6. Investigation of bacterial interactions: Competition by toxin production 71
6.3. Deterministic competition
6.3.1. Experimental competition parameters: Growth rate and toxin
6. Investigation of bacterial interactions: Competition by toxin production
0.0 0.005 0.01 0.1
T1
yfp cei cei
PSOS T2
pMO2
chromosomal DNA
SYFP pMO2
a b
Extinction Coexistence
(10%<C<90%) C/SYFP wins
(C>90%) SRFP wins (C<10%)
CpMO3 SYFP
.00 .25 .50 .75 1.0
Competition outcome
CpMO3 SYFP CpMO3 SYFP CpMO3 SYFP
Figure 6.5.: Alternative competition scenario without toxin release
a The plasmid pMO2 carries the colicin operion in which the cea gene is replaced by a yfp gene. The transformation of pMO2 into the S wild type strain yields the SYFP strain that lyses in response to SOS activation but is unable to release any toxin. bCompetition outcome comparison shows that SYFP (right) performs worse compared to CpMO3 (left) in competition with the SRFP strain due to missing toxin action.
population, on MitC concentration was investigated.
As discussed earlier, the response dynamics of single cells to SOS stress (by MitC) have been investigated previously in liquid conditions using time-lapse microscopy [20]. The individual single cell dynamics led to a collective response that was strongest 75 min after induction and was found to increase with the external stress level (see section 2.2).
In order to verify that these results were also valid under the experimental conditions of the competition experiments on solid growth media, the degree of phenotypic het-erogeneity was assessed using high-resolution microscopy (see 3.5). The results on solid growth medium were qualitatively similar, although lower inducer concentrations yielded similar results compared to liquid conditions (Fig. 6.4 b). Without external inducer a low but steady producer fraction (7.0± 1.5%) was detected. At low inducer concentra-tions, the mean producer fraction increased to 14.5 ± 1.9% (average of 0.005 and 0.01 µg/ml MitC conditions) over the time-course of the experiment and stayed relatively constant. At high induction (0.1 µg/ml MitC), however, a synchronized response peak-ing at 57.8 ±3.2% toxin producers was observed, followed by a collective decrease due to cell lysis.
Applying the phenomenological model from chapter 4, this behavior can be interpreted as the inducer setting the switching rates and thereby altering the steady state of toxin producers r+ds . Without external inducer, the producer fraction stays constant. At low induction, the population can settle to the new steady state. At high induction, however, the switching rate is so large that the switching process eventually drives the system to the absorbing boundary COF F =CON = 0.
To further support the hypothesis that indeed toxin production was responsible for the success of the C strain at intermediate producer fraction, competition experiments were performed in which the C strain was replaced by the SYFP strain unable to produce
6.3. Deterministic competition
the toxin. This SYFP strain contained the colicin E2 operon in which the cea gene was replaced by a yfp gene on the pMO2 plasmid (see Fig. 6.5 a). Consequently, it was able to produce the Cei and Cel proteins upon SOS response but without any toxin released upon lysis. The qualitative competition results (Fig. 6.5 b) clearly showed that in contrast to the C strain, the non-toxic mutant was unable to dominate over the SRFP strain, although it was even faster in growth (see table A.2 in the appendix).
This further supported the hypothesis that the observed shift in competition outcome distribution with varying inducer concentration was due to the change in toxin-producer fraction.
Taken together, at intermediate inducer concentration, there was no significant decrease in growth rate compared to the uninduced case, i.e. the cost of toxin production for the C is sufficiently low. Nonetheless, the increase in toxin producer fraction already cre-ated a sufficiently large toxin action on the S strain such that C could succeed. At high induction however, the production cost was too high and a prolonged toxin benefit could not be established. Therefore, it was hypothesized that only varying the toxin producer fraction should be sufficient to alter the overall competition outcome. In order to inves-tigate the sole influence of a variation of toxin producer fraction without any distorting effects, the computational model (chapter 5) was applied to the C-S interaction.
6.3.2. Simulation parameters: Switching rate, toxin sensitivity/effectivity, and growth rate
In addition to the experiments, the computational model presented in chapter 5 was used to simulate to competition dynamics. For each condition a set of replicate simu-lations was performed. One result of the experimental analysis was that the fraction of toxin producers was mainly responsible for the observed shift in competition outcome with varied inducer concentration. In order to corroborate these findings, the simula-tions were performed for a range of switching rates sC that determined the fraction of toxin producers2. Due to the close relation between sC and the fraction of toxin pro-ducers, both terms are used interchangeably.
