1
Supplemental Materials
2
Table of Contents
3
4
5
6
7
8
9
Dynamic Multi-species Metabolic Modeling framework ............................................ 2
10
11
12
13
14
15
16
17
18
19
Modeling Subsurface Iron-Reducing Community ...................................................... 12
20
21
22
23
Parameter Sensitivity Analysis ......................................................................................... 20
24
List of Assumptions ............................................................................................................... 22
25
DMMM and the Prediction of Metabolic States ........................................................... 25
26
Supplemental Figures .......................................................................................................... 26
27
28
References ................................................................................................................................ 28
The formulation of the DMMM framework ............................................................................... 2
Sample Implementation of the DMMM framework ................................................................ 5
Advantage of the DMMM framework ........................................................................................... 8
DMMM vs. Monod-kinetic Model .............................................................................................................8
DMMM vs. Stolyar Model .............................................................................................................................9
DMMM vs. Experimental Studies .......................................................................................................... 10
Using DMMM to model Rhodoferax and Geobacter Species .............................................. 12
Nutrient Uptake Parameters .................................................................................................................. 13
Simulation of Cell-Death ............................................................................................................... 16
List of Simulation Parameters..................................................................................................... 17
Acetate Uptake Parameters .................................................................................................................... 17
Ammonium Uptake Parameters............................................................................................................ 17
Fe(III) Uptake Parameters....................................................................................................................... 18
Simulations under Natural Conditions ............................................................................................... 18
Simulations During Acetate Addition ................................................................................................. 19
Ammonium Affinity......................................................................................................................... 20
Rhodoferax’s Fe(III) Affinity......................................................................................................... 20
Rhodoferax’s Acetate Affinity ...................................................................................................... 21
29
1
1
Dynamic Multi-species Metabolic Modeling framework
2
The formulation of the DMMM framework
3
A community metabolic model must account for the metabolic exchanges
4
between species and with the environment, as well as the changes in biomass of the
5
modeled species. The Dynamic Multi-species Metabolic Modeling (DMMM) framework
6
extends the dynamic flux balance analysis (dFBA) formulation to the community realm.
7
A mathematical formulation of the DMMM framework describes a community of N
8
microbial species coexisting in an environment containing MEX metabolites.
9
10
The growth rate (dX/dt) of every microbial species in the community is given by:
11
12
dX j
dt
 jX j
(1)
13
 14
15
The consumption/production rate (dS/dt) of every metabolite in the environment is given
by:
16
17
N
dSi
  j 1 Vij X j
dt
(2)
18
 19
Here, Xj is the biomass of the jth species in the community; Si is the concentration of the
20
ith metabolite in the environment. The specific growth rate (μj) of the jth microbial
21
species, and Vij , the specific consumption/production rate of the ith metabolite due to the
22
actions of the jth microbial species, are calculated using the FBA:

