Modeling metabolic systems: the need for dynamics

Through the looking glass: attempting to predict future opportunities and challenges in experimental biology

To celebrate its centenary year, Journal of Experimental Biology (JEB) commissioned a collection of articles examining the past, present and future of experimental biology. This Commentary closes the collection by considering the important research opportunities and challenges that await us in the future. We expect that researchers will harness the power of technological advances, such as '-omics' and gene editing, to probe resistance and resilience to environmental change as well as other organismal responses. The capacity to handle large data sets will allow high-resolution data to be collected for individual animals and to understand population, species and community responses. The availability of large data sets will also place greater emphasis on approaches such as modeling and simulations. Finally, the increasing sophistication of biologgers will allow more comprehensive data to be collected for individual animals in the wild. Collectively, these approaches will provide an unprecedented understanding of 'how animals work' as well as keys to safeguarding animals at a time when anthropogenic activities are degrading the natural environment.

A protocol for dynamic model calibration

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

Consolidated bioprocessing (CBP) of cellulose is a cost-effective route to produce valuable biochemicals by integrating saccharification, fermentation and cellulase synthesis in a single step. However, the lack of understanding of governing factors of interdependent saccharification and fermentation in CBP eludes reliable process optimization. Here, we propose a new framework that synergistically couples population balances (to simulate cellulose depolymerization) and cybernetic models (to model enzymatic regulation of fermentation) to enable improved understanding of CBP. The resulting framework, named the unified cybernetic-population balance model (UC-PBM), enables simulation of CBP driven by coordinated control of enzyme synthesis through closed-loop interactions. UC-PBM considers two key aspects in controlling CBP: (1) heterogeneity in cellulose properties and (2) cellular regulation of competing cell growth and cellulase secretion. In a case study on Clostridium thermocellum, UC-PBM not only provides a decent fit with various exometabolomic data, but also reveals that: (i) growth-decoupled cellulase-secreting pathways are only activated during famine conditions to promote the production of growth substrates, and (ii) starting cellulose concentration has a strong influence on the overall flux distribution. Equipped with mechanisms of cellulose degradation and fermentative regulations, UC-PBM is practical to explore phenotypic functions for primary evaluation of microorganisms' potential for metabolic engineering and optimal design of bioprocess.

An Improved Scatter Search Algorithm for Parameter Estimation in Large-Scale Kinetic Models of Biochemical Systems

Background:

Mathematical models play a central role in facilitating researchers to better understand and comprehensively analyze various processes in biochemical systems. Their usage is beneficial in metabolic engineering as they help predict and improve desired products. However, one of the primary challenges in model building is parameter estimation. It is the process to find nearoptimal values of kinetic parameters which may culminate in the best fit of model prediction to experimental data.

Methods:

This paper proposes an improved scatter search algorithm to address the challenging parameter estimation problem. The improved algorithm is based on hybridization of quasi opposition-based learning in enhanced scatter search (QOBLESS) method. The algorithm is tested using a large-scale metabolic model of Chinese Hamster Ovary (CHO) cells.

Results:

The experimental result shows that the proposed algorithm performs better than other algorithms in terms of convergence speed and the minimum value of the objective function (loglikelihood). The estimated parameters from the experiment produce a better model by means of obtaining a reasonable good fit of model prediction to the experimental data.

Conclusion:

The kinetic parameters’ value obtained from our work was able to result in a reasonable best fit of model prediction to the experimental data, which contributes to a better understanding and produced more accurate model. Based on the results, the QOBLESS method can be used as an efficient parameter estimation method in large-scale kinetic model building.

Phenomenological models as effective tools to discover cellular design principles

Microbes have proved useful to us in many different ways. To utilize microbes, we have mostly focused on maximizing growth, to improve yield of chemicals derived from the microbes. However, to truly tap into their potential, we should also aim to understand microbial physiology. We present a historical perspective of the developments in the field of Microbial Biotechnology, focusing on how the growth-modelling approaches have changed. Starting from simple empirical growth models, we have evolved towards mechanistic and phenomenological models which use molecular and physiological details to drastically improve prediction power of these models. Lastly, we explore the as of yet unsolved questions in microbial physiology, and discuss how the ability to monitor microbial growth at single cell resolution using the lab-on-a-chip technologies is uncovering previously unobservable causal principles underlying microbial growth.

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming

Motivation

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP).

Results

Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs.

Availability and Implementation

The software is implemented in Matlab, and is provided as supplementary information .

Contact

hyunseob.song@pnnl.gov.

Supplementary information

Supplementary data are available at Bioinformatics online.

