Modeling environmental impacts of engineered
nanomaterials : the value of “generic models”
of individual organisms
Roger M. Nisbet
University of California, Santa Barbara
Work with: Tin Klanjscek, Shannon Hanna, Trish Holden, Ben Martin, Ed
McCauley, Bob Miller, Erik Muller, John Priester, Louise Stevenson, and many
others
Funding: US Environmental Protection Agency and National Science
Foundation (through UC CEIN).
The need for theory in ecotoxicology
• Contaminants impact individual organisms, populations,
communities and ecosystems.
• Contaminants are one component of environmental stress, that typically
acts simultaneously with others (e.g. temperature, pH, food
availability……….)
• Gereral theory is required because testing cannot match rate of
introduction of new chemicals:
- 75,000+ chemicals registered for commercial use in US
- less than 1000 have undergone complete toxicity testing
- overwhelming costs of tests ($2-$4 million for in vivo studies)
The need for theory in ecotoxicology
• Contaminants impact individual organisms, populations,
communities and ecosystems.
• Contaminants are one component of environmental stress, that typically
acts simultaneously with others (e.g. temperature, pH, food
availability……….)
• Biology-based theory is required because testing cannot match rate of
introduction of new chemicals:
- 75,000+ chemicals registered for commercial use in US
- less than 1000 have undergone complete toxicity testing
- overwhelming costs of tests ($2-$4 million for in vivo studies)
• Dynamics of budgets of energy and elemental matter should be a
component of this theory.
• Kooijman’s DEB theory offers a powerful framework for this.
Nanotechnology has made the challenge tougher
Definition
Engineered nanomaterial (ENM) consists of intentionally produced
particles with a characteristic dimension between 1 and 100nm and
possessing properties that are not shared by non-nanoscale particles
with the same chemical composition”
Examples
- metal oxides – TiO2 and ZnO, (sunscreeen); Ag (antibacterial)
- Quantum Dots (electronics)
Properties
- Size and shape dependent due to: large surface/volume
- Often manufactured with coatings
Ecological/environmental impact?
- May impact biogeochemical fluxes (nutrient cycling)
- Toxicity (e.g designed for antibacterial/antifungal properties)
Information on potential ENM hazard
few/year
100’s/year
1000’s/year 10,000’s/day 100,000’s/day
High Throughput Bacterial,
Cellular, Yeast, Embryo or
Molecular Screening
Expensive in vivo testing and
ecological experiments
Challenge for theorists: to use information from molecular and cellular studies
to prioritize, guide design, and interpret ecological studies
Dynamic Energy Budget (DEB) Models
Organism
Resources
Growth
Development
Reproduction
Survival
Metabolic
Products
DEB model equations describe the kinetics of the “reactor” that converts
resources into “products”
Kooijman’s “standard” DEB model
Food
Feces
X
JEA
Reserve
ME
Mobilization
somatic
maintenance
growth
MV
k
JEC
1-k
Maturity
Maintenance
Maturity or
Reproduction
MH
MER
Kooijman’s “standard” DEB model*
i-state variables
 Reserve biomass at time t
 Structural biomass at time t
 “Cumulative reproduction”, i.e. total carbon allocation to
reproduction buffer by time t
 Total allocation to “maturity” by time t .
 Hazard rate at time t, i.e. instantaneous “risk” of mortality
 Aging acceleration at time t – related to level of damage
inducing compounds
Parameters
Total of ~12 parameters. Of these some are expected to be
broadly invariant across taxa and others scale in predictable way
with size. This opens the way to generality. For many
applications, fewer state variables and parameters suffice.
S.A.L.M. Kooijman (2010) Dynamic Energy Budget models for metabolic organization.
Cambridge University Press.
