Modeling Bacterial War

E. scolopes is a species of small squids, commonly known as the Hawaiian bobtail squid, living off the coast of Hawaii. Early in its life cycle, it forms a life-long symbiosis with bacteria Vibrio fischeri . The squids need the bioluminescent bacteria for a form of camouflage called counter-illumination, which helps the squid blend in with the moonlit ocean surface at night while out hunting. Scientists also find that the bacteria is crucial in squid’s development as a juvenile and health as an adult organism.

Symbiosis between Hawaiian bobtail squid and Vibrio fischeri.

What we are interested in is the microbial component of the symbiosis. V. fischeri is very abundant in the ocean, and some strains of it have evolved what’s called Type VI Secretion System (T6SS). When I first heard of this, my mind was blown — what T6SS does is it allows a bacterium to put together a spear, and shoot it at another cell and kill it. I knew bacteria can swim and swarm, but the ability to shoot and kill adds a whole new level of complexity. What’s also fascinating is that these spears, commonly called sheaths, are very similar to that of bacteria phages’. One theory is that at one point in the evolution of bacteria, some species co-opted bacteria phages’ DNA to build T6SS molecular machine – we may have on our hand a classic example of what doesn’t kill you makes you stronger!

As a computational mathematician, I approached the questions in T6SS-dependent interactions using a bit of mathematical modeling and computation. Collaborating with Steph Smith and Prof. Alecia Septer from UNC, Chapel Hill, we developed a model for the dynamics of T6SS on the subcellular level. Growing and competing different strains of V. fischeri on a Petri dish, Steph found that some strains consistently win, while others consistently lose. A while ago, her colleagues in the Septer Lab have found that V. fischeri activates T6SS activity after being exposed to viscous media, like the agarose pads on the Petri dish. And we started to wonder, if the activation process has anything to do with the consistent winning/losing in the different strains. It turns out the timing of activation is crucial when a population is competing against another — naturally, the population that can activate faster has the upper hand.

Steph also measured how many T6SS structures each cell has in a population over time. This information can help us understand quite a few things. First, since the cells activate T6SS over time, we would expect the number of cells that have any T6SS structures at all increases over time, so does the average number of T6SS structures per cell. In fact, this is exactly what we observed in the cell cultures of V. fischeri strains.

What’s more, the distribution of the number of T6SS per cell can also tell us quite a lot about the underlying process that produce and fire them. We found the this distribution is very similar to a Poisson distribution, albeit the mean of the distribution depends on the strain. This hint led us to model the subsequent processes of T6SS structure assembly and firing as independent stochastic processes with constant rates, which predicts the T6SS structure number follows the Poisson distribution.

Now that we have the subcellular model, we still need to somehow predict how a population of such cells would behave, when they engage in battles using the T6SS. To do this, I plugged the subcellular model into an agent-based model (ABM) so that every single cell is undergoing activation, assembly, and firing independently.

The hybrid ABM is off to a good start when we see in simulations of two strains of competing bacteria that the T6SS-dependent killing creates an emergent spatial structure (see movies below) that resembles coarsening, or phase separation, in physical systems such as magnetic fluids and liquid crystal. This has been observed in other microbiological systems such as V. cholerae and has been investigated by biologists, physicists, as well as applied mathematicians. However, what these previous studies didn’t capture is the effect of activation on the competition outcomes and spatial organization. Part of the reason was that the previously investigated organisms were engineered to have heightened T6SS activity, since they don’t naturally up-regulate their T6SS expression under lab conditions. Fortunately, the microbes we worked with, V. fischeri, do this under regular lab conditions as long as they are exposed to a viscous medium. Our experiments, and the hybrid model we developed based on their results, filled in this gap in our knowledge about how T6SS functions in inter-cellular competitions. And on top of that, it opens up a new avenue to describe, model, and investigate the processes that regulates T6SS, and tie them into inter-cellular dynamics on the population level.

We recently submitted our manuscript on the work and the preprint is available on bioRxiv.

Two strain of bacteria, both equipped with T6SS and ready to kill, grow from random initial condition within a confined geometry (periodic boundary condition). Both populations are initially fully activated.
Two strain of bacteria, both equipped with T6SS and ready to kill, grow from random initial condition without spatial limit. Between the antagonistic strains, a line forms (Dienes line). If the opposing strains have comparable killing ability, then the line will remain stable over time.