2
1
Maximize  j  c T v j
2
subject to A j v j  0
(3)
v j min  v j  v j max

3
1  i  M EX (number of metabolites)
1  j  N (number of microbial species)
4

5
In Equation Set 3, cT is the objective function; in our simulations, growth
6
maximization is used as the objective function. Aj is the stoichiometric matrix of the jth
7
microbial species. vj is the reaction flux vector of the jth microbial species. vjmax and vjmin
8
are the flux capacity constraints of the jth microbial species based on the corresponding
9
genome-scale model. For the components of vjmax and vjmin corresponding to external
10
metabolites, the uptake/production constraints (Vjmax,Vjmin) to these fluxes can be
11
calculated based on the environmental concentration of these metabolites, using either the
12
On/Off method (if the uptake kinetics are not available) or the Michaelis–Menten kinetics
13
method (if kinetics are available) . It is important to note that a separate FBA model is
14
used for each microbial species in the community – N FBA models are required for a
15
community of N member species. The flux constraints and the reaction network itself
16
forms a viable solution space, and the solution in this space where the objective function
17
(specific growth rate) is maximal is selected by linear programming. If no viable optimal
18
solution is found for species j, then it is concluded that species j does not have sufficient
19
nutrients to survive at this time, and Equation 8 is used to calculate the death rate (as a
20
negative specific growth rate).
3
1
By integrating the growth rates of all microbial species within the community, as
2
well as the production/consumption rates of all metabolic species in the environment, the
3
DMMM framework can dynamically predict the temporal changes in metabolite and
4
biomass concentrations in a complex microbial community.
5
A small sample implementation of the DMMM framework is included in the next
6
section to further illustrate the simulation process. The DMMM framework is
7
implemented in MATLAB as an add-on to the COBRA toolbox (Becker et al., 2007).
8
This allows the user to easily incorporate new species into the DMMM framework. The
9
MATLAB code for the DMMM framework can be downloaded from Supplemental
10
Materials.
11
12
4
1
Sample Implementation of the DMMM framework
2
A sample implementation of the DMMM framework is provided here to clarify the
3
algorithm.
4
consisting of two microbial species, A and B, and three substrates, Met1, Met2, Met3
5
(Figure S1). The numbers of microbial and metabolic species are arbitrary in this
6
example. The maximal numbers of microbial and metabolic species depend on the
7
limitation of the computational hardware.
8
simulation step size (hrs) is given, this particular implementation of the DMMM
9
framework execute the following routines during each simulation step:
This sample implementation assumes the existences of a community
After a simulation length (hrs) and a
10
11
R1:
The concentration of Met1, Met2, and Met3 are used to calculate the upper and
12
lower constraints to V1A, V2A, V3A, V1B, V2B, and V3B, where Vij represent the ith
13
reaction flux of the species j. Two calculation methods are commonly used:
14
i. On/Off methods
15
if [Meti] > 0, then -∞< Vij <∞
16
if [Meti] <= 0, then Vij =0
17
18
j. Michaelis–Menten kinetics
v iconstraint 
19
Vi,max  Si
Si  K i s
20

5
1
R2:
The FBA models of species A and B calculates the specific growth rates, μ A and
2
μB, as well as the reaction fluxes V1A, V2A, V3A, V1B, V2B, and V3B. The models
3
can be described by the following equations.
Maximize  j  c T v j
subject to A j v j  0
4
v j min  v j  v j max
1  i  M EX (number of metabolites)
5

1  j  N (number of microbial species)
6
The constraints to the reaction fluxes (including the uptake constraints) and the
7
 reaction network itself forms a viable solution space, and the point in this space
8
where specific growth rate is maximized is selected using linear programming. If
9
the linear programming method provides a solution, then continue to routine R3.
10
If the linear program method fails for species j (indicating that the cells does not
11
have the required nutrients to survive under the conditions at this time), then a
12
special cell-death routine RD is executed to calculate the rate of death rd of the
13
species j, and μj is set to rd.
14
15
R3:
The rate of change in the biomass of A and B are calculated with the equation:
dX j
16
dt
 jX j
Calculate ∆Xj by integrating dXj/dt over the simulation step.
17
 Calculate the new Xj at the end of the simulation step with Xj new = Xj old +∆Xj.
18
19
20
21
R4:
The rate of change in the concentration of external metabolite i is with the
equation:
6
N
dSi
  j 1 Vij X j
dt
1
Calculate ∆Si by integrating dSi/dt over the simulation step.
2
 Calculate the new Si at the end of the simulation step with Sinew = Siold +∆Si.
3
4
Only the rates of change of external metabolites are integrated since all internal
5
metabolites still follow the internal steady state assumption.
6
7
RD:
The cell death RD routine is a special user-defined routine that is called upon
8
when the environmental concentrations of substrates are insufficient to sustain the
9
current biomass concentration of the organism. This routine is flexible and can be
10
redefined for each individual organism to reflect its specific mechanism of cell-
11
decay. The RD routine produces the rate of cell death rd, which should be
12
considered a negative growth rate. The specific method used to calculate rd is
13
described in the main text. After completion of RD, return to R3.
14
15
16
After routine R4 is completed, time advances one step-size. The routine R1 is initiated
17
again. This continues until the simulation length is reached. At each time point, the flux
18
constraints to each organism varies base on the substrate concentration at that particular
19
time, and leading to dynamic variations in the growth rate. This procedure is illustrated
20
in Figure S1.
21
22
7
1
Advantage of the DMMM framework
2
The usage of the DMMM framework to model microbial communities holds significant
3
advantages over the traditional Monod-kinetic models, the Stolyar community metabolic
4
model (Stolyar et al., 2007) mentioned in the main text, as well as pure experimental
5
methods.
6
DMMM vs. Monod-kinetic Model
7
The Monod-kinetic model can model relatively simple metabolism quite well. For
8
example, if an organism is treated as having only one limiting substrate, S, then the
9
organism’s growth with respect to S can be modeled fairly accurately by:
10
   max 
[S]
[S]  Ks
11
If an organism is treated as having two limiting substrates, S1 and S2, then the

