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Computer Assisted Simulations and Molecular Graphics Methods in Molecular Design. 1. Theory and Applications to Enzyme Active-Site Directed Drug Design O. T A P I A , M. P A U L I N O and F.M.L.G. STAMATO Department of Physical Chemistry, Uppsala UniversiO,, Box 5"32, 751 21 UPPSALA, Sweden. (Received: 10 June 1994; in final form: 5 July 1994) Abstract. A survey is presented of model building techniques, computer-assisted molecular dynamics simulations and a new theory of enzyme catalysis. Some aspects of the theoretical formalism are given. Enzyme active-site directed drug design is illustrated with examples taken from molecular modeling studies using FAD-containing disulphide oxidoreductases, proteinases and carbonic anhydrases. Key words. Drug design, enzyme catalysis, molecular graphics, molecular modeling, computer simulation methods.

1. Introduction Molecular graphics and computer-assisted simulations [1] are invaluable techniques for the design of drugs, drug receptors and transport molecules. These methods offer a practical way for determining average geometric structures, atomic fluctuation patterns and thermodynamic properties of biomacromolecules, ligands and molecular complexes. Computer-assisted molecular design is benefiting from techniques and results drawn from at least four important contemporary fields of research: (i) Structural chemistry, including high resolution X-ray crystallography [2, 3] and NMR [4, 5] methodologies [6], which produce atomic resolution characterizations of ligands (drugs), proteins, nucleic acids and molecular complexes; (ii) Genetic engineering and molecular immunology; (iii) Information technology, with recent breakthroughs in graphic work stations and the concomitant progress in software design; (iv) Theoretical chemistry, which provides the basis for the design of sound computer-assisted simulation tools, such as modern classical (statistical) mechanics techniques and advanced ab-initio quantum chemistry; this latter allows the calculation of analytical gradients (forces) and Hessian matrices - the elements of which are second-order derivatives of the total energy with respect to geometric parameters - that, once diagonalized, provide essential information to characterize the nature of the stationary points on the energy hypersurface. The integration of tools and methods coming from all these areas is influencing the development of modern molecular chemotherapy and shaping a new research field, molecular biotechnology [7] and, more broadly, molecular engineering. Software, based on molecular dynamics (MD) techniques, is now available to refine the structure of proteins obtained from either X-ray diffraction or multiMolecular Engineering 3: 377-414, 1994. © 1994 Kluwer Academic Publishers. Primed in the Netherlands.

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dimensional NMR measurements [8-10]. Other classes of computer programs address the problems of automated protein sequence alignments, secondary structure predictions, and model building of proteins; in the latter case, coordinates of high-resolution structures serve as templates to propose models for new homologous proteins of unknown 3D structure. Genetic engineering techniques are generating proteins and their sequences in huge quantities. This pace is not matched by the production of experimentally determined 3D structures. X-ray crystallography is still limited by the ability to obtain suitable crystals. Thus, the demand put on the structural chemist to generate structural knowledge can be satisfied by resorting to reliable model building techniques. In this paper, a number of cases are examined and limitations emphasized. For a recent overview on engineering and design see reference [11]. Computerized drug design is still promising but not yet here [12]. Progress has been made, as this paper intends to illustrate, but, there is still some way to go before the fundamentals of receptor-ligand interactions [13, 14] are fully understood. Up till now there have been excellent descriptive schemes that serve to organize most of the experimental data. This is better illustrated by the present state of the theory of enzyme catalysis. In the same way as an enzyme (E) and a substrate (S), by forming a complex (E-S), undergo specific conformational changes resulting in the formation of the active site, the activated enzyme-substrate complex, a drug (D) and a receptor (R), via a specific complex (R-D), would undergo conformational changes to attain an active state. The analogy is not superficial. For competitive inhibitors of enzymes, the binding site acts as the receptor and the inhibitor as a drug [15, 16]. This issue is extensively analyzed in the first section of this review. Particular attention is paid to a recent theoretical approach of chemical reactions which seems to be better adapted to discuss the connection between kinetics and molecular events in proteins and solvent in general [17-21]. Selected examples are examined in Section 2, while reference [22] gives an overview of pharmacologically relevant proteins. 1.1. ENZYMES AND CATALYSIS

The understanding of the electronic and molecular determinants of an enzyme's catalytic activity is being radically transformed by the results obtained from modern protein engineering techniques. In the light of present experimental knowledge, it is convenient to make a distinction between those primary conditions, giving a protein its catalytic nature, from those determining its catalytic efficiency. These factors must be treated separately in a theoretical description and interpretation of the catalytic phenomenon. Theoretical chemistry has contributed to a better understanding of enzyme catalysis by introducing basic concepts and increasingly accurate calculations [2325]. The current understanding of enzyme catalysis is dominated by the seminal hypothesis launched by Pauling [26]: the binding site of enzymes is complementary to the activated complex rather than to the substrate of the reaction to be catalyzed. This idea brought into focus the transition state theory of activated processes which provided a successful descriptive picture. In the standard theory of enzyme catalysis [27, 28], Pauling's activated complex is mapped on to the transition state

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of the absolute reaction rate theory [29]. This leads naturally to the dictum: the enzyme should bind the transition state more tightly than the substrate, by a factor corresponding to the increase in the rate of reaction due to the enzyme. As a consequence, enzymes are not expected to have high affinities for their substrates. If they do, the enzyme would not be a catalyst; for a general description see Creighton [28]. It is this view which will be critically examined in this paper. Enzyme catalysis is a complex process. The turnover of enzymes may be selectively influenced by nutritional factors, organelle distribution, cellular differentiation, environmental conditions and metabolic abnormalities of different origins (genetic or not). Rates of turnover in vivo vary with respect to molecular size, isoelectric point, hydrophobicity, the N-terminal amino acid, thermal stability, conformational changes induced by protein-protein interactions, protein-lipid interactions, and the concentration of coenzymes, allosteric factors, and enzyme substrates [30]. Catalytic efficiency is the issue in all these cases. The molecular mechanisms of reactions catalyzed by enzymes are not single step processes; besides the chemical interconversion, a number of other steps are necessary for a complete kinetic description. In Nature, it is not unusual to find that the step where the fundamental chemistry takes place is not the rate-limiting one. The rate-limiting step is commonly displaced towards other molecular events, such as loop or domain isomerization, proton translocation, enzyme regeneration,etc. Thus, besides the primary catalytic step, defined as the fundamental chemical interconversion step, an enzyme performs a number of concurrent processes which determine its efficiency. If the factors determining the primary step are not in place, the enzyme loses its activity. While, if only the efficiency factors are absent the enzyme will retain catalytic activity, although at a noticeably lower rate compared with the wild-type. In the approach presented here, Pauling's activated complex is mapped onto the quadratic zone around the transition structure [17, 31-33]. The concept of precursor and successor complexes, widely used in thermal electron transfer theory [34], is introduced to describe the chemical interconversion step [21]. The structure of such complexes is determined by the geometry of the corresponding saddle point of index one (SP-il) [35, 36] which is obtained from a diagonalization of the Hessian. While in the past such structures were difficult to obtain, contemporary computational quantum chemistry offers a unique way to determine them with high accuracy [19-21, 31-33]. Thus, an independent source of information is available concerning the geometry, stereochemistry, charge distribution, and the reactive fluctuation pattern (dynamics); this latter is embodied in the eigenvector associated with the unique negative eigenvalue obtained after diagonalizing the Hessian (see Section 1.3). The theoretical studies of SP-ils for the interconversion step, in reactions catalyzed by several proteins, strongly suggest that the transition structure for the system in vacuo, identified with the geometry of the SP-il, fits in the cavity of the enzyme when this is complexed with transition state analogs or slow substrates [17, 19, 21, 31-33]. To quote three examples: alcohol dehydrogenases present a generic endo transition structure (TS) for hydride transfer; carbonic anhydrases show that zinc tetra co-ordination is required to obtain a reactive primary step for the interconversion of bicarbonate into carbon dioxide and hydroxide ion; and

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most importantly, in Rubisco (1,5-bis-phosphate ribulose carboxylase/oxygenase) the bifunctionality could be rationally described with the SP-il obtained with ab initio MO techniques [19, 21, 32, 37, 38]. In these examples, the substrates are always molded into a geometry similar to the one calculated for the corresponding SP-il. This geometry is different from the one describing the ground state reactants, it corresponds to the geometry of a precursor complex. Thus, from the in vacuo perspective, the reactant-enzyme binding process can be thought of as a substrate being deformed and molded into a geometry determined by the corresponding SP-il in order to fit into the active site; this does not imply structural identity. The work required to deform, or orient appropriately the molecular moieties, comes from ligand binding. This is a recast of Haldane's dictum: catalysis is binding. If the enzyme-substrate (precursor) complex successfully adapts to a neighboring SP-il geometry in the quadratic zone, two things may happen: (i) the concentration of the active species may increase with respect to that found in solution; (ii) the activation energy for the unimolecular primary event may be lower than the overall activation energy in solution. Such a binding process determines the more fundamental condition for catalysis to occur by increasing the concentration of the precursor complex. The induced fit theory [27] is actually one mechanism which describes the molecular events leading to the formation of a complementary surface to enclose the SP-il. The whole idea of transition state analogues reflects the point made in the present approach. Here, all the interaction free energy is used in binding since the molecule has, by construction, the proper surface complementarity to the active site [39-44]. Such molecules are ideal inhibitors, and sometimes may become useful drugs.

