Dynamic models of multi-trophic interactions in microbial food webs.

Abstract

Non-steady-state mechanistic models were developed to examine the dynamics of organic pollutant utilization, microbial competition, inhibition and predation in a multi trophic system populated by bacteria of different growth rates and protozoa in a continuously mixed flow reactor and a batch reactor. The levels of substrate and cells were modeled during the biodegradation of naphthalene (a moderately bioavailable semi-volatile organic pollutant) by two bacteria in the presence of a predator assuming other nutrients were present in excess. The model predicts that multiple bacteria and predator species can co-exist in the system only if they differ in inhibition capacity, selective predation rate, and/or ability to employ predation defense mechanisms. These models further predict that predation can enhance the process of bioremediation, similar to what has been observed in some experimental studies. Together, these results provide a mechanistic model framework to support the idea that increased species diversity may increase the ability of microbial ecosystems to biodegrade pollutants.

Full text

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Journal of Environmental Science and Health, Part A (2012) 47, 1391–1406
Copyright C ?Taylor & Francis Group, LLC
ISSN: 1093-4529 (Print); 1532-4117 (Online)
DOI: 10.1080/10934529.2012.672316
Dynamic models of multi-trophic interactions in microbial
food webs
MENKA MITTAL and KARL J. ROCKNE
Department of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, Illinois, United States
Non–steady-statemechanisticmodelsweredevelopedtoexaminethedynamicsoforganicpollutantutilization,microbialcompetition,
inhibition and predation in a multi trophic system populated by bacteria of different growth rates and protozoa in a continuously
mixed flow reactor and a batch reactor. The levels of substrate and cells were modeled during the biodegradation of naphthalene
(a moderately bioavailable semi-volatile organic pollutant) by two bacteria in the presence of a predator assuming other nutrients
were present in excess. The model predicts that multiple bacteria and predator species can co-exist in the system only if they differ
in inhibition capacity, selective predation rate, and/or ability to employ predation defense mechanisms. These models further predict
that predation can enhance the process of bioremediation, similar to what has been observed in some experimental studies. Together,
these results provide a mechanistic model framework to support the idea that increased species diversity may increase the ability of
microbial ecosystems to biodegrade pollutants.
Keywords: Microbial food web, predation, bioremediation, biodegradation, protozoa.
Introduction
Environmental scientists have a growing interest in the re-
lationship between microbial population dynamics and or-
ganic matter cycling in the biosphere. Although a wide
variety of research has been undertaken over the past few
decades to understand the metabolic diversity of the mi-
crobes and the metabolic reactions they perform in the
cycling of organic matter, we still lack systematic knowl-
edge about how these processes occur concurrently. An
ongoing problem in predicting the fate of organic contami-
nants in the soil/sediment environment is that macro-scale
phenomenaareprimarilygovernedbycomplexmicro-scale
processes that are difficult to isolate and characterize in a
heterogeneous environment.
It is clear that nature is much more complex and dy-
namic on biological, temporal and physical scales than can
be accounted for in linear closed form and/or steady-state
models, and thus an approach utilizing coupled dynamic
non-steady state models is needed for better predictive ca-
pacity. Often the failure of models to adequately predict
behavior is attributed to using overly simplistic assump-
tions based on small-scale and short-term laboratory ex-
periments. Thus the variation of model parameters is fre-
quently unrealistically narrow. Further, in the microbial
Address correspondence to Karl J. Rockne, 842 W. Taylor St.
(m/c 246), Chicago, IL 60607, USA; E-mail: krockne@uic.edu
Received November 16, 2011.
realm multi-trophic interactions are frequently ignored, in
spite of the numerous studies that have demonstrated that
predation by protozoa can alter the abundance of bacterial
species and can also change the morphological as well as
taxonomical structure of the bacterial community.[1–15]
It has been demonstrated that grazing of bacteria by
protozoa can enhance the breakdown of carbon thus af-
fecting the process of bioremediation[16,17]by increasing
the metabolic activity of the bacterial prey;[18]as well as
allowing the co-existence of multiple prey species utilizing
the same common resource through selective predation.[19]
Hobular et al.[20]reported an increase in chemical oxygen
demand due to the presence of bacterivorous ciliates in a
petrochemical activated sludge process.
Rogerson and Berger[21]reported an increase in the
degradation rate of crude oil in a batch culture due to graz-
ing by the ciliate Colpidium colpoda. In addition, a model
food chain investigated by Mattison and Harayama[16]
demonstratedanenhancementintoluenemineralizationby
Pseudomonas sp. in the presence of the bacterivorous flag-
ellate Heteromita globosa, which the authors attribute to
predation-induced changes in taxonomical as well as mor-
phological structure of the bacterial community. All these
results suggest the importance of understanding the role of
protozoa in the process of bioremediation.The focus of the
present research is on a microbial bioremediation food web
consisting of bacteria and their predators in soil/sediment
with a bioavailability-limited organic contaminant as the
sole microbial food source.

