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Mechanistic Modeling of Biochemical Systems without A Priori Parameter Values Using the Design Space Toolbox v.3.0.

ABSTRACT: Mechanistic models of biochemical systems provide a rigorous description of biological phenomena. They are indispensable for making predictions and elucidating biological design principles. To date, mathematical analysis and characterization of these models encounter a bottleneck consisting of large numbers of unknown parameter values. Here, we introduce the Design Space Toolbox v.3.0 (DST3), a software implementation of the Design Space formalism enabling mechanistic modeling without requiring previous knowledge of parameter values. This is achieved by using a phenotype-centric modeling approach, in which the system is first decomposed into a series of biochemical phenotypes. Parameter values realizing phenotypes of interest are subsequently predicted. DST3 represents the most generally applicable implementation of the Design Space formalism and offers unique advantages over earlier versions. By expanding the Design Space formalism and streamlining its distribution, DST3 represents a valuable tool for elucidating biological design principles and designing novel synthetic circuits.

SUBMITTER: Valderrama-Gomez MA

PROVIDER: S-EPMC7287267 | biostudies-literature | 2020 Jun

REPOSITORIES: biostudies-literature

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Mechanistic Modeling of Biochemical Systems without A Priori Parameter Values Using the Design Space Toolbox v.3.0.

Valderrama-Gómez Miguel Á MÁ Lomnitz Jason G JG Fasani Rick A RA Savageau Michael A MA

iScience 20200523 6

Mechanistic models of biochemical systems provide a rigorous description of biological phenomena. They are indispensable for making predictions and elucidating biological design principles. To date, mathematical analysis and characterization of these models encounter a bottleneck consisting of large numbers of unknown parameter values. Here, we introduce the Design Space Toolbox v.3.0 (DST3), a software implementation of the Design Space formalism enabling mechanistic modeling without requiring ...[more]

PMID: 32531747

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Project description:BackgroundThe 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.ResultsThree 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.ConclusionsThe 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.

Project description:The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.

Dataset Information

Mechanistic Modeling of Biochemical Systems without A Priori Parameter Values Using the Design Space Toolbox v.3.0.

Publications

Mechanistic Modeling of Biochemical Systems without A Priori Parameter Values Using the Design Space Toolbox v.3.0.

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