Codes for software programs and mathematical models developed by our research.

## Mathematical models for biological oscillators

**SA_Drosophila_Clock**Matlab codes for the mathematical model of the Drosophila circadian clock and its parameter estimation using the simulated annealing (SA) method. See Jeong et al, Systematic modeling-driven experiments identify distinct molecular clockworks underlying hierarchically organized pacemaker neurons,*PNAS*(2022) for details.**24h_model2019**

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.

**Phosphoswitch_Clock**

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.

**Systems_pharmacology**

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.

**PER_p53**

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.

**dual_strain_synthetic_oscillator**

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.**Collective_phospho_circadian**

The code simulates the system describing the transcriptional-translational feedback loop (TTFL) of PER protein by using delayed Gillespie algorithm. See “Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping “, Chae et al. (2023), i*Science*for details.

## Bayesian inference algorithms

**MBI**

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.

**Delay**

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

**EKMCMC**

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.

## Stochastic analysis

**Feedme**

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.**ASSISTER**

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,for details.*PLoS Com Biol*(2021)**CASTANET**

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,for details.*Commun Biol*(2021)

## Causality Inference

**ION**

MATLAB code for inferring networks of biochemical systems from oscillatory data. See Tyler*et al.*, Inferring causality in biological oscillators,for details.*Bioinformatics*(2021)**GOBI**

MATLAB code for accurate and broadly applicable causal inference method for time-series data. See Park*et al.*, A general model-based causal inference method overcomes the curse of synchrony and indirect effect,*Nature Communications*(2023) for details.

## Diagnosis for sleep disorders

**OSA-phenotyping**

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.**MCQ_I**

The computational code for predicting the classification via RF based on either the MCQI-6 or the MCQI-14.