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Mittal and Rockne
At present, the role of predation in the process of biore-
mediation is poorly understood and is rarely incorporated
in biodegradation models. We present here an examination
of several critical geochemical, biological and predation
processes that affect bioremediation through sensitivity
analysis of the model predictions accounting for both the
“top down” control of the bacterial community structure
by predation, as well as the “bottom up” control by
substrate bioavailability limitation.
Process stoichiometry
A series of stoichiometric models for substrate, bacteria
and ciliates (a model protozoan bacterial predator) were
developed to represent the utilization of organic carbon by
microbes and predation of microbes by ciliates. The poly-
cyclic aromatic hydrocarbon (PAH) naphthalene (C10H8)
was chosen as a model organic contaminant substrate for
microbes. Although naphthalene is not technically a PAH,
it is typically included within the PAH class[22]and has suf-
ficient bioavailability to support a microbial community[23]
unlike some of the higher molecular weight PAHs with
severely limited bioavailability.
Vibrio sp. VS NAP (referred to hereafter as VS NAP)
and Pseudomonas putida str. NCIB (referred to hereafter
as NCIB) were chosen as the model PAH degrading bac-
terial species based on the criteria that both species should
employ a similar di-oxgyenase attack for complete PAH
biodegradation and mineralization, both should grow in
similar, free-living (i.e., non-biofilm) conditions, and, most
importantly, the species should have significantly different
biodegradation rates. In the present study, VS NAP is a
fast-growing, free-living PAH biodegrading bacterium and
NCIB is a model slow-growing, free-living bacterium able
to biodegrade PAHs.
Overallstoichiometricequations(Ro)werebasedoncon-
sumption of naphthalene as the electron donor, oxygen as
the electron acceptor, and ammonia as the source of nitro-
genusingthemethodofRittmanandMcCarty.[24]Bacterial
growthyieldsweredeterminedfromenthalpicdatawithO2
as the electron acceptor. Phosphorous and other nutrients
were assumed to be present in non-limiting quantities. Cell
mass was represented by the general formula C5H7O2N.
The overall reactions (Ro) are:
VS NAP – Fast-growing bacteria:
0.0208C10H8+ 0.205O2+ 0.009NH+
→ 0.009C5H7O2N + 0.071H2O + 0.172CO2
NCIB – Slow-growing bacteria:
4+ 0.009HCO−
3
(1)
0.0208C10H8+ 0.205O2+ 0.009NH+
→ 0.009C5H7O2N + 0.071H2O + 0.172CO2
The stoichiometry of bacteria predation by protozoa is
not as direct as the consumption of a defined electron
donor, therefore protozoa cell mass was represented by
4+ 0.009HCO−
3
(2)
thegeneralbacterialcellstoichiometricformulaC5H7O2N,
and the overall predation stoichiometry is thus:
0.05C5H7O2N + 0.2025O2→ 0.009C5H7O2N
+0.162CO2+ 0.04NH+
4+ 0.041HCO−
3+ 0.035H2O
(3)
Mass balances
The supply of organic carbon and nutrients and boundary
fluxeswererepresentedeitherbyacontinuouslymixedflow
reactor (CMFR) or by a batch reactor (Batch) system as
models of open and closed soil/sediment environments, re-
spectively. Mass balances of substrate (S) consumption,
population growth of bacteria (X), and their ingestion
by protozoa (Z) were developed for both systems. In the
CMFR case, a well mixed habitat of constant volume is re-
plenished by a nutrient medium with excess concentrations
of other nutrients and an initial concentration of substrate
(S0)thatbalancesaconstantoutflowatadilutionrateofD.
In the batch case, substrate is initially present at its highest
concentration and decreases as it is utilized.
OursimplestmodelsystemofSutilizationbyeachbacte-
rial specie without predation pressure with substrate either
dissolved in the reactor influent (CMFR only) or dissolved
into the aqueous phase from crystalline substrate (Batch
only). The inclusion of substrate supply through dissolu-
tion in the batch reactor system was necessary to produce
a non-trivial response (i.e., limited solubility would rapidly
limit the growth of bacteria and thus predation). Mass bal-
ancesonsubstrate(S)underthesetwocasesarerepresented
as follows:
CMFR:dS
dt= D(S0− S) − rut,sb
Batch:dS
dt= ksol(SSAT− S) − rut,sb
where S is the substrate concentration (mg L−1) at any
time t, S0is the substrate concentration in the feed (mg
L−1), D (d−1) represents the dilution rate, ksol(d−1) is the
rate of solubilization (for batch reactor only) and SSAT
(mg L−1) is the saturation concentration of the substrate.
The parameter rut,sbis the rate of substrate utilization by
bacteria.
Substrate utilization is typically thought to follow the
Monod kinetic regime, an empirical hyperbolic relation-
ship between kinetic rate and substrate concentration with
a “half-saturation” constant (Ks). Our objective here was
to develop equations that are fully mechanistic, and we
thusmodeledsubstrateutilizationusingthedual-resistance
model developed by Merchuck and Ansejo,[25]which pro-
vides a physical meaning to the half-saturation constant
(Ks1,b). In this model, the overall bacterial growth rate
(µsyn) is a function of the intrinsic maximum growth rate
(ˆ µb) limited by the transport of the substrate from the bulk
(4)
(5)