Regulation-Structured Dynamic Metabolic Model Provides a Potential Mechanism for Delayed Enzyme Response in Denitrification Process

In a recent study of denitrification dynamics in hyporheic zone sediments, we observed a significant time lag (up to several days) in enzymatic response to the changes in substrate concentration. To explore an underlying mechanism and understand the interactive dynamics between enzymes and nutrients, we developed a trait-based model that associates a community's traits with functional enzymes, instead of typically used species guilds (or functional guilds). This enzyme-based formulation allows to collectively describe biogeochemical functions of microbial communities without directly parameterizing the dynamics of species guilds, therefore being scalable to complex communities. As a key component of modeling, we accounted for microbial regulation occurring through transcriptional and translational processes, the dynamics of which was parameterized based on the temporal profiles of enzyme concentrations measured using a new signature peptide-based method. The simulation results using the resulting model showed several days of a time lag in enzymatic responses as observed in experiments. Further, the model showed that the delayed enzymatic reactions could be primarily controlled by transcriptional responses and that the dynamics of transcripts and enzymes are closely correlated. The developed model can serve as a useful tool for predicting biogeochemical processes in natural environments, either independently or through integration with hydrologic flow simulators.

Metabolic engineering with multi-objective optimization of kinetic models

Kinetic models have a great potential for metabolic engineering applications. They can be used for testing which genetic and regulatory modifications can increase the production of metabolites of interest, while simultaneously monitoring other key functions of the host organism. This work presents a methodology for increasing productivity in biotechnological processes exploiting dynamic models. It uses multi-objective dynamic optimization to identify the combination of targets (enzymatic modifications) and the degree of up- or down-regulation that must be performed in order to optimize a set of pre-defined performance metrics subject to process constraints. The capabilities of the approach are demonstrated on a realistic and computationally challenging application: a large-scale metabolic model of Chinese Hamster Ovary cells (CHO), which are used for antibody production in a fed-batch process. The proposed methodology manages to provide a sustained and robust growth in CHO cells, increasing productivity while simultaneously increasing biomass production, product titer, and keeping the concentrations of lactate and ammonia at low values. The approach presented here can be used for optimizing metabolic models by finding the best combination of targets and their optimal level of up/down-regulation. Furthermore, it can accommodate additional trade-offs and constraints with great flexibility.

BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology

Background

Dynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions.

Results

Here we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker’s yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation.

Conclusions

This suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from the BioPreDyn-bench website, https://sites.google.com/site/biopredynbenchmarks/.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0144-4) contains supplementary material, which is available to authorized users.

Dynamic modelling of mixotrophic microalgal photobioreactor systems with time-varying yield coefficient for the lipid consumption

Microalgae have been suggested as a promising feedstock for producing biofuel because of their potential for lipid production. In this study, microalgal photobioreactor systems under mixotrophic conditions were investigated, for the purpose of developing a mathematical model that predicts biomass and lipid production. The model was developed based on the Droop model, and the optimal input design using D-optimality criterion was performed to compute the system input profile, to estimate parameters more accurately. From the experimental observations, the newly defined yield coefficient was suggested to represent the consumption of lipid and nitrogen within the cell, which reduces the number of parameters with more accurate prediction. Furthermore, the lipid consumption rate was introduced to reflect the experimental results that lipid consumption is related to carbon source concentration. The model was validated with experiments designed with different initial conditions of nutrients and input changes, and showed good agreement with experimental observations.

d-OptCom: Dynamic multi-level and multi-objective metabolic modeling of microbial communities

Most microbial communities change with time in response to changes and/or perturbations in environmental conditions. Temporal variations in interspecies metabolic interactions within these communities can significantly affect their structure and function. Here, we introduce d-OptCom, an extension of the OptCom procedure, for the dynamic metabolic modeling of microbial communities. It enables capturing the temporal dynamics of biomass concentration of the community members and extracellular concentration of the shared metabolites, while integrating species- and community-level fitness functions. The applicability of d-OptCom was demonstrated by modeling the dynamic co-growth of auxotrophic mutant pairs of E. coli and by computationally assessing the dynamics and composition of a uranium-reducing community comprised of Geobacter sulfurreducens, Rhodoferax ferrireducens, and Shewanella oneidensis. d-OptCom was also employed to examine the impact of lactate vs acetate addition on the relative abundance of uranium-reducing species. These studies highlight the importance of simultaneously accounting for both species- and community-level fitness functions when modeling microbial communities, and demonstrate that the incorporation of uptake kinetic information can substantially improve the prediction of interspecies flux trafficking. Overall, this study paves the way for the dynamic multi-level and multi-objective analysis of microbial ecosystems.