12
organism’s growth can be modeled with:
13
   max 
[S1 ]
[S2 ]

[S1 ]  K s1 [S2 ]  K s2
14
For an organism with i limiting substrates, the organism’s growth is modeled with the

15
General Monod Model:
16

i
max

1
[Si ]
[Si ]  K si
17
For example, if we assume that each of the substrates are available at their saturation

18
concentration (Ks), the Monod model would predict a growth rate of 1/2n of the
19
maximum, even though it is clear that the substrate concentrations are sufficient to allow
20
the organism to grow at ½ the maximum. Moreover, the yield in the presence of multiple
8
1
substrates needs to be experimentally determined for each combination, as there are no
2
known mechanisms to compute the yields accurately for different metabolic states. Since
3
n is generally related to the metabolic complexity, the Monod-kinetic model does not
4
scale up well with complex metabolisms. Realistically, prediction accuracy often
5
becomes unacceptable when i > 2. Since the DMMM framework is based on constraint-
6
based models, it is capable of handling significantly more complex metabolisms. For
7
example, the Geobacter sulfurreducens model used in this paper contains 727 reactions,
8
55 of which are exchange reactions (i = 55).
9
metabolic network of Geobacter has many modes of operation such acetate-limiting
10
ammonium-utilization mode, iron-limiting ammonium-utilization mode, acetate-limiting
11
nitrogen fixation mode, iron-limiting nitrogen fixation mode. The DMMM framework
12
automatically selects the modes of operations based on the substrate concentrations at
13
each time point. This is unachievable for traditional models.
14
It is also important to note that the
DMMM vs. Stolyar Model
15
Stolyar et al. published the first constraint-based metabolic model of a mutualistic
16
microbial community in 2007 (Stolyar et al., 2007). In the Stolyar model, the CBMs of
17
Desulfovibrio vulgaris and Methanococcus maripaludis are directly connected.
18
authors assumed that the species are interdependent, thereby justifying their usage of a
19
pair of arbitrary biomass flux weights (authors used 10:1, 1:1, 1:10) as the objective
20
function.
21
Another caveat of this model is that it cannot predict the dynamic shifts in population and
22
their metabolite concentrations. While this approach may be appropriate when the
The
This objective function is inappropriate for most microbial communities.
9
1
microorganisms are inter-dependent, it is inappropriate in ecological settings where the
2
community composition is dynamic.
3
In comparison, the DMMM framework does not rely on arbitrary objective function –
4
instead, the FBA problems representing each organisms are solved separately, allowing
5
the usage of more established objective functions such as maximization of biomass flux.
6
The DMMM framework is not restricted to mutualistic communities; it is capable of
7
predicting the dynamic shifts in community composition and metabolites’ concentration.
8
9
DMMM vs. Experimental Studies
10
While no model can ever achieve the accuracy of real experimental studies, usage of
11
metabolic modeling has proved to be a valuable analytical tool. The DMMM framework
12
allows scientists to consider thousands of possible reactions and metabolites
13
simultaneously, this together with necessary experimental work, can provide significant
14
insights that are otherwise overlooked due to the limitation on the processing capacity of
15
the human brain. Furthermore, the DMMM framework allows scientists to observe the
16
emergent properties of the complex microbial community, which are difficult (if not
17
impossible) to predict without.
18
The DMMM framework allows complex experiments to be performed in silico prior to
19
real experiments. These simulations can guide the formation of new hypothesis, which
20
allows in situ and in vivo experiments to be performed selectively. Furthermore, this
21
approach allows scientists to test otherwise difficult-to-prove hypothesis. For example, a
