Classical and Three-Dimensional QSAR in Agrochemistry - American

Chapter 7

QSARs from Mathematical Models Systemic Behavior of Pesticides D. A. Kleier

Downloaded by MONASH UNIV on October 4, 2013 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/bk-1995-0606.ch007

Stine-Haskell Research Center, DuPont Agricultural Products, P.O. Box 30, Newark, DE 19714

Quantitative structure-activity relationships (QSAR's) are usually established by a statistical analysis of a matrix of property data for a series of compounds. QSAR's can also be established by experimentally validating a mathematical model. Such a first principles model has been developed for phloem systemicity of a compound as a function of its physical properties such as partition coefficients and acid dissociation constants. This model has been validated by both systematic experimental studies, and general observations concerning the phloem systemicity of pesticides. The mathematical model can account for the sensitivity of systemicity to plant parameters and has recently been used to design a phloem systemic pro-nematicide.

Mathematical modeling of an idealized system can provide simple relationships that capture the essence of the more complex, real world system being modeled. We have developed such a relationship for the movement of both ionizable and non-ionizable compounds in the plant vascular system (7). This relationship enables a deeper understanding of the delicate balance of physical properties required for phloem systemicity. Phloem systemic compounds move in that part of the plant vascular system known as the sieve tubes (2). Phloem sap moving through these tubes carries photosynthates, especially sucrose, from mature leaves to sinks in both the roots and in meristematic tissue. Compounds that can enter the phloem and be retained there are transported along with these photosynthates. What is the value of a phloem systemic pesticide? First of all, phloem systemic insecticides and fungicides can control pests far from the site of a foliar application (3). Furthermore, since phloem systemic pesticides would normally be applied foliarly, their performance should not depend upon soil conditions, nor should they require rain for activation. They should also have less chance of leaching into ground water. Such compounds may also provide more flexibility to the farmer. For example, the need for

0097-6156/95/0606-0098$12.00/0 © 1995 American Chemical Society In Classical and Three-Dimensional QSAR in Agrochemistry; Hansch, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.


7. KLEIER

QSAR from Mathematical Models

99

prophylactic soil treatments should be lessened by the availability of a phloem systemic curative material that could be applied to the leaf canopy as needed. Over the past several years a great deal of information has been collected concerning the relationship of chemical structure to phloem mobility (4-10). First of all, the vast majority of compounds known to be phloem mobile are acidic in nature. These materials include benzoic acids, naphthoxyacetic acids, sulfonylureas and maleic hydrazide to name just a few. The phloem mobility of weak acids has been attributed (11) to entrapment of the dissociated acids in the phloem sap which is relatively basic compared to the surrounding tissue. Any QSAR model should take this effect into account. There are a few compounds known to be phloem mobile that are not acidic. These include herbicides such as amitrole and some quaternized nitrogen heterocycles such as N-methylpyridinium halides (8,70). Most, if not all, non-acidic, phloem mobile compounds have logKQ values of zero or below. We set out to develop a quantitative structure-activity relationship that would not only explain the phloem mobility of both acidic and hydrophilic compounds as a function of physical properties, but would also be sensitive to the type and growth stage of the plant to which the compounds had been applied (7). QSAR's are traditionally developed by establishing an empirical relationship between some descriptor of biological activity and multiple descriptors of chemical structure. Empirical QSAR's start with experimental data and use statistical methods such as linear regression to establish the relationship. The resultant relationship should be consistent with fundamental laws. Alternatively, QSAR's can be constructed starting from these fundamental laws. This deterministic or ab initio approach starts with a physical model of a biological system, then uses basic physico-chemical laws to develop a structure-activity relationship. QSAR's developed in this manner should be validated by experiments. Our QSAR for phloem mobility was developed using a mixed or semi-empirical method. We first developed a deterministic model for the plant vascular system, and then used a statistical method to estimate some of the key parameters needed to apply the model in a practical sort of way. In this paper we will first briefly review our simple model for the plant vascular system. We will then describe the QSAR that results from a mathematical development of this model. The relationship relates mobility to a compound's acid dissociation constant as well as to its octanol-water partition coefficients. We will then review the performance of the model for pesticides. Finally, we will describe the application of the QSAR to the design of novel phloem mobile pesticides. W

Description of the Model A cross sectional view of the plant vascular system (72) reveals that the sieve tubes which transport phloem sap in one direction, and the xylem elements that carry the transpiration stream in the opposite direction are in intimate contact in most higher plants. As a result compounds moving in the phloem can be lost to the xylem and carried off in the opposite direction. This limits net transport for compounds that are highly permeable.

