Effect of transcription cooperativity on population behavior

There are many factors that affect the population behavior of cells. Except for the ways of cellular communication and the cellular environment, which have been considered in the previous studies, transcription cooperativity (or Hill coefficient) that has been little considered before is also an important factor. This article investigates the effects of Hill coefficient on dynamical behavior in a synthetic multicellular system, where individual oscillators are an integration of repressilators and hysteresis-based oscillators and they are coupled through a quorum-sensing mechanism. By bifurcation analysis and numerical simulation, we find that because of the variety of Hill coefficient the system can show five kinds of typical dynamical structures on cell density, which suggests that Hill coefficient has great influences not only on the systems ability to oscillate and the modes of oscillation but also on the occurrence of multistability. Properly increasing Hill coefficient, the system evolves along the route from monostability to switches among monostability, bistability and multistability, from non-oscillation to simple oscillation, from a single oscillating mode to switches among a variety of oscillating modes. Our results may be the foundation for understanding complicated collective behaviors of cells.