Water mediated ligand functional group cooperativity: The contribution of a methyl group to binding affinity is enhanced by a COO- group through changes in the structure and thermodynamics of the hydration waters of ligand-thermolysin complexes

Article

pubs.acs.org/jmc

Water Mediated Ligand Functional Group Cooperativity: The

Contribution of a Methyl Group to Binding Aﬃnity is Enhanced by a

COO⁻Group Through Changes in the Structure and

Thermodynamics of the Hydration Waters of Ligand−Thermolysin

Complexes

Nader N. Nasief,*^,†Hongwei Tan,^‡Jing Kong,*^,§,‡and David Hangauer*^,†

^†Department of Chemistry, University at Buﬀalo, The State University of New York, Buﬀalo, New York 14260, United States

^‡Center for Computational Research, New York State Center of Excellence for Bioinformatics & Life Sciences, University at Buﬀalo,

The State University of New York, Buﬀalo, New York, 14203, United States

^§Q-Chem Inc., The Design Center, Suite 690 5001 Baum Boulevard, Pittsburgh, Pennsylvania 15213, United States

S

* Supporting Information

ABSTRACT: Ligand functional groups can modulate the contributions of one

another to the ligand−protein binding thermodynamics, producing either positive

or negative cooperativity. Data presented for four thermolysin phosphonamidate

inhibitors demonstrate that the diﬀerential binding free energy and enthalpy caused

by replacement of a H with a Me group, which binds in the well-hydrated S2′

pocket, are more favorable in presence of a ligand carboxylate. The diﬀerential

entropy is however less favorable. Dissection of these diﬀerential thermodynamic

parameters, X-ray crystallography, and density-functional theory calculations

suggest that these cooperativities are caused by variations in the thermodynamics

of the complex hydration shell changes accompanying the H→Me replacement.

Speciﬁcally, the COO⁻reduces both the enthalpic penalty and the entropic

advantage of displacing water molecules from the S2′ pocket and causes a

subsequent acquisition of a more enthalpically, less entropically, favorable water

network. This study contributes to understanding the important role water plays in ligand−protein binding.

Snyder et al provided new insight into the hydrophobic eﬀect

through analyzing the thermodynamics of water molecules in

carbonic anhydrase active site.⁹An intriguing characteristic of

water molecules in active sites is their ability to participate in

extended H-bond networks,¹⁰which can have favorable

enthalpies (due to multiple H-bonds) and unfavorable

entropies (due to reduction in mobility). Perturbations of

such networks by incremental structural changes in the ligand

can have their own enthalpy−entropy compensation eﬀects that

are layered upon those of the bound complexes and the

unbound ligands. Investigating the thermodynamic consequen-

ces of these perturbations is therefore crucial for understanding

the relative enthalpy, entropy, and free energy of binding across

series of congeneric ligands.

Understanding structure−activity and structure−thermody-

namics relationships is also contingent upon unraveling the

details of another important aspect in ligand−protein binding:

cooperativity among ligand functional groups. Changes in the

binding thermodynamics across a series of ligand congeners can

be inﬂuenced by the presence of other functional groups in the

INTRODUCTION

■

Interpreting the changes in the binding free energy across a

series of congeneric ligands (aka the structure−activity

relationship (SAR)) is one of the central pillars in the practice

of medicinal chemistry. These free energy changes are the net

result of enthalpy and entropy changes that often oppose each

other (enthalpy−entropy compensation). A deeper under-

standing of the changes in the binding thermodynamics across

congener series^1,2(structure−thermodynamics relationship) is

consequently fundamental to fully comprehend SAR relation-

ships. Binding thermodynamics are determined by the

thermodynamic status of the solvated ligand−protein complex

relative to that of the solvated uncomplexed ligand and protein.

Thermodynamic changes can therefore be produced when the

solvated ligand−protein complex and/or the solvated un-

complexed ligand systems are perturbed by ligand structural

modiﬁcations. One of the most versatile elements of these

systems, which can be easily perturbed, is water. Water is a

major player in ligand−protein binding whose role in the

binding process is not yet fully understood.³In recent years,

there has been growing awareness of many of the previously

unexplored aspects of water involvement in ligand−protein

binding.⁴⁻⁸For example, a very recent study published by

Received: April 4, 2012

Published: August 15, 2012

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Figure 1. Schematic representation of the interactions between the phosphonamidate inhibitors (blue) and thermolysin; H-bonds are shown as

dotted lines, water molecules are shown as blue balls, and the enzyme hydrophobic pockets are represented as red curves. (A) ZG^PLG: three

crystallographic water molecules are shown in the S2′ pocket; others are not shown; diagram is based on one of the crystal structures discussed later

in this paper. (B) ZG^PLL: two of the three water molecules shown in the S2′ pocket of ZG^PLG are displaced by the isobutyl side chain; diagram is

based on the crystal structure of ZG^PLL (3FWD).

ligand. For example, the improvement in the binding free

energy across a series of congeneric thrombin inhibitors, in

which the hydrophobic side chain binding the S3 pocket was

systematically varied, was shown to be more pronounced in the

presence of a ligand NH₂group capable of forming a H-bond

with the protein.¹¹The NH₂group and the hydrophobic side

chain in this series of thrombin inhibitors are therefore

synergistic; in other words, they demonstrate positive

cooperativity. Two ligand functional groups are said to be

cooperative when their simultaneous existence in the ligand

structure contributes more, or less, favorably to the binding free

energy than the sum of the contributions of these groups when

present individually. Cooperativity between ligand groups X

and Y, for instance, can be evaluated using double mutant

cycles¹²⁻¹⁵by comparing the binding free energy change

may arise from introducing conformational bias in one of the

ligand side chains by another, or from modifying the ligand

binding mode.¹²One of the potential sources of cooperativity

which, to the best of our knowledge, has not been explored is

the inﬂuence of a ligand functional group on the structural

changes caused by another group in the hydration layers of the

uncomplexed ligand and/or the ligand−protein complex

(water-mediated cooperativity). For instance, water displace-

ment, reorganization, and other structural changes in the

hydration shells caused by a ligand group X can be either

facilitated or hindered by another ligand group Y. This could

occur when group Y directly interacts with the water molecules

being displaced, reorganized, etc., by group X or indirectly

perturbs the extended H-bond networks that these water

molecules might participate in. The inﬂuence of group Y on the

hydration shell changes produced by group X might

consequently cause the diﬀerential binding energy of the H→

occurring when both groups exist in the ligand (ΔΔG_(H,H→X,Y)

)

with the sum of the binding free energy changes occurring

when each group exists individually (ΔΔG_(H,H→X,H)

+

X replacement to be more, or less, favorable (ΔΔG_(H,Y→X,Y)

ΔΔG_(H,H→X,H), positive cooperativity; ΔΔG_(H,Y→X,Y)

ΔΔG_(H,H→X,H), negative cooperativity).

<

>

ΔΔG_(H,H→H,Y)). When ΔΔG_(H,H→X,Y)has a more negative

value than ΔΔG_(H,H→X,H)+ ΔΔG_(H,H→H,Y), groups X and Y are

synergistic (i.e., ΔΔG_(H,H→X,Y)< ΔΔG_(H,H→X,H)

+

In this study, we tested the hypothesis that cooperativity can

be mediated by changes in the hydration shells. Thermolysin

(TLN), a Zn-endopeptidase¹⁸⁻²⁰obtained from Bacillus

thermoproteolyticus, was selected as a biological model system

to test this hypothesis. One reason for selecting this system was

that, in the course of investigating hydrophobic binding in the

thermolysin S1′ and S2′ pockets, the binding of ZG^PLG¹⁶to

thermolysin was found to leave the S2′ pocket well hydrated,

with a number of water molecules hydrogen-bonded to the

protein and to each other (Figure 1a; details are provided

later). Following the hypothesis, it appeared that some of these

water molecules can be displaced, and/or rearranged, by the

introduction of a hydrophobic side chain capable of binding the

S2′ pocket. For example, the crystal structure of the previously

reported thermolysin inhibitor, ZG^PLL,^21,22shows that an

isobutyl side chain displaces some water molecules from the S2′

pocket (Figure 1b). Because these water molecules form H-

bonds with Asn112, which is in turn H-bonded to the ligand

COO⁻, it was postulated that the waters that are displaced or

rearranged as a consequence of side chain binding to the S2′

pocket could be inﬂuenced by the presence of the COO⁻and

their thermodynamics could be modulated by this group, giving

ΔΔG_(H,H→H,Y), positive cooperativity). On the contrary, when

ΔΔG_(H,H→X,Y)has less negative value than ΔΔG_(H,H→X,H)

+

ΔΔG_(H,H→H,Y), groups X and Y are antagonistic (i.e.,

ΔΔG_(H,H→X,Y)> ΔΔG_(H,H→X,H)+ ΔΔG_(H,H→H,Y), negative

cooperativity). Another way to estimate the amount of

cooperativity is through comparing either the diﬀerential

binding energy¹⁶caused by the replacement of the ligand H

with group X in the presence “ΔΔG_(H,Y→X,Y)” and absence of

group Y “ΔΔG_(H,H,→X,H)”, or the diﬀerential binding energy

caused by the H→Y replacement in the presence

“ΔΔG_(X,H→X,Y)” and absence of group X “ΔΔG_(H,H→H,Y)”. If,

for example, ΔΔG_(H,Y→X,Y)has more negative value than

ΔΔG_(H,H→X,H), groups X and Y show positive cooperativity and

vice versa.

Cooperativity can be produced if the strength of direct

ligand−protein interactions is modiﬁed. For example, mutual

reinforcement of direct ligand−protein interactions,¹⁷which

might be associated with reducing the residual mobility of the

ligand, can cause positive cooperativity (e.g., thrombin

inhibitors).¹¹Cooperativity can be also mediated by other

factors which inﬂuence the binding process. For example, it

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rise to variations in the side chain contribution to the binding

thermodynamics (i.e., cooperativity).

The synthesis of intermediates 6a−d is illustrated in Scheme

2. Boc protected ^L-leucine was coupled to the hydrochloride

The approach used to investigate the potential cooperativity

between side chains that bind in the S2′ pocket and the ligand

COO⁻group was to compare the changes in binding aﬃnities

and thermodynamic proﬁles associated with the introduction of

these S2′ side chains in the presence, and absence, of the

COO⁻group. The side chain that was selected for this initial

investigation was a Me group. The phosphonamidate ligands

8a:ZG^PLG and 8b:ZG^PLA, both of which have the terminal

COO⁻group, as well as their analogues 8c and 8d, which lack

the COO⁻, were therefore synthesized and analyzed by kinetic

assay, isothermal titration calorimetry, and X-ray crystallog-

raphy in order to answer the following questions: (1) Is there

cooperativity between the ligand methyl group which binds in

the thermolysin S2′ pocket and the ligand terminal COO⁻

group? (2) Is this cooperativity positive or negative? (3) Is this

cooperativity enthalpically, or entropically, driven? (4) Does

the aqueous environment of the S2′ pocket play a role in this

cooperativity? To better reveal the origin of cooperativity, a

detailed theoretical approach, along with an initial computa-

tional analysis, was used to analyze the diﬀerential thermody-

namic parameters caused by the H→Me group replacement.

Additional inhibitors, with various larger alkyl side chains

binding the S2′ pocket, are currently under investigation and

will be reported in subsequent publications.

a

Scheme 2. Synthesis of Intermediates 6a−d

a

(a) 1.2 equiv PyBop, 1.5 equiv amino acid/amine HCl, 4 equiv DIEA,

anhydrous DMF, rt, 2−5 h, 72−80%; (b) 3 M HCl/MeOH, rt, 1.5−2

h, 99%; (c) HCl/AcOEt, rt, 1.5−2 h, 99%.

salts of glycine ethyl ester and ^L-alanine methyl ester to give 5a

and 5b, respectively, and coupled to methylamine hydro-

chloride and ethylamine hydrochloride to give 5c and 5d,

respectively. Either EDCI/HOBT or PyBop in anhydrous DMF

were used eﬀectively to achieve the coupling in presence of

diisopropylethylamine. Compounds 6a−d were obtained as

hydrochloride salts upon the removal of the Boc groups from

intermediates 5a−d. To remove the Boc groups, either 3 M

HCl/MeOH solution was used (5b−d) or HCl gas was

bubbled into an ethyl acetate solution of the Boc protected

intermediate (5a to avoid transesteriﬁcation with MeOH).

Intermediate 4 was coupled to each of the intermediates 6a−

d in anhydrous dichloromethane using PyBop as the coupling

reagent to give 7a−d (Scheme 3). Compounds 7a−d were then

hydrolyzed using lithium hydroxide to give the ﬁnal compounds

8a−d either as dilithium salts (when the carboxylate group is

present: 8a and 8b) or monolithium salts (when the

carboxylate group is absent: 8c and 8d). All the ﬁnal

compounds (8a−d) were puriﬁed by reverse-phase HPLC to

at least 95% purity.

RESULTS AND DISCUSSION

Chemistry. The synthesis of the intermediate 4 is illustrated

in Scheme 1. Commercially available benzylcarbamate was

■

a

Scheme 1. Synthesis of Intermediate 4

Binding Aﬃnity. The inhibition constants (K_i) for

compounds 8a−d were determined in a standard thermolysin

biochemical assay using 2-furanacryloyl-Gly-Leu-NH₂as a

substrate.²⁴The assay was carried out in high salt

concentration, which improves the enzyme activity as well as

the substrate binding to the enzyme. More details about the

assay condition are given in the Experimental Section. The K_i

and the corresponding free energy of binding values for the

thermolysin inhibitors 8a−d are provided in Table 1.