However, while the growth rates rC and rS for both strains and the lysis rate dCON of the CON state were known, one remaining free parameter was the toxin sensitivity sS which was hard to determine experimentally. The parametersS combines the toxin effectivity and toxin sensitivity of the susceptible strain S and is therefore interchange-ably called toxin effectivity depending on the focus. In order to take into account its effect, sS was varied in addition to sC simultaneously. As a first result, it is worth
not-2 Please note that in the simulations for this chapter, a different functional relationship between toxin producer fraction and sC was used compared to the definition from chapter 4. F racSS =
CON
CON+COF F = 1+s/ds/d However, this did not change the simulation results qualitatively.
6. Investigation of bacterial interactions: Competition by toxin production
Con +
C
colicin diffusion rC sC
rS
S sS Sstop dCon
Ø Computational model
S dominance
Coexistence
C dominance
Extinction
b a
Figure 6.6.: Computational model
aThe computational model featured reproduction and state switch reactions of bothC(green) and S (magenta) strain as well as lysis of the CON strain. See chapter 5 for details3. b The model could reproduce the four distinct competition outcomes taking into account S (bright magenta),Sstop (dark magenta),C(green), andCON (white) cells. The scale bar corresponds to 1 mm on the computational grid.
ing that the computational model was able to reproduce the four different experimental competition outcomes (Fig. 6.6 b).
The system was simulated for a range ofsC and sS values, generating phase diagrams for each of the four competition outcomes (see Fig. 6.7). Dominance of the C strain was maintained for a broad range of toxin effectivitiessS for intermediate inducer con-centrations. Accordingly, S dominance was most prominent under conditions in which C failed. Similarly, coexistence was mostly found in regions, in which C could not dominate: at low toxin producer fractions or low toxin effectivity. Extinction events occurred under conditions in which toxin is effective and prolonged toxin production is ensured. Despite the capability of the model to generate extinction outcomes, it could not reproduce the high incidence of extinction events seen in experiments at high in-ducer levels. A more detailed model taking into account synchronous toxin responses was able to generate high extinction probabilities. However this will not be discussed in this thesis and the interested reader is referred to the original publication [141].
By comparing the competition outcome of experiments (see Fig. 6.3) and simula-tions (see Fig. 6.8 a), the free toxin effectivity parameter of the simulation was fixed to sS = 1500. Then focusing on the exclusive variation of the switching rate sC, the simulations underlined that only varying the switching rate was sufficient to explain the observed changes in outcome distribution. This will be discussed in more detail in the following.
3 The death reaction of growth inhibited SStop cells was considered in the simulation but with a negligible rate and therefore not shown in the scheme.
6.3. Deterministic competition
S success [%] 0 25 50 75 100
0.0 50.0 99.01
Toxin producer fraction [%]
3.0 1.5 0
Toxin effectivity sS [103]
0 25 50 75 100 C success [%]
0.0 50.0 99.01
Toxin producer fraction [%]
3.0 1.5
Toxin effectivity sS [103] 0
Coexistence [%] 0 25 50 75 100
3.0 1.5
Toxin effectivity sS [103] 0
0.0 50.0 99.01
Toxin producer fraction [%]
Extinction [%] 0 25 50 75 100
3.0 1.5
Toxin effectivity sS [103] 0
0.0 50.0 99.01
Toxin producer fraction [%]
Figure 6.7.:Toxin effectivity sS and switching rate sC parameter variation
The phase diagram for the simultaneous sC and sS parameter variation shows the outcome probability for the four outcomes S and C domination, coexistence, and extinction.
0 50 100
Outcome distributions [%] 0.0 50.0 99.01Toxin producer fraction [%]
0 25 50 75 100
0.0 50.0 99.01
Final fraction of C strain [%]
Toxin producer fraction [%]
a b
Figure 6.8.: Outcomes of switching rate variation for constant sS = 1500
aThe final C strain abundance changes with increasing producer fraction, determined by the switching rate, similar to experiments. b Translating the C strain abundance into distinct outcomes, the change in outcome distribution is even more evident. Color code as in Fig. 6.3 b.
By increasingsC and keepingsS constant (1500), which is the computational equivalent of increasing the inducer concentration, qualitative changes similar to the experimen-tally obtained ones could be observed (Fig. 6.8 a). At low and very high sC values, domination of the C strain could not be observed, while C was successful for interme-diatesC values. In particular, at approximately half of the C population producing the toxin, mostly C dominance was found (see Fig. 6.8 a, middle boxed outcome distribu-tion). However, similar to the experiments the presence of the three other competition outcomes was conserved. The classification into distinct outcomes (see Fig. 6.8 b) made
6. Investigation of bacterial interactions: Competition by toxin production
it even more evident: C domination was only found at intermediate inducer concentra-tions, i.e. balanced division of labor.
