University of Groningen Understanding enzymic binding

University of Groningen

Understanding enzymic binding affinityTalhout, Reinskje

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Citation for published version (APA):Talhout, R. (2003). Understanding enzymic binding affinity: thermodynamics of binding of benzamidiniumchloride inhibitors to trypsin. s.n.

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CHAPTER 1 Inhibitor-Enzyme Interactions: an

Introduction

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Thermodynamics of Binding of Benzamidinium Chloride Inhibitors to Trypsin

2

1.1 Biomolecular Recognition in Water

1.1.1 Water

Water, the most abundant molecule on the earth’s surface and in the atmosphere, is paramount to

the existence of terrestrial life.1 The apparent molecular simplicity of water, which can act as a

solvent as well as a reactant, is deceiving. Water, with its small molecular size, has the unique ability

to form an extensive network of (almost) tetrahedrally connected hydrogen bonds. In bulk water,

three to four hydrogen bonds per molecule are formed.2 Its three-dimensional hydrogen bonding

capacities and relatively small size give bulk water its anomalous properties as well as its specific

hydration pattern of solutes.2,3 In comparison to organic solvents, water has a low compressibility

and a small thermal expansion coefficient.4 This makes the aqueous medium ‘stiffer’, with a lower

tendency to expand with temperature than nonpolar media, enlarging the temperature window over

which biomolecular complexes are stable and functional. The high heat capacity, due to the various

degrees of freedom, makes it an excellent temperature regulator on the surface of the earth as well as

in living organisms. Furthermore, its high dielectric constant, together with its excellent solvation

properties of polar and charged groups, serves to moderate attractive forces between biomolecules.

This necessitates multiple favourable interactions, which ensures the specificity required for the

formation of the specific three-dimensional scaffolds for biochemical functions. One of these

favourable interactions, which is unique for water, is the hydrophobic interaction (Section 1.1.6.2).

The interaction of water with solutes is crucial to our understanding of a broad range of chemical,

biological and physical processes in aqueous solution.5

1.1.2 Noncovalent Interactions in Water

Specific binding is fundamental to the molecular organisation of living matter.6 Within each cell of an

organism, a large number of covalent and noncovalent interactions, each with its specific purpose,

continuously occurs coordinated and regulated in space and time. Cells are able to survive and

function partly due to specific, noncovalent binding of molecules within the heavy molecular traffic

in and around cells. Interactions in the cell, which is highly crowded with other molecules

(300-500 g l-1 or >50% of the total volume), are quite different from those in dilute aqueous solutions

due to excluded volume effects as well as specific chemical interactions.7-9 Timely binding of the

correct molecular partners is critical in signal transduction, the expression of genetic information, the

assembly of cellular components, and all other cellular activities. Molecular recognition is also

central to many diseases and medical therapies. Furthermore, it is remarkable that living organisms

can survive in extreme conditions of pH and temperature.10 Therefore, the recognition properties of

biologically active molecules have attracted the interest of many scientists over the years.11

CHAPTER 1: Inhibitor-Enzyme Interactions: an Introduction

3

Water plays a key role in governing biomolecular binding interactions.12,13 The unique properties of

water compared to other solvents, described in the previous section, also emerge in the dehydration

of both reactants upon complex formation. This step involves not only the rupture and reformation

of hydrogen bonds to functional groups, but also the reorganisation of the water structure at the

interface.14 Association in solution is in direct competition with solvation, and water is very good at

solvating ions and hydrogen bond donors and acceptors.15 Therefore, biomolecular assembly

processes occurring in aqueous media are governed, to a large extent, by the differential interaction

of water molecules with the unassembled and assembled components of a system.10,16 Specific

interactions are the result of formation and breakage of many individual bonds, comprising salt

bridges, hydrogen bonds, hydrophobic interactions, π- π interactions,17 cation-π18,19 and aromatic-

aromatic20 interactions. Furthermore, solvation and desolvation contributions, and the mutual spatial

complementarity in van der Waals interactions are of utmost importance. For protein-ligand

complexes, additional effects are determined by intramolecular changes of receptor and ligand

during complex formation.21

Water molecules are able to complement substituents in an interaction with a receptor, since

water can act as both hydrogen bond donor and acceptor, imposes few steric constraints on

hydrogen bond formation and is not very space-consuming.21,22 Thus, water can directly bridge

energetically unfavourable voids on an interface and provide (multiple) hydrogen bonds or

contribute indirectly to stability by holding bridging water molecules in the right position through a

network of hydrogen bonds.23 The versatile character of water as a mediator eventuates in a larger

adaptability of biomolecular surfaces and may thus lead to an increased affinity. However, it also

leads to a loss in selectivity, since different numbers of water molecules may be taken up to

complement the binding site.24 Some of these water molecules may be highly conserved in ligand-

protein complexes of homologous proteins, even be present in free protein and thus sometimes be

considered an integral part of the protein, which changes the binding site characteristics.25 Water

molecules located close to binding surfaces are more ordered than those contained in the bulk

solvent, and as such behave differently.16 These locally structured water molecules can be retained or

released during a binding interaction with different thermodynamic consequences. In general, it is

assumed that the entropic cost of trapping a water molecule between two interfaces is that high26 that

two more compatible interfaces would give a higher binding affinity. However, sometimes the

enthalpic gain of extra water-mediated hydrogen bonds can outweigh this entropic penalty of

immobilising a water molecule.27,28 The net thermodynamic result of water inclusion is, still, highly

unpredictable and it is a new challenge to drug design to explicitly incorporate water.12,23,25,27


4

1.1.3 Thermodynamics of Binding

The Gibbs energy of binding, which describes the tendency of a molecular system to associate, is

arguably one of the most important general concepts in physical chemistry:

STHG ∆−∆=∆ (1.1)

where ∆G is the Gibbs energy of binding, ∆H the enthalpy of binding, T the absolute temperature

and ∆S the entropy of binding. ∆G reflects two opposing fundamental effects at the molecular level:

the tendency to fall to lower energy (bond formation, negative ∆H), offset by the equally natural

tendency for thermal motion to disrupt structures (bond breakage, positive ∆S). There is a crucial

distinction between the binding energies that are observed in solution and the fundamental forces

between molecules in the gas phase: solvent binds to all solutes and has to be displaced when the

solutes bind to one another.29 ∆H primarily reflects the strength of the noncovalent interactions

between the reactants relative to those existing with the solvent.30,31 ∆S, on the other hand, mainly

reflects two contributions concerning the order of the system: changes in solvation entropy and

changes in conformational entropy. Upon binding, water is released and a gain in solvent entropy is

observed, which is particularly important for hydrophobic groups. At the same time, the ligand and

certain groups in the protein lose conformational freedom, resulting in a negative change in

conformational entropy.

Different structural and chemical characteristics reflect themselves in different

thermodynamic signatures.16,32,33 Of course, in typical systems consisting of a multitude of weak,

noncovalent interactions, the observed binding thermodynamics are the result of the signatures of all

these separate interactions. This renders the interpretation of thermodynamical data somewhat

ambiguous, since, as Alan Cooper34 puts it, “heat does not come in different colours”. The canonical

picture for protein-ligand interaction comes down to burial in the complex of relatively nonpolar

regions of the molecular surfaces. Within the buried interface of the complex, the shape and charge

of the interacting polar groups are complementary.6 It is difficult to assess which interactions are the

driving force.8 In the next three sections, the interactions that are most important in enzyme-inhibitor

interactions, together with their thermodynamics, will be considered in more detail.