1.1.1. Thermodynamic Treatment

A solvent favoring the formation of a precursor complex,e.g, one which may sustain the reactive fluctuation pattern, will increase the reaction rate. If the reaction mechanism is not changed by the solvent, it is rather obvious that in solution, a complex having a geometry not too far away from the one characterizing the SP-il (transition structure) in vacuo should form first. The reactive fluctuation pattern of such a complex has the required information to achieve the reaction; this is a full quantum mechanical effect which will not be analyzed here [20]. Instead, a simple kinetic scheme may help the description of this process [17, 19, 21]. Let E be the environment and S the reactants assumed to be in chemical equilibrium with the solvated precursor E-Si. The structure and curvarture of Si are in (or not far from) the quadratic zone of the generic TS without solvent; here it is implicit that there is a fundamental invariance towards solvation of the structure and fluctuation pattern of the SP-il in vacuo. The following equilibrium results: ka g

~- S (

kd

) E-si,

K r = [E-Si]/[E][S]

=

kJkd

(1)

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Now, the interconversion step corresponds to the change from the precursor complex St to the successor complex S, via the transition structure symbolized by

k+

E-Si,

k-

, E-S,

(2)

This is a unimolecular process. The release of product (P) closes the reaction mechanism: ks

,E + P

(3)

the dissociation rate ks, of the solvated successor complex (E-S,), is usually faster than k÷. Of course, such a situation is not general but it goes beyond the traditional transition state theory scheme. A steady state analysis of equations (1) to (3) produces an expression for the observed rate constant kobs [34]: llkob, = 1/ka + (llKrk+){1 + k_/ks}

(4)

Under thermodynamic equilibrium between R and Si, there are a number of alternatives depending on the actual values of the kinetic parameters. For instance, the following inequalities are usually fulfilled: kd ~>k+ and ks ~>k_. When the interconversion step is rate-limiting, the observed rate constant is the product of the equilibrium constant and the forward rate constant:

kobs ICrk+

(5)

where the equilibrium constant Kr depends upon the nature of the solvent. Thus, for a given solvent that favors the stability of the reactive complex, the reaction would be faster compared with those solvents that shift the equilibrium towards the separated reactants. The solvent can also modify the intrinsic unimolecutar process, namely, k÷. Observe that the intrinsic activated process can be described with the early theory of Kramer. It is at this level that dynamical effects, originating from the coupling with the surrounding medium, must be theoretically treated (see re*. [21 ] and Ehrenberg and Tapia [45] for details on Kramer's like approaches). Note that a contact can be made with the standard transition state theory. One can apply such a theory to get an explicit equation for the forward rate k+, while k_ = 0 and ks ~> k+ [21]. For a bimolecular reaction, where A + B = S and C + D = P, St corresponds to the reactive precursor complex between A and B that the environment may modulate. The equilibrium between reactant and precursor complex is solvent dependent. The free energy difference between ground state reactants and the activated complex can be changed as a function of the nature of the solvent. The chemical interconversion process is unimolecular. The activated complex in the present approach involves the precursor and

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successor complexes as well as the SP-il. Solvent effects can differently modulate the magnitudes of the energy difference between these complexes as well as the gap with respect to the SP-il energy. We assume that it is the geometry and fluctuation pattern of the SP-il as obtained in vacuo which is invariant to passive solvent effects [17, 19, 21, 46]. Note that, if there were an equilibrium, it would be achieved not with the transition state but with the associated precursor complex. Departures from the standard absolute rate theory can easily be taken into account [21]. At the microscopic level, not all events exciting the precursor complex towards the saddle point structure would lead to the formation of the successor complex. Microscopic friction effects may be important in lowering the limiting value that could be obtained from the transition-state-theory rate constant. The coupling of dynamical behavior between the activated complex and the solvent is important. The solvent (or surrounding medium) must fluctuate in phase when the activated complex is vibrating between the extreme structures formed by the precursor and successor complexes [19, 21]. It is worth noting that high levels of noise may inhibit a chemical interconversion. In some cases, it may be that the reaction kinetics is fully determined by the association process, i.e. kd ~ k+, and kob s ~ k,. This type of reaction is fully solvent dependent and the interconversion step is no longer rate-limiting. Another extreme situation may be found if k= ~ ka and ks ~ k _ in which case, obviously, kob= "~ k=. Still, in both cases, the heart of the process is the primary interconversion event but the kinetics reflects other aspects of the overall process. It is worth noting that the stereochemistry and chirality [47, 48] are also determined by the SP-il structure. Note, for example, that in the hydrolysis of ester groups, the transition structure is almost tetrahedral around the carbon-center in the carboxylate moiety whereas in the free reactants the carboxylate moiety is planar, as it is in the product (acid form). If bulky groups are linked to the ester function, they ought to reorganize in order to achieve a geometry resembling the first order saddle point. It is therefore not surprising to find that the solvent E may play a central role in the kinetics of this process. A rationalization of solvent effects on chemical reactions can be started at this point. We do not pursue this issue any further here as it is beyond the scope of this article. We note, however, that the use of the symbol E for the environment has a double objective. It stands for a general environment, but also stands for the enzyme considered as a very specific surrounding medium to the atoms undergoing the chemical inter-conversion step. In this case, E can also change conformation once the precursor complex is formed. Let IF represent the enzyme in its active complex with the substrate; conformational changes take place during the binding process. Note that the enzyme does not bind the substrate in the gound conformational state, S, but it does bind a particular precursor complex g,-. The geometry of this complex corresponds to the complex obtained by productive binding. Although in particular cases it may happen that a non-productive binding is found; even in this latter case, the substrate is molded into a geometric configuration that differs from the gound state but differs also from the SP-il geometry. In most cases, S and Si are not in equilibrium inside the protein. The difference with the standard view now becomes apparent. For a generic situation, the elementary mechanistic sequence is:

ASSISTED SIMULATIONSAND MOLECULARGRAPHICS ka

E + S ~

kd

k+

~ ~--Si "-

383

ks

~ ~_-Sf~----~ E + P

k-

and Kr =

[E-SI]/[EI[S]

=

ka/kd

(1 ')

with a final, usually slow, step for isomerization of the enzyme, back to E. The only invariant in this scheme is Sir, the S P - i l or transition structure. Enzyme catalysis is now described differently. Let Kr(x) be the equilibrium constant in the surrounding medium X , cf. eqns. (1) and (1'). First, the enzyme environment selects the structure of the reactants in a conformation adequate for the reaction so that the equilibrium constant K r ( X ) compared with the same equilibrium in solution K r ( E ) elicits an increase of the equilibrium concentration of the precursor complex. Structural complementarity is the key factor. The process can be described with a thought experiment. First, the substrate S and enzyme E are separately molded into the conformation attained after binding, S; and ~, respectively. Work is then carried out by the enzyme-substrate complex interaction to mold the system into a geometric neighborhood of the activated complex. Since Si should be almost the same in solution and inside the enzyme, the activation energy in solution can be lowered in the enzyme if there is an excess of binding energy over the molding work. We assume for simplicity a uniform binding of the three structure S;, Sis and S~. Thus, the largest is this excess of binding energy over the molding work, the lowest will be the activation energy. The activation energy is always measured from the E + S level. The scheme presented in Figure 1 can help visualizing this description [17, 19, 21]. Second, the surface complementarity of the SP-il and the enzyme's active site imposes a dynamic constraint: the enzyme must fluctuate in phase with the vibration associated with the passage via the saddle point Sil. If the active site atoms were tightly bound by the enzyme, it would freeze the reactive vibrations of the activated complex, thus substrate atoms belonging to groups other than those defining the SP-il may tigthly bind to the enzyme. What enzyme catalysis requires is perfect dynamical "pairing" of both surfaces. From the in vacuo perspective, the enzyme-substrate free energy has been employed in binding the reactants as a precursor complex thereby producing the required conformational changes in the protein. The concentration of the precursor complex increases accordingly. Third, general acid and base groups may intervene to increase the efficiency of the primary and/or other steps, either by changing the entropy factor, or modifying the activation energies between the structures involved in the activated complex. If the precursor complex resembles the saddle point structure, in the present view, they are bound to the enzyme with almost equal strength. The geometry of the successor complex is likely to be highly deformed when compared with the free products. For an experimental illustration see for example Matthews and coworker recent paper on a mutant T4 lysozyme [49]. Knowles' principle of matching of internal states [50] is reflected by the free energy gaps prevalent between the precursor, successor and SP-il species in the

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/

/

+ I u.,,or.,

[

Solvation

,o,v.,o. k. i

/ / ff/ "/

//

=

IIII I

~f ~ nneat~llyzedpath \ /"',,\

',

°,,,/\ ",. \

//

1I I~=~r N Deaetivati°n

ka

E+ R

solvent or enzyme catalyzed path

\ ks X, _ _

I v E+ P

Fig. 1. Energy diagram representing a generic chemical interconversion via precursor (Si), transition state ($if) and successor ($f) complexes. The energy profile in the uniform binding energy approximation is displayed below. Since the activated complex, constructed around the geometry of the transition structure, contains the information about the actual interconversion, it is taken as an invariant feature of the reaction path. The energy is renormalized due to the activated complex interaction with its surrounding medium. The process of activation of the reactants to jump into the precursor complex structure is sketchily indicated; it is at this level where a thermodynamic equilibrium, or a stationary state when product concentration is zero at the beginning of the reaction, may be assumed. Before global equilibrium is attained, the deactivation energy of the successor and the enzyme (or general environment) is sketchily indicated at the right hand side. The kinetics parameters of this model are also indicated. Note that the pathway inside the given environment E and IFare generic. The energies entering this scheme can also be thought of as free energies.

active e n z y m e . W h e n the e n z y m e catalyzes the reaction in the opposite direction, a similar analysis holds. In the activated complex zone, a fine-tuning of free e n e r g y gaps can be achieved by specific functional groups, that are usually lining the c o r r e s p o n d i n g active site; these groups can have different interaction energies with the p r e c u r s o r and successor complexes. Janos H a j d u (personal c o m m u n i c a t i o n [51]) has recently p o i n t e d out that there is a n e w type of e n z y m e s which instead of being selective rate accelerators (Paulingtype catalysts), they w o r k as reaction selectors (non-Pauling enzymes); for an example o f such e n z y m e see H a j d u and coworkers p a p e r [52]. This type of e n z y m e s enter in the general description presented here without further ado. F o r a m o r e detailed analysis o f this t h e o r y see Tapia et al. [17, 19, 21]. 1.1.2. Active Site and Binding Site T h e active site is the physical region delimited by those a t o m s participating in the chemical interconversion process. Such a process usually involves a r e d u c e d set of the substrate atoms: the active atomic space. T h e protein groups lining this region have a surface c o m p l e m e n t a r y in shape to the SP-il. T h e regions o c c u p i e d by o t h e r moieties o f the substrate(s), that are usually b o u n d to the e n z y m e , define


