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. 2017 Dec 19;8(6):e01466-17. doi: 10.1128/mBio.01466-17

TABLE 1 .

Rules, parameters, and parameter values used in the agent-based model

Rule Biofilm
process
Rule implemented
in model
Parameter value
and rate (per min)
Comment(s)
1 NTHI
replication
NNTHI and concentration of
nutrient (Nc) in a
compartment increases
and decreases by 1,
respectively (NNTHI
NNTHI + 1; Nc
Nc – 1)
NTHI replication rate
(krepli) of 0.0167 NTHI
cells/min (k1 = krepli ×
NNTHI × Nc)
Based on 1 division/60
min (46); for slowdown
of growth rate due to
biofilm aging, we assumed
replication rate in NHTI
biofilm decreased by ½
after 3 days
2 eDNA
production
No. of eDNA strands
(NeDNA) in a compartment
increases by 1 (NNTHI
NNTHI + 1) at rate
of kdnaprod at every
MC step
kdnaprod = 0.003
molecules/min until 72 h
(k2 = kdnaprod)
Rate was calculated using
measurements in reference
47; see also Text S1
3 eDNA diffusion eDNA strands in a
compartment but not
attached to eDNA
network move to
nearest neighboring
compartments with
diffusion rate of
DeDNA
We used DeDNA value of
10 μm2/min (k3 =
DeDNA/l02 × NeDNA;
NeDNA ≡ no. of eDNA
in compartment)
DeDNA calculation
assumes eDNA strands
are 1.8 × 104 bp
(see Text S1 for details)
4 Diffusion of
planktonic NTHI
Planktonic NTHI
(pNTHI) in a
compartment diffuse
to nearest
neighboring
compartments with
diffusion rate DpNTHI
We used DpNTHI of 10
μm2/min (k4 = DpNTHI/l02 ×
NpNTHI; NpNTHI is the
no. of pNTHI cells in a
compartment)
DpNTHI calculation assumes
Stokes-Einstein formula
(48); see Text S1 for details
5 NTHI dispersion NTHI in biofilm in a
compartment (NNTHI)
disperses to
supernatant in same
compartment with
rate of kdispers; if
compartment is part
of eDNA network, rate is 5
times smaller
kdispers is taken to be
0.001 molecules/min
[k5 = kdispers × (NNTHI)2]
NTHI disperses into supernatant;
AI-2-induced quorum sensing along
with Tfp appear to regulate
this effect (34); we
assumed density-dependent
rate to represent positive
feedback in quorum sensing (49);
we hypothesized that dispersion
rate is lower when a compartment
is part of eDNA network;
this can arise due to adherence
of NTHI to eDNA by Tfp as
well as trapping NTHI via
encasement created by
eDNA network; we also
tested a variant of the
model where NTHI
dispersion occurred at
higher rates in
compartments farther from
substrate at z = 0; results
were qualitatively similar
to our model (Fig. S7)
6 eDNA binding eDNA network-bound
strands in a compartment
bind free eDNA strands
in adjacent compartments
that are not part of the
eDNA network
kdnastick = 0.003 [k6 =
kdnastick × NeDNA(network) ×
NeDNA(free); NeDNA(network)
no. of network-bound eDNA
in chosen
compartment; NeDNA(free)
no. of free eDNA in an
adjacent compartment]
See main text, rule ii,
in the section describing
construction of the agent-
based in silico model
7 Tfp-driven NTHI
movement on eDNA
network
NTHI in a
compartment moves
to an adjacent
compartment when
both compartments
belong to the eDNA
network
kTfpdna = 3.12 μm/min
(k7 = kTfpdna × NNTHI)
In biofilms formed by
P. aeruginosa, the bacteria
move on eDNA tracks via
Tfp movements; avg
displacement ≈5 μm/100 s
(3.12 μm/min) (20). It is
currently unknown whether
NTHI moves on eDNA
strands using Tfp.
8 Replication of
planktonic NTHI
NpNTHI and Nc in a
compartment increases and
decreases by 1, respectively
(NpNTHI → NpNTHI + 1;
NcNc – 1)
pNTHi replication rate
(krepli) = 0.0167 NTHI
particles/min (k8 =
krepli × NpNTHI)
Same as rule 1
9 eDNA
production by
planktonic NTHI
Same as rule 2 Same as rule 2 Same as rule 2
10 Nutrient addition At intervals of 16 h
and 8 h, nutrient
densities in all
compartments are
reset to 2 (Nc
Nc = 2)
NAa This rule represents change
of medium in biofilm static
culture every 16 h and 8 h
11 NTHI removal
from supernatant
At intervals of 16 h and
8 h, planktonic NTHI
in each compartment
is removed
(probability of 0.8)
NA This rule represents
removal of NTHI in
supernatant when medium
in biofilm static culture is
replaced every 16 h and 8 h
Ab Mass movement
of NTHI
Excess NTHI cells
above nthres (NNTHI
nthres) in compartment
are transferred to
adjacent
compartment with
room for that
amount; transfer is
done at every MC
step at time interval
Δt of 0.1 min
Transfer of excess NTHI to
neighboring compartments
represents mass movement
of NTHI due to physical
forces between bacteria due
to tight packing of finite-
sized NTHI particles;
similar movements have
been considered in other in
silico biofilm models (50)
Bb Nutrient
diffusion
Nutrient concentration is
homogenized at
every MC step at
time interval Δt of
0.1 min
We assumed nutrient
diffusion (D) of
100–1,000 μm2/s
Nutrient variable in model
represents range of
molecule sizes, from small
metabolites to large
proteins; nutrient particles
travel rate (DΔt)½ of ≈24–
77 μm in Δt, so
homogenization of nutrients
in simulation box (128 μm × 40
μm) is reasonable
a

NA, not applicable.

b

Rules A and B are implemented at every MC step.