Computer-Assisted Drug Design - American Chemical Society

9 The Conformational Parameter in Drug Design: The Active Analog Approach

Downloaded by UNIV OF GUELPH LIBRARY on May 17, 2012 | http://pubs.acs.org Publication Date: November 28, 1979 | doi: 10.1021/bk-1979-0112.ch009

GARLAND R. MARSHALL, C. DAVID BARRY, HEINZ E . BOSSHARD, RICHARD A. DAMMKOEHLER, and DEBORAH A. DUNN Departments of Physiology and Biophysics, of Pharmacology and of Computer Science and the Computer Systems Laboratory, Washington University, St. Louis, MO 63110

Molecular recognition plays a central role in biological systems and is the basis of the specificity seen in antigen -antibody, substrate-enzyme, hormone-receptor, and drug-receptor interactions. The importance of this problem had been recognized by scientists like Pasteur and Ehrlich at the end of the nineteenth century. Structure-activity relations in which one probes the basis of recognition by chemically modifying one of the partners form a significant segment of medicinal chemistry. Attempts to correlate activity with physical properties such as solubility, refractive index, etc. are a reasonable approach to defining the characteristic properties associated with activity in a given biological assay (1). In most systems, these correlations reflect the effective concentration of the drug in the critical biophase rather than the critical features necessary for bimolecular recognition. We would like to concentrate on what can be deduced regarding bimolecular recognition from structure-activity data. A major dichotomy between quantitative structure-activity relations (QSAR) and the active analog approach (AAA) exists on two levels. First, potency is the primary raison d'etre of QSAR and depends on a multitude of parameters such as distribution, metabolism, transport, recognition, affinity, etc. On the other hand, good pharmacological data implying recognition at a common receptor site is the criterion for inclusion in AAA regardless of the relative potency if one can be convinced the activity lies in the compound tested and not some contaminant, etc. The purpose is to deduce the minimal recognition requirements as a basis for understanding how a diverse set of chemical structures can activate the same receptor. Secondly, recognition is critically dependent on the three-dimensional arrangement of electron density in a molecule and the determination of the receptor-bound conformation is a logical goal in attempting to deduce recognition requirements. QSAR has traditionally neglected the conformational parameter although the use of steric parameters has become increasingly more sophisticated 0-8412-0521-3/79/47-112-205$05.50/0 © 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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(2)· A number of approaches to the conformational parameter have been taken. Crystallographic determinations of the molecular structure have been made, and proposals relèvent to the receptor-bound conformation have been based on the crystal structures. Alternatively, spectroscopic determinations of the solution conformation have been made in attempts to correlate this three-dimensional shape with biological activity. Theor e t i c a l calculations have also been used to determine the most probable conformer. Each of these approaches makes the tacit assumption that the conformer of minimum energy is directly correlated with the receptor-bound conformer. This assumption deserves to be challenged based on pure logic as well as experimental observation Q). Each method deals with molecules i n a symmetrical force f i e l d due to other similar molecules, solvent or vacuum. Biological systems are characterized by stereospec i f i c i t y due to interactions with asymmetric molecules, e.g. enzymes or receptors. The close proximity to an asymmetric force f i e l d characteristic of binding of a small molecule to a receptor must express i t s e l f i n the conformation assumed by the ligand. Aliosteric effects in enzymes have shown that small molecules are capable of inducing conformational changes i n large proteins; certainly the converse situation is to be expected. Experimental data relevant to this issue have become abundant. One example (Fig. 1) is ribonuclease S in which s u b t i l i s i n cleavage hydrolyzes the peptide bond between residues 20 and 21 of the 124 residue enzyme Ribonuclease A. The Speptide (residues 1-20) can be dissociated and reassociated. The crystal structure of both ribonuclease A and S have been determined and residues 2-13 form two-three turns of α-helix (4.)· dissociated state, S-peptide contains l i t t l e detectable helix either by circular dichroism (5) or by NMR (6>2)· Either the S-protein induces the bound conformation during the association or a conformer too limited i n concen tration to be detected by spectroscopy i s preferentially bound. It has been argued (g) on kinetic grounds that the induced-fit or "zipper" hypothesis is more l i k e l y , but no relevant experimental data exists on this or other systems to our knowledge. Several cases exist where analogs with essentially equiva lent biological activity have been shown to have different conformations i n solution. Data exist for somatostatin (9), gramicidin S (10) and angiotensin II (11). One would assume that the analogs assume a similar conformation during activation and that the solution conformation of, at least, one of the analogs must be irrelevant to the biological activity, i f not both. A similar argument can be made in the case of gammaaminobutyric acid i n which requirements for recognition by the presynaptic uptake system clearly rest in one conformer while I n

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In Computer-Assisted Drug Design; Olson, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


