Gupta, ChinmayaLópez, José ManuelAzencott, RobertBennett, Matthew R.Josić, KrešimirOtt, William2017-05-242017-05-242014Gupta, Chinmaya, López, José Manuel, Azencott, Robert, et al.. "Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations." <i>The Journal of Chemical Physics,</i> 140, no. 20 (2014) AIP Publishing: http://dx.doi.org/10.1063/1.4878662.https://hdl.handle.net/1911/94379Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlehttp://dx.doi.org/10.1063/1.4878662