. Significantly large structural ensembles must be generated for the complex, MDM2, and peptide for evaluating the BFE with sufficient accuracy. When the complex structure is not experimentally available, it is necessary to construct it and to conduct much longer MD simulations for the complex. However, in the examination of a peptide obtained by applying a slight modification to MIP, which is described above, the complex structure is available for MDM2-MIP and the modified peptide is similar to MIP. As a consequence, it is expected that we can construct the MDM2−peptide complex structure and carry out the MD simulations without severe difficulty. A case where the complex structure is unknown and cannot readily be constructed is to be investigated in the next stage. Another subject to be considered is the refinement of the force field. As described above, the values of ΔΔF obtained through AMBER99SB and AMBER14SB are different as ΔΔF(AMBER14SB) − ΔΔF(AMBER99SB) ∼ −3.58 kcal/mol, and this difference may not be acceptably small. Further, the calculation method for −TΔΔSC using the MD simulations is to be improved for increasing the accuracy of ΔΔF.

It is desired that the binding pocket (i.e., vacant space) of isolated MDM2 (Figure 7(A)) be completely filled by the

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CONCLUDING REMARKS We have developed a reliable theoretical method using our accurate statistical-mechanical theory for hydration of biomolecules16 and investigated the physical origins of the large difference between the MDM2-p53NTD6 and MIP9 complexes in the binding free energy (BFE). In principle, the BFE is calculable by employing the molecular dynamics (MD) simulation alone, though it is quite time consuming. As a matter of fact, the BFE for the complex of MDM2 and the transactivation domain of p53 (TAD-p53) was calculated using a special MD simulation technique.56 (p53NTD is included in TAD-p53 possessing 17 residues.) We note, however, that the statistical mechanical theory16 provides the following great advantages: The BFE can be decomposed into a variety of energetic and entropic components, and these components provide physical insights into the binding mechanism. The change in energy originating from hydrophobic hydration (i.e., cavity creation in water) upon binding, ΔεVH,1, opposes the binding. This opposing factor is larger for MDM2-MIP than for MDM2-p53NTD. Decreases in MDM2−peptide van der Waals (vdW) and electrostatic (ES) interaction energies (Δ(EvdW + EES)) drive the binding, but an increase in the sum of MDM2-water, peptide−water, and water−water vdW and ES interaction energies (Δ(εVH,2,vdW + εVH,2,ES)) opposes it. The change in total energy, Δ(εVH,1 + EvdW + εVH,2,vdW + EES + εVH,2,ES), is positive, and it is larger for MDM2-MIP (13.70 and 21.30 kcal/mol for MDM2-p53NTD and MDM2-MIP, respectively; see Tables 2 and 3). The loss of the conformational entropy defined for MDM2 and the peptide opposes the binding, but the two complexes share almost the same value of the loss. Upon binding, the excluded volumes generated by MDM2 and the peptide overlap, and the total volume available for the translational displacement of water molecules (not limited to those near MDM2 and the peptide) increases by the overlapping volume. As a consequence, the entropic correlation among water molecules in the system, which is referred to as the “water crowding”,52,53 is significantly mitigated, leading to a large gain of water entropy. This water-entropy gain is the pivotal driving force in the binding, and it is considerably larger for MDM2-MIP than for MDM2-p53NTD.

Figure 7. (A) Binding pocket in isolated MDM2. A snapshot structure in the MD simulation is shown here. (B) Part of the binding pocket which remains vacant even after the binding: It is near the Cterminus of MIP. The molecular images are created using the Visual Molecular Dynamics (VMD).54