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the post-synaptic receptor recognizes another conformer (12)· The relevance of solution conformation to biological activity has been questioned i n the case of TRH and enkephalin (13)· A conformation for LHRH deduced from empirical energy calculation has been proposed to be responsible for the biological activity (14), but an analog [D-Phe ,Aib ]-LHRH which cannot assume this conformation has excellent binding activity (15). With regard to crystal data, numerous examples such as acetylcholine exist where many conformers have been found depending on the conditions of crystallization and, certainly, the activity at both muscarinic and cholinergic receptors cannot be explained on the basis of a single conformer. In summary, methods which have focused on a single conformer of a flexible molecule have been misleading regardless of the methodology. One must examine the multitude of possible conformations available to flexible molecules in order to adequately sample the possible receptor-bound conformation induced on binding to the receptor. The magnitude of this task has prevented most investigators from pursuing this approach. The active analog approach recognizes the necessity to consider a l l possible conformations as potential activation states. Active Analog Approach. The concept of pharmacophore i n which the recognition requirements are defined as the three dimensional arrangement of functional groups essential for recognition and activation i s a central concept (Fig. 2). By chemical modification, the medicinal chemist has identified chemical groups essential for activity. Substitution of groups by similar chemical functions retaining activity led to the concept of bioisosterism. The definition of the three dimensional arrangement of the groups essential for activity completes the designation of the pharmacophore. Such pharmacophoric patterns have been proposed for a number of systems (16,17). The i n i t i a l task i s , therefore, the deduction of the pharmacophore. Based on the known structureactivity data, a hypothesis concerning the possible pharmacophoric groups is proposed. The set of possible conformations for each compound shown to activate the receptor under examination is calculated. For each allowed conformation, the relative position of the proposed essential groups i s determined. This can be expressed as an orientation map in which each point represents one possible arrangement of the essential groups, i.e. a possible pharmacophoric pattern. For three groups, these points can be plotted i n three-dimensions where each point represents a specific triangle (Fig. 3). The intersection of a l l the orientation maps for the active analogs yields the possible pharmacophoric patterns available to the entire set of analogs. A null result would indicate either incorrect identification of essential groups or inclusion of incorrect pharmacological information. Use of sufficient number of analogs of


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+ S protein Figure 1.

S peptide

Dissociation of S-peptide from ribonuclease S with associated loss of the helical conformation of a segment of the peptide

Figure 2. The three-dimensional recognition requirements essential for activity —the designated groups A , B, and C and their correct spatial orientation comprise the pharmacophore. The number of groups is not limited to three which is chosen for convenience of presentation.

Figure 3. Orientation space map for a molecule with essential groups A , B, and C. Each axis represents the distance between two points.



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diverse chemical structures can uniquely determine the pharmaco phore. This information can be used as a frame of reference for orienting molecules i n the correct receptor-bound conformation as a prelude to mapping the functional volume (excluded volume map) available to drugs which bind. The pharmacophore also serves as a criterion for judging a novel structure for recogni tion by the receptor. The other criterion i s the volume required by the drug when presenting the pharmacophore. Lack of a c t i v i t y i n a drug which was capable of presenting the pharmaco phore and f i t t i n g within the excluded volume space would seriously compromise the proposed pharmacophore unless a l t e r native explanations such as distribution or metabolism could be demonstrated. A logical extension of mapping the volume available for binding to the receptor i s to map the volume which i s not a v a i l able, i.e. receptor essential volume. Certainly, a number of drugs with potential activity may be prevented from interaction by the presence of bulky substituents. Knowledge of the pharma cophore and the excluded volume map allows the unique volume required by the inactive analog to be located i n space. Unfor tunately, only one segment of this unique volume need be required by the receptor to prevent binding (Fig. 4) and, thus, the total unique volume cannot be used indescriminately. One scheme which we are investigating normalizes the number of observations of inactivity associated per volume segment by the unique volume associated with each observation. A unique volume requirement of only one volume segment based on an inactive analog would yield a predicted probability of inactivity 1, i f that segment were required by a new test compound. In a similar manner, the pharmacophore can provide a three-dimensional frame work for QSAR studies and a basis for correlations across a series of different basic structures. This discussion should provide the rationale for the follow ing material i n which some of the problems which arise i n the implementation are presented as well as results illustrated from the various biological systems under exploration. β

Systematic Conformational Search. A major d i f f i c u l t y arises due to the computational com plexity of determining a l l possible conformations at a given grid, i.e. minimal difference between two conformers. Let us compute the number of operations necessary for a molecule of Ν atoms with M rotatable bonds each of which w i l l be sampled R times, i.e. the angular difference between conformers i s 360/R degrees. Each atom must be rotated to determine i t s position i n space which takes operations and then i t must be checked against a l l other atoms for possible Van der Waals collisions which requires P2 operations for each check and N(N-l)/2 pairwise checks. The total number of operations involved in the search i s therefore:


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PARTIALLY MAPPED RECEPTOR BIOPHASE


VOLUME UNION OF ACTIVE COMPOUNDS

RECEPTOR Figure 4. Schematic drug-receptor interaction in which the pharmacophore has been defined and the extra volume requirements of inactive molecules capable of presenting the pharmacophore indicated. If one molecule requires several discrete areas, then one cannot distinguish if all are essential to the receptor, or only a segment of any one, as a single conflict is sufficient to prevent binding.