22
scientist designing an environmental biotechnology strategy might want to study the
10
1
effect of increasing groundwater flow rate, which would be very difficult to evaluate in
2
situ.
3
4
11
1
Modeling Subsurface Iron-Reducing Community
2
Using DMMM to model Rhodoferax and Geobacter Species
3
The DMMM framework was used to evaluate competition between Geobacter and
4
Rhodoferax species in anoxic environments in which Fe(III) is the primary electron
5
acceptor available to these organisms (Figure 2). This represents conditions in uranium-
6
contaminated subsurface environments, because Fe(III) is expected to be the predominant
7
electron acceptor under anoxic conditions (Lovley, 1991) and the concentration of U(VI)
8
contaminants in the groundwater is not significant enough to sustain growth as the sole
9
acceptor (Finneran et al., 2002). While the concentration profiles of all metabolites that
10
are either secreted into or consumed from the environment and the biomass of the
11
organisms in the community can be calculated, our study focuses on acetate, and Fe (III),
12
which are the electron donor and acceptors of these two organisms, as well as
13
ammonium, which can significantly affect growth yield (Figure 2).
14
Geobacter sulfurreducens and Rhodoferax ferrireducens served as models for
15
Geobacter and Rhodoferax species because genome-scale metabolic models of these
16
organisms are available (Mahadevan et al., 2006; Risso et al., 2009; Sun et al., 2009).
17
These models have been used to successfully predict the biomass yield of these two
18
species under multiple physiological conditions (Mahadevan et al., 2006; Risso et al.,
19
2009; Sun et al., 2009; Segura et al., 2008). The energetic of G. sulfurreducens and R.
20
ferrireducens has been discussed in detail (Mahadevan et al., 2006; Risso et al., 2009).
21
The ATP maintenance requirement value for G. sulfurreducens and R. ferrireducens was
22
set to 0.45 mmol ATP/gDW (Mahadevan et al., 2006; Risso et al., 2009; Sun et al.,
23
2009).The simulations were performed using the maximization of biomass yield as a
12
1
cellular objective (Varma & Palsson, 1994; Varma & Palsson, 1995). As in the dynamic
2
FBA (dFBA) formulation (Mahadevan et al., 2002), the nutrient uptake/production flux
3
constraints (mmol/gDW/hr) used in the FBA models of the individual species are
4
calculated using the Michaelis-Menten expressions.
5
6
7
Nutrient Uptake Parameters
The acetate transport kinetics of G. sulfurreducens have been determined by
8
measuring [14C]-labeled acetate uptake (Richter et al., Submitted).
9
acetate uptake mechanisms, each with different saturation constants, Ks (mM), and
10
specific uptake rates, Vmax, were identified. All three of these uptake systems were
11
observed to be up-regulated under acetate-limited growth, suggesting that they are co-
12
expressed (Risso et al., 2008). Hence, the overall acetate consumption rate of G.
13
sulfurreducens was calculated using the experimentally identified uptake parameters for
14
these uptake systems (Equation 4).
Three different
15
The Vmax for acetate uptake of R. ferrireducens was calculated from regression
16
analysis of batch growth data (Finneran et al., 2003). We have performed BLAST
17
analysis on the Rhodoferax ferrireducens genome against the acetate permease gene
18
(ActP) in E. coli and four predicted acetate transporter genes (GSU2352, GSU1070,
19
GSU1068, GSU0518) in Geobacter sulfurreducens.
20
ferriducens Rfer3782 gene showed similarity to all these acetate transporter genes, but is
21
most similar to E. coli’s ActP gene. Therefore, we assumed the Ks of Rhodoferax on
22
acetate to be the same as that of E. coli, 0.0054 mM (Gimenez et al., 2003) (Equation 5).
23
In the following equations, [S] represents the concentration of substrate S, and VSA
We found that the Rhodoferax
13
1
represents the uptake rate of substrate S by organism A (Gs or Rf for G. sulfurreducens
2
and R. ferrireducens respectively).
3
4
5

