Mechanism of One-to-Many Molecular Recognition Accompanying

Article pubs.acs.org/JPCB

Mechanism of One-to-Many Molecular Recognition Accompanying Target-Dependent Structure Formation: For the Tumor Suppressor p53 Protein as an Example Tomohiko Hayashi, Hiraku Oshima, Satoshi Yasuda, and Masahiro Kinoshita* Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan S Supporting Information *

ABSTRACT: The new type of molecular recognition, in which an intrinsically disordered region (IDR) of a protein binds to many different target proteins with target-dependent structure formation, is indispensable to the expression of life phenomena and also implicated in a number of diseases. According to the prevailing view, the physicochemical factors responsible for the binding are also target dependent. Here we consider an IDR of the tumor suppressor p53 protein, p53CTD, as an important example related to carcinogenesis and analyze its binding to four targets accompanying the formation of target-dependent structures (i.e., helix, sheet, and two different coils) using our statistical-mechanical method combined with molecular models for water. We find that all of the seemingly different binding processes are driven by a large gain of the translational, configurational entropy of water in the system. The gain originates from sufficiently high shape complementarity on the atomic level within the p53CTD−target interface. It is also required that the electrostatic complementarity be ensured as much as possible to compensate for the dehydration. Such complementarities are achieved in harmony with the portion of the target to which p53CTD binds, leading to a large diversity of structures of p53CTD formed upon binding: If they are not achievable, the binding does not occur. This finding is made possible only by calculating the changes in thermodynamic quantities upon binding and decomposing them into physically insightful components.

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INTRODUCTION Molecular recognition1 has been a central issue in a variety of fields related to chemistry, physics, and biology. Conventionally, it implies that a ligand binds to a particular receptor with high selectivity and the binding is often described by the lockkey2 or induced-fit3 model. Recently, a new type of recognition has attracted much attention: Molecular recognition feature (MoRF) is an intrinsically disordered region of a protein which binds to a target protein or multiple target proteins, and binding to multiple targets is accompanied by target-dependent structure formation of the MoRF.4 This one-to-many molecular recognition plays imperative roles in the biochemical reaction network in a cell and is regarded as one of the factors indispensable to the sustenance of life.4 The extreme Cterminal peptide region of the tumor suppressor p53 protein, p53CTD, is an important example of MoRF. It is known that p53CTD recognizes a multitude of biomolecules and acts as a principal regulator for the tumor-suppressing activity of p53.5,6 Therefore, the research on p53CTD may lead to the development of anticancer therapeutic methods. It is mysterious that p53CTD forms a large diversity of structures upon binding. When the targets are S100B(ββ)7 and Cyclin A,8 portions of p53CTD form a helix and a coil, respectively. When Lys382 of p53CTD is acetylated, upon binding to a sirtuin (Sir2-Af2)9 and CBP bromodomain,10 portions of p53CTD form a sheet and a coil, respectively. Despite extensive experimental and theoretical studies, there are still lots of © XXXX American Chemical Society

controversial aspects, and many of the issues remain unresolved even for the conventional types,1 not to mention that very little is known about the new types. Figure 1 illustrates the structure formations of p53CTD in binding to the four different target proteins: p53CTD binds to S100B(ββ),7 Sir-Af2,9 CPB bromodomain,10 and Cyclin A8 in systems 1, 2, 3, and 4, respectively. It has been suggested that the physicochemical factors promoting the binding as well as the structure of p53CTD formed are target dependent.12 Further, the emphasis has been placed on p53CTD−target intermolecular interactions: The physicochemical factors responsible for the binding are salt bridge and contact of hydrophobic portions (i.e., the so-called hydrophobic interaction) in system 1,7 hydrogen bonding and van der Waals (vdW) interaction in system 2,9 contact of hydrophobic portions in system 3,10 and hydrogen bonding and vdW interaction in system 4.8 The p53CTD−target electrostatic interaction has also been pointed out as a dominant driving force of the binding in system 1.13 The salt bridge, hydrogen bonding, and vdW interaction are p53CTD−target direct interactions, and the effect of water is considered only through the contact of hydrophobic portions. Taken together, according to the prevailing view,7−10,12,13 the physicochemical factors Received: September 1, 2015

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DOI: 10.1021/acs.jpcb.5b08513 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

Supporting Information. Hence, the changes in thermodynamic quantities under the isochoric condition are almost the same as those under the isobaric one (e.g., the change in system energy is almost equal to that in system enthalpy). The free-energy function G for a solute molecule immersed in water at infinite dilution is defined as G = EC − TSC + μH

(1)

where EC, SC, and μH are the conformational energy, conformational entropy, and hydration free energy (i.e., excess chemical potential) of the solute, respectively, and T is the absolute temperature. “Conformational” signifies “solute intramolecular”. The quantity μH is given by μH = εVH − TS VH

Figure 1. Images of structure formations of p53CTD in binding to the four different target proteins. In systems 1, 2, 3, and 4, respectively, p53CTD binds to S100B(ββ), Sir-Af2, CPB bromodomain, and Cyclin A. S100B(ββ) is present as a dimer, and two p53CTDs bind to it. The structures of the two protomers of S100B(ββ) are essentially identical. In our theoretical calculations, the complex of the dimer and a p53CTD is regarded as the target, and the process where one more p53CTD binds to it is considered. This figure was drawn using the VMD.11

(2)

where εVH and SVH are the hydration energy and entropy, respectively, and the subscript “VH” denotes hydration under the isochoric condition. It should be noted that μH is independent of the solute insertion condition, isobaric or isochoric.22 Substituting eq 2 into eq 1 yields G = EC − TSC + εVH − TS VH

(3)