1.1.4 Salt Bridges

Electrostatic interactions occur between charged or dipolar ligands and counter-charged binding

sites on a macromolecule.29 Their strengths depend on both the inverse distance of approach of the

charges, and the dielectric constant of the surrounding medium. A decrease in solvent polarity

causes a considerable increase in association constants due to the reduction in dielectric shielding.19

The dielectric constant at a binding site may differ considerably from the dielectric constant of bulk

solvent.35 For example, the nonpolar interiors of enzymes provide the living cell with the equivalent


5

of an organic solvent, in which strong electrostatic interactions between substrate and specific polar

groups of the enzyme can occur.36

The net effect of a salt bridge is a delicate balance between the high cost of desolvating the

charged groups and the interionic attraction. Although ion pairing may be expected to be associated

with a favourable enthalpic contribution, frequently entropy drives the binding due to the release of

highly ordered water molecules from hydration shells surrounding the interacting groups. This

behaviour can in part be explained by the chelate effect, since less translational entropy is lost by

coordination with a polydentate macromolecule than by coordination with several monodentate

water molecules. The magnitude of the entropy change is likely to be dependent on the number of

coordination sites present on the macromolecule, and there are examples of ion pair formation that

are enthalpically driven.16 Even if salt bridges are destabilising, they do provide specificity in the

overall binding process.35

1.1.5 Hydrogen Bonds

Hydrogen bond formation, with its relatively strong directional character, is particularly important

in biological binding interactions.21,37 Hydrogen bonds result from an electrostatic attraction of a

hydrogen atom bound to an electronegative atom with another electronegative atom or a π-electron

system. Distances of 2.5-3.2 Å between the hydrogen-bond donor and acceptor and angles of

130-180° are typically found.2 The more polar the solvent is, the weaker the hydrogen bonds are

because of the increasing competitive solvation of donor and acceptor sites by polar solvent

molecules. The strength of a hydrogen bond depends on its microscopic environment, since the

shielding of electrostatic interactions depends on the local dielectric constant of the surrounding

medium. As a consequence, multiple hydrogen bonding can lead to observable, but strongly

medium-dependent association.

It is difficult to make generalisations regarding the contribution of a single hydrogen bond to

binding affinity, since distances and angles differ and hydrogen bonds between the reactants and

water have to be broken. Reasonable estimates for the strength of a single hydrogen bond are in the

order of 10-40 kJ mol-1, but contributions to binding thermodynamics often are much smaller than

this due to the nature of hydrogen bond exchange.16,29 Despite indications from the behaviour of

small model compounds, which suggest that hydrogen bonds should be at best thermodynamically

neutral in aqueous systems, some experiments show that, in protein folding, hydrogen bonding

might be as significant as hydrophobic interactions.33,38 Data from protein mutant studies,14,21,38 host-

guest complexes,14 and model compounds14 yield estimates for the contribution of a single hydrogen

bonds to the Gibbs energy of binding or protein stability of approximately -2.5 to -7.5 kJ mol-1.14 In

contrast, values of -10 to -20 kJ mol-1 have been reported for charge-assisted hydrogen bonds and salt

bridges. The interpretation of the experimentally determined apparent binding contributions suffers

from one important problem common to all these studies: the measured quantities correspond to the

intrinsic contribution of an interaction only if superimposed effects can be excluded.


6

1.1.6 Hydrophobic Effects

Hydrophobic effects are unique for the solvent water and refer to the anomalous behaviour of

nonpolar solutes in aqueous solutions. They influence a wide range of molecular phenomena in

aqueous solutions, ranging from relatively simple processes, as the solubility of nonpolar gases in

water, to the more complex protein folding, membrane formation and protein-ligand association,

including conformational changes of the receptor upon ligand binding.39,40 Hydrophobic effects

comprise two distinct processes: hydrophobic hydration and hydrophobic interactions. Hydrophobic

hydration (Section 1.1.6.1) indicates the typical solvation pattern of nonpolar solutes by water.

Hydrophobic interactions (Section 1.1.6.2) can be partly understood as the minimisation of the effect

of hydrophobic hydration as a result of the interactions between nonpolar solutes.

1.1.6.1 Hydrophobic Hydration

Hydrophobic hydration refers to the anomalous thermodynamics of transferring a nonpolar

molecule from either the gas or the liquid phase into water, which are characterised by a large

positive Gibbs energy, dominated by a large negative entropy around room temperature, and a large

positive heat capacity. This entropic effect was first described in 1945 by Frank and Evans in a classic

paper41 on the thermodynamics of solution of hydrocarbons in water.

In Figure 1.1, the thermodynamics of transfer for the simple nonpolar solute n-pentane from

liquid n-pentane into water are compared to those for the transfer from n-pentane from its gaseous

into its liquid phase. For the transfer of gaseous n-pentane into liquid n-pentane, ∆G is favourable

and dominated by ∆H, T∆S is small, and both the enthalpy and the entropy are relatively

independent of temperature. The mixing of a nonpolar solute and water is quite different to

solvation in simpler solutions. ∆G of transferring nonpolar molecules from a nonpolar phase into

water is large and positive. The enthalpy and entropy of this transfer process increase with

increasing temperature and are compensating to a large extent, leading to an only moderate increase

of the Gibbs energy. Therefore, around room temperature, transfer is entropically disfavoured, but

only up to a critical temperature TS, were the entropic contribution to the transfer vanishes. TS

depends on the nature of the compound to be transferred. At temperatures above TS, the entropy of

transfer becomes favourable.

It can be shown that the effect of hydrophobic hydration is strongest, i.e. ∆G is maximal, at

TS.39 TH, the temperature above which the enthalpy of transfer becomes unfavourable, is around

room temperature. The low value of TH indicates that this transfer process, as a measure of

hydrophobicity, is dominated by entropy only at low temperatures, whereas at high temperatures it

is dominated by enthalpy.42 For small molecules such as benzene and pentane, TH and TS are,

respectively, approximately 25 °C and 113 °C.39,43 The complete thermodynamics of solute parti-

tioning into water can be expressed in terms of these two temperatures provided that ∆Cp is

independent of temperature.39


7

Figure 1.1. (A) The transfer of n-pentane from its liquid phase into water, and (B) the transfer of

n-pentane from the gas phase into an n-pentane liquid phase. (Adapted from Southall et al.)39


8

Over the full temperature range for liquid water, from the melting point to the boiling point, there is

a large positive heat capacity change upon transfer of nonpolar solutes into water. The curvature of

the Gibbs energy with temperature can be expressed in terms of the heat capacity ∆Cp:

2

2

pT

GTC

∂∆∂−=∆ (1.2)

Also, the strong temperature dependence of the entropy and enthalpy are a consequence of this large

∆Cp. Changes in enthalpy and entropy upon variation of the temperature are, respectively, given by

Equation 1.3 and 1.4:

p/ CTH ∆=∂∆∂ (1.3)

SCTST ∆+∆=∂∆∂ p/ (1.4)

Enthalpy-entropy compensation arises from the relative magnitudes of ∆S and ∆Cp.44,45 When |∆Cp|