Finally, the computational model was used to assess the influence of a change in relative growth rate of the strains. To this end, the growth rate of the competitor (S) strain was systematically varied and expressed in terms of the growth rate rC of theC strain.
By simultaneously varying the toxin sensitivity sS of the competitor, two dimensional outcome phase diagrams could be obtained (Fig. 6.9). The phase diagrams showed a diagonal area of coexistence that divided the regions in which mainlyC orS dominate.
This diagonal represented a trade-off between growth rate and sensitivity. Below the separating region, strains were sensitive and slow, and consequently succumbed to the toxin producer (see highlighted square SRF P). However, being equally sensitive but faster in growth enabled it to cross the diagonal thereby overcoming the toxin action and to thrive in competition (see highlighted square SN F P).
0.5 1.0 1.5
Relative competitor growth rate [rC] 0 25 50 75 100 C success [%]
3.0 1.5 0
Toxin sensitivity sS [103]
Rrfp Rnfp
Snfp Srfp
[%]
0.5 1.0 1.5
Relative competitor growth rate [rC]
Rrfp Rnfp
Snfp Srfp
0 25 50 75 100 Competitor
success
3.0 1.5 0
Toxin sensitivity sS [103]
Coexistence [%]
0.5 1.0 1.5
Relative competitor growth rate [rC]
Rrfp Rnfp
Snfp Srfp
0 25 50 75 100
3.0 1.5 0
Toxin sensitivity sS [103]
Extinction [%]
0.5 1.0 1.5
Relative competitor growth rate [rC]
Rrfp Rnfp
Snfp Srfp
0 25 50 75 100
3.0 1.5 0
Toxin sensitivity sS [103]
Figure 6.9.: Toxin sensitivity sS and competitor (S) growth rate rS parameter variation The growth rate of the competitor (S) strain was varied and is expressed in terms of theC growth rate rC.
Conclusion
Taken together, the theoretical model allowed to investigate various competition pa-rameters: switching rate sC, toxin effectivity / sensitivity sS, and growth rate rS. The most important result was that only varying the switching rate and thereby the toxin producer fraction within the C strain population was enough to reproduce the exper-imentally observed shift in outcome distribution. The explanation for this effect is a balanced division of labor between toxin production and reproduction which is only successful at intermediate levels.
Furthermore, the computational model allowed exploration of experimentally inacces-sible parameter combinations that yielded outcome phase diagrams. In particular the simulations allowed to draw conclusions on how the system changes if only one of the parameters was changed while the others are kept constant (see Fig. 6.10). Focusing on
6.3. Deterministic competition
0.00 0.25 0.50 0.75 1.00
0.00 0.25 0.50 0.75 1.00
Toxin producer fraction
Competition outcome
a
0.00 0.25 0.50 0.75 1.00
0.50 0.75 1.00 1.25 1.50
Competitor growth rate [rC]
Competition outcome
b
0.00 0.25 0.50 0.75 1.00
0 500 1000 1500 2000 2500 3000 Toxin effectivity / sensitivity sS
Competition outcome
c
Figure 6.10.:The effect of simulation parameter variation on competition outcome The effect of the variation of the toxin producer fraction via switching rate (a), the competitor growth raterS (b), and toxin effectivity/ sensitivitysS(c) on the competition outcome of sim-ulations is displayed for the four different outcomes: C success (green), S success (magenta), coexistence (blue), and extinction (black). Points denote average values of competition out-come for 48 simulation replicates, error bars denote standard error the mean, and the lines are polynomial splines as guide for the eye. Simulation conditions: a: rC = 0.0729, rS = 0.0607, sS = 1500, sC varied. b: rC = 0.0729, rS varied, sS = 1500, sC = 0.015. c: rC = 0.0729, rS = 0.8rC,sS varied,sC = 0.015.
the C strain, the optimum behavior of the producer fraction manifested in an inverted u-shaped relation (Fig. 6.10 a). With increasing competitor growth rate, C’s success declined (Fig. 6.10 b), while C became more successful with higher toxin effectivity/
sensitivity (Fig. 6.10 c). The behavior of the S strain followed the opposite trend and coexistence was found in regions in which neither S nor C were completely advanta-geous.
After exploring the parameter space of the model, the question arose how well the pre-dicted competition outcomes reflect the actual dynamics. These will be answered in the next section.
6. Investigation of bacterial interactions: Competition by toxin production