ARCHIVES OF BIOCHEMISTRY AND BIOPHYSICS Vol. 194, No. 2, May, pp. 552-557, 1979

Inhibition of Chymotrypsin by Alkyl Phosphonates: A Quantitative Structure-Activity Analysis

CARLO SILIPO,tj’ CORWIN HANSCH,*s2 CIRO GRIECO,? AND ANTONIO VITTORIA?

*Departme& of Chemistry, Pomona College, Claremont, California 91711, and the tlnstitute oj Pharmaceutical and Toxicological Chemistry, University oj’Naples, Naples, Italy

Received October 13, 1978; revised December 27, 1978

A quantitative structure-activity relationship has been formulated for 53 alkyl phos- phonates [R,OPO(CH,)SR,] inhibiting chymotrypsin: log k, = 1.47MR,,~, + 0.34MRs,,, + 1.250$ - 1.061 - 3.43 log (p.10 Mh~Ka + 1) - 5.26; log p = -3.85. In this so-called bilinear model, ki is the bimolecular rate constant (Mm’ s-l), p is a disposable parameter evaluated by a computerized iterative procedure, MR is the molar refractivity of a substituent, 4 is Taft’s polar parameter, and Z is an indicator variable for substituents containing a sulfonium group. The correlation coefficient for this equation is 0.985. This quantitative structure-activity relationship is compared with those previously formulated for the action of chymotrypsin on acylamino acid ester substrates.

In continuing our analysis (1, 2) of the interactions of ligands with chymotrypsin, we consider in this report the inhibition by thiophosphonates (I)

P3 9

3

pzo PH

R20’ ‘CH3 P2 PI

I

from the studies of Aaviksaar and his col- leagues (3-9). We have oriented the general structure for the phosphonate esters in I to parallel that of the acyl esters of amino acids which we have used in the preceding papers in this series (1, 2). We describe this paral- lelicity with the nomenclature of Hein and Niemann (10) who discuss the space around the active site in terms of the four groups attached to the a-carbon of amino acid

1 Visiting Scientist from the University of Naples. * To whom all correspondence should be addressed. 3 Abbreviations used: p3, Enzymic space; u*, Taft’s

polar parameter; r, hydrophobicity; MR, molar refrac- tivity; k;, bimolecular rate constant.

esters. We have placed the -SR, leaving group in the phosphorylation of chymotryp- sin in p3 space,3 just as the -OR, leaving group in the acylation of chymotrypsin is accommodated there. Oxygen, the smallest of the four groups attached to phosphorus, has been placed in pn open space where, by analogy, the smallest of the four groups at- tached to the a-carbon of amino acid esters is also located. The small methyl group com- mon to all congeners has been positioned in the relatively weakly bonding (1) p, space. The fourth group, the relatively large -OR, moiety, is finally assigned to p2 space which normally accommodates the cr-alkyl group of amino acid esters. We have formulated Eqs. [l]-[5] from the data of Aaviksaar et al. in Table I.

EXPERIMENTAL PROCEDURES

552

The substituent constants employed in this study were taken from our previous report (1) or calculated as outlined in that study (1). Since c* values for sub- stituents of the type (CH,),SC,H, and (CH,),S+(CH,)Et were not all available, they were estimated by using the fall-off factor of 2.73 of Wells (11) for the reduction of the inductive effect resulting from the interposition of each methylene group. Fortunately, o* (1.60) for -CH,CH,S+(CH,)Et has been determined by Yarv et al. (12). The u* values for the (CH,),SEt and

0003-9861/79/060552-06$02.00/O Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.