peptide. We find for MDM2-MIP that part of this pocket near the C-terminus of MIP is still vacant as illustrated in Figure 7(B). Since L10 (Leu) and M11 (Met) of MIP possess significantly large values of |ΔVex,n| and play essential roles in the exhibition of high affinity for MDM2, it is probably not profitable to mutate them. Instead, if the hydrogen atom covalently bound to Cα (i.e., Hα) in M11 is replaced by a bulkier, nonpolar group, the vacant space could be filled almost completely. If the surface of the vacant space was charged, the contact of a nonpolar side chain to the surface of the vacant space would undergo the energetic dehydration. However, we find that the surface is rather nonpolar, and such a problem does not arise. Though the water-entropy gain is a significant quantity, the BFE is influenced by the other physical factors as well. Once a candidate peptide is chosen through the modification of MIP, we have to construct the structure of MDM2 to which the peptide is bound (i.e., the complex structure), conduct sufficiently long MD simulations for the complex and the peptide, and estimate the BFE using our theoretical method developed in this study. When the BFE is lower than that for MDM2-MIP, the binding affinity of the peptide for MDM2 is worth measuring by experiments. Issues To Pursue in Future Studies. As demonstrated in our recent publication,16 the hydration free energy of a biomolecule with a fixed structure, the key quantity in our theoretical method, can be calculated for a force field given with sufficient accuracy and moderate computational effort. We note that the hydration free energy is strongly dependent on the biomolecule structure. Our major concern is in the MD simulations necessitated for taking account of the structural fluctuation of a biomolecule. The MDM2−peptide complex structure determined in an experiment is an essential part of I


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17K07307, 17H05878, and 26440026 to T.N.) from Japan Society for the Promotion of Science (JSPS). This work was also supported by “Priority Issue on Post-K Computer” (Building Innovative Drug Discovery Infrastructure through Functional Control of Biomolecular Systems) (Project IDs: hp150269, hp160223, hp170255, and hp180191) from Ministry of Education, Culture, Sports, Science and Technology (MEXT), by Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS) (Project IDs: JP17am0101109 and JP18am0101109) from Japan Agency for Medical Research and Development (AMED), by Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Engine” (No. 18H05426) from MEXT, and by RIKEN Dynamic Structural Biology Project (to M.I.).

By analyzing the efficiency of packing of peptide and MDM2 residues within the binding interface, we find that the third, seventh, and tenth residues shared by the amino-acid sequences of p53NTD and MIP, F3 (Phe), W7 (Trp), and L10 (Leu), play essential roles in the achievement of shape complementarity. This should be a significant factor leading to the exhibition of high binding affinity of p53NTD and MIP for MDM2. The twelfth residue, E12 (Glu), which is also shared by the amino-acid sequences of the two peptides, plays only minor roles in the achievement of shape complementarity. Especially for MDM2-MIP, E12 is directed outward and not within the binding interface, and the role of E12 is probably not to enlarge the binding affinity but to increase the solubility in water. The fact that MIP possesses higher affinity than p53NTD can be ascribed to the presence of W4 in MIP. We have also discussed how to design a peptide which binds to MDM2 even more strongly than MIP. Our suggestion is to apply a modification to one of the residues of MIP rather than to change its amino-acid sequence by multiple mutations. We find for MDM2-MIP that part of the binding pocket of MDM2, which is located near the C-terminus of MIP, is exposed to water. The replacement of the hydrogen atom covalently bound to Cα (i.e., Hα) in M11 (Met) by a bulkier group, for instance, could lead to the contact of the group with the part mentioned above and to a larger decrease in the total excluded volume. We intend to perform a more detailed analysis using our theoretical method developed in this study and test the binding affinity of a modified MIP designed accordingly. Last, we add that there is no reason why our theoretical method is inapplicable to the general receptor− ligand binding processes.

