Computational Analysis of Sphingolipid Pathway Systems. In: Chalfant C, Poeta MD, editors. Sphingolipids as Signaling and Regulatory Molecules. New York: Springer; 2010. pp. 264-75. [PMID: 20919661 DOI: 10.1007/978-1-4419-6741-1_19]

The three-legged stool of understanding metabolism: integrating metabolomics with biochemical genetics and computational modeling

Traditional biochemical research has resulted in a good understanding of many aspects of metabolism. However, this reductionist approach is time consuming and requires substantial resources, thus raising the question whether modern metabolomics and genomics should take over and replace the targeted experiments of old. We proffer that such a replacement is neither feasible not desirable and propose instead the tight integration of modern, system-wide omics with traditional experimental bench science and dedicated computational approaches. This integration is an important prerequisite toward the optimal acquisition of knowledge regarding metabolism and physiology in health and disease. The commentary describes advantages and drawbacks of current approaches to assessing metabolism and highlights the challenges to be overcome as we strive to achieve a deeper level of metabolic understanding in the future.

Identification of Metabolic Pathway Systems

The estimation of parameters in even moderately large biological systems is a significant challenge. This challenge is greatly exacerbated if the mathematical formats of appropriate process descriptions are unknown. To address this challenge, the method of dynamic flux estimation (DFE) was proposed for the analysis of metabolic time series data. Under ideal conditions, the first phase of DFE yields numerical representations of all fluxes within a metabolic pathway system, either as values at each time point or as plots against their substrates and modulators. However, this numerical result does not reveal the mathematical format of each flux. Thus, the second phase of DFE selects functional formats that are consistent with the numerical trends obtained from the first phase. While greatly facilitating metabolic data analysis, DFE is only directly applicable if the pathway system contains as many dependent variables as fluxes. Because most actual systems contain more fluxes than metabolite pools, this requirement is seldom satisfied. Auxiliary methods have been proposed to alleviate this issue, but they are not general. Here we propose strategies that extend DFE toward general, slightly underdetermined pathway systems.

Modeling of nonlinear biological phenomena modeled by S-systems

A central challenge in computational modeling of biological systems is the determination of the model parameters. In such cases, estimating these variables or parameters from other easily obtained measurements can be extremely useful. For example, time-series dynamic genomic data can be used to develop models representing dynamic genetic regulatory networks, which can be used to design intervention strategies to cure major diseases and to better understand the behavior of biological systems. Unfortunately, biological measurements are usually highly infected by errors that hide the important characteristics in the data. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. This paper addresses the problem of state and parameter estimation of biological phenomena modeled by S-systems using Bayesian approaches, where the nonlinear observed system is assumed to progress according to a probabilistic state space model. The performances of various conventional and state-of-the-art state estimation techniques are compared. These techniques include the extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and the developed variational Bayesian filter (VBF). Specifically, two comparative studies are performed. In the first comparative study, the state variables (the enzyme CadA, the model cadBA, the cadaverine Cadav and the lysine Lys for a model of the Cad System in Escherichia coli (CSEC)) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data. In the second comparative study, the state variables as well as the model parameters are simultaneously estimated. In this case, in addition to comparing the performances of the various state estimation techniques, the effect of the number of estimated model parameters on the accuracy and convergence of these techniques is also assessed. The results of both comparative studies show that the UKF provides a higher accuracy than the EKF due to the limited ability of EKF to accurately estimate the mean and covariance matrix of the estimated states through lineralization of the nonlinear process model. The results also show that the VBF provides a relative improvement over PF. This is because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the VBF yields an optimum choice of the sampling distribution, which also utilizes the observed data. The results of the second comparative study show that, for all techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The VBF, however, still provides advantages over other methods with respect to estimation accuracy as well convergence.

