Integrated mechanistic pharmacokinetics/pharmacodynamics model of 5-fluorouracil (5-FU) anti-tumor activity
The code is used to implement the model in paper 'Computational analysis of 5-fluorouracil anti-tumor activity in
colon cancer using a mechanistic
pharmacokinetic/pharmacodynamic model' which is accepted for publication in PLOS Compuatational Biology.
Author: Chenhui Ma, Alex Almasan, Evren Gurkan-Cavusoglu
Note: The code is created by using Matlab® ver. R2022a
The entire model is composed of PK, cellular, and tumor growth inhibition (TGI) sub-models (shown in figures below), the last two of which constitute the PD model. The PK model is used to compute the concentration-time profile, and the TGI model focuses on the kinetics of tumor growth post-treatment.
The resistance analysis is discussed in detail in the manucript. The main functions in the folder are for resistance analysis are @Resistance_main_oncluster.m and Resistance_main_plot.m, which run on the cluster using Matlab Parallel computing to save extensive computational time. @Resistance_main_oncluster.m is served to execute the seven scenarios. For each scenario, based on the sampled N parameter sets, the N time courses of tumor volume, anabolites and DSBs are computed and stored, which are futhered processed and dispalyed in Fig 5, which is generated by function @Resistance_main_plot.m. The rest of the functions in the folder are called by the two main functions. Their associated roles are indicated by their function names.
We first applied gradient-based optimization to preliminarily identify the optimal values of the model parameter to gain a general idea about the magnitudes of the parameters. Such useful information allows us to assign prior distribution to each parameter before conducting the MCMC analysis. Functions for estimating parameters for each submodel are included. The main functions are kinetics_dNTP_main.m kinetics_DSB_main.m kinetics_PKand3to10_main.m kinetics_TumorVolume_main.m. kinetics5_para_estimation.m called the fmincon function to search for the local minimizers and configured a GlobalSearch object contains properties that affect how run repeatedly runs a local solver to generate a GlobalOptimSolution object. We conducted the sequential parameter estimation because it is computationally infeasible to estimate all the parameters once and all.
We utilized the Bayesian inference method to estimate the expected values of the model parameters as the Bayesian inference can capture the uncertainty of model parameters given the experimental data. We used the Robust adaptive Metropolis algorithm(RAM) in place of the naïve MH algorithm. Specifically, the Markov chain Monte Carlo (MCMC) technique is applied to obtain the approximated expected values. MCMC_main_dNTP_DSB.m, MCMC_main_PK.m, and MCMC_main_TGI.m are the main functions for conducting MCMC analysis for the three submodels. The RAM is defined in the function MyRAM.m. The joint posterior distributions for the parameters defined in the three submodels are provided in the files, @Target_fun_LE_Cellular, @Target_fun_LE_dNTP_DSB, @Target_fun_LE_PK , and @Target_fun_LE_TGI.
We plotted the mean time courses of model variables defined in the PK, cellular, and nine TGI models, and associated 0.7 credible regions of model simulations based on samples generated by MCMC analysis. The main scripts are @MyStaAnalysis_Cellular, @MyStaAnalysis_PK, and @PlotAllTGI. The functions for plotting time courses and MCMC analysis are organized into the folder 'MCMC_Plot234_Ea_EDSB'.
The functions @DoseDifference main and @Dose_difference_AUCe_damage, which are in the same folder as MCMC analysis, were used to carry out the three tasks.
The global sensitivity analysis is conducted by applying Morris screening and Sobol analysis.
We computationally experiment dosage regimens that are different from Table3 in the paper.
The folder named as "TimeCourses_DSB_Anabolites" includes the precomputed time courses of DSB and 5-FU anabolites using the predefined cellular model for each of nine TGI models to speed up the process of estimating parameters in TGI models.
We also employed the MCMC technique with uniform prior distributions.
The data used in the analysis are from the literature as cited in the paper. These papers are also listed below:
[1] Berne MH, Gustavsson BG, Almersj ̈o O, Spears PC, Fr ̈osing R. Sequential Methotrexate/5-FU: FdUMP Formation and TS Inhibition in a Transplantable Rodent Colon Adenocarcinoma;16(3):237–242. doi:10.1007/BF00293984.
[2] Falzacappa MVV, Ronchini C, Faretta M, Iacobucci I, Di Ror`a AGL, Martinelli G, et al. The Combination of the PARP Inhibitor Rucaparib and 5FU Is an Effective Strategy for Treating Acute Leukemias;14(4):889–898. doi:10.1158/1535-7163.MCT-14-0276.
[3] Adams ER, Leffert JJ, Craig DJ, Spector T, Pizzorno G. In Vivo Effect of 5-Ethynyluracil on 5-Fluorouracil Metabolism Determined by 19F Nuclear Magnetic Resonance Spectroscopy;59(1):122–127.
[4] Kamm VJ, Rietjens IM, Vervoort J, Heerschap A, Rosenbusch G, Hofs HP, et al. Effect of Modulators on 5-Fluorouracil Metabolite Patterns in Murine Colon Carcinoma Determined by in Vitro 19F Nuclear Magnetic Resonance Spectroscopy;54(16):4321–4326.
[5] van Laar JA, van der Wilt CL, Rustum YM, Noordhuis P, Smid K, Pinedo HM, et al. Therapeutic Efficacy of Fluoropyrimidines Depends on the Duration of Thymidylate Synthase Inhibition in the Murine Colon 26-B Carcinoma Tumor Model;2(8):1327–1333.
[6] Noordhuis P, Holwerda U, Van Laar JaM, Van der Wilt CL, Peters GJ. A Non-Radioactive Sensitive Assay to Measure 5-Fluorouracil Incorporation into DNA of Solid Tumors;23(8-9):1481–1484. doi:10.1081/NCN-200027699.
[7] Spears CP, Shahinian AH, Moran RG, Heidelberger C, Corbett TH. In Vivo Kinetics of Thymidylate Synthetase Inhibition of 5-Fluorouracil-Sensitive and -Resistant Murine Colon Adenocarcinomas;42(2):450–456.
[8] Tattersall MH, Harrap KR. Changes in the Deoxyribonucleoside Triphosphate Pools of Mouse 5178Y Lymphoma Cells Following Exposure to Methotrexate or 5-Fluorouracil;33(12):3086–3090.
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