385

the binding site(s); in some particular cases, the solvent may complete the surface of the active site. The necessary and sufficient condition for primary enzyme catalysis is related to the way the substrate is bound. If the SP-il for the primary step is an invariant, the protein active site must acquire a shape as complementary as possible to the shape of the SP-il. This can be achieved by binding the substrates with the conformation of a precursor complex. Productive binding is equivalent to trapping a particular precursor complex geometry; this binding is intimately related to specificity requirements due to the special stereochemistry imposed on the moieties outside the active atomic space by the geometry of the SP-il. Thus, specificity and primary catalysis are intrinsically interlinked. This type of behavior is nicely illustrated for instance by specific catalytic antibodies controlling exo end endo pathways of the Diels-Alder reaction [44]. Let us use the serine proteases to illustrate the points made above. The active site is partly formed by the enzyme, and partly by the solvent. They have a catalytic triad: serine-histidine-aspartate that is presumed to be essential for catalysis. Interestingly, although all three residues have been mutated into none active residues the protein still presents catalytic activity. The reaction is 1000 times faster in the presence of the mutant enzyme than in absence of it [53]. One simple explanation follows from the present binding theory: the incumbent peptide group is molded into a geometry resembling the one characteristic for OC-NH bond breaking as it binds to the protein. As water is present at the active site, the primary reaction can still proceed, albeit less efficiently than the wild-type. This explanation was first advanced in the discussion to of paper by one of us [54]. The active site is formed sometimes in a relatively complex process, that may or may not include induced fit. This has been confirmed experimentally in different systems. Thus, with liver alcohol dehydrogenase (LADH), the active site at the instant when interconversion occurs is in a deep pocket inside the protein, shielded from the bulk solvent. When the process starts, the enzyme is open and the binding sites are solvated. Coenzyme binding initiates, with the first conformational change, the formation of the active site. The substrate moves through a barrel-like structure lined mainly with hydrophobic residues until it binds to the catalytic zinc, and the enzyme achieves a final closed conformation [55-57]. At the chemical interconversion step the protein has changed conformation, water has leaked out into the solution and the protein active site surface becomes complementary in shape to the SP-il in vacuo [31, 58]. For alcohol oxidation, the interconversion step (hydride transfer) is not rate-limiting. The catalytic process is controlled by coenzyme release. 1.1.3. Transition Structure Invariance. H a m m e t ' s L F E R Logically, the analysis carried out above can be summarized in the following postulate: For a given interconversion reaction, taking place in any solvent or surrounding media with the same mechanism f o r the primary step, the in vacuo transition structure and its fluctuation pattern are the fundamental invariants. Differences in degree, but not in essence, are of course present for different surrounding media.

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One of the interesting results obtained from analytical gradient ab initio MO studies is a sort of geometric invariance of the fragments participating in a first order saddle point geometry. This is seen when the fragments are found in different reactions and therefore geometric comparisons can be performed [18, 19, 21, 32, 591 . The invariance of the transition structure (TS), or SP-il structure, can be used to derive a mathematical relationship between the activation free energy (rate) of a system and the free energy for an equilibrium process involving a common molecule. This is possible if there is a common fragment in the TSs of the corresponding interconversion processes. Consider a chemical compound that can intervene in two different processes. One may be the equilibrium between its acid form and the corresponding conjugated base for which the equilibrium constant is Ka. The second can be an interconversion process. Using the kinetic view, the equilibrium constant Ka is written as the ratio between the forward and backward kinetic constants, K~ = ka+/ka_ ; where Ka is is the conjugated acid dissociation constant corresponding to the common fragment. Thus, from absolute rate theory, ka+ ~ e x p (~Ga+ ~ / k B T ) . Now, for a family of related compounds undergoing the same type of equilibria and interconversion as the parent molecule, if in the chemical reaction the TS-ffagment is equal to the one found for the acid-base equilibrium, and its electronic structure does not change in the family of molecules, then a AAG due to substituent effects within the family will be equally reflected in both processes; all other things being equal. One can then write a relationship between the activation free energy for the interconversion step, AGicx~. and A G a + x # : AGic~* = F{AG,+x~ }

(6)

where x stands for a given member of a family of compounds, and ic refers to the interconversion step; F has a particular functional form. The simplest function can be taken as a proportionality constant r, namely, AGicx* = r(iXGa+x*). Now: log kicx = r log ka+ = r log Ka ka_ = r log Ka + constant

(7)

Equation (6) is based only upon the principle of fragment invariance in the transition structure. It is then obvious that for cases where the fragments are strongly perturbed by the x-substituent, those molecules do not necessarily fulfill a relationship of type (7). For example, it is well known that o-substituents in benzoic acid cannot be correlated with the m- and p- in the base-catalyzed hydrolysis of their esters. The explanation follows trivially from the present theory. Note that equation (7) is nothing but Hammett's relationship; for a modern review and references to the pioneers of this field see the text by Shaik et al. [60]. The linear free energy analysis of structure-reactivity correlations have been considered to give quantitative measures of the transition state structure [27, 60]. In practice, Hammett plots are obtained when the rate constant of a given reaction is plotted against the equilibrium constant of a reference process and the reactant is varied using different substituents. The slope of the resulting line is considered to be a measure of the similarity of the rate process to the reference equilibrium

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process. This similarity coefficient is often denoted by the parameter a or 13 and it is utilized to measure the extent to which the transition state resembles the reactant or the product. For this reason this coefficient was thought to provide a quantitative measure of transition state structure when its value lies between 0 and 1. This principle is commonly termed the Leffler-Hammond postulate. These basic ideas lead to all the key models developed over recent years for predicting changes in transition state structure [60]. In fact, the idea of invariant transition structures gives a simple rationale to these empirical equations. What is actually changing is the structure of the precursor or successor complex involved in the reaction. Recent work by Sinot et al. [61] can easily be interpreted in the present theoretical approach. The use of Hammett-like equations in QSAR has been discussed by Hansch and Klein [62].

1.1.4. Drug-Receptor Complexes An essential factor determining drug action is its binding to the receptor. Drug design, of course, must encompass properties other than receptor interactions, e.g. pharmacokinetics, pharmacodynamics and adverse toxicity to target cells or organisms [63-65]. For those cases where the drug is targeted as an inhibitor of a particular protein, binding as a transition-state-analog offer a definite geometric template on which to design especial drugs. Wolfenden and Kati [66] have tested the limits of protein-ligand binding discrimination with transition state analogs. Most hydrophilic drugs that act inside the cell are structural analogs of natural substrates normally transported into the cell by carrier proteins [67], which modulate the binding between a receptor and a drug. A similar mechanism has been proposed for the chemoprevention of cancer using protease inhibitors [16]. In enzyme catalysis, the binding of the substrate is inseparable from the activation of the enzyme to form the active site compatible with the primary chemical interconversion step. Molecular evolution can be described as a process of adapting the protein structure in order to get surface complementarity with something invariant: the transition structure. A similar approach may be valid when describing drug-receptor binding. Thus, for those drugs having large conformational spaces, binding to the receptor can be done with a geometric structure in the neighborhood of a particular SP-il rather than with a minimum energy structure. If the drug cannot perform work on the receptor to activate it, the situation is close to an antagonistic effect. If the drug can change its internal state, one may imagine the existence of a passage via a saddle point of index one on a conformational hypersurface, or if the drug is metabolized a transition state structure may be the active species. The receptor would bind the drug molded in a geometric arrangement characteristic of the precursor complex associated with the SP-il responsible for the interconversion process. This mechanism may be operating for histamine in complexes with its receptors [68]. If these ideas are correct, attention must be focused on saddle points connecting two molecular basins (valleys) on the potential energy hypersurface and assume drug-receptor binding to be fairly analogous to the binding of the activated complex in enzyme reactions. Drugs targeted towards particular enzymes can totally or partially occupy the

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binding site (not necessarily the active site) of the enzyme. Examples of such binding are discussed below for glutathione reductase, trypanothione reductase and some other systems. Here, molecular modeling and computer-assisted simulations have helped in the design. 1.2. COMPUTER SIMULATION TECHNIQUES

Molecular dynamics simulation schemes for the study of biomolecules are based upon a partitioning of a larger complex system into two portions or subsystems: the system of interest or generalized solute and its surrounding medium [69]. Two general techniques are usually employed to perform such simulations for the system of interest. One of them considers the generalized solute as a microcanonical ensemble; in which case, the total energy is conserved. This procedure has been extensively used in the literature [70-72]. The other procedure considers the generalized solute as "open" in the sense of energy exchange with the surrounding medium, temperature being the controlled variable [73]. If both subsystems have a local thermal equilibrium with small fluctuations in local temperatures, then, on the time scale of atomic motions, energy exchange between them would ensure global thermal equilibrium. According to the premises used to get separability of both systems, the generalized solute looks like a Brownian particle. Time dependent processes associated with a velocity dependent dragging force and the Langevin stochastic force are two sources of interactions. In order to make them explicitly appear in the formalism it is necessary to resort to the theory of generalized Langevin equations. In phase space, the coordinates of a particle are represented by the point (Pe, re ), where Pe is the linear momentum and re the cartesian space position vector of the i-th particle. Ps represents the set of N-particles momenta of the system of interest: P, -- (Pl, • • •, PN); and R, describes the spatial positions: R, = ( r l , . . . , rN). The time evolution of P, is given by the generalized Langevin equation: Ps = - O V ( R s ) / O R s - O(Vm~)m/OR~ + F~(t) + f dt'Op(t - t ' ) P s ( t ' )

(8)

The first term describes the internal forces which in this case are derivable from the potential energy function of the system of interest, i.e. the intramolecular force field; the second term is a static-like force created by the surrounding medium, the symbol (...)m represents a statistical mechanical averaging over the space variables of the surrounding medium (m) with fixed coordinates for the system of interest; in numerical simulations, this term contributes forces with avoid implosion or explosion of the subsystem when the surrounding medium particles are only implicitly considered. The other two terms are time dependent: The stochastic Langevin Fs(t) and delayed (memory) force terms. These are the subject of specific modeling in practical simulations. The memory matrix ~(~-) is related to the autocorrelation matrix of the stochastic force Fs (t):

• s (,r) = (Fs

F ; (0))(L(0), P ; (0))-1

(9)


389

This equation is an expression of the second fluctuation-dissipation theorem. The scalar product is defined in terms of matrix elements with the help of standard statistical mechanical correlation functions: = f dFof(Fo) Fi(t)(t)F*j(O) = (F~ (t), F*(0))

(10)

where the star indicates the complex conjugation. Fo = (Ps, Rs) is a point in phase space for the system of interest. The time integral of ~s (t) is a generalized matrix friction function: y(t) = f dt'c~(t - t')