T. Sousa et al (2010)., Philosophical Transactions of the Royal Society B, 365:3413-3428.
Kooijman’s “standard” DEB model equations
d
dt
d
dt
d
dt
d
dt
M E  J EA  J EC
M V  J VG  (k J EC  J EM ) yVE
M H  (1  k ) J E C  J E J
M ER  0
w ith
if M H  M H
p
if M H  M H
p
, else
dt
J E A  c (T ) f { J E A m } L
J E C  c (T ){ J E A m } L
d
2
2
, else
d
dt
MH 0
M E R  (1  k ) J E C  J E J
if M H  M H
b
else J E A  0
ge 
L 
1



ge
gL m 
J E M  c (T )[ J E M ] L
3
J E J  c (T ) k J M
H
PLUS ODEs for aging acceleration and hazard rates
Kooijman’s “standard” DEB model equations
d
dt
d
dt
M E  J EA  J EC
M V  J VG  (k J EC  J EM ) yVE
COLLECTION
OF MESSY
ODEs
d
dt
d
dt
M H  (1  k ) J E C  J E J
M ER  0
w ith
if M H  M H
p
if M H  M H
p
, else
dt
J E A  c (T ) f { J E A m } L
J E C  c (T ){ J E A m } L
J E M  c (T )[ J E M ] L
2
3
J E J  c (T ) k J M
H
d
2
, else
d
dt
MH 0
M E R  (1  k ) J E C  J E J
if M H  M H
b
ge 
L 
1



ge
gL m 
else J E A  0
Dynamics of structured populations
•
•
•
Environment: E-state variables - experienced by all organisms
- Resources
- Toxicants
- Metabolic products
Individual Organism: i-state variables
- DEB state variables – ODEs in previous slides
Population dynamics: p-state variables – Book-keeping
- population size, age structure, distribution of i-state variables
- many mathematical representations possible (IBMs, PDEs, IDEs etc.)
- special assumption (ontogenetic symmetry) yields ODEs
Population modeling involves assumptions on interactions of individuals
and their environment
Messages from some UC CEIN Projects
1) Phytoplankton I. Ontogeny symmetry assumed.
Suborganismal and population properties consistent
2) Phytoplankton II. Metabolic products important
Algal-produced compounds mitigate toxicity.
3) Bacteria. Metabolic products important.
Suborganismal data can help model selection.
4) Individual Population projection for mussels.
Ontogeny asymmetry.
Population response more sensitive than individual
response
5) Phytoplankton-zooplankton interactions. Ontogeny
important and metabolic products important?
Effects of ENMs on
phytoplankton
populations
Kooijman’s “standard” DEB model*
i-state variables
 Reserve biomass at time t
 Structural biomass at time t
 “Cumulative reproduction”, i.e. total carbon allocation to reproduction
buffer by time t
 Total allocation to “maturity” by time t .
 Hazard rate at time t, i.e. instantaneous “risk” of mortality
 Aging acceleration at time t – related to level of damage inducing
compounds
Parameters
Total of 3 parameters + 2 parameters for toxic effects. Of these some are
expected to be broadly invariant across taxa and others scale in
predictable way with size. This opens the way to generality. For many
applications, fewer state variables and parameters suffice.
S.A.L.M. Kooijman (2010) Dynamic Energy Budget models for metabolic organization.
Cambridge University Press.
T. Sousa et al (2010)., Philosophical Transactions of the Royal Socitey B, 365:3413-3428.
Marine phytoplankton population growth*
•Study of 4 phytoplankton species exposed to TiO2 and ZnO particles
•No effect with TiO2
•ZnO effect probably due to Zn2+
Toxicity described by two quantities
(NEC and one other)
* R.J. Miller et al. (2010) Environmental Science & Technology 44: 7329–7334
Marine phytoplankton population growth*
•Study of 4 phytoplankton species exposed to TiO2 and ZnO particles
•No effect with TiO2
•ZnO effect probably due to Zn2+
Toxicity described by two quantities
(NEC and one other)
DEB model
* R.J. Miller et al. (2010) Environmental Science & Technolgy 44: 7329–7334
Marine phytoplankton population growth*
•Study of 4 phytoplankton species exposed to TiO2 and ZnO particles
•No effect with TiO2
•ZnO effect probably due to Zn2+
Toxicity described by two quantities
(NEC and one other)
DEB model
* R.J. Miller et al. (2010) Environmental Science & Technology 44: 7329–7334
Marine phytoplankton population growth*
Isochrysis galbana
Membrane permeability (Cell death )
RF
Relative fluorescence (RF)
Mitochondrial membrane potential
ZnO mg L-1 (ppm)
ZnO mg L-1 (ppm)
Reactive oxygen species (ROS)
production
Dynamic Energy Budget
(DEB) modeling of NEC
NEC = 223 ± 56 ppb
ZnO mg L-1 (ppm)
Expt data from Cole, Cherr
et al., in prep
18
BUT – it’s not always that simple
(Expts by L. Stevenson on silver ENMs and a freshwater alga)
Per capita growth rate of algal cultures by age
1
7
14
New culture
One week old
Two weeks old
Days
Particles aggregate in
older batch cultures
-0.4
-0.2
0.0
Per capita5 mg/L
growth
rate AgNPs
of algal cultures
citrate-coated
5 mg/L citrate-coated AgNP
-0.6
-0.8
20
40
60
80
100
per capita growth rate (ug/L chl a per day)
0.2
Size of AgNPs (nm)
0
nanoparticle diameter (nm)
120
Diameter of AgNPs per age of algal culture (nm)
New culture
One week7old Two weeks14old
1
Days
Smaller particles more toxic
than aggregates
Hypothesis: algae excrete soluble organic compounds that interact with
particles and dissolved metals
ADDITIONAL FEEDBACK TERM(S) + NEW E-STATE INTERACTIONS
2
1
-2
-1
0
5 mg/L AgNP data
Control data & fit
only ions inactivated
only NPs inactivated
NPs & ions inactivated
-3
log10(chlorophyll a concentration (mg/L))
DOC mitigation of AgNP and Ag+
5
10
15
Day
20
25
Effects of Cd-Se quantum
dots on bacterial populations
(Pseuomonas aerigunosa)
Contrasting QD toxicity with toxicity of dissolved Cd1-3
Strategy: Use DEB models to charcterize differences in bacterial growth response to