In Classical and Three-Dimensional QSAR in Agrochemistry; Hansch, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

100

CLASSICAL AND THREE-DIMENSIONAL QSAR IN AGROCHEMISTRY

Our simple model of the plant vascular system captures the essence of these transport and permeation processes. Following Tyree, et al. (7) the model consists of two coaxial pipes as shown in Figure 1. The inner pipe of radius r represents the sieve

B. Velocity Profile

A. Plant Dimensions I


0.5 L

Leaf

I

Distance S from Leaf Tip

Petiole &Stem

0.5 L

0.5 L

Root

Sieve Tube, Radius, r

Velocity

Figure 1. Simple model of plant vascular system (Reprinted with permission from Reference 13.) tubes which carry phloem sap from the top of the model plant to the bottom. The outside pipe representing the apoplast carries xylem sap in the opposite direction. The pipes are separated by a permeable membrane. It is assumed that compound is applied to an annulus located at the top of the model plant. This annulus represents the apoplast of the leaf. The model provides for permeation of the compound from this annulus into the sieve tube which it surrounds. Once entrained, the model then provides for movement by mass flow of the phloem sap towards the bottom of the model plant. The model also provides for loss in transit via permeation back into the surrounding apoplast where the xenobiotic can be swept back to the leaf with the transpiration stream. The very important acid trapping effect is accounted for by a) assigning a higher pH to the phloem sap than to the surrounding apoplast, b) providing for correspondingly higher degrees of acid dissociation within the phloem consistent with the pH differential and c) assigning reduced permeabilities to charged conjugate bases resulting from acid dissociation (7). For most of the simulations performed we have taken the pH of the phloem to be 8 and that of the surrounding apoplast to be 6.


7. KLEIER

101

QSARfromMathematical Models

The total length L of the plant is divided into three parts: leaf, petiole & stem, and root. The root length is taken as half that of the plant (L / 2). The upper half of the plant is divided into a leaf of length /, and a petiole and stem of length (L / 2) - J. What distinguishes these three parts of our model plant is the phloem sap velocity profile within them. The velocity at the leaf tip is taken as zero, and is assumed to rise linearly to a velocity v at the base of the leaf. Within the petiole and stem the phloem sap velocity is assumed to remain at a constant value of v . In the root we assume a linear decrease in velocity back to a value of zero at the root tip. We use the concentration factor, Cf as the dependent variable of this model. It is defined as the stoichiometric concentration of xenobiotic in the phloem at a distance S from the leaf tip at time t relative to that in the leaf apoplast. 0

0


y

Cf(S,t) = {[HA] + [A-] } / {[HA] + [A"] } S

s

0

(Equation 1)

0

Here [HA] and [A"] are respectively the concentrations of the undissociated acid H A and conjugate base A" within the phloem sap at a distance s from the leaf tip. [HA]o and [A"] are the corresponding concentrations at the point of application within the leaf apoplast. Since the leaf apoplast is considered to be a reservoir of xenobiotic, [ H A ] and [A~] are assumed independent of time. Large values of Cf at large distances s from the leaf tip indicate high phloem mobility. The differential equations describing the movement of xenobiotic for this model are essentially statements of the conservation of mass of the xenobiotic. These equations account for both the downward mass flow along the axis of the sieve tube, as well as radial permeation of xenobiotic through the cylindrical surface of the sieve tube. An analytical solution to the differential equations describing the movement of xenobiotic is possible for this model and has been described elsewhere (1,13). The solution expresses the dependence of the concentration factor Cf upon both distance s and time t, and parametrically upon properties of both the plant and xenobiotic. According to this model a steady state is established throughout the length of the plant within a short time, usually within a few multiples of L / v (13). We have thus chosen to use the steady state concentration factor evaluated at a point deep within the root (S = 0.9L) as a measure of a compound's phloem mobility. In the steady state limit (t = oo) the concentration factor evaluated at this point is given by S