(11)

for a review and references, the reader is referred to the paper: [46, 56, 69]. In thermal equilibrium, f(F0) is a probability density function in phase space. In the canonical ensemble this function is given by: /(F, 0) =/(Fo) = e x p ( - f l H ) / f dF0 exp(-/3H)

(12)

with/3 = 1/kB T; kB stands for the Boltzman constant, T is the absolute temperature and H is the Hamiltonian of the system of interest: which is the sum of the kinetic energy and the potential energy. This distribution function is used to carry out the statistical averaging ( ( . . . ) ) . The (classical) partition function Z is given by Z = fdr0 exp(-/3H)

(13)

This function of temperature and volume is related to the Helmholz free energy. 1.2.1. Force Fields

The potential energy function, V(Rs), describes the interactions between the atoms in the system of interest. For a protein or nucleic acid, the potential is composed of terms representing covalent bond stretching, bond angle bending, quadratic dihedral bending which takes care of out-of-plane and out-of-tetrahedral configuration motion, sinusoidal dihedral torsion, interatomic repulsive forces and van der Waals attractive interactions which make up for the Lennard-Jones potential used in normal liquid simulations and Coulomb interactions. Empirical parameter sets have been developed and used for example in C H A R M M [74], GROMOS [75] or A M B E R computer programs from P. Kollman's group. The algorithm commonly used in the GROMOS package to couple the system of interest to a thermal bath at temperature To leads to: [~, = - O V ( R , ) / a R s - (1 - To/T)Ps(t). T

(14)

the matrix y is usually taken as a diagonal scalar matrix: T1. The set of parameters used initially [76] corresponds to an electroneutral system where the presence of counterions is mimicked by spreading a counter charge onto the fully charged

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side-chains, including the the N- and C- termini, in such a way as to retain Hbonding capabilities. This scheme has been referred to as the none-inertial solvent (NIS) model. More recently we have included terms representing O(Vms)m/OR~ as well as simple representation of the memory kernel: /,,

=

-OV(R~)/OR~-

a(Vms)mlORs

(Ps)¢ • Y' ( z) - Ps(t). y ( 1 -

To/T)

(15)

the term (Ps), is a time average over the interval z, after each of these intervals the microscopic friction coefficient y'(z) is recalculated by using knowledge about atomic surface accessibility. The term O(Vms)m/OR, is evaluated by using atom solvent surface accessibility [77] calculated at selected points of the MD trajectory. Note that the integration of the equations above does not ensure a correspondence with a canonical ensemble. For further discussions on this topic we refer the reader to the paper by Bonomi [78] and the recent book by Hoover [79] where the Nose-Hoover method is thoroughly discussed. 1.2.2. Free Energy Calculations and Thermodynamic Cycles Free energy calculations on chemical and biological systems have gained increased attention in drug design. The technique has quantitative power and can be used, among other things, to predict trends in free energy differences for binding processes and mutation effects on protein structure and stability [24, 80]. The Helmholz free energy for a molecular system is related to the partition function and volume (v) of the system of interest: A = - k B Tln(Z/v)

(16)

For a system having two possible equilibrium thermodynamic states, a and b say, the difference in free energy is given by: ~dtab =

Aa - Ab = --kB T ln(Za/Zb)

(17)

where now Za and Zb are the partition functions for states a and b. Note that the possibility of identifying such states can be related to the fact that each one of them can be assigned a Hamiltonian Ha and Hb, respectively. Furthermore, both have the same volume. Then, using a A-weighted linear combination of these Hamiltonians one can construct a model Hamiltonian, H(A) that can be transmuted from Ha for h = 0 to Hb for h = 1: H ( , q = (1 - A ) H a +

(18)

The free energy at a given value of lambda now follows from a formula similar to eq. (16): A(A) = - k B T l n Z(A) + kB T i n V. The second term does not depend upon the coupling parameter. To get the variation of free energy due to this A-

ASSISTED SIMULATIONSAND MOLECULARGRAPHICS process, the partial derivative of the free energy is first calculated: at constant volume. Now, using standard rules for integration:

AA,,b =

(OA(A)/OA)V dh

391

(3A(h)/Oh)v

(19)

This integral is transformed into the ensemble average of the mechanical property of the system which can be evaluated with a molecular dynamics or a Monte Carlo simulation. The formula for the partial derivative reads now as:

M , b = f (OA(h)/Oh)v da = f {(OH(h)/Oh)v)a dh

(20)

the integration is still between zero and one in the variable lambda, but now the statistical average is performed with the Hamiltonian H(A). The last equality represents the essence of the thermodynamic integration method. For mutation processes where the h-dependence resides only in the potential energy V(Rs) and not in the kinetic energy term, one gets:

(OH(h)/Oh)V = (OV (h)/Oh)u

(21)

In this case, a more simple perturbation method can be used too. For an H(X)-system depending linearly on A, the thermodynamic integration can be even more simplified. In this case (OV(h)/Oh)v is independent of the parameter A, it can be written as the difference of the potential energy functions Va-Vb. The h-dependence remains only at the statistical average level in the integration formula:

N4av = f (Va - Vv)xdh ~- £~(Va - Vb)~,ZXhk

(22)

Where the index k runs over the number of windows selected for the numerical integration. Note that the statistical average (Va - Vb)xk is carried out with H(ak). The main problem associated with this technique is the difficulty in getting an adequate sampling of the phase space. For a detailed review on the exploration of the phase space of molecular systems to get reliable free energy differences, the reader is referred to several important papers [10, 81-83]. Free energy thermodynamic cycles are extremely useful to work out quantitative information about important processes in physical chemistry. Consider the prediction of the inhibition constants in a series of inhibitors (I) bound to the same binding site of the protein P. Differential solvation effects are actually one of the most important factors. As the inhibitor binds to the protein, it displace s a given amount of solvent from the binding site. The free energy cycle represented in the Scheme below permits expressing the dissociation free energy in the solvent (s),

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O. T A P I A E T AL.

I(v) + P(v) c

~ I - P(v)

3G~olvl

6G°(v)

3Gsolv2

$

;

I(s) + P(s)

c

~ I - P(s)

8G°(s)

namely 8G~(s), in terms of the dissociation free energy for the same complex in vacuo, namely 6G~(v), and the solvation free energies of the protein, inhibitor, and P-I complex: - 3 G ~ ( s ) : -3G~,(v) +

(6G~o,~- 3G~olv~)

(23)

If a comparison is made with another inhibitor I', that binds at the same binding site than I, the difference in dissociation free energy is given by: - 33G

= - (6G3 (s) -

8G~, (s)) = - 6(G~ (v) -

3G~, (v))

+ (6G~o,v2 - 6G~olv2, ) - (6Gso1~1 - 3 G ~ o l v l , )

(24)

the in vacuo 88 free energy term, (SG3(v) - 3G~,(v)), can be obtained by using the h-technique; the inhibitor I is mutated into I at the binding site of P. The term (SG~o~v~ - 8GsolvV) is reduced to the difference in solvation free energy of I and I'; since P is assumed to conserve its conformation its solvation energy cancels out in the 86-calculation. The term (3G~olv2- 6Gso~v2,) reflects the difference in solvation energy of the complex I'-P with I-P. Now, 8G~o~vl and 3Gsolv2 are a sum of a solvent-solvent cavity term (Gcav) solute-solvent van der Waals term ( G v d W ) and a solvent-solute electrostatic polarization term (Gpol). The first two are related to the solvent accessible area. They contain solvophobic forces: hydrophobic effects (hyd) and in the present case they represent solvation-desolvation process of the surfaces involved in the complex. The solvation free energy can be written as: - 3G~(s)

= - 363(v)

+ (3G~o,v2 -

- 6(SGhyd + 6Gpol)

3Gsoivl)

= - 6a~(v)

(25)

the difference in solvation free energies ( 3 G s o l v 2 - 8Gsolvl) is basically represented by the work required to solvate-desolvate the surface contact in the complex, 88Ghyd; and the electrostatic polarization forces 88Gpol [84]. The equation above implies a linear free energy relationship between 8Ga (s) and 86Ghyd. There is a particular case that can easily be handled. This is the one where the two complexes I-P and I'-P have almost the same accessibility surface and the electrostatic term is relatively unchanged. The term (SGsoiv2 - 3 G s o l v 2 , ) cancels out. For inhibitors differing in surface terms of hydrophobic residues only, 88G only depends upon the change in hydrophobicity term. The application to the prediction of genetically engineered proteins is relatively simple. Once an in vacuo MD simulation has disclosed invariance of the mutant configuration space with respect to the wild-type and the structure in solution is similar to that in vacuo the difference in free energies can be traced back to


393

changes basically involving the mutated residues. For competitive inhibitors the inhibition constant Ki is the inverse of the dissociation constant of the enzymeinhibitor complex (Kd). The change of lid will follow the change in hydrophobicity if the mutation involves neutral and/or hydrophobic residues. The inclusion of electrostatic contributions can be done semiquantitatively by using well defined calculation schemes [46, 56, 84]. Recently, Aqvist [85] has proposed a promising empirical procedure to calculate inhibitor binding constants, and Ben-Naim has given an overview on solvation problems from small to biomolecules [86]. 1.3. QUANTUMCHEMICALTECHNIQUES The forces acting on the nuclei of the system, in principle, are derived from quantum mechanics. For a system described by the Hamiltonian H(r,X), where r stands for the electron coordinate position vector operators and X represents the nuclei coordinates, the forces can be calculated by using the Hellman-Feynman formula: F~, = - O V ( X ) / O X k : - ( * ( r ; X) [0H/0Xk [~(r; X))

(26)

where ~(r; X) is the total electron wave function for a fixed nuclear configuration; H is the sum of a nuclear Hamiltonian, Hn, and an electronic one, He, in the Coulomb representation. This latter includes the inter-nuclear Coulomb interaction and Hn only contains terms associated with the nuclear kinetic energy operators. If quantum mechanical effects of nuclear dynamics are negligible, then the nuclear motion is treated classically. Let K be the classical kinetic energy for the nuclei, then the total energy W is given by: W = V(X) + K = (~(r; X)I He [g~(r; X)) + K

(27)

Quantum chemical techniques are available to obtain upper bounds to the expectation value (~(r; X)[ He ]'¥(r; X)). For a one-determinant representation of the wave function, built upon a set of molecular orbitals (MOs), the variational principle leads to the Hartree-Fock (HF) theory. The orbital eigen-equations are nonlinear in the sense that the effective one-electron operator (Fockian) is a function of the occupied MO manifold; for this reason the system is solved selfconsistently by imposing the invariance of the orbitals generating the occupied manifold. When the MOs are expanded as linear combinations of functions (usually centered at the atomic nuclei; a basis set) the variational principle leads to matrix equations of the Roothaan type. If the matrix elements are analytically or numerically calculated the method is dubbed ab initio. The physical nature of the problem determines the type of basis set to be selected. For a general description of quantum chemical methods applied to biochemical systems the reader is referred to the book by N~iray-Szab6 et al. [87]. The nature of relevant stationary points on the energy hypers~arface V (X) can be determined by calculating the matrix of second derivatives of the energy with respect to the nuclear coordinates, the Hessian. This Hessian is diagonalized to

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O. TAPIA ET AL.

characterize the nature of the stationary points. For a minimum, all eigenvalues are positive. A first order saddle point is defined by the existence of only one negative eigenvalue. Levy and Perdew [88] showed that for some approximate formulations, such as Hartree-Fock, the change in the error of the energy upon geometry change, is zero through second order perturbation term for Coulomb Hamiltonians. This may explain why approximate energy curves often closely parallel exact curves and give accurate geometries. Thus, minimal basis sets might be good enough to obtain adequate geometries in a number of cases; absolute energies are usually unreliable.

