1

Chemical concentration, activity,

fugacity, and toxicity:

dynamic implications

Jon Arnot and Don Mackay

Trent University

McKim Conference

Duluth, MN

September, 2007

Overview

• Building on Part I by Don Mackay

– Four chemicals, log KOW = 2, 4, 6, 8

– Two organisms, fish and mammal

• Objectives

– Reference point for acute “baseline” toxicity (narcosis)

– Data quality

• Assumptions vs reality

– Dynamic profiles and “complicating” factors

(biotransformation rates, absorption efficiency)

• Internal vs external concentrations and activities

2

• Lethality is “well defined”

• Toxic Ratio (TR) or “excess toxicity” =

CBRX (mmol.kg-1) / CBRN (mmol.kg-1)

• If CBRN = 3 mmol.kg-1 and TR > ~10 then

chemical “x” has greater “potency”

Reference point for hazard identification

Equilibrium partitioning (EqP)

Complete bioavailability

No biotransformation or growth dilution

EqP = activity in exposure medium = activity in organism

log BCF = 1.0 log KOW - 0.9

0

2

4

6

8

10

0 2 4 6 8 10

log KOW

log

BC

F

log (1/LC50) = 1.0 log KOW - 1.4

log activity = 0.06 log KOW - 1.6

-2

0

2

4

6

8

0 2 4 6 8 10

log KOW

log

(1/L

C50

mol.

m-3

)

-2

-1.5

-1

-0.5

0

log

act

ivit

y

3

• Illustrations using a kinetic mass balance model

1. Fish

2. Mammal

• Exposure concentrations based on EqP assumptions to

exert a toxic effect at 3 mmol.kg-1 or 3 mol.m-3 whole

body concentration, i.e., narcosis

• Four chemicals, each with three different metabolic

biotransformation rates (0, 0.1, 1.0 d-1)

Series of toxicity “experiments”

70% water20% NLOM

10% lipid

Dietary intake; kD

Respiratory exchange; k1 and k2

Fecal egestion; kE

Metabolic biotransformation; kM

Growth dilution; kG

Two organisms – same properties and

processes (air vs water)

NLOM equivalent to

3.5% lipid

(both 100 g)

4

Model

kD

k1

k2

kM

kG

kE

CB = ((k1 • CWD ) + (kD • CD)) / (k2 + kE + kM + kG)

kT

Time

Co

ncentr

atio

n

Time

Co

ncentr

atio

n steady state

A B C D

Log Kow 2 4 6 8

Concn in fish mol/m3 or mmol/kg 3 3 3 3

BCF (fish/water) 1.14E+01 1.07E+03 1.07E+05 1.07E+07

Concn in water mol/m3 2.63E-01 2.80E-03 2.80E-05 2.80E-07

Concn in water g/m3 2.63E+01 4.20E-01 5.61E-03 7.01E-05

Activity in water and fish 0.033 0.042 0.056 0.070

Equilibrium partitioning: fish

Chemical

5

0

1

2

3

4

0 0.25 0.5 0.75 1

time (d)

Cfi

sh (

mo

l.m

-3)

k M = 0 d-1

; t99 = 8.4 h

k M = 0.1 d-1

; t99 = 8.3

h

k M = 1.0 d-1

; t99 = 7.8 h

Chemical A

Cwater = 0.263 mol.m-3

activity in fish ≈ activity in water ≈ 0.03

No big difference!

short

0

1

2

3

4

0 10 20 30 40time (d)

Cfi

sh (

mo

l.m

-3)

k M = 0 d-1

; t99 = 18.7 d; amax = 0.04

k M = 0.1 d-1

; t99 = 13.3 d; amax = 0.028

k M = 1 d-1

; t99 = 3.7 d; amax = 0.008

Chemical B

Cwater = 0.0028 mol.m-3

awater = 0.04

substantial differences in activity and tsteady state

6

0

1

2

3

4

0 10 20 30 40time (d)

Cfi

sh (

mo

l.m

-3)

k M = 0 d-1

; t99 = 18.7 d; amax = 0.04

k M = 0.1 d-1

; t99 = 13.3 d; amax = 0.028

k M = 1 d-1

; t99 = 3.7 d; amax = 0.008

Chemical B

Cwater = 0.0028 mol.m-3

awater = 0.04

substantial differences in activity and tsteady state

Need to increase Cwater !!

activity in fish ≠ activity in water!!

Factor of 5; awater ~ 0.2

Chemical CCwater = 0.028 mmol.m-3

awater = 0.056

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80time (d)

Cfi

sh (

mol.

m-3

)

k M = 0 d-1

; t99 = 294 d; amax = 0.008

k M = 0.1 d-1

; t99 = 40 d; amax = 0.001

k M = 1.0 d-1

; t99 = 4.5 d;

amax = 10-4

big differences in activity and tsteady state

7

Chemical CCwater = 0.028 mmol.m-3

awater = 0.056

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80time (d)

Cfi

sh (

mol.

m-3

)

k M = 0 d-1

; t99 = 294 d; amax = 0.008

k M = 0.1 d-1

; t99 = 40 d; amax = 0.001

k M = 1.0 d-1

; t99 = 4.5 d;

amax = 10-4

big differences in activity and tsteady state

Need to increase Cwater !!

