6 The Design of Transition State Analogs P. R. ANDREWS
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Department of Physical Biochemistry, The John Curtin School of Medical Research, Australian National University, Canberra, A.C.T. 2600, Australia
The transition state of an enzymically catalyzed reaction is bound to the enzyme much more tightly than its substrate(s), and may therefore be used as a template for the design of potent and specific enzyme inhibitors (1,2,3,4). Such inhibitors are known as transition state analogues, and have considerable potential as highly selective drugs. They may, for example, be specifically designed to inhibit enzymes which are vital to abnormal or invading cells, but of no importance to the host. Alternatively they may take advantage of quantitative biochemical differences between normal and abnormal tissue. Two major phases may be distinguished in the design of transition state analogues. They are (i) determination of the transition state structure, and (ii) specification of stable molecules which mimic the geometric and electronic properties of the transition state. Determination of Transition State Structure Unlike the substrate(s) and product(s) of a reaction, transition state structures cannot be studied directly, and the structures employed in analogue studies are commonly derived from intuitive interpolations between reactant(s) and product(s) on the basis of an assumed reaction mechanism. The intermediates obtained in this way may differ radically from the actual transition states. Efforts to deduce transition state structures theoretically have until recently been retarded by the failure of even the more sophisticated molecular orbital treatments to predict accurate activation energies, and the need to avoid geometric and mechanistic assumptions has made the calculation of reaction pathways prohibitively expensive. The introduction of efficient gradient methods for minimizing energy with respect to all geometric parameters, coupled with the advent of faster computers, has now virtually overcome the latter problem, and careful parameterization of semiempirical molecular orbital methods has led to more 0-8412-0521-3/79/47-112-149$05.00/0 © 1979 American Chemical Society In Computer-Assisted Drug Design; Olson, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.
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accurate calculated energies. The use of computers to determine the structures of transition states for enzyme catalyzed reactions has thus become a r e a l i s t i c p o s s i b i l i t y . The Reaction Coordinate. To calculate the reaction pathway, an internal coordinate which varies monotonically from reactant(s) to product(s) i s chosen as the reaction coordinate,e.g. the length of a making or breaking bond may be used. The energies at various points along the reaction pathway are then obtained by constraining the reaction coordinate to appropriate fixed values while minimizing the energy with respect to a l l other geometric variables. The high point on the reaction pathway thus obtained provides an estimate of the location and structure of the transition state, which may then be precisely located and identified by minimizing the energy gradient with respect to a l l geometric variables, including the reaction coordinate (5). Because of the complexity of many reaction surfaces i t may sometimes be necessary to calculate reaction pathways for several starting geometries and reaction coordinates; a number of alternative transition state structures may thus be located. The lowest energy transition state obtained in this way i s appropriate to the gas phase reaction, and does not necessarily correspond to the transient species for the reaction i n solution. Similarly, there i s no v a l i d j u s t i f i c a t i o n for assuming that the pathway catalyzed by the enzyme i s the calculated minimum energy reaction pathway. There i s , however, good reason to suppose that one of the calculated low energy reaction pathways w i l l be that catalyzed by the enzyme. The calculations may thus provide two or more alternative reference reactions with their corresponding transition states, one of which w i l l be selectively stabilized at the active site of the enzyme. Calculation Methods. Of the alternative molecular orbital methods available, the MINDO/3 method (6) has proved especially successful for calculating reaction pathways (7). Dewar estimates that the relative energies of alternative transition states are predicted to within 5 kcal/mol, and that the structures of transition states are probably reproduced to a few hundredths of an Angstrom i n bond lengths, and a few degrees i n angles (7). Unresolved differences between the energies and geometries of the transition state structures obtained for bimolecular. reactions using ab initio, MINDO/3 and other techniques (8) suggest that any molecular orbital method must s t i l l be applied with caution, but provided that alternative reaction pathways within 5-10 kcal/mol of the minimum energy pathway are considered, i t seems l i k e l y that an accurate representation of the transition state structure for an enzyme catalyzed reaction w i l l be obtained using MINDO/3. Versions of MINDO/3 suitable for various computers are available from the Quantum Chemistry Program Exchange (9,10,11).