Data in Table 1 were analyzed by the double mutant cycle

shown in Figure 2. This cycle reveals that there is positive

cooperativity between the Me and the COO⁻groups, which

account for 5.1 kJ/mol improvement in binding caused by

combining the Me and the COO⁻groups in 8b

(ΔΔG_{(H,H→Me,COO)}− (ΔΔG_(H,H→Me,H)+ ΔΔG_{(H,H→H,COO)}) =

−5.1 kJ/mol). Cooperativity were also estimated by comparing

the diﬀerential binding energy of H→Me in the presence and

absence of the COO⁻group (ΔΔG_{(H,COO→Me,COO)}vs

ΔΔG_(H,H→Me,H)). This comparison showed that the Me group

is more favorable in the presence of the COO⁻group by 5.1

kJ/mol, representing the amount of cooperativity between

a

(a) 0.5 equiv Na₂CO₃, 1.5 equiv 37%HCHO, H₂O, heated until

dissolved, stirred at rt, overnight, 74%; (b) excess Ac₂O, 6 equiv

pyridine, THF, rt, 2 h, 67%; (c) 3−4 equiv P(OCH₃)₃, reﬂux, 3 h,

98%; (d) 10% NaOH 6 equiv, rt, 2 h, 77%.

heated in an aqueous basic formaldehyde solution to give

benzyl N-(hydroxymethyl) carbamate 1.²³The terminal

hydroxyl group of intermediate 1 was acetylated using acetic

anhydride to give benzyl N-(acetoxymethyl) carbamate 2.

Intermediate 2 was converted to dimethyl N-benzyloxycarbonyl

aminomethylphosphonate 3 by reﬂuxing with trimethyphos-

phite. Intermediate 4 was obtained by the hydrolysis of one of

the two methyl phosphonate esters in 3 using 10% NaOH

solution.

these two groups (i.e., ΔΔG_{(H,COO→Me,COO)}− ΔΔG_(H,H→Me,H)

−5.1 kJ/mol).

=

ITC Data.²⁵Isothermal titration calorimetry (ITC) was used

to dissect the changes in binding aﬃnities caused by the

replacement of H with Me, both in the presence and the

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a

Scheme 3. Synthesis of Ligands 8a−d

a

(a) 1.2 equiv PyBop, 1.5 equiv 6a−d, 4 equiv DIEA, anhydrous DCM, rt, 6 h−overnight, 45−75%; (b) LiOH, 2−4 equiv, H₂O/MeCN, rt, 2 h−

overnight, 60−95%.

free energy in absence of the COO⁻group) are given in Table

2. Absolute ITC values of the four inhibitors under

Table 1. The K_iand the Corresponding ΔG Values of the

Thermolysin Inhibitors 8a−d

compd

K_i(nM)

SD

36.0

ΔG_K(kJ/mol)

SD

0.2

i

Table 2. Binding Thermodynamic Values of 8b Relative to

8a and 8d Relative to 8c as Determined by ITC

8a

8b

8c

8d

472

19.1

902

289

−36.1

−44.0

−34.5

−37.3

0.55

197

35.1

0.1

0.4

0.3

ΔΔG_K(kJ/mol)

ΔΔH (kJ/mol)

−TΔΔS (kJ/mol)

d

8b−8a

8d−8c

−5.6

−2.2

−13.3

2.5

7.7

−4.7

investigation are not given because these values reﬂect not

only the thermodynamics of the binding process, and any

associated molecular changes, but also the thermodynamic

signal of the dipeptide Val-Lys displacement from the enzyme

active site by the inhibitors.²²This dipeptide is produced by

autoproteolysis of thermolysin in the enzyme concentrated

solutions used in ITC experiments. The Val-Lys displacement

contributions to the observed ITC values are assumed to be the

same for all of the inhibitors, consequently, they are canceled

out in the relative values given in Table 2.

The experimentally determined values of enthalpy can be

inﬂuenced by the buﬀer ionization capacity if the ligand and/or

the protein undergo protonation/deprotonation upon bind-

ing.²⁶The buﬀer ionization capacity is, however, anticipated to

equally aﬀect the observed enthalpies of ligands which pick up/

lose the same number of protons upon binding. Because the

thermolysin inhibitors 8b and 8a have the same ionizable

groups, the binding of either 8b or 8a to the enzyme

presumably causes the ligand−protein system to pick up/lose

the same number of protons. The ionization contributions to

the observed enthalpies of 8b and 8a are therefore equal and

canceled out in their relative value. The same applies to 8d and

8c relative to each other, as they also have the same ionizable

groups. Changes in the protonation state that these ligands may

undergo upon binding are currently under investigation.

Table 2 shows that the replacement of H with Me group in

absence of the COO⁻group causes an entropy-driven

enhancement of binding free energy (favorable diﬀerential

entropy dominates unfavorable diﬀerential enthalpy:

−TΔΔS_8d−8c(−TΔΔS_(H,H→Me,H)) = −4.7 kJ/mol; ΔΔH_8d−8c

(ΔΔH_(H,H→Me,H)) = 2.5 kJ/mol). The replacement of H with

the Me group in the presence of the COO⁻group, however,

Figure 2. Double mutant cycle showing positive cooperativity of −5.1

kJ/mol between the COO⁻group and the Me side chain.

Cooperativity

ΔΔG_{(H,H→H,COO)}

=

ΔΔG_{(H,H→Me,COO)}

−

(ΔΔG_(H,H→Me,H)

+

=

)

=

−5.1 kJ/mol. Also cooperativity

ΔΔG_{(H,COO→Me,COO)}− ΔΔG_(H,H→Me,H)= −7.9 − (−2.8) = −5.1 kJ/

mol. ΔΔG_{(H,COO→Me,COO)}: the diﬀerential binding free energy of the

H→Me replacement in presence of the COO⁻group. ΔΔG_(H,H→Me,H)

:

the diﬀerential binding free energy of the H→Me replacement in

absence of the COO⁻group.

absence of the ligand COO⁻group, into their enthalpic and

entropic components. Binding enthalpies, entropies, and free

energies of 8b relative to 8a (diﬀerential enthalpy, entropy, and

binding free energy in the presence of the COO⁻group) and of

8d relative to 8c (diﬀerential enthalpy, entropy, and binding

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causes an enthalpy-driven enhancement of binding free energy

(favorable diﬀerential enthalpy dominates unfavorable diﬀer-

ential entropy: ΔΔH_8b−8a(ΔΔH_{(H,COO→Me,COO)}) = −13.3 kJ/

mol; −TΔΔS_8b−8a(−TΔΔS_{(H,COO→Me,COO)}) = 7.7 kJ/mol).

The presence of the COO⁻group, therefore, improves the

enthalpic contribution of the Me group by 15.8 kJ/mol

(enthalpic positive cooperativity: ΔΔH_{(H,COO→Me,COO)}

−

ΔΔH_(H,H→Me,H)= −13.3 − 2.5 = −15.8 kJ/mol). This large

enthalpic positive cooperativity is substantially compensated by

an entropic negative cooperativity of 12.4 kJ/mol

(−TΔΔS_{(H,COO→Me,COO)}− (−TΔΔS_(H,H→Me,H)) = 7.7 −

(−4.7) = 12.4 kJ/mol). The data of the binding free energies

calculated from the dissociation constants K_ds, that were

determined in ITC experiments, shows positive cooperativity

between the Me and the COO⁻groups of −3.4 kJ/mol

(ΔΔG_{(H,COO→Me,COO)}− ΔΔG_(H,H→Me,H)= −5.6 − (−2.2) =

−3.4 kJ/mol). The magnitudes of the ITC-determined free

energy cooperativity and the kinetically determined coopera-

tivity are reasonably comparable (−3.4 vs −5.1 kJ/mol). Free

energy cooperativity can be also obtained when both the

enthalpic and the entropic cooperativities are added together as

shown in eq 1.

Figure 3. Theoretical thermodynamic cycle showing the relative

binding of ligands 8a and 8b, or 8c and 8d, to thermolysin (TLN). It

also shows the mutations 8a→8b or 8c→8d, in both the free

(mutation a) and the enzyme-bound (mutation b) states (Y = H in the

ligand pair 8c and 8d, and = COO⁻in the ligand pair 8a and 8b). The

hydration state of each species is illustrated as a number (n, n^ζ, n′, n′′,

ζ

or n*) of H₂O molecules and are marked by , ′, *, or ′′ to indicate

that the properties of the hydration water molecules might be diﬀerent

from one species to another. All species exist in the bulk water phase

which could exchange water with these species upon binding, or upon

the mutation of one species to another. The thermodynamic

parameters of each system (e.g. G₁, H₁, −TS₁), the binding

thermodynamic parameters (e.g. ΔG_8b/8d, ΔH_8b/8d, −TΔS_8b/8d), as

well as the thermodynamic parameters of mutations “a” and “b” are

shown.

free energy cooperativity

= enthalpic cooperativity + entropic cooperativity

= −15.8 + 12.4

= −3.4kJ/mol

(1)

Dissecting the Diﬀerential Thermodynamic Parame-

ters Associated with the H→Me Replacement. The

diﬀerential thermodynamic parameters caused by the structural

modiﬁcation H→Me were examined using the thermodynamic

cycle shown in Figure 3.²⁷This thermodynamic cycle includes

four systems: (1) the uncomplexed solvated ligand 8a, or 8c,

together with the uncomplexed solvated TLN, (2) the solvated

ligand−protein complex 8a−TLN, or 8c−TLN, (3) the

uncomplexed solvated ligand 8b, or 8d, together with the

uncomplexed solvated TLN, and (4) the solvated ligand−

protein complex 8b−TLN, or 8d−TLN. Both (1)→(2) and

(3)→(4) represent the binding of 8a and 8b (or 8c and 8d) to

TLN, respectively; while (1)→(3) and (2)→(4) represent the

mutation of the uncomplexed 8a→8b (or 8c→8d) and the

mutation of the 8a−TLN→8b−TLN (or 8c−TLN→8d−

TLN) complexes respectively (mutations a & b). As illustrated

in Figure 3, mutations “a” and “b” can be accompanied with

signiﬁcant changes in the hydration states of the uncomplexed

ligand and the ligand−protein complex.

mutation of the complex of one of these analogues with the

protein to the complex of the other, relative to the

thermodynamics of the mutation of the uncomplexed ﬁrst

analogue to the other. The thermodynamic parameters of

mutations “b” and “a” can be partitioned, according to the

structural changes taking place in these mutations, into more

basic terms²⁸as described in the next sections. In these

sections, changes in these basic terms caused by the presence of

the COO⁻group, and how these changes aﬀect the diﬀerential

thermodynamic parameters, will be investigated in order to ﬁnd

out the term(s) that might be responsible for the

experimentally observed enthalpy, entropy, and free energy

cooperativities between the Me and the COO⁻groups.

ΔΔG_(H,Y→Me,Y)= ΔG_8b/8d− ΔG_8a/8c

= ΔG_{b(H,Y→Me,Y)}− ΔG_{a(H,Y→Me,Y)}

(2A)

ΔΔH_(H,Y→Me,Y)= ΔH_8b/8d− ΔH_8a/8c

The thermodynamic cycle in Figure 3 shows that a

diﬀerential binding parameter such as ΔΔG_(H,Y→Me,Y)(Y =

H/COO⁻), which is by deﬁnition equal to the diﬀerence

between the binding free energies of the Me and the H

analogues (ΔG_8b/8d− ΔG_8a/8c), is equal to [G₄− G₃− (G₂−

G₁)]. Rearranging [G₄− G₃− (G₂− G₁)] to [(G₄− G₂− (G₃

− G₁)], which is equal to ΔG_{b(H,Y→Me,Y)}− ΔG_{a(H,Y→Me,Y)}, we

can equate ΔΔG_(H,Y→Me,Y)with ΔG_{b(H,Y→Me,Y)}− ΔG_{a(H,Y→Me,Y)}

as well (eq 2A: ΔG_{b(H,Y→Me,Y)}, the free energy change caused by

mutation “b”; ΔG_{a(H,Y→Me,Y)}, the free energy change caused by

mutation “a”). Similar equations can be written for both

ΔΔH_(H,Y→Me,Y)and −TΔΔS_(H,Y→Me,Y)(eqs 2B and 2C). The

thermodynamic cycle shown in Figure 3, therefore, enables one

to express the diﬀerential binding thermodynamics of two

closely related analogues in terms of the thermodynamics of the

= ΔH_{b(H,Y→Me,Y)}− ΔH_{a(H,Y→Me,Y)}

(2B)

−TΔΔS_(H,Y→Me,Y)

= −TΔS_8b/8d− (−TΔS_8a/8c

= −TΔS_{b(H,Y→Me,Y)}− (−TΔS_{a(H,Y→Me,Y)}

Where Y = H (8c, 8d) or COO⁻(8a, 8b)

)

(2C)

1. Dissecting the Thermodynamic Parameters of Muta-

tion “b”. The fact that the free energy, enthalpy, and entropy

are state functions (dependent on the initial and ﬁnal states, but

not on the path taken to reach the ﬁnal state) can be utilized to

dissect the thermodynamic parameters of mutations “a” and

“b”. In mutation “b”, going from the 8c−/8a−TLN to the

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Figure 4. (a) Overlay of the crystal structures 8a−TLN and 8b−TLN. Ligand 8a and water molecules that belong to its complex are shown in green.

Ligand 8b and water molecules that belong to its complex are shown in blue. Protein atoms of both complexes are shown in the following colors: C

(gray), O (red), and N (blue). Some water molecules and protein residues are not shown for clarity. No conformational or binding mode changes

but signiﬁcant changes in hydration layer are observed. (b) Overlay of the crystal structures 8c−TLN and 8d−TLN. Ligand 8c and water molecules

that belong to its complex are shown in green. Ligand 8d and water molecules that belong to its complex are shown in blue. No conformational or

binding mode changes, but signiﬁcant changes in hydration layer, are observed.