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Multi-trophic interactions in microbial food webs
1393
liquid phase to the cell surface in response to the concen-
tration gradient. The consumption of soluble substrate by
bacteria is thus:
−dS
where Kt is the overall mass transfer coefficient (m s−1)
to the cell surface and Scis the substrate concentration at
the cell surface. The specific cell surface area per unit cell
control volume assuming a spherical cell of diameter (dc)
is:
?
πd3
dt=cell surface area
control volumeKt(S− Sc)
(6)
cell surface area
control volume
=
πd2
c
c
?6
??Xb
ρc
?
=6Xb
dcρc
(7)
where ρcis the cell density. Substituting, we get:
−dS
dt=6Xb
dcρcKt(S− Sc)
(8)
Assuming the growth rate (µsyn) is limited by and pro-
portional to the substrate flux to the cell (X), and the pro-
portionality constant between substrate utilization and cell
mass growth is Yb(the yield of X per unit mass of S con-
sumed), we get:
?
ˆ µb+
Assuming that the Scis relatively small compared to the
bulk phase (Sc<<S) and dividing the right-hand side of
Eq. (9) by [6YbXb
µsyn.b=
ˆ µb
6YbXb
dcρcKt
?
?
(S− Sc)
?
6YbXb
dcρcKt
(S− Sc)
(9)
dcρcKt] we get:
µsyn.b=
ˆ µbS
ˆ µb
?6YbXb
dcρcKt
?+ S
(10)
Eq.10canbemadeequivalenttoaMonodkineticregime
once we substitute the first term in the denominator with
the constant Ks1,b:
Ks1,b=
ˆ µb
?
6YbXb
dcρcKt
?
(11)
Ks1,bis the ratio of the metabolic capacity of the cell (ˆ µb)
to the substrate bioavailability (Kt). We then incorporate
this kinetic term into the rate of substrate utilization:
ˆ qsbS
Ks1,b+ SXb
where Xbdenotes the bacterial cell concentration (mg L−1)
and b = v or p indexes the bacterial species VS NAP and
NCIB respectively, ˆ qsbis the specific rate of substrate uti-
lization derived from bacterial synthesis:
rut,sb=
(12)
ˆ qsb=
ˆ µb
Yb
(13)
where ˆ µbrepresents the maximum growth rate of bacteria
(d−1) and b = v or p indexes the bacterial species VS NAP
and NCIB respectively, and Yb(mg mg−1) and Ks1,b(mg
L−1) are as described above. Based upon this analysis, the
mass balance on cells (X) is thus:
CMFR:dXb
dt
= D(X0,b− Xb) +?µsyn,b− Kd1,b
Batch:dXb
dt
?Xb
(14)
=?µsyn,b− Kd1,b
?Xb
(15)
whereX0,brepresentstheinitialbacterialcellconcentration
(mg L−1), Xbbacterial cell concentration at time t, Kd1,b
represents the endogenous decay rate of bacteria (d−1) and
b = v or p indexes VS NAP or NCIB, respectively, and
µsyn,bis the specific growth rate (d−1) as derived in Eqs. 10
and 11.
Eqs. 14–15 provide the mass balances of X for the sim-
ple system of single microbial substrate utilization in the
absence of predation. Including predation results in the
following (the S mass balance in Eqs. 4–5 are not changed
by inclusion of predation):
Cells(CMFR):dXb
dt
= D(X0,b− Xb)
?− rut,bc
= Xb
+ Xb
?µsyn,b− Kd1,b
dt
(16)
Cells(Batch):dXb
?µsyn,b− Kd1,b
?− rut,bc
(17)
where rut,bcis the rate of ingestion of bacteria by ciliates
and is represented by:
rut,bc=
ˆ qb(Xb− Xbt)
Ks2,bc+ (Xb− Xbt)Zc
(18)
and ˆ qbis the maximum specific bacterial ingestion rate of
protozoa as:
ˆ qb=
ˆ µc
Yc
(19)
where ˆ µc is the maximum growth rate of ciliates (d−1),
Ycis the yield (mg mg−1) of protozoa on bacterial cells,
Xbtrepresents the threshold bacteria concentration below
whichthereisnopredation, Ks2,bcrepresentsthebiokinetic
“half saturation” constant (mg L−1) and Zcrepresents the
protozoa cell concentration (mg L−1).
Protozoan(ciliate)population(Zc)increasesbyingesting
bacterial cells according to the saturation kinetic rate as
follows:
CMFR:dZc
dt
= D(Z0,c− Zc) + µsyn,bcZc− Kd2,cZc
(20)
Batch:dZc
dt
= µsyn,bcZc− Kd2,cZc
(21)

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Mittal and Rockne
where Z0,c(mgL−1)istheinitialconcentrationofprotozoa,
Kd2,cdenotes the endogenous decay rate of the protozoa
(d−1), and the specific protozoa growth rate is µsyn,bc(d−1).
The specific protozoa growth rate µsyn,bc was devel-
oped using a mechanistic model of bacterial cell predation
by analogy with the Michaelis-Menton (M-M) enzymatic
catalysis mechanism. We posit that the protozoa-bacteria
interaction can be modeled analoguous to the M-M model
withbacteria(X)equivalenttothesubstratefortheenzyme
whichuponcontactwiththeprotozoa(Z)formsa“contact
complex” denoted CC:
X + Z
k1
→CC
(22)
The CC thus can be seen as analogous to enzyme-
substrate complex in the M-M model. The rate at which
protozoa contacts a bacterial cell is given by k1, which is
a function of the speed and charge of the bacterial cell.
However, successful digestion of microbial cells by ciliate
protozoa is more complex, with subsequent capture, in-
gestion, digestion, and clearance stages influenced by the
different properties of bacterial prey such as size, shape,
speed, charge, taste, enzymatic resistance and toxicity. If
due to inappropriate size, shape, speed, taste or charge the
protozoa is not able to capture the bacterial cell, the CC
reverts back to separate protozoa and bacterial cells as:
CC
k2
→ X + Z
(23)
After successful capture of the bacterial cell, the process
ofingestiontakesplace.However,iftheprocessofingestion
isunsuccessful,e.g.,theingestedbacterialcellisegestedout
by the protozoa due to its shape and speed the CC reverts
back to the free state:
CC
k3
→ X + Z
(24)
The bacteria cell may be ejected out of the protozoa
body due to cyst/spore formation or some other microbial
toxicity or enzymatic resistance factor that yields a viable
bacterium:
CC
k4
→ X + Z
(25)
After successful digestion, the bacterial cell is digested
and metabolic products (MP) are released in the environ-
ment at a clearance rate (k5), while protozoa return to their
original state:
CC
k5
→ Z+ MP
(26)
If Z is the total protozoa concentration in the system
and CC is the concentration of the contact-complex, the
difference of the two (Z-CC) is the concentration of free
protozoa in the system. The net rate of CC formation can
be expressed as:
d (CC)
dt
− {[k2+ k3+ k4](CC) + k5(CC)}
= k1(Z− (CC)) X
(27)
If we hypothesize that the clearance rate k5is the rate-
limiting step, we know from chemical kinetics theory that
all upstream reactions are at steady state, i.e., the rate of
CC formation of a complex equals the rate of breakdown
and Eq. 27 = 0, we get:
k1(Z− (CC)) X = {[k2+ k3+ k4](CC) + k5(CC)}
Or, re-organizing as:
(28)
(Z− (CC)) X
CC
=k2+ k3+ k4+ k5
k1
(29)
If we substitute for the left-hand side of Eq. 29, the ratio:
Ks2,bc=k2+ k3+ k4+ k5
k1
(30)
and solve for CC in Eq. 29, we get the following:
CC =
XZ
Ks2,bc+ X
(31)
Now, our interest is in the rate of formation of metabolic
products (MP). The forward velocity (µc) of this reaction
can be expressed as:
µc= k5CC
(32)
If the bacterial cell concentration is very high (X>>Z)
so that essentially all the predators (ciliates) are present as
CC, that is, CC = Z, the maximum reaction velocity ˆ µcis
defined as:
ˆ µc= k5Z
(33)
Combining Eqs. 31–33, we get the familiar M-M form
for X predation:
µc=
ˆ µcX
Ks2,bc+ X
(34)
A heterogeneous remediation environment will contain
different bacterial species that compete for the same sub-
strate and other common resources necessary for growth.
Two species can coexist in a system only if they exploit
their environment differentially.[26]Thus, if two species are
present in an environment with a common substrate they
must be exerting some interference effect on each other in
order to utilize the substrate in a different manner. We con-
sider here a two bacterial species system for simplicity, with
a mass balance on substrate:
CMFR:dS
dt= D(S0− S) − rut,sv− rut,sp
dt= ksol(SSAT− S) − rut,sv− rut,sp
(35)
Batch:dS
(36)
Whererut,svandrut,sparetheS utilizationratesbyVSNAP
and NCIB, respectively as in Eq. (13). The mass balance