Cd(II) and CdSe Quantum dot (QD) exposure
1. Data from J. Priester et al. Environmental Science and Technology 43:2589-2594 (2009).
2. T. Klanjscek, J. Priester, P.A. Holden and R.M. Nisbet, PlosONE, 7(2): e26955. doi:10.1371/journal.pone.0026955)
3. T. Klanjscek, J. Priester, P.A. Holden and R.M. Nisbet, Ecotoxicology, in review
Contrasting QD toxicity with toxicity of dissolved Cd1-3
Strategy: Use DEB models to charcterize differences in bacterial growth response to
Cd(II) and CdSe Quantum dot (QD) exposure
• New feedback to environment required to fit
DEB model to control (zero Cd) curve
1. Data from J. Priester et al. Environmental Science and Technology 43:2589-2594 (2009).
2. T. Klanjscek, J. Priester, P.A. Holden and R.M. Nisbet, PlosONE, 7(2): e26955. doi:10.1371/journal.pone.0026955)
3. T. Klanjscek, J. Priester, P.A. Holden and R.M. Nisbet, Ecotoxicology, in review
Kooijman’s “standard” DEB model
i-state variables
 Reserve biomass at time t
 Structural biomass at time t
 “Cumulative reproduction”, i.e. total carbon allocation to reproduction
buffer by time t
 Total allocation to “maturity” by time t .
 Hazard rate at time t, i.e. instantaneous “risk” of mortality
 Aging acceleration at time t – related to level of damage inducing
compounds
 Acclimation energy – new variable
E-state variables

Environmental degradation – new variable
Parameters
Total of 6 DEB parameters + variable number of other parameters
depending on submodel. Of these some are expected to be broadly
invariant across taxa and others scale in predictable way with size. This
opens the way to generality. For many applications, fewer state variables
and parameters suffice.
Contrasting QD toxicity with toxicity of dissolved Cd1-3
Strategy: Use DEB models to charcterize differences in bacterial growth response to
Cd(II) and CdSe Quantum dot (QD) exposure
• New feedback to environment required to fit
DEB model to control (zero Cd) curve
• Model with toxic effect on resource
assimilation and mortality best fits response
to Cd (II) and to ROS data
1. Data from J. Priester et al. Environmental Science and Technology 43:2589-2594 (2009).
2. T. Klanjscek, J. Priester, P.A. Holden and R.M. Nisbet, PlosONE, 7(2): e26955. doi:10.1371/journal.pone.0026955) (2012)
3. T. Klanjscek, J. Priester, P.A. Holden and R.M. Nisbet, Ecotoxicology DOI 10.1007/s10646-012-1028-7 (2013)
Modeling the effect of QDs
Rule of the game: no change in Cd toxicity model
Cd2+ interferes with assimilation and
enters the cell → previous toxicity model
QD dissolution
introduces Cd2+
in environment
CdSe
CdSe
CdSe
QDs associate
with the cell
Associated QDs produce ROS
affecting membrane processes
ROS produced
inside the cell
affect all cellular
processes
Toxicity mechanism for Quantum Dots
• Model selection from fitting
growth trajectories not
possible
• Measurements of Reactive
Oxygen Species (ROS)
allow model selection
Effects of metal oxide
nanoparticles on
populations of marine
mussels (Mytilus spp.)
Effects of ZnO NPs on mussel physiology
(Expts. By Shannon Hanna)
Adult marine mussels, Mytilus galloprovincialis, were exposed to ZnO NPs for 12
weeks at concentrations up to 2 mg L-1.