In Computer-Assisted Drug Design; Olson, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.
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For reactions involving large molecules, the time required to compute a reaction pathway with MINDO/3 remains prohibitive. The development of reliable empirical methods for preliminary studies of reaction surfaces w i l l be necessary to alleviate this problem.
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Design of Stable Analogues The long p a r t i a l bonds and abnormal hybridization of transition state structures preclude precise correspondence between the functional groups of an analogue and those of the transition state, but a range of plausible analogues can usually be derived by inspection of the transition state structure; additional alternatives may be obtained from chemical or crystal structure f i l e s . Choice of the best analogues for synthesis i s then based on a comparison of their molecular structures with that of the transition state. For this purpose, computed transition state structures and other points on the reaction pathway may conveniently be stored in a molecule library f i l e , either as cartesian coordinates or as geometric variables; i t may also be convenient to store a connectivity matrix, since the presence of p a r t i a l bonds i n the transition state structure may not be s e l f evident from the interatomic distances. Molecular Manipulation and Superimposition* To f a c i l i t a t e molecular comparisons, a variety of computer graphic techniques are available for three-dimensional manipulation and display of the stored structures in the library f i l e (12,13). In our laboratory l a t e r a l stereo pair views of either single line or b a l l and stick models are displayed on a Tektronix 4014 graphics terminal linked to a Univac 1100/42 computer. The three-dimensional images of the analogues, derived using standard geometric parameters (14,15), are superimposed on that of the transition state structure using interactive graphics routines to manipulate either molecule. We automate this process by running a stepwise minimization of the extent of misfit between the two molecules. Various functions may be used for the minimization, which i s carried out with respect to the six degrees of intermolecular rotational and translational freedom as well as appropriate conformational variables i n the analogue molecule. The simplest function appears to be the sum of the squares of the distances between corresponding atoms i n the two molecules. In our hands this function has proved most useful when hydrogen atoms are excluded, isoelectric groups are equated, and atoms separated by more than a given distance (e.g. 1 A) are a r b i t r a r i l y assigned a separation of that distance. Analogues which optimally match the transition state structure are chosen for synthesis, which may i t s e l f be computer assisted (Wipke, this Symposium) . Inhibitory a c t i v i t i e s against the enzyme may then be measured in vitro and/or in vivo, and
In Computer-Assisted Drug Design; Olson, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.
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structure-activity relationships determined. Design of further analogues may then prove desirable on the basis of these data. Example : Inhibition of Chorismate Mutase
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The Claisen rearrangement of chorismate to prephenate, catalyzed by chorismate mutase, i s illustrated below. It
is the f i r s t specific step i n the biosynthetic pathways leading to tyrosine and phenylalanine in bacteria and other organisms (16). The enzyme i s absent i n man and thus provides a potential target for bacteriostatic action, although this potential i s limited by the a b i l i t y of bacteria to scavenge aromatic amino acids i n the bloodstream. The enzyme provides a clear example of the design principles described above, i l l u s t r a t i n g both advantages and limitations of most of the techniques discussed. Transition State Calculation. MINDO/3 calculations have been used to describe the reaction surface for the isomerization of chorismate i n both the neutral and dianionic forms (17). Two alternative structures were obtained i n each case (Figure 1). One, which results from clockwise rotation of the sidechain around the breaking C-0 bond, adopts a chair-like configuration; the other results from anticlockwise rotation, which leads to a boat-like structure. Both are asymmetric structures in which the breaking C-0 bond (ca. 1.45 A) i s significantly shorter than the making C-C bond (ca. 1.95 A). The enthalpy difference between these alternative reaction pathways (