> > |∆S| at all temperatures, the temperature dependence of ∆S is practically equal to ∆Cp. This

means that the temperature dependence of both ∆H and T∆S is a constant factor equal to ∆Cp, which

results in the value of ∆G being relatively temperature-independent. In contrast, if ∆H and ∆S were

constant (∆Cp = 0), then no such compensation would occur and ∆G would vary much more rapidly

with T. Such a buffering of ∆G may well be of considerable importance, since biological systems

depend on a delicate balance of interactions, the extent of which is determined by ∆G, rather than by

∆H and ∆S. This ‘thermodynamic homeostasis’ allows an organism to withstand much greater

fluctuations in environmental conditions than might otherwise be the case.33,34

Large and negative entropies and large and positive heat capacities are considered hallmarks

of hydrophobic hydration.27 However, the hydration of virtually any solute, nonpolar, polar or ionic,

is accompanied by a decrease in entropy, and can be reproduced by almost any solvation model (see

below).46 Furthermore, although the large positive Gibbs energy of mixing of hydrocarbons with

water is dominated by entropy at 25 °C, it is dominated by enthalpy at higher temperatures where

∆G is maximal. Therefore, where hydrophobicity is strongest, the entropic contribution is

negligible.47 A more general perspective of what is unique about hydrophobicity, one that applies

over the full range of temperatures for liquid water, is the large heat capacity. The large and positive

heat capacity change is what truly distinguishes the hydrophobic effect from other solvation effects:

in contrast to nonpolar groups, the hydration of polar groups is accompanied by a smaller, but

significant decrease in the heat capacity change.46,48,49

In the absence of a full molecular understanding, an explanation for hydrophobic hydration

is usually sought through considering unusual properties of liquid water, especially the hydrogen

bonding interactions between water molecules.39,40,50 Models of water are useful to explore the

principles of hydrophobic hydration, which gives a consistent physical picture that accounts for the

qualitative difference observed between hydration shell and bulk parameters.51 Muller treats the


9

transfer of a solute into water as a process in which hydrogens that participated in hydrogen bonds

in the bulk now become a part of the hydration shell of the solute.47,52 Each hydrogen bond has two

accessible states: a lower energy state in which the hydrogen bond is intact, and an upper energy

state in which the hydrogen bond is broken, both in the bulk and in the solvation shell. In the

Mercedes-Benz model, water molecules are represented as two-dimensional Lennard-Jones disks,

with three hydrogen-bonding arms, arranged as in the Mercedes-Benz logo.47,53 It captures two

aspects of water physics in a simple way: Lennard-Jones interactions for long-range attractions and

short-ranged repulsions, and an orientation dependent interaction to mimic hydrogen bonding

effects. Despite its relative simplicity of using only two dimensions, adopted for ease of computation

and clarity of interpretation, the Mercedes-Benz model qualitatively predicts both the anomalous

properties of pure water and the anomalous hydration thermodynamics of nonpolar molecules.33

Classically, hydrophobic hydration has been interpreted as not so much due to direct

solvent-solute interactions, but rather to the reorganisation of the bulk water hydrogen-bonding

network as a result of the insertion of a nonpolar solute, which does not satisfy the hydrogen

bonding capability of water. In the interfacial region of relatively planar (surfaces of relatively high

(> 15 Å) radius of curvature) nonpolar solutes, as well as nonpolar liquid-water interfaces, three-

fourth of the bulk average number of hydrogen bonds is still present, which is more than the one-

half expected for a physical wall without structural consequences for the surrounding water.4,54 For

smaller solutes, the interfacial water can reorganise in such a way that no hydrogen bonds are lost by

avoiding the hydrogen bonding vectors to point toward the nonpolar solute, which results in water

molecules that tend to orient their OH-bonds tangentially to the surface of the solute.40 Thus, relative

to bulk water, structural reorganisation occurs in the interfacial region to maximise the total number

of hydrogen bonds and thereby optimise the hydrogen-bonding network. This reorganisation

results, in comparison to bulk water, in a decreased number of microstates able to adopt this

hydrogen-bond maximising pattern in a hydration shell, and therefore in a decreased entropy.

With large solutes, water wastes hydrogen bonds by pointing them at the nonpolar surface,

since it is geometrically impossible to form the maximal number of hydrogen bonds to other waters

in the vicinity of a large inert surface; in this case, the enthalpy of hydration is positive and the

change in heat capacity is negligible. This change in mechanism explains why the energetic costs per

unit surface area for creating planar oil water interfaces is three times higher than that for

transferring small nonpolar solutes into water.39 Real solutes are expected to be somewhere in

between, but for nonpolar cavities, hydration properties may be quite different. For a concave

nonpolar cavity, the number of hydrogen bonds between the hydration waters is expected to be even

smaller than the three-fourth of the bulk average number encountered for a planar surface.

In conclusion, around a nonpolar solute, the dynamic, loose hydrogen bond network of the

bulk water phase looses orientational degrees of freedom in order to preserve the maximum number

of hydrogen bonds, each of which has an energy of about 25 kJ mol-1. This partial immobilisation of

the water molecules leads to some low-entropy structure, which accounts for the observed negative

∆S of transfer and may be suggestive of clathrate structures.29


10

Figure 1.2. The first hydration shell of water molecules around a nonpolar solute at (A) room

temperature and (B) higher temperatures). (Taken from Southall et al.)39

For instance, Frank and Evans suggested that the hydrated nonpolar atoms and molecules are

covered with a layer of partially water molecules, called frozen patches or icebergs.41 However,

neither simulations nor experimental studies have supported substantial changes in structural and

hydrogen bonding properties of the hydration shell with respect to bulk water.40

That ∆H increases rapidly with temperature (∆Cp is large and positive) presumably reflects

the breaking or weakening of hydrogen bonds at higher temperatures as the nonpolar molecule is

introduced.16,42 Thus, at higher temperatures, the structure ‘melts’ with a compensating increase in

enthalpy and entropy (Figure 1.2). The Mercedes-Benz model gives a physical interpretation for TH

and TS, the temperatures at which the transfer enthalpy and entropy, respectively, are zero. TH is the

temperature at which hydrogen bond reorganisations are balanced by solute–solvent interactions

and TS is the temperature at which the relative hydrogen bonding strengths and numbers of shell

and bulk water molecules reverse roles.47

This classical view of hydrophobic hydration, however, is not generally accepted. A different

view considers the small size of the water molecule and not low-entropy-structure formation in the

hydration shell, to be the essence of the hydrophobic effect.58 On a molecular basis, the hydration of

small molecules may be considered as a two-step process: cavity59 formation in bulk water to

accommodate the solute, followed by the insertion of the solute molecule in this cavity with the

corresponding interactions.

ic GGG ∆+∆=∆ • (1.5)

where • denotes the Ben-Naim standard state, ∆Gc refers to the work of forming a cavity and ∆Gi

refers to the work done by the attractive forces between the solvent and solute molecules. ∆Gi

produces both the solvent reorganisation term ∆Gr and the interaction term Ea between solute and

solvent molecules. The degree of orientational freedom of water molecules in the hydration shell of

the solute molecule is obviously smaller than that in bulk water,58 but it is thought that this solvent


11

reorganisation entropy term is exactly balanced by the corresponding enthalpy term.45,60-62 Since ∆Gr

is therefore zero, only averages over the solute-solvent interaction energy Ea contribute to ∆Gi. Since

both ∆Gc and Ea primarily depend on the density of the solvent, which is not very temperature-

dependent for water, ∆G• is also not very temperature-dependent.42

According to Ben-Naim, the solubility of small solute molecules is largely dependent on the

work required to form a suitable cavity in the solvent.3,40 In comparison to the cavity term, the solute-

solvent interaction term is quite small.42 The larger the nonpolar solute, as represented by its solvent-

accessible surface area, the more pronounced the effect of hydrophobic hydration. This can be

explained by the cavity term being related to the chance of finding a naturally occurring, transient

cavity of that size in the solvent, which, in turn, is related to the molecular size and the density of the

solvent. Therefore, large cavities are more likely in solvents consisting of large molecules. Water

molecules are among the smallest of all solvent molecules, and, according to the small-size model,

the Gibbs energy cost of opening a cavity of a given size is therefore larger for water than for other

solvents. Water has the smallest molecular size, but also the lowest packing density of all common

solvents, the latter because of the unique hydrogen-bonding network of water (Section 1.1).