BUT, exceed water

solubility limits

i.e., awater > 1 X

Chemical DCS

S = Cwater = 0.074 µmol.m-3

awater = 0.07

0.0

0.1

0.2

0.3

0.4

0 20 40 60 80time (d)

Cfi

sh (

mm

ol.

m-3

)

k M = 0 d-1

; t99 = 321 d; amax = 10-4

k M = 0.1 d-1

; t99 = 40 d; amax = 10-5

k M = 1.0 d-1

; t99 = 4.5 d;

amax ~ 10-6

huge differences in activity and tsteady state

8

Chemical DCS

S = Cwater = 0.074 µmol.m-3

awater = 0.07

0.0

0.1

0.2

0.3

0.4

0 20 40 60 80time (d)

Cfi

sh (

mm

ol.

m-3

)

k M = 0 d-1

; t99 = 321 d; amax = 10-4

k M = 0.1 d-1

; t99 = 40 d; amax = 10-5

k M = 1.0 d-1

; t99 = 4.5 d;

amax ~ 10-6

No chance!

huge differences in activity and tsteady state

A B C D

Log Kow 2 4 6 8

Concn in mammal mol/m3 or mmol/kg 3 3 3 3

BCF (mammal/air) 1.26E+03 1.77E+05 2.65E+07 3.53E+09

Concn in air mol/m3 2.39E-03 1.70E-05 1.13E-07 8.49E-10

Concn in air g/m3 2.39E-01 2.54E-03 2.26E-05 2.12E-07

Activity in air and mammal 0.033 0.042 0.056 0.070

Chemical

Equilibrium partitioning: mammal

9

0

1

2

3

4

0 5 10 15 20time (d)

Cm

amm

al (

mol.

m-3

)

k M = 0 d-1

; t99 = 9.5 d; amax = 0.03

k M = 0.1 d-1

; t99 = 7.9 d; amax = 0.03

k M = 1.0 d-1

; t99 = 3 d

amax = 0.01

Chemical A

Cair = 0.0024 mol.m-3 aair = 0.03

Lower concentrations in air compared to water

“minor”

differences

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80time (d)

Cm

amm

al (

mo

l.m

-3) k M = 0 d

-1; t99 = 331 d; amax = 0.01

k M = 0.1 d-1

; t99 = 40 d; amax = 10-3

k M = 1.0 d-1

; t99 = 4.5 d;

amax = 10-4

Chemical B

Cair = 0.017 mmol.m-3

aair = 0.04

10

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80time (d)

Cm

amm

al (

mo

l.m

-3) k M = 0 d

-1; t99 = 331 d; amax = 0.01

k M = 0.1 d-1

; t99 = 40 d; amax = 10-3

k M = 1.0 d-1

; t99 = 4.5 d;

amax = 10-4

Chemical B

Cair = 0.017 mmol.m-3

aair = 0.04

Maximum activity in mammal ≠ activity in air!!

Need to increase Cair !!

BUT, exceed air

solubility limits, i.e.,

vapor pressure

Chemical C

Cair = 0.11 µmol.m-3

aair = 0.056

0.0

0.5

1.0

1.5

2.0

0 20 40 60 80time (d)

Cm

amm

al (

mm

ol.

m-3

)

k M = 0 d-1

; t99 = 436 d; amax = 10-4

k M = 0.1 d-1

; t99 = 41.7 d; amax = 10-5

k M = 1.0 d-1

; t99 = 4.6 d;

amax = 10-6

“same story”

~ 560x

~ 5,600x

~ 56,000x

11

Chemical D

PSS = Cair = 0.22 nmol.m-3

aair = 0.07

0

1

2

3

4

0 20 40 60 80time (d)

Cm

amm

al (

um

ol.

m-3

) k M = 0 d-1

; t99 = 442 d; amax = 10-6

k M = 0.1 d-1

; t99 = 42 d; amax = 10-7

k M = 1.0 d-1

; t99 = 4.6 d;

amax = 10-8

“same story”

A view to a kill (96 h LD50)

kM

Organism Parameter Units 0 d-1 0.1 d-1 1 d-1

Fish CD (mg/kg) 165,000 200,000 580,000

Fish t99 (d) 294 40 4.5

Mammal CD (mg/kg) 102,000 124,000 360,000

Mammal t99 (d) 436 42 4.6

Chemical C; fed 2x/d

Inhalation exposure is assumed “irrelevant”

not at steady state or equilibrium!

BMFs are larger in the mammal

12

A view to a kill (96 h lethal dose)

Chemical C; but 0.5 * ED

Have to double the dose!

kM

Organism Parameter Units 0 d-1 0.1 d-1 1 d-1

Fish CD (mg/kg) 330,000 400,000 X

Fish t99 (d) 294 40 4.5

Mammal CD (mg/kg) 204,000 248,000 720,000

Mammal t99 (d) 436 42 4.6

• Uptake times can be long and can exceed standard test

durations, combined exposure routes may be necessary

• Exposure concentrations and activities “rarely”

approximate internal concentrations and activities

• Metabolites that may be toxic will further complicate

interpretation of toxicity measurements

• Need to measure both internal and external

concentrations to identify “more potent” chemical

• Need for a quality toxicity dataset

• Uncertain data result in uncertain models

Summary

13

Careful inspection of the toxicity data can

support Ferguson’s proposal that activity

be used to interpret toxicity data such that

“the disturbing effect of phase distribution

is eliminated from the comparison of

toxicities”

Ferguson 1939

Thank you!