Codes for software programs and mathematical models developed by our research.
Mathematical models for biological oscillators
A systems pharmacological model for mammalian circadian clock of monkeys used to simulate the effect of the circadian clock modulator (Mathematica). See Kim et al., Systems approach reveals photosensitivity and PER2 level as determinants of clock‐modulator efficacy, Mol Syst Biol (2019) for details.
Mathematical models for mammalian circadian clock with the phosphoswitch (Mathematica). See Zhou, Kim et al, Mol Cell (2015) and Narasimamurthy R et al, PNAS (2018) for details.
A systems pharmacology model for mammalian circadian clock of mice (Mathematica). See Kim JK, et al, Validating Chronic Pharmacological Manipulation of Circadian Rhythms, CPT:Pharmacometrics & Systems Pharmacology (2013) for details.
- Kim-Forger model
The detailed mathematical model for mammalian circadian clock (Mathematica, Matlab and XPPAUT). See Kim JK and Forger DB, A Mechanism for Robust Circadian Timekeeping via stoichiometric balance, Mol Syst Biol (2012) for details.
A mathematical model describing molecular interactions between PER and p53 (Mathematica). See Gotoh and Kim et al., Model-driven experimental approach reveals the complex regulatory distribution of p53 by the circadian factor Period 2, PNAS (2016) for details.
Mathematical model of dual strain synthetic oscillator (Mathematica). See Ye and Kim et al., Emergent genetic oscillations in a synthetic microbial consortium, Science (2015) for details.
Bayesian inference algorithms
Moment-based Bayesian inference method (MBI) for inferring cell-to-cell heterogeneity in the non-Markovian signaling process. See Kim et al., Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: the rate-limiting step number, Science Advances (2022) for details.
Bayesian inference algorithm (R code) that estimates reaction rates and delay distribution of Birth-Death process with time delay. See Choi et al., Bayesian inference of distributed time delay in transcriptional and translational regulation, Bioinformatics (2019) for details
R package that performs the Bayesian inference for enzyme kinetics with the total quasi-steady-state approximation model. See Choi et al., Beyond the Michaelis-Menten equation: Accurate and efficient estimation of enzyme kinetic parameters, Scientific Reports (2017) for details.
- Hierarchical Bayesian inference for systems with delay
Hierarchical Bayesian inference algorithm (Python code) that estimates reaction rates and delay distribution of Birth-Death process with time delay over heterogeneous population. See Cortez et al., Hierarchical Bayesian models of transcriptional and translational regulation processes with delays, Bioinformatics (2021) for details.
Matlab code for the calculation of exact moments of biochemical reaction networks with feed-forward structures. See Kim and Sontag, Reduction of Multiscale Stochastic Biochemical Reaction Networks using Exact Moment Derivation, PLoS Com Biol (2017) for details.
Matlab code for efficient and accurate simulations of stochastic biochemical systems containing rapid reversible binding reactions. See Song et al., Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities, PLoS Com Biol (2021) for details.
Matlab code to analytically derive stationary distributions for a given stochastic biochemical reaction networks using network translation and propensity factorization based on chemical reaction network theory. See Hong et al., Derivation of stationary distributions of biochemical reaction networks via structure transformation, Commun Biol (2021) for details.
MATLAB code for inferring networks of biochemical systems from oscillatory data. See Tyler et al., Inferring causality in biological oscillators, Bioinformatics (2021) for details.
Diagnosis for sleep disorders
A computational package (Python) that can phenotype obstructive sleep apnea (OSA) patients based on their polysomnography (PSG) data. See Ma et al., Combined unsupervised‑supervised machine learning for phenotyping complex diseases with its application to obstructive sleep apnea, Scientific Reports (2021) for details.