It was suggested by Lee that the low solubility of nonpolar solutes in water stems from the

fact that water molecules are small in size (in comparison to most organic solvents), rather than from

their capability to form hydrogen bonds.63 This small size would lead to small interstitial spaces

available in water, and thereby a smaller chance that a large cavity is formed. The hydrogen bonds,

on the other hand, would aid the dissolution process by decreasing the density of water, which leads

to larger interstitial spaces.64 Calculations on a reference liquid with the same molecular size and

bulk density as the model water liquid TIP4P but devoid of hydrogen bonding capability affirm this

hypothesis. The Gibbs energy cost of forming a given-sized cavity in this reference liquid is similar

to that in TIP4P water, indicating that the bulk density and not the presence of hydrogen bonds

determines the energetic cost of forming a cavity.51,58 For both this Lennard- Jones liquid and water,

opening a cavity to bring together many small packets of free volume into a single larger cavity,

leads to an entropy cost.

The unfavourable cavity term contribution to the Gibbs energy is derived from a decreased

number of solvent microstates associated with the larger cavities and this work is not compensated

for by strong solute-water interactions, which are present for soluble compounds such as salts,

sugars and alcohols. There is no simple analogue in terms of the number of hydrogen bond

interactions or specific clathrate structures for this entropic phenomenon.51 The origin of this effect is

intrinsically geometrical and entropic; it bears no direct relation to the formation and breakage of

hydrogen bonds.45 An energy increase with increasing temperature causes a breakdown of some of

the hydrogen bonds, which then promotes a more efficient packing of molecules.63 Since the chance

of forming a cavity fluctuates primarily with the volume, this mechanism keeps the energy of cavity

formation rather independent of temperature.

Thus, there are two ‘schools’ in the discussion of hydrophobic hydration: one that stresses

the importance of the hydrogen-bond reorganisation upon inserting a solute, the other that of the

size of the water molecule. It seems that part of the confusion in the discussion on hydrophobic


12

hydration is due to the fact that different definitions of this effect are used: the large and positive

heat capacity or the large and positive Gibbs energy of dissolution (see e.g. the discussion with Sharp

following the article of Lee45). For the first, the hydrogen bonding reorganisation upon inserting a

solute is crucial, while for the second the small size of the molecule is the determining factor.

Of course, these two properties of water go together. According to Lee, the characteristic

hydrogen-bonding properties of water molecules do not directly affect the Gibbs energy, since the

enthalpy and entropy of solvent reorganisation are compensating. However, these properties do

affect the Gibbs energy indirectly, by decreasing the packing density of water and thereby increasing

the chance of forming an appropriate-sized cavity. Therefore, the hydrogen-bonding network aids

the dissolution process and the ultimate cause of hydrophobicity is the small size of water.63 A

synthesis of both opinions on hydrophobic hydration could thus be that cavity formation is indeed

entropically costly and that water reorientation effects contribute to the temperature-dependence of

the thermodynamic parameters.39

1.1.6.2 Hydrophobic Interaction

Hydrophobic interactions often are characterised by small (frequently positive) enthalpy changes,

large positive entropy changes, and a negative contribution to ∆Cp. Thus, one of the main

fingerprints indicating that hydrophobic interactions are involved in chemical or biological processes

is a temperature dependence of the thermodynamic parameters that is more or less the opposite of

that shown in Figure 1.1.43 The classical understanding of hydrophobic interactions is that nonpolar

groups associate with each other, minimising their contact area with water. Regardless the specific

cause of the positive Gibbs energy and the large and positive heat capacity upon solvating a

nonpolar molecule in water, which we discussed in the previous section, the aggregation of nonpolar

solutes will (partially) remove the effects of hydrophobic hydration. For these solvent-induced

attractive forces between nonpolar molecules in water, the term hydrophobic interaction has been

introduced.40 Water molecules in a concave, nonpolar cavity are entropically less constrained than

their bulk water counterparts (Section 1.1.6.1). Complexation of a nonpolar guest with a concave

cavity is enthalpy-driven with an adverse entropic contribution; the change in heat capacity remains

negative. This phenomenon has been called nonclassical hydrophobic interaction55-57 and has been

extensively studied for cavities where arene-arene interactions play an important role.55

The heat capacity upon transferring nonpolar solutes from water to a nonpolar phase is

directly proportional to the number of water molecules in the first hydration shell, which can be

approximated by taking into account the surface area.65 The contribution of hydrophobic interactions

to ∆Cp in protein folding and other interaction processes could thus be regarded as proportional to

the size of the hydrophobic surface area buried during these processes.10,27,33,34 However, the wider

applicability of such correlations is now being questioned. Some of the discrepancy may be

attributed to immobilised water molecules on the interface or the interacting

components.16,27,66 Furthermore, good correlations are only obtained in case of rigid-body

binding models67 and discrepancies are observed for small ligands.67,68


13

1.1.7 Enthalpy-Entropy Compensation upon Varying the Substituent

Gibbs energy changes for binding may occur with virtually all possible net favourable combinations

of enthalpic and entropic changes, which leads to an absence of correlation between ∆G and ∆H.30,66

However, for a series of related compounds with only moderate changes in their structures, the

entropy and enthalpy of binding do not vary independently. Introducing a small structural variation

in a compound may hardly change the Gibbs energy of binding, whereas the enthalpy and entropy

may vary considerably. Such enthalpy-entropy compensation upon varying a substituent is a

common phenomenon when studying weak (comparable to thermal energy) interactions,32,34,69

although some counter-examples31 (anti-compensation) do exists.

This common thermodynamic behaviour has often been thought to reflect a major role of the

compensating enthalpic and entropic contributions of hydration effects and was thus interpreted as a

diagnostic test for the involvement of water molecules in the association process,70,71 but it can also

occur in other solvents, e.g. alcohols.62,72 It has been suggested that compensation is an intrinsic

property of complex interacting systems and is particularly apparent in aqueous systems were

noncovalent interactions dominate.32,34 This phenomenon is often thought to be the outcome of

compensating solute-induced molar shifts in the solvent.70,71 Alternatively, a valuable distinction

between the environmental and the chemical part of a physical process has been made by Grunwald

and Steel.62 The Gibbs energy for solvent reorganisation accompanying the binding process is taken

to be zero due to complete enthalpy-entropy compensation.42,60 Therefore, if the magnitudes of the

enthalpy and entropy of solvent reorganisation dominate the binding process, i.e. the magnitudes of

the chemical process are modest, enthalpy-entropy compensation is observed.

