Mathematical modeling in cellular biology aims to predict the behavior of biological systems. This aspect is particularly important in synthetic biology, where novel biological entities are being designed and implemented. Often, only an intuitive, qualitative prediction is available of how the planned device will function – while quantitative characterization is performed after experimental implementation. Ideally, mathematical modeling should offer the advantage of predicting the quantitative behavior of the system, minimizing the necessity for experimental optimization and fine-tuning. In this work, we present a kinetic model of an experimentally implemented, functioning synthetic system and we show that our model allows for analysis and prediction of the timing of events in the system and facilitates system optimization. Finally, we demonstrate how the model aids the design of system modifications.

For our analysis we used the synthetic cellular logic-gates system developed by Regot et al. (

2011), who implemented their system in cells of the yeast

*Saccharomyces cerevisiae*, exploiting endogenous Mitogen-Activated Protein Kinase (MAPK) signaling pathways. Such logic-gate units are intended as a first step on the way to the construction of a biological computation device. The novelty of this system lies in the concept of using communicating populations of cells: in each cell type, only a single logic operation is implemented, but the different cell types communicate with each other by secreting diffusible signaling molecules, such that more complicated functions can be achieved by mixing of cells that perform different basic operations. The advantage of this kind of implementation is that the chemical output synthesized by a population of engineered cells – the concentration of the signaling molecule that “wires” the different cell types into a functional circuit – is robust to noise arising in single cells, since it is averaged over the whole population (Li and You,

2011). It also enables the construction of many different functions from a limited number of engineered cells, by just mixing them in different combinations. The attractiveness of this system prompted us to analyze it deeper and to explore the possibilities of its further development.

In the system studied in this work, cell-to-cell communication is based on one of the best studied cell communication systems, i.e., the mating response of haploid yeast cells (Elion,

2000). In the mating process,

*MAT*α cells produce the α-factor mating pheromone and express an alpha-factor receptor while

*MAT* alpha cells produce alpha-factor and an α-factor receptor. Binding of the cognate pheromone to its receptor stimulates a G-protein-coupled sensing device including a MAPK cascade, which in turn initiates a cascade of events that lead to mating and cell fusion (Dohlman and Thorner,

2001; Hohmann,

2002). Another extensively studied signaling pathway used here is the High Osmolarity Glycerol (HOG) MAPK signaling network (de Nadal et al.,

2002; Hohmann,

2002). Several mathematical models of the pheromone-response pathway and the HOG signaling pathway have been already published (Kofahl and Klipp,

2004; Klipp et al.,

2005; Schaber et al.,

2006; Zi et al.,

2010), providing approaches on which we can now build further. Both pathways have previously been used in synthetic biology to demonstrate the feasibility of redirecting signal transduction (Park et al.,

2003) as well as building artificial cell communication systems (Chen and Weiss,

2005).

In their work, Regot et al. (

2011) have constructed and described 16 different types of engineered cells. In this study, we present kinetic models of four of these cells, which can be arranged in various combinations to perform five different logic operations (IDENTITY, NOT, OR, IMPLIES, NAND). All data necessary for model construction and parameterization have been obtained from previously published literature. The results from the work of Regot et al. are used only for model validation. The verified model is then employed for the identification of individual processes with highest impact on the functioning of the logic gates, for analyzing how culture density influences the system output and for determining the major sources of noise in the system. Finally it serves to propose how the current system could be transformed to operate on three discrete values.