How to turn a genetic circuit into a synthetic tunable oscillator, or a bistable switch

Abstract

Systems and Synthetic Biology use computational models of biological pathways in order to study in silico the behaviour of biological pathways. Mathematical models allow to verify biological hypotheses and to predict new possible dynamical behaviours. Here we use the tools of non-linear analysis to understand how to change the dynamics of the genes composing a novel synthetic network recently constructed in the yeast Saccharomyces cerevisiae for In-vivo Reverse-engineering and Modelling Assessment (IRMA). Guided by previous theoretical results that make the dynamics of a biological network depend on its topological properties, through the use of simulation and continuation techniques, we found that the network can be easily turned into a robust and tunable synthetic oscillator or a bistable switch. Our results provide guidelines to properly re-engineering in vivo the network in order to tune its dynamics.

Figure 1. Re-engineering the topology in order to turn IRMA into an oscillator or a switch.

Comparison between the topology of the actual version of the network (A) and the re-engineered topologies (B)–(E); in all the cases we only consider the galactose growing condition. A thicker line corresponds to an increase of the strength of the corresponding interaction; the strength is intended in terms of Michaelis-Menten coefficient and/or Hill coefficient and/or maximal transcriptional velocity. The parameters in red are the ones that we are varying from the nominal value. (A) Topology of IRMA. In galactose growing conditions, the topology consists of one delayed positive and one negative feedback loop, since the protein-protein interaction between Gal4 and Gal80 is switched off. (B) Re-engineering of IRMA in order to turn it into an autonomous oscillator, Scenario 1. Tuning the parameters v₂, k₆, h₂ and h₆ we increase the strength of the following interactions: Cbf1 on Gal4, Swi5 on Ash1 and Ash1 on Cbf1. Both the original positive and the negative feedback lops are present. (C) Re-engineering of IRMA in order to turn it into an autonomous oscillator, Scenario 2. Tuning the parameters v₂, k₁, k₂, k₆, h₃ and h₆ we increase the strength of the following interactions: Cbf1 on Gal4, Swi5 on Ash1 and Ash1 on Cbf1. The original positive feedback loop is removed. (D) Re-engineering of IRMA in order to turn it into an autonomous oscillator, Scenario 3. The topology is identical to the one in Scenario 2 with the addition of a positive auto-feedback-loop on Swi5. The tuned parameters are: v₂, k₁, k₂, k₆, h₃ and h₆. (E) Re-engineering of IRMA in order to turn it into a bistable switch, Scenario 4. Properly tuning the parameters v₂, k₁, k₂, h₁ and h₃ we increase the strength of the following interactions: Cbf1 on Gal4, Swi5 on Cbf1. The negative feedback loop is removed.

Figure 2. Turning IRMA into an oscillator: time simulations.

In silico oscillations simulating the mathematical model using the parameters of Scenario 1 A, Scenario 1 B, Scenario 2 and Scenario 3. (A) Scenario 1 A, simulations of the DDEs model; parameters v₂, k₆, h₂ and h₆ were varied from their nominal values (Table 1, Scenario 1 A column). Period of the oscillations = 120 minutes. (B) Scenario 1 B, simulations of the DDEs model; parameters k₆, h₂ and h₆ were varied from their nominal values like in Scenario 1 A (Table 1, Scenario 1 B column), while v₂ was tuned according to the continuation results in Figure S1 E in order to increase the values of CBF1. Period of the oscillations = 120 minutes. (C) Scenario 2, simulations of the ODEs model; parameters v₂, k₁, k₂, k₆, h₃ and h₆ were varied form their nominal values (Table 1, Scenario 2 column). The negative feedback loop was removed. Period of the oscillations = 110 minutes. (D) Scenario 3, simulations of the ODEs model; parameters v₂, k₁, k₂, k₆, h₃ and h₆ were varied form their nominal values (Table 1, Scenario 3 column). The negative feedback loop was removed. A positive auto-feedback loop was introduced on Swi5. Period of the oscillations = 133 minutes.

Figure 3. Viability of tuning parameter v₂ in vivo: methionine modulates IRMA genes expression.

Expression levels of IRMA genes at different methionine concentrations in glucose (white bars) or in galactose/raffinose (grey bars). The control is the standard complete medium, YEP, which contains 140 mM of methionine. Data represent the 2^−DCt (mean of two experiments±Standard Error).