ELSEVIEi Chemometrics and Intelligent Laboratory Systems 24 (1994) 185-191

C~emometrics and intelligent. laboratory systems

Receptor mapping with multiple binding modes: binding site of a PCB-degrading enzyme

&efan BaE *, Viktor HorEik, L’ubor mazurka Department of Biochemical Technology, Faculty of Chemical Technology, Slovak Polytechnic University, Radlinskzho 9,

81237 Bratislava, Slovak Republic

Received 19 August 1993; accepted 10 April 1994

Abstract

The binding site of a polychlorinated biphenyl (PCB)-degrading enzyme has been mapped using the published data on biodegradation rates of individual PCB congeners by the Acinetobacter P6 strain. As in other approaches to the problem, additivity of contributions of individual parts of the PCB molecules to the global binding energy was assumed. The ~m~unds were allowed to bind to the enzyme in various bin~mg modes. In the search for the correlation between the structure of individual PCB wngeners and their biodegradation rates the approach to select one binding mode for each PCB congener failed. Its modification, the consideration of simultaneous occurrence of all possible binding modes for each PCB congener in proportions given by the binding energy provided satisfactory results. The resulting map of the binding site consists of four binding points corresponding to the positions (2 and 61, 5, 2’, (3’ and 4’1, with both phenyl rings having a perpendicular orientation. The first binding point is attractive: the ~~o~nes in the positions 2 and 6 are pr~ably hydropho~ical~ bonded to the ~unte~a~s in the binding site of the degrading enzyme. The other binding points are repulsive.

1, induction

Polychlorinated biphenyls (PCBs) are mixtures of chemicals with interesting physical and chemi- cal properties: they have low vapour pressures, low water solubility, excellent dielectric proper- ties, stability to o~dation, flame resistance and relative inertness. These properties, which have made them an attractive chemical product for

* Corresponding author.

over 50 years, also caused their persistence in the environment. Microbial degradation seems to be a promising tool for their removal from contami- nated water and soil. The rate parameters of this process are important characteristics enabling the estimation of the period needed for their removal from the environment [l].

In this work we attempt to find the relation between the structure of a series of PCBs and their microbial degradability and, simultaneously, to obtain an estimate of the geometry of the binding site of dioxygenase which is assumed to be responsible for bi~egradation of PCB. The

0169-7439/94/$07.00 8 1994 Elsevier Science B.V. All rights reserved SS’ZX 0169-7439(94)00034-G

186 t? Balrii et al. /Chemometrics and Intelligent Laboratory Systems 24 (1994) 185-191

task is identical to revealing the spatial organisa- tion of an unknown receptor using the data on binding of a series of bioactive compounds; there- fore the approach will be referred to as receptor mapping. Due to the structure of PCB only inter- actions of the same type are expected, hydropho- bic binding being assumed to play a dominant role. Since we have no direct information about the structure of the enzyme, we have to use, as exhaustively as possible, the known structure of PCB molecules. We can exploit one more fact that follows from the reaction mechanism of PCB biodegradation: the enzymatic reaction starts in the non-chlorinated positions ortho and metu where the aromatic ring is split and gradually degraded to chlorobenzoic acids [l]. Therefore the acceptable binding modes of a PCB congener should have non-chlorinated ortho and metu po- sitions localised at the same place within the binding site of the enzyme. The geometry of the binding site and a quantification of the underly- ing interactions should help to predict the elimi- nation rate for any of 209 PCB congeners.

2. Theoretical

2.1. Receptor mapping with multiple binding modes

The present approach to receptor mapping is based on the following assumptions. The binding strength of the tested compounds to the receptor is expressed in terms of the association constant K which is connected with the Gibbs free energy through the equation

AG=RTIn K (1)

The total free energy of binding is assumed to be the sum of partial interaction energies for all contacts between parts of the ligand molecule and parts of the receptor molecule (binding points) 121:

AG = C AG, k

(2)

where the index k goes over all contacts. To take

into account the number of ways a molecule can bind to the receptor, we determine for each com- pound its possible binding modes, i.e., the man- ner in which the compound is geometrically em- bedded in the binding site. The interaction en- ergy for the jth mode of the ith congener is

AGii = RT In Kij = c vijk AG, k

(3)

where the subscripts i,j,k designate ith com- pound, its jth binding mode and the index k goes over all the binding points. The variable vijk indicates the occurrence of a structural feature (1 if present, 0 otherwise) in the kth binding point for the jth mode of the ith congener. Here AG, are the partial interaction energies and they rep- resent the adjustable parameters. For their opti- misation two approaches can be used.

