Figure 1. Amount of activated Ste12 at steady state as a response to α-pheromone concentrations. Error bars show one standard deviation.

Our part of the collaboration with RHiT was helping them with stochastic modelling of the trigger system for mating in yeast. The full mechanism has been quite well studied, but it is very complicated[1]. In RHiTs model, the final steps of the mechanism is activation of the Ste12 protein by the Fus3 enzyme. To simplify the model, production of Fus3 in the model was described by a sigmoid curve found in experiments[2] with respect to the concentration of α-pheromone. Inactive Ste12 was quickly activated by the presence of Fus3, so the outcome of active Ste12 followed a similar sigmoid curve, giving the expected switch behaviour. The resulting plot is shown in Figure 1. Each point is the average of 100 trajectories with the error bars indicating one standard deviation.

The equations used in the model are given in the table below. The parameters are taken from[1] and are modelled using mass action solvers, except Fus3 → Fus3PP, which use a sigmoid function. Timesteps in the model are minutes.

Reaction

Propensity

Comment

Fus3 → Fus3PP

*

Activation of Fus3

Fus3PP → Fus3

150

Deactivation of Fus3

Fus3PP + Ste12 → Fus3Ste12

18

Activation of Ste12 through complexation with Fus3

Fus3Ste12 → Fus3PP + Ste12

10

Deactivation of Ste12 by release of Fus3

Bar1 + Fus3Ste12 → aBar1 + Fus3Ste12

0.1

Activation of Bar1 enzyme

aBar1 → Bar1

0.1

Deactivation of Bar1

aBar1 → ø

0.01

Export of active Bar1

* The function for Fus3 activation is given by 200*α⁶/(α⁶ + 150⁶) where α is the concentration of α-phermone in nM

The initial amounts are given in the table below.

Species

Amount

Fus3

200

Fus3PP

0

Ste12

200

Fus3Ste12

0

Bar1

200

aBar1

0

A .zip file of the full model can be downloaded here.