In the vision of Williams and co-workers,73 enthalpy-entropy compensation is a consequence

of weak associations, where the binding enthalpy is much lower than that for typical covalent bond

strengths, rather than some unique feature of solvation. Compensation is the natural outcome of the

fact that bound species will necessarily have less freedom of motion in a tighter complex,74,75 and

serves to underline the importance of the formulation of the Gibbs energy of binding as in

Equation 1.1. When the complex formation is considered as a bimolecular association, and solvent

molecules are neglected, each component loses three degrees of translational and rotational freedom,

while six new vibrational degrees of freedom are created.21,32 Thus, when two molecules associate,

there is an entropic cost as a consequence of lost degrees of motion for the molecules constrained in

the complex. This cost must be paid for by favourable interactions between the molecules and by the

increased entropy of the solvent. The limiting value for the entropy loss upon reaching an essentially

rigid complex is 50-60 kJ mol-1 (T∆S at 25 °C) for molecules of low molecular mass.76,77


14

50-60

-∆H

(kJ

mol

-1)

-T∆S (kJ mol-1)

Figure 1.3. General form of the extent of exothermicity of an association process of two molecules as a

function of the entropic cost at a temperature T (adapted from Searle et al.).73

For weaker interactions, considerable residual motion is often retained and the entropic cost is some

fraction of this limiting value. In fact, it is thought to be a sensitive function of the exothermicity of

the interaction: an increase in exothermicity of association is offset by an increased adverse entropy

of restricted motion.78,79 The origin of this phenomenon is found in the depth of- and the density of

states in- the potential well of the associated state: the stronger the interaction, the deeper and

shallower the well, the less energy levels can be occupied and thus the lower the entropy.73,74 The

converse is true for weaker interactions, which can occur with a relatively small loss of entropy.

From theoretical considerations, confirmed by experimental data, the general form of an enthalpy-

entropy curve has been deduced, which is shown in Figure 1.3.32

The direction of the curvature arises from the fact that the adverse entropy of a bimolecular

association is limited, as stated above, whereas its exothermicity can increase far beyond this

limitation. It is noted that for real systems in solution, usually only part of the theoretical curve is

accessible and that each experimental data point is a composite of interactions involving solvent and

solute (e.g. desolvation also plays a role).73,80-82 This curve is also useful in considering interactions

like the classical chelate effect.29 It is clear that the cooperativity in binding affinity of two exothermic

interactions is largest to the right part of the curve, where the limiting entropy is reached. The

advantage for binding of added exothermic interactions will outweigh the extra cost in entropy.83 A

corollary of this is that for deletion studies, such as mutation studies of proteins, the estimated

contribution of the deleted group to the Gibbs energy of binding, will necessarily be too large.82


15

It is convenient to consider two types of enthalpy-entropy compensation: weak and strong

compensation.84 Weak compensation means that upon varying the substituent, the changes in

enthalpy and entropy will have the same sign. However, at times the correlation of enthalpy with

entropy approaches the precision of a linear relationship characteristic of that particular reaction

series. Strong compensation indicates this linear correlation between enthalpy and entropy with a

slope TC defining a compensation temperature and an abscissa ∆H0:62,71

STHH ∆⋅+∆=∆ C0 (1.6)

Strong compensation is encountered for several phenomena, such as protein-protein interactions,85

protein-ligand interactions86,87 and host-guest chemistry.88,89 Sometimes, linear enthalpy-entropy

compensation is just the outcome of the systems that were selected. When a homologous series of

compounds is chosen,90 linear compensation often is no more than the manifestation of this source of

additivity.91,92 Furthermore, when the range of Gibbs energies that can be observed is small due to

practical or biological reasons, ∆G is more or less constant in comparison to its constituents and

therefore an apparent linearity between enthalpy and entropy is observed.34,84,92 Also, ∆H and ∆S are

usually derived from the same set of data and therefore not statistically independent, leading to

highly correlated errors in both quantities that can lead to linear plots with high correlation

coefficients. In these cases, the apparent compensation temperature is equal (within a certain

confidence interval) to the temperature at which the measurement is performed.84,93 A simple

statistical test to verify that the observed enthalpy-entropy compensation is not a computational

artefact is to check whether the compensation temperature is outside this confidence interval.93 Using

this test, only three from thirty-seven sets of data that showed linear entropy-enthalpy

compensation, had a compensation temperature outside this confidence interval.93 Furthermore, data

plotted in the ∆H-∆G plane only show chemical effects, since in that case errors propagate in a

random manner.93,94 When such trivial reasons for strong enthalpy-entropy compensation can be

excluded, an intriguing extra-thermodynamic phenomenon is encountered the origin of which is not

completely understood.71,84,91 In these cases, the compensation temperature is the temperature at

which the Gibbs energies of binding of all compounds within the data set are equal.70,71,84

From Equation 1.1 and Equation 1.6, Equations 1.7 and 1.8 are readily obtained:

STTHG ∆⋅−∆=∆ ) -( C0 (1.7)

HT

TH

T

TG ∆⋅+∆⋅=∆ ) -1(

C0

C

(1.8)

These two relations imply that upon substituent variation at temperatures below the compensation

temperature, a decrement in ∆H, with the accompanying decrement in ∆S, leads to a decrement in

∆G, whereas an increment in ∆S, with the accompanying increment in ∆H, leads to an increment in

∆G. At temperatures above the compensation temperature, the reverse is the case.95 In other words,


16

linear enthalpy-entropy compensation implies that at temperatures below the compensation

temperature, a higher binding affinity can only be achieved by a more favourable enthalpy of

binding and not by a more favourable entropy of binding, whereas the opposite is true at

temperatures above the compensation temperature. Also, the reaction constant ρ, which is a measure

of the sensitivity of the reaction to changes in the substituent constant, changes sign at the

compensation temperature. Thus, close to the compensation temperature it is not safe to say that

changes in the substituent do not influence the rate or binding constant.

A major point of debate is whether this compensation temperature indicates any further

physical relevance regarding the mechanism of binding.84,92 Linear enthalpy-entropy compensation

is only present if one mechanism truly dominates the reaction or binding or if the compensation

temperatures of the different mechanisms are the same.71 An absence is usually thought to indicate a

complex interplay of effects or the occurrence of more than one mechanism within the series.96 In the

theory developed by Linert,97,98 the compensation temperature is related to the vibrational spectrum

of the surrounding medium (the solvent, or, in case of large host-molecules, their cavities and

surroundings), which acts as a constant temperature heat-bath. The thermal energy corresponding to

the compensation temperature signifies the predominantly active frequency (ν) of the vibrational

spectrum of the heat bath:

k

hT

ν⋅= C (1.9)

and TC is thus a natural outcome of the interplay between medium and complex.99 At this

temperature, the maximum energy transfer from heat bath to reactants takes place and the minimum

selectivity can thus be seen as a resonance phenomenon. Experimental examples of compensation

temperatures and the corresponding heat bath frequencies have been given for several different

processes in different solvents.97,99

Regardless of the actual molecular origin, enthalpy-entropy compensation seems to occur in

almost any noncovalent macromolecular interacting system, and indeed frustrates attempts to

characterise such interactions.33,34 However, like enthalpy-entropy compensation with change in

temperature (Section 1.1.6) confers thermodynamic stability and buffering against environmental

challenges, enthalpy-entropy compensation with change in substituent confers thermodynamic

stability and buffering against mutational challenges that may be of significant advantage in the

evolution and function of biomolecular systems. Living organisms depend on a delicate interplay

and balance of intermolecular interactions, and anything that upsets this balance is likely to be a

disadvantage in evolutionary terms.