8d−/8b−TLN complexes, can be achieved through diﬀerent

paths each of which comprises a number of hypothetical steps

and artiﬁcial intermediate states. In each step, one or more of

the structural changes associated with the mutation is

accomplished. High-resolution crystal structures for the

complexes of the four ligands with thermolysin were taken so

that the structural diﬀerences between 8c−TLN and 8d−TLN

complexes and between 8a−TLN and 8b−TLN complexes

could be determined.²⁵Superimposing the crystal structures of

each ligand pair (Figure 4) reveals the following: (1) No

change in the binding mode occurs due to the replacement of

H with Me in either pairs of ligands. (2) No signiﬁcant

conformational change in the enzyme occurs due to the H→

Me replacement in either pairs of ligands. (3) Signiﬁcant

changes in the hydration layer of the S2′ pocket and the nearby

regions take place as the H is replaced by Me in both 8c−TLN

and 8a−TLN complexes. It should be noted that an accurate

comparison of the hydration shell of a ligand−protein complex

Figure 5. Thermodynamic cycle showing that the mutation of 8a−

TLN→8b−TLN, or 8c−TLN→8d−TLN, can be achieved via either

two (I and II) or three (III, IV and II) hypothetical steps. Step I: The

change in the complex hydration state from (n*H₂O)* to (n″H₂O)′′.

Step II: The replacement of H with Me group. Step III: Removal of

some water molecules from the complex hydration shell. Step IV: The

appearance of a number of new water molecules, which are either

captured from the bulk solvent or experience reduction in their

mobility, in the hydration shell. Thermodynamic parameters of each

step are shown.

with the hydration shell of another requires the two complexes

to have comparably high resolutions because the detection of

crystallographic water molecules is highly dependent on the

structure resolution.²⁹This requirement was reasonably fulﬁlled

in the crystal structures obtained for the four ligands in

question (resolution ranges from 1.6 to 1.28 Å).²⁵

Because no conformational or binding mode changes were

observed in the crystal structures, mutation “b” can be

accomplished in two steps; the ﬁrst involves the changes

taking place in the complex hydration shell (step I, Figure 5)

and the second involves the replacement of H with Me (step II,

Figure 5). Changes in the hydration shell that can be detected

by X-ray crystallography involve the disappearance of some

crystallographic water molecules which exist in the initial but

not in the ﬁnal complex, and the appearance of others which

exist in the ﬁnal but not the initial complex. The disappearance

of crystallographic water molecules can be attributed to the

transfer of these water molecules to the bulk solvent (i.e., water

displacement) or to increase in their motions, while the

appearance of new water molecules can be attributed to the

acquisition of these water molecules from the bulk solvent or to

decrease in their motions.

visible by X-ray crystallography. These regions often have polar

groups which can form strong H-bonds with water. (2) Regions

potentially hydrated with disordered water molecules which are

not visible by X-ray crystallography.³⁰⁻³³(3) Void regions.

Regions that belong to both the second and the third categories

are typically apolar pockets which do not provide suﬃcient H-

bonding groups to make strong interactions with water.

Whether these apolar pockets are actually empty or have

disordered waters is controversial and diﬃcult to determine.³⁴

Fortunately, we will not have to deal with this case in the

current study because crystallographic data shows that the S2′

pocket is hydrated with ordered waters. Because almost all of

the water molecules in the ﬁrst hydration layer of the area we

are interested in could be detected by X-ray crystallography, our

discussions will be focused only on these waters.

As a relevant background for the discussion that follows, it is

helpful to consider that regions in protein active sites can be

roughly categorized according to their hydration status to: (1)

Regions hydrated with ordered water molecules which are

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Figure 6. Schematic representation of the complex active site showing the most important water molecules and the H-bond networks among them;

(a) The crystallographic complex 8c−TLN (b) An artiﬁcial state produced by the removal of two water molecules from the S2′ pocket of the 8c−

TLN crystallographic complex. (c) An artiﬁcial state produced by the incorporation of new crystallographic water molecules in the active site (the

ones detected in the 8d crystallographic complex, but not in the 8c complex). (d) The 8d−TLN crystallographic complex produced by the

replacement of the H of ligand 8c in the artiﬁcial state c with Me group. Hs of the water molecules and polar groups were intuitively placed where

they can form H-bonds or where the H-bonds they form can maximize the energetic beneﬁt. a→b corresponds to step III in Figure 5; b→c

corresponds to step IV in Figure 5, and c→d corresponds to step II in Figure 5.

Considering the thermodynamic principle that nature adopts

the status that maximizes the free energy beneﬁt, the fact that

the S2′ pocket is hydrated with ordered water molecules

indicates that this hydration status is more favorable than either

the hydration of this pocket with disordered waters or its being

void. We can therefore conclude that perturbing this hydration

status, for example through the transfer of crystallographic

waters from the S2′ pocket to the bulk solvent (to create a void

area), is unfavorable in terms of free energy (ΔG > 0), and vice

versa. The free energy of transferring water molecules to

protein cavities hydrated with crystallographic water molecules

was previously studied and shown to be negative.^35,36Ordered

waters in the active site adopt an entropically unfavorable status

because of their restricted motions which allow their crystallo-

graphic detection. For these waters to remain in the active site,

their free energy must be favorable. This can be accomplished

only if these waters can form stronger interactions, and

consequently have more favorable enthalpy, in the active site

relative to the bulk solvent. The transfer of ordered water

molecules to the bulk is therefore entropically favorable, due to

a relative increase in the motions of these waters in the bulk

solvent, and enthalpically unfavorable due to the weaker

binding they experience there (binding opposes motions). The

unfavorable free energy anticipated for the transfer of

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Figure 7. Schematic representation of the complex active site showing the most important water molecules and the H-bond networks among them.

(a) The crystallographic complex 8a−TLN. (b) An artiﬁcial state produced by the removal of two water molecules from the S2′ pocket of the 8a−

TLN crystallographic complex. (c) An artiﬁcial state produced by the incorporation of new crystallographic water molecules in the active site (the

ones detected in the 8b complex, but not in the 8a complex). (d) The 8b−TLN crystallographic complex produced by the replacement of the H of

ligand 8a in the artiﬁcial state c with Me group. Hs of water molecules and polar groups were intuitively placed where they can form H-bonds or

where the H-bonds they form can maximize the energetic beneﬁt. a→b corresponds to step III in Figure 5, b→c corresponds to step IV in Figure 5,

and c→d corresponds to step II in Figure 5.

crystallographic water molecules to the bulk water can therefore

be attributed to the enthalpic penalty which overcompensates

the favorable entropy of displacing these waters from the active

site (the magnitude of the unfavorable enthalpy is larger than

that of the favorable entropy; |ΔH| > |−TΔS|).

Conversely, the aforementioned appearance of new crystallo-

graphic water molecules in the complex, which is caused by

either the transfer of water molecules to the complex or the

restriction of their motions, is anticipated to have an opposite

thermodynamic proﬁle (enthalpically favorable and entropically

unfavorable). Because some of the changes in the hydration

layer are entropic in nature and others are enthalpic, it is

appropriate to partition the ﬁrst step of mutation “b” into two

steps: one involves the entropically favorable, enthalpically

unfavorable changes (e.g., crystallographic water displacement;

step III, Figure 5), and the other involves the enthalpically

favorable, entropically unfavorable changes (e.g., crystallo-

graphic water acquisition from the bulk solvent; step IV,

Figure 5). The mutation of 8c−/8a− to 8d−/8b−thermolysin

complexes, along with its potential steps, is described by the

thermodynamic cycle shown in Figure 5. This thermodynamic

cycle was used to write equation set 3.

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Figure 8. Schematic representation of parts of the model systems which were constructed based on 8c−TLN and 8a−TLN active sites and used for

calculations; all of the water molecules included in a model, along with the H-bond networks among them, are shown. (a) The model system of 8c−

TLN before and after the removal of the two red-colored water molecules from the S2′ pocket. Partial charges of the water molecules atoms are

shown in blue, each close to its corresponding atom. (b) The model system of 8a−TLN before and after the removal of the two red-colored water

molecules from the S2′ pocket. Partial charges of the water molecules atoms are shown in blue, each close to its corresponding atom. In both a and b,

the numerical values of the partial charges of all of the water molecules’ atoms decrease when the two water molecules are removed from the S2′

pocket.

removed from the active site of the 8c−TLN (8a−TLN)

ΔG_{b(H,Y→Me,Y)}= ΔG_{b‐solv(H,Y→Me,Y)}+ ΔG_{b‐Me(H,Y→Me,Y)}

complex (the initial state). Second, water molecules which

= ΔG_{b‐Wdisp(H,Y→Me,Y)}+ ΔG_{b‐Wstrct(H,Y→Me,Y)}

+ ΔG_{b‐Me(H,Y→Me,Y)}

appear in the 8d−TLN (8b−TLN) complex, but not in the

8c−TLN (8a−TLN) complex, are incorporated into the

complex hydration shell. Third, the H in 8c (8a) is replaced

by Me to give 8d (8b). A schematic representation of the S2′

pocket and its adjacent regions in 8c−TLN, the two artiﬁcial

intermediates produced by the ﬁrst two steps of this mutation,

and 8d−TLN are shown in Figure 6. In this ﬁgure, a→b of

Figure 6 corresponds to step III/Figure 5, b→c of Figure 6

corresponds to step IV/Figure 5, and c→d of Figure 6

corresponds to step II/Figure 5. An analogous representation

for the 8a−TLN→8b−TLN three-step mutation is shown in

Figure 7. As illustrated in these ﬁgures, the region of the active

site being investigated is characterized by the presence of many

crystallographic water molecules which are, together with the

ligand and the protein polar groups, involved in a web-like H-

bonding network. Many of these water molecules form chains

or polygonal structures³⁷that are presumably stabilized by the

mutual reinforcement (cooperativity) of the H-bonds formed

among their water molecules. Mutual reinforcement of H-

bonds in these structures can be attributed to resonance-

(3A)

ΔH_{b(H,Y→Me,Y)}= ΔH_{b‐solv(H,Y→Me,Y)}+ ΔH_{b‐Me(H,Y→Me,Y)}

= ΔH_{b‐Wdisp(H,Y→Me,Y)}+ ΔH_{b‐Wstrct(H,Y→Me,Y)}

+ ΔH_{b‐Me(H,Y→Me,Y)}

(3B)

−TΔS_{b(H,Y→Me,Y)}= −TΔS_{b‐solv(H,Y→Me,Y)}

− TΔS_{b‐Me(H,Y→Me,Y)}= −TΔS_{b‐Wdisp(H,Y→Me,Y)}

− TΔS_{b‐Wstrct(H,Y→Me,Y)}− TΔS_{b‐Me(H,Y→Me,Y)}

(3C)

Details of the Mutations of 8c−TLN→8d−TLN and 8a−

TLN→8b−TLN Complexes. As previously noted in Figure 5,

mutation “b” can be carried out in three steps (steps III, IV, and

II). First, water molecules which do not exist in the 8d−TLN

(8b−TLN) complex (the ﬁnal state of the mutation) are

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enhancement (π-bond cooperativity)³⁸⁻⁴¹and/or polarization-

enhancement (σ-bond cooperativity) of these H-bonds.⁴¹⁻⁴⁴π-

Bond cooperativity is exempliﬁed in the 8c−TLN complex by

the mutual reinforcement of the H-bonds formed by the CO

and the NH₂of the Asn112 amide (Figure 6a). σ-Bond

cooperativity is observed in water arrangements which can

adopt homodromic patterns^45,46(Figure 6a, c). The reinforce-

ment of H-bonds by the π- and the σ-bond cooperativities can

be responsible for a great deal of the favorable free energy,

favorable enthalpy, and unfavorable entropy which crystallo-

graphic waters presumably have in ligand−protein complexes.

A. Water Displacement from the S2′ Pocket. The ﬁrst step

in the mutation 8c−TLN→8d−TLN involves the removal of

two water molecules from the S2′ pocket of the 8c−TLN

complex (Figure 6a) to produce the artiﬁcial state shown in

Figure 6b (corresponds to step III/Figure 5). This step creates

the cavity required to accommodate the Me group when it

replaces the H of 8c. Similarly, two water molecules are

removed from the S2′ pocket of the 8a−TLN complex to

create a cavity for the Me group (Figure 7a). The removal, or

displacement, of ordered water molecules from the S2′ pocket

(i.e., their transfer to the bulk solvent) involves breaking the H-

bonds they form with other water molecules and with the

protein (e.g., with the Asn111 and the Asn112 residues) as well

as reducing the σ- and π- bond cooperativities in the complex

H-bond network. This loss of H-bonding correlates with an

enthalpic penalty. It is not likely that this enthalpic penalty is

fully compensated when the displaced waters form new H-

bonds in the bulk solvent because, as it was previously

mentioned, water molecules are anticipated to experience

weaker H-bonding in the bulk water than when ordered in the

complex. Consequently ΔH_{b‑Wdisp(H,Y→Me,Y)}> 0. With regard to

the entropy and the free energy of this water displacement step,

it was pointed out earlier that the displacement of crystallo-

graphic water molecules, such as those in the S2′ pocket, from

the ligand−protein complex is favorable in terms of entropy

and unfavorable in terms of free energy (−TΔS_{b‑Wdisp(H,Y→Me,Y)}

< 0, ΔG_{b‑Wdisp(H,Y→Me,Y)}> 0).