The first one assumes that only one of possible binding modes for a certain congener is encoun- tered. One binding mode for each compound is chosen and the contributions AG, are calculated using multiparameter linear regression. This pro- cedure is repeated for all possible combinations of the binding modes. The final results have to fulfil the condition that the most favourable bind- ing modes for all compounds should be encoun- tered [2]. In addition to good statistical quality, an acceptable solution should comprise for each congener the binding mode that is energetically more favourable than the remaining binding modes for the given congener. This combinatorial approach is conceptually similar to that used by Crippen [2], although he used a different mathe- matical approach for optimisation of the partial interaction energies AG,.

The simplicity of our problem allowed us to go beyond this concept, which is apparent from the second approach. Here the possibility of multiple binding modes of the same compound is consid- ered and this seems to be a better description of the physical reality. It is assumed that each bind- ing mode of the same compound can be encoun- tered with some probability. The interaction of the ligand (D) and the receptor (R) with the

3. Bal& et al. /Chemometrics and Intelligent Laboratory Systems 24 (1994) 185-191 181

possibility of several binding modes can be writ- ten schematically as

D+R 2 DR,

D+R 2 DR,

. . . . . . . . . Kll

D+R - DR, (4)

where 12 is the number of binding modes for a certain compound. DR, in Scheme 4 are the 1:l ligand-receptor complexes, differing in the ge- ometry of binding, i.e. in each complex the ligand is bound in a different orientation and its parts have contacts to different binding points consti- tuting the binding site. Equations derived for one compound are valid also for the others (with respect to this and also for clarity’s sake the subscript i is omitted in all equations). Each equilibrium in Scheme 4 represents the interac- tion of the enzyme R with the ligand D in the ith binding mode and is characterised by the partial association constant Kj:

Kj = [DRj] /[DI[RI (5) The experimentally measured equilibrium con- stant K reflects the total concentration of ligand D and not its different modes of binding. The concentration of [DR] encompasses all complexes of D and R:

K= [DRl/[DI[Rl

= (W,I+ P%I + - * - + WRnI)/PI[Rl

= iKj (6) j=l

The expression of the partial association constant Fj in terms of partial interaction energies AG, is given by Eq. 3. Its combination with Eq. 6 results in

(7)

This is the final equation that is to be used for finding the values of the partial interaction ener-

gies AG, from the experimental values of the drug-receptor association constants Ki using non-linear regression analysis. The number of data points is equal to the number of experimen- tally determined association constants and the number of adjustable parameters is given princi- pally by the number of binding points. Combina- torial load from the first approach has been sub- stituted by a single run of non-linear regression analysis in the second approach. Since the com- plexity of the problem was not reduced in the physically more realistic second approach, it is transferred now to finding the proper first esti- mates of the partial interaction energies AG,.

2.2. Mapping the PCB-degrading enzyme

Assuming Michaelis-Menten kinetics, of the enzymatic degradation reaction is

v = vm,[Sl/(Kn + PI)

the rate

(8)

where [S] is the concentration of the substrate OTB&,, is the maximal reaction rate and K, is the Michaelis constant. For a small concentra- tion of substrate ([Sl -z K,):

v = v,[S]/K, = k[S] (9)

where k is the observed elimination rate constant of the first order. When the covalent steps in the degradation reaction are much slower than the formation of the non-covalent complex, K, is equal to the inverse value of the association con- stant K for the non-covalent binding of the sub- strate to the enzyme. Then

Ki = ki/v_ (10)

Providing we can assume the same and constant maximal rate v,, for all congeners, the elimina- tion rate parameter kj is proportional to the association constant for non-covalent complex formation and can be used directly in Eq. 7, v,, being an additional adjustable parameter. Al- though AG, stands for the partial interaction energies, they are the only adjustable parameters and the constant terms v,, and RT can be

188 s Bal& et al. / Chenwmetrics and Intelligent Laboratory Systems 24 (1994) 185-191

incorporated into them. Then Eq. 7 can be rewritten, using Eq. 10, as

ni Im+l \

ki = C exp j=l

(11)

Here ni is the number of binding modes for the ith congener and m is the number of binding points.