1.1.8 Drug Design

The design of ligands for biological and synthetic receptors is a subject of continuing intellectual and

practical interest. A thorough understanding of molecular recognition is crucial for the design of


17

molecules that can mimic or disrupt the association of biological molecules, and insight into the

interactions responsible for such association may often be gained from molecular simulations and

modelling. To fully understand protein-ligand interactions requires the structure and conformation

of the ligand, the protein, and the protein-ligand complex to be completely characterised, since

conformational changes may accompany binding. The contribution of an individual functional group

to the binding thermodynamics can be estimated by comparison of related systems in which small

structural variations are introduced in this functional group of either the ligand or the protein.29,68,100

However, when introducing such a structural variation, even minor, one always has to be careful

with the interpretation, since changing one interaction might also induce changes at other positions.

Therefore, the noncovalent forces governing biomolecular interactions are most accurately assessed

when both structural aspects and the thermodynamics of binding are known.16,101 This is the case in

the present study, where thermodynamic data are interpreted with the help of crystal structures and,

in particular, molecular dynamics simulations (performed by Dr. Alessandra Villa).

The search for new lead structures in drug development proceeds via two complementary

approaches: experimental screening and rational design.21,102 Experimental screening implies a trial

and error testing of large libraries of synthetic and natural compounds on their possible activity.

Rational design can be divided into methods used when the three-dimensional structure of the

complex is either known or not known. Structure-based drug design uses three-dimensional

visualisation of drug candidates bound to a target receptor to direct structural modifications that

increase the binding affinity.14,21,27 For unknown structures, quantitative structure-activity

relationships (QSAR) may prove helpful to establish a relation between the molecular structure and

the biological activity of known compounds, and thus also predict the binding constant of potentially

active candidates.103,104 Input substituent parameters can represent steric (e.g. Sterimol103,105 or

Taft103,104 parameters), hydrophobic (e.g. n-octanol-water partition coefficients)103,106 and electronic

(e.g. Hammett substituent constants)103,104 properties of the molecule.

The difficulties in predicting ligand binding thermodynamics from three-dimensional

structures have renewed interest in an empirical determination.66 The integration of structure-based

drug design with empirical chemistry provides a two-fold understanding of drug-binding energies.

When both the structure and thermodynamics of a large data set of complexes are known, so-called

scoring functions can be retrieved. The purpose of these functions is to partition the Gibbs energy of

binding in the separate contributions of the different interactions, which will eventually lead to an

approximation of the value of each separate interaction. These functions can then be used to predict

the binding affinity of new ligands.14,107

High binding affinity is often achieved by preshaping conformationally constrained lead

compounds to the geometry of the binding site, and by incorporating a high degree of

hydrophobicity into the designed ligands.21,30 Conformationally constrained ligands exhibit high

specificity and improved affinity compared with identical but otherwise flexible counterparts

because of a smaller conformational entropy loss upon binding. For instance, the entropy of binding

of tailor-made thrombin inhibitors decreases linearly with the number of rotational bonds in the

molecule.86 However, the high specificity of conformationally constrained compounds limits their


18

ability to adapt to mutational changes in the target or to closely related targets. Enthalpy-entropy

compensation may frustrate attempts to improve binding affinities, since the achievement of high

binding affinity requires the synergy of favourable enthalpic and entropic contributions to the

binding affinity.33,34 However, for medicinal chemistry the potential advantage is that modifications

implemented to affect other properties of the drug, e.g. solubility, toxicity and stability, can be

introduced without compromising binding affinity too much.

1.2 Serine Proteinases

1.2.1 Catalytic Mechanism

Amide bonds are very stable in water due to electron delocalisation, water being a poor nucleophile

and amines being poor leaving groups. Proteinases are very effective catalysts for their hydrolysis, to

which artificial catalysts are not even close.15 Three invariant residues within the serine proteinases,

His57, Asp 102 and Ser195 (from which the name serine proteinases is derived), together form a

hydrogen-bonded constellation, which is referred to as the catalytic triad (or charge relay

system).29,108 Thanks to the presence of this triad, the cleavage of peptide bonds (and synthetic ester

substrates) by serine proteinases is accelerated around 1010 times in comparison to water.108-110 This

triad is not formed in the native enzyme. Only upon binding of substrate or inhibitor, do the

catalytically crucial Asp102-His57 and His57 N2-Ser195 OG hydrogen bonds become strong.111-113

Molecular Dynamics simulations on acyl-chymotrypsin indicate that the side chains of the catalytic

triad residues are significantly less flexible than other side chains in the protein.114

The scissile bond of the peptide substrate is hydrolysed in two steps (acylation and

deacylation) via the acyl-enzyme mechanism (Figure 1.4). After formation of the noncovalent

enzyme-substrate (ES) Michaelis complex, the scissile peptide bond is attacked by the hydroxyl

group of Ser195. The nucleophilicity of Ser195 OG is enhanced by general base catalysis of His57 N2,

which takes up the proton. The resulting imidazolium ion is stabilised electrostatically by the

unsolvated negatively charged Asp102, which also serves to orient His57 in the Nδ1-protonated

tautomeric form.115 Thus, the first tetrahedral intermediate (TI1) is formed, which subsequently

decomposes to the acyl-enzyme intermediate (EA) upon releasing the amine leaving group. Next, the

acyl-enzyme intermediate is hydrolysed via the second tetrahedral intermediate (TI2) to the enzyme-

product complex (EP).

1.2.2 Biological Function and Inhibitors

Serine proteinases are involved in the regulation of a wide range of physiologically important

processes including digestion (trypsin, elastase), blood coagulation (thrombin, factor Xa), and

fertilisation (plasmin).116-118


19

ON

N

OH

O

Asp102

:

His57

Ser195 Ser195

His57

Asp102

O

N

R

O

R'

H

OR' R

H O

N

HN

NO

ES

nucleophilicattack

TI1

R'

H

N

HN

NO

O

Asp102

His57

Ser195

OR

O

OR

O

Ser195His57

Asp102

OH

N

NO

OH

:

EA EA

N

NO

HO

Asp102

His57

Ser195

OR

H O

O

O

R

OH

Ser195

His57

Asp102

O

ON

N

OH

TI2 EP

Figure 1.4. Catalytic mechanism of peptide bond cleavage by serine proteinases.

Cascades of consecutive limited proteolytic reactions catalyse the irreversible cleavage of peptide

bonds. This class of enzymes is, however, not only physiologically crucial, but also a potential

hazard.119 If uncontrolled, the protein components of cells and tissues can be destroyed. Nature

therefore evolved control mechanisms for proteinases. Almost all proteinases are biosynthesised as

largely inactive precursors or zymogens, which are stored and activated (by proteolysis of a single

peptide bond) on demand. Furthermore, ten percent of the proteins in plasma are very high

affinity120 proteinase inhibitors.