TABLE I

PARAMETERS USEDIN THE FORMULATIONOF EQS. [l]-[5]

SR:,

R,O-P=O

k,

1 SC,H,, OMe, 2 SC,H,, OCH(Me),, 3 SC&, OC,H,, 4 SCJL, O&H,, 5 SC,H,, OCH(Me)CH,Me, 6 SC&, OCH,CH(Me),, 7 SC,H,, OCH,C(M& 8 SC&. OWL, 9 SC& OC,H,,,

10 SC& OCH,CH,CH(M& 11 S&H.,. O(CH,):,CH(Me),, 12 S&H.., OC,H,.,, 18 SC&,, OGH,,, 14 SC,H.,. O(C~,MWMel,. 15 SCJL. OCH(Me)Wlr),,. 16 SC,H,, OC,H,,, 17 SC& OC,,H, ,a 1X SC,H.,, OCH(Me)(CH,I,Mr 19 SC,H,, O(CH,),CH(Me),. 20 SC,H,, OC,H;. 21 SC,H,. OC>H;, 22 S&H,,, OC,H,. 23 SC,H,.l, OC,H,. 24 S(CH,),SC,H,. OMe. 25 SC&,. OC,H,. 26 S(CH,),SC,H,. OC,H,. 27 S&H,,, OC,H,, 28 %H,,, OC>H;, 29 S(CH,),SC,H,. O&H,, 30 S(CH,),SC,H,, OCIH.,. 31 SCH,SC,H.. OCIH,, 32 S(CHJ,SC,H., O(‘,H,, 33 S(CH,),SC,H,, OCJL 34 S(CH,),SC,H,. OCJ,,, 35 S(CH,),SC,H,. OGH,.,, 36 S(CH,),SC,H,. OGH,,. 37 S(CH,),SC,H,, OCH(Me)C(Me),, 3X S(CH,),SC,H,. OGH,.,. 39 S(CH,),SC,H,. OGH, /. 40 S(CH,),SC,H,. OC,H,,.

41 S(CH,),kMe)C,H,,

42 S(CH,l,S(Me)C,H,, 43 S(CH,),,S(MeK,H,, 44 S(CH,),S(Me)C,H,, 4.i S(CH,),S0le)C,H., 46 S(CH,),S(Me)C,H,, 47 S(CH,GXMeGH,, + 48 S(CH,),S(Me)C,H,, f 49 S(CH,),S(Me)C,H,, 50 S(CH,),S(Me)C,H,, + 51 %CH,),S(Me)C,H,,

+ 52 S(CH,),S(Me)C,H,, 53 S(CH,),%Me)C,H,,

OC>H,, OC~H.,. OC,H;. OMe, OC,H;.

OGH,. OGH,,, OWL, 'X8,,, OC.,H,,, OGH,,, OGH,.,. OGH,,.

Me Me Me Me Ml? Me Me Me

Me Me Me Me Me Me Mr Me Me

Me Mr. Ml? Me Me Me MP Me Me Me Me Me Me Mle Me Me Me Me Mt? Me Me Ml? Me

Me

M?

.Me

MC2

Me

Me

.Me

.Me

MC!

Me

Me

Me

Me

-3.33 -3.31 0.02 2.7; 0.79 -0.13 u (8) -2.57 ml.97 0.60 2.7; 1.71 -0.13 u (6, -2.6% -2.64 0.04 2.7i 1.25 -0.13 0 (3) -2.04 -1.97 0.07 2.7i 1.71 -0.13 0 (8) -1.46 -1.31 0.15 2.7; 2.17 -0.13 0 (6, 8)

1.33 -1.31 0.02 2.7i 2.17 -0.13 0 (6, 8) -1.15 -0.69 0.46 2.7; 2.63 -0.13 0 (8) -0.99 ml.31 0.32 2.7: 2.17 -0.13 0 (5, HI -0.55 -0.69 U.14 2.7: 2.6X -0.13 0 (Xl -0.55 -0.69 0.14 2.7: 2.63 -0.13 u (6. 8) -0.29 -0.17 0.12 2.7: 3.09 -0.13 0 (6, 8) -0.27 -0.37 0.10 2.7: 4.47 -0.13 0 (5, 8)

I~.02 0.0X 0.10 2.7: 4.01 -0.13 u (5, Xl 0 06 0.0x 0.W 2.T 4.01 -0.13 u (6. hl 0.13 -0.17 0.30 2.r 3.U9 --Il. 13 0 (a) 0.1X 0.14 0.u.l 2.7'7 3.55 -U.13 0 (5. Xl 0.22 -0.17 u.39 2.T :3.09 -0.13 u (2. Xl 0.38 0.0X 0.Z 2.T 4.01 -0.13 0 (8) 0.39 u.14 0.2.~ 2.7 :3.5.5 -0.13 0 (6. Xl

