TABLE 1 .
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; Nc → Nc – 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 |
NA, not applicable.
Rules A and B are implemented at every MC step.