20

Uncontrolled proteolysis plays an important role in diseases as pancreatitis121,122 (trypsin) and

vascular clotting121 (thrombin, factor Xa), which makes proteinases important targets for medicinal

chemistry. The primary specificity of serine proteinases is for arginine or lysine. Many natural

proteinase inhibitors are small peptides with an arginine or lysine residue, which bind very tightly in

the specificity pocket because they are locked in a conformation similar to the pretransition state

Michaelis complex of a flexible peptide substrate.29,111,119,123,124 In fact, the conformation of the bovine

pancreatic trypsin inhibitor (BPTI)-trypsin complex is well along the reaction coordinate towards the

tetrahedral intermediate state of the acyl-enzyme complex.29 However, the complex is very rigid and

tight; the carbonyl carbon of the “scissile” bond of BPTI, is, with a distance of 2.7 Å, in closer than

van der Waals contact with Ser195 OG.119,125 Therefore, polypeptide inhibitors do not hydrolyse

under physiological conditions since water cannot reach the reaction centre and the amino leaving

group that should be released upon cleavage cannot diffuse away. Under these circumstances,

nature has given us the choice opportunity to study interactions and conformational changes

occurring in the first step of the catalytic cleavage of a peptide bond.

Synthetic proteinase inhibitors are also often based on arginine and lysine groups.121,126 In

particular, the benzamidinium group, which can be thought of as a structural mimic of the arginine

group, is a potent small-molecular inhibitor.127 It is also the primary component of many larger

inhibitors that have been designed to have more elaborate interactions with the enzyme.68,107,128,129

1.2.3 Trypsin as a Model System

In 1876, the word enzyme was introduced by W. Kühne to describe pancreatic trypsin.130,131 Trypsin

is the archetype of a large group of enzymes belonging to the serine proteinases, with over 240

recognised examples the most abundant in nature.109 It is a globular protein of 223 α-amino acid

residues with a well-defined calcium binding site,123,124 folded in two interconnected six-stranded

antiparallel β-barrel domains, with the catalytic residues located at their junction.112,132 Other trypsin-

like serine proteinases have a core similar to trypsin with large segments attached to it that modify

the specificity.108,123 Convergent evolution has resulted in at least four different structural contexts

containing the catalytic triad. The different serine proteinase classes are distinguished by the absence

of any conserved secondary and tertiary motifs, but in each case, the catalytic serine and histidine

maintain an identical geometric orientation. To a lesser extent, adjacent groups that stabilise the

transition state are also arranged similarly.133

Figure 1.5 shows a schematic representation of the binding site of trypsin. The primary

binding pocket of trypsin, S1, defined by the residues Asp189, Ser190 and Gly219, is a cavity that is

approximately 10 Å deep and 4 Å by 6 Å wide.110 S3/S4, defined by the residues Leu99 and Trp215, is

a hydrophobic binding pocket on the surface of the enzyme. When a peptide substrate binds to the

enzyme, the binding pocket not only provides specificity by preferentially binding an arginine or

lysine side chain to the negatively charged Asp189 at the base of the pocket, but also helps align the

scissile bond relative to the catalytic triad and the oxyanion hole. Mutant studies showed that the

presence of a negative charge at the base of the binding pocket is essential for efficient catalysis.133


21

S3/S4

Trp215

Leu99

Asp189

Gly219 Ser190

Ser195

His57

Asp102

S1

Gly193

Figure 1.5. Schematic representation of the binding site of trypsin showing the binding pockets and

relevant α-amino acids mentioned in the text.

The oxyanion hole, consisting of the two backbone NH’s from Gly193 and Ser195, activates the

carbonyl oxygen of the scissile bond and stabilises the negative charged developed on it in the

activated complex leading to the tetrahedral intermediate.109

The importance of the specific three-dimensional spatial arrangement of the α-amino acid

residues of the active site was elegantly demonstrated by the synthesis of artificial peptide enzymes

or pepzymes. These polypeptides in general hardly possess any detectable fixed conformation in

solution. Due to the absence of a proper scaffold to align the catalytic machinery, enzyme-like

features are very limited.110,134 Although there was one group claiming that two different cyclic

polypeptides mimicking the trypsin and chymotrypsin active sites possessed nearly the same

catalytic activity and specificity as chymotrypsin and trypsin,135 these results were not confirmed by

two independent other groups that tried to reproduce them.15,136,137

Crystal structures of trypsin in different functional states are remarkably similar with respect

to their three-dimensional structures.125,129,138,139 Changing the conditions of preparation and/or

adding different types of inhibitors leads to crystals with different space groups and unit cell

dimensions. However, these different structures show only little variation in backbone coordinates.

Therefore, binding of inhibitors to trypsin seems in accordance with the lock and key model,

meaning that upon binding no significant conformational changes occur in the enzyme. The crystal

structures of benzamidinium-trypsin and benzylammonium-trypsin will be discussed in detail in

Chapter 2. Also, structures of complexes of trypsin with a wide range of inhibitors derived from the

parent compound benzamidinium, are known. For these reasons, complexes of trypsin with new

inhibitors are feasible targets for computational studies as well.


22

1.3 Isothermal Titration Calorimetry

As we saw in the previous sections, the enthalpic and entropic contributions to the Gibbs energy of

binding can provide information on the binding mechanism. The introduction of a small structural

variation in the inhibitor often results in only a small change in the Gibbs energy of binding, whereas

the enthalpy and entropy may vary considerably.32,34,69,83 Large changes in ∆H and ∆S may indicate

changes in binding mode that are not apparent from the resulting modest changes in ∆G. Knowing

whether a structural variation is enthalpically or entropically favourable, especially in a series of

closely related inhibitors, gives information on the nature of the associated noncovalent interactions.

The temperature dependence of the enthalpy of binding also gives valuable information on the

burial of surface area upon complex formation in aqueous solution.27

The enthalpy change accompanying a chemical process can be determined either directly or

indirectly. Indirect methods inevitably involve calculation of the thermodynamic quantities from

theoretical relationships, such as van ‘t Hoff analyses, where enthalpy changes upon binding are

calculated from the temperature dependence of the binding constant. Both direct and indirect

methods, when put into practice carefully, have been shown to agree within statistically significant

margins.140 However, several measurements in a wide temperature range have to be performed,

which is often not experimentally feasible and leads to large errors in the parameters resulting from

van ‘t Hoff analysis, in particular for ∆Cp.67,141,142 Since isothermal titration calorimetry (ITC) is the

only method that allows direct characterisation of the heat involved in any process,143 it is an ideal

technique to acquire a complete thermodynamic description of a binding process.67,144 The advantage

of ITC over indirect methods such as kinetic techniques is that it is efficient and non-invasive.10,16,30,145

One experiment, if designed carefully, provides both the binding constant and the enthalpy of

binding from which the Gibbs energy and entropy of binding are readily calculated. Furthermore,

chemical modification or immobilisation of the reactants is not required and the system is not

disturbed by, for instance, a spectral probe. The development of these calorimeters has gone a long

way since it was first described by Théophile de Donder, founder of the Brussels School of

Thermodynamics, in 1920.146,147 At present, the new generations of calorimeters are so sensitive that

nanocalories can be measured, meaning that only very small amounts of reactants are necessary.148

With ITC, one directly measures the energetics (via heat effects) associated with processes

occurring at constant temperature. When binding is studied, the goal is to generate a binding

isotherm, a curve that represents the degree of saturation in terms of the ligand concentration.149 To

this purpose, small aliquots of ligand are titrated by a computer-controlled stirring syringe into the

macromolecule solution in the sample cell (Figure 1.6). After each injection, the heat released or

absorbed is measured with respect to a reference cell solely filled with buffer. The heat change is

monitored by the electrical power needed to maintain a small temperature difference between both

cells, which are placed in an adiabatic jacket.