Gs
VAc

13.3[Acetate]
2[Acetate]
2.67[Acetate]


[Acetate]  0.77 [Acetate]  0.167 [Acetate]  0.012
(4)
Rf
VAc

1.71[Acetate]
[Acetate]  0.0054
(5)
6
7
Ammonium serves as a nitrogen source for G. sulfurreducens and R. ferrireducens,
8
and it was assumed that maximum ammonium uptake rates were equal to the
9
stoichiometric ammonium requirement at their respective maximum growth rates, and is
10
calculated with FBA.
While the Km value of the ammonium transport systems in
11
Geobacter and Rhodoferax have not be experimentally characterized, the Km value of the
12
AMT ammonium transport system (used by Geobacter species) commonly ranges
13
between 1 – 50 μM (Winkler, 2006). Raey et al. has reported the Km value for nine
14
microbial species ranges between 5 – 74.4 μM, with majority at the range between 20 –
15
30 μM (Reay et al., 1999). Based on these reasons, the Km values for ammonium was
16
assumed to 25 μM for both of these organisms. (Equation 6, 7)
17
18
19

Gs
VNH

4
0.468[Ammonium]
[Ammonium]  0.025
(6)
Rf
VNH

4
0.127[Ammonium]
[Ammonium]  0.025
(7)
20

14
1
Fe(III) serves as the extracellular electron acceptor of both Geobacter and
2
Rhodoferax species. Chemostat data showed that the Km for Geobacter Fe(III) transport
3
is 1 mM, and we have calculated that the maximal Fe(III) uptake rate of Geobacter to be
4
568 mmol/gDw/hr.
5
Rhodoferax is assumed to be the same as that of Geobacter’s. (Equation 8, 9).
6
7

8
The affinity and the maximal rate of the Fe(III) transport in
Gs
VFe(III)

568[Fe(III)]
[Fe(III)] 1
(8)
Rf
VFe(III)