To conﬁrm that the removal of water molecules from the S2′

pocket reduces the σ- and π-bond cooperativities in the active

site H-bond network, and as an initial eﬀort to investigate the

role these cooperativities play in stabilizing this network, the

polarization of water molecules in the active site was studied

using QM calculations. Model systems were constructed based

on the crystal structures of 8c−TLN and 8a−TLN. These

model systems included parts of the Tyr193, Leu202, Asn111,

and Asn112 residues, the terminal part of the ligand, and many

of the water molecules shown in Figures 6a and 7a. The model

systems were optimized using the DFT/B3LYP method⁴⁷⁻⁴⁹

with 3-21G basis, and the partial charges of their atoms were

calculated using B3LYP functional and triple-ζ cc-pVTZ basis.⁵⁰

The two S2′ pocket water molecules were then removed from

each model, and the new partial charges of the remaining atoms

were then calculated. The results show that, after water

removal, a signiﬁcant global decrease in the polarization of the

remaining water molecules’ atoms takes place. For example, in

the model representing 8c−TLN, the average partial negative

charge on the O atoms decreases from −0.685 to −0.478, and

the average partial positive charge on the H atoms decreases

from +0.353 to +0.258 (Figure 8a). Also, in the model

representing 8a−TLN, the average partial negative charge on

the O atoms decreases from −0.70 to −0.52, and the average

partial positive charge on the H atoms decreases from +0.33 to

+0.25 (Figure 8b). This indicates an underlying decrease in the

cooperativity among the H-bonds formed by the water

molecules left after the removal of the two S2′ waters (i.e., a

less polarized O or H atom is less capable of participating in H-

bonds).⁵¹

Inﬂuence of the COO⁻Group on the Thermodynamics of

Water Displacement. Comparing the structures of the two

crystallographic complexes 8a−TLN and 8c−TLN reveals that

one of the two water molecules whose displacement from the

S2′ pocket is discussed herein, in the presence of the COO⁻

group, forms one less H-bond than in absence of this group

(Figure 7a vs Figure 6a). The presence of the COO⁻in the

8a−TLN complex also causes the H-bond network of this

complex to be less interconnected than that of the 8c−TLN

complex (e.g., in Figure 7a, the southern H-bond network is

isolated from the northern one). This indicates a potential

reduction in the σ- and π-bond cooperativities in the 8a−TLN

complex (relative to 8c−TLN), which can be translated into a

decrease in the binding (and an increase in the mobility) of the

water molecules in the active site, including those that are

displaced from the S2′ pocket. Both the formation of one less

H-bond by one of the S2′ waters and the decrease in the σ- and

π-bond cooperativity can cause the displacement of water from

the S2′ pocket to have a smaller enthalpic penalty and a less

favorable entropic change in the presence vs absence of the

COO⁻group (ΔH_{b‑Wdisp(H,COO→Me,COO)}< ΔH_{b‑Wdisp(H,H→Me,H)}

−TΔS_{b‑Wdisp(H,COO→Me,COO)}> −TΔS_{b‑Wdisp(H,H→Me,H)}).

;

To qualitatively support this, the interaction energy of these

water molecules in the complex was calculated in each of the

two model systems shown in Figure 8. The enthalpic penalty of

removing a water molecule from the ligand−protein complex is

the sum of the penalty of losing the interactions of this water in

the complex and the smaller-in-magnitude advantage of

forming new interactions in the bulk solvent. Because the

interaction energy of water in the complex is the only

component that varies when the COO⁻group exists (i.e.,

interactions with the bulk solvent is the same), the diﬀerence

between the calculated interaction energies of the two water

molecules of interest in the model that has the COO⁻group

and the model that does not have it can be qualitatively

correlated with −(ΔH_{b ‑ W d i s p ( H , C O O → M e , C O O )}

−

ΔH_{b‑Wdisp(H,H→Me,H)}). Dispersion-corrected DFT energy calcu-

lations show that the interaction energy of the two S2′ water

molecules in the model system that has the COO⁻group is 9.3

kcal/mol less favorable than their interaction energy in the

model system that lacks this group (E_int,COO− E_int,No‑COO= 9.3

kcal/mol; Supporting Information Table 1). This indicates that,

as was predicted based upon structural data, the enthalpic

penalty of the removal of the indicated two water molecules

from the complex in the absence of the COO⁻group is larger

than the enthalpic penalty of their removal in the presence of

this group (−(ΔH_{b‑Wdisp(H,COO→Me,COO)}− ΔH_{b‑Wdisp(H,H→Me,H)}

)

correlates with the 9.3 kcal/mol diﬀerence in interaction energy

→ ΔH_{b‑Wdisp(H,COO→Me,COO)}< ΔH_{b‑Wdisp(H,H→Me,H)}).

B. Crystallographic Water Gain. The removal of two water

molecules from the S2′ pocket, which produces the

intermediates shown in Figures 6b and 7b, most likely causes

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the conﬁgurations of the remaining water molecules in these

intermediates to become unstable. This is because for the rest

of the crystallographic water molecules to remain ﬁxed at their

particular positions without the level of enthalpic support

provided by the σ- and π-bond cooperativity in the original

complexes would be costly in terms of free energy. New water

molecules are therefore captured from the bulk solvent or

become more ordered so as to be detectable by X-ray

crystallography, allowing the water conﬁgurations of Figures

6b and 7b to regain stability (Figures 6c, 7c). Two of the new

water molecules appear close to where the two water molecules

that were previously removed had existed. These water

molecules, together with others left in the S2′ pocket, form a

heptagonal (Figure 6c) or a semicircular (Figure 7c) structure

which can hydrate the Me group when it replaces the ligand H.

It is not uncommon for hydrophobic side chains in protein

systems to be hydrated with similar polygonal water structures

(e.g., the methyl side chain of Ala92 of the human lysozyme,⁵²

the Val3 side chain in the human insulin,⁵³etc.), particularly

when these water structures are anchored on the protein by one

or more polar groups (e.g., Asn111 CO group). These water

structures can restore a great deal of the σ-bond cooperativity,

which was lost upon the removal of the previously described

water molecules from the S2′ pocket ( Figure 6c).

complex region shown in Figures 6 and 7, both in absence and

presence of the COO⁻group, shows that 12 water bridges are

gained in the presence of the COO⁻, while only 6 are gained in

its absence (the water bridges counted are those having four or

fewer water molecules bridging two ligand/protein polar atoms:

Supporting Information Figure 1). Correlating these structural

features with the thermodynamic proﬁle of this step, we can

conclude that the COO⁻group causes the water gain step to be

more enthalpically favorable and more entropically unfavorable

(ΔH_{b‑ Ws trc t(H, COO→ M e , C OO)}< ΔH_{b ‑ Wst r ct( H, H → M e , H )}

−TΔS_{b‑Wstrct(H,COO→Me,COO)}> −TΔS_{b‑Wstrct(H,H→Me,H)}).

;

It is important to note that when a particular ligand−protein

complex mutation is compared with another with respect to the

number of crystallographic water molecules gained or lost,

experimental variations that could lead to artifacts should be

taken into account. For example, even slight variations in

resolution among ligand−protein complexes could lead to

variations in the number of the detected crystallographic water

molecules and may consequently cause an apparent gain or loss

of water. It is therefore more appropriate that, for each complex

involved in a mutation, the percentage of ordered water

molecules observed in the region of interest, relative to the

entire complex, be determined and used to calculate a “water

gain/loss index” for this mutation. This water gain/loss index is a

ratio of the percentage determined for the ﬁnal complex of the

mutation to the percentage determined for the initial complex

(eq 4: the water gain/loss index for the 8c−TLN→8d−TLN

mutation). The use of percentages, rather than numbers, of

water molecules eliminates the experimental variability among

diﬀerent crystallographic complexes (normalization). If the

water gain/loss index for a particular mutation is larger than 1, it

can be concluded that this mutation causes gain of crystallo-

graphic water and vice versa.

Other new water molecules appear in the intermediates

shown in Figures 6c and 7c. For example, additional new waters

could be found near the COO⁻group of Asp226 in Figure 6c.

In Figure 7c, the additional new waters appear in two regions:

one is bordered by Asn111 and Thr129 and the other lies

between the Asp226 COO⁻and the ligand COO⁻groups.

These new waters in Figure 7c, together with others, form an

intricate water network which bridges many of the protein polar

groups and the ligand COO⁻together. It is possible that the

appearance of these additional new waters in the crystal

structures is caused by reducing their motions due to stronger

binding they might experience following the removal of the two

waters from the S2′ pocket: water displacement from the S2′

pocket could be communicated to other regions of the active

site through H-bond networks, bringing about the appearance

of new waters in these regions (e.g., the network extending

from the Asn112 NH₂to the Asp226 COO⁻; Figure 6b). The

H-bonds formed by the new water molecules can be mutually

cooperative. They can also reinforce several existing H-bonds in

the active site through σ-bond cooperativity (Figure 7c). As

noted earlier, this water gain step is anticipated to be

enthalpically favorable due to the formation and the reinforce-

ment of the H-bonds in the complex active site and entropically

unfavorable due to restricting the motions of the water

molecules which join the crystallographic water inventory

(ΔH_{b‑Wstrct(H,Y→Me,Y)}< 0, − TΔS_{b‑Wstrct(H,Y→Me,Y)}> 0).

water gain/loss index

= percentage of water molecules observed in the

investigated area in 8d−TLN/percentage of water

(4)

molecules observed in the same area in 8c−TLN

The water gain/loss indexes for both the 8c−TLN→8d−TLN

́

and the 8a−TLN→8b−TLN mutations in a sphere of 10 Å

radius around the terminal Me group of 8c were calculated and

found to be 0.98 and 1.14, respectively (Supporting

Information Table 2). The water gain/loss index of the 8c−

TLN→8d−TLN mutation indicates that the net gain of water

observed in this mutation might be an artifact caused by a

global enhancement of the detection of water molecules in the

8d−TLN complex. The water gain/loss index of the 8a−TLN→

8b−TLN mutation, on the contrary, suggests that the water

gain in this mutation is genuine and reﬂects an improvement in

the organization of water molecules in the S2′ pocket and the

nearby region. The water gain/loss index might be correlated

with the thermodynamic proﬁle of the overall hydration shell

changes (i.e., ΔH_{b‑solv(H,Y→Me,Y)}and −TΔS_{b‑solv(H,Y→Me,Y)}; step I/

Figure 5: net water gain→ favorable enthalpic change and

unfavorable entropic change; and vice versa). This correlation,

together with the fact that the water gain/loss index of the 8a−

TLN→8b−TLN mutation is larger than that of the 8c−TLN→

8d−TLN mutation, leads to the conclusion that the presence of

the COO⁻group causes the thermodynamics of the overall

hydration shell changes to be enthalpically favorable and

entropically unfavorable relative to when this group is absent

Inﬂuence of the COO⁻Group on the Gain of Crystallo-

graphic Waters. The water gain step in both the 8a−TLN→

8b−TLN and the 8c−TLN→8d−TLN mutations (i.e., Figure

7b→7c and Figure 6b→6c) reveals that the intermediate shown

in Figure 7b, which has the COO⁻group, gains more

crystallographic water molecules than the intermediate shown

in Figure 6b which lacks this group (e.g., two more waters per

the complex region shown in Figure 6 and 7). This step, in the

presence of the COO⁻group, produces a more developed H-

bond network as well. The number of water chains bridging the

ligand and/or the protein polar atoms can be taken as a

measure of how developed the active site H-bond network is.

Counting the bridging water chains gained in this step in the

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(ΔH_{b ‑ s o l v ( H , C O O → M e , C O O )}

Article

<

ΔH_{b ‑ s o l v ( H , H → M e , H )}

;

second step of this mutation (i.e., mutation b). First, the eﬀect

of the presence of the COO⁻group on the H-bonding status of

the two water molecules being displaced from the S2′ pocket

can be illustrated by superimposing the crystal structures of the

8a−TLN complex and the 8c−TLN complex (the initial states

of the mutations 8a−TLN→8b−TLN and 8c−TLN→8d−

TLN). Figure 9 shows that the COO⁻group pushes water

−TΔS_{b‑solv(H,COO→Me,COO)}> −TΔS_{b‑solv(H,H→Me,H)}). Because the

hydration shell changes include both water displacement and

water gain, the decrease in ΔH_{b‑solv(H,Y→Me,Y)}caused by Y

COO⁻compared to YH comprises the decreases in both

ΔH_{b‑Wdisp (H,Y→Me,Y)}and ΔH_{b‑Wstrct(H,Y→Me,Y)}, and the increase in

−TΔS_{b‑solv(H,Y→Me,Y)}comprises the increases in both

−TΔS_{b‑Wdisp (H,Y→Me,Y)}) and −TΔS_{b‑Wstrct (H,Y→Me,Y)}

.

Are Changes in the Hydration Shell Responsible for the

Observed Cooperativity? Investigating whether or not the

decrease in ΔH_{b‑solv(H,Y→Me,Y)}and the increase in

−TΔS_{b‑solv(H,Y→Me,Y)}caused by the COO⁻group are responsible

for the experimentally observed enthalpic and entropic

cooperativities requires substituting the thermodynamic

parameters of mutation “b” in equation set 2 with their

fundamental components given by equation set 3. Doing so, we

can write equation set 5. Equation 5B shows that the decrease

in ΔH_{b‑solv(H,Y→Me,Y)}caused by the COO⁻group decreases

ΔΔH_(H,Y→Me,Y). Because this is in agreement with the

Figure 9. Overlay of the crystal structures 8a−TLN and 8c−TLN.

Ligand 8a and the water molecules that belong to its complex are

shown in blue. Ligand 8c and the water molecules that belong to its

complex are shown in green. Protein atoms of both complexes are

shown in the following colors: C (gray), O (red), and N (blue). Some

water molecules and protein residues are not shown for clarity. In

ligand 8a complex, water no. 1 is pushed by the COO⁻group toward

water no. 2 as indicated by the red arrow. Water no. 2 ceases to appear

in the crystal structure (probably displaced). Water no. 3 loses its 3.1 Å

H-bond with water no. 2 and cannot form a H-bond with water no. 1

(O−−O distance is 4.4 Å). Water no. 3 and water no. 4 are the ones

being displaced by the Me group in both the mutations 8c−TLN→

8d−TLN and 8a−TLN→8b−TLN.

experimental data (ΔΔH_{(H,COO→Me,COO)}− ΔΔH_(H,H→Me,H)

=

−15.8 kJ/mol), we conclude that changes in the hydration shell

of the complex can be responsible for the enthalpic positive

cooperativity between the Me and the COO⁻groups. Similarly,

the increase in −TΔS_{b‑solv(H,Y→Me,Y)}caused by the COO⁻group

increases −TΔΔS_(H,Y→Me,Y)(eq 5C). Because this is also in

agreement with the experimental data (−TΔΔS_{(H,COO→Me,COO)}

− (−TΔΔS_(H,H→Me,H)) = 12.4 kJ/mol), we can conclude that

changes in the hydration shell of the complex can cause the

entropic antagonism (entropic negative cooperativity) between

the Me and the COO⁻groups.

molecule no. 1 toward water no. 2 which cannot stay in its

position anymore because, if it did, it would be in steric clash

with water no 1. As a consequence, water no. 3 has one H-bond

less in the 8a−TLN complex than in the 8c−TLN complex,

and the H-bond network that water no. 3 used to participate in

(i.e., in the 8c−TLN) is disrupted (water no. 3 and water no. 4

are the ones being removed in the water displacement step of

the mutations 8c−TLN→8d−TLN and 8a−TLN→8b−TLN).

