Modeling Gene Expression with Differential Equations

By Ting Chen, Hongyu L. He, George M. Church. 1998

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Citations in the corpus

Current approaches to gene regulatory network modelling (2007, methodology): “The discrete model approaches we consider include Boolean network based models [56-58] and Petri nets [59-62], the dynamic systems are based on difference or differential equations [63-65].”
Genetic network inference: from co-expression clustering to reverse engineering (2000, background): “, 1999), linear transcription model (Chen et al., 1999), weight matrix model (Weaver et al.”
A model of periodic oscillation for genetic regulatory systems (2002, background): “…remarks in Section V. Mathematical models that extract functional information from observations or experiments are useful for discovering higher order structures of an organizm and gaining deep insights into both static and dynamical behaviors of biological systems [2], [14], [18], [20]–[23].”
Modeling and Simulation of Genetic Regulatory Systems: A Literature Review (2002, unknown): “Related work taking ordinary differential equations and difference equations as their point of departure has come up recently (Chen et al ., 1999b; D’haeseleer et al ., 2000; Noda et al ., 1998; van Someren et al ., 2000; Weaver et al ., 1999; Wessels et al ., 2001).”
Inferring qualitative relations in genetic networks and metabolic pathways (2000, methodology): “Chen et al. (1999) and D'haeseleer et al. (1999) proposed inference methods based on linear differential equations.”
Inferring gene networks from time series microarray data using dynamic Bayesian networks (2003, methodology): “Several methods have been proposed for modelling gene networks including: Boolean networks,(1,2) Bayesian networks (BNs) and differential equations.(6,7) In particular, researchers have paid great attention to BNs, which model causal relationships between variables based on probabilistic measure.”
Identifying Causal Structure in Large-Scale Kinetic Systems (2018, background): “Nowadays, differential equations are universally used in scientific fields as diverse as physics, neuroscience [e.g. Friston et al., 2003], genetics [e.g. Chen et al., 1999], bioprocessing [e.g. Ogunnaike and Ray, 1994], robotics [e.g. Murray, 2017], or economics [e.g. Zhang, 2005].”
Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks (2003, background): “…refined level of detail is a mathematical description of the biophysical processes in terms of a system of coupled differential equations that describe, for example, the processes of transcription factor binding, diffusion, protein and RNA degradation, etc.; see, for instance, Chen et al. (1999).”
Molecular characterization of Mycobacterium abscessus strains isolated from a hospital outbreak. (2000, unknown): “insight has yet to be established (49-51).”
On Learning Gene Regulatory Networks Under the Boolean Network Model (2003, background): “…and Mian, 1999; Friedman et al., 2000; Hartemink et al., 2001), neural networks (Weaver et al., 1999; Vohradsky, 2001), differential equations (Chen et al., 1999; Mestl et al., 1995), and models including stochastic components on the molecular level (McAdams and Arkin, 1997) (see (Smolen et…”