1.4. MOLECULAR GRAPHICS TECHNIQUES

Molecular graphics techniques have grown at a fast pace with the development of protein crystallography. From the wire models of Kendrew up to the present advanced molecular graphics techniques, impressive progress has been achieved. A lively review of this subject has been made by Olson and Goodsell [89]. In our laboratory, Nilsson [90] has produced MD-FRODO, which is an enhancement of F R O D O , previously developed by Alwyn Jones, and from TOM [91] which has a docking facility added to FRODO. The program supports the display and analysis of molecular dynamics trajectories. Topology has also contributed to the study of protein structures. Thus, Arteca et al. [92] have implemented knot-theoretical methods to analyze the backbone of proteins. The method is rather abstract in form and for a pedagogical introduction to knot theory, it is advisable to read the paper by V.F.R. Jones [93]. The concept of surface fractality has also been implemented to analyze the surfaces of proteins. Actually, it was used to build up a molecular complex between the retinol binding protein and transthyretin [94, 95]. The basic idea is that at the atomic level of resolution a surface does not necessarily have a dimension equal to two, its fractal dimension is somewhat larger due to protrussions and involutions in 3D. The degree of roughness presented by a protein surface changes with the folding pattern. Surfaces with high roughness can have better interactions with small molecules or other surfaces with a similar degree of roughness. Smooth surfaces simply glide on top of one another. Unfortunately, the fractality index has not yet found widespread applications. One of the most useful graphics programs for display purposes is RIBBONS [96, 97]. Several commercial programs are available with excellent graphics interfaces [89].

2. Enzyme Active-Site Directed Drug Design The acceleration of the rate of specific reactions by enzymes was attributed to the work done by the protein to mold the reactants into a configuration belonging to the quadratic zone of the SP-il (transition state) describing the primary interconversion step. Molecules that can be easily molded, or already have such conformation may act as inhibitors if they bind at the binding site or at the active site or both. The interaction energy between the protein and this type of ligands will


395

then be fully transformed into binding energy. These are usually dubbed: transition state analogs. Such TS-analogs are being designed and tested for clinical use in a number of enzyme systems. Here, we will review some aspects of this vast subject. 2.1. FAD-CONTAININGDISULPHIDE OXIDO-REDUCTASES The parasitic protozoa Trypanosoma and Leishmania cause a variety of diseases both in man and in domestic animals [98]. In humans, T. Cruzi is responsible for the American trypanosomiasis (Chagas' disease), while African sleeping sickness is caused by T. brucei gambiense and T. brucei rhodesiense. In cattle, nagana is produced by T. congolense. These parasites may be selectively susceptible to oxidative stress by the reduced oxygen metabolites superoxide, hydrogen peroxide and hydroxide radical. In mammalian cells, one of the mechanisms used to eliminate free radicals involves the enzymatic couple glutathione reductase(GR)/glutathione peroxidase. Glutathione peroxidase reduces H202 to water by using the oxidation of glutathione (GSH). High levels of GSH are maintained by GR-catalyzed reduction of GSSG, the oxidized glutathione. In trypanosomatid parasites, another member of the FAD-containing disulphide oxido-reductases, trypanothione reductase (TpR) maintains the level of reduced trypanothione (TSH) [99]. G R does not exists in the parasite. It is the reduced TSST which increases the level of GSH by chemically reacting with GSSG, thereby exerting a function similar to GR. TpR, which is found in parasitic protozoa such as Trypanosoma and Leishmania, is structurally related to glutathione reductase [100]. Furthermore, although the catalytic mechanism seems to be closely related, the enzymes have a striking degree of mutually exclusive substrate specificity. This fact offers the possibility to design selective antiparasitic drugs [98, 101]. Besides structural knowledge - see [100] for an excellent overview and references on X-ray structures - a good understanding of the mechanism at both molecular and electronic level, is desirable to help design new and hopefully effective drugs. The X-ray diffraction studies together with molecular modeling yield invaluable knowledge on the active site topography, as well as putative inhibitor binding sites. We discuss here results obtained from docking model substrates to GR and a model-built structure from T. congolense [102]. The modelbuilt structure is a fairly good representation of TpR's 3D structure as shown by a comparison made in our group. The overall reaction implies the transfer of two electron equivalents from reactants and a proton from the solvent to form the products. The active site of glutathione reductase provided an example of near transition-state structure for hydride transfer between the nicotinamide and the isoalloxazine moieties [103]. The global fold of G R is displayed in Figure 2, with a ribbon representation of the dimer. The dimer contact region is at the center and on the sides, the isoalloxazine ring of FAD is visible.

2.1.1. The Active-Site Structure The active site of GR is located at the interface between the two monomers; it includes, as fundamental electronic components, FAD and the amino acid resi-

396

O. TAPIA ET AL.

Fig. 2. Glutathione reductase. Coordinates are taken from the Brookhaven PDB and the ribbon picture was constructed with a SG-graphics workstation. The protein corresponds to a model-built dimer of glutathione reductase where Gly-418 has been "mutated" into the bulkier tryptophan. The mutated system has recently been studied by Perham and coworkers who showed that cooperativity is induced by this single mutation [154]. The tryptophans can be seen at the center making a stacking interaction with a phenylalanine. A bridged electron transfer interaction connecting both active sites is a possible interaction that might be responsible for cooperativity.

dues: Cys-58 and Cys-63. They are involved in the redox active disulfide bridge [100, 104, 105]. The active site, at the level of the coenzyme, is occupied by the nicotinamide ring which lies almost parallel to the plane of the isoalloxazine moiety of the F A D . On the opposite side of the isoalloxazine ring the active disulphide bridge which provides the active site for the substrate is found. This spatial distribution m a y help actual electron transfer via this molecular device. The protons required to complete a nominal hydride are obtained from proton relay systems found in the neighborhood of the active site [102] but, according to the view discussed in Section 1, such systems only influence the efficiency of the enzyme rather and not the intrinsic catalytic power. 2.1.2. NADPH Binding Site Tyr-197-which has a flexible side chain-is located within the N A D P H binding site and in the absence of N A D P H , the active site is open to the solvent. After binding of the nicotinamide, the site is closed by a m o v e m e n t of this side chain. This isomerization forms the active site surface required for the electrons to be transferred from N A D P H to F A D . A t the nicotinamide binding site, an ion-pair formed by Lys-66 and Glu-201


397

acts as a source of catalytic efficiency. The premises for an alternative e-transfer pathway have been previously discussed by us [102]. Basically, the system would have two different pathways to accomplish the hydride transfer step. The same situation is found in the TpR active site. The numbering of the residues is altered, of course, due to residue insertions and deletions [102]o Here, the disulfide bridge links Cys-51 to Cys-56 and the nearby proton relay system is composed now by His-460' and Glu-465' and the ion-pair at the nicotinamide binding site is formed between Lys-59 and Glu-201. Tyr-197 performs the same role as in GR.

2.1.3. Substrate Binding Site Let us now examine the substrate binding site of both TpR and GR. Oxidized glutathione, GSSG, is formed of two halves of L-glutamyl-L-cysteinylglycine, GSH, linked by a disulfide bridge. GSSG binds to an asymmetric site located at the dimer interface of glutathione reductase making the two halves distinguishable. They are designated GS-I and GS-II, the former being covalently linked to the enzyme during catalysis. Accordingly, the amino acid residues of GSSG are named Glu-1, Cys-1, Gly-1 and Glu-ll, Cys-ll and Gly-ll. The pocket for the glycine residue in the so called GS-I moiety in GSSG can be opened by the side chain movement of Tyr-114. In the substrate binding site, there is a proton relay system consisting of residues His-467' and Glu-472' belonging to the second subunit. Most of the structural features discussed above can be seen in Figure 3 in which the modeled and crystallographic structures are depicted. The latter came to our attention only rather recently and from the similarity of the two structures the quality of the modeling can be observed. The plane of the isoalloxazine ring can be seen in the neighborhood of His-467'. When the disulfide bridge of TSST is reduced, unlike GSSG, the molecule is not separated in two independent units; the spermidine bridge still connects them

[1061. The model of GR in its complex with GSSG was constructed by using the reported relative orientation and contacts made by GSSG at the GR active site {104] and the Brookhaven Protein Data Bank (PDB) coordinates. The Molecular Mechanics method of Allinger (MM2) was adapted to the calculation of the polypeptide structures of GSSG and TSST, generating a new series of parameters named MM2G [107]. Some parameters of this first generation force field were modified and a better agreement between the derived geometries and the crystallographic structures is obtained with this method for certain peptides. A model for the structure of trypanothione was also obtained by the same molecular mechanics procedure. The molecular model of GSSG was docked with the program TOM into the 3D structure of GR, imposing as geometrical constraints the structural data described for the GR-GSSG complex [104]. This docked complex was used as a template to build the TSST-TpR complex. Similarly, GSSG was docked at the TpR active site and TSST was docked at the G R active site. Four different substrate-enzyme complexes were generated: TpR-TSST, GR-

398

O. TAPIA ET AL.

Fig. 3. Partial view of the binding and active site for the substrate GSSG. A comparisonbetween the model-builtdocked and X-ray structures is presented.