The physical meaning of εVH is the solute−water interaction energy generated upon solute insertion, which is accompanied by the energy change due to the structural reorganization of water especially near the solute.20 SVH is the change in water entropy upon solute insertion. G is independent of the solute insertion condition. EC is calculated on the basis of a molecular mechanical potential. It is decomposed into the bonded and nonbonded components as

which drive the binding are target dependent, and water plays only a secondary role. In the present study, we investigate the one-to-many molecular recognition by p53CTD using our statisticalmechanical method combined with molecular models for water and show that all of the seemingly different binding processes illustrated in Figure 1 share the same binding mechanism guided by water. This result is in marked contrast with the prevailing view7−10,12,13 explained above. Unlike in the previous studies,7−10,12,13 we analyze not only the effect of the p53CTD−target direct interactions but also that of hydration to its full extent, by evaluating the changes in thermodynamic quantities upon binding and decomposing them into physically insightful components. The molecular theories of hydration, which are much more suited to the quantification and decomposition than the molecular dynamics simulations, have been quite successful in studies on a variety of biological selfassembly processes such as protein folding/unfolding, protein− protein binding, and protein aggregation.14−21 Our method is a hybrid20 where only advantageous aspects of these theories are judiciously utilized: We calculate the hydration energy εVH by the three-dimensional reference interaction site model (3DRISM) theory14,15 and the hydration entropy SVH by the angledependent integral equation theory (ADIET)16,17,19,20 combined with the morphometric approach (MA).18 The hybrid has an achievement that the binding free energy calculated for an RNA aptamer and a partial peptide of a prion protein is almost in perfect agreement with the experimental one.20

EC = E B + EvdW + E ES

(4)

where EB is the bonded energy comprising the bond-stretching, angle-bending, and torsional terms, EvdW the van der Waals (vdW) interaction energy (the vdW energy is represented by the Lennard-Jones (LJ) interaction potential), and EES the electrostatic interaction energy. We decompose εVH as εVH = εVH,vdW + εVH,ES (5) where εVH,vdW and εVH,ES are the vdW and electrostatic contributions to εVH, respectively. For the decomposition of εVH, we first calculate the hydration energy of a hypothetical solute molecule whose partial charges are all switched to zero, εVH,vdW. We then obtain εVH,ES from εVH,ES = εVH − εVH,vdW. Substituting eqs 4 and 5 into eq 3 yields

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G = E T − TSC − TS VH

(6a)

E T = E B + (EvdW + εVH,vdW ) + (EES + εVH,ES)

(6b)

where ET is referred to as the system energy: It comprises EB and the vdW and electrostatic components denoted by (EvdW + εVH,vdW) and (EES + εVH,ES), respectively. Paths for Calculating Binding Free Energy. The freeenergy function and its constituents defined above are applicable to p53CTD, its target proteins, and complexes. Hereafter, a complex is referred to as “p53CTD:target”. We consider the thermodynamic cycle explained in Figure 2. Path II, which represents the p53CTD−target binding to be considered, is decomposed into paths I and III. For path I, p53CTD and its target in the complex (in the final state) are simply separated with no structural changes, and the resulting structures are employed as the isolated molecules (in the initial

MODEL AND THEORY Free-Energy Function. The change in system free energy upon solute−solute binding in water is independent of the condition, isobaric or isochoric, but the changes in system energy and entropy are not.22 We consider the isochoric condition because it is free from the effect of compression or expansion of the bulk water and more suited to physical interpretation of a change in a thermodynamic quantity of hydration. Moreover, we have found that the p53CTD−target binding occurs almost with the system volume unchanged under the isobaric condition as described in section S4 of B


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The Journal of Physical Chemistry B ΔIIIG = G(p53CTDstructured ) − G(p53CTDdisordered ) = ΔIIIE B + ΔIII(EvdW + εVH,vdW )

+ ΔIII(E ES + εVH,ES) − T ΔIIISC − T ΔIIIS VH

We note that ΔIIG = ΔIG + ΔIIIG and ΔIISC = ΔIIISC. ΔMSC (M = II, III) comprises the conformational-entropy losses of p53CTD and the target, ΔMSC(p53CTD) and ΔMSC(target), respectively, but ΔMSC(target) is neglected in the presentation of calculation results as the tables. Hereafter, the free-energy change upon p53CTD−target binding for path II, ΔIIG, is referred to as “binding free energy”. Calculation of Conformational Energy. EC (= EB + EvdW + EES) is calculated on the basis of a molecular mechanical potential. We employ the Amber99SB force field23 for calculating EC. For the acetylated Lys residues in systems 2 and 3, we prepare the general Amber force field (GAFF)24 combined with restrained electrostatic potential (RESP) charges25 which are based on the HF/6-31G* level of the quantum chemical theory, using the antechamber module in AMBER12 program26 and the Gaussian09 program.27 Calculation of Hydration Entropy. The ADIET16,17,28−30 combined with a multipolar model for water16,28 has been applied to analyses on hydrophobic and hydrophilic hydrations with success. A water molecule is modeled as a hard sphere with diameter dS = 0.28 nm in which a point dipole and a point quadrupole of tetrahedral symmetry are embedded. The dependence of water−water and solute−water interaction potentials and correlations on the molecular orientations is mathematically handled in an explicit manner. The effect of molecular polarizability is taken into account by means of the self-consistent mean field theory.16,28 The dielectric constant of bulk water is a good measure of the validity of a theory: It is calculated to be ∼83 that is in good agreement with the experimental value, ∼78. The hydration free energies of spherical, nonpolar solutes calculated are in quantitatively excellent accord with those obtained from Monte Carlo simulations using such water models as the TIP4P and the SPC/E.17 A more detailed description of the ADIET is given in section S1 of Supporting Information. In the present study, we have to consider a large solute molecule with complex polyatomic structure. The application of the ADIET to such a solute becomes nontrivial due to the mathematical complexity. Fortunately, it has been shown that in general the hydration entropy SVH is fairly insensitive to the solute−water interaction potential.31 For this reason, in calculating SVH only the geometric characteristics of the solute become essential: The solute can be modeled as a set of fused, neutral hard spheres, in which case the diameter of an atom in the solute is set at the corresponding σ-value for the LJ potential. As a consequence, the MA18,32 becomes a very powerful tool. We employ the method in which the ADIET is combined with the MA (ADIET-MA) for calculating SVH. In the MA, the solute geometry is characterized by the four measures, Vex, A, X, and Y, and SVH is expressed as their linear combination18,32 (i.e., the morphometric form):