568[Fe(III)]
[Fe(III)] 1
(9)
For both organisms, the maximization of biomass is assumed to be the optimization
9 objective function. This is the most commonly used objective function for modeling
10
microbial growth; however, there are other possibilities (Schuster et al., 2008; Carlson,
11
2007; Molenaar et al., 2009; Hoffmann & Holzhutter, 2009).
12
15
1
Simulation of Cell-Death
2
There is no known mechanism for dissimilatory Fe(III)-reducing microorganisms to
3
generate ATP from acetate utilization once Fe(III) has been depleted in the subsurface.
4
Under such nutrient limitation conditions, energy required for sustaining metabolic
5
activity without any growth (non-growth ATP maintenance requirements) cannot be met
6
leading to cell death (Pirt, 1982; Russell & Cook, 1995; Rittmann & McCarty, 2001).
7
Similarly, insufficient electron donor can also lead to cell death. Traditionally, the rate of
8
cell death, rD, due to failure to meet maintenance energy requirements is modeled using
9
the following equation (Pirt, 1982; Russell & Cook, 1995):
10
r D  (q S  m S )Y
11
(10)
12
13
Here, qS (mmol S/gDW/hr) is the uptake rate of limiting substrate S, mS (mmol
14
S/gDW/hr) is the uptake rate of substrate S required to maintain the current biomass, Y is
15
the biomass yield on substrate S. When qS is less than mS, rD becomes negative (death
16
rate).
17
In metabolic models, the non-growth-related maintenance energy is represented
18
with an ATP maintenance flux (mATP) with the unit mmol ATP/gDW/hr. mS is calculated
19
by multiplying the mATP by the number of ATP produced per acetate (RATP/S). RATP/S can
20
be found using FBA. Finally, Equation 8 is used to calculate rD.
21
16
1
List of Simulation Parameters
2
Acetate Uptake Parameters
G. sulfurreducens
Ks,1
0.012 mM
Ks,2
0.017 mM
Ks,3
0.78 mM
Vmax,1
2.7 mmol/gDW/hr
Vmax,2
2 mmol/gDW/hr
Vmax,3
13 mmol/gDW/hr
(Richter et al., Submitted; Esteve-Nunez et al.,
2005)
R. ferrireducens
Ks
Vmax
0.012 mM
Assumed to be the same as G. sulfurreducens
1.7 mmol/gDW/hr
(Finneran et al., 2003)
3
4
Ammonium Uptake Parameters
G. sulfurreducens
Ks
0.025 mM
Assumed based on literature values.
(Reay et al., 1999)
Vmax
0.47 mmol/gDW/hr
Calculated by FBA
R. ferrireducens
Ks
0.025 mM
Assumed based on literature values.
(Reay et al., 1999)
Vmax
0.13 mmol/gDW/hr
Calculated by FBA
5
17
1
Fe(III) Uptake Parameters
G. sulfurreducens
Ks
1 mM
Vmax
568 mmol/gDW/hr
(Esteve-Nunez et al., 2005)
Calculated from chemostat data.
(Esteve-Nunez et al., 2005)
R. ferrireducens
Ks
1 mM
Vmax
568 mmol/gDW/hr
Assumed to be same as Geobacter.
Calculated from chemostat data.
(Esteve-Nunez et al., 2005)
2
3
Simulations under Natural Conditions
[Fe(III)]init
10 mmoles/l
(Anderson et al., 2003; Vrionis et al.,
2005; Yabusaki et al., 2007; Petrie et al.,
2003)
Acetate Turnover
0-0.54 μM/hr
Rate
(Balba & Nedwell, 1982; Chapelle &
Lovley, 1990; Crill & Martens, 1986;
Hansen et al., 2001; Kuivila et al., 1989;
Lovley & Klug, 1983; Lovley & Klug,
1986)
Ammonium Concentration
0 – 400 μM
(Mouser et al., 2009)
[G. sulfurreducens]init
105 cells/L
(Holmes et al., 2007)
[R. ferrireducens]init
105 cells/L
(Holmes et al., 2007)
Dilution rate
0.00141 hr-1
Calculated based on geometry
18
(Anderson et al., 2003; Petrie et al.,
2003; Vrionis et al., 2005; Yabusaki et
al., 2007)
1
2
Simulations During Acetate Addition
[Fe(III)]init
10 mM
(Anderson et al., 2003; Petrie et al.,
2003; Vrionis et al., 2005; Yabusaki et
al., 2007)
Acetate Injection Rate
4.2 - 7 μM/hr
(Anderson et al., 2003; Vrionis et al.,
2005)
[NH4]init (excess)
400 μM
(Mouser et al., 2009)
[NH4]init (limiting)
5 μM
(Mouser et al., 2009)
[G. sulfurreducens]init
105 cells/L
(Holmes et al., 2007)
[R. ferrireducens]init
105 cells/L
(Holmes et al., 2007)
Dilution rate
0.00141 hr-1
Calculated based on geometry
(Anderson et al., 2003; Vrionis et al.,
2005)
3
4
19
1
Parameter Sensitivity Analysis
2
Ammonium Affinity
3
We have performed sensitivity analysis on the ammonium uptake affinity parameters by
4
performing the acetate injection simulations under both high and low ammonium
5
conditions using various ammonium Km values.
6
We first compared the acetate amendment simulations under both high (400 μM) and low
7
(5 μM) ammonium conditions using ammonium Km of 1, 10, 50, 100, 500 μM for both
8
organisms (Figure S2, S3). Then, we compared the acetate amendment simulations under