-3.W -2.92 0.14 1.84 1.23 -0.10 0 (ii) -2.x9 ~-2.79 u.10 2.31) I.23 -0.12 0 GO -2.jlj -2.62 0.04 :i.u 1.23 -0.16 0 (:i) -2.82 -2.X u.u5 S.ti!j 1.2.5 -0.17 0 (:I) -2.5 -2.53 O.Zh 3.hli 0.m 0.2x 0 (4) -2.18 -2.21 o.u;1 4.16 1.2.; -U.li 0 (iI1 -2.11 -1.W 0.25 :3.sli 1.25 0.28 0 (4)

1.99 -2.03 0.04 4.62 1.2.5 -0.15 0 (3) -1.W -1.92 U.12 ,>.U? 1.25 -0 19 ” (3) -1.55 -1.85 0.30 4.9li 1.25 -0.10 u ii)

1.34 ml.70 0.36 j.42 1.23 -0.111 0 17) -1.27 -1.ti6 u.39 3. 10 1.25 u..5ti 0 (71 -1.25 ml.18 0.07 3.36 1.71 IJ.Zb U (4) -u..52 0.33 0.01 3.,5i 2.17 0.2x u (4)

0.0x 0.09 0.01 :i. 5’i 2.63 0.2x u C-1) 0.2x 0.77 0.49 3.42 3.w -0.10 0 01) 0.44 0.86 0.4% 3.5’4 4.01 0.2x u (4) 0.44 0.61 0.17 :3.5; 3.09 0.2x u (‘v 0.53 0.63 0.10 4.49 3.09 0.04 IJ (9) 0.67 0.61 U.Uti :3.5i 3.09 u.2n u (4.X) U.i4 0.92 0.18 3.56 3.55 u.2n u (4)

-2.M

-2.66

-2.07

-1.31

-1.Z

-0.3

0.15

0 31

0.44

0.93

l.ti4

1.70

1.77

-2.45

-2.36

-2.1:i

-1.X)

-1.02

-0.35

(1.11

0.31

0.02

0.93

1.69

I.45

1 75

0.21

0.30

0.06

0.19

0.24

0. In

0.04

0 00

0.42

0.00

0.05

0.25

U.O2

3.14

610

4.72

4.26

4.26

4.26

ti.10

4.26

5.E

4.26

4.26

4.26

4.26

1.25 1.25

1.25

U.i!l

1.Z

1.71

3.U9

2.17

3.w

2.m

4.01

3.09

3.,i.z

0.21 1 (7)

il.03 1 (7)

0.39 I (7)

l.RU 1 (41

I.60 1 (il

1.60 1 (4)

0.03 1 (9)

1.60 1 (4)

0.21 1 (9)

1.60 1 (4)

1.60 1 (4)

1.60 1 (4)

1.60 1 (4)

n The units of k, are M-‘s-‘. b From Refs. (3-Y). ’ Frnm Eq. 151.

554 SILIPO ET AL.

(CH,),SEt were assumed to be the same as that of

-CH,CH:,. We have not employed stepwise regression analysis but instead have derived all possible equations for the variables considered. In the calculation of MR

for the charged sulfonium group, MR for neutral S was

used because reliable MR values are not available. The

indicator variable in Eq. [5] takes care of any discrepancy in the value of MR,,,,.

model gives a slightly lower ideal MR,,,, value. For Eq. [3], ,~3 is estimated by an iterative procedure; hence we cannot place confidence limits on the optimum value of MRoK, as we can with the parabolic model.

To formulate Eq. [4] we have added the next 21 congeners of Table I to the first 19 and refit the data:

RESULTS log ki = 1.42( +0.12)MR,,RL

Aaviksaar and his co-workers have limited the changes in I almost entirely to the addition of CH, groups along with posi- tion isomerism. This means that 7~ and MR are almost perfectly collinear for the data in Table I; hence there is no point in in- vestigating both parameters and we have therefore limited our consideration to MR. The reason for selecting MR is that our earlier studies showed MR to be much superior to n for correlation analysis with chymotrypsin (1, 2).