Second, the gain of ordered water molecules and the other

associated changes can be considered as compensatory changes

that occur secondary to the removal of the two water molecules

from the S2′ pocket (e.g., to partially neutralize the unfavorable

free energy of water removal from the S2′ pocket). These

compensatory changes could be mediated by the charge

redistribution that was shown by calculations to occur in the

system after the removal of the water molecules from the S2′

pocket (Figure 8). Both the COO⁻group in the 8a−TLN

complex and the water molecules which occupy the same

region in the 8c−TLN complex are involved in transmitting

this charge redistribution eﬀect through the H-bond network

they participate in. Because the COO⁻group in the 8a−TLN

complex, due to being ionized and due to having π-electrons,

could be more responsive to charge redistributions than the

water molecules in the 8c−TLN complex and in turn more

eﬃcient in relaying this eﬀect to other parts of the system, the

subsequent compensatory changes in the system might be more

prominent when the COO⁻is present than when it is absent.

More detailed computational studies are being carried out in

order to investigate this eﬀect, and their results will be reported

in due course.

ΔΔG_(H,Y→Me,Y)= ΔG_{b‐solv(H,Y→Me,Y)}+ ΔG_{b‐Me(H,Y→Me,Y)}

− ΔG_{a(H,Y→Me,Y)}

(5A)

ΔΔH_(H,Y→Me,Y)= ΔH_{b‐solv(H,Y→Me,Y)}+ ΔH_{b‐Me(H,Y→Me,Y)}

− ΔH_{a(H,Y→Me,Y)}

(5B)

−TΔΔS_(H,Y→Me,Y)

= −TΔS_{b‐solv(H,Y→Me,Y)}− TΔS_{b‐Me(H,Y→Me,Y)}

− (−TΔS_{a(H,Y→Me,Y)}

)

(5C)

What Could Cause the COO⁻to Produce This Eﬀect? To

understand why the COO⁻group is responsible for inﬂuencing

the hydration shell of the ligand−protein complex in such a way

that could produce cooperativity, we need to investigate how

the COO⁻group in the 8a−TLN complex, but not the water

molecules which occupy the same region in the 8c−TLN

complex, could cause: (1) one of the water molecules being

displaced in the ﬁrst step to have an incomplete set of H-bonds

(one H-bond less). (2) The gain of more water molecules and

the formation of a more developed H-bond network in the

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Figure 10. Thermodynamic cycle describing the mutation of the uncomplexed ligand 8a→8b or 8c→8d via two steps (I and II). Step I:

Reorganization of the hydration waters (blue) in order to create a cavity for the Me group. Step II: The replacement of H with Me to produce the

ﬁnal state of the mutation. The changes in the number of rotatable bonds as the H in 8a is replaced by Me to give 8b and as the H in 8c is replaced

by Me to give 8d are shown. The thermodynamic parameters of each step are shown on the arrow representing this particular step of the mutation.

C. The Replacement of H with Me. The ﬁnal step in this

mutation involves the replacement of the Hs of 8c and 8a with

Me groups to give the 8d−TLN and 8b−TLN complexes,

respectively (Figures 6d and 7d; corresponds to step II/Figure

5). These Me groups interact favorably with surrounding water

molecules, and to a lesser extent with the protein, through

dispersion forces. The interactions of the Me groups with their

hydrating waters can provide additional stabilization to the

heptagonal and the semicircular water structures as depicted in

Figures 6d and 7d. The Me interactions with both water and

the protein can give rise to some favorable enthalpy

(ΔH_{b‑Me(H,Y→Me,Y)}< 0). On the other hand, the H→Me

replacement is not anticipated to signiﬁcantly inﬂuence the

entropy (−TΔS_{b‑Me(H,Y→Me,Y)}≈ 0). The conformational

entropy, for instance, is not likely aﬀected by this functional

group replacement, even when the ligand acquires an additional

rotatable bond in the 8c−TLN→ 8d−TLN mutation (i.e.,

NH−CH₂CH₃). This additional rotatable bond is already

restricted as the ligand Me group is enclosed in the heptagonal

water structure shown in Figure 6d, and the H-bond network

among the water molecules of this heptagonal structure would

be greatly disrupted if this bond were to rotate freely.

It was previously mentioned that cooperativity can be caused

by the mutual reinforcement of direct ligand−protein

interactions.¹⁰Reinforcement of the Me interactions with the

protein by the COO⁻group, however, does not seem to be the

origin of the cooperativity observed in this study. There are two

reasons for this. First, the Me group has only few interactions

with the protein (i.e., 2−3 contacts within 3.6−4.3 Å, Figure 6d,

7d), and reinforcement of such few interactions would not be

anticipated to produce large cooperativity terms like those

observed here. Second, unlike the cooperativity studied in ref

10, which is proportional to the ligand−protein hydrophobic

contact, analogues for ligands 8a−d with larger side chains that

make more contacts with the protein (e.g., sec-butyl) do not

show this proportionality (some even show diminished

cooperativity).⁵⁴It can therefore be concluded that the

cooperativity observed here and that observed in ref 10 have

diﬀerent molecular origins and that the presence of the COO⁻

group does not signiﬁcantly change ΔH_{b‑Me(H,Y→Me,Y)}(i.e.,

ΔH_{b‑Me(H,COO→Me,COO)}− ΔH_{b‑Me(H,H→Me,H)}≈ 0).

2. Dissecting the Thermodynamic Parameters of Muta-

tion “a”. Even though we could attribute the cooperativity

observed in this study to changes in the ligand−protein

complex hydration waters, the unbound ligand thermodynamics

still need to be analyzed because other terms arising from such

analysis could also be implicated in the cooperative behavior

being investigated here. In this section, we dissect the

thermodynamic parameters of mutation “a” (Figure 3) into

their basic components. Mutation “a” can be achieved in two

steps as shown in Figure 10. First, water molecules reorganize

and form a small cavity capable of accommodating the Me

group that is to replace the ligand H. Water molecules at the

cavity−water interface are not capable of using their full H-

bonding capacity if some of their Hs/lone pairs of electrons

face the empty cavity and later the hydrophobic surface of the

Me group. They, consequently, tend to restrict their motions

and assume orientations that maximally preserve their H-bonds

(e.g., H-bonded to adjacent water molecules or to ligand H-

bonding group). The increase in the order of the interfacial

water molecules correlates with an unfavorable entropic change

(−TΔS_{a‑solv(H,Y→Me,Y)}> 0) and represents the basis for the

classical entropy-driven hydrophobic eﬀect. The eﬃciency in

preserving the H-bonds by increasing the order of water

molecules around a nonpolar solute largely depends on the size

and the shape of the solute. With small side chains like the Me,

H-bonds among the interfacial waters are most likely well

preserved.⁵⁵The formation of a cavity in the bulk water for the

incoming Me group is therefore anticipated to be accompanied

with little change in enthalpy (ΔH_{a‑solv(H,Y→Me,Y)}≈ 0). Given

that −TΔS_{a‑solv(H,Y→Me,Y)}> 0, and ΔH_{a‑solv(H,Y→Me,Y)}≈ 0, we can

conclude that ΔG_{a‑solv(H,Y→Me,Y)}> 0. Both the entropy and the

free energy of the formation of cavities in water were

extensively studied by Graziano and were shown to be

unfavorable.⁵⁶⁻⁵⁸

The second step in Figure 10 involves the replacement of H

with Me. This replacement produces some interactions

between the Me and the aqueous medium (e.g., dispersion

forces). This step might therefore have some negative enthalpy

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Table 3. The Enthalpic and Entropic Terms Constituting the Diﬀerential Enthalpy and the Diﬀerential Entropy, The

Anticipated Inﬂuence of the COO⁻on Each Term, And The Inﬂuence Required to Consider Such Term a Cause for the

a

Experimentally Observed Cooperativity

a

The signs shown in the table are the algebraic signs of the diﬀerence between the enthalpic, or the entropic terms, in presence and absence of the

COO⁻(e.g., (ΔH_{b‑solv(H,COO→Me,COO)}− ΔH_{b‑solv(H,H→Me,H)}). (+) increase in the thermodynamic term; (−) decrease in the thermodynamic term.

change (ΔH_{a‑Me(H,Y→Me,Y)}< 0). To investigate the entropic term

ΔΔH_(H,Y→Me,Y)= ΔH_{b(H,Y→Me,Y)}− (ΔH_{a‐solv(H,Y→Me,Y)}

associated with this step, we need to consider the inﬂuence of

+ ΔH_{a‐Me(H,Y→Me,Y)}

)

the replacement of H with Me on the ligand conformational

entropy. When H is replaced by Me in absence of the COO⁻

group (8c→8d), a larger conformational space becomes

accessible to the ligand as it acquires an additional rotatable

bond. This causes favorable entropic change

(−TΔS_{a‑Me(H,H→Me,H)}< 0). On the other hand, the replacement

of H with Me in presence of the COO⁻group (8a→8b) would

limit the ligand conformational space because: (1) No

additional rotatable bonds are acquired in presence of the

COO⁻. (2) Some of the ligand conformers become more

sterically demanding when two functional groups simulta-

neously exist at the ligand terminal end (i.e., the COO⁻and the

Me groups). Reducing the ligand conformational space in the

presence of the COO⁻correlates with an unfavorable entropic

change (−TΔS_{a‑Me(H,COO→Me,COO)}> 0) and leads us to conclude

that the COO⁻group increases −TΔS_{a‑Me(H,Y→Me,Y)}

(−TΔS_{a‑Me(H,COO→Me,COO)}− (−TΔS_{a‑Me(H,H→Me,H)}) > 0).

Whether or not this increase in −TΔS_{a‑Me(H,Y→Me,Y)}can be

one of the factors responsible for the observed entropic

cooperativity depends on how this variation aﬀects the

diﬀerential entropy. To evaluate this, the thermodynamic

parameters of mutation “a” in equation set 2 were substituted

with their basic components obtained from the dissection of

this mutation [e.g., ΔG_{a(H,Y→Me,Y)}is equal to, and can, in turn,

be substituted with (ΔG_{a‑solv(H,Y→Me,Y)}+ ΔG_{a‑Me(H,Y→Me,Y)}], and

equation set 6 was subsequently written.

(6B)

−TΔΔS_(H,Y→Me,Y)

= −TΔS_{b(H,Y→Me,Y)}− (−TΔS_{a‐solv(H,Y→Me,Y)}

− TΔS_{a‐Me(H,Y→Me,Y)}

)

(6C)

Equation 6C shows that the potential increase in

−TΔS_{a‑Me(H,Y→Me,Y)}caused by the COO⁻group decreases

−TΔΔS_(H,Y→Me,Y). Because ITC data demonstrates that

−TΔΔS_(H,Y→Me,Y)increases in presence of the COO⁻group

[−TΔΔS_{(H,COO→Me,COO)}− (−TΔΔS_(H,H→Me,H)) = 12.4 kJ/

mol], the variation in −TΔS_{a‑Me(H,Y→Me,Y)}caused by the COO⁻

group cannot be responsible for the observed entropic negative

cooperativity.

The presence of the COO⁻might also inﬂuence water

reorganization which occurs in the ﬁrst step of this mutation.

For example, the COO⁻group, being polar and ionized, might

form strong charge-assisted H-bonds with the reorganized

water molecules as well as help these water molecules to form

stronger H-bonds among themselves. This decreases

ΔH_{a‑solv(H,Y→Me,Y)}(ΔH_{a‑solv(H,COO→Me,COO)}< ΔH_{a-solv(H,H→Me,H)}).

The stronger binding experienced by these water molecules in

the presence of the COO⁻might be accompanied by additional

restriction in their motions which is reﬂected as an increase in

−TΔS_{a ‑ s ol v (H , Y → M e , Y )}(−TΔS_{a‑ so lv( H, C OO → Me , C OO )}

>

−TΔS_{a‑solv(H,H→Me,H)}). The experimentally determined enthalpic

positive cooperativity (= −15.8 kJ/mol) cannot be attributed to

the COO⁻inﬂuence on ΔH_{a‑solv(H,Y→Me,Y)}, nor can the entropic

negative cooperativity (= 12.4 kJ/mol) be attributed to the

COO⁻inﬂuence on −TΔS_{a‑solv(H,Y→Me,Y)}. This is because, as we

ΔΔG_(H,Y→Me,Y)= ΔG_{b(H,Y→Me,Y)}− (ΔG_{a‐solv(H,Y→Me,Y)}

+ ΔG_{a‐Me(H,Y→Me,Y)}

)

(6A)

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can conclude from eqs 6B and 6C, the potential decrease in

ΔH_{a‑solv(H,Y→Me,Y)}and the increase in −TΔS_{a‑solv(H,Y→Me,Y)}

caused by the COO⁻should increase ΔΔH_(H,Y→Me,Y)and

decrease −TΔΔS_(H,Y→Me,Y), respectively, not decrease

ΔΔH_(H,Y→Me,Y)and increase −TΔΔS_(H,Y→Me,Y)as we observe

in the ITC data.