3. Results and discussion

3.1. Quantum-mechanical characterisation of PCB molecules

The analysis of the structure of PCB was done with the help of the semi-empirical quantum- mechanical method AMl. The optimisation of geometry in vacua terminated for all congeners in the structure where both rings are mutually ro- tated and the angle is dependent on the substitu- tion positions of chlorines. No significant defor- mations of the phenyl rings were observed under the influence of chlorine substitution in various positions. From the course of optimisation it was obvious that the main way the molecule gets to its minimum is the mutual rotation of rings about the 11’ bond. Summarising the last two facts we can conclude that the conformational analysis without optimisation of geometry of the phenyl rings will be sufficient to get an approximate picture of the energetic states of all possible conformations of PCB. Here the energy of a molecule is calculated for certain values of the dihedral angle of the two rings. Molecular confor- mations for the dihedral angle in the range O-180” are symmetrical to those with an angle of 180- 360” regardless of chlorine substitution on both rings. Therefore the calculations in the interval O-180” will be sufficient for complete analysis.

It follows from the results obtained in this way (Fig. 1) that the individual congeners do not differ significantly in the range of the dihedral angle in which the rings move practically freely. The extent of flat minima on the curve of ener- getic profiles is approximately 60-120” for all congeners. In the following we will consider only

0 50 100 150 200

dihedral angle Fig. 1. The dependence of energy on the dihedral angles for the PCB congeners (IUPAC Nos.) 18 (01, 26 (A), 27 (Xl,

and 35 (0).

two approximate positions of the rings which we will call coplanar and perpendicular. Whilst the coplanar position corresponds fully to the desig- nation with the dihedral angle being zero, the perpendicular position encompasses a rather broad interval of the dihedral angles (60-120”) as given by the flat minima on the energy-dihedral angle curve.

Individual congeners differ significantly in the height of the energetic barrier in a coplanar con- figuration of rings. Its magnitude would be cer- tainly lower if full geometry optimisation would be undertaken. Nevertheless, we assume that the approximate approach will suffice for our pur- pose. The height of the barrier is influenced only by the substitution and number of chlorines in the ortho positions of both rings. According to this criterion all congeners can be divided into six groups: (1) without any ortho chlorines (the bar- rier 2.7 kcal/mol), (2) with one ortho chlorine (35 kcal/mol), (3) with two ortho chlorines on the same ring (67 kcal/mol) and (4) on different rings (66 kcal/mol for the contacts Cl-H and 914 kcal/mol for the contacts Cl-Cl and H-H), (5)

s Balk? et al. /Chemometrics and Intelligent Laboratory System 24 (1994) 185-191 189

with three (946 kcal/mol) and (6) four o&o chlorines (1827 kcal/mol).

3.2. Mapping the binding site

For this purpose the data on degradation rates of individual PCB congeners by the strain Acine- tobacter P6 [3] were used (Table 1). For construc- tion of the binding site we can take advantage of the experimental information that the enzymatic splitting of the phenyl ring starts in the non-chlo- rinated positions ortho and meta [l]. For all binding modes these positions have to be located at the same place in the binding site. This will reduce the number of possibilities in which PCB can bind to the enzyme. Two congeners (19 and 20, Table 1) have all ortho and meta position pairs chlorinated and cannot be degraded by the same route as the rest of congeners. They were excluded from analysis. The suggested model of the binding site in principle copies the shape of the biphenyl skeleton in the conformation where

