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Active modulation of surfactant driven flow instabilities by swarming bacteria

Models based on surfactant driven instabilities have been employed to describe pattern formation by swarming bacteria. However, by definition, such models cannot account for the effect of bacterial sensing and decision making. Here we present a more complete model for bacterial pattern formation which accounts for these effects by coupling active bacterial motility to the passive fluid dynamics. We experimentally identify behaviours which cannot be captured by previous models based on passive population dispersal and show that a more accurate description is provided by our model. It is seen that the coupling of bacterial motility to the fluid dynamics significantly alters the phase space of surfactant driven pattern formation. We also show that our formalism is applicable across bacterial species.


I. Introduction
Bacteria are perhaps the simplest living systems capable of complex behaviour involving sensing and coherent, collective behaviour and an example of which is the phenomena of swarming, where bacteria colonizes a semi-solid surface (typically, nutrient loaded agar) in geometric patterns characteristic of different species [2] [3].
Swarming involves several, possibly collective, decision making steps such as quorum sensing [4]. The swarming patterns produced by the Gram-negative bacteria Pseudomonas aeruginosa (PA) are unique due to the presence of long straight segments (tendrils) in its swarming pattern [ Figure 1 a)]. The tendrils produced by swarming PA are typically of the order of a centimetre with a width of 4-5 mm and their motion during swarming can be easily tracked with time-lapse imaging using regular digital cameras. This enables us to study the motion of the tendrils and their response to various environmental perturbations with relative ease compared to isotropically swarming bacteria [5] and other bacterial species which form dense fractal-like patterns [3]. The motion of single bacterial cells on the agar surface can also be observed using GFP expressing bacteria leading to the generation of motility data spanning multiple spatial (microns to cm) and temporal (seconds to days) scales. Such multi-scale imaging data helps to link individual behaviour to the collective behaviour of the swarm.
The swarming pattern produced by PA is unique in two major aspects. Firstly, the typical tendril length (~ cm) is nearly 4 orders of magnitude compared to the micron-sized individual swarm member. Considering the large stochastic fluctuations likely to be experienced by a micron sized individual member, it is remarkable that collective motion of these individuals produces such long straight segments. The long directional persistence leading to this highly anisotropic collective motion is worthy of detailed mathematical modelling. Secondly, The observation and analysis of the response of the tendrils to perturbations introduced into the swarming medium (agar) reveals a remarkable ability of PA swarm to sense its spatial environment which will be described in detail in the sections II and IV.
Indeed, there have been several attempts to model the swarming pattern of PA based on a highly mechanistic multiscale model [6], as a population dispersal phenomenon using spatial kernels [7] and based on Marangoni forces [8]. While generic models such as the Vicsek model [9] can explain large directional persistence in collections of stochastically moving particles, one would like to have a more detailed model involving experimentally accessible parameters of the system which produces statistically identical patterns as seen in the experimental system. The surfactant driven models [1] have come close to explaining the rich features of the PA swarm. We have been able to use this model to explain our experimental data of PA swarm's response to various perturbations. This leads to the most obvious question as to what is then the role of bacteria in this phenomenon. Are all the features exhibited by a swarm colony due to a passive non-intelligent phenomenon or are the bacteria taking advantage of the passive forces to ease their movement to niche locations while modulating the passive forces to avoid non conducive environment. We design our experiments to probe this active component of phenomena to further understand the ability of the bacteria to modulate the swarming pattern.

A. Awareness of the Presence of Sister Tendrils
The swarming tendrils display self-avoidance [10] [11]. This behaviour is also seen in growing Bacillus subtilis tendrils [12] and in P.dendritiformis by Avraham Be'er et al [13] who used the term sibling rivalry to describe this behaviour. In this case swarm fronts emerging from two locations in the same swarm plate lead to the formation of a zone of inhibition unpopulated by either of the advancing swarm fronts which can be viewed as a form of self-avoidance. However, there is a crucial difference between the self-avoidance seen in the PA system compared with the Paenibacillus system. As [14] showed the zone of inhibition is due to mutually lethal secretions produced by the swarming P. dendritiformis resulting in the death of bacteria in the region between the advancing fronts producing the zone of inhibition. In the case of PA, the advancing sister tendrils sense each other and typically one of them retracts back (complete reversal) or changes its direction. [Appendix B] This is a form of true self-avoidance and not a consequence of lethal secretions killing off the bacteria in the advancing front [12]. In other words, It can be thought of as the bacteria on one of the advancing tendrils sense the presence of another tendril advancing towards it and initiate changes in the motility profile which result in a change in the swarming direction. Thus, the selfavoidance phenomena in PA is significantly more complex and requires coordination far more in extent to that described previously in the case of P. dendritiformis and requires deeper study.

B. Awareness of the Presence of Inert Objects
we found strong evidence of the advancing tendril detecting the presence of the obstacle and changing its direction as it approached the obstacle [ Figure 1 (c)]. The bulk of our studies were conducted with the inert polymeric material PDMS. However, in order to check the material dependence of the obstacle, we also conducted more limited studies with obstacles made of glass. We did rigorous statistical analysis of experimental data to quantify the detection of inert obstacles by advancing swarm tendrils. The detection of obstacles was also observed with change in nutrient media (From PGM to M9) as with change of obstacle material.
The above mentioned experimental observations lead us to believe a presence of complex collective intelligence that would probably enable the bacteria to sense spatial features. In the next section, we describe this model and verify if our experimental observations can indeed be simulated using the model.