Figure 2. Thermodynamic cycle considered in our theoretical analyses. The binding process represented by path II is decomposed into paths I and III. In path I, neither p53CTD nor its target exhibits any structural change. Path III represents the target-dependent structural change of p53CTD from a disordered state to a well-defined structure. This figure was drawn using the VMD.11

state): In path I, p53CTD and its target exhibit no structural changes at all upon binding. In path III, p53CTD undergoes a target-dependent structural change from a disordered state (an ensemble of structures: p53CTDdisorderd) to a well-defined structure (strictly, portions of p53CTD are structured) (p53CTDstructured). The target is assumed to undergo no structural change. In a strict sense, however, upon binding, its residues within the p53CTD−target interface of the complex lose side-chain flexibilities. Though this loss of the target is neglected as an approximation in the presentation of calculation results as the tables, the effect of this approximation is discussed in the Binding Free Energy section. Only some of the residues of p53CTD are structured (the others remain flexible) in each complex, and the conformational-entropy loss of p53CTD in path III is estimated using a simple but physically reasonable manner19,20 explained in the Estimation of ConformationalEntropy Change upon Binding section. We denote the change in quantity X for path M by ΔMX (M = I, II, III). The changes in system free energy for paths I and II, ΔIG and ΔIIG, are formally expressed as ΔIG = G(p53CTD: target) − {G(p53CTDstructured ) + G(target)} = ΔI(EvdW + εVH,vdW ) + ΔI(E ES + εVH,ES) − T ΔIS VH

(7)

ΔIIG = G(p53CTD: target) − {G(p53CTDdisordered ) + G(target)} = ΔIIE B + ΔII(EvdW + εVH,vdW ) + ΔII(E ES + εVH,ES) − T ΔIISC − T ΔIIS VH

(9)

(8)

Some of the notations are as follows: G(target) denotes the free-energy function for the target protein, ΔIEES is ascribed to p53CTDstructured−target electrostatic interactions, ΔIεVH,ES represents the changes in p53CTDstructured−water, target− water, and water−water electrostatic interactions for path I, and ΔISVH denotes the change in water entropy for path I. ΔIEB = 0 and ΔISC = 0 for path I. The change in system free energy for path III, ΔIIIG, is expressed as

S VH/kB = C1Vex + C2A + C3X + C4Y

(10)

In eq 10, kB is the Boltzmann constant, Vex the excluded volume (EV) generated by the solute, and A the water-accessible surface area. The water-accessible surface is the surface that is accessible to the centers of water molecules. The EV is the C


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The Journal of Physical Chemistry B volume that is enclosed by this surface. X and Y are the integrated mean and Gaussian curvatures of the wateraccessible surface, respectively. The water molecules near the solute contribute to SVH through C2A, C3X, and C4Y. The EV term, C1Vex, represents the contribution from the water molecules in the bulk. In the conventional view of hydrophobic hydration, the EV term is not taken into account (see section S5 of Supporting Information).21,35,36 In the MA, the solute shape enters SVH only via Vex, A, X, and Y. Hence, the four coefficients (C1−C4) can be determined in much simpler geometries: They are calculated using the values of SVH of hardsphere solutes. The ADIET combined with the multipolar model for water is employed in the calculation. C1−C4 are determined by the least-squares fitting applied to the following equation:

residue there are two dihedral angles which can rotate, and each angle has three stable values. Since the number of possible combinations is 32 = 9, the backbone contribution to SC is kB ln(9). On the basis of the computer simulation study by Doig and Sternberg,48 we regard the contribution from the side chain to SC as 1.7kB per residue. Hence, for a p53CTD with Nr residues structured upon binding, the conformational-entropy loss ΔIISC(p53CTD) (= ΔIIISC(p53CTD)) is given by ΔIISC(p53CTD)/kB = −Nr(ln 9 + 1.7)