GSSG, TpR-GSSG and GR-TSST, which allowed for comparisons of the substrate binding site in both enzymes and provided a deeper understanding of their exclusive substrate specificity. The results have been checked with the crystallographic structure of GR in its complex with an inhibitor (GSSG retro) the coordinates of which have recently been made available through the PDB. A picture of this latter structure is presented in Figure 4. It can be seen that the S-S-bridge of the retro form is far away from the active disulphide bridge of the enzyme. However, the binding site of GSSG is occupied (partially) by this inhibitor.

2.1.4. Substrate Binding and Substrate Specificity As described by Pai and Schulz [104], the binding site for oxidized glutathione in GR involves side chains belonging to both subunits. GSSG makes contacts with Args -37, 38, -347 and -478', which at physiological pH represent four positively charged groups. There are also two negatively charged residues Glu-472' and Glu473' in the vicinity. Taken together with the carboxylate groups of GSSG the whole region is electroneutral. The GR-GSSG complex has the ce-carboxylate group of Glu-1 interacting with Arg-347 and a bound water molecule, while the amino group is directed towards the bulk solvent. The sulfur atom of Cys-1 binds within van der Waals distance of Cys-58 ST and His-467'. Its backbone is also in contact with the end of the side chain of Tyr-114. This residue moves nearly 1.0 A away from the crystallographic position it occupies in the apo-enzyme [104]. Many of these features are apparent


399

Fig. 4. Binding of the retro analogue. Note the extremely large distance between the catalytic S-S bridge of the enzyme and that of the inhibitor.

in Figure 3. Gly-1 is fairly well buried and its carboxylate makes contact with Arg37. The pocket of Gly-1 can be opened by the a chain movement of Tyr-ll4, the amide group of Gly-1 pointing towards the hydroxyl group of Tyr-114, but it is too far away to interact strongly. On the other hand, Glu-ll makes direct contacts only with residues from the other subunit of the enzyme. Its a-amino group is held by three hydrogen bond acceptor groups: Thr-469' O, Glu-472' Oel and Glu473' Oe2. The a-carboxylate receives a hydrogen bond from Met-406' N and from two solvent molecules which make contact with the enzyme at Lys-67 and Ser470', respectively. Cys-II makes weak contacts with the end of the side chains of Leu-ll0, Tyr-ll4 and His-467' and seems to be held in place primarily by the disulfide bond to Cys-I. In TpR, the distribution of the charged residues has been drastically altered in comparison with the substrate binding site of GR. It contains a series of neutral or negative amino acid residues: Glu-17, the TpR counterpart of G R Ala-34; Trp20 (Arg-37 in GR), Asn-21 (Arg-38 in GR) and Ala-342 (Arg-347 in GR). Arg471', which is conserved in GR, is no longer pointing towards the substrate binding region due to the existence of a longer C-terminus in TpR. TSST, presents drastic changes in the glycyl moiety compared to the glutathione parent structure. One carboxylate in each molecule GS-I and GS-II is neutralized when binds covalently to spermidine forming TSST, while the carboxytates from the glutamyl moieties are preserved. One of these carboxylates and the positively charged nitrogen atom of spermidine bind in the above mentioned region of TpR corresponding to the GSSG binding site in GR: the carboxylate group of Glu-17

400

o . TAPIA ET AL.

would interact with the positively charged nitrogen group of the spermidine bridge. However, we note that [108] indicate that it is unlikely that the positive nitrogen interacts with Glu-17. An X-ray structure of TpR-TSST would resolve this issue. The 03' of Ser-469' interacts with Glu-1 carboxylate which results in a global electroneutral region in TpR which should favor TSST binding and destabilize the binding of negatively charged substrates such as GSSG. The fourth carboxylate group Glu-ll, common to all the substrates, binds close to Lys-67 in GR. This interaction is preserved in the TpR model. TSST creates large steric hindrance when it is docked in the active site cavity of GR, at the place described above for GSSG and without moving side chains. Moreover, even if we allow for side chain relaxation, the positively charged nitrogen atom of spermidine would have to bind at a highly positively charged region in GR, which is clearly unfavorable. Thus, one of the factors determining the specificity of GR for GSSG may be due to this repulsive electrostatic effect. GSSG docked at the active site of TpR cannot be stabilized by the interactions set up by its four terminal carboxylate groups with the array of positively charged residues, which are missing in TpR. Furthermore, Glu-17 is replaced by Ala-34, thereby introducing an additional destabilizing factor. The model results are consistent with site-directed mutagenesis studies [109], where the substrate specificity of E. coli GR has been changed from GSSG to TSST by introducing the appropriate residues of TpR in the active site of GR. Trypanothione reductase in its complex with TSST and NADPH is one example of extensive modeling before X-ray crystallographic structures were determined. In preliminary comparisons of model and experiment, the agreement has been good. Further comparisons are possible now as the substrate interactions between TpR and Nl-glutathionylspermidine disulphide have been identified on the complex which has been solved at a nominal 2.8 ~ by Hunter and coworkers [110, 111]. 2.2. PROTEINASE INHIBITORS

A number of plant and animal viruses rely on virus-encoded proteinase action at various stages in their replication. These proteinases are highly substrate-selective and and show high specificity. These molecules are potential targets for inhibition of viral replication. Inhibitors of viral proteinases may emerge as major antiviral chemo-therapeutic agents [112, 113]. 2.2.1. Carboxypeptidase Inhibitors Protease inhibitors are involved in important biological processes, e.g. hormone and neuropeptide processing, defense mechanisms, fertilization and virus replication. Protein engineering is being used to tailor proteins with specific properties that can transform such molecules into useful drugs or target-oriented inhibitors to control a variety of biological processes [114-116]. In particular, potato carboxypeptidase inhibitor (PCI) has been the target of a number of experimental and theoretical studies. PCI is a 39-residue protein; its 3D structure is known in aqueous solution and in a crystal complex with carboxypeptidase A (CPA). The


401

inhibitory mechanism of PCI is via strongly competitive binding to the active site of CPA; the Ki is in the nM range. The functional importance of the primary contact site with CPA (the C-terminal tail composed of residues 35-38) together with the short stretch of residues located around Trp-28, referred to as the secondary binding site (residues 28-31), have been experimentally probed by chemical modification studies [117]. Molecular dynamics studies with the none inertial solvent model [118, 119] were carried out to study the possibility offered by this technique as a tool to help design mutants [120]. The theoretical and experimental work has recently been reviewed by [121], and the reader is referred to this paper for further details. There is, however, one point of interest concerning the theoretical framework adopted here that deserves a short comment. The theory predicts that this inhibitor can be turned into a full substrate (or at least into a weak inhibitor) if the last residue Gly-39 at the C-terminus is replaced by a highly substrate-selective one. The experimental test will be crucial for the theory developed around SP-il in vacuo.

2.2.2. Serine Proteases The serine proteases constitute a widespread family of enzymes whose function appears to be the transfer of acyl groups from one molecule to another. These enzymes were among the first to be extensively studied with structural, kinetic and theoretical methods. Most of our understanding of enzyme catalysis and specificity derives from such studies. 3D structures have been solved for each mechanistic class; these studies were recently extended using site-directed mutagenesis to characterize amino acid residues required for enzyme function [122]. In the active site there is an invariant triad of amino acid residues: a reactive serine, which gives the name to the family, an histidine and an aspartate. They have a similar geometric disposition, conforming a proton relay structure. This invariance is striking. The three dimensional structure and primary composition can be fairly different from one family member to the other but the catalytic triad is always in place. For subtilisin, a major result was obtained from a genetically engineered mutant where the triad was eliminated: the catalytic activity of this molecule was not fully suppressed. As was discussed in Section 1.1, the catalytic triad can be thought of as a molecular device enhancing the catalytic efficiency of the protein. The primary interconversion step is the peptide bond breaking° The binding of the substrate in a conformation related to the transition structure activates the system. Efficiency or catalytic enhancement is achieved via a general base catalyzed nucleophilic attack of the substrate by the hydroxide oxygen atom of the reactive serine on the carbonyl carbon atom. The efficient form of the enzyme is currently assumed to be the deprotonated serine residue. Under standard conditions, an acyl-enzyme intermediate is formed; this intermediate derives from the tetrahedra! transition structure for peptide bond breaking. The deacylation step regenerates the enzyme, which otherwise would remain inhibited. The deacylation reaction also employs a tetrahedral transition structure which is the mechanistic inverse of that produced during acylation; thus, the principle of microscopic reversibility is

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fulfilled. The collapse of the second tetrahedral intermediate yields the enzymeproduct complex. Besides the substrate binding site, there is a factor anchoring the transition structure in a correct orientation, the oxyanion hole. This is formed by the backbone amide hydrogens donated by neighboring Gly and Ser residues. The hole provides a surface complementary to those atoms intervening at the active site. In the standard description, it is assigned a stabilizing role for the developing negative charge on the substrate carbonyl oxygen atom. A considerable amount of experimental evidence is accumulating showing that enzymes use this type of machinery to boost catalytic efficiency. Catalytic structures similar to the serine protease triad appear to be ubiquitous. They have been identified in enzymes belonging to several different families. In the acetylcholineesterase from Torpedo californica [123], a Glu replaces the Asp residue of the serine protease triad. Furthermore, the relation of the triad (at the surface of these proteins) to the rest of the enzyme approximates a mirror image to that found in the former, although the detailed structures are different. A serine protease-like catalytic triad was also found in the catalytic center of a triacylglycerol lipase [124]; the active serine being buried under a short helical fragment of a surface loop. It is also found in the molecular structure of the acyl-enzyme intermediate formed between penicillin G and the Glu-1 66-Asn mutant of the RTEM-1 class A/3-1actamase from E. coli. Strynadka et aI. [125] revealed that the substrate is covalently bound to O y of Ser-70 as an acyl-enzyme intermediate similar to that formed in the catalytic mechanism of serine proteases. As a result of this mutation, the deacylation step was prevented and the acyl-enzyme intermediate was trapped. A striking structural similarity was also found after superimposing the side chains of Glu-166, Asp-170 and their bound water molecules of this stable intermediate with the side chains of the corresponding catalytic Asp215 and Asp-32 and their bound water molecules in the active site of endothiapepsin (Pearl, 1993). In the catalytic process of the corresponding enzymes, both configurations act in the same way: in the aspartic proteinase, the two aspartate residues activate their bound water molecule to perform a nucleophilic attack on the peptide carbonyl of the substrate, while in the/3-1actamase, the activated water attacks the ester carbonyl of the acyl-enzyme. These activated water molecules perform a role equivalent to the reactive Ser of the serine proteases. More recently, Strynadka et al. [126] made a structural and kinetic characterization of an exocellular/3-1actamase-inhibitor protein. However, a clear picture of how does this protein inhibit /3-1actamase activity is not yet available. These authors announced the determination of the 1 : 1 molecular complex of the/3-1actamase-inhibitor protein with TEM-1 at 2.8A resolution which will be a stringest test for the modeling work caried out on this system [126]. The quantum-mechanical interpretation of the catalytic mechanism of serine proteases has attracted considerable attention. Early work on the catalytic mechanism was mainly focused in the characterization of the initial proton transfer step. The interpretation of NMR measurements was controversial; some authors favored a single proton transfer mechanism, while others suggested instead that a double proton transfer was most feasible. Efforts were made to solve this problem through quantum chemical in vacuo calculations, the first of which were reported by


