Developing A Multi-scale Drug Model To Investigate The Synergistic Effects Of Drug Combinations

Cancer is currently the world's largest public issue and it greatly threatens the human's health.Rational combination therapy can achieve better efficacy than single drug,which has received great attention.Due to the complexity of anticancer drugs and clinical trials,the clinical research on which has never stopped.Especially,using model to explain and predict the synergistic effects of combination drugs has attracted more and more attention of researchers.In the modeling of biological systems,many mathematical methods have been widely used.However,a single-level model is not enough to describe a complex biological system.Agent based model(ABM)and differential equation(DE)are two commonly used methods for system modeling.Although these two methods have brought great help to scientific researchers.However,there are still shortcomings cannot be ignored for DE and ABM methods.For instance,DE method is not able to descript the immune system model detailed enough in multi-dimensions and multi-scale though it is good at estimating parameters with excellent mathematical methods.Besides,it is difficult for ABM to estimate key parameter for model by incorporating experimental data,leading to a poor result in parameter estimation.Meanwhile,the ABM has high dependence on powerful computer hardware and software resources when it faced a complex system.To address these issues and integrate the advantages of these two commonly used models,a new effective method called an Multi-Scale Agent-based Drug Model(MSABM)is created in this paper.Firstly,an agent-based model were developed to predict drug synergy with various phenotypes and types of cancer cells.Secondly,the key parameters were optimized using the Linear regression(LR)and particle swarm optimization algorithm(PSO).The detail process of this study is explained in the following content.In the modeling phase,we divided one kind of cancer cell population into four different states,just as quiescence,migration,proliferation and dead phenotypes,based on the cell biology and literatures.At the same time,the interactions between different scales are defined.Finally,we employed the advantages of ABM technology built a multi-scale prediction model in multi-level combined with the phenotypes switch chart and the equations under the effect of single drug or combination drug.In the parameter estimation phase.We make step-by-step estimates of the parameters in the model.First,using linear regression to estimate the apoptosis rate of tumor cells combined with biological experimental data.Then,we estimate the overall parameters by employing the particle swarm optimization.Through the combination of local and global methods,the efficiency of parameter optimization is increased.In the experimental results analysis phase.In this paper,three kinds of drug combinations were used to verify the model.The study found that the linear regression has less relative error than the robust regression by comparing the simulated data with the experimental data.There is no significant difference between the experimental data and the prediction data through the statistical significance test.In addition,we found that most of the predicted CI value are within the synergy interval.In summary,it is proved that the model has strong predictive ability.The growth and survival of cancer cells are greatly related to their surrounding microenvironment.To understand the regulation under the impact of anti-cancer drugs and their synergistic effects,we have developed a multiscale agent-based model that can investigate the synergistic effects of drug combinations with three innovations.First,it explores the synergistic effects of drug combinations in a huge dose combinational space at the cell line level.Second,it can simulate the interaction between cells and their microenvironment.Third,it employs both local and global optimization algorithms to train the key parameters and validate the predictive power of the model by using experimental data.The research results indicate that our multicellular system can not only describe the interactions between the microenvironment and cells in detail,but also predict the synergistic effects of drug combinations.