Ni

Figure 5. Chlorpromazine which antagonizes a central dopamine receptor has 4 degrees of rotation freedom that position the side chain rehtive to the phenothiazine ring. Shown is the crystal structure (41).


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l

Number of Operations = (Ν Ρ + "^"-u χ

R

A

'

An estimate of the number of operations required for rotation of a point is given by examining the formulation of Gibbs (18) and others (19). T


V

X

-

X

< i - o>

+

X

o

where Τ is a matrix (3 χ 3) whose elements are functions of the direction cosine and the sine and cosine of the angle of rota tion; is the vector (3 χ 1) whose elements are the coordi nates of atom i , and X is a vector of a point along the axis of rotation. P^ requires 9 multiplications and 12 additions, or 21 operations in our simplified analysis. Ρ2 be derived for the formula for a distance check between two atoms i and j . Q

c

a

n

D

ij

2

=

[ X

X

X

X

i " j> i " j

]

"

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ij

2

Since the calculation can u t i l i z e the squared radius as a criterion, the number of operations required i s only 3 multiples and 6 additions without a square root, and Ρ 2 * l l 9. Our formula can be simplified to: s

e c

u a

t o

9N(N - 1 M Number of operations = (21 Ν + — ^ — ^ ) R As an example (20) relevant to an application to be discussed later, l e t us consider the phenothiazine neuroleptic chlorpromazine shown i n Fig. 5 which has four rotatable bonds (M=4) which determine the orientation of the nitrogen-containing sidechain relative to the phenothiazine ring. If we assume R=64 or a grid of approximately 5.6 degrees, then R = 64 or 16,777,216 possible conformations to be examined. If we consider the methyl groups bonded to nitrogen as spheres of rotation, then the number of atoms N=34 and the number of operations = 5763 R = 9.67 χ 1 0 . If one has a computer of moderate capability such as a DEC 20/40 which can perform a floating point multiplication in 2.5 microseconds, then such a calculation should take approximately 241,718 seconds or 67 hours. Over the past several years, num erous improvements i n the algorithms used i n systematic confor mational search have been developed (21) leading to a reduction on the order of (M + 1) 2 . A prototype system on a DEC 20/40 written in Fortran without any optimization completed this search i n under 6 minutes CPU time. Out of the 16,777,216 possible conformations, only 78,670 were sterically allowed. The number capable of presenting the appropriate pharmacophore to the receptor was less than 50. A f a c i l i t y for computer-aided M

10

M



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drug design i s being established at Washington University which has an array processor coupled to a 32-bit host computer as the computation engine for the systematic search of conformational space. Estimates indicate that problems of eight to ten rotatable bonds should be approachable u t i l i z i n g this hardware, enabling consideration of most molecules of pharmacological interest. While the combinatorial nature of a systematic search presents formidable computational demands, both the increased performance and a v a i l a b i l i t y of computational hardware as well as the increased understanding resulting in algorithmic improve ments make this approach feasible. A number of other problems such as the determination of conformations using lanthanide shift reagents (22) logically require the determination of a l l possible answers, and avoidance of problems such as local minima associated with minimization i s necessary. Strategy. Because systematic search i s a combinatorial problem, the choice of the order of processing molecules to determine the pharmacophore can dramatically affect the computational demands. Determination of the orientation map for the most s t e r i c a l l y constrained molecule with the least number of variables places limits on the possible pharmacophores which translate into distance constraints on subsequent molecules. These distance constraints can be used to effectively truncate the combina t o r i a l search tree eliminating much of the computation. Since the object is to determine i f overlap in pharmacophoric patterns between a set of molecules can occur, conformations which cannot satisfy a l l molecules are not of interest. An extension of this concept to assist i n looking for possible pharmacophoric groups derives from the construction of a distance range matrix for each molecule (2L2). A matrix of the maximum and minimum pairwise distance between atoms is constructed analytically through use of distance geometry (24) as shown i n Fig. 6. A minimum condition for selection of a pair of groups as recognition sites is that the ranges i n this matrix overlap for a l l active mole cules. In fact, one can limit the search to the range consist ing of the smallest maxima and largest minima which contains a l l possible distances common to the set of molecules. When faced with a set of flexible molecules with too large a number of variables, one must turn to chemical modification to reduce the number of variables to a managable set. In the case of peptide hormones, introduction of proline eliminates the torsional degree of freedom φ by introducing a cyclic con straint, but adds the necessity of considering both cis and trans isomers of the amide bond. Replacement of the α-proton of an amino acid by a methyl group has been shown to reduce the number of possible combinations of values for the φ and ψ torsional rotation to essentially two (25). Introduction of a c y c l i c constraint in a linear flexible molecule reduces the


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Computer-Assisted Drug Design - American Chemical Society

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