ΔG _{b ‑ W d i s p ( H , H → M e , H )}= ΔH_{b ‑ W d i s p ( H , H → M e , H )}−

TΔS_{b‑Wdisp(H,H→Me,H)}; ΔH_{b‑Wdisp(H,H→Me,H)}is unfavorable but

p a r t i a l l y c o m p e n s a t e d b y t h e f a v o r a b l e

−TΔS_{b‑Wdisp(H,COO→Me,COO)}), free energy cooperativity can be

viewed as an outcome of all the enthalpy−entropy

compensation eﬀects. As these enthalpy−entropy compensa-

tions largely depend on the structural details of the system, the

type and the magnitude of the free energy cooperativity appears

to be highly context-dependent and therefore requires an in-

depth experimental and theoretical analysis of the individual

system under consideration in order to be well understood.

Table 3 summarizes the enthalpic and the entropic terms that

constitute both the diﬀerential enthalpy and the diﬀerential

entropy respectively. It also shows the inﬂuence of the COO⁻

group on each term and the kind of change that, if a term

underwent in presence of the COO⁻group, could produce the

experimentally observed cooperativity. As shown in the table,

the only enthalpic term which is inﬂuenced by the COO⁻

group in a manner clearly correlating with the experimental

enthalpic cooperativity, is the enthalpy of the modiﬁcations in

the complex hydration shell “ΔH_{b‑solv(H,Y→Me,Y)}”. The existence

of another enthalpic term (i.e., ΔH_{a‑solv(H,Y→Me,Y)}), inﬂuenced by

the COO⁻in a manner opposite to what would be contributive

to the experimentally observed cooperativity, indicates that the

inﬂuence of the COO⁻group on ΔH_{b‑solv(H,Y→Me,Y)}is large

enough to overcome this term and still produces cooperativity

(ΔH_{b‑solv(H,COO→Me,COO)}− ΔH_{b‑solv(H,H→Me,H)}≤ −15.8 kJ/mol).

The same applies to the entropy of the complex hydration shell

modiﬁcations “−TΔS_{b‑solv (H,Y→Me,Y)}” which is shown to be the

sole term whose inﬂuence by the COO⁻group can rationalize

the experimental entropic antagonism. The presence of other

terms opposing the experimental cooperativity indicates that

the inﬂuence of the COO⁻group on −TΔS_{b‑solv(H,Y→Me,Y)}is also

large enough to overcome these opposing terms and still

produces the observed 12.4 kJ/mol negative cooperativity

[−TΔS_{b‑solv(H,COO→Me,COO)}− (−TΔS_{b‑solv(H,H→Me,H)})] ≥ 12.4

kJ/mol).

It should be noted that the free energy cooperativity is the

net result of the two underlying enthalpic and entropic

cooperativities (eq 1). Even though the magnitude of each of

these cooperativities is large, the free energy cooperativity is

comparatively smaller because the enthalpic and the entropic

cooperativities in part compensate each other. Because the

magnitude of the enthalpic positive cooperativity is larger than

that of the entropic negative cooperativity, the free energy

shows positive cooperativity. It is not necessary, however, for

the enthalpic cooperativity to be the favorable cooperativity

term or to be greater than the entropic cooperativity. The kind,

as well as the magnitude, of cooperativity is highly dependent

on the structural details of the system and on how this system

responds to the structural perturbations being studied. This

indicates that in other ligand−protein binding cases the free

energy cooperativity could be positive, negative, or nonexistent

(i.e., additivity) depending upon the details.

free energy cooperativity

= ΔΔG_{(H,COO→Me,COO)}− ΔΔG_(H,H→Me,H)

= ΔG_{b‐solv(H,COO→Me,COO)}− ΔG_{b‐solv(H,H→Me,H)}

= ΔG_{b‐Wdisp(H,COO→Me,COO)}− ΔG_{b‐Wdisp(H,H→Me,H)}

+ ΔG_{b‐Wstrct(H,COO→Me,COO)}− ΔG_{b‐Wstrct(H,H→Me,H)}

(7)

CONCLUSIONS

■

In this study, we have demonstrated that the contribution of

the Me side chain, which binds in the thermolysin S2′ pocket,

to the ligand binding aﬃnity can be enhanced by about an

order of magnitude in the presence of a ligand COO⁻group

(positive cooperativity). This positive cooperativity is the net

result of a large favorable enthalpic cooperativity term (−15.8

kJ/mol) and a smaller unfavorable entropic cooperativity term

(12.4 kJ/mol). To determine the origin of these individual

cooperativities, the diﬀerential thermodynamic parameters of

the Me group, in the absence and presence of the COO⁻group,

were dissected into fundamental components, and the inﬂuence

of the COO⁻on each of these components was investigated.

An approach based on investigating the mutations of 8a and 8c

to 8b and 8d, respectively, in both the enzyme-bound and the

unbound states, was used to achieve this.

The crystallographic data of the 8a−, 8b−, 8c−, and 8d−

thermolysin complexes were used to compare the structural

changes occurring in the complex when the Me group is

introduced into the ligand in the absence of the COO⁻group,

with the changes occurring when this group is introduced into

the ligand in presence of the COO⁻. This comparison revealed

that the changes occurring in the hydration shell of the complex

(e.g., displacement of two water molecules from the S2′ pocket

and acquisition of others at new sites) in the presence of the

COO⁻group are more enthalpically, and less entropically,

favorable than those occurring in absence of this group. For

example, with regard to the enthalpically favorable, entropically

unfavorable acquisition of new crystallographic waters by the

complex, the presence of the COO⁻causes the complex to

acquire more of these waters and to form a more extensive H-

bond network characterized by enhanced σ-bond cooperativity.

This correlates with the improved diﬀerential enthalpy and the

worsened diﬀerential entropy observed in the ITC data when

the COO⁻is present.

Another aspect which greatly adds to the intricacy of the free

energy cooperativity evaluation is that this cooperativity is

produced by multiple enthalpy−entropy compensation eﬀects.

Each of these eﬀects yields a free energy term that contributes

to the overall free energy cooperativity. To illustrate this, the

inﬂuence of the COO⁻group in question on the diﬀerential

binding energy components is assumed to be negligible except

for ΔG_{b‑solv(H,Y→Me,Y)}which is composed of ΔG_{b‑Wdisp(H,Y→Me,Y)}

and ΔG_{b‑Wstruct(H,Y→Me,Y)}. Upon the basis of this assumption,

and using eqs 2A and 3A, eq 7, which shows the free energy

terms contributing to cooperativity, can be derived (for detailed

derivation, see Supporting Information). Because each of the

four free energy terms in eq 7 represents the net eﬀect of an

enthalpy−entropy compensation relationship (e.g.,

In addition, a smaller enthalpic penalty, and a reduced

entropic advantage, for the displacement of two water

molecules from the S2′ pocket, in the presence of the COO⁻

group, were indicated to contribute to the positive enthalpic

and the negative entropic cooperativities, respectively. Both

structural data and calculation results were found to support

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Laboratories, Inc. (Andover, MD) on one of the following

instruments: Varian Gemini 300 MHz, Varian Inova 400 MHz, or

Varian Inova 500 MHz. H NMR data is reported in the following

this smaller enthalpic penalty, which is accompanied by the

smaller entropic advantage. For example, crystal structures

reveal that the COO⁻group causes one of the two displaced

waters to form one less H-bond than what it forms in the

absence of this group. The COO⁻of 8a also interferes with the

interconnectedness of the active site H-bond network, causing

an enthalpic destabilization of the S2′ water molecules as well

as the other waters in the active site. The thermodynamic

implications of these data are consistent with the results of the

QM calculations of the interaction energies of the two displaced

waters in model systems representing the 8a−TLN and 8c−

TLN complexes. Such calculations showed that these waters

have weaker interactions in presence of the COO⁻. Enthalpi-

cally less-stabilized waters like those in 8a−TLN are likely to

have a higher degree of mobility, which is reﬂected as a

decrease in the entropic advantage of water displacement from

the 8c−TLN S2′ pocket.

1

format: chemical shift (ppm values in relation to TMS or appropriate

solvent peak), multiplicity (s = singlet, d = doublet, t = triplet, q =

quartet, dd = doublet of doublets, d of t = doublet of triplets, complex

= combinations of peaks resulting from diﬀerent molecular

conformations, m = multiplet, br = broad peak) coupling constant(s),

and integration. Low resolution ESI mass spectrometry was performed

on a Thermo Finnigan LCQ Advantage instrument using 60%

methanol in water with 1% acetic acid or 60% acetonitrile in water

with 0.1% triﬂuoroacetic acid as the mobile phase. Preparative and

semipreparative HPLC instrumentation included a Milton Roy

gm4000 gradient programmer, Milton Roy Constametric I and III

pumps, a Rheodyne 7125 injector with a 5.00 mL sample loop, and a

Knauer variable wavelength detector set at 218 nm with a preparative

ﬂow cell. All ﬁnal compounds tested were at least 95% pure by HPLC

analysis.

Synthesis of Benzyl N-(Hydroxymethyl) Carbamate (1):²³Benzyl

carbamate (6 g, 40 mmol) was added to a solution of 37% formalin

(4.4 g, 56 mmol) and sodium carbonate (2.2 g, 20 mmol) in 65 mL of

water. The mixture was heated until all the solids were dissolved and

then cooled to room temperature and stirred overnight. The

precipitated solid was then ﬁltered, dried, and redissolved in

dichloromethane. The solution was dried using anhydrous magnesium

sulfate, and the solvent was removed under vacuum to give the

product as a white solid, which was used in the next step without

It was also revealed in the current study that cooperativity

among ligand functional groups can be more intricate than

what might have been appreciated in the past. This is because

the binding free energy is determined by a complex interplay

among a number of enthalpy−entropy compensation eﬀects.

Consequently, ligand functional group cooperativity can be

highly dependent on the structural details of the system being

investigated and on how this system responds to structural

perturbations in the ligand. Cooperativity might therefore be

positive, negative, or nonexistent.

1

further puriﬁcation (5.40 g, 74.6%). H NMR (CDCl₃-d) δ 4.10 (s,

1H), 4.71 (d, J = 6.5 Hz, 2H), 5.13 (s, 1H), 6.07 (s, 1H), 7.36 (s, 5H).

m/z (LCMS, ESI): found 181.2 [M + H]⁺, C₉H₁₁NO₃requires 180.1.

Synthesis of Benzyl N-(Acetoxymethyl) Carbamate (2). Com-

pound 1 (3.62 g, 20 mmol) was dissolved in 25 mL of anhydrous THF

and was added slowly to an ice-cooled stirred solution of 23 mL of

acetic anhydride and 6.5 mL of anhydrous pyridine under argon. The

mixture was stirred at rt for 2 h, and then the solution was diluted with

150 mL of ethyl acetate and washed with 1N HCl (3× 150 mL) and

brine (2× 150 mL). The organic layer was dried with anhydrous

magnesium sulfate, and the volatile materials were removed under

vacuum to give an oily residue, which was puriﬁed with ﬂash

chromatography (2.95 g, 66.1%) of the pure product. ¹H NMR

(CDCl₃-d₁) δ 2.08 (s, 3H), 5.16 (s, 2H), 5.23 (d, J = 7.5 Hz, 2H), 6.08

(s, 1H), 7.38 (s, 5H). m/z (LCMS, ESI): found 246.0 [M + Na]⁺,

C₁₁H₁₃NO₄requires 223.1.

To the best of our knowledge, this is the ﬁrst time water

molecules within binding cavities have been shown to be

involved in cooperativity among ligand functional groups.

Snyder et al., though, suggested that changes in binding aﬃnity

among closely related analogues can be signiﬁcantly inﬂuenced

by changes in the number and organization of water molecules

localized in and beyond the active site in the bound complex.⁹

Studies like the one presented herein can set the stage and

provide direction for more in-depth experimental and

theoretical studies which may further analyze and better

quantify the contributions of the individual thermodynamic

factors to the relative binding and the SARs in ligand congener

series. Some of the general considerations suggested by this

study are: (1) High-resolution crystal structures for the

complexes of closely related analogues (e.g., congeneric ligand

series) can reveal important changes in the complex hydration

shell that might occur when the ligand structure is modiﬁed.

(2) These hydration shell changes can have a signiﬁcant eﬀect

on the thermodynamic parameters of binding as determined by

ITC. (3) Changes in the hydration water of the ligand−protein

complex can produce cooperativity among ligand side chains.

(4) The consideration of the changes of the water structures, in

response to ligand structural modiﬁcation, can assist SARs

analyses and contribute to a better understanding of the

underlying science of ligand−protein binding. This enhanced

fundamental understanding may be useful for improving the

accuracy of scoring functions in predicting binding aﬃnity.

Synthesis of Dimethyl N-Benzyloxycarbonyl-aminomethyl-phos-

phonate (3). A mixture of compound 2 (2.90 g, 13 mmol) and

trimethylphosphite (4.6 mL, 39 mmol) was reﬂuxed for 3 h. The

volatile materials were removed by distillation at 60 °C under reduced

pressure to give the product as an oily residue, which was used in the

next step without further puriﬁcation (3.44 g, 97.5%). ¹H NMR

(CDCl₃-d₁) δ 3.62 (dd, J = 6.5 Hz, J_H−P= 11 Hz, 2H), 3.72 (d, J_H−P

=

11 Hz, 6H), 5.09 (s, 2H), 5.83 (s, 1H), 7.32 (m, 5H). ³¹P NMR

(CDCl₃-d₁) δ 25.32, m/z (LCMS, ESI): found 296.1 [M + Na]⁺,

C₁₁H₁₆NO₅P requires 273.1.

Synthesis of Methyl N-Benzyloxycarbonyl-aminomethyl-phos-

phonate (4). Compound 3 (3.28 g, 12 mmol) was shaken vigorously

with 10% NaOH (14.5 mL, 3 equiv) until it was completely dissolved.

