The E. coli Whole-Cell Modeling Project

The Escherichia coli whole-cell modeling project seeks to create the most detailed computational model of an E. coli cell in order to better understand and predict the behavior of this model organism. Details about the approach, framework, and current version of the model are discussed. Currently, the model includes the functions of 43% of characterized genes, with ongoing efforts to include additional data and mechanisms. As additional information is incorporated in the model, its utility and predictive power will continue to increase, which means that discovery efforts can be accelerated by community involvement in the generation and inclusion of data. This project will be an invaluable resource to the E. coli community that could be used to verify expected physiological behavior, to predict new outcomes and testable hypotheses for more efficient experimental design iterations, and to evaluate heterogeneous data sets in the context of each other through deep curation.

Quorum-Sensing Synchronization of Synthetic Toggle Switches: A Design Based on Monotone Dynamical Systems Theory

Synthetic constructs in biotechnology, biocomputing, and modern gene therapy interventions are often based on plasmids or transfected circuits which implement some form of “on-off” switch. For example, the expression of a protein used for therapeutic purposes might be triggered by the recognition of a specific combination of inducers (e.g., antigens), and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off. The robustness of such a design is hampered by molecular (“intrinsic”) or environmental (“extrinsic”) noise, which may lead to spontaneous changes of state in a subset of the population and is reflected in the bimodality of protein expression, as measured for example using flow cytometry. In this context, a “majority-vote” correction circuit, which brings deviant cells back into the required state, is highly desirable, and quorum-sensing has been suggested as a way for cells to broadcast their states to the population as a whole so as to facilitate consensus. In this paper, we propose what we believe is the first such a design that has mathematically guaranteed properties of stability and auto-correction under certain conditions. Our approach is guided by concepts and theory from the field of “monotone” dynamical systems developed by M. Hirsch, H. Smith, and others. We benchmark our design by comparing it to an existing design which has been the subject of experimental and theoretical studies, illustrating its superiority in stability and self-correction of synchronization errors. Our stability analysis, based on dynamical systems theory, guarantees global convergence to steady states, ruling out unpredictable (“chaotic”) behaviors and even sustained oscillations in the limit of convergence. These results are valid no matter what are the values of parameters, and are based only on the wiring diagram. The theory is complemented by extensive computational bifurcation analysis, performed for a biochemically-detailed and biologically-relevant model that we developed. Another novel feature of our approach is that our theorems on exponential stability of steady states for homogeneous or mixed populations are valid independently of the number N of cells in the population, which is usually very large (N ≫ 1) and unknown. We prove that the exponential stability depends on relative proportions of each type of state only. While monotone systems theory has been used previously for systems biology analysis, the current work illustrates its power for synthetic biology design, and thus has wider significance well beyond the application to the important problem of coordination of toggle switches.

For the last decade, outstanding progress has been made, and considerable practical experience has accumulated, in the construction of elementary genetic circuits that perform various tasks, such as memory storage and logical operations, in response to both exogenous and endogenous stimuli. Using modern molecular “plug-and-play” technologies, various (re-)programmable cellular populations can be engineered, and they can be combined into more complex cellular systems. Among all engineered synthetic circuits, a toggle, a robust bistable switch leading to a binary response dynamics, is the simplest basic synthetic biology device, analogous to the “flip-flop” or latch in electronic design, and it plays a key role in biotechnology, biocomputing, and proposed gene therapies. However, despite many remarkable properties of the existing toggle designs, they must be tightly controlled in order to avoid spontaneous switching between different expression states (loss of long-term memory) or even the breakdown of stability through the generation of stable oscillations. To address this concrete challenge, we have developed a new design for quorum-sensing synthetic toggles, based on monotone dynamical systems theory. Our design is endowed with strong theoretical guarantees that completely exclude unpredictable chaotic behaviors in the limit of convergence, as well as undesired stable oscillations, and leads to robust consensus states.

Modeling a minimal cell

One important aim of synthetic biology is to develop a self-replicating biological system capable of performing useful tasks. A mathematical model of a synthetic organism would greatly enhance its value by providing a platform in which proposed modifications to the system could be rapidly prototyped and tested. Such a platform would allow the explicit connection of genomic sequence information to physiological predictions. As an initial step toward this aim, a minimal cell model (MCM) has been formulated. The MCM is defined as a model of a hypothetical cell with the minimum number of genes necessary to grow and divide in an optimally supportive culture environment. It is chemically detailed in terms of genes and gene products, as well as physiologically complete in terms of bacterial cell processes (e.g., DNA replication and cell division). A mathematical framework originally developed for modeling Escherichia coli has been used to build the platform MCM. A MCM with 241 product-coding genes (those which produce protein or stable RNA products) is presented. This gene set is genomically complete in that it codes for all the functions that a minimal chemoheterotrophic bacterium would require for sustained growth and division. With this model, the hypotheses behind a minimal gene set can be tested using a chemically detailed, dynamic, whole-cell modeling approach. Furthermore, the MCM can simulate the behavior of a whole cell that depends on the cell's (1) metabolic rates and chemical state, (2) genome in terms of expression of various genes, (3) environment both in terms of direct nutrient starvation and competitive inhibition leading to starvation, and (4) genomic sequence in terms of the chromosomal locations of genes.

