CADLIVE toolbox for MATLAB: automatic dynamic modeling of biochemical networks with comprehensive system analysis

MLAGO: machine learning-aided global optimization for Michaelis constant estimation of kinetic modeling

BACKGROUND

Kinetic modeling is a powerful tool for understanding the dynamic behavior of biochemical systems. For kinetic modeling, determination of a number of kinetic parameters, such as the Michaelis constant (K_m), is necessary, and global optimization algorithms have long been used for parameter estimation. However, the conventional global optimization approach has three problems: (i) It is computationally demanding. (ii) It often yields unrealistic parameter values because it simply seeks a better model fitting to experimentally observed behaviors. (iii) It has difficulty in identifying a unique solution because multiple parameter sets can allow a kinetic model to fit experimental data equally well (the non-identifiability problem).

RESULTS

To solve these problems, we propose the Machine Learning-Aided Global Optimization (MLAGO) method for K_m estimation of kinetic modeling. First, we use a machine learning-based K_m predictor based only on three factors: EC number, KEGG Compound ID, and Organism ID, then conduct a constrained global optimization-based parameter estimation by using the machine learning-predicted K_m values as the reference values. The machine learning model achieved relatively good prediction scores: RMSE = 0.795 and R² = 0.536, making the subsequent global optimization easy and practical. The MLAGO approach reduced the error between simulation and experimental data while keeping K_m values close to the machine learning-predicted values. As a result, the MLAGO approach successfully estimated K_m values with less computational cost than the conventional method. Moreover, the MLAGO approach uniquely estimated K_m values, which were close to the measured values.

CONCLUSIONS

MLAGO overcomes the major problems in parameter estimation, accelerates kinetic modeling, and thus ultimately leads to better understanding of complex cellular systems. The web application for our machine learning-based K_m predictor is accessible at https://sites.google.com/view/kazuhiro-maeda/software-tools-web-apps , which helps modelers perform MLAGO on their own parameter estimation tasks.

Robustness analysis of the detailed kinetic model of an ErbB signaling network by using dynamic sensitivity

The ErbB receptor signaling pathway plays an important role in the regulation of cellular proliferation, survival and differentiation, and dysregulation of the pathway is linked to various types of human cancer. Mathematical models have been developed as a practical complementary approach to deciphering the complexity of ErbB receptor signaling and elucidating how the pathways discriminate between ligands to induce different cell fates. In this study, we developed a simulator to accurately calculate the dynamic sensitivity of extracellular-signal-regulated kinase (ERK) activity (ERK*) and Akt activity (Akt*), downstream of the ErbB receptors stimulated with epidermal growth factor (EGF) and heregulin (HRG). To demonstrate the feasibility of this simulator, we estimated how the reactions critically responsible for ERK* and Akt* change with time and in response to different doses of EGF and HRG, and predicted that only a small number of reactions determine ERK* and Akt*. ERK* increased steeply with increasing HRG dose until saturation, while showing a gently rising response to EGF. Akt* had a gradual wide-range response to HRG and a blunt response to EGF. Akt* was sensitive to perturbations of intracellular kinetics, while ERK* was more robust due to multiple, negative feedback loops. Overall, the simulator predicted reactions that were critically responsible for ERK* and Akt* in response to the dose of EGF and HRG, illustrated the response characteristics of ERK* and Akt*, and estimated mechanisms for generating robustness in the ErbB signaling network.

S-system-based analysis of the robust properties common to many biochemical network models

Robustness is a key feature to characterize the adaptation of organisms to changes in their internal and external environments. A broad range of kinetic or dynamic models of biochemical systems have been developed. Robustness analyses are attractive for exploring some common properties of many biochemical models. To reveal such features, we transform different types of mathematical equations into a standard or intelligible formula and use the multiple parameter sensitivity (MPS) to identify some factors critically responsible for the total robustness to many perturbations. The MPS would be determined by the top quarter of the highly sensitive parameters rather than the single parameter with the maximum sensitivity. The MPS did not show any correlation to the network size. The MPS is closely related to the standard deviation of the sensitivity profile. A decrease in the standard deviation enhanced the total robustness, which shows the hallmark of distributed robustness that many factors (pathways) involve the total robustness.

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.