23

sample cell reference cell

∆T

feedback heaterfeed

back

hea

ter

adiabatic jacket

stepper motor

Figure 1.6. Schematic representation of the ITC, adapted from Holdgate.16

Because the amount of uncomplexed macromolecule available progressively decreases after each

successive injection, the magnitude of the raw data peaks becomes progressively smaller until

complete saturation is reached. The heat per injection dQ for binding of ligand L to a macromolecule

M to form the noncovalent complex ML is equal to:

VHMLddQ ⋅∆⋅= ][ (1.10)

where V is the volume of the cell.148,150 This heat change can be differentiated with respect to the total

concentration of ligand in the cell after each injection (the variable under experimental control) to

yield a binding isotherm that can be fitted to the enthalpogram.151 The ability of ITC to obtain a good

estimate of the binding constant depends on the unitless c-value:16,67

nKc ⋅⋅= ]M[ (1.11)

where K is the binding constant, [M] is the concentration of (macro)molecules in the cell and n is the

stoichiometry of binding. This value may range between 1 and 1000; for very low values, the titration

curves become shallow and nondescript, while for very high values the transition region between

ligand binding and saturation is devoid of data points. Routinely, binding constants between 103 and

108 can be measured accurately and conveniently.10


24

1.4 Aim and Outline of this Thesis

This study will be primarily devoted to the interactions of the serine proteinase trypsin with several

artificial inhibitors. A thorough knowledge of the factors that determine inhibitor-enzyme binding

affinity is of fundamental scientific interest as well as a prerequisite for structure-based drug

design.14,27 In that method, the structure of the binding site, preferably complexed with a lead

inhibitor, is used for an intelligent design of new high-potency inhibitors by maximising favourable

interactions with the enzyme. One approach to evaluate the contribution of a specific part of the

inhibitor is to study the influence of small structural variations in this group on the thermodynamics

of binding.29,68,100

This thesis describes an isothermal titration calorimetry study of the noncovalent

interactions governing the binding thermodynamics of benzamidinium-based inhibitors to the serine

proteinase trypsin. There have been many studies of the binding of different benzamidinium

derivatives to trypsin. However, in terms of understanding the origin of the differences in binding

affinity observed, these previous studies have in general had two major drawbacks. First, only the

binding constant is normally reported. This can easily lead to the erroneous conclusion that specific

structural variations do not influence binding significantly. With our approach that yields the

complete thermodynamics of binding, we indeed often encounter enthalpy-entropy compensation

upon varying the substituent, which results in ∆G being relatively constant in comparison to the

changes in ∆H and T∆S. Second, the structural variations are often large, which makes it difficult to

infer the precise reason for the change in binding thermodynamics and mechanism. For these

reasons, it is of interest to study the effect of small structural variations in the benzamidinium

derivatives in detail. In this study, the binding of benzamidinium derivatives has been studied using

ITC. For most of these compounds, binding constants have been reported, but a calorimetric study

has, to our knowledge, not been reported. In fact, only few calorimetric studies on the binding of

benzamidinium derivatives to serine proteinases have been reported whatsoever68,86 and these

studies involve complicated derivatives and the comparison of relatively large structural changes.

Crystal structures and, in particular, molecular dynamics simulations performed by Dr. Alessandra

Villa, have been most helpful in interpreting part of the thermodynamic data.

Chapter 1 has set the stage by highlighting the relevance for in particular drug discovery of

understanding the noncovalent interactions that determine molecular recognition in biological

processes and the thermodynamic signatures that accompany these interactions. Isothermal titration

calorimetry is advocated as an efficient and non-invasive technique to uncover these thermodynamic

patterns. Furthermore, trypsin is introduced as an ideal model system to study inhibitor-enzyme

interactions.

Chapter 2 presents the binding thermodynamics of the parent compound benzamidinium

chloride, which show the signature of the hydrophobic effect. Structural variations unravel the

nature of the interactions of both the amidinium and the phenyl group with the enzyme. A model

system of the amidinium Asp189 salt bridge is presented.


25

Chapter 3 reports the influence of the inductive and resonance effects of the p-substituent on

the binding thermodynamics. Differences in hydrophobicity of the phenyl ring and different

interactions with bulk water are argued to induce this effect. Furthermore, it is clear that additional

interactions of the substituent contribute to the binding affinity. In Chapter 4, the importance of these

additional effects on the binding of p-substituted benzamidinium chlorides to trypsin is highlighted.

Chapter 4 discusses the role steric and hydrophobic effects of a p-alkyl substituent play in

determining the interaction between the inhibitor and the enzyme. To this end, thermodynamics,

quantitative structure-activity analysis and molecular dynamics simulations (performed by Dr.

Alessandra Villa) of a series of systematically varied p-alkyl substituents are helpful. The increased

binding affinity and the hydrophobic behaviour encountered upon elongating a linear tail correlate

with interactions of the tail with the hydrophobic S3/S4 cleft on the surface of the enzyme. The

decreased binding affinity upon increasing the steric bulk on the first carbon of the substituent does

not induce a substantial disturbance of the binding pocket and its surroundings. In Chapter 5, the

fundamental reason for the influence of sterically demanding substituents is found to be the

dehydration of the protein.

Chapter 5 deals with the influence of the p-alkyl substituent on the dehydration of the

catalytic triad. Buffer-dependent thermodynamic experiments show that a larger substituent induces

a larger decrease in the fraction of protonated residues, most likely due to a pKa shift of His57 N2.

Molecular dynamics simulations corroborate that His57 N2 is (partially) dehydrated in

p-alkylbenzamidinium-trypsin complexes and that this dehydration is accompanied by a stronger

hydrogen bond between Ser195 OG and His57 N2. This effect is strongest for the most bulky

substituents.

Chapter 6 describes the synthesis and aggregation behaviour of p-n-alkylbenzamidinium

chloride surfactants. The aggregation behaviour gives valuable information concerning the self-

interaction of p-n-alkylbenzamidinium chlorides. Since these compounds have high Krafft

temperatures, mixed solutions with both cationic and anionic cosurfactants were studied. Analysis of

the thermodynamics of mixed cationic solutions shows, in comparison to surfactants without

electron delocalisation in the head group, a lowering of the Gibbs energy of aggregation that is

enthalpically driven. Mixing with anionic cosurfactants results in the formation of (pseudo-)

catanionic surfactants.

Chapter 7 reviews the most important conclusions from this thesis and, based on that,

suggests new research projects in the field of binding of benzamidinium-based inhibitors to trypsin.


26

1.5 References and Notes

(1) Ball, P. H2O. A Biography of Water; Weidenfeld & Nicholson: London, 1999.

(2) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures; Springer-Verlag: Berlin,

1991.

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