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Scheiner and Lipscomb [127]. All such calculations found that double proton transfer was energetically more favorable than single proton transfer. It was also shown that, in vacuo, the presence of the substrate and one water molecule localized in the active site favor the zwitterionic structure resulting from single proton transfer and destabilizes the intermediate structure which leads to double proton transfer [128]. When electrostatic surrounding effects [129] and reaction field terms [130] were introduced the numerical results suggested that environmental effects stabilize the zwitterionic form which resulted from a single proton transfer mechanism. Furthermore, once the proton transfer energies are corrected for known deficiencies in calculated proton affinities, single proton transfer becomes favored over double proton transfer. A sequence of molecular arrangements corresponding to different steps in the catalytic mechanism of serine proteases has been studied [131] within the framework of ISCRF theory of protein core effects [56]. This scheme was devised to take explicit account of the protein electric field and the reaction field response. The residues of the catalytic triad (Ser, His and Asp) were modeled with methanol, imidazole and formate anion, respectively; the substrate was represented by a methyl acetate molecule. Protein-substrate interactions were optimized at each step of the reaction path. The ionization state of the acidic and basic side chains, together with the amino terminus, were used to simulate pH effects. The main experimental features concerning the catalytic activity were fairly well reproduced in these simulations. Some other aspects of the catalytic mechanism of the serine proteases were submitted to ab initio HF MO studies at a 3-21G basis set level [132]. Analytical gradient were used to optimize the geometry of the molecular partners and to probe the interactions between the substrate and the model active site. Reaction fields of graded strengths were used to sense the response of the active site atoms to protein surrounding effects. The catalytic triad was reduced to a model dyad, simulated with ammonia and methanol, while methyl acetate (MeAc) represented the substrate. One water molecule was added to the model as a local solvation effect. This molecule plays a central role in the rupture of the acylated enzyme. However, this latter step was not studied in that particular paper. The reaction pathways of MeAc interacting with the alcohol and alcoholate were studied to probe the intrinsic properties of this system at the particular level of wave function representation. The presence of the dyad altered the interaction potential of the reactive system. The canonical form in vacuo is significantly more stable than the di-ionic one, however, the reaction field produced significant stabilizing effects favoring the catalytic di-ionic form. The effect of inducing a tetrahedral conformation in the substrate was studied. A planar substrate is strongly repelled at distances shorter than 3.A, while a tetrahedral one can approach the catalytic dyad in the native configuration without apparent steric hindrance. Incidentally, the above ab initio results are interesting with regard to the binding theory discussed in Section 1.1. The energy required to deform the substrate is drawn from the interaction between the substrate and the model active site; the forces between the substrate and the dyad are attractive when the substrate is tetrahedrally deformed but are repulsive when the substate retains its planar conformation.

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Schr6der et al. [133] have recently discussed the results of semiempirical MO calculations of model compounds relevant to the catalytic mechanism of serine proteases (methanol, methoxy anion, acetic acid, acetate anion, methylimidazole in neutral and protonated forms, N-methylacetamide, methylamide, water and hydroxide ion). This work aimed at determining which of the parameter sets in the AM1 and PM3 methods was most appropriate for the study of amide and ester catalysis by serine proteases. In order to evaluate the errors in the semiempirical models, 6-31 G*/MP2 calculations were performed. Heats of formation, atomic charges, proton affinities and the properties of hydrogen bonds between pairs of molecules relevant to the catalytic mechanism were calculated. Tetrahedral complexes formed from hydroxide and methoxide attack on N-methylacetamide were examined. The AM1 and PM3 methods were found to be very similar in terms of calculated heats of formation and proton affinities. However, PM3 was much better at producing hydrogen-bond geometries. Based on the conclusions of the preceding paper, further studies on the actual reaction pathway of amide and ester hydrolysis catalyzed by serine proteases were performed using the PM3 method [134]. The formation of the tetrahedral intermediate of the acylation reaction was found to be the rate-limiting step with both substrates. The attack of serine hydroxide on the scissile carbonyt bond of the substrate in the acylation reaction and the nucleophilic attack by water in the deacylation step were both found to be concomitant with proton transfer, at variance with previous work which suggested that proton transfer was approximately complete prior to nucleophilic attack [135]. The effect of the environment on catalysis was estimated by calculating molecular mechanical interaction energies in both a noncovalent trypsin-peptide complex and a model for the transition state, in which a covalent bond is imposed between 03, of Ser and the carbonyl carbon of the substrate. The environment itself, excluding the key active site residues and interactions, was found to be important in stabilizing the substrate. It also stabilized better covalent complexes than noncovalent ones. Compared to the oxyanion hole, the Asp residue, which participates in the catalytic triad, was found to be more important in poising the tetrahedral intermediate, and presumably also the transition state. A molecular dynamics simulation was also performed on the noncovalent complex, to test the importance of motion in the active site in the early stages of catalysis. Recently, several site-directed mutagenesis studies were envisaged in order to characterize the essential amino acid residues for enzyme function. The importance of the catalytic triad in trypsin-catalyzed hydrolysis was underscored by the substantial reduction in catalytic rate observed upon the systematic mutation of each residue [136]. The importance of binding energies in enzymatic reactions was also demonstrated; the binding free energy of the precursor complex decreased by 4 kcal/mol upon mutation of Ser-195 or His-57. A similar result was obtained for subtilisin, by studying the effects of mutations of the active site residues and the oxyanion hole, which, in this case, is formed by the side-chain of Asn-155, the amide group of Ser-221 and the side chain hydroxyl of Thr-220. The reduction in precursor complex binding energy was 4 kcal/mol for Asn-1 55-Ala, 2 kcal/mol for Thr-220-Ala and 6 kcal/mol for the double mutant Thr-200-Ala/Asn-155-Ala [137]. Similarly, the mutation of Ash-155 in combination with the catalytic His


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[138] or Ser [139] resulted in a stabilization loss of the precursor complex for the reaction similar to that determined by the single mutations of the active site residues. The outcome of these mutational studies is that the observed effect in precursor complex stability are only additive when the residues function in an independent manner and when the rate-limiting step and mechanism remain unchanged. The removal of the entire catalytic triad in trypsin did not eliminate catalysis [136]. The reason for this behavior is that the serine side-chain is not essential to form the transition structure for peptide bond breaking, as was discussed in Section 1.1. The results of these site-directed mutagenesis studies prompted a theoretical investigation of mutations on an enzymatic reaction. It was demonstrated that free energy perturbation calculations, using molecular dynamics [140] or a different implementation of the free energy simulation method [24], were able to predict, in good agreement with experiment, the free energy differences of both binding and activation for catalysis of a tripeptide substrate by native subtilisin and a subtilisin mutant (Asn-155-Ala). MD free energy perturbation calculations were also performed to study the binding and catalysis of a tetrapeptide substrate by native subtilisin and the subtilisin mutant Thr-220-Ala. It was seen [141] that the solvation of the mutant is disfavored over the native enzyme in all three cases studied (enzyme alone, enzyme-substrate noncovalent complex and tetrahedral intermediate). 'Mutations' of the substrate P~ side chain rather than changes to protein residues were also performed for a-lytic protease, a bacterial serine protease. MD free energies were calculated on different substrates for this enzyme in several situations: gas phase, solution, noncovalent Michaelis complex and a tetrahedral structure representing a transition state intermediate for acylation by the enzyme (or more properly, a precursor complex since a saddle point of index 1 structure was not determined). Various substrates were studied, with P! = Gly, Ala, Val and Leu. The calculations showed the enzyme catalyzes more effectively the substrate with P~ = Ala than with P1 = Gly, Val or Leu, in qualitative agreement with experiment. The calculated relative solvation free energy of Gly ~ Ala and Ala ~ Val 'mutations' were also in qualitative agreement with experimental values in comparable model systems. However, this study was not as successful as the one by Rao et al. [140] in that the level of qualitative agreement with experiment was not that good. The authors suggested that this was due to the difficulty in qualitatively simulating the predominantly van der Waals and hydrophobic effects as compared to the hydrogen bonding and electrostatic effects which dominated in Rao's work [140]. A 60ps long molecular dynamics trajectory was performed by Avbelj et al. [143] to simulate the behavior of a serine protease (Streptomyces griseus protease A). Special care was taken to represent the full environment of the proteins in the crystal. Thus, all hydrogen atoms, water molecules and counterions present in the experimental system were explicitly introduced in the simulation, as well as neighboring protein molecules generated by the appropriate crystallographic symmetry. For nonbonded interactions, a cut-off radio longer than the customary one was used. The main purpose of this work was to test the reliability of contem-