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Multi-trophic interactions in microbial food webs
1395
on cells is thus:
CMFR:
dXv
dt
dXp
dt
dXv
dt
dXp
dt
= D(X0,v− Xv) +?αµsyn,v− Kd1,v
= D?X0,p− Xp
=?αµsyn,v− Kd1,v
=?µsyn,p− Kd1,p
where α denotes the interference effect of NCIB on VS
NAP and ranges from 0–1 with a value of 0 meaning no
interference (i.e., NCIB does not inhibit the growth of VS
NAP) and a value of 1 means NCIB completely inhibits
the growth of VS NAP.
The model incorporates a selectivity parameter given
that protozoan predators have the ability to selectively
graze on one type of bacterial species over another. Se-
lectivity may be a function of some or all of the following
factors: bacteria size, motility, cell surface charge and hy-
drophobicity, capsulated cell growth mode and enzymatic
resistance or toxicity towards the predator. The substrate
dynamics can be represented the same as in Eqs. 4–5 and X
and Z mass balances are as follows:
?Xv
?Xp
?+?µsyn,p− Kd1,p
?Xv
?Xp
(37)
Batch :
(38)
Cells(CMFR):
dXv
dt
= D(X0,v− Xv) +?αµsyn,v− Kd1,v
× Xv− (1 − ε)rut,vc
= D?X0,p− Xp
?
?
dXp
dt
?+?µsyn,p− Kd1,p
× Xp− εrut,pc
(39)
Cells(Batch):
dXv
dt
dXp
dt
=?αµsyn,v− Kd1,v
=?µsyn,p− Kd1,p
?Xv− (1 − ε)rut,vc
?Xp− εrut,pc
(40)
where ε is the selectivity parameter denoting the preference
of protozoa for one bacterial species over another.
The selectivity parameter (ε) ranges from 0–1, where 0
means no predation on NCIB and full grazing on VS NAP
and a value of 1 means protozoa select wholly NCIB as
their source of food with no predation on VS NAP. A value
of ε = 0.5 means there is no preference. Protozoa (Z) mass
balances are:
Ciliates(CMFR):dZc
dt
= D(Z0,c− Zc) +??1 − ε?µsyn,vc
+εµsyn,pc− Kd2,c
Ciliates(Batch):dZc
dt
+εµsyn,pc− Kd2,c
where all terms are as defined previously.
?Zc
?Zc
(41)
=??1 − ε?µsyn,vc
(42)
Various bacterial species have the capacity to em-
ploy predation defense mechanisms by shifting towards
smaller cell size[27]or forming filaments/flocs and/or ag-
gregates.[4,9,14,27–30]Based on these studies, we include in
the model the formation of grazing-resistant floc cell forms
by the slow-growing cell to protect against predation.[3,30]
This is arbitrary; however, as it is possible that the faster
growing bacterium could also form flocs; but the growth
rate will already favor the dominance of the faster growing
bacterium, leading to rapid extinction of the slower grow-
ing bacterium. Because the cells in different forms (flocs
or free living) may have different S utilization rates, the S
mass balance must be modified as well as the bacterial (X)
and protozoa (Z) mass balances:
CMFR:dS
dt= D(S0− S)−rut,sv−rut,sp1−rut,sp2
Batch:dS
dt= ksol(SSAT− S) − rut,sv− rut,sp1− rut,sp2
(43)
(44)
dXv
dt
= D(X0,v− Xv) +?αµsyn,v− Kd1,v
×Xv− (1 − ε)rut,vc
= D?X0,p1− Xp1
× Xp1+ Rd− Rf− εrut,p1c
= D?X0,p2− Xp2
× Xp2− Rd+ Rf
=?αµsyn,v− Kd1,v
=?µsyn,p1− Kd1,p
×Xp1+ Rd− Rf− εrut,p1c
=?µsyn,p2− Kd1,p
= D(Z0,c− Zc) +??1 − ε?µsyn,vc
+εµsyn,p1c− Kd2,c
=?(1 − ε)µsyn,vc+ εµsyn,p1c− Kd2,c
?
CMFR:dXp1
dt
?+?µsyn,p1− Kd1,p
?+?µsyn,p2− Kd1,p
?Xv− (1 − ε)rut,vc
?
?Xp2− Rd+ Rf
?
(45)
?
dXp2
dt
dXv
dt
Batch:dXp1
dt
(46)
dXp2
dt
CMFR:dZc
dt
?Zc
(47)
?Zc
(48)
Batch:dZc
dt
whereXp1, denotes the concentration of dispersed free-
living NCIB cells, Xp2 denotes the concentration of
NCIB cells in flocs, and rut,sp1 and rut,sp2 are the rate
of substrate utilization by dispersed and floc NCIB cells,
respectively:
rut,sp1=
ˆ qp1S
Ks1,p1+ S
ˆ qp2S
Ks1,p2+ S
(49)
rut,sp2=
(50)

