Computing intrinsic noise of the genetic regulation modeled by Hill functions

Riccardo Ziraldo,Lan Ma

doi:10.15744/2455-7625.3.101

Abstract

Intrinsic noise embedded in stochastic gene regulation due to low copy number of species has been studied using the approach of theoretical modeling and computational simulation, including the standard methods of stochastic simulation algorithm (SSA) and linear noise approximation (LNA). At average cell level, Hill functions are widely used as a compact format to represent gene regulation involving multi-transcription-factor binding and cooperativity. Heuristic SSA and LNA methods (hSSA and hLNA) have been applied to study stochastic models employing Hill functions. It is however unclear which modeling and simulation method is suitable to characterize intrinsic noise of Hill-type gene regulation with sufficient accuracy and computational efficiency. In this work, we perform noise analysis of two gene regulatory models represented by second-order activating and inhibitory Hill functions, seeking to evaluate the performance of five existing noise modeling methods. Specifically, SSA and LNA are applied to the full models that are expanded from the Hill functions containing only elementary reactions, while hSSA and hLNA are applied to reduced models where the Hill function is heuristically used. In addition, we characterize intrinsic noise using the slow-scale LNA (ssLNA) method that is recently proposed to deal with models with both fast and slow time scales. Using SSA as ground truth, we find that hSSA and hLNA underestimate the level of intrinsic noise in the Hill-type models, despite of high computational efficiency. The ssLNA approach calculates noise with comparable accuracy as SSA and LNA, while requesting much less computational resources. In addition, the chemical Langevin equation (CLE) under the same slow-scale framework simulates single-cell stochastic trajectories as accurately as SSA yet with significantly lower computational demands. This study shows that ssLNA complemented by slow-scale CLE offers a computational platform that out-performs the other four methods in characterizing intrinsic stochasticity of the Hill-type genetic models.

Highlights

Gene regulation is among the most important yet intricate biological processes
We focus on exploring the intrinsic noise of two theoretically basic and useful genetic models, namely the second-order Hill-type gene activation and gene inhibition networks
To compare with the standard approach of stochastic simulation algorithm (SSA) and linear noise approximation (LNA), we explore the performance of heuristic SSA (hSSA) and heuristic LNA (hLNA) in quantifying the intrinsic stochasticity of Hilltype gene regulations, where the fast binding/unbinding processes are assumed to reside at quasi-steady states

Summary

Introduction

Gene regulation is among the most important yet intricate biological processes. Mathematical modeling of gene regulatory networks has provided helpful insights in understanding natural genetic networks and designing synthetic genetic circuits. One type of widely accepted approach for modeling gene regulation is through deterministic rate equations (i.e. ordinary differential equations) [1,2]. In the formulation of complex transcriptional events regulated by transcription factors, Hill-type rate law has been shown to successfully approximate the multibinding-site mechanism and cooperativity [3,4,5]. The application of Hill functions to represent activating or inhibitory regulation by transcription factors greatly reduces the complexity of deterministic modeling of gene regulation [6,7]. It is noteworthy that the deterministic models using ordinary differential equations only reflect the macroscopic behavior of genetic networks averaged over many cells, while neglecting the intrinsically random nature of gene regulation in a single cell, namely the stochasticity inherent in gene expression [8,9]

Methods

Results

Conclusion