Basic measurements on individuals(2 food levels)
1) weights of shell, gonad, somatic tissue
2) Zn distribution within organism
3) Tank clearance rates  information on food consumed.
used to estimate
parameters
4) Iindividual clearance rates
5) Oxygen consumption rates.
Population level prediction
Aims to extract enough information to project effects on lifetime reproduction
(previous experience in Muller, E.B. et al. Ecotoxicology 19: 38-47 (2010))

R 

 ( a ) S ( a ) da
0 fecundity survival
at age a
to age a
From DEB model
EC50 EXPECTED LIFE-TIME PRODUCTION
OF REPRODUCTIVE MATTER
- EC50 for a given food level
- MUCH SMALLER THAN
FOR INDIVIDUAL RATES
(e.g. 1.5 mg/l for feeding)
- Consequence of ontogenic
asymmetry
Phytoplanktonzooplankton
interactions
80
80
60
60
40
40
Phytoplankton-zooplankton interactions
DEB-IBM predicts effects of ontogeny asymmetry*
20
20
X m a x = 2 *K
0
X m a x = 5 *K
0
140
140
120
120
100
100
60
20
Feeding
X m a x = 2 0 *K
4
S u rviva l
B io m a ss
% reduction compared to control
140
1 4102 0
120
100
100
80
80
60
60
40
40
20
X m a x = 2 *K
20
0
X m a x = 2 *K
0
140
140
120
120
100
100
80
80
60
60
40
40
20
X m a x = 1 0 *K
20
0
X m a x = 1 0 *K
0
0
X m a x = 5 *K
X m a x = 5 *K
le n g th (m m )
X m a x = 1 0 *K
0
112400
6800
4600
X m a x = 5 *K
1
X m a x = 2 0 *K
8 0 06 0
6 0 04 0
18000
2400
500
0
X m a x = 2 0 *K
X m a x = 1 0 *K
X m a x = 2 0 *K
X m a x = 1 0 *K
M e a n le n g th
Physiological Mode
of Action
M a tu ra tio n flu x / R e p ro d u c tio n flu x
1.Reproduction
(direct)
120
160
1 0 02.Feeding
140
80
120
3.Maintenance
16000
48004.Growth costs
60
20
4 05.Control
X m a x = 2 *K
X m a x = 5 *K
0
300
20
1 4 00
200
X m a x = 2 *K
X m a x = 5 *K
120
160
100
140
80
120
16000
100
4800
60
20
40
0
20
0
0
X m a x = 2 0 *K
X m a x = 1 0 *K
X m a x = 2 0 *K
X m a x = 1 0 *K
95
90
M a tu ra tio n flu x / R e p ro d u c tio n flu x
75
50
25
0
95
90
75
50
25
0
95
90
X m a x = 5 *K
200
400
75
M e a n fo o d d e n sity
50
25
0
200
95
90
400
X m a x = 2 *K
75
*
600
X m a x = 2 0 *K
50
800
25
1000
Maturation
Reproduction
X m a x = 1 0 *K
0
1200
X m a x = 5 *K
140
c u m u la tive re p ro d u c tio n
% reduction compared to control
X m a x = 5 *K
1 0 0 08 0
0
X m a x = 5 *K
X m a x = 2 *K
4600
1 2 0100 0 X m a x = 1 0 *K
Growth
X m a x = 2 *K
110200
0
X m a x = 2 0 *K
X m a x = 2 0 *K
8 0 06 0
20
400
0
200
200
6800
3
X m a x = 2 *K
2400
2
112400
120
6 0 04 0
20
400
0
200
140
0
120
18000
1
1 2 0100 0 X m a x = 2 *K
1 0 0 08 0
110200
3
1 4 00
Maturity
B io m a ss
maintenance
M e a n fo o d d e n s ity
140
A b u n d a n ce
M e a n le n g th
140
Reserve
4
X m a x = 2 0 *K
40
20
3
X m a x = 1 0 *K
60
5
40
Somatic
maintenance
X m a x = 5 *K
80
80
2
X m a x = 2 *K
160
ECx reproduction
0
140
10
120
20
100
tim e (d )
Unpublished work by Benjamin Martin
80
60
40
20
X m a x = 2 *K
X m a x = 5 *K
30
Take home messages
1. Structured population models (or IBMs) can help relate
sub-organismal information (cheap and fast) to
population dynamics (slow, expensive and important)
2. Abstract representation of individual organism
(Kooijman’s DEB theory) has practical value
3. Experiments are revealing new feedbacks involving
metabolic products
4. Ontogeny asymmetry impacts levels at which toxic
effects impact populations