The validity of employing eq 12 was corroborated in our earlier work.19,20 Upon binding, some of the residues of the target should lose the flexibilities of their side chains, leading to a loss of conformational entropy ΔIISC(target) = ΔIIISC(target). Unlike in the transition from a disordered state to a structure whose portions are well-defined (i.e., in the case of p53CTD), however, the backbone exhibits essentially no flexibility even before binding. Therefore, the loss scaled by kB can be approximated to −1.7Nr where Nr is the number of residues losing the flexibilities of their side chains upon binding: ΔIISC(target)/kB = −1.7Nr. Structure Modeling for p53CTD:Target Complex. We investigate the binding of p53CTD with its four target proteins, S100B(ββ),7 Sir2-Af2,8 CPB bromodomain,9 and Cyclin A,10 and the four pairs are referred to as systems 1, 2, 3, and 4, respectively. The three-dimensional structures for p53CTD− target complexes are taken from the Protein Data Bank (PDB), and the corresponding PDB codes are 1DT7, 1MA3, 1JSP, and 1H26, respectively. The structures were determined by nuclear magnetic resonance (NMR) for systems 1 and 3 and by X-ray crystallography for systems 2 and 4. There are 40 and 20 NMR models registered in the PDB codes for systems 1 and 3, respectively. S100B(ββ) is present as a dimer, and two p53CTDs bind to it. The structures of the two protomers of S100B(ββ) are essentially identical. In our theoretical calculations, the complex of the dimer and a p53CTD is regarded as the target, and the process where one more p53CTD binds to it is considered. The structure of a p53CTD:CyclinA complex in system 4 is obtained from that of p53CTD:CyclinA:CDK2 in 1H26 by removing the CDK2 domain. The missing hydrogen atoms for systems 2 and 4 are added using the LEaP module in the AMBER12 program.26 In the binding experiments, the portion of p53CTD used varies from system to system: The numbers of residues in the four systems are 22, 18, 20, and 11, respectively (see column 2 in Table 1). In systems 2 and 4, only the structures of 9 residues in the complexes were detected in the X-ray crystallography (see column 3 in Table 1). This was probably due to the structural fluctuations of the other 9 and 2 residues in systems 2 and 4, respectively: We therefore assume that they do not participate in the binding, and the portions displayed in column 3 are considered for p53CTD in our theoretical calculations. It is important to note that for system 2 there are missing residues within the target Sir2-Af2 (those from Ser30 to Asp39) in the PDB code, and they are added on the basis of a de novo modeling procedure using the MODELLER program;49 the resultant 10 structures generated are adopted. We consider a stable structure (or an ensemble of the stable structures determined by NMR) in each system. In the real system, however, the structure of p53CTD-target complex fluctuates around the stable one in aqueous solution. Karino and Matubayasi50 examined the variations of the thermody-

S VH/kB = C1(4πR3/3) + C2(4πR2) + C3(4πR ) + C4(4π ) (11a)

R = (dU + dS)/2

(12)

(11b)

Here, dU denotes the diameter of a hard-sphere solute, and sufficiently many different values of dU are considered (0.6dS ≤ dU ≤ 10dS). Equation 11a,b comes from the application of eq 10 to hard-sphere solutes. Once C1−C4 are determined (C1 = −0.1968 Å−3, C2 = 0.0452 Å−2, C3 = 0.2567 Å−1, and C4 = −0.3569), SVH of a solute molecule with any structure is obtained directly from eq 10 only if its four geometric measures are calculated. A description of the MA is also provided in section S2 of Supporting Information. The high reliability of the ADIET-MA has been demonstrated in solving a variety of important problems related to protein folding33 and denaturation,34−38 protein−protein39 or protein−ligand40 binding, and binding of an RNA aptamer and a partial peptide of a prion protein.20 Calculation of Hydration Energy. In contrast with SVH, the hydration energy εVH is largely influenced by the solute− water interaction potential. Hence, the MA cannot be applied to the calculation of εVH . We employ the 3D-RISM theory14,15,31,41 for calculating εVH. The LJ potential parameters and partial charges are assigned to the solute atoms. The 3DRISM theory has been qualitatively successful in elucidating important subjects in biological systems such as the hydration properties of peptides and proteins,31,42 receptor−ligand binding processes,43,44 association of protein molecules,45,46 and discrimination of the relative propensities of proteins to aggregate.47 However, the theory is not suited to the investigation of hydrophobic hydration (see section S5 of Supporting Information). As an important example, the theory underestimates the absolute value of the water-entropy change upon protein folding though the hydration-energy change remains quantitatively reliable.31,41 In fact, we have found the following: If the water-entropy change upon binding is calculated by the 3D-RISM theory in the present study, due to the underestimation, all of the binding processes in systems 1 through 4 do not occur: ΔIIG becomes positive. It follows that the 3D-RISM theory and the ADIET-MA are best suited to calculations of εVH and SVH, respectively. (A more detailed description of the 3D-RISM theory is provided in section S3 of Supporting Information.) Estimation of Conformational-Entropy Change upon Binding. The conformational entropy SC for p53CTDstructured is considered to be essentially zero. SC for p53CTDdisorderd is estimated in the following manner. For the backbone, per D


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Energy section) and the generalized Born implicit solvent model.52,53 The structures thus obtained are used in our calculations. For systems 1 and 3, the value of a thermodynamic quantity reported in the present article is calculated by averaging the values for the structures satisfying ΔIIG < 0: The numbers of the structures considered in systems 1 and 3 are 27 and 8, respectively. Structured and Fluctuating Residues of p53CTD in Each Complex. The conformational-entropy loss of the p53CTD calculated, ΔIISC(p53CTD), depends on the value of Nr assumed (Nr is the number of residues structured upon binding; see eq 12). For systems 2 and 4, only the 9 residues of p53CTD in the complexes detected in the X-ray crystallography are considered to be structured as explained above. In system 1, the 10 residues from Thr377 to Lys386 form a helix, and the positions of the next 2 residues of Thr387 and Glu388 are almost fixed relative to the target in all of the 40 NMR models registered in the PDB code. Therefore, we assume that the 12 residues from Thr377 to Glu388 are structured. In system 3, since the positions of the 8 residues from Arg379 to Lys 386 are almost fixed relative to the target in all of the 20 NMR models registered in the PDB code, these residues are assumed to be structured. In summary, we assume that the numbers of residues structured upon binding are 12, 9, 8, and 9 in systems 1, 2, 3, and 4, respectively. It should be noted that the portions of p53CTD assumed to be structured do not necessarily form well-defined secondary structures such as αhelix or β-sheet. Structure Modeling of Disordered p53CTD. The disordered state of p53CTD is modeled as a set of random coils. For such a short polypeptide, the random-coil set gives a reasonably good model of the disordered state, as shown in our earlier works.19,20 The structural data for the complexes include 22, 9, 20, and 9 residues of p53CTD in systems 1, 2, 3, and 4, respectively (see Table 1). We generate a total of 100 random coils for each system by assigning random numbers to the dihedral angles, φ and ψ, for the main chain (ω is set at 180°). The random numbers are limited to the following ranges: −180° ≤ φ ≤ −30°, −180° ≤ ψ ≤ −150°, and −90° ≤ ψ ≤ 180°. These ranges correspond to the allowed regions in the Ramachandran map. For glycine, the ranges allowed are −180° ≤ φ ≤ −30°, 30° ≤ φ ≤ 180°, and −180° ≤ ψ ≤ 180°. The structures thus obtained are slightly modified in accordance with the minimization techniques described above. All of the calculations are carried out using the AMBER12 program.26 The value of a thermodynamic quantity presented in the present article is the average of 100 values.

