A Hill type equation can predict target gene expression driven by p53 pulsing

Abstract

Many factors determine target gene expression dynamics under p53 pulsing. In this study, I sought to determine the mechanism by which duration, frequency, binding affinity and maximal transcription rate affect the expression dynamics of target genes. Using an analytical method to solve a simple model, I found that the fold change of target gene expression increases relative to the number of p53 pulses, and the optimal frequency, 0.18 h^-1 , from two real p53 pulses drives the maximal fold change with a decay rate of 0.18 h^-1 . Moreover, p53 pulses may also lead to a higher fold change than sustained p53. Finally, I discovered that a Hill-type equation, including these effect factors, can characterise target gene expression. The average error between the theoretical predictions and experiments was 23%. Collectively, this equation advances the understanding of transcription factor dynamics, where duration and frequency play a significant role in the fine regulation of target gene expression with higher binding affinity.

Keywords: fold change; hill equation; mRNA dynamical model; p53 pulse; target gene expression patterns.

Fig. 1

mRNA half‐life changes mRNA dynamics. K_A = 21 nm, A = 60 nm and β = 18. (A) Strongly pulsing (α = 1); (B) weakly pulsing (α = 0.18); and (C) rising dynamics (α = 0.01)

Fig. 2

Optimal expression dynamics. (A) 2 input pulses, T = 5.5 h, Δ = 2.75 h, β = 18, A = 60 nm, n = 1.8. (B) 2 input pulses, T = 5.5 h, K_A = 4.9 nm, β = 18, A = 60 nm, n = 1.8. (C) 20 input pulses, T = 5.5 h, Δ = 2.75 h, β = 18, A = 60 nm, n = 1.8. (D) 20 input pulses, T = 5.5 h, K_A = 4.9 nm, β = 18, A = 60 nm, n = 1.8.