title: Modeling delayed processes in biological systems.
abstract: Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated with a delayed process but instead use an estimated average delay time. In an effort to examine the validity of this approach, we study systems with significant delays by explicitly incorporating intermediate steps. We show that such explicit models often yield significantly different equilibrium distributions and transition times as compared to DDEs with deterministic delay values. Additionally, different explicit models with qualitatively different dynamics can give rise to the same DDEs revealing important ambiguities. We also show that DDE-based predictions of oscillatory behavior may fail for the corresponding explicit model.
authors.affiliation: Department of Bioengineering and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251-1892, USA.
authors.forename: Jingchen
authors.initials: J
authors.lastname: Feng
authors.affiliation: Department of Physics and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251-1892, USA.
authors.forename: Stuart A
authors.initials: SA
authors.lastname: Sevier
authors.affiliation: Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251-1892, USA.
authors.forename: Bin
authors.initials: B
authors.lastname: Huang
authors.affiliation: Graduate Program in Systems, Synthetic and Physical Biology and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251-1892, USA.
authors.forename: Dongya
authors.initials: D
authors.lastname: Jia
authors.affiliation: Department of Bioengineering and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251-1892, USA.
authors.forename: Herbert
authors.initials: H
authors.lastname: Levine
mesh_terms: D003198:Computer Simulation; D008954:Models, Biological; D015203:Reproducibility of Results; D013997:Time Factors