Stochastic Modeling of the Quorum Sensing Network in Agrobacterium tumefaciens Brendan Davis*, Leigh Nicholl, David Brown, and Phoebe Lostroh, Departments of Mathematics and Biology For years, prokaryotes were thought to be simple, single cell organisms without communicate or interact. We now know bacteria, such as Agrobacterium tumefaciens, use small, autoinducing molecules to sense population densities. This “quorum sensing” (QS) model works on a positive feedback loop and signals the bacteria to insert a tumor inducing (Ti) plasmid into the nucleus of a plant cell by horizontal gene transfer. Here, we used a stochastic model to mathematically evaluate the quorum sensing system. We found under certain conditions the model acted as a “bistable switch”, turning the system “on” and “off” at random. When a second cell was introduced to the model it increased the probability of the system turning “on”. We also found that by manipulating various variables we could alter the frequency of the QS network turning “on”. With this research, we are able to better understand the coordination involved in the infection of host plants by Agrobacterium tumefaciens. Thus, we can predict possible treatments for the progression of tumors in plants that are infected by crown gall disease. This type of model has implications to many other mathematical models in which this “bistable” phenomenon may be observed, as well as applications to other quorum sensing networks.
Quorum sensing is how bacteria communicate in response to cell density through the uptake and release of small signaling molecules called autoinducers. Through this form of signaling, bacteria dictate biofilm formation, motility, and pathogenesis, among many other cellular responses. Gram-negative bacteria employ N-acyl homoserine lactone molecules as their signaling molecule of choice, which then initiate a signaling cascade to turn on specific promoters. Previous research looking at bacterial behavior in the bistable regime has been largely from a deterministic point of view. Our two-cell model instead takes a stochastic approach, incorporating random noise into the system. Three models were observed: one with only one positive feedback loop, one with two feedback loops and no dimerization of the transcription factor, and one all-encompassing model with both feedback loops and dimerization. Two parameter values were varied in computer-run time trials: signal movement between the two cells and autoinducer turnover, or how quickly molecules were being replaced in the extracellular environment. As signal movement increased, the cells were more likely to enter the on state, and to enter it together. As autoinducer turnover increased, the cells were less likely to enter the on state and also less likely to turn on together. These results point to the potential to suppress QS by decreasing signal movement and increasing the affinity of the autoinducer to return to its parent cell, which could hold importance for research in the field of pathogenesis and microbial food spoilage. Future research will focus on acquiring accurate parameter rates, examining the role of negative feedback loops, and suppressing QS through inhibition of dimerization and blocking the second amplifying feedback loop from being initiated.