s

0

0

0

0

C (0.9L,oo) = {([H+] f

x {5([H+]

i+

oPHA

K ) / ( [ H + ] + K )} a

0

a

+ KaP -)} / {[H+]i(b + A

xexp{-c([H+]iPHA+ KaP -)/([H+] A

i +

P h a

) + K (b + p -)} a

A

K )} a

(Equation 2) where b = r v / 2/, and c = (2.609L - 21) I r v . The plant parameters appearing in Equation 2 include the hydrogen ion concentrations within both the phloem sap and the apoplast, [H ]j and [ H ] , respectively, as well as the length and velocity parameters illustrated in Figure 1. The xenobiotic parameters include the acid dissociation 0

+

0

+

0


102


constant, K , as well as the permeability PHA of the xenobiotic and that of its conjugate base PA". The permeabilities are essentially rate constants for diffusion across the sieve tube membranes, and are very seldom reported in the literature. In order to make practical applications, we assume a log linear relationship between the permeability of a species and its octanol-water partition coefficient. a


log pi = a log Kow,i + b

(Equation 3 )

The decreased permeability of a negatively charged conjugate base, A", relative to its undissociated parent acid, H A , is taken into account by using a log Kow,A~ value in Equation 3 which is 3.7 log units less than log K Q W , H A (^5). The slope and intercept of this relationship are also plant parameters and could be related to membrane thickness and viscocity in a completely deterministic model (14). We have taken a more empirical approach at this point. The parameters in equation 3 have either been determined by linear regression of permeability data or simply assigned to account for the systemic properties of a set of xenobiotics. For example, the parameters for the socalled Nitella membranes (a = 1.20, b = -5.86) have been determined by linear regression using permeabilities measured (16) for a series of organic molecules through the cell membrane of the large single celled organism known by this name. The socalled Grayson parameters (a = 1.20, b = -7.5) have been assigned in order to provide a good account of the phloem mobility of a series of xenobiotics including a large number of pesticides (14). Predictions of the Model: Dependence of the Concentration Factor, Cf, upon K and

a

In Figure 2 we display the dependence of the concentration factor evaluated using Equation 2 upon K Q W , H A and Ka for a standard 15 cm. plant with Nitella membranes. Large values of log Cf correspond to high predicted mobility. Lipophilic, non-acidic compounds appear in the upper right hand corner of this contour surface. LogCf values in this region are generally much less than -4. Thus, a herbicide like diuron with a L o g K Q = 2.8 and a p K > 12 is not predicted to move well in the phloem. As we move along the top edge of the plot from diuron towards less lipophilic, but still nonacidic compounds, phloem mobility is predicted to increase until an optimum is reached at logKow ~ -2.0. This is where marginally phloem mobile, non-dissociable compounds such as oxamyl and N-alkyl pyridiniums reside. The highest mobility is predicted for compounds that reside on the elevated diagonally running ridge near the center of the plot. On this ridge reside weak acids with pKa values near 5 and logKow values near zero. Compounds that reside here have logCf > 0, and hence are predicted to actually concentrate in the phloem at long distances from the point of application. This is the region where compounds known for their phloem mobility such as the sulfonylurea, metsulruron-methyl, reside. It should be noted, however, that the model does not predict phloem mobility for all acids. Very lipophilic acids such as acifluorfen are not predicted by this model to be phloem mobile. While the general shape of this plot does not change with plant parameters, the position, breadth and height of the ridge are quite sensitive to parameters such as pH differential, membrane parameters, and plant dimensions. W

a



7. KLEIER

103

QSARfromMathematical Models

Figure 2. Contour plot for log Cf as a function of l o g K and p K . Plant parameters are L = 15 cm, / = 5 cm, r = 5 mm, v = 1.8 cm/min. The membrane parameters (Equation 3) are a = 1.20 and b = -5.86. The pH of the phloem sap was taken as 8.0 and that of the surrounding apoplast as 6.0. P U A A = phenylureidoacetic acid, N-but-Pyr = N-butylpyridinium bromide, JR522 is illustrated in Figure 3 (vide infra). o w H A