Table 1. Residues Considered in Binding Experiments (exptl), those Registered in Protein Data Bank (PDB), and those Assumed to be Structured in the Complex in Each System (Structured)a P53CTD sequence 367

367

382*

388

403

- S HLKSKKGQS T SRHK K LMFKT E GPDS D -COO− system

exptl (no. of residues)

PDB (no. of residues)

structured (no. of residues)

1 2 3 4

“S367, E388” (22) “K372, G389” (18) “S367, K386” (20) “S376, K386” (11)

“S367, E388” (22) “R379, T387” (9) “S367, K386” (20) “S378, K386” (9)

“T377, E388” (12) “R379, T387” (9) “R379, K386” (8) “S378, K386” (9)

“S367, E388”, for example, represents the residues from Ser367 to Glu388. Asterisk indicates that in system 2 or 3, the amino group of side chain of Lys382 is acetylated.

a

namic quantities in the course of equilibrium structural fluctuation for the native structure of a protein. They found that the protein intramolecular energy and hydration energy are compensating, and the protein structure fluctuates with the hydration entropy and system energy (corresponding to SVH and ET in the present study, respectively) almost completely unchanged. The compensation should hold for both of the vdW and electrostatic components of the intramolecular energy and hydration energy. Therefore, our conclusions on ΔSVH, Δ(EvdW + εVH,vdW), Δ(EES + εVH,ES), and ΔET are not altered at all even in a quantitative sense by accounting for the structure fluctuation of the complex. Structure Refinement for p53CTD:Target Complex. The structures are slightly modified using a standard energy minimization to remove the unrealistic overlaps of protein atoms. The complexes in systems 1 and 2 include ions (Ca2+ and Mg2+, respectively). For system 1, we lay positional restraints in the harmonic form on the ions and on the heavy atoms in any residue which possesses at least one atom within a distance of 4 Å from an ion. The force constant for the restraints is 10.0 × 10−2 kcal/(mol Å2). For systems 2 and 4, the harmonic positional restraints are laid on all of the heavy atoms with a force constant of 5.0 × 10−2 kcal/(mol Å2). We perform 100 steps of the steepest-descent energy minimization followed by the limited memory Broyden−Fletcher−Goldfarb−Shanno (L-BFGS)51 minimization which is continued until the root-mean-square forces acting on the complex atoms become weaker than 1.0 × 10−2 kcal/(mol Å2). The minimization is carried out using the AMBER12 program26 with Amber99SB force field23 (GAFF/RESP24,25 for the acetylated Lys mentioned in the Calculation of Conformational

Table 2. Changes in System Free Energy and Its Energetic and Entropic Components with Standard Errors for Path Ia (in kcal/ mol) system

ΔIG

ΔIET

−TΔISVH

ΔIVex

1 2 3 4

−54.53 ± 2.83 −66.27 ± 1.36 −57.13 ± 4.95 −59.32

−0.57 ± 1.42 1.91 ± 1.36 11.96 ± 2.46 13.29

−53.96 ± 2.57 −68.18 ± 0.01 −69.09 ± 4.76 −72.61

−1100 ± 23 −1265 ± 0 −1137 ± 49 −1168

ΔG = ΔET − TΔSVH − TΔSC; the entropic components are −TΔSVH and −TΔSC, and the superscript “I” denotes the value for path I. ΔG: change in system free energy. ΔET: change in system energy = ΔEC + ΔεVH. ΔSVH: change in water entropy. ΔSC: change in the conformational entropy of p53CTD and its target. T: absolute temperature. ΔEC corresponds to the change in system energy in vacuum, and ΔεVH represents the dehydration, the factor arising from the presence of water (see Table 3 for more details). ΔSC = 0 for path I. ΔVex: change in excluded volume generated by p53CTD and its target (in Å3). 27, 10, and 8 structure models are considered for systems 1, 2, and 3, respectively, and the standard errors arise from the consideration of these multiple models (there is only a single structure model in system 4). a

E


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The Journal of Physical Chemistry B Table 3. Components of Change in System Energy with Standard Errors for Path Ia (in kcal/mol) system

ΔIET

ΔI(EvdW+εVH,vdW)

ΔI(EES+εVH,ES)