The mixture was stirred at room temperature for 2 h, then diluted with

water, extracted with ethyl acetate (2× 30 mL), and acidiﬁed to pH 1

with 2N HCl. The aqueous solution was extracted with dichloro-

methane (2× 100 mL) and ethyl acetate (2× 50 mL). The

dichloromethane layers were combined, washed with brine (2× 50

mL), and dried using anhydrous magnesium sulfate. The ethyl acetate

layers were also combined, washed with brine (2× 25 mL), and dried

with anhydrous magnesium sulfate. The organic layers were then

combined, and the volatile solvents were removed under high vacuum

EXPERIMENTAL SECTION

■

Chemistry. General Methods. Reagents were obtained from

commercial suppliers and used without further puriﬁcation. Anhydrous

solvents were purchased as sealed bottles from either Fisher-Acros

(AcroSeal) or Aldrich (Sure-Seal) and were maintained under an

argon atmosphere. All amino acids used are ^Lunless otherwise noted.

Proton, phosphorus, and carbon nuclear magnetic resonance was

performed in deuterated solvents purchased from Cambridge Isotope

1

to give the product as a pure white solid (2.26 g, 72.7%). H NMR

(CDCl₃-d₁) δ 3.64 (d, J_H−P= 11 Hz, 2H), 3.71 (d, J_H−P= 11 Hz, 3H),

5.12 (s, 2H), 5.7 (br s, 1H), 7.35 (m, 5H), 11.8 (br s, 1H). ³¹P NMR

(CDCl₃-d₁) δ 24.12, m/z (LCMS, ESI): found 282.1 [M + Na]⁺,

C₁₀H₁₄NO₅P requires 259.1.

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General Procedure for Amide Coupling; Compounds 5a−d. To a

cooled solution of the carboxylic acid (1 equiv), the amine/amino acid

HCl (1.5 equiv) and PyBop (1.2 equiv) in anhydrous DMF was added

diisopropylethylamine (4 equiv) gradually. The reaction mixture was

stirred at rt for 2−5 h, diluted with ethyl acetate (50 mL for every 5

mL of DMF), then extracted with 1N HCl (3×), saturated sodium

bicarbonate (3×), and brine (2×). The organic layer was then dried

with anhydrous sodium sulfate, and the solvent was evaporated under

vacuum to give the products which were puriﬁed by ﬂash

chromatography.

(N-(tert-Butoxycarbonyl)-^L-leucinyl)-glycine Ethyl Ester (5a).

Using the above procedure, Boc-^L-leucine (2.5 mmol, 579 mg) was

reacted with glycine ethyl ester HCl (3.75 mmol, 524 mg) to give

compound 5a (603 mg, 76.3%). ¹H NMR (DMSO-d₆) δ 0.86 (d, J = 7

Hz, 3H), 0.88 (d, J = 7 Hz 3H), 1.19 (t, J = 7 Hz, 3H), 1.38 (s, 9H),

1.43 (t, J = 7.5 Hz, 2H), 1.58−1.66 (m, 1H), 3.76 (dd, J = 17, 6 Hz,

1H), 3.87 (dd, J = 17, 6 Hz, 1H), 4.01 (q, J = 7 Hz, 1H), 4.08 (q, J = 7

Hz, 2H), 6.89 (d, J = 8.5 Hz, 1H), 8.21 (t, J = 6 Hz, 1H). m/z (LCMS,

ESI): found 339.1 [M + Na]⁺, C₁₅H₂₈N₂O₅requires 316.2.

(N-(tert-Butoxycarbonyl)-^L-leucinyl)-alanine Methyl Ester (5b).

Using the above procedure, Boc-^L-leucine (2.5 mmol, 579 mg) was

reacted with alanine methyl ester HCl (3.75 mmol, 524 mg) to give

compound 5b (578 mg, 73.1%). ¹H NMR (DMSO-d₆) δ 0.86 (d, J = 7

Hz, 3H), 0.88 (d, J = 7 Hz 3H), 1.28 (d, J = 7 Hz, 3H), 1.37 (s, 9H),

1.39 (t, J = 7.5 Hz, 2H), 1.58−1.66 (m, 1H), 3.61 (s, 3H), 3.99 (q, J =

7 Hz, 1H), 4.26 (m, 1H), 6.82 (d, J = 8.5 Hz, 1H), 8.21 (d, J = 7 Hz,

1H). m/z (LCMS, ESI): found 339.1 [M + Na]⁺, C₁₅H₂₈N₂O₅

requires 316.2.

2H), 1.60 (m, 1H), 2.65 (d, J = 5 Hz, 3H), 3.70 (t, J = 8 Hz, 1H), 8.29

(br, 3H), 8.64 (q, J = 4 Hz, 1H). m/z (LCMS, ESI): found 289.0 [2M

+ H]⁺, C₇H₁₆N₂O requires 144.1.

N′-Ethyl-^L-leucinamide Hydrochloride (6d). Compound 5d (400

mg, 1.55 mmol) was converted to 6d using 3N HCl/MeOH as

described in the above procedure (297 mg, 98.5%). ¹H NMR (DMSO-

d₆) δ 0.93 (d, J = 6.5 Hz, 3H), 0.95 (d, J = 6.5 Hz, 3H), 1.10 (t, J = 7

Hz, 3H), 1.59 (t, J = 7 Hz, 2H), 1.67 (m, 1H), 3.10−3.25 (m, 2H),

3.72 (t, J = 8 Hz, 1H), 8.31 (br, 3H), 8.68 (t, J = 4 Hz, 1H). m/z

(LCMS, ESI): found 339.0 [2 M + Na]⁺, C₈H₁₈N₂O requires 158.1.

General Procedure for the Synthesis of Compounds 7a−d: To a

cooled solution of (4), 6a−d (1.5 equiv) and PyBop (1.2 equiv) in

anhydrous DCM was added diisopropylethylamine (4 equiv)

gradually. The reaction mixture was stirred at rt for 6 h to overnight.

The reaction mixture was then diluted up to 25 mL DCM, extracted

with 5% citric acid (2× 12 mL), saturated sodium bicarbonate (2× 12

mL), and brine (2× 10 mL) and dried over anhydrous sodium sulfate.

The solvent was then evaporated under reduced pressure, and the

residue was puriﬁed by semipreparative HPLC.

Ethyl-N-(N-(N-(benzyloxycarbonyl)-(R/S)-aminomethylphos-

phonyl)-^L-leucinyl)-glycinate Methyl Ester (7a). Compound 4 (0.5

mmol, 130 mg) was reacted with 6a (0.75 mmol, 190 mg) according

to the general procedure described above (PyBop: 0.6 mmol, 312 mg.

DIEA: 2 mmol, 0.35 mL.) to give 7a as two diastereomers with an

approximate ratio of 3:2 as determined by ³¹P NMR (153 mg, 66.8%).

¹H NMR (CDCl₃) δ 0.90−0.98 (complex, 6H), 1.23 and 1.26 (2t, J =

7 Hz, 3H), 1.52−1.63 (m, 2H), 1.76 (m, 1H), 3.45−4.05 (complex,

9H), 4.14 and 4.16 (2q, J = 7 Hz, 2H), 5.10 (complex, 2H), 5.97 and

6.10 (2 × br, 1H), 7.34 (m, 5H), 7.75 and 7.80 (complex, 1H). ³¹P

NMR (CDCl₃) δ 27.69 and 28.50 (approximately 3:2). m/z (LCMS,

ESI): found 480.2 [M + Na]⁺, C₂₀H₃₂N₃O₇P requires 457.2.

Methyl-N-(N-(N-(benzyloxycarbonyl)-(R/S)-aminomethylphos-

phonyl)-^L-leucinyl)-alaninate Methyl ester (7b). Compound 4 (0.5

mmol, 130 mg) was reacted with 6b (0.75 mmol, 190 mg) according

to the general procedure described above (PyBop: 0.6 mmol, 312 mg.

DIEA: 2 mmol, 0.35 mL.) to give 7b as two diastereomers with an

approximate ratio of 3:2 as determined by ³¹P NMR (134 mg, 58.5%).

¹H NMR (CDCl₃) δ 0.90−0.96 (complex, 6H), 1.36 and 1.38 (2d, J =

7 Hz, 3H), 1.49−1.60 (m, 2H), 1.75 (m, 1H), 3.40−4.15 (complex,

9H), 4.50 (m, 1H), 5.10 (complex, 2H), 6.01 and 6.15 (2 × br, 1H),

7.33 (m, 5H), 7.62 and 7.67 (2d, J = 7 Hz, 1H). ³¹P NMR (CDCl₃) δ

27.61 and 28.04 (approximately 3: 2). m/z (LCMS, ESI): found 480.2

[M + Na]⁺, C₂₀H₃₂N₃O₇P requires 457.2.

N-(N-(Benzyloxycarbonyl)-(R/S)-aminomethylphosphonyl)-N′-

methyl-^L-leucinamide Methyl Ester (7c). Compound 4 (0.5 mmol,

130 mg) was reacted with 6c (0.75 mmol, 135 mg) according to the

general procedure described above (PyBop: 0.6 mmol, 312 mg. DIEA:

2 mmol, 0.35 mL.) to give 7c as two diastereomers with an

approximate ratio of 3:2 as determined by ³¹P NMR (138 mg, 71.6%).

¹H NMR (CDCl₃) δ 0.93 (complex, 6H), 1.44−1.64 (m, 2H), 1.65−

1.80 (m, 1H), 2.75 and 2.77 (2d, J = 5 Hz, 3H), 3.40−3.95 (complex,

7H), 5.10 (complex, 2H), 5.96 (br, 1H), 7.087 and 7.17 (2t, J = 5 Hz,

1H), 7.35 (m, 5H). ³¹P NMR (CDCl₃) δ 27.89 and 28.21

(approximately 3:2). m/z (LCMS, ESI): found 408.1 [M + Na]⁺,

C₁₇H₂₈N₃O₅P requires 385.2.

N-(N-(Benzyloxycarbonyl)-(R/S)-aminomethylphosphonyl)-N′-

ethyl-^L-leucinamide Methyl Ester (7d). Compound 4 (0.5 mmol, 130

mg) was reacted with 6d (0.75 mmol, 146 mg) according to the

general procedure described above (PyBop: 0.6 mmol, 312 mg. DIEA:

2 mmol, 0.35 mL.) to give 7d as two diastereomers with an

approximate ratio of 3:2 as determined by ³¹P NMR (93 mg, 46.7%).

¹H NMR (CDCl₃) δ 0.97 (complex, 6H), 1.13 and 1.16 (2d, J = 6.5

N′-methyl-N-(tert-Butoxycarbonyl)-^L-leucinamide (5c). Using the

above procedure, Boc-^L-leucine (2.5 mmol, 579 mg) was reacted with

methylamine HCl (3.75 mmol, 253 mg) to give compound 5c (473

mg, 77.4%). ¹H NMR (DMSO-d₆) δ 0.85 (d, J = 6.5 Hz, 3H), 0.88 (d,

J = 6.5 Hz, 3H), 1.39 (s, 9H), 1.30−1.45 (m, 2H), 1.57 (m, 1H), 2.58

(d, J = 4 Hz, 3H), 3.92 (m, 1H), 6.82 (d, J = 8.5 Hz, 1H), 7.75 (q, J =

3.5 Hz, 1H). m/z (LCMS, ESI): found 267.1 [M + Na]⁺, C₁₂H₂₄N₂O₃

requires 244.2.

N′-Ethyl-N-(tert-butoxycarbonyl)-^L-leucinamide (5d). Using the

above procedure, Boc-^L-leucine (2.5 mmol, 579 mg) was reacted with

ethylamine HCl (3.75 mmol, 306 mg) to give compound 5d (416 mg,

1

64.5%). H NMR (DMSO-d₆) δ 0.89 (d, J = 6 Hz, 3H), 0.91 (d, J =

6.5 Hz, 3H), 1.04 (t, J = 7 Hz, 3H), 1.42 (s, 9H), 1.36−1.46 (m, 2H),

1.61 (m, 1H), 3.04−3.15 (m, 3H), 3.93 (m, 1H), 6.82 (d, J = 8.5 Hz,

1H), 7.75 (t, J = 3.5 Hz, 1H). m/z (LCMS, ESI): found 281.1 [M +

Na]⁺, C₁₃H₂₆N₂O₃requires 258.2.

General Procedure for Boc Deprotection: Compounds 6a−d. The

Boc-protected compound was dissolved either in 3N HCl/MeOH or

in ethyl acetate. When the compound was dissolved into ethyl acetate,

HCl gas was bubbled into the solution. The solution was stirred for

1.5−2 h. The volatile materials were removed under vacuum to give

the product as hygroscopic solid, which was puriﬁed with semi-

preparative HPLC.

L-Leucinyl-glycine Ethyl Ester Hydrochloride (6a). Compound 5a

(554 mg, 1.75 mmol) was converted to 6a using HCl/ethyl acetate as

described in the above procedure (426 mg, 99.1%). ¹H NMR (DMSO-

d₆) δ 0.90 (d, J = 7 Hz, 3H), 0.92 (d, J = 7 Hz 3H), 1.19 (t, J = 7 Hz,

3H), 1.59 (m, 2H), 1.77 (m, 1H), 3.81 (t, J = 7 Hz, 1H), 3.83 (dd, J =

17, 5.5 Hz, 1H), 3.98 (dd, J = 17, 5.5 Hz, 1H), 4.00 (d of q, J = 7, 2

Hz, 2H), 8.42 (br, 3H), 9.17 (t, J = 6 Hz, 1H). m/z (LCMS, ESI):

found 217.0 [M + H]⁺, C₁₀H₂₀N₂O₃requires 216.1.

