An improved hybrid of particle swarm optimization and the gravitational search algorithm to produce a kinetic parameter estimation of aspartate biochemical pathways

Improved Gravitational Search Algorithm Based on Adaptive Strategies

The gravitational search algorithm is a global optimization algorithm that has the advantages of a swarm intelligence algorithm. Compared with traditional algorithms, the performance in terms of global search and convergence is relatively good, but the solution is not always accurate, and the algorithm has difficulty jumping out of locally optimal solutions. In view of these shortcomings, an improved gravitational search algorithm based on an adaptive strategy is proposed. The algorithm uses the adaptive strategy to improve the updating methods for the distance between particles, gravitational constant, and position in the gravitational search model. This strengthens the information interaction between particles in the group and improves the exploration and exploitation capacity of the algorithm. In this paper, 13 classical single-peak and multi-peak test functions were selected for simulation performance tests, and the CEC2017 benchmark function was used for a comparison test. The test results show that the improved gravitational search algorithm can address the tendency of the original algorithm to fall into local extrema and significantly improve both the solution accuracy and the ability to find the globally optimal solution.

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.

Utility of constraints reflecting system stability on analyses for biological models

Simulating complex biological models consisting of multiple ordinary differential equations can aid in the prediction of the pharmacological/biological responses; however, they are often hampered by the availability of reliable kinetic parameters. In the present study, we aimed to discover the properties of behaviors without determining an optimal combination of kinetic parameter values (parameter set). The key idea was to collect as many parameter sets as possible. Given that many systems are biologically stable and resilient (BSR), we focused on the dynamics around the steady state and formulated objective functions for BSR by partial linear approximation of the focused region. Using the objective functions and modified global cluster Newton method, we developed an algorithm for a thorough exploration of the allowable parameter space for biological systems (TEAPS). We first applied TEAPS to the NF-κB signaling model. This system shows a damped oscillation after stimulation and seems to fit the BSR constraint. By applying TEAPS, we found several directions in parameter space which stringently determines the BSR property. In such directions, the experimentally fitted parameter values were included in the range of the obtained parameter sets. The arachidonic acid metabolic pathway model was used as a model related to pharmacological responses. The pharmacological effects of nonsteroidal anti-inflammatory drugs were simulated using the parameter sets obtained by TEAPS. The structural properties of the system were partly extracted by analyzing the distribution of the obtained parameter sets. In addition, the simulations showed inter-drug differences in prostacyclin to thromboxane A2 ratio such that aspirin treatment tends to increase the ratio, while rofecoxib treatment tends to decrease it. These trends are comparable to the clinical observations. These results on real biological models suggest that the parameter sets satisfying the BSR condition can help in finding biologically plausible parameter sets and understanding the properties of biological systems.

We propose a new method to analyze the properties of biological dynamic models, which we named TEAPS (Thorough Exploration of Allowable Parameter Space). TEAPS can thoroughly determine combinations of parameter values for ordinary differential equations with which an initial state in a certain range converges to a particular fixed point. This stable and resilient behavior is a characteristic shared with many biological systems, including metabolic systems and intracellular signaling systems. Therefore, this thorough search outlined the possible parameter space as biological systems for target models, which helps to understand the system constraints when the target systems behave dynamically. The obtained parameter space can be used as an initial space for parameter tuning. For models that include a large number of parameters, the parameter space to be searched in the parameter tuning process is too large; therefore, narrowing down the space by TEAPS potentially contributes to the analysis of the dynamics of complicated biological models. Thus, our approach can partly overcome the current problem in parameter tuning and can advance the computational dynamic analyses of biological systems.

Dynamic chaotic gravitational search algorithm-based kinetic parameter estimation of hepatocellular carcinoma on 18F-FDG PET/CT

Background

Kinetic parameters estimated with dynamic ¹⁸F-FDG PET/CT can help to characterize hepatocellular carcinoma (HCC). We aim to evaluate the feasibility of the gravitational search algorithm (GSA) for kinetic parameter estimation and to propose a dynamic chaotic gravitational search algorithm (DCGSA) to enhance parameter estimation.

Methods

Five-minute dynamic PET/CT data of 20 HCCs were prospectively enrolled, and the kinetic parameters k₁ ~ k₄ and the hepatic arterial perfusion index (HPI) were estimated with a dual-input three-compartment model based on nonlinear least squares (NLLS), GSA and DCGSA.

Results

The results showed that there were significant differences between the HCCs and background liver tissues for k₁, k₄ and the HPI of NLLS; k₁, k₃, k₄ and the HPI of GSA; and k₁, k₂, k₃, k₄ and the HPI of DCGSA. DCGSA had a higher diagnostic performance for k₃ than NLLS and GSA.

Conclusions

GSA enables accurate estimation of the kinetic parameters of dynamic PET/CT in the diagnosis of HCC, and DCGSA can enhance the diagnostic performance.

Modeling cholesterol metabolism and atherosclerosis

Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.

Temperature drift compensation of a FOG based on an HKSVM optimized by an improved hybrid BAS-GSA algorithm

In this paper, the optimal hybrid kernel support vector machine is employed to propose a compensation strategy intended for the temperature drift of a fiber optical gyroscope (FOG). First, the mode of the hybrid kernel with an interpolation and extrapolation capability is constructed, which consists of the radial basis function and the polynomial kernel function. Second, the combination model of the beetle antennae search algorithm and gravitational search algorithm that has both local and global search capability is proposed to optimize the structure-related parameters of a hybrid kernel support vector machine (HKSVM). Finally, the proposed approach is trained and tested using the experimental data of temperature drift at two different rates of temperature change (10°C/min and 5°C/min). In addition, the proposed method is validated against those conventional compensation algorithms. According to the research results, the compensation error (mean squared error) of the proposed approach is reduced by 92% compared to the traditional support vector machine based on the radial basis function.