ΔIEvdW

ΔIεVH,vdW

ΔIEES

ΔIεVH,ES

1 2 3 4

−0.57 ± 1.42 1.91 ± 1.36 11.96 ± 2.46 13.29

−6.63 ± 0.99 −20.28 ± 0.39 −16.11 ± 2.39 −13.11

6.05 ± 1.70 22.19 ± 1.55 28.06 ± 4.13 26.40

−55.27 ± 1.39 −74.46 ± 0.00 −61.92 ± 3.30 −70.30

48.64 ± 1.00 54.18 ± 0.40 45.81 ± 1.69 57.19

−1349.09 ± 21.91 −136.70 ± 1.87 −191.85 ± 21.41 −657.49

1355.14 ± 22.10 158.88 ± 2.71 219.92 ± 20.34 683.88

ΔET: change in system energy = Δ(EvdW + εVH,vdW) + Δ(EES + εVH,ES). The superscript “I” denotes the value for path I. ΔE: change in intramolecular energies of p53CTD and its target plus p53CTD−target intermolecular energy (change in intramolecular energies of p53CTD and its target is zero for path I). ΔεVH: change in water−water, water−p53CTD, and water−target interaction energies. The subscripts “vdW” and “ES”, respectively, denote the contributions from van der Waals and electrostatic interactions. The intramolecular, intermolecular, and interaction energies include the effects of hydrogen bonding and salt bridge. 27, 10, and 8 structure models are considered for systems 1, 2, and 3, respectively, and the standard errors arise from the consideration of these multiple models (there is only a single structure model in system 4). a

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RESULTS AND DISCUSSION Large Gain of Water Entropy upon Binding. We consider path I where the conformational entropies of p53CTD and its target remain unchanged. Table 2 presents the changes in system free energy and its energetic and entropic components. The entropic component, which arises solely from the water-entropy gain in path I, takes a very large, negative value. The energetic component representing the change in system energy is positive but relatively much smaller (systems 3 and 4) or almost zero (systems 1 and 2). The change in system energy can further be decomposed into physically insightful components as displayed in Table 3. The binding is driven by a large gain of water entropy. The large water-entropy gain upon binding (ΔISVH > 0) can be interpreted as follows. As illustrated in Figure 3, p53CTD

dehydration mentioned in Table 2 is as follows (also see Table 3 and Figure 3). Upon binding, a decrease in energy occurs due to a gain of p53CTD−target van der Waals (vdW) attractive interactions (ΔIEvdW < 0). However, the binding is unavoidably accompanied by a loss of p53CTD−water and target−water vdW attractive interactions followed by an increase in energy. The binding brings contact of unlikecharged portions of p53CTD and its target and a gain of p53CTD−target electrostatic attractive interactions, leading to a large decrease in energy (ΔIEES ≪ 0). However, oxygen and hydrogen atoms of water carry negative and positive partial charges, respectively, and the binding is unavoidably accompanied by a large increase in energy due to a loss of portionwater (“positively charged portion”−“water oxygen”; “negatively charged portion”−“water hydrogen”) electrostatic attractive interactions. About half of the total increase in energy is canceled out by a decrease in energy brought by the structural reorganization of water20 (i.e., change in the water− water interaction energy). Nevertheless, the losses described above are still large enough to compensate for the gains: ΔIεVH,vdW > 0, ΔIεVH,ES ≫ 0, |ΔI(EvdW + εVH,vdW)| ≪ |ΔIEvdW|, and |ΔI(EES + εVH,ES)| ≪ |ΔIEES|. Moreover, ΔI(EvdW + εVH,vdW) and ΔI(EES + εVH,ES) are also compensating, leading to a small value of |ΔIET|. We refer to ΔεVH (= ΔIεVH,vdW + ΔIεVH,ES) as “dehydration”. Here, it is interesting to note the following: In Table 3, for instance, |ΔIEES| in system 1 is almost an order of magnitude larger than that in system 2; however, ΔIεVH,ES in system 1 is also almost an order of magnitude larger than that in system 2, and ΔIεVH,ES is larger than |ΔIEES| in both of the two systems. In what follows, we describe the reasons for negative ΔI(EvdW + εVH,vdW) and positive ΔI(EES + εVH,ES). It is required by the entropic EV effect that the p53CTD−target interface be packed as closely as possible. A closer packing also leads to lower p53CTD−target vdW interaction energy. However, this is not true for the p53CTD−target electrostatic interaction energy because a closer packing does not necessarily result in closer unlike-charged portions and more separated like-charged portions. Thus, ΔI(EvdW + εVH,vdW) always works in favor of the entropic EV effect and becomes negative, whereas ΔI(EES + εVH,ES) takes a positive value when the priority is given to the water-entropy gain as in the present case. In other words, the electrostatic complementarity is often less perfect than the shape complementarity. We never claim that the electrostatic complementarity is unimportant: When charged portions are buried within the interface, it is crucial to compensate for the dehydration by assuring as much electrostatic complementarity as possible.

Figure 3. Cartoon illustrating the overlap of excluded volumes and the dehydration accompanying p53CTD−target binding. The structure of p53CTD does not necessarily become more compact upon binding. The presence of “water molecule hydrating solute” means that the water molecule interacts with the solute (p53CTD or its target) through van der Waals and electrostatic attractive potentials.

and its target generate spaces which the centers of water molecules cannot enter. The volume of an excluded space is referred to as “excluded volume (EV)”. Upon the p53CTD− target binding, the two EVs overlap, and the total EV decreases by this overlapped volume, leading to a corresponding increase in the total volume available to the translational displacement of water molecules in the system. This is followed by a larger number of accessible configurations of water.20,21 The large water-entropy gain given in Table 2 originates primarily from this entropic EV effect. In the real system, p53CTD and its target possess polyatomic structures. The p53CTD−target interface is closely packed with the achievement of high shape complementarity on the atomic level. Dehydration, Shape Complementarity, and Electrostatic Complementarity. The physical meaning of the F


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Table 4. Changes in System Free Energy and Its Energetic and Entropic Components with Standard Errors for Path IIa (in kcal/mol) system 1 2 3 4