III. Model
Recent model [1] based on marangoni forces arsing due to surfactants produced by bacteria showed that varying parameters in the swarm environment like wettability , diffusion and some active parameters like the growth of the bacteria and surfactant production can lead to branching patterns qualitatively similar to those seen in the experiments. The equations are as follows

. a) single swarm colony simulation b) multi swarm colony simulation c) swarm colony simulation in the presence of obstacle
To our surprise, the above model could effectively capture the obstacle avoidance and sister colony avoidance which we had previously thought of being an active bacterial intelligence in play. This brings to light the complexity of the phenomena and the need to delineate the active and passive components of the phenomenon to understand it better.
We further went on to design experiments to probe the "activity" of the bacteria in the swarm which is summarised in the following section.

IV. Experiments to probe bacterial activity A. Retraction of the cells at the tip of the tendrils
The above model explains the avoidance of sister colony branches due to decrease in gradients of surfactants that causes marangoni force. But it fails to capture the spontaneous retraction of the high density bacterial cluster from the tips towards the centre of the colony (figure 3 b(i), c(i)). This is seen in both edge of the petriplate and sister colony interactions. This retraction is quite unlike the reverse marangoni forces that might occur due to gradient inversion near the no flux boundaries due to accumulation of surfactants (figure 3 b(ii), c(ii)). Specifically, we see that the advancing speed for bacteria swarming is less than the retracting speed while it is the opposite in the case of a purely surfactant driven flow indicating a crucial difference enabled by activity.

B. Flagella deficient mutant
The flgM mutant of PA is mutant characterised by the absence of flagella, yet it induces avoidance response in wild type PA as shown in Figure 4 (a). Our LC/MS data revealed that flagella mutant secretes similar amounts of Rhamnolipids (surfactants produced by PA) as the wild type. Also the growth rate of the flagella mutant is expected to be similar due to similar nutrient conditions as that of wild type. The model mentioned in the previous section cannot explain the absence of fingers in the swarm colony of the mutant. This reaffirms the importance of flagella motility of the bacteria in swarm phenomena which is backed by some reports [15] in literature.

C. Response to antibiotics
The above model does not capture the aversion of the bacteria to the antibiotics. The ability of the bacteria to change the direction of swarm near the antibiotics is a clear evidence of the bacterial activity and possibly an emerging collective intelligence. The response may be change in direction or retraction as show in Figure 4 (b) and this may not be due to passive forces as the control experiment with addition of water in place of antibiotic showed no such perturbation in the pattern. It would be interesting to see how the bacteria drive against the passive forces to change direction.

V. Conclusion
The swarming is a complex phenomenon of entangled passive and active forces. Many features of bacterial swarming that may arise purely due to passive forces are often mistaken to be an active intelligence. Our primary interest is to understand the emergence of collective intelligence in bacteria and it is important to probe the actual activity of the bacteria. We report some experiments that

A. Swarming Motility Assay
For swarming assay, we used Peptone growth medium (PGM). Composition of PGM 0.6% agar plates are 6 grams of bacteriological agar (Bacto agar), 3.2 grams of peptone, and 3 grams of sodium chloride (NaCl) added in 1 litre of distilled water. The medium was autoclaved at 121°C for 30 minutes. After autoclaving the media, 1 mL of 1M CaCl2 (Calcium chloride), 1 mL of 1 M MgSO4 (Magnesium sulphate), 25 ml of 1M KPO4 and 1 mL of 5 mg/mL cholesterol were added into the medium and mixed properly. 25 mL PGM were poured in each 90mm Petri-plates and allowed them to solidify at room temperature (RT) for a half an hour under the laminar hood flow with the lid opened. And all the plates were kept at room temperature for 16-18 hours for further drying.

B. Swarming
2ul of a planktonic culture of Wild type PA or flgM mutant with OD >2.8 is inoculated at the centre of 90 mm petri-plate containing PGM-0.6% agar. The wild type PA14 forms the pattern as shown in FIG.  1 a) over a period of 24 hours in a 90 mm petri-plate. FlgM is a transposon insertion mutant in the flgM gene of PA14 and is part of P. aeruginosa transposon insertion library [16].

C. Preparation of PDMS (Poly DiMethyl Siloxane) obstacle
We have used Sylgard 184 from Dow Corning. It has two parts: an elastomer part and the curing agent. The two parts i.e. elastomer: curing agent is mixed in the ratio of 10:1. This mixture is stirred well. The air bubble cause due to stirring is removed by degassing the PDMS mixture in a desiccator connected to vacuum pump. An acrylic template is made to obtain different shapes of the obstacle. The air bubble free PDMS mixture is then poured into the template and cured for 12 hours. The cured PDMS solidifies and is removed from the acrylic template. These PDMS obstacles are then sterilised in autoclave.
The sterilised obstacle blocks are placed in an appropriate position in the petri-plate. The nutrient agar is then poured around the obstacle such that the obstacle is half immersed in the nutrient agar while held intact in its original position. The nutrient agar with the obstacle is allowed to dry under the laminar hood.