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porary MD algorithms and force fields in reproducing observed protein structures. A strong influence of the ionic medium on the protein's behavior was elicited after a thorough analysis of deviations from experimental values shown by the conformation of substructural elements and individual residues. The nature and size of the observed deviations were discussed, in order to characterize their origins and thus improve the prediction of the properties of protein molecules within experimental accuracy. Unfortunately, the trajectory is apparently still too short to get a proper evaluation of the MD methodology. 2.2.3. Aspartic Proteases Besides renin, this family has among its members fungal enzymes such as penicillopepsin, endothiapepsin, and rhizopuspepsin. Their sequences contain two aspartates that are essential for catalysis. Tom Blundell and coworkers have produced a beautiful example of rational design of renin inhibitors. The modeling studies of this group and those of others based on the homology of renin with other aspartic proteases, showed that renins may assume tertiary structures that are similar to those of other members of the family [144]. The use of transition state analogs to produce useful drugs has been instrumental in obtaining successful results. 2.3. CARBONICANHYDRASES For carbonic anhydrases, the rate limiting step does not correspond to the chemical interconversion step. The fundamental chemical process catalyzed by the enzyme takes place at the coordination sphere of the metal. It consists of a fairly simple chemical reaction between the hydroxide ion and carbon dioxide to form bicarbonate and the enzyme catalyzes the decomposition of bicarbonate at the same active site. Quantum chemical studies show that along both reaction directions there are finite activation energies. Even for this simple system, the search of SP-ils is not trivial. Early studies with minimal and more complex models had failed to find a transition structure for this simple reaction. Semiempirical AM1 studies [145] were successful in finding a maximum along a reaction coordinate although no Hessian diagonalization was reported. In the study of a minimal model system in vacuo, the transition structure was found at a high basis set level. This result suggested an alternative mechanism where direct nucleophilic attack was not necessary in order to accomplish interconversion [146]. The saddle point structure remained when some structural features found in the real enzyme were added to the molecular model. The coordination shell in the enzyme can be expected to be the source of strong interactions and a transition structure was identified with three ammonia molecules that provided, together with the reactants, a full complement of valence electrons to the zinc cation [18]. Zinc, in carbonic anhydrases, not only can participate in the reversible hydration of carbon dioxide and in bicarbonate dehydration but also catalyzes hydroxylation of carbonyl containing molecules such as formaldehyde. In order to identify the simplest molecular model capable of describing this interconversion process, the


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transition structure and the transition vector for the hydroxylation of formaldehyde at the coordination sphere of a bare-zinc cation were numerically identified [18]. One important objective was to explore the possibility of invariance in the transition structure and transition vector fluctuation pattern for hydroxylation of carbon dioxide and carbonyl bond containing compounds. The result was a striking confirmation of the initial hypothesis. Theoretical evidence showed that the transition structures for hydroxylation of carbon dioxide and formaldehyde were, to within minor geometrical differences, closely related in both reactions. A rotary mechanism, where the reactants use two (vacant) coordination sites of the zinc coordination sphere, was the unifying feature. Later on, the same microscopic motions were found for direct water attack both onto carbon dioxide and formaldehyde. The intramolecular proton transfer pathway, which is always present as an alternative, appears to be excluded due to its high activation barriers compared to the zinc-sensitive barriers of the rotatable model. The rotary model enforces a space requirement in the coordination sphere of zinc. In a coordination shell with four fixed ligands the reactive subsystem will have more difficulties than one with three ligands to accommodate the molecular motions required by the fluctuations along the transition vector; the former may introduce strong steric effects. Three fixed ligand positions occupy one hemisphere around the metal thereby leaving the space for unhindered incoming/outgoing of molecules. In carbonic anhydrases, three histidines coordinate the metal plus one exchangeable water molecule in a distorted tetrahedral arrangement. This stereochemistry appears optimal in view of the present mechanistic model. Furthermore, after analyzing entries in the Protein Data Bank for a number of zinc containing enzymes, one finds a distorted tetrahedral arrangement to be the characteristic coordination sphere. One can then understand that one extra monodentate ligand would block one position at the coordination sphere of zinc and may actually act as a competitive inhibitor. Based on the rotary mechanism in carbonic anhydrases, it was predicted that a replacement of the residue Thr-199 by a non-hydrogen bonding residue, would be likely to permit the reactants to rotate more freely in the coordination sphere of zinc, thereby opening the possibility for bidentate ligation of bicarbonate and consequent inhibition [18, 146, 147]. 3. Conclusions An extended survey of computer-assisted molecular modeling has been presented. The methods used by different workers show a wide range of complexity. They include energy minimization procedures, with classical force fields or MO (semi)empirical quantum chemical analytical gradient methods, that generate fairly accurate geometries and molecular properties, MD-based techniques, such as free energy perturbation approaches; various levels of structure analysis using topologically grounded methods and fractal theory, protein model-building from homologous sequences using advanced graphics programs and finally advanced computational quantum chemistry whose results help understand the electronic aspects of chemical reactivity, kinetics and drug-receptor interactions. A change in perspective has been introduced to discuss the sources of enzyme

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catalytic activity. From a molecular viewpoint, there are important differences between the traditional and the approach presented here. The present approach emphasizes microscopic dynamical aspects that are most relevant to model building and underlines the fact that enzyme and substrate may suffer geometric modifications upon binding. Prime catalytic sources are distinguished from those determining catalytic efficiency. Based on the idea that the reference system should be defined in vacuo, and noting that it is the saddle point of index 1 describing the prime interconversion step which is a fundamental invariant, the experimental data can be described and used on a more firm structural basis. The very idea of enzyme prime catalytic power is reinforced by the construction of catalytic antibodies: complementarity with respect to transition state analogs endow catalytic power [40-44, 148, 149]. For such systems, the efficiency is seldom as good as a wild-type enzyme. For real enzymes, one can imagine that molecular evolution first led to a protein structure that was adapted to entrap the fundamental invariant of the chemical interconversion step and thereafter, a gain in efficiency as a concomitant process. The present theory leads to the conclusion that it was not the enzyme which enforced the transition structure, but the other way around. The inhibitory power of transition state analogs, as shown by the work summarized by Wolfenden and Karl [66] speaks in favor of the basic tenets of the theory. We note that these authors rejected the idea found in earlier formulations that enzymes could act by combining with an activated form of the substrate, which might approach the transition state structure. The formulation given here may overcome some of these criticisms. In discussing the mechanism of an enzyme,tit should be clear that the simple kinetic data is not always sufficient to disentangle a detailed molecular mechanism. In most cases kcat/Km does not reflect the chemistry, namely, what is going on at the chemical interconversion step, but describes the overall process. The protein surface complementary of the active site (as defined here) is an essential ingredient in the present theory. Initially proposed by L. Pauling, the theoretical studies carried out so far show that such complementarity is actually with respect to a fundamental invariant of the reaction in vacuo: the region of the reactive hypersurface where the information of the interconversion step resides. This region involves definite structures belonging to the quadratic zone and also reactive fluctuation patterns. A modification of such complementarity may modify the balance between alternative pathways in a given catalytic process. For instance, in glutathione reductase, the mutation of Tyr-197 for a glycine produce a change in the mechanism. It changes from a ping-pong to an ordered sequential mechanism with reduced activity. From the molecular nature of the mutated residues, a change in surface complementarity is apparent. On the other hand, for trypanothione reductase compared to GR, the tyrosine is conserved, and no alteration is produced in the nature of the mechanism for NADPH oxidation. The efficiency of the protein in catalysis appears to be controlled by electrostatic factors. A nice illustration of this is provided by the beautiful work of Warshel et al. [150] for serine proteases. Another example is given by the drastic lose in activity of GR from E. colt when the proton shuttle formed by the residues His439' and Glu-465' in the substrate active site is altered. The mutant His-439'-Ala and His-439'-Glu retain a very low percentage of the wild-type activity (0.3 and


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Fig. 5. 5a. Trypanothione (TSST) docked (grey) in the model-built structure of trypanothione reductase. The geometric conformation of GSSG was used to make the complex that is displayed in grey. 5b. In white, the in v a c u o energy minimized structure of TSST has been superposed on the grey structure. The S-S bridge in the white structure moves away the putative active conformation of TSST; clear differences (discussed in the text) in the binding site are apparent. Comparisons in vacuo of the grey and white structures show clear deformation of the substrate.

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1%, respectively) as reported by Deonarain et al. [151]. Other examples are discussed in Section 2. For trypanothione reductase a comparison of the substrate in vacuo and docked to the enzyme can be made. In Figure 5 are displayed the binding site and the docked substrate and fully geometry optimized substrate. The docked conformation of TSST has an energy much above the one calculated for the free structure and the substrate appears strained if a comparison is made with the same structure in vacuo. A similar situation holds for the substrates reported by Fairlamb and coworkers [106] when they are submitted to this type of conformational energy calculation. A delicate point arises when chemically modified cofactors and/or substrates are used to probe enzyme catalytic properties. It is not uncommon to find that a relatively small modification may totally change the binding to the protein. This is the case, documented by X-ray crystallography, of pyridine adenine dinucleotide in liver alcohol dehydrogenase. The binding site of the adenine moiety is the same as for NAD but the pyridine ring binds far away from the active site of the normal cofactor. This type of result puts limits on the design of transition-state analogue inhibitors when they are used to discriminate protein-ligand binding as discussed by Wolfenden and Kati [66]. The problems of ab initio model building are well illustrated in all the examples discussed here. However, Nature is always more subtle. Actually, it is becoming more and more evident that we do not yet know all the structural motifs Nature has produced during the course of molecular evolution [152]. Of course, in modelbuilding, one is on safer ground when a high level of protein sequence similarity (or even better, identity) is found in a given family. As the number of experimentally determined structure increases, model-building will become more and more reliable, as illustrated by the progress being made in constructing realistic drugreceptor models. Finally, it is appropriate to mention the important field of bioactive peptide design. These molecules are relevant to medicinal chemistry. They are usually targeted to interact with enzymes, ion-channel ionophores, antibiotics, hormones, etc. The reader is referred to the review of Benedetti in this field to get a complete view of the role played by molecular engineering [153].

Acknowledgements The authors are deeply indebted to Dr. Richard Garret for reading and corrections to this paper. Prof. David Shugar is thanked for invaluable comments. We are grateful to Dr. J. Andres for help with references on the theory of chemical reactions. This work has received important financial support from SAREC. O.T. thanks NFR for sustained support. References 1. B. Honig: Curt. Opin. Struct. Biol. 3, 223 (1993). 2. J. R. Helliwell: Macromoleeular crystallography with synchrotron radiation; Cambridge University Press: Cambridge, UK (1992).

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