Parameter estimation of biological phenomena: an unscented Kalman filter approach

Recent advances in high-throughput technologies for biological data acquisition have spurred a broad interest in the construction of mathematical models for biological phenomena. The development of such mathematical models relies on the estimation of unknown parameters of the system using the time-course profiles of different metabolites in the system. One of the main challenges in the parameter estimation of biological phenomena is the fact that the number of unknown parameters is much more than the number of metabolites in the system. Moreover, the available metabolite measurements are corrupted by noise. In this paper, a new parameter estimation algorithm is developed based on the stochastic estimation framework for nonlinear systems, namely the unscented Kalman filter (UKF). A new iterative UKF algorithm with covariance resetting is developed in which the UKF algorithm is applied iteratively to the available noisy time profiles of the metabolites. The proposed estimation algorithm is applied to noisy time-course data synthetically produced from a generic branched pathway as well as real time-course profile for the Cad system of E. coli. The simulation results demonstrate the effectiveness of the proposed scheme.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Intervention in Biological Phenomena via Feedback Linearization

The problems of modeling and intervention of biological phenomena have captured the interest of many researchers in the past few decades. The aim of the therapeutic intervention strategies is to move an undesirable state of a diseased network towards a more desirable one. Such an objective can be achieved by the application of drugs to act on some genes/metabolites that experience the undesirable behavior. For the purpose of design and analysis of intervention strategies, mathematical models that can capture the complex dynamics of the biological systems are needed. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of biological phenomena. Due to the complex nonlinear dynamics of the biological phenomena represented by S-systems, nonlinear intervention schemes are needed to cope with the complexity of the nonlinear S-system models. Here, we present an intervention technique based on feedback linearization for biological phenomena modeled by S-systems. This technique is based on perfect knowledge of the S-system model. The proposed intervention technique is applied to the glycolytic-glycogenolytic pathway, and simulation results presented demonstrate the effectiveness of the proposed technique.

Fuzzy intervention in biological phenomena

An important objective of modeling biological phenomena is to develop therapeutic intervention strategies to move an undesirable state of a diseased network toward a more desirable one. Such transitions can be achieved by the use of drugs to act on some genes/metabolites that affect the undesirable behavior. Due to the fact that biological phenomena are complex processes with nonlinear dynamics that are impossible to perfectly represent with a mathematical model, the need for model-free nonlinear intervention strategies that are capable of guiding the target variables to their desired values often arises. In many applications, fuzzy systems have been found to be very useful for parameter estimation, model development and control design of nonlinear processes. In this paper, a model-free fuzzy intervention strategy (that does not require a mathematical model of the biological phenomenon) is proposed to guide the target variables of biological systems to their desired values. The proposed fuzzy intervention strategy is applied to three different biological models: a glycolytic-glycogenolytic pathway model, a purine metabolism pathway model, and a generic pathway model. The simulation results for all models demonstrate the effectiveness of the proposed scheme.

Analysis of operating principles with S-system models

Operating principles address general questions regarding the response dynamics of biological systems as we observe or hypothesize them, in comparison to a priori equally valid alternatives. In analogy to design principles, the question arises: Why are some operating strategies encountered more frequently than others and in what sense might they be superior? It is at this point impossible to study operation principles in complete generality, but the work here discusses the important situation where a biological system must shift operation from its normal steady state to a new steady state. This situation is quite common and includes many stress responses. We present two distinct methods for determining different solutions to this task of achieving a new target steady state. Both methods utilize the property of S-system models within Biochemical Systems Theory (BST) that steady states can be explicitly represented as systems of linear algebraic equations. The first method uses matrix inversion, a pseudo-inverse, or regression to characterize the entire admissible solution space. Operations on the basis of the solution space permit modest alterations of the transients toward the target steady state. The second method uses standard or mixed integer linear programming to determine admissible solutions that satisfy criteria of functional effectiveness, which are specified beforehand. As an illustration, we use both methods to characterize alternative response patterns of yeast subjected to heat stress, and compare them with observations from the literature.

Intervention in biological phenomena modeled by S-systems

Recent years have witnessed extensive research activity in modeling biological phenomena as well as in developing intervention strategies for such phenomena. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of biological phenomena. In this paper, two different intervention strategies, namely direct and indirect, are proposed for the S-system model. In the indirect approach, the prespecified desired values for the target variables are used to compute the reference values for the control inputs, and two control algorithms, namely simple sampled-data control and model predictive control (MPC), are developed for transferring the control variables from their initial values to the computed reference ones. In the direct approach, a MPC algorithm is developed that directly guides the target variables to their desired values. The proposed intervention strategies are applied to the glycolytic-glycogenolytic pathway and the simulation results presented demonstrate the effectiveness of the proposed schemes.