Global parameter estimation methods for stochastic biochemical systems

<p>Abstract</p> <p>Background</p> <p>The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.</p> <p>Results</p> <p>Three parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.</p> <p>Conclusions</p> <p>The parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data.</p

Impact of kinetic isotope effects in isotopic studies of metabolic systems

Background: Isotope labeling experiments (ILEs) are increasingly used to investigate the functioning of metabolic systems. Some enzymes are subject to kinetic isotope effects (KIEs) which modulate reaction rates depending on the isotopic composition of their substrate(s). KIEs may therefore affect both the propagation of isotopes through metabolic networks and their operation, and ultimately jeopardize the biological value of ILEs. However, the actual impact of KIEs on metabolism has never been investigated at the system level. Results: First, we developed a framework which integrates KIEs into kinetic and isotopic models of metabolism, thereby accounting for their system-wide effects on metabolite concentrations, metabolic fluxes, and isotopic patterns. Then, we applied this framework to assess the impact of KIEs on the central carbon metabolism of Escherichia coli in the context of C-13-ILEs, under different situations commonly encountered in laboratories. Results showed that the impact of KIEs strongly depends on the label input and on the variable considered but is significantly lower than expected intuitively from measurements on isolated enzymes. The global robustness of both the metabolic operation and isotopic patterns largely emerge from intrinsic properties of metabolic networks, such as the distribution of control across the network and bidirectional isotope exchange. Conclusions: These results demonstrate the necessity of investigating the impact of KIEs at the level of the entire system, contradict previous hypotheses that KIEs would have a strong effect on isotopic distributions and on flux determination, and strengthen the biological value of C-13-ILEs. The proposed modeling framework is generic and can be used to investigate the impact of all the isotopic tracers (H-2, C-13, N-15, O-18, etc.) on different isotopic datasets and metabolic systems. By allowing the integration of isotopic and metabolomics data collected under stationary and/or non-stationary conditions, it may also assist interpretations of ILEs and facilitate the development of more accurate kinetic models with improved explicative and predictive capabilities

Understanding Regulation of Metabolism through Feasibility Analysis

Understanding cellular regulation of metabolism is a major challenge in systems biology. Thus far, the main assumption was that enzyme levels are key regulators in metabolic networks. However, regulation analysis recently showed that metabolism is rarely controlled via enzyme levels only, but through non-obvious combinations of hierarchical (gene and enzyme levels) and metabolic regulation (mass action and allosteric interaction). Quantitative analyses relating changes in metabolic fluxes to changes in transcript or protein levels have revealed a remarkable lack of understanding of the regulation of these networks. We study metabolic regulation via feasibility analysis (FA). Inspired by the constraint-based approach of Flux Balance Analysis, FA incorporates a model describing kinetic interactions between molecules. We enlarge the portfolio of objectives for the cell by defining three main physiologically relevant objectives for the cell: function, robustness and temporal responsiveness. We postulate that the cell assumes one or a combination of these objectives and search for enzyme levels necessary to achieve this. We call the subspace of feasible enzyme levels the feasible enzyme space. Once this space is constructed, we can study how different objectives may (if possible) be combined, or evaluate the conditions at which the cells are faced with a trade-off among those. We apply FA to the experimental scenario of long-term carbon limited chemostat cultivation of yeast cells, studying how metabolism evolves optimally. Cells employ a mixed strategy composed of increasing enzyme levels for glucose uptake and hexokinase and decreasing levels of the remaining enzymes. This trade-off renders the cells specialized in this low-carbon flux state to compete for the available glucose and get rid of over-overcapacity. Overall, we show that FA is a powerful tool for systems biologists to study regulation of metabolism, interpret experimental data and evaluate hypotheses.Intelligent SystemsElectrical Engineering, Mathematics and Computer Scienc

On the identifiability of metabolic network models.

Item does not contain fulltextA major problem for the identification of metabolic network models is parameter identifiability, that is, the possibility to unambiguously infer the parameter values from the data. Identifiability problems may be due to the structure of the model, in particular implicit dependencies between the parameters, or to limitations in the quantity and quality of the available data. We address the detection and resolution of identifiability problems for a class of pseudo-linear models of metabolism, so-called linlog models. Linlog models have the advantage that parameter estimation reduces to linear or orthogonal regression, which facilitates the analysis of identifiability. We develop precise definitions of structural and practical identifiability, and clarify the fundamental relations between these concepts. In addition, we use singular value decomposition to detect identifiability problems and reduce the model to an identifiable approximation by a principal component analysis approach. The criterion is adapted to real data, which are frequently scarce, incomplete, and noisy. The test of the criterion on a model with simulated data shows that it is capable of correctly identifying the principal components of the data vector. The application to a state-of-the-art dataset on central carbon metabolism in Escherichia coli yields the surprising result that only 4 out of 31 reactions, and 37 out of 100 parameters, are identifiable. This underlines the practical importance of identifiability analysis and model reduction in the modeling of large-scale metabolic networks. Although our approach has been developed in the context of linlog models, it carries over to other pseudo-linear models, such as generalized mass-action (power-law) models. Moreover, it provides useful hints for the identifiability analysis of more general classes of nonlinear models of metabolism.1 december 201