+ 0.35( ?O. 10)MRsK,,

+ 1.21(?0.42)&

- 3.30(*0.88) log (/3.10”~~‘~~ + 1)

- 5.18(t0.45), [4]

In attacking the structure-activity rela- tionship we considered at the outset the first 19 compounds in Table I in which SR, is constant and changes occur only in OR,. Correlation analysis yields Eqs. [ lJ- [31:

log ki = l.OO( ?0.25)MR,,,,,

where n = 40, r = 0.981, s = 0.253, ideal MRoHz = 3.75, log /3 = -3.87. The second set of 21 congeners contains changes in the SR, moiety as well as in the OR,. Two new terms are needed in Eq. [4]. There is enough variation in the electronic effects of R, of SR, to warrant the use of Taft’s polar pa- rameter u*, and a term in MR for SR, is now needed to account for variation in this group. If we use the parabolic model with the same terms in place of the bilinear model, we find a poorer correlation (r = 0.974; s = 0.290).

-3.62(+0.72), [l]

where n = 19, r = 0.902, s = 0.503.

log ki = 2.87( +0.84)MR,,,,

- 0.35( 20.15) (MR,,,,)’

The parameters of Eqs. (31 and [4] and the quality of fit are quite close. Note that the optimum value for MR,,, is almost identical for each equation. The positive coefficient with (T< shows, as one would expect, that electron withdrawal by R, of SR, favors phosphorylation.

-5.80(?1.1), [2]

where ‘a = 19, r = 0.961, s = 0.331, ideal MROKI = 4.15 (3.7 to 5.4);

log ki = 1.60(*0.22)MR,,,,

- 3.85(?1.17) log (p.lOU”““X + 1)

-4.76(?0.51), [3]

Finally, we can combine the last 13 con- geners in Table I to get Eq. [5]:

log ki = 1.47(tO.lO)MR,,,,

+ 0.34( +O.O9)MR,,,

+ 1.25(*0.19)a$

- 1.06(cO.31)1

where n = 19, r = 0.978, s = 0.258, ideal MRoH, = 3.72, log ,Z3 = -3.86. In these expressions ki (M-l s-l) is the bimolecular rate constant. We have employed the so- called parabolic (13) model in Eq. [2] for activity dependence on log P and used Ku- binyi’s bilinear model (14, 15) in Eq. [3]. The bilinear model gives a sharper fit (compare standard deviations). As usual, the bilinear

- 3.43(*0.74) log (p.lOMK(“wL + 1)

- 5.26(?0.38), [5]

where n = 53, r = 0.985, s = 0.243, ideal MRoKI = 3.71, log p = -3.85. One addi- tional term (Z) is needed to include the last 13 congeners of Table I with the first 40 to formulate a single correlation equation. Z takes the value of 1 for all charged sul-

ALKYL PHOSPHONATE INHIBITION OF CHYMOTR.YPSIN 555

TABLE II

SQUARED CORRELATION MATRIX OF VARIABLES

CONSIDERED IN THE DERIVATION OF EQ. 151

MR,,,, MRsR:, cr$ I

M&xc, 1.00 0.03 0.00 0.00

MRsR,, 1.00 0.10 0.36 a? 1.00 0.60 I 1.00

fonium substituents; its negative value shows the deleterious effect of the positive charge on the inhibition reaction, The pa- rameters of Eq. 151 are in good agreement with those of Eqs. [3] and [4], showing that all three subsets of Table I behave in a paral- lel fashion in the inhibition of chymotrypsin. Again, using the parabolic model in place of the bilinear model yields a slightly inferior correlation (r = 0.979, s = 0.389).

DISCUSSION

Equation [5] appears to be a robust ex- pression based on more than 10 data points per variable. It is a good correlation which explains 97.1% of the wide variation (lOO,OOO-fold) in ki.