9
both high and low ammonium conditions when Geobacter and Rhodoferax have 50 times
10
difference between their Km values (50 μM vs 1 μM, 1 μM vs 50 μM) and when they
11
have equal Km values (25 μM vs 25 μM) (Figure S4, S5).
12
These comparisons showed that the community composition is insensitive to the
13
organisms’ ammonium affinity under high ammonium condition, and is only minimally
14
affected by the ammonium affinity when the Rhodoferax’s affinity is 50 times greater
15
than that of Geobacter’s.
16
17
Rhodoferax’s Fe(III) Affinity
18
Since we have assumed Rhodoferax Fe(III) uptake kinetics to be the same as that of
19
Geobacter’s, we performed sensitivity analysis on the Vmax and the Km of Rhodoferax
20
on Fe(III).
21
ammonium conditions using different values of Rhodoferax Fe(III) Km (10 times lower,
22
10 times higher, and equal to that of Geobacter’s).
We compared acetate injection simulations under both high and low
Then, we compared acetate
20
1
simulations under both high and low ammonium conditions using Rhodoferax Fe(III)
2
Vmax 10 times lower, 10 times higher, and equal to that of Geobacter’s.
3
simulations showed that the dynamic behavior of the community is not changed by the
4
variations in these parameters (all curves overlap; simulations not shown).
These
5
6
Rhodoferax’s Acetate Affinity
7
Since we have assumed Rhodoferax Acetate affinity to be the same as that of E.coli’s, we
8
performed sensitivity analysis on this parameter.
9
simulations using different acetate affinities for Rhodoferax ranging from the lowest
We compared acetate amendment
10
Geobacter acetate affinity (777 μM) to the highest E. coli affinity (5.4 μM).
The
11
simulations showed that under ammonium poor condition, the community composition is
12
insensitive to this parameter; under ammonium rich condition, the community
13
composition is only minimally sensitive to this parameter (Figure S6, S7).
14
21
1
2
List of Assumptions
3
This section summarizes the assumptions made in our simulation.
4
5
1. Cells were assumed to be in internal steady state. This is the basic assumption of
constraint-based metabolic modeling.
6
7
8
2. The relationship between substrate concentration and the upper limit of substrate
uptake rates follow Michaelis-Menten relationship.
9
a. Acetate uptake Ks of Rhodoferax ferrireducens is the same as Geobacter
10
sulfurreducens, because they must compete for acetate in the same
11
environment.
12
13
b. Ammonium uptake Ks of both Rhodoferax ferrireducens and Geobacter
sulfurreducens are the same as that of Escherichia coli.
14
15
16
17
3. Our simulations model uranium-contaminated subsurface sediment as a
18
chemostat. This implies the assumption of spatial homogeneity, as well as greatly
19
simplifies the transport process. However, our ability to accurately predict the
20
trend shift in community composition suggests that biological interactions are the
21
dominant factor in the Rifle system.
22
4. In the Rifle site, bromide tracer is injected along-side acetate during
23
bioremediation for analytical purpose. The half-life of the bromide tracer after the
22
1
injection stops range between 10 to 50 days (Yabusaki et al., 2007). Assuming
2
the decay of bromide is a first-order reaction, the in situ dilution rates are
3
calculated to be between 0.0029 hr-1 and 0.0006 hr-1 by solving the first order rate
4
equation using the following equations:
dS Br
  D  S Br
dt
ln( S Br , final / S Br ,initial)
D
t final  tinitial
5
D
ln( 2)
thalflife
6
We chose 0.0014 hr-1 as the dilution rate, which is representative of the Rifle
7
system.
8
5. The physical density (mass/volume) of the intracellular contents of G.
9
sulfurreducens and R. ferrireducens are assumed to be the same. The average
10
mass of G. sulfurreducens (g/cell) is measured experimentally. The average mass
11
of R. ferrireducens is calculated based on volume ratio of the two cells. The
12
volumes of the cells are calculated based on the published cell dimensions
13
(Finneran et al., 2003; Caccavo et al., 1994). Cells are assumed to be rod-shaped.
14
6. Growth-independent maintenance requirements of both Geobacter sulfurreducens
15
and Rhodoferax ferrireducens were extrapolated from experimental data at low
16
growth rate, and hence, we believe this is appropriate for modeling the observed
17
growth rates. However, we have performed additional simulations based on a