L-Leucinyl-alanine Methyl Ester Hydrochloride (6b). Compound

5b (554 mg, 1.75 mmol) was converted to 6b using 3N HCl/MeOH

as described in the above procedure (408 mg, 95.0%). ¹H NMR

(DMSO-d₆) δ 0.90 (d, J = 6 Hz, 3H), 0.93 (d, J = 6.5 Hz 3H), 1.33 (d,

J = 7 Hz, 3H), 1.57 (m, 2H), 1.73 (m, 1H), 3.64 (s, 3H), 3.77 (t, J = 7

Hz, 1H), 4.35 (m, 1H), 8.29 (br, 3H), 9.01 (d, J = 6.5 Hz, 1H). m/z

(LCMS, ESI): found 217.1 [M + H]⁺, C₁₀H₂₀N₂O₃requires 216.2.

N′-Methyl-^L-leucinamide Hydrochloride (6c). Compound 5c (428

mg, 1.75 mmol) was converted to 6c using 3N HCl/MeOH as

Hz, 3H), 1.46−1.66 (m, 2H), 1.67−1.82 (m, 1H), 3.25 (complex,

2H), 3.40−4.1 (complex, 7H), 5.16 (complex, 2H), 6.05 (br, 1H),

7.14 and 7.22 (2t, J = 5 Hz, 1H), 7.38 (m, 5H). ³¹P NMR (CDCl₃) δ

27.80 and 28.20 (approximately 3:2). m/z (LCMS, ESI): found 422.1

[M + Na]⁺, C₁₈H₃₀N₃O₅P requires 399.2.

General Procedure for the Synthesis of Compounds 8a−d. 0.2

mmol of the phosphonamidate ester (7a−d) was vigorously shaken at

rt with 1−2 mL of 0.4 M LiOH aqueous solution until all the solid

1

described in the above procedure (313 mg, 99%). H NMR (DMSO-

d₆) δ 0.88 (d, J = 6 Hz, 3H), 0.90 (d, J = 6 Hz, 3H), 1.55 (t, J = 7 Hz,

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Journal of Medicinal Chemistry

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dissolved (acetonitrile was used as a cosolvent whenever needed). The

solution was stirred for 2−24 h and concentrated under reduced

pressure. The ﬁnal compound was then separated as a pure mono- or

dilithium salt using semipreparative HPLC.

complexes. Each of these model systems consisted of the terminal part

of the ligand, the part of the protein that directly interacts with the

chosen part of the ligand and a number of the crystallographic water

molecules that solvate the part of the ligand−protein complex that was

included in the model. Water molecules were chosen in such a way

that important water polygonal and chain structures were kept intact.

The two water molecules that are displaced by the Me group were

included. Each model consisted of about 100 atoms in total. The

positions of the hydrogen atoms were added manually and further

optimized with DFT/B3LYP method⁴⁷⁻⁴⁹with 3-21G basis. The

positions of all the heavy atoms except the two water molecules

displaced by the methyl were constrained in the original positions of

the crystal structure during the DFT optimization. After geometry

optimizations, a duplicate pdb ﬁle was generated for each model, and

the two water molecules displaced by the Me group were removed

from that second ﬁle. The total energies of the four models and their

Mulliken electronic charges were calculated with B3LYP functional

with dispersion correction using the exchange-dipole moment

method^63,64and triple-ζ cc-pVTZ basis.⁵⁰The total energies of the

removed water molecules were similarly calculated. Values of the

calculated total energies and interaction energies are provided in Table

2 in the Supporting Information. Calculations were done using Q-

Chem Program.⁶⁵

N-(N-(N-(Benzyloxycarbonyl)-aminomethylphosphonyl)-^L-leucin-

yl)-glycinate Dilithium (8a). Compound 7a (91 mg, 0.2 mmol) was

reacted with 4 equiv LiOH (2 mL of 0.4 M aqueous solution) for 6 h

to give 8a as dilithium salt (72 mg, 81.8%). ¹H NMR (D₂O) δ 0.73 (d,

J = 6.5 Hz, 3H), 0.74 (d, J = 6.5 Hz, 3H), 1.33 (m, 2H), 1.55 (m, 1H),

3.13 (complex, 2H), 3.50−3.65 (complex, 3H), 4.97 (complex, 2H),

7.26 (m, 5H). ¹³C NMR (D₂O) δ 21.08, 22.42, 23.99 (3C,

CH(CH₃)₂), 38.90 and 40.71 (d, J_C−P∼ 543 Hz, 1C, CH₂P), 43.15,

43.29 (2C, CH₂CH(CH₃)₂and CH₂COO), 54.16 (1C, CHCO),

67.16 (1C, PhCH₂O−), 127.82, 128.42, 128.83, and 136.43 (6C, Ph),

158.31 (1C, Cbz C=O), 176.39 and 177.93 (2C, 2CO). ³¹P NMR

(D₂O) δ 17.56. m/z (LCMS, ESI): found 434.1[M + Li]⁺and 466.1

[M − Li + 2Na]⁺, C₁₇H₂₄N₃O₇PLi₂requires 427.2.

N-(N-(N-(Benzyloxycarbonyl)-aminomethylphosphonyl)-^L-leucin-

yl)-alaninate di-Lithium (8b). Compound 7b (91 mg, 0.2 mmol) was

reacted with 4 equiv LiOH (2 mL of 0.4 M aqueous solution) for 5 h

1

to give 8b as dilithium salt (72 mg, 81.8%). H NMR (D₂O) δ 0.73

(complex, 6H), 1.17 (d, J = 7.5 Hz, 3H), 1.26−1.36 (m, 2H), 1.53 (m,

1H), 3.13 (complex, 2H), 3.50 (q, J = 5 Hz, 1H), 3.97 (q, J = 7 Hz,

1H), 4.97 (complex, 2H), 7.28 (m, 5H). ³¹P NMR (D₂O) δ 17.57. m/

z (LCMS, ESI): found 436.1[M − Li + 2H]⁺and 442.1 [M+ H]⁺,

C₁₈H₂₆N₃O₇PLi₂requires 441.2.

ITC and X-ray Crystallography Data. Experimental details of

ITC and X-ray crystallography will be published elsewhere by Biela, A.

et al.²⁵

N-(N-(Benzyloxycarbonyl)-aminomethylphosphonyl)-N′-methyl-

L-leucinamide Lithium (8c). Compound 7c (77 mg, 0.2 mmol) was

reacted with 2 equiv LiOH (1 mL of 0.4 M aqueous solution) for 2 h

ASSOCIATED CONTENT

* Supporting Information

■

S

1

to give 8c as monolithium salt (68.5 mg, 90.7%). H NMR (D₂O) δ

A table containing the computational data used to calculate the

interaction energies of the S2′ water molecules in the complex

before their displacement, another table containing the

crystallographic data used to calculate the water gain/loss

indexes of the mutations discussed in this paper, and a ﬁgure

corresponding to Figures 6c and Figure 7c providing details

about how water bridges were counted. Mathematical

derivations for equation 7 are also provided. This material is

available free of charge via the Internet at http://pubs.acs.org.

0.72 (complex, 6H), 1.2−1.4 (m, 2H), 1.49 (m, 1H), 2.55 (s, 3H),

3.12 (complex, 2H), 3.47 (m, 1H), 4.98 (complex, 2H), 7.29 (m, 5H).

¹³C NMR (D₂O) δ 22.599, 23.78, and 25.52 (3C, CH(CH₃)₂), 27.21

(1C, −NHCH₃), 40.29 and 42.09 (2 × d, J_C−P∼ 540 Hz, 1C, CH₂P),

44.63 and 44.69 (1C, CH₂CH(CH₃)₂), 55.65 (1C: CHCONH−),

68.59 (1C, PhCH₂O−), 129.28, 129.85, 130.23, and 137.87 (6C, Ph),

159.72 (1C, Cbz CO), 180.11 (1C, CO). ³¹P NMR (D₂O) δ

17.40. m/z (LCMS, ESI): found 384.2 [M + Li]⁺and 761.3 [2M +

Li]⁺, C₁₆H₂₅N₃O₅PLi requires 377.2.

N-(N-(Benzyloxycarbonyl)-aminomethylphosphonyl)-N′-ethyl-^L-

leucinamide Lithium (8d). Compound 7d (80 mg, 0.2 mmol) was

reacted with 2 equiv LiOH (1 mL of 0.4 M aqueous solution) for 24 h

to give 8d as monolithium salt (47 mg, 60%). ¹H NMR (D₂O) δ 0.73

(complex, 6H), 0.93 (t, J = 7 Hz, 3H), 1.2−1.4 (m, 2H), 1.48 (m, 1H),

3.00 (complex, 2H), 3.11 (complex, 2H), 3.46 (m, 1H), 4.97

(complex, 2H), 7.28 (m, 5H). ³¹P NMR (D₂O) δ 17.29. m/z (LCMS,

ESI): found 408.1[M − Li + Na + H]⁺, C₁₇H₂₇N₃O₅PLi requires 391.2

Biological Assay. The inhibition constants of the thermolysin

phosphonamidate inhibitors 8a−d were determined photometrically at

345 nm using 2-furanacryloyl-Gly-Leu-NH₂as a substrate.²⁴The assay

was carried out on a Cary 100/300 UV/vis spectrophotometer at 25.0

0.2 °C. A 0.05 M Tris buﬀer containing 0.02 M CaCl₂, 2.5 M

NaBr,¹⁶and 1.25% DMF was used in all measurements. Buﬀer pH was

AUTHOR INFORMATION

Corresponding Author

■

*Correspondence regarding the synthesis, the kinetic assay, and

the interpretation of the experimental data should be addressed

to either N.N. at nnnasief@yahoo.com, or D.H. at hangauer@

bu ﬀ alo.edu, phone 716-645-4183. Correspondence regarding

the computational data should be addressed to J.K. at jkong@q-

chem.com.

Author Contributions

N.N. and D.H. contributed the design of the project, the

synthesis of the compounds, the kinetic assay and the

interpretation of the experimental data. N.N. was the ﬁrst to

propose the dissection of the diﬀerential thermodynamic

parameters through theoretical mutations. H.T. and J.K.

contributed the computational data and their interpretation.

The use of the computational data to support the conclusions

of this paper was mutually done by all authors.

adjusted to 7.3

0.5 at room temperature prior to use. The

concentration of the enzyme stock solution was determined by UV

absorbance at 280 nm (ε1% = 17.65 cm⁻¹).⁵⁹The concentrations of

the stock solutions of the substrate and the inhibitors were determined

based on accurately weighed samples. The enzyme concentration in all

the ﬁnal assay solutions was approximately 8 nM, the substrate

concentration in the ﬁnal assay solutions was 0.8 M, and the inhibitors’

concentrations were in the range of 0.5−10 K_ifor each inhibitor. The

inhibition constant (K_i) for the inhibitor was taken to be the average of

at least three K_ideterminations, each of which was calculated from the

experimentally determined IC₅₀using Cheng−Prusoﬀ equation⁶⁰(K_m

= 3.9 0.6 mM). The IC₅₀values were determined from υ₀/υ_ivs [I]

plots^16,61for inhibitors 8a, 8c, and 8d (υ₀/υ_i= [I]/IC₅₀+ 1) or

Henderson plots⁶²for inhibitor 8b (at least six diﬀerent inhibitor

concentrations [I] were used to construct each plot).

Notes

The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENTS

■

We kindly acknowledge Adam Biela, Michael Betz, Andreas

Heine, and Prof. Gerhard Klebe, the Department of

Pharmaceutical Chemistry, Philipps University Marburg,

Germany, for making the ITC values and the crystal structures

3T8G, 3T74, 3T73, and 3T8F available to use prior to

Quantum Mechanical Calculations. Two model systems were

built from the X-ray crystal structures of 8c−TLN and 8a−TLN

8300

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Journal of Medicinal Chemistry

Article

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(25) At the time of the initial submission of this paper, details of the

ITC and the crystallographic data were intended to be submitted

elsewhere by Biela, A., et al.; and while this paper was in the peer-

review stage, the paper which includes these data was submitted and

published in: Biela, A.; Betz, M.; Heine, A.; Klebe, G. Water Makes

the Difference: Rearrangement of Water Solvation Layer Triggers

Nonadditivity of Functional Group Contributions in Protein−Ligand

Binding. ChemMedChem 2012, 7, 1423−1434.

publication. This project was designed, and the hypothesis to

be tested was put forth by N.N. and D.H. The compounds were

synthesized, and the kinetic assay was run by N.N. under the

supervision of D.H. These compounds were sent to Prof. G.

Klebe’s lab for ITC and crystal structures. The complete set of

data, including ITC and crystal structures, was initially and

independently analyzed by N.N. and D.H., and initial drafts of

this manuscript, all of which proposed the involvement of water

in the observed cooperativity, were shared with Prof. G. Klebe’s

lab prior to their analysis of the data, and prior to the

preparation of their manuscript. Although, Prof. Klebe’s lab was

in agreement with our overall conclusions, they analyzed the

data diﬀerently, and it was therefore mutually agreed that the

two research groups should publish separately. Both groups

provided each other with their submitted manuscripts in the

spirit of a good collaboration. H.T. and J.K. contributed the

computational data and their interpretation. The use of the

computational data to support the conclusions of this paper was

mutually done by all authors. The computational part of the

work was supported by National Institutes of Health through a

grant (R44GM084555).

ABBREVIATIONS USED

■

Boc: tert-butyloxycarbonyl; DCM: dichloromethane; DIEA:

diisoproplyethylamine; DMF: N,N-dimethylformamide; EDCI:

1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochlor-

ide; HOBT: hydroxybenzotriazole; HCl: hydrochloric acid;

HPLC: high pressure liquid chromatography; ITC: isothermal

titration calorimetry; TLN: thermolysin; NMR: nuclear

magnetic resonance; ZG^PLG: N-carbobenzyloxy-Gly^p-L-Leu-

Gly; ZG^PLA: N-carbobenzyloxy-Gly_p-L-Leu-L-Ala; ZG^PLG: N-

carbobenzyloxy-Gly^p-L-Leu-L-Leu

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Article Doi

Water mediated ligand functional group cooperativity: The contribution of a methyl group to binding affinity is enhanced by a COO- group through changes in the structure and thermodynamics of the hydration waters of ligand-thermolysin complexes

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