You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Optimization-based models have been used to predict cellular behavior for over 25 years. The constraints in these models are derived from genome annotations, measured macro-molecular composition of cells, and by measuring the cell's growth rate and metabolism in different conditions. The cellular goal (the optimization problem that the cell is trying to solve) can be challenging to derive experimentally for many organisms, including human or mammalian cells, which have complex metabolic capabilities and are not well understood. Existing approaches to learning goals from data include (a) estimating a linear objective function, or (b) estimating linear constraints that model complex biochemical reactions and constrain the cell's operation. The latter approach is important because often the known observed biochemical reactions are not enough to explain observations, and hence there is a need to extend automatically the model complexity by learning new chemical reactions. However, this leads to nonconvex optimization problems, and existing tools cannot scale to realistically large metabolic models. Hence, constraint estimation is still used sparingly despite its benefits for modeling cell metabolism, which is important for developing novel antimicrobials against pathogens, discovering cancer drug targets, and producing value-added chemicals. Here, we develop the first approach to estimating constraint reactions from data that can scale to realistically large metabolic models. Previous tools have been used on problems having less than 75 biochemical reactions and 60 metabolites, which limits real-life-size applications. We perform extensive experiments using 75 large-scale metabolic network models for different organisms (including bacteria, yeasts, and mammals) and show that our algorithm can recover cellular constraint reactions, even when some measurements are missing.

Cited Abstract(s):
[1]: Genome-scale models of metabolism and macromolecular expression (ME-models) explicitly compute the optimal proteome composition of a growing cell. ME-models expand upon the well-established genome-scale models of metabolism (M-models), and they enable a new fundamental understanding of cellular growth. ME-models have increased predictive capabilities and accuracy due to their inclusion of the biosynthetic costs for the machinery of life, but they come with a significant increase in model size and complexity. This challenge results in models which are both difficult to compute and challenging to understand conceptually. As a result, ME-models exist for only two organisms (Escherichia coli and Thermotoga maritima) and are still used by relatively few researchers. To address these challenges, we have developed a new software framework called COBRAme for building and simulating ME-models. It is coded in Python and built on COBRApy, a popular platform for using M-models. COBRAme streamlines computation and analysis of ME-models. It provides tools to simplify constructing and editing ME-models to enable ME-model reconstructions for new organisms. We used COBRAme to reconstruct a condensed E. coli ME-model called iJL1678b-ME. This reformulated model gives functionally identical solutions to previous E. coli ME-models while using 1 5 the number of free variables and solving in less than 10 minutes, a marked improvement over the 6 hour solve time of previous ME-model formulations. Errors in previous ME-models were also corrected leading to 52 additional genes that must be expressed in iJL1678b-ME to grow aerobically in glucose minimal in silico media. This manuscript outlines the architecture of COBRAme and demonstrates how ME-models can be created, modified, and shared most efficiently using the new software framework.

[2]: The production of acetate by aerobically growing E. coli is examined. The problem is formulated in terms of a flow network that has as its objective maximal ATP synthesis. It is found that when loads are imposed and flux constraints exist either at the level of NADH turnover rate or the activity of a key Krebs cycle enzyme, switching to acetate overflow is predicted. Moreover, the result found for the latter constraint can be shown to be formally equivalent to a correlation experimentally determined for the specific rate of acetate production by E. coli K-12.

[3]: Large-scale integration of metabolite and protein structural data with existing networks of human metabolism provides insights into gene function and how drugs affect metabolic response.

[4]: Metabolic reconstructions remain limited in their scope and content, and improvements in biochemical knowledge and collaborative research are required.
The ability of engineers to predict microbial behavior was facilitated in 1990 by the observation that overflow metabolism---an industrially-relevant metabolic behavior---in could be predicted by a relatively simple network of reactions with capacity-constrained flows [2] . Since then, this constrained optimization model of cellular metabolism (often called COBRA) has been applied to over @math species across the tree of life [4] . Metabolic reconstructions today are genome-scale''---i.e., they account for the majority of metabolic genes annotated in the organism's genome---and consist of hundreds to thousands of biochemical reactions and metabolites. For example, the most recent reconstruction of human metabolism includes 13,543 metabolic reactions involving 4,140 metabolites [3] , while the latest multiscale model of metabolism and protein expression for [1] consists of 12,655 reactions and 7,031 components including macromolecules like protein, RNA (ribonucleic acid), and ribosome.