Table 1 Structure of the studied PCB congeners and their biodegrada- tion rate constants [3]. The congeners are sorted according to the magnitude of the rate constants

No. IUPAC No. Substitution k(h-‘1’ position of Cl

1 8 2,4’- 0.982 2 14 3,5- 0.964 3 5 2,3- 0.928 4 30 2,4,6- 0.920 5 12 3,4- 0.882 6 26 2,3’,5- 0.826

.7 28 2,4,4’ - 0.804 8 33 2,3’,4’ - 0.772 9 29 2,4,5- 0.648

10 21 2,3,4- 0.640 11 31 2,4’,5- 0.608 12 15 4,4’- 0.504 13 61 2,4,5,6- 0.380 14 11 3,3’- 0.370 15 4 2,2’ - 0.280 16 40 2,2’,3,3’- 0.146 17 18 2,2’,5- 0.102 18 10 2,6- 0.082 19 52 2,2’,5,5’- 0.070 20 54 2,2’,6,6’- NDb

a First-order rate constants; strain Acinetobacter P6. b No degradation determined.

Fig. 2. All binding modes for the tested PCB congeners (Table 1) regarded as different orientations of the molecules within the same binding site. A designation of binding points (these are equivalent to the positions of chlorine substitution) is depicted in one of the binding modes. Thick line on every picture represents the non-substituted o&o and meta posi- tion necessary for initiation of the enzyme attack,

both phenyl rings are either perpendicular or coplanar. It consists of eight binding points that are located near the carbons of the biphenyl skeleton so as to be able to account for possible binding of chlorines in every position (except the fixed ortho and meta positions where no chlo- rines can occur). The acceptable binding modes for all tested PCB congeners are given in Fig. 2.

The combinatorial approach assuming the presence of only one binding mode failed. Al- though many good correlations have been found by multivariate linear regression analysis, in no case the selected set of binding modes of individ- ual congeners consisted of the most energetically

190 .?. BaE et al. /Chemometrics and Intelligent Laboratory Systems 24 (1994) 185-191

Table 2 The values of parameters AG, for given binding sites (2 and 61, 5, 2’, (3’ and 4’) and a constant term of the skeleton

AG,,,,, in Eq. 11; statistical indices of the non-linear regres- sion are n = 16, r = 0.951, and s = 0.249

Designation of Value of Standard parameter parameter deviation

26 0.3147 0.097 5 - 1.1996 0.298 2’ - 1.6389 0.433 3’4’ -0.1828 0.080 const - 0.8635 0.099 Fig. 3. The proposed model of the binding site of dioxygenase

with outlined regions of attraction (+) and repulsion (- ).

favourable binding modes. Usually only for about half of all PCB congeners the best binding modes were encountered in the selection providing oth- erwise satisfying agreement with the experimental data.

Non-linear regression analysis of the experi- mental elimination rate parameters (Table 1) ac- cording to Eq. 11 has been tried with many ran- domly chosen sets of the first estimates of the partial interaction energies AG,. Testing the sig- nificance of the eight binding points and coupling them in different ways led to the proposal of the binding site that best fitted the experimental data (Table 2). The number of binding points has been reduced to four, which with one constant term gives the total number of five adjustable parame-

ters. The term vijk (Eq. 11) for the coupled posi- tions (2 and 6) and (3’ and 4’) takes the values 0, 1 or 2 according to how many chlorines occupy them. One binding point, corresponding to the positions 2 and 6, is attractive: the chlorines in these positions, if present, form probably the hydrophobic bonds with the parts of the enzyme macromolecule within the binding cavity. The other three binding points for the positions 5, 2’, (3’ and 4’) are repulsive (Fig. 3). Two congeners (2 and 18, Table 1) did not fit the suggested model, probably because they do not meet the assumption of the constant maximum rate v,, and were excluded from correlation.

Having determined the partial binding ener-

Table 3 Experimental and calculated values of the degradation rate constants and the contribution of individual binding modes (Fig. 2) to the total rate constant for a certain congener

No.

1

IUPAC No.