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Mittal and Rockne
The parameter rut,p1cis the rate of utilization (d−1) of
dispersed NCIB cells by protozoa:
rut,p1c=
ˆ qp1c(Xp1− Xbt)
Ks2+ (Xp1− Xbt)Zc
(51)
Rfand Rdare the rates of floc formation and floc break
up, respectively, and are assumed to depend on substrate
and cell mass concentration as follows:[31]
Rf= K3SXp1
Rd= K4Xp2
(52)
(53)
K3and K4are the floc formation (ml mg S−1d−1) and floc
break up rates (d−1), respectively.
Parameterization and numerical simulation
Themassbalanceequationshavenoclosed-formanalytical
solutions.Thusnumericalsimulationwasrequiredfortheir
analysis.Measuredexperimentalvalueswerechosenforthe
model parameters where known, and best guesses based
upon literature-derived experimental values were chosen
for all other parameters as our “base case” simulation val-
ues (Table 1). These values were then varied by an order of
magnitude plus or minus the base case to determine output
Table 1. Parameter values used for the base case simulations.
ParameterDefinitionValue (units)
Indices:
b
Index for bacterial species (v: Vibrio, p:
pseudomonad)
Index for ciliate species
c
Environmental Parameters
D
α
ε
K3
K4
Functions
rut,sb
(rut,sv,rut,sp,rut,sp1,rut,sp2)
ˆ qs
µsyn,b
(µsyn,v,µsyn,p,µsyn,p1,µsyn,p2)
rut,bc
(rut,vc,rut,pc,rut,p1c)
ˆ qb
µsyn,bc
Dilution rate
Interference effect of Vibrio on Pseudomonad
Selectivity parameter
Constant parameter for flocculation
Constant parameter for rate of floc breakup
0.2 (d−1)
1.0
0.5
0.05 (ml mg S−1d−1)
0.01 (d−1)
Rate of substrate utilization (s) by bacteria (b)(mg L−1d−1)
(mg mg−1d−1)
(d−1)
Maximum specific rate of substrate utilization
Specific growth of bacterial cells due to
synthesis
Rate of bacterial ingestion(mg mg−1d−1)
(mg mg−1d−1)
(d−1)
Maximum specific rate of bacterial ingestion
Specific growth rate of ciliates due to synthesis
on bacterial cells (b)
Substrate Parameters
S0
ksol
SSAT
Ks1,b
Initial substrate concentration
Solubilization rate of substrate
Saturation concentration
Substrate conc. at which bacterial conc. is half
of its maximum growth
(0.02 mg mL−1)
1.0 (d−1)
0.02 (mg mL−1)
0.002 (mg mL−1)
?Ks1,v, Ks1,p, Ks1,p1, Ks1,p2
Bacterial Growth Parameters
ˆ µb(ˆ µv,ˆ µp,ˆ µp1,ˆ µp2)
Yb
X0,b
Kd1,b
Ciliates Parameters
Z0,c
ˆ µc
Yc
Ks2,bc(Ks2,vc, Ks2,pc)
?
Maximum specific growth rate of bacterial cells
Yield of bacterial cells
Initial concentration of bacterial cells
Endogenous decay rate of bacterial cells
1.64 (d−1), 1.04 (d−1), 1.04 (d−1), 0.52 (d−1)
0.51, 0.51, 0.51, 0.38 (mg mg−1)
7.5 × 106(cells mL−1), 7.5 × 106(cells mL−1)
0.05 (d−1), 0.05 (d−1)
?Yv,Yp,Yp1,Yp2
?Kd1,v, Kd1,p
?
?X0,v, X0,p
?
?
Initial concentration of ciliate cells
Maximum growth rate of ciliate cells
Yield of ciliate cells
Substrate conc. at which bacterial conc. is half
of its maximum growth
Endogenous decay rate of ciliate cells
8 × 104(cells mL−1)
0.75 (d−1)
7.03 × 10−3(ciliates per bacterium)
9.13 × 10−4(bact mL−1)
0.01 (d−1)
Kd2,c

Page 7

Multi-trophic interactions in microbial food webs
1397
0
10
20
30
40
50
60
70
80
90
100
01000200030004000
Predator/Prey Volume Ratio
Ingestion Rate (bact flag-1d-1)
Fig. 1. Ingestion rate versus predator/prey volume ratio from
published experimental studies.
sensitivity of simulations conducted using the computer
program STELLA (v8) employing a fourth-order Runge-
Kuttaalgorithmwithadaptivestep-sizecontroltosolvethe
differential equations simultaneously.
Thebacterialyieldvalues(Yv,Yp)forVSNAPandNCIB
on naphthalene and protozoa cell yields were calculated
from the stoichiometric equations developed here in Eqs.
1–3. The yield for NCIB dispersed cells compared to flocs
form are different, based on the ratio of yield of dispersed
cells to floc cells. The maximum growth rate of dispersed
VS NAP and NCIB (ˆ µv, ˆ µp) were measured in the micro-
biology laboratory at Rutgers University.[32]We calculated
the value of growth rate of NCIB floc cells (ˆ µp2) according
to the ratio of growth rate of dispersed cells and floc cells
described in Lee et al.[31]
The half saturation constant for the NCIB floc cells was
calculated on the basis of the ratio of the half saturation
constant for dispersed and floc cells given in Lee et al.[31]
Parameters for ciliophora protozoa growth rate from Mat-
tisonandHarayama[16]wereadopted,exceptthemaximum
specific growth rate of ciliates which were very high com-
pared to other literature values. A literature search of over
40 studies was performed to determine more typical values
for the maximum growth rate of ciliates on bacteria[32]and
0
0.2
0.4
0.6
0.8
1
02040
Time (d)
6080100
Substrate
0
0.2
0.4
0.6
0.8
1
02040
Time (d)
6080 100
Substrate
10-6
10-4
10-2
100
102
104
106
02040
Time (d)
6080 100
Normalized VS NAP(X/X0)
10-6
10-4
10-2
100
102
104
106
02040
Time (d)
6080100
Normalized NCIB (X/X0)
No PredationPredation
a)
b)
c)
d)
Fig. 2. Effects of predation on the relative abundance of A) substrate in the presence of VS NAP or B) NCIB. Also shown are the
relative abundance of C) VS NAP cells or D) NCIB cells in a CMFR (a single prey system) when each grown on naphthalene.