a

0

Tasteful Rules for Rendering Xenobiotics Phloem Systemic How can the properties of a lipophilic compound such as diuron be altered in order to make it phloem mobile? Either the compound's l o g K o or p K or both can be lowered in order to move it into the loftier regions of the concentration factor contour diagram (Figure 2). Molecular modifications of diuron such as sugar conjugation (colloquially termed "sweetening") should lower the l o g K and according to the model improve phloem mobility. Quaternization, or "salting", is another modification that significantly lowers the l o g K o of compounds possessing basic nitrogens, and, as suggested by studies on pyridiniums (8, 10), should improve phloem mobility. Diuron, which does not possess a nitrogen basic enough to be quaternized, cannot be "salted", but it can be "soured" by acid functionalization. For example, the addition of a carboxylic group is predicted to be a very effective modification for increasing the phloem mobility of phenylurea herbicides as shown in the Table I. While neither diuron nor defenuron is predicted to move well in the phloem, both acid derivatives, P U A A and C P M U , are predicted to have concentration factors greater than 1.0, and hence both compounds are expected to be highly phloem mobile in a plant with parameters similar to the one simulated. Cf values greater than 1.0 can be attributed to the acid trapping effect. The predictions of the table are consistent with studies performed on both one-leaf bean (phaseolus vulgaris) and mustard plants (sinapis alba) plants by Neumann, et al. (17). The expected high phloem mobility of P U A A is also indicated by its location on the elevated ridge in Figure 2. Unfortunately, the acid derivatives of defenuron are devoid of herbicidal activity. In fact, it is anticipated that loss of useful intrinsic biological activity will be a rather general problem for pesticides that have been modified to improve phloem systemicity. The physical properties required for pesticidal activity are often incompatible with those required for phloem systemicity. One possible solution to this W

a

o w

W


104


Table I. Physical Properties and Theoretical Concentration Factors for Phenylureas Structure

Name

logK^

pK

a

Cf

CI


Cl

^

^

/

ϊ

^

^

^

ο ^11^ y Ν Ν

Diuron

2.8

>12

0.00

Defenuron

1.1

>12

0.00

4.76

36.1

4.2

32.4

ο î ^ N ^ ^ f " ο

Phenylureido 0.77 Acetic Acid (PUAA)

4-Carboxyphenyl, methylurea (CPMU)

1.10

a

Plant parameters for these simulations are identical to those described in the caption to Figure 2.

quandary is the use of phloem mobile pro-pesticides. For example, if a substituent (e.g., acid group, sugar) that facilitates movement in the phloem could be removed near the site of action, effective control might be realized. Realization of this stragegy might necessitate modifying not only the crop protection chemical but also the crop to be protected. The modification of the chemical would be designed to enhance phloem systemicity; that of the plant to ensure activation at the site where protection is needed. The Pro-pesticide Approach to the Design of Phloem Systemic Nematicides A highly phloem mobile nematicide would be a very useful crop protection chemical. Such a compound could be sprayed on the leaves of a plant and still control nematodes that feed on the roots. This was the motivation behind the design and synthesis (18) of the following derivative of oxamyl: In Classical and Three-Dimensional QSAR in Agrochemistry; Hansch, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

7. KLEIER

105

QSAR from Mathematical Models

Oxamyl


Figure 3. Structure of JR522. The right hand side of this structure is oxamyl itself, a known effective nematistat. The substituent on the left is a glucuronylmethyl group which is predicted to improve the mobility of oxamyl by lowering both its p K and logKow- This mobilophore consists of both a sugar and an acid functionality and hence might be termed "sweet and sour". Figure 2 illustrates the location of both oxamyl and the glucruonide (designated as JR522) on the concentration factor surface for a short plant with Nitella membranes. For this simulated plant oxamyl falls in a region that is not predicted to be particularly well suited for phloem translocation (logCf < -4). On the other hand the glucuronide with lowered p K and logKow is predicted to lie on a contour with a logCf value of between -3 and -4. Our experience has been that compounds with predicted logCf values in this region usually exhibit phloem systemicity. Furthermore, since the glucuronide resides on a less steep portion of the Cf surface than does oxamyl, its predicted mobility will be less sensitive to changes in plant parameters. Experiments with transgenic tobacco plants that have been engineered to hydrolyze the glucuronide in a root specific manner (18,19) are consistent with the expectation that JR522 will be phloem mobile. At a foliar application rate of 1 gm/1 the glucruonide provides significantly greater control than oxamyl itself when applied at over 10 gm/1. We believe this to be due to the enhanced phloem mobility of the glucuronide coupled with root specific generation of the active substance near the target pest. a

