Computational Molecular Biology 2025, Vol.15, No.4, 193-207 http://bioscipublisher.com/index.php/cmb 199 Figure 1 Main features of IDESS: (i) simulation of biocircuit dynamics by Semi-Lagrangian (PIDE model) or SSA Algorithms, (ii) parameter estimation from experimental data for model identification, and (iii) automated design of biocircuits, delivering synthetic gene circuits (topology and parameters) with predefined target behaviors. IDESS applies CPU and GPU parallel implementations of stochastic simulation and global optimization to accelerate computing (Adopted from Sequeiros et al., 2023) If the goal is to develop genetic logic circuits or leans more towards synthetic design, iBioSim is a good open-source tool. It integrates functions such as logic circuit modeling, ordinary differential equations and stochastic simulation, and is suitable for researchers who want to draw circuit diagrams and run models (Myers et al., 2009). In contrast, Tellurium is more popular among users who prefer the Python environment. It integrates Antimony language, roadrunner solver, etc., and can directly load models, run simulations, optimize parameters and plot using scripts (Choi et al., 2018). Unlike COPASI, Tellurium does not rely on a graphical interface but is more suitable for scenarios such as batch analysis, automation, and flexible computing. 5.3 Visualization and model optimization strategies After building the model and running the simulation, the diagrams drawn are often the ones that can best help people "understand" the system's behavior. Complex multi-variable dynamic processes are hard to understand the patterns just by numbers, but good visualization can immediately bring the problem to light. For instance, a curve of protein concentration varying over time can visually reveal the period and amplitude of the oscillation. Phase diagrams can display the switching trajectories of the system between different states. The heat map can immediately reveal which parameters have the greatest impact on the output (Madsen et al., 2019). Time series diagrams, phase diagrams and heat maps are the three most commonly used forms, each with its own application - the former is used to observe dynamics, while the latter two are used to assess the stability and sensitivity of the system. Especially during the parameter adjustment stage, researchers often rely on graphs to determine whether the system's direction is reasonable. However, visualization is not only for presenting results but can also, in turn, guide model optimization. For instance, in a high-dimensional parameter space, we can draw the distribution of the objective function to see if there are regions similar to "basins", which can help select the initial point or algorithm. If there are too many parameters, principal component analysis can also be used to project the high-dimensional information into a two-dimensional graph to see which parameters dominate the system behavior. These graphs are often more
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