Evolutionary dynamics of metabolic

resistance against ALS herbicides

Otto Richter1, Dirk Langemann2 and Roland Beffa3

1 Technische Universität Braunschweig, Institut für Geoökologie 2Technische Universität Braunschweig, Institut Computational Mathematics 3 BAYERCrop Science, Frankfurt am Main

Contents

•Mechanism of metabolic resistance against ALS inhibitors

•Polygenic inheritance model

•Gene expression

•Approach of Renton

•Derivation from metabolic model

•Time discrete model for weed development

•Assessment of management strategies

•Low dose or high dose?

Metabolic pathways

2 y1 y2 Valiney3

z1 z2

Leucine

ALS

x1 x2x3 x4 Isoleucine

Inhibitor

I2 I3 I4

P450 GST ABC

Breakdown products

Threonine

y4

z3

Pyruvate

I1

x5

y5

z4

2 y1 y2 Valiney3

z1 z2

Leucine

ALS

x1 x2x3 x4 Isoleucine

Inhibitor

I2 I3 I4

P450 GST ABC

Breakdown products

Threonine

y4

z3

Pyruvate

I1

x5

y5

z4

Note that phase I products may still act as inhibitor to ALS

(Werck-Reichardt et al. 2000).

Kinetic model

inputKI

IV

dt

dI

P

P

1

14501

G

GST

P

P

KI

IV

KI

IV

dt

dI

2

214502

ABC

ABS

G

GST

KI

IV

KI

IV

dt

dI

3

3

2

23

),,(2 511 yIyv

dt

dyALS

Oxidation of herbicide by cytochrome P450 monooxygenase (1.term).

Gluthatione conjugation of oxidized herbicide

Vacuolar transport of oxidized and conjugated herbicide

2 PYR 2-acetolactate

Key reaction of branched amino acids synthesis

ALS Kinetics

22

22

22

max

)1()1(

)1()1(

,,,)1()1(

)1(),,(

IV

IVss

ALS

ccLL

K

I

K

V

K

S

cL

VIVSv

Pyr Val ALS inhibitor

P450 activity low

(poor metabolizer)

0 50 100 1500

0.2

0.4ALS activity

µM

ol/m

in/m

g

0 50 100 1500

50Inhibitor

0 50 100 1500

2

4intermediates

Concentr

ation

0 50 100 1500

50Ox. inhibitor

0 50 100 1500

20

40cumulated valine

Concentr

ation

Time [min]

0 50 100 1500

50conj. inhibitor

Time [min]

P450 activity high

GST activity low

0 50 100 1500

0.2

0.4ALS activity

µM

ol/m

in/m

g

0 50 100 1500

50Inhibitor

0 50 100 1500

2

4intermediates

Concentr

ation

0 50 100 1500

50Ox. inhibitor

0 50 100 1500

20

40cumulated valine

Concentr

ation

Time [min]

0 50 100 1500

50conj. inhibitor

Time [min]

0 50 100 1500

0.2

0.4ALS activity

µM

ol/m

in/m

g

0 50 100 1500

50Inhibitor

0 50 100 1500

2

4intermediates

Concentr

ation

0 50 100 1500

50Ox. inhibitor

0 50 100 1500

20

40cumulated valine

Concentr

ation

Time [min]

0 50 100 1500

50conj. inhibitor

Time [min]

P450 and GST activity high

(rapid metabolizer)

Simulated dose response curves

10-2

10-1

100

101

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Herbicide concentration

Cum

ula

ted v

alin

e

10-2

10-1

100

101

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Herbicide concentration

Cum

ula

ted v

alin

eGST Aktivität

P450 Aktivität

Logistic dose-response

function

10 4 0.001 0.01 0.1 1 100.0

0.2

0.4

0.6

0.8

1.0

Inhibitor concentration

Vali

ne

Vali

nem

ax

)]log()(log(exp[1

1)(

edbdS

Polygenic inheritance model

Number of loci: ng

Number of biotypes: m=3ng

……………………………………

Biotype 1

Biotype 2

Biotype g

Genetic submodel

Evolutionary dynamics

t

mRRR ),,( 1

m

i itotal RR1

total

i

t

iR

RWRRg )(

iAi SpK

m

i iKK1

K

K

LK

KDJ i

i

max

)(hSuJR iii

)(expmax RgTh

RAS i

a

totalHi

wHtsAFttF pSppSS ))1(()1(

Seedlings

Young plants

Adult plants

Heredity function

Number of seeds

Index „i“ refers to biotype

Number of seeds

spring next year

Survival probability as a function of

application rate h

Heredity transmission matrix

Genetics: evaluation of

heredity transmission matrices

t

Xv )02/11(

t

xv )12/10(

t

XX vvV 1

t

Xx

t

xX vvvvV 2

t

xx vvV 3

imiii VVVW 21

000

04/12/1

02/11

1V

02/11

2/12/12/1

12/10

2V

12/10

2/14/10

000

3V

General case

Langemann, Richter and Vollrath 2012

Heredity transmission matrix

of biotype1, ng=3, m=27

Heredity transmission matrix of biotype 42

ng=4, m=81

Gene expression:

general approach of Renton

],,,[ 321 ngxxxxgt genotype

]2,1,0[ix

0: no resistant gene at locus i

1: one resistant gene at locus i

2: two resistant genes at locus i

epis

ng

xgrxxxxfr

ng

i i

ng

2

1max321

)(]),,,([

21

1

00

)(

i

i

i

i

xif

xifdom

xif

xg

with ]1,0[dom

resistance factor

Renton et al. 2011

epistasis factor

Derivation from metabolic

model

33

22

11

yx

yx

yx

gt

],[, hlyx ii

P450: low/ high metabolizer

GST: low/ high metabolizer

ABC: low/ high transport capacity

Assignment of resistance factor to genotypes

hh

hh

hh

gtmaxrr

ll

ll

ll

gtminrr

ll

ll

hh

gt max3.0 rr

)]()((exp[1

1),(

sEDrLogdLogbrdS

Dose dependent dynamics

of biotypes

0 10 20 30 40 500

20

40

60

80

100

120

Time

Wee

dde

nsit

y

0 10 20 30 40 500

20

40

60

80

100

120

Time

Wee

dde

nsit

y

0 10 20 30 40 500

20

40

60

80

100

120

Time

Wee

dde

nsit

y

0 10 20 30 40 500

20

40

60

80

100

120

Time

Wee

dde

nsit

y

4500 5500

6500 8000

Biotype 1

Biotype 27

Biotype 26

Threshold

Evolution of population

dose-response curves

D=1000

Evolution of biotypes

D=1000

Evolution of biotypes

D=4000

Evolution of biotypes

D=8000

Thank you for your attention!

Low dose vs high dose

8 9 10 11 12 13 14 150

100

200

300

400

500

600

Time

Wee

dde

nsit

y

8 9 10 11 12 13 14 150

100000

200000

300000

400000

500000

600000

700000

Time

See

dde

nsit

y

S1={ Dmax, Dmax, Dmax,Dmax,…}

S2={0.2 Dmax, 0.5 Dmax, Dmax,…}

S1

S2

S1 S2