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(1) Vogelstein, B.; Lane, D.; Levine, A. J. Surfing the p53 Network. Nature 2000, 408, 307−310. (2) Royds, J. A.; Iacopetta, B. p53 and Disease: When the Guardian Angel Fails. Cell Death Differ. 2006, 13, 1017−1026. (3) Vousden, K. H.; Lane, D. P. p53 in Health and Disease. Nat. Rev. Mol. Cell Biol. 2007, 8, 275−283. (4) Lane, D. P. p53, Guardian of the Genome. Nature 1992, 358, 15−16. (5) Shadfan, M.; Lopez-Pajares, V.; Yuan, Z.-M. MDM2 and MDMX: Alone and Together in Regulation of p53. Transl. Cancer Res. 2012, 1, 88−89. (6) Kussie, P. H.; Gorina, S.; Marechal, V.; Elenbaas, B.; Moreau, J.; Levine, A. J.; Pavletich, N. P. Structure of the MDM2 Oncoprotein Bound to the p53 Tumor Suppressor Transactivation Domain. Science 1996, 274, 948−953. (7) Chène, P. Inhibiting the p53-MDM2 Interaction: An Important Target for Cancer Therapy. Nat. Rev. Cancer 2003, 3, 102−109. (8) Shiheido, H.; Takashima, H.; Doi, N.; Yanagawa, H. mRNA Display Selection of an Optimized MDM2-Binding Peptide That Potently Inhibits MDM2-p53 Interaction. PLoS One 2011, 6, No. e17898. (9) Nagata, T.; Shirakawa, K.; Kobayashi, N.; Shiheido, H.; Tabata, N.; Sakuma-Yonemura, Y.; Horisawa, K.; Katahira, M.; Doi, N.; Yanagawa, H. Structural Basis for Inhibition of the MDM2:p53 Interaction by an Optimized MDM2-Binding Peptide Selected with mRNA Display. PLoS One 2014, 9, No. e109163. (10) Chène, P.; Fuchs, J.; Carena, I.; Furet, P.; Echeverría, C. G. Study of the Cytotoxic Effect of a Peptidic Inhibitor of the p53-Hdm2 Interaction in Tumor Cells. FEBS Lett. 2002, 529, 293−297. (11) Bernal, F.; Tyler, A. F.; Korsmeyer, S. J.; Walensky, L. D.; Verdine, G. L. Reactivation of the p53 Tumor Suppressor Pathway by a Stapled p53 Peptide. J. Am. Chem. Soc. 2007, 129, 2456−2457. (12) Hu, B.; Gilkes, D. M.; Chen, J. Efficient p53 Activation and Apoptosis by Simultaneous Disruption of Binding to MDM2 and MDMX. Cancer Res. 2007, 67, 8810−8817. (13) Bernal, F.; Wade, M.; Godes, M.; Davis, T. N.; Whitehead, D. G.; Kung, A. L.; Wahl, G. M.; Walensky, L. D. A Stapled p53 Helix Overcomes HDMX-Mediated Suppression of p53. Cancer Cell 2010, 18, 411−422. (14) Baek, S.; Kutchukian, P. S.; Verdine, G. L.; Huber, R.; Holak, T. A.; Lee, K. W.; Popowicz, G. M. Structure of the Stapled p53 Peptide Bound to Mdm2. J. Am. Chem. Soc. 2012, 134, 103−106. (15) Chang, Y. S.; Graves, B.; Guerlavais, V.; Tovar, C.; Packman, K.; To, K.-H.; Olson, K. A.; Kesavan, K.; Gangurde, P.; Mukherjee, A.; Baker, T.; Darlak, K.; Elkin, C.; Filipovic, Z.; Qureshi, F. Z.; Cai, H.; Berry, P.; Feyfant, E.; Shi, X. E.; Horstick, J.; Annis, D. A.; Manning, A. M.; Fotouhi, N.; Nash, H.; Vassilev, L. T.; Sawyer, T. K. Stapled α−Helical Peptide Drug Development: A Potent Dual Inhibitor of MDM2 and MDMX for p53-Dependent Cancer Therapy. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, E3445−E3454.

ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org/. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jcim.9b00226.

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REFERENCES

Information on the integral equation theories, calculation of hydration energy and entropy of a biomolecule with a fixed structure, changes in thermodynamic quantities of hydration upon binding under isochoric and isobaric conditions, molecular dynamics simulations, estimation of conformational-entropy losses of biomolecules upon binding, force-field effects on the calculation results, and calculation results for the MDM2-DI binding. (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel: +81-774-38-3503. E-mail: [email protected]. ORCID

Mitsunori Ikeguchi: 0000-0003-3199-6931 Masahiro Kinoshita: 0000-0001-8060-045X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Grant-in-Aid for Scientific Research (No. 17H03663 to M.Kinoshita, No. 19K14674 to T.H., Nos. 18H04550 and 18K19397 to M.Kinoshita, and Nos. J


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