Page 8

1398
Mittal and Rockne
an analysis was also performed to determine whether there
is a correlation between ingestion rate and predator-prey
volume ratio (Fig. 1).
No trend was observed between the ingestion rate
of protozoa and predator-prey volume ratio, which was
somewhat unexpected based upon results presented in
the literature. The average maximum protozoa growth
rate of 0.75 d−1from all 40 studies was adopted as
the base case in the present study. In the present study,
the maximum growth rate of Euplotes plicatum (Phy-
lum Ciliophora, Class Spirotrichea, Subclass Hypotrichia)
on NCIB grown on naphthalene was 0.5 d−1and the
maximum growth rate of Cyclidium spp. (Phylum Cilio-
phora, Class Oligohymenophora, Subclass Hymenostom-
ata) was 0.78 d−1fed with VS NAP when grown on
naphthalene.[32]
CMFR simulations were first run with variable dilution
rates to determine washout conditions (data not shown). A
value of 0.5 d−1resulted in washout of the protozoa cells
(the slowest growing community member and thus rate
limiting), leaving only VS NAP in the system. Therefore,
a value of 0.2 d−1for the dilution rate was adopted as the
base case for subsequent simulations.
Results and discussion
Effects of predation in single prey system
In the absence of predation, simulations for a CMFR
(Fig. 2) and a batch reactor (Fig. 3) containing either
VS NAP or NCIB showed that the organic contaminant
(naphthalene) will be rapidly consumed in less than ten
days in the presence of either of the cultures in either of the
reactors. However, when grazing pressure is exerted by cil-
iates in a single prey system, the fast-growing bacteria (VS
NAP)followstheclassicpredator-preycycle,whereasslow-
growing bacterium (NCIB) goes to extinction in a CMFR
(Fig. 2B).
Thus, in the presence of ciliates, naphthalene concen-
tration in the effluent from a CMFR will oscillate with
increases and decreases in biomass but if NCIB is present
as the prey species the naphthalene concentration will re-
bound as biomass washout will occur.
In the batch base case, the substrate solubilization rate is
such that a rapid increase in concentration (back to satu-
ration level at t = 0) occurs in the presence of ciliate preda-
tors. Rapid depletion of NCIB or VS NAP occurs within
0
0.2
0.4
0.6
0.8
1
1.2
020 40
Time (d)
60 80100
Substrate
0
0.2
0.4
0.6
0.8
1
1.2
02040
Time (d)
6080100
Substrate
10-6
10-4
10-2
100
102
104
106
02040
Time (d)
60 80100
Normalized VS NAP
10-6
10-4
10-2
100
102
104
106
02040
Time (d)
6080100
Normalized NCIB
No PredationPredation
c)
d)
b)
a)
Fig. 3. Effects of predation on the relative abundance of A) substrate in the presence of VS NAP or B) NCIB. Also shown are relative
abundance of C) VS NAP cells or D) NCIB in a batch reactor when each bacterial specie was grown on naphthalene.

Page 9

Multi-trophic interactions in microbial food webs
1399
10-6
10-4
10-2
100
102
104
106
0 100 200
Time (d)
300 400500
Normalized Ciliates (Z/Z0)
0
0.2
0.4
0.6
0.8
1
1.2
0100 200
Time (d)
300 400 500
Normalized Substrate
10-6
10-4
10-2
100
102
104
106
0100 200
Time (d)
300 400500
Normalized NCIB (X/X0)
10-6
10-4
10-2
100
102
104
106
0100200
Time (d)
300400500
Normalized VSNAP (X/X0)
α = 0α = 0α = 0.1α = 0.1 α = 1α = 1
a)
b)
d)c)
Fig. 4. Effect of competitive interference of NCIB on VS NAP on the relative abundance of A) substrate, B) NCIB, C) VS NAP and
D) Ciliates in a CMFR when bacteria were grown on naphthalene.
10 days. Predation is sufficient to lead to near extinction;
no “rebound” of prey is observed by 100 d in the simu-
lation, even as the ciliate predator levels decrease through
endogenous decay and starvation.
Effects of inter-species interference
The behavior of a system gets more complex due to inter-
species interference in the presence of predators. In a
CMFR, there exist three possible outcomes of the inter-
action, depending upon the magnitude of the interference
effect (Fig. 4). If there is no interference effect of one specie
on another then the bacteria population decreases to an
insufficient density to support the ciliate predator leading
to washout (Fig. 4D, α = 0).
However, if we assume that the superior prey NCIB in-
hibits the growth of the other prey VS NAP by 10% (α =
0.1), biomass washout does not occur (Fig. 4B-D, α = 0.1).
NCIB and the ciliates start to exhibit population fluctu-
ations for approximately 320 d whereas VS NAP goes to
extinction. In this system, NCIB is able to compete for
naphthalene and withstand predation with perpetual fluc-
tuations and out-compete VS NAP. Thus, the system will
consistofonlyNCIBandtheciliatesafteroneoscillationof
VS NAP prior to eventual NCIB extinction after t = 320 d.
This result alone demonstrates the utility of simulation.
It is not possible a priori to predict this stable oscillation
rangethroughothermeans.IfNCIBcompletelyinhibitsVS
NAP, biomass washout occurs and naphthalene rebounds
back in the environment. In marked contrast to the CMFR
simulationresults,thereisnosignificantdifference(i.e.sim-
ulation results overlap) in organic contaminant (naphtha-
lene) concentration with time due to the interference effect
of NCIB on VS NAP in the batch case (Fig. 5).
In all cases (α = 0, 0.1, and 1), prey levels are decreased
rapidly to near extinction. However, with a 10% interfer-
ence effect of NCIB on VS NAP, VS NAP is able to with-
stand predation pressure exerted by ciliates and oscillates
with perpetual fluctuations with ciliates after almost 300
d. But this does not cause a significant change in naph-
thalene concentration. Ciliate levels then decrease through
endogenous decay and starvation (Fig. 5).

