Identification of Metabolic Pathway Systems

Understanding biochemical design principles with ensembles of canonical non-linear models

Systems biology applies concepts from engineering in order to understand biological networks. If such an understanding was complete, biologists would be able to design ad hoc biochemical components tailored for different purposes, which is the goal of synthetic biology. Needless to say that we are far away from creating biological subsystems as intricate and precise as those found in nature, but mathematical models and high throughput techniques have brought us a long way in this direction. One of the difficulties that still needs to be overcome is finding the right values for model parameters and dealing with uncertainty, which is proving to be an extremely difficult task. In this work, we take advantage of ensemble modeling techniques, where a large number of models with different parameter values are formulated and then tested according to some performance criteria. By finding features shared by successful models, the role of different components and the synergies between them can be better understood. We will address some of the difficulties often faced by ensemble modeling approaches, such as the need to sample a space whose size grows exponentially with the number of parameters, and establishing useful selection criteria. Some methods will be shown to reduce the predictions from many models into a set of understandable “design principles” that can guide us to improve or manufacture a biochemical network. Our proposed framework formulates models within standard formalisms in order to integrate information from different sources and minimize the dimension of the parameter space. Additionally, the mathematical properties of the formalism enable a partition of the parameter space into independent subspaces. Each of these subspaces can be paired with a set of criteria that depend exclusively on it, thus allowing a separate sampling/screening in spaces of lower dimension. By applying tests in a strict order where computationally cheaper tests are applied first to each subspace and applying computationally expensive tests to the remaining subset thereafter, the use of resources is optimized and a larger number of models can be examined. This can be compared to a complex database query where the order of the requests can make a huge difference in the processing time. The method will be illustrated by analyzing a classical model of a metabolic pathway with end-product inhibition. Even for such a simple model, the method provides novel insight.

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems

Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, which renders the inference of parameter values for complex dynamic models challenging. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms. In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.

Mathematical models of lignin biosynthesis

BACKGROUND

Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in several reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount.

RESULTS

Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon.

CONCLUSIONS

Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded.

The best models of metabolism

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.

Stepwise inference of likely dynamic flux distributions from metabolic time series data

MOTIVATION

Most metabolic pathways contain more reactions than metabolites and therefore have a wide stoichiometric matrix that corresponds to infinitely many possible flux distributions that are perfectly compatible with the dynamics of the metabolites in a given dataset. This under-determinedness poses a challenge for the quantitative characterization of flux distributions from time series data and thus for the design of adequate, predictive models. Here we propose a method that reduces the degrees of freedom in a stepwise manner and leads to a dynamic flux distribution that is, in a statistical sense, likely to be close to the true distribution.

RESULTS

We applied the proposed method to the lignin biosynthesis pathway in switchgrass. The system consists of 16 metabolites and 23 enzymatic reactions. It has seven degrees of freedom and therefore admits a large space of dynamic flux distributions that all fit a set of metabolic time series data equally well. The proposed method reduces this space in a systematic and biologically reasonable manner and converges to a likely dynamic flux distribution in just a few iterations. The estimated solution and the true flux distribution, which is known in this case, show excellent agreement and thereby lend support to the method.

AVAILABILITY AND IMPLEMENTATION

The computational model was implemented in MATLAB (version R2014a, The MathWorks, Natick, MA). The source code is available at https://github.gatech.edu/VoitLab/Stepwise-Inference-of-Likely-Dynamic-Flux-Distributions and www.bst.bme.gatech.edu/research.php .

CONTACT

mojdeh@gatech.edu or eberhard.voit@bme.gatech.edu.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Effects of Storage Time on Glycolysis in Donated Human Blood Units

Background: Donated blood is typically stored before transfusions. During storage, the metabolism of red blood cells changes, possibly causing storage lesions. The changes are storage time dependent and exhibit donor-specific variations. It is necessary to uncover and characterize the responsible molecular mechanisms accounting for such biochemical changes, qualitatively and quantitatively; Study Design and Methods: Based on the integration of metabolic time series data, kinetic models, and a stoichiometric model of the glycolytic pathway, a customized inference method was developed and used to quantify the dynamic changes in glycolytic fluxes during the storage of donated blood units. The method provides a proof of principle for the feasibility of inferences regarding flux characteristics from metabolomics data; Results: Several glycolytic reaction steps change substantially during storage time and vary among different fluxes and donors. The quantification of these storage time effects, which are possibly irreversible, allows for predictions of the transfusion outcome of individual blood units; Conclusion: The improved mechanistic understanding of blood storage, obtained from this computational study, may aid the identification of blood units that age quickly or more slowly during storage, and may ultimately improve transfusion management in clinics.

Perspective: On the importance of hydrodynamic interactions in the subcellular dynamics of macromolecules

An outstanding challenge in computational biophysics is the simulation of a living cell at molecular detail. Over the past several years, using Stokesian dynamics, progress has been made in simulating coarse grained molecular models of the cytoplasm. Since macromolecules comprise 20%-40% of the volume of a cell, one would expect that steric interactions dominate macromolecular diffusion. However, the reduction in cellular diffusion rates relative to infinite dilution is due, roughly equally, to steric and hydrodynamic interactions, HI, with nonspecific attractive interactions likely playing rather a minor role. HI not only serve to slow down long time diffusion rates but also cause a considerable reduction in the magnitude of the short time diffusion coefficient relative to that at infinite dilution. More importantly, the long range contribution of the Rotne-Prager-Yamakawa diffusion tensor results in temporal and spatial correlations that persist up to microseconds and for intermolecular distances on the order of protein radii. While HI slow down the bimolecular association rate in the early stages of lipid bilayer formation, they accelerate the rate of large scale assembly of lipid aggregates. This is suggestive of an important role for HI in the self-assembly kinetics of large macromolecular complexes such as tubulin. Since HI are important, questions as to whether continuum models of HI are adequate as well as improved simulation methodologies that will make simulations of more complex cellular processes practical need to be addressed. Nevertheless, the stage is set for the molecular simulations of ever more complex subcellular processes.