Single Cell Model

The single-cell model of our system is composed of 4 interconnected modules. The design of the modules were based on the papers [] and on the feedback received from the experimentalists on the expected behaviour of the pathway, taking into consideration only the aspects relevant to our project. The single-cell model helped us understand in detail whether and how our synthetic circuit works and get a feeling of how it is related to concentration of our input substance.

Overview

The single cell mathematical model is developed on a scheme favouring the temporal order of processes. The changes in the species concentrations in time is given by a system of non-linear ordinary differential equations. The single cell model was simulated using numerical Matlab solvers.

The initial set of parameters used in the model were obtained as described below.

• Initial concentrations were obtained from the literature.
• The rates uptil Fus3 phosphorylation were obtained from fitting the model to the data presented in [Yu et al 2008].
• The rates for the gene expression module were obtained from the literature.

The description of the individual modules and their use within the scope of this project is given in the sections below.

Receptor Activation

Figure 1: Molecular mechanism of the modified yeast pathway.

G - Protein Cycle

The G- protein is a heterotrimer consisting of three subunits:G-alpha,G-beta and G-gamma. The interaction of G-alpha with the activated receptor leads to conformational changes that result in the release of GDP from G-alpha and the association of GTP with the nucleotide binding site. The related conformational change also leads to the release of G-beta-gamma, which in turn is capable of binding and activating components of the mating pheromone response pathway. Regulators of G protein signalling (RGS proteins) can accelerate the hydrolysis of G-alpha-GTP. The principle regulator of the G – Protein cycle is the Sst2 that interacts with G-alpha-GTP and increases its GTPase activity.

One of the most essential steps in the pheromone signal transmission is the ability of G-beta-gamma to bind to the scaffold protein Ste5. Absence of free G-beta-gamma results in the complete attenuation of the signal. Hence the choice of the promoter of G-alpha plays a key role in signal transmission. The effects of different promoters on the signal transmission characteristics were studied.

MAPK Cascade

MAPK Cascade description

The released heterodimer can bind and activate other components of the pathway. The most essential step in the pheromone single transmission is the ability of to bind to the scaffold protein Ste5. The function of a scaffold protein is to localise and tether all required components in one particular area in the cell as well as to coordinate the feedbacks. The Ste5 recruits Ste11 to the plasma membrane and activates the MAPK cascade. The first step in the cascade is the phosphorylation of the serine and threonine residues in the N-terminal kinase region of MAPKKK Ste11 by a membrane-associated kinase Ste20 resulting in Ste11 activation. The activated Ste11 phosphorylates the MAPKK Ste7 and activates it in this way. Analogically, the activated Ste7 activates two other MAPKs: Fus3 and Kss1. The Ste7-dependent activation of Fus3 takes place by phosphorylation of threonine and tyrosine residues in the activating loop. After double-phosphorylation, activated Fus3 rapidly dissociates from the scaffold protein Ste5. The Ste5 remains tethered to the plasma membrane acting as platform and enables phosphorylation of many Fus3 molecules. (Supady, 2009)

MAPK cascade reduced model

A simplified structure to model the MAPK cascade to fit the project requirements. The G-Protein subunits can bind to the scaffold protein ‘C’ building a complex ‘D’ that activates the MAPK cascade which further leads to the activation of Fus3. The activated Fus3 can get de-activated. Sst2a mediated feedback, promotes the dissociation of complex D into G-beta-gamma and the scaffold complex and therefore can be interpreted as a negative feedback of Fus3pp on the scaffold protein recruitment.

A simplified structure was used in place of the full structure as shown in the model by edda klipp as there were no key investigations that needed to be performed on the cascade. The reduced model successfully captured the dynamics of the pathway.

Gene Expression

For the gene expression, a reaction based model represented in the figure is used. In this model, the mRA synthesis is proportional to the concentration of the regulator of gene expression, activated Ste12. The protein synthesis is proportional to the mRNA concentration. The protein synthesis is represented in two stages, the synthesis of nascent-GFP which is proportional to the mRNA concentration and the synthesis of mature-GFP which is proportional to the nascent-GFP concentration. The mRNA and protein degradations are proportional to their concentrations. This reaction based model is first interpreted with deterministic semantics and then using stochastic semantics.