Page 10

1400
Mittal and Rockne
10-6
10-4
10-2
100
102
104
106
0 100 200
Time (d)
300400 500
Normalized Ciliates
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200
Time (d)
300400500
Substrate
10-6
10-4
10-2
100
102
104
106
0100 200
Time (d)
300 400500
Normalized NCIB
10-6
10-4
10-2
100
102
104
106
0 100200
Time (d)
300400500
Normalized VS NAP
α = 0α = 0α = 0.1α = 0.1α = 1α = 1
d)
c)
b)
a)
Fig. 5. Effect of competitive interference of NCIB on VS NAP on the relative abundance of A) substrate, B) NCIB, C) VS NAP and
D) Ciliates in a batch reactor when cultures were grown on naphthalene.
Effects of selective predation
The CMFR system is sensitive to selective predation
(Fig. 6). When we assume that ciliates exhibit no prefer-
encebetweenVSNAPandNCIB(ε =0.5),thesimulations
demonstrates that the three species can coexist together
with perpetual population fluctuations through t = 500 d.
The balance between growth rate and predation is such
that numerical domination of one bacterial species invites
its replacement by another due to preferential predation.
When NCIB increases due to its predation resistance, the
ciliates die back paving way for the fast-growing bacterium
VS NAP to rebound.
This process continuesin a series of quasi-cycles through
a period of 500 d. Now if we assume that ciliates select
NCIBby3:1overVSNAP(ε =0.75),thesimulationsshow
that due to the low growth rate, NCIB is again not able to
support ciliates and rapidly decreases to extinction. With
less predation on VS NAP, it reaches a stable value. Ciliate
levelsdecreaseatanearfirstorderrateasthepreferredprey
(NCIB) is extinct. Even though it feeds on VS NAP, it is
notsufficienttosustaintheciliateduetoendogenousdecay.
With a fast degrader present, nearly all of the naphthalene
is degraded.
If we assume that ciliates selectively predate VS NAP by
a 3:1 ratio (ε = 0.25), the simulations demonstrate that VS
NAP and ciliate populations oscillate and NCIB reaches
a stable value due to less predation pressure. Due to high
growth rate, VS NAP is able to withstand the predation
pressure. The presence of the slow-growing naphthalene
degrader utilizes all the naphthalene present and keeps the
organic carbon concentration low.
Surprisingly, there is no significant effect of selective pre-
dationonnaphthaleneutilization(Fig.7)inabatchsystem,
as shown by the nearly overlapping simulation results. Due
to a low growth rate, NCIB is not able to withstand the
predation pressure exerted by ciliates and decreases to ex-
tinction by t = 10 d for all levels of predation (even ε =
0.75).VSNAPisresponsiblefornaphthaleneutilizationfor
a certain period of time (t ∼ 25 d) but after that VS NAP is
not able to withstand predation pressure even with a high
growth rate and finally goes to extinction. Ciliates also de-
crease due to endogenous decay and biomass decreases in

Page 11

Multi-trophic interactions in microbial food webs
1401
10-6
10-4
10-2
100
102
104
106
0100200
Time (d)
300 400500
Normalized Ciliates (X/X0)
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200
Time (d)
300 400500
Normalized Substrate
10-6
10-4
10-2
100
102
104
106
0 100200
Time (d)
300 400500
Normalized NCIB (X/X0)
10-6
10-4
10-2
100
102
104
106
0 100 200
Time (d)
300400 500
Normalized VSNAP (X/X0)
ε= 0.5ε= 0.5 ε = 0.75 ε = 0.75ε = 0.25ε = 0.25
a)
b)
c)
d)
Fig. 6. Effects of selective predation by ciliates on the relative abundance of A) substrate, B) NCIB, C) VS NAP, and D) ciliates in a
CMFR when bacteria were grown on naphthalene. With ε = 0.5 there is no selection between prey. With ε = 0.75 or 0.25, the ciliate
preferentially selects NCIB and VS NAP, respectively.
the system, causing organic contaminant concentration to
rebound back in the environment.
Effects of floc formation
Surprisingly, the simulations demonstrated that there was
no visible difference in predicted naphthalene concentra-
tion or VS NAP and ciliate levels when there were dis-
persed NCIB cells compared to the case of floc formation
inaCMFR(resultsnotshown).Thisislikelyduetothefact
that substrate responds more strongly to the fast-growing
VS NAP. In turn, VS NAP levels increase by an order
of magnitude leading to a growth response by the ciliate
predator. It is likely however, that a difference would have
occurred if the fast-growing VS NAP formed flocs because
S levels respond more strongly to this species.
Interestingly, there is a dramatic change in the taxonom-
ical structure of the bacterial community when flocs form.
When NCIB exists as dispersed cells, it rapidly decreases to
extinction. In contrast, when NCIB forms flocs, the bacte-
rial community consists of both VS NAP as well as NCIB
primarily in the form of flocs. Even when NCIB cells form
flocs, there is no significant difference (i.e., nearly overlap-
ping results) in the utilization of naphthalene because the
growth rate and yield of NCIB floc is very low, and thus
does not significantly change the naphthalene utilization
rate. Thus,flocsperform the functionofrefugeand prevent
the extinction of NCIB.
In marked contrast, the formation of flocs by NCIB
changes both the biomass and substrate levels in a batch
reactor (results not shown). When there was no floc
formation, biomass extinction and decay occurs and the
organic contaminant (naphthalene) persists in the envi-
ronment. However, when NCIB forms flocs, they keep the
naphthalene concentration low in the environment as they
are guarded against predation. Then, as NCIB floc lev-
els increase by several orders of magnitude, the naphtha-
lene solubilization rate becomes limiting and total NCIB
levels reach 100 times initial values. Ciliates decrease at a
very slow rate subsisting on the remaining dispersed NCIB
cells.