It is of interest to compare Eq. [5] with Eq. [6] which correlates interaction with chymotrypsin of acylamino acid esters II. Congeners II are normal substrates for

R/‘NHCOR, p2 PI

II chymotrypsin, while congeners I are inhibi- tors. Aaviksaar et al. have called the phos- phonates “quasi-substrates” because they acylate the enzyme and hence are expected to have structural dependence on K, and k, similar to that of substrates. Since de- acylation does not occur, there is no depend-

ence upon k, such as normal substrates have. It is of interest to compare correlation equations for ki with those for K,,, and k,lK, for substrates. Equation [6] correlates (2) binding of congeners II:

log l/K,, = 1.13(?0.12)MR,

+ 0.48(-+0.11)MR,

+ 0.77(?0.11)MR,

- 0.54( ?0.27)1,

+ 1.29( +0.23)a%

- 0.055( *O.Ol)MR, .MR,.MR,

- 1.68(?0.48), [6]

where n = 84, r == 0.977, s = 0.333. This equation is not as sharp a correlation as Eq. [5] (compare values of a). Probably the major reason for this is that K, values for Eq. [6] are from a variety of laboratories while all of the data for Eq. [5] are from the same laboratory. In addition, the molecular changes in the congeners correlated by Eq. [6] are much more varied. There are many instances where hetero atoms are used. In Eq. [6] the subscripts with MR correlate with pl, p2, and p3 space of the enzyme as shown in II. There are three terms in Eq. [6] not present in Eq. 1.51; since MR, is constant in congeners I, no term for it appears in Eq. [5]. The indicator variableI, is given the value of 1 when R = isopropyl; this struc- ture does not occur among the phosphonates. In Eq. [6] we have the cross-product term MR, .MR,. MR, which brings out the inter- action between binding in p,, p2, and p3 space. Putting large groups in two of these spaces inhibits binding in the third, No cross-product term (e.g., MRoK2. MR,,:,) is found for Eq. [5] which is not surprising since all of the congeners contain the small CH, group and only a few contain two large groups.

The correspondence between coefficients of & in Eqs. [5] and [6] is very close in- deed, indicating the same dependence of re- action upon electron withdrawal. Also, the dependence of the reaction on MR, is close in the two equations. The coefficient for MR, in Eq. [6] does not. differ greatly from that for MR,,, of Eq. [3]; this suggests that the

556 SILIPO ET AL.

formation of enzyme-substrate complex in the phosphorylation step is more important than the acylation step.

A more proper comparison might be that between ki and k,lK,. Relatively little of the latter type of data exists, though a set of 20 congeners has been characterized by Bere- zin and his colleagues (16). We have formu- lated Eq. [7] from the data in Table III for congeners of type II:

log kz/K, = 1.78(+0.21)MR,

+ 0.44(&0.18)MR,

- 2.13( 20.4611

-1.06(-cO.70), [7]

where n = 20, r = 0.990, s = 0.372. The standard deviation of Eq. [7] is rather high, but since there is a 107-fold range in k,lK,, it is possible to obtain a high value of r. The indicator variable I is, as usual, assigned the

value of 1 when R, =isopropyl. No exponen- tial or cross-product terms are needed in Eq. [7] since large R, groups were not studied.

Unfortunately, MR, and MRoR, are the only common terms for comparison in Eqs. [5] and [7]. Bearing in mind the rather large structural differences between congeners I and II, it is surprising that the dependence of log ki and log k,lK, on MR is so similar. All things considered, the agreement is about as close as one could expect.

There is so little variation in R:, for the data set on which Eq. [7] is based (either in (T* or MR) that it is not possible to include this term in the correlation.