18
recent publication suggesting that Geobacter metallireducens (Lin et al., 2009)
19
could have much lower maintenance energy requirement. These simulations with
20
the lower values does not change the overall competition dynamics significantly
23
1
as Rhodoferax maintenance energy requirement is assumed to be same as the
2
Geobacter species. We have also evaluated the case where Rhodoferax species
3
has a higher maintenance energy requirement. However, in this case, the
4
simulations cannot explain the observed dominance of Rhodoferax species in
5
Rifle site under natural conditions in ammonium rich environments. Therefore,
6
Rhodoferax maintenance energy requirement is likely to be either lower or similar
7
to the Geobacter species.
8
9
24
1
2
DMMM and the Prediction of Metabolic States
3
growth of Geobacter sulfurreducens alone under ammonium excess and limiting
4
conditions. Under ammonium limiting conditions, the final biomass is about 30% lower
5
than the final biomass under ammonium excess conditions, which is reflective of the cost
6
of nitrogen fixation. This shift in metabolic state also lead to changes in acetate and
7
Fe(III) utilization (Figure S8). Furthermore, we are able to see an acetate-limited phase
8
where the growth rate is significantly reduced (apparent in the ammonium-excess case,
9
between 250-350 hrs) as well as a iron-limited death phase (350-500 hrs) (Figure S8).
To highlight the model’s ability to identify multiple metabolic states, we simulated the
10
11
25
1
Supplemental Figures
2
Figure S1. The Dynamic Multi-species Metabolic Modeling Framework
3
The DMMM framework consists of four major steps: [1] Calculation of the substrate uptake constraints based on current substrate
4
concentration. [2] Solve the FBA problems for the member species of the community. This generates the specific growth rates and
5
external reaction fluxes of the member species. If the FBA problem is infeasible for one or more of the member species, then a special
6
cell-death simulation routine is used to generate the specific death rate. [3] Calculate dX/dt for each member species. Integrating over
7
this rate to generate the dynamic profile of biomass concentrations. [4] Calculate dSi/dt for each member species. Integrating over
8
this rate to generate the dynamic profile of metabolite concentrations.
9
10
Figure S2. Sensitivity to Ammonium Affinity 1 (Ammonium Rich: 400 μM)
11
The growth of the iron reducers during acetate amendment was simulated using Km values of 1 (blue), 10 (red), 50 (cyan), 100
12
(green), 500 (magenta) μM. The blue and red curves is not visible in some panels because it is covered by the cyan curves.
13
14
Figure S3. Sensitivity to Ammonium Affinity 1 (Ammonium Poor: 5 μM)
15
The growth of the iron reducers during acetate amendment was simulated using Km values of 1 (blue), 10 (red), 50 (cyan), 100
16
(green), 500 (magenta) μM.
17
18
Figure S4. Sensitivity to Ammonium Affinity 2 (Ammonium Rich: 400 μM)
19
The growth of the iron reducers during acetate amendment was simulated using Geobacter and Rhodoferax Km value pairs of (25 and
20
25 μM (blue), 1 and 50 μM (red) , 50 and 1 μM (green)).
21
22
Figure S5. Sensitivity to Ammonium Affinity 2 (Ammonium Poor: 5 μM)
23
The growth of the iron reducers during acetate amendment was simulated using Geobacter and Rhodoferax Km value pairs of (25 and
24
25 μM (blue), 1 and 50 μM (red) , 50 and 1 μM (green)).
25
Figure S6. Sensitivity to Rhodoferax’s Acetate Affinity (Ammonium Rich: 400 μM)
26
1
The growth of the iron reducers during acetate amendment was simulated using low and high Rhodoferax acetate affinity (Km = 777
2
μM vs. Km = 12 μM). Red line is the low affinity simulation; blue line is high affinity simulation.
3
Figure S7. Sensitivity to Rhodoferax’s Acetate Affinity (Ammonium Poor: 5 μM)
4
The growth of the iron reducers during acetate amendment was simulated using low and high Rhodoferax acetate affinity (Km = 777
5
μM vs. Km = 12 μM). Red line is the low affinity simulation; blue line is high affinity simulation.
6
Figure S8. Growth of Geobacter alone under ammonium-excess and limited
7
conditions
8
The growth of Geobacter alone under ammonium-limiting and excess conditions was simulated to highlight the model ability to
9
predict multiple metabolic states.
10
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