Amino acid supplementation decreases plasmid retention in Escherichia coli

The effect of amino acid supplementation on plasmid stability in Escherichia coli B/r was tested experimentally. Comparisons of experimental results to computer-predicted values were made using a detailed, structured single-cell model. The plasmid, pDW17 (a pBR322 derivative with a mutated tac promoter controlling the beta-lactamase gene), was used. In chemostat cultures, the amino acid supplemented cultures were always less stable than those grown in minimal medium. This effect was not a growth rate effect, as increasing growth rate improves stability for both cultures in minimal medium and in amino acid supplemented medium. The computer model also predicted a decrease in stability due to amino acid supplementation. The model also predicts that amino acid supplementation, combined with moderately strong plasmid-encoded protein expression, results in a depletion of low-molecular-weight organics compared with plasmid-free cells. In minimal medium the same level of plasmid-encoded protein synthesis results in a strong reduction in amino acid pools compared with plasmid-free cells. With amino acid supplementation the growth differential between plasmid-bearing and plasmid-free cells may be due to an "energy limitation," while in minimal medium the size of the growth rate differential may be due to a "building block" limitation.

A genomically/chemically complete module for synthesis of lipid membrane in a minimal cell

A minimal cell is a hypothetical cell defined by the essential functions required for life. We have developed a module for the synthesis of membrane precursors for a mathematical minimal cell model. This module describes, with chemical and genomic detail the production of the constituents required to build a cell membrane and identifies the corresponding essential genes. Membranes allow selective nutrient passage, harmful substance exclusion, and energy generation. Bacterial membrane components range from lipids to fatty acids with embedded proteins and are structurally similar to eukaryotic cell membranes. Membranes are dynamic structures and experimental analyses show great variations in bacterial membrane composition. The flexibility of the model is such that different membrane compositions could be obtained in response to simulated changes in culture conditions. The model's predictions are in close agreement with the observed biological trends. The model's predictions correspond well with the experimental values of total lipid content in cells grown in chemostat culture, but less well with data from batch growth. Cell shape and size results agree especially well for data for growth rate relative to maximum growth rate larger than 0.5; and DNA, RNA, and protein predictions are consistent with experimental observations. A better understanding of the simplest bacterial membrane should lead to insights on the more complex behavior of membranes of higher species as well as identification of potential targets for antimicrobials.

A modular minimal cell model: purine and pyrimidine transport and metabolism

A more complete understanding of the relationship of cell physiology to genomic structure is desirable. Because of the intrinsic complexity of biological organisms, only the simplest cells will allow complete definition of all components and their interactions. The theoretical and experimental construction of a minimal cell has been suggested as a tool to develop such an understanding. Our ultimate goal is to convert a "coarse-grain" lumped parameter computer model of Escherichia coli into a genetically and chemically detailed model of a "minimal cell." The base E. coli model has been converted into a generalized model of a heterotrophic bacterium. This coarse-grain minimal cell model is functionally complete, with growth rate, composition, division, and changes in cell morphology as natural outputs from dynamic simulations where only the initial composition of the cell and of the medium are specified. A coarse-grain model uses pseudochemical species (or modules) that are aggregates of distinct chemical species that share similar chemistry and metabolic dynamics. This model provides a framework in which these modules can be "delumped" into chemical and genetic descriptions while maintaining connectivity to all other functional elements. Here we demonstrate that a detailed description of nucleotide precursors transport and metabolism is successfully integrated into the whole-cell model. This nucleotide submodel requires fewer (12) genes than other theoretical predictions in minimal cells. The demonstration of modularity suggests the possibility of developing modules in parallel and recombining them into a fully functional chemically and genetically detailed model of a prokaryote cell.

Structured model to predict intracellular amino acid shortages during recombinant protein overexpression in E. coli

Recombinant protein overexpression and the classical stringent response have been shown to induce the same proteases. Since the stringent response was the result of an intracellular amino acid shortage, it was hypothesized that the overexpression of the recombinant protein also caused an intracellular amino acid shortage. A structured non-segregated kinetic mathematical model of recombinant Escherichia coli was developed to predict intracellular amino acid shortages during recombinant protein overexpression, and thus the induction of the stringent response. Two model recombinant proteins were examined, chloramphenicol acetyl-transferase (CAT) and an 'average protein'. The model predicted an aromatic amino acid shortage during CAT overexpression, as predicted based on the CAT's amino acid content. The model also predicted a shortage of the intracellular alanine family amino acid pool during CAT overexpression. This was unexpected due to the relatively low content of alanine family amino acids in CAT compared to the average E. coli protein. The model predicted alanine, glutarate, and aspartate family amino acid shortages during recombinant 'average protein' overexpression. Additionally, the model predicted a decrease in the ribosome pool at induction for both recombinant proteins, which agrees with published experimental results. Thus, the structured kinetic model was able to predict amino acid shortages, that could potentially cause a stringent response and elevated protease activity.

Single-cell models: promise and limitations

This article describes the development of single-cell models, their uses and accomplishments, the barriers to the greater adoption, and a perspective on challenges to the biochemical engineering community where the single-cell model approach may be used advantageously. In particular, it may become an important tool in relating genomic information to cellular regulation and dynamics.

Mathematical models of metabolic pathways

There have been recent advances in metabolic flux analysis. In particular, the marriage of traditional flux balancing with NMR isotopomer distribution analysis holds great promise for the detailed quantification of physiology. Nevertheless, flux analysis yields only static snap-shots of metabolism. To robustly predict the time evolution of metabolic networks, dynamic mathematical models, especially those that contain a description of both gene expression as well as enzyme activity, must be utilized. When mechanistic control and regulatory information is not available, heuristic-based methods, such as the cybernetic framework, can be employed to describe the action of these control mechanisms. In the 'high-information' future, as more biological information becomes available, such heuristic-based approaches can be replaced by mechanistic mass-action representations of physiology that stem directly from genetic sequence.