a

Summary A simple model of the plant vascular system has been developed which enables the prediction of the phloem mobility of xenobiotics as a function of their physical properties in a variety of plant types. The predictions of this model are consistent with the vast majority of reports on this subject. The model can be used to design phloem systemic xenobiotics including phloem systemic pro-pesticides. Acknowledgments The author is grateful to Dr. Francis Hsu for introducing the author to this area of research, for his efforts to validate the mathematical model, and for his promotion of modeling as a tool for the design and discovery of new pesticides. The author is grateful to Dr. King Mo Sun for his artful synthesis of the glucuronide of hydroxymethyloxamyl. I would also like to thank Dr. Tariq Andrea for useful


106


discussions on the mathematical development of the simple model of the plant vascular system. Finally, I would like to thank former colleagues, James R. Sanborn and B. Terence Grayson, as well as my managers, John B. Carr, Russ F. Bellina and James V . Hay for their encouragement to pursue this area of research. References


1. 2.

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18. 19.

Kleier, D. A. Plant Physiol. 1988, 86, 803-810. Grimm, E. and Neumann, S. In Modern Selective Fungicides-Properties, Applications and Mechanisms of Action; Lyr, H., Ed.; Longman Scientific & Technical: Essex, England, 1987; pp 13-29. Edgington, L. V., Ann. Rev. Phytopathol. 1981, 19, 107-24. Bromilow, R.; Rigitano, R. L. O.; Briggs, G. G.; Chamberlain, K. Pestic. Sci. 1987, 19, 85-99. Rigitano, R. L. O.; Bromilow, R. H.; Briggs, G. G.; Chamberlain, K. Pestic. Sci. 1987, 19, 113-133. Chamberlain, K.; Butcher, D. N.; White, J. C. Pestic. Sci. 1986, 17, 48-52. Tyree, M.; Peterson, C. Α.; Edgington, L. Plant Physiol. 1979, 63, 367-374. Hsu, F.; Kleier, D. A. Plant Physiol. 1986, 86, 811-816. Lichtner, F. In Phloem Transport; Cronshaw, J.; Lucas, W. J.; Giaquinta, R. J. Eds.; Alan R. Liss, New York, 1986, pp 601-608. Price, C. E.; Boatman, S. G.; Boddy, B. J. J. Exp. Botany,1975, 26, 521-532. Crisp, C. Pestic. Chem., 1972,1,211-264. Kuhn, W. Angewandte Chem, Int. Ed., Eng. 1990, 29, 1-19. Kleier, D. A. Pestic. Sci. 1994, 42, 1-11. Grayson, B. T.; Kleier, D. A. Pestic. Sci. 1990, 30, 67-79. Scherrer, R. A. In Pesticide Synthesis through Rational Approaches, Magee, P. S.; Kohn, G. K.; Menn, J. J. Eds.; ACS Symposium Series, American Chemical Society, Washington, D. C. 1984, No. 255, 225-246. Collander, R., Physiol. Planta 1954, 7, 420-445. Neumann, S.; Grimm, E.; Jacob, F. Biochem. Physiol. Pflanzen, 1985, 180, 257-268. Hsu, F.; Sun, Κ. M.; Kleier, D. Α.; Fielding, M., Pestic. Sci., 1995, in press. Yamamoto, Y. T.; Taylor, C. G.; Acedo, G. N.; Cheng, C. L.; Conkling, M. A. Plant Cell, 1991, 3, 371-382.

RECEIVED

April 26, 1995


Classical and Three-Dimensional QSAR in Agrochemistry - American

Recommend Documents