8

In(k,,)

-0.018

tn(k,,rJ

0.043

Contribution of the given binding mode to the total rate constant (%/lOO)

0.08 0.46 0.46 3 5 - 0.075 4 30 - 0.083 5 12 -0.126 6 26 -0.191 7 28 - 0.218 8 33 - 0.259 9 29 - 0.434

10 21 - 0.446 11 31 - 0.498 12 15 - 0.685 13 61 - 0.968 14 11 - 0.994 15 4 - 1.273 16 40 - 1.924 17 18 - 2.283

-0.199 0.70 - 0.234 1.00 -0.173 0.50 - 0.468 0.23

0.030 0.47 - 0.096 0.09 - 0.285 0.23 - 0.213 0.71 - 0.468 0.23 - 1.046 1.00 - 1.055 0.50 - 0.783 0.77 - 1.495 0.50 - 2.107 0.77 - 1.924 0.23

0.21 0.08

0.15 0.35 0.77 0.47 0.07 0.03 0.44 0.44 0.77 0.22 0.07 0.77

0.50 0.23 0.50 0.23 0.77

$. Bali? et al. / Chemometrics and Intelligent Laboratory Systems 24 (1994) 185-191 191

gies AG, for individual positions, it is straightfor- ward to calculate the elimination rate parameters for individual binding modes (Fig. 2) as the terms under summation in Eq. 11. For illustration 2,4’- dichlorobiphenyl (compound 1, IUPAC No. 8, Table 1) with its three possible binding modes (Fig. 2) has been chosen. The elimination rate parameters can be calculated using AG, given in Table 2 for each of the binding modes outlined consecutively in the first row of Fig. 2 (the brack- eted numbers correspond to the number of the binding mode) as follows: (1) the ortho chlorine is massively repulsed by the binding point 2’ (num- bering in Fig. 2) with AG, = - 1.6389, the para chlorine is neither attracted nor repulsed by the binding point 4 (AG, = 0), the constant term is -0.8635, the elimination rate parameter is exp[ - (1.6389 + 0.8635)]= 0.0819, (2) the ortho chlorine is attracted by the binding point 2 with AG, = 0.3147, the para chlorine is repulsed by the binding point 4’ with AGk = -0.1828, the elimination rate is exp(0.3147 - 0.1828 - 0.8635) = 0.4811, (3) the ortho chlorine is attracted by the binding point 6 with AG, = 0.3147, the para chlorine is repulsed by the binding point 4’, therefore the elimination rate parameter will be the same as for the second binding mode. The calculated elimination rate is given by the sum of the elimination rates for individual binding modes (Eq. 11) as k, = 0.0819 + 2 x 0.4811 = 1.0441 (Table 3). The contributions of individual binding modes to the total rate constant are easily calcu- lated as 0.0819/1.0441 z 0.08 and 0.4811/1.0441 = 0.46 and are also summarised in Table 3.

The site which would fit the coplanar confor- mation of PCB (this feature was implemented

through an additional parameter for the energy repulsions in planar conformation) did not im- prove the correlation. Therefore we assume that the site can be occupied by PCB with the phenyl rings in the perpendicular position. The term perpendicular has a rather broad definition in this context: it encompasses the dihedral angles from 60 to 120” where the energy-dihedral angle dependences (Fig. 1) have flat minima.

Although further research is needed we hope that the presented results illustrate the usefulness of the present approach to receptor mapping with multiple binding modes. If future results confirm this belief the approach can contribute to a better understanding of tions.

chemico-biological interac-

Acknowledgments

The research was supported by grants Nos. l/990969/93 and l/712/93 from Slovak Grant

Agency.

References

[l] D.A. Abramowicz, Aerobic and anaerobic biodegradation of PCE3s: a review, Critical Reviews in Biotechnology, 10 (1990) 241-251.

[2] G.M. Crippen, Distance geometry approach to rationalis- ing binding data, Journal of Medicinal Chemists, 22 (1979) 988-997.

[3] K. Furukawa, K. Tonomura, A. Kamibayshi, Effect of chlorine substitution on the biodegradability of polychlori- nated biphenyls, Applied and Environmental Microbiology, 35 (1978) 223-227.