An interesting parameter in the phos- phonate Eq. [5] is I which is assigned the value of 1 for all phosphonium substituents. Its negative coefficient shows these analogs to be about lo-fold less effective inhibitors, all other factors being equal. The cause of

TABLE III

PARAMETERS USEDINTHEFORMULATIONOFEQ. ['7]"

Log k,lK,”

No. RI R2 R3 Observed’ Calculated” IA log k,/K,I MR, MR, I

1 L-NHCOMe, i-&H,, i-O&H,

2 L-NHCOMe, i-&H,, OEt

3 L-NHCOMe, i-&H,, OMe 4 L-NHCOCH,Cl, i-&H,, OMe

5 L-NHCOPh, Me, OEt

6 L-NHCOPh, i-&H,, OMe

7 L-NHCOMe, Et, OMe

8 L-NHCOPh, Et, OMe

9 L-NHCOMe, WL OMe

10 L-NHCOPh, ‘XL OMe

11 L-NHCOMe, CaH,, OMe

12 L-NHCOMe, CH,Ph, OEt

13 L-NHCOMe, CH,Ph, OMe 14 L-NHCO-furyl, CH,Ph-kOH, OMe

15 L-NH-Ala-COMe(L), CH,Ph, OMe

16 L-NHCOMe, CH,Ph-I-OH, OEt

17 L-NHCOPh, CHzPh, OMe

18 L-NH-Leu-COMe(L), CH,Ph-COH, OMe 19 L-NHCOPh, CH,Ph-I-OH, OEt

20 L-NHCOPh, CH,Ph-lOH, OMe

u See structure II. b The units of k,lK, are mM-'s-l. c From Ref. (16). d From Eq. [‘7].

-0.26 0.15 0.41 1.49 1.50 1

0.14 0.15 0.01 1.49 1.50 1

0.29 0.15 0.14 1.49 1.50 1 0.47 0.36 0.10 1.98 1.50 1

1.06 1.48 0.42 3.46 0.56 0

1.19 1.02 0.17 3.46 1.50 1 1.32 1.44 0.12 1.49 1.03 0

2.36 2.32 0.04 3.46 1.03 0

2.55 2.28 0.27 1.49 1.50 0

3.46 3.16 0.30 3.46 1.50 0

3.48 3.10 0.38 1.49 1.96 0

4.57 4.95 0.38 1.49 3.00 0

5.02 4.96 0.06 1.49 3.00 0

5.08 5.80 0.72 2.67 3.18 0

5.29 5.78 0.49 3.34 3.00 0

5.46 5.27 0.18 1.49 3.18 0 5.94 5.83 0.11 3.46 3.00 0

6.53 6.72 0.19 4.73 3.18 0 6.59 6.15 0.44 3.46 3.18 0

6.70 6.15 0.55 3.46 3.18 0

ALKYL PHOSPHONATE INHIBITION OF CHYMOTRYPSIN 557

this lower activity may be attributable to a conformational change induced in the en- zyme. It has been shown (17) that ligands having either a positive or negative charge, when added to chymotrypsin, produce a sudden drop in activity of the enzyme fol- lowed by slow inactivation.

An interesting aspect of the indicator var- iable for the sulfonium analogs is that, re- gardless of the number of CH, units separat- ing the positive charge from the P-S bond of the leaving group, a single indicator var- iable suffices to correlate log ki. Of course, af correlates the electronic effect of the positive charge on the leaving group. The point of importance is that the positive charge must interact with the enzyme at different points, yet the overall effect is much the same for each congener after cor- rection is made for the a: effect.

Aaviksaar and his co-workers have shown (8) that a subset of the congeners of Table I gives a good bilinear fit when plotted against 7~. The fact that both rr and MR give ex- cellent correlations is to be expected since perfect collinearity in these parameters ex- ists between homologous series. Only on the basis of our earlier studies (1, 2, 18) are we justified in the use of MR rather than rr for the correlation of the phosphonates. As before, we interpret the correlation with MR to mean that hydrophobic partitioning with its attendant desolvation is not the pri- mary force in the interaction of ligands with chymotrypsin. This suggests a polar nature for the residues constituting the binding sites. The role of MR is that of modeling dispersion forces through which binding occurs. MR is also a measure of substituent bulk which may be responsible for causing conformational changes in the enzyme.

In summary we can say that correlation analysis brings out the great similarity in the interaction of chymotrypsin with acyl- amino acid substrates and the phosphonates which are quasi-substrates. The corre- spondence between the two structure-

activity relationships is surprisingly close considering the stereoelectronic differences in the two systems.

ACKNOWLEDGMENTS

This work was supported bg Grant CA 11110 from the National Cancer Institute.

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