Table 2 Successive dynamical models introduced in this article. We recall for each step the main feature and the form of the mRNA stationary distribution. The full network model (step 3) is used for simulations, while the simplified one (step 4) is used to derive the approximate statistical likelihood

1

Single-gene, discrete [29]

◇ All molecules are discrete

◇mRNA distribution: Beta-Poisson

↓

Abundant species treated continuously

2

Single-gene, PDMP (1)

◇ Only the promoter is discrete

◇ mRNA distribution: Beta

↓

Introduction of interactions via k _on, k _off

3

Network (2), normalized version (4)

◇ Both accurate and fast to simulate

◇mRNA distribution: unknown

↓

Timescale separation of Protein/mRNA (d ₀≫d ₁)

4

Simplified network (7)

◇ mRNA is removed from the network

◇ Conditional mRNA distribution: Beta (8)