Page 12

1402
Mittal and Rockne
10-6
10-4
10-2
100
102
104
106
0 100200
Time (d)
300 40050
Normalized Ciliates
0
0.2
0.4
0.6
0.8
1
1.2
0100 200
Time (d)
300 400500
Substrate
10-6
10-4
10-2
100
102
104
106
0 100200
Time (d)
300400 50
Normalized NCIB
10-6
10-4
10-2
100
102
104
106
0100 200
Time (d)
300400500
Normalized VS NAP
ε= 0.5ε= 0.5ε = 0.75ε = 0.75ε = 0.25ε = 0.25
a)
b)
c)
d)
Fig. 7. Effects of selective predation by ciliates on the relative abundance of A) substrate, B) NCIB, C) VS NAP, and D) ciliates in a
batch reactor when bacteria were grown on naphthalene. With ε = 0.5 there is no selection between prey. With ε = 0.75 or 0.25, the
ciliate preferentially selects NCIB and VS NAP, respectively.
Interestingly,thesystembehaviorisquitedifferentforthe
case of NCIB floc formation compared to selective preda-
tiononVSNAP.RecallinallcasesNCIBgoestoextinction
in the batch system. Floc formation ability appears to pro-
tect the prey to a much greater extent than just preferential
predation.This is explained by thefact that floc refuge pro-
tectsabsolutely,independentofpredatorlevels.Incontrast,
selective predation only protects absolutely at low predator
levels.
Effects of floc formation coupled with selectivity
and competitive interference
Several insights into the interrelationships between selec-
tive predation, competitive interference and floc formation
as a defense mechanism against predation emerge from the
observed behavior of the most complex (and realistic) sys-
tem studied in comparison with other modeling studies in
the literature and established models in biochemical engi-
neering applications.[33,34]In a CMFR, the most sensitive
parameteristheflocformationdefensemechanismadopted
by NCIB, followed by the interference effect of NCIB on
VS NAP and selective predation by ciliates (Fig. 8). For-
mation of flocs by NCIB allows the two bacterial species to
co-exist together along with the ciliates but does not make
a significant difference on the naphthalene utilization rate
by the bacterial species (Fig. 8, circles vs. squares).
We can see nearly coincident lines for circles and squares
for substrate and both VS NAP and ciliates. When NCIB
inhibits the growth of VS NAP but was a preferred prey for
ciliates, the bacterial community is dominated by VS NAP
andNCIB exists onlyin the form offlocs that are protected
againstpredation.However,flocNCIBgraduallydecreases
in a first-order rate and eventually becomes extinct. Thus,
both competitive inhibition of VS NAP together with the
defense mechanism of floc formation employed by NCIB
were not enough to counteract the preferential predation
of NCIB by the ciliate.
In contrast, when the competitive interference effect of
NCIB on VS NAP was 50% but VS NAP is the preferred

Page 13

Multi-trophic interactions in microbial food webs
1403
Fig. 8. The effects of floc formation coupled with interference effect and selectivity on the relative abundance of A) substrate, B) Total
NCIB, C) Dispersed NCIB, D) Floc NCIB, E) VS NAP and F) ciliates in a CMFR when bacteria were fed with naphthalene.
prey by a 3:1 ratio (ε = 0.25), the bacterial community
structureshiftsandbecomesdominatedbyNCIBwithfluc-
tuationsinVSNAPandciliateabundance.Allthreespecies
co-exist in the environment, causing maximum utilization
of organic contaminant (naphthalene). Thus, in a CMFR,
the selective predation by predators is an important fac-
tor determining the utilization of substrate by bacterial
species.
In a batch reactor, the most important factor affecting
the utilization of naphthalene was the formation of floc by
NCIB and the preference of ciliates for their prey (Fig. 9).
When there was no floc formation, both NCIB and VS

Page 14

1404
Mittal and Rockne
Fig. 9. The effects of floc formation coupled with competition and selectivity on the relative abundance of A) substrate, B) Total
NCIB, C) Dispersed NCIB, D) Floc NCIB, E) VS NAP and F) ciliates in a batch reactor when bacteria were fed with naphthalene.
NAP becomes extinct and the organic contaminant persist
in the environment. Ciliate levels decrease due to endoge-
nous decay. However, when NCIB forms flocs, NCIB exists
in the environment as it is guarded against predation and
is responsible for naphthalene utilization. However, naph-
thalene utilization is not significantly affected with any in-
terference of NCIB on VS NAP or selective predation by
ciliates.IncontrasttotheCMFRcase,flocNCIBandciliate
levels are insensitive to inhibition and selective predation
in the batch system. But floc formation is a very sensi-
tive parameter in a batch system in contrast to a CMFR
system.

Page 15

Multi-trophic interactions in microbial food webs
1405
Conclusions
In all of the systems simulations in the present study, the
presenceofthepredatorundercertainconditionscanresult
in the stable coexistence of two prey species which would
not occur in the absence of predation. Further, this co-
existence in many cases resulted in the enhancement of the
naphthalene degradation rate. Co-existence depends upon
the difference in biokinetic or morphological properties of
the prey species. Selective predation by ciliates and the de-
fense mechanisms adopted by prey are important factors
in determining the taxonomical structure of the bacterial
community, which in turn affects the bioremediation pro-
cess.
Competitive interference of one bacterial species by a
competitor for the same resource is also an important fac-
tor in determining the microbial community structure of
the system. As we have seen in our simulations, floc for-
mation by NCIB allows co-existence with VS NAP along
withtheciliatesinbothbatchandCMFRsystems.Thisco-
existence of predation-resistant bacteria results in reducing
the oscillations of substrate in response to decreases in the
non-resistantbacteriainresponsetociliateincrease.Thisis
an important implication for bioremediation applications
where effluent standards must be met. Keeping the sub-
strate level below this standard is of utmost importance
and a simple view that predation increases degradation is
not sufficient to adequately safeguard against concentra-
tion oscillations exceeding standards.
Most macroscopic predator-prey systems studied in na-
turewithobservedco-existenceoftwopreyspeciestypically
are reported to result from differences between the prey
competitors in resource use. In our simulations of a micro-
bial ecosystem, it is not only the partitioning of resource
use alone (or predation alone) that allows the co-existence
of two prey species together, but rather both mechanisms
operating simultaneously. Thus, these models predict sim-
ilar results as are found in experimental studies of macro-
scopic predator-prey ecosystems; that grazing by protozoa
may enhance the process of bioremediation under certain
conditions and that predation plays the dominant role in
determining the structure of the bacterial community.
Acknowledgments
This project was funded by Grant OCE-0120453 from the
National Science Foundation.
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