ΔIIG −16.53 −31.85 −16.85 −18.45

± ± ± ±

2.67 1.48 4.06 0.53

ΔIIET

−TΔIISC

14.06 ± 2.49 3.98 ± 1.47 29.18 ± 2.74 37.82 ± 0.48

27.45 20.59 18.30 20.59

−TΔIISVH −58.04 −56.42 −64.33 −76.86

± ± ± ±

2.83 0.59 3.89 0.53

ΔIIGexp (−4.29, −4.06) (−3.78, −3.57) −3.86 −4.97

ΔG = ΔET − TΔSVH − TΔSC; the superscript “II” denotes the value for path II, and ΔIIGexp is the experimentally determined value of ΔG. ΔIISC = ΔIISC(p53CTD). See Table 2 for the notation. (−4.29, −4.06), for example, represents that the value is in the range from −4.29 to −4.06. As argued in the text, ΔIIG should be sufficiently lower than ΔIIGexp: This requirement is certainly met. 27, 10, and 8 structure models are considered for systems 1, 2, and 3, respectively (there is only a single structure model in system 4). 100 random coils are considered for the disordered state of p53CTD. The standard errors arise from the consideration of these multiple structure models and random coils. a

Table 5. Changes in System Free Energy and Its Entropic Components with Standard Errors for Path IIIa (in kcal/mol) system 1 2 3 4

ΔIIIG

ΔIIIET

−TΔIIISC

−TΔIIISVH

ΔIIIVex

± ± ± ±

14.63 ± 1.95 2.07 ± 0.56 17.22 ± 1.70 24.53 ± 0.48

27.45 20.59 18.30 20.59

−4.08 ± 1.87 11.76 ± 0.59 4.77 ± 2.42 −4.25 ± 0.53

−50 ± 33 218 ± 10 83 ± 38 −53 ± 9

38.00 34.42 40.29 40.87

1.90 0.59 2.95 0.53

a ΔG = ΔET − TΔSVH − TΔSC; the superscript “III” denotes the value for path III. ΔVex: change in excluded volume generated by p53CTD (in Å3). ΔIIISC = ΔIIISC(p53CTD) (=ΔIISC). See Table 2 for the notation. 100 random coils are considered for the disordered state of p53CTD, and the standard errors arise from the consideration of these multiple random coils.

of ΔIIG with ΔIIGexp in system 2 may arise from these uncertain points. Here, we emphasize the success in our earlier work20 on the binding free energy for an RNA aptamer and a partial peptide of a prion protein. The calculated value was almost in perfect accord with the experimentally measured one. The disordered state of the peptide before binding was modeled as a set of random coils, and the conformational-entropy loss upon binding was estimated using eq 12. The reasons for the success should be as follows: It is definite that all of the residues of the peptide are structured upon binding, and no conformationalentropy loss for the aptamer needs to be considered because its structure remains rigid (it possesses no flexible side chains like those in a protein) during the binding process. These strong points are absent in the present case. Nevertheless, it is definite that ΔIIET > 0, ΔIISC < 0, ΔIISVH > 0, and ΔIISVH is substantially larger than |ΔIISC|. Our conclusion, “all of the seemingly different binding processes shown in Figure 1 are driven by ΔIISVH”, is not likely to be influenced by the imperfect consideration of ΔIISC(target) and the uncertain points described above. Characteristics of p53CTD Structural Change upon Binding. The changes in system free energy and its energetic and entropic components for path III are presented in Table 5. A conformational-entropy loss is caused by the structural change of p53CTD from a disordered state to a well-defined structure. Interestingly, it does not always accompany a waterentropy gain. This result can readily be understood because the EV of p53CTD does not necessarily decrease upon binding as shown in Table 5. The change in system energy ΔIIIET is positive because on the whole the dehydration dominates for path III. For these reasons, the change in system free energy is positive. This result is consistent with the experimental fact that p53CTD is intrinsically disordered in its isolated state; namely, p53CTD cannot be structured without its target. Physical Picture of Molecular Recognition by MoRFs. The p53CTD−target binding is characterized by sufficiently high shape complementarity on the atomic level as the first priority together with as much electrostatic complementarity as

Thermodynamics of Binding for Path II. We discuss path II in Figure 2. Path II includes the target-dependent structure formation of p53CTD upon binding. Table 4 presents the changes in system free energy and its energetic and entropic components. The water-entropy gain still acts as the strong driving force of the binding even when the negative effect, the conformational-entropy loss of p53CTD, is taken into account: The gain is far larger than the loss. The change in system energy (ΔIIE) takes a positive value regardless of the system. Binding Free Energy. The theoretical value ΔIIG is compared with the experimental one7−10 ΔIIGexp in Table 4 for each system. We remark that ΔIIGexp cannot be exactly the same as ΔIIG, since the standard state is 1 mol/L and the activity coefficient is set at unity for ΔIIGexp while the standard state is the infinite dilution for ΔIIG. More importantly, it is required that ΔIIG be sufficiently lower than ΔIIGexp. This is because the conformational-entropy loss of the target upon binding ΔIISC(target), which is difficult to be quantified unlike that for a small peptide, is not incorporated in ΔIIG. The requirement is certainly met. The number of residues structured within p53CTD upon binding is in the range from 8 to 12. If we assume that the number of residues structured within the target upon binding is also in this range, the conformational-entropy loss accompanying the rearrangement of side chains of these residues give rise to −TΔIISC(target) which is in the range from 8 to 12 kcal/mol (these values come from the use of ΔIISC(target)/kB = −1.7Nr). If −TΔIISC(target) is taken into account, the agreement between ΔIIG and ΔIIGexp is significantly improved. Further, as mentioned above, we assume that the numbers of residues structured within p53CTD upon binding are 12, 9, 8, and 9 in systems 1, 2, 3, and 4, respectively. It is possible that these numbers are underestimated. For system 2, there are the following uncertain points: (i) the missing residues within Sir2Af2 (from Ser30 to Asp39) are added on the basis of a de novo modeling procedure; and (ii) since a large portion within p53CTD (i.e., 9 residues) was not detected in the X-ray crystallography, we assume that this portion does not participate in the binding (see Table 1). The worst agreement G


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and vdW components of system energy is positive (ΔIIET > 0; see Table 4), opposing the p53CTD−target binding. The binding undergoes conformational-entropy losses for p53CTD and the target (the loss for the former dominates), which also acts as a factor against the binding. We have concluded that the binding is driven by a large gain of configurational entropy of water. This gain originates from an increase in the total volume available to the translational displacement of water molecules in the system. The p53CTD− target interface in each system is closely packed with the achievement of high shape complementarity on the atomic level, leading to the large water-entropy gain. Though there are uncertainties in the conformational-entropy losses for p53CTD and the target upon binding, it is definite that ΔIIET > 0, ΔIISC < 0, and ΔIISVH > 0, and that ΔIISVH is substantially larger than |ΔIISC|, demonstrating the robustness of our conclusion. We have also shown that p53CTD cannot be structured without its target and its structure is intrinsically disordered in its isolated state, which is in line with the experimental fact. A closer packing of the p53CTD−target interface leads to not only higher water entropy but also lower p53CTD−target vdW interaction energy. However, it does not necessarily lead to lower p53CTD−target electrostatic interaction energy. This is because closer unlike-charged portions and more separated like-charged portions cannot always be assured by the closer packing. Thus, the electrostatic complementarity is not perfect though it is required to compensate for the energy increase due to the dehydration. Taking together, the p53CTD−target interface is featured by sufficiently high shape complementarity on the atomic level as the first priority together with as much electrostatic complementarity as possible. Such complementarities are achieved in harmony with the portion of the target to which p53CTD binds, leading to a large diversity of structures of p53CTD formed upon binding. The structure of p53CTD in the complex can take a less compact structure than its disordered state. If the complementarities are not achievable, the binding does not occur. This is our interpretation of the one-to-many molecular recognition. It is important to examine the generality of our conclusion drawn for the four binding processes shown in Figure 1. To this end, we are planning to further investigate the molecular recognition by a variety of intrinsically disordered regions (IDRs) of proteins, especially in cases where their targets are also IDRs. The binding of a protein to DNA or RNA is also of great interest. Our hybrid is expected to act as a useful theoretical tool in these investigations.

possible within the p53CTD−target interface. Such complementarities are achieved in harmony with the portion of the target to which p53CTD binds, leading to a large diversity of structures of p53CTD formed upon binding. The structure of p53CTD in the complex can be less compact than its disordered state. We then consider the general processes of the molecular recognition by an intrinsically disordered protein or region which constructs a well-defined structure only after the binding to its target is implemented. On the basis of the results from our earlier works20,39,40 and the present study, we believe that the receptor−ligand or protein−protein binding is always accompanied by a large gain in water entropy. However, it is not improbable that the conformational-entropy loss becomes larger than the water-entropy gain. In such a case, the binding occurs if the electrostatic complementarity is almost perfect and the change in total energy takes a sufficiently large, negative value. Here, we make an important remark. As explained in section S4 of Supporting Information, when the two biomolecules are hydrophobic, unlike p53CTD and the four targets considered in the present study, the bulk water is compressed upon binding in experiments performed under the isobaric condition. The compression makes significantly large, negative contributions to the changes in water entropy and enthalpy. Consequently, it is possible that the change in system entropy measured superficially become negative even though the binding is entropically driven.

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CONCLUSIONS We have investigated the binding processes for the extreme Cterminal peptide region of the tumor suppressor p53 protein (p53CTD) and its four different target proteins as an important example of the one-to-many molecular recognition accompanying the formation of target-dependent structures: p53CTD forms a helix, a sheet, and two different coils upon binding to the four targets, respectively (see Figure 1). Changes in thermodynamic quantities upon binding are calculated using a hybrid of statistical-mechanical theories combined with molecular models for water. We calculate the hydration energy εVH by the three-dimensional reference interaction site model (3D-RISM) theory14,15 and the hydration entropy SVH by the angle-dependent integral equation theory (ADIET)16,17,19,20 combined with the morphometric approach (MA).18 This hybrid, which we believe is currently the most reliable theoretical method, enables us to decompose the thermodynamic quantities into physically insightful components and thereby elucidate the mechanism of the one-to-many molecular recognition by p53CTD. Contrary to the prevailing view,7−10,12,13 we find that all of the four binding processes share the same binding mechanism in which water plays a pivotal role. The binding brings a large gain of p53CTD−target electrostatic attractive interaction. However, it accompanies an even larger loss of p53CTD−water and target−water electrostatic attractive interactions. This loss is partly compensated by a large gain of water−water electrostatic attractive interaction, but the net change in the electrostatic component of system energy is positive. A similar discussion can be made for p53CTD−target, p53CTD−water, target− water, and water−water van der Waals (vdW) attractive interactions, but the net change in the vdW component of system energy is negative. The effect caused by water is referred to as “dehydration”. Importantly, the sum of the electrostatic

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b08513. Further information on the angle-dependent integral equation theory, morphometric approach, three-dimensional reference interaction site model theory, changes in thermodynamic quantities of hydration under isochoric and isobaric conditions, and so-called hydrophobic effect or hydrophobic interaction (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. H


Article

The Journal of Physical Chemistry B Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The computer program for the morphometric approach was developed with R. Roth and Y. Harano. This work was supported by JSPS (Japan Society for the Promotion of Science) Grant-in-Aid for Scientific Research (B) (No. 25291035, M.K.) and by Grant-in-Aid for JSPS fellows (H.O.).

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Mechanism of One-to-Many Molecular Recognition Accompanying

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