Calibrating spatiotemporal models of microbial communities to microscopy data: A review.

Spatiotemporal models that account for heterogeneity within microbial communities rely on single-cell data for calibration and validation. Such data, commonly collected via microscopy and flow cytometry, have been made more accessible by recent advances in microfluidics platforms and data processing pipelines. However, validating models against such data poses significant challenges. Validation practices vary widely between modelling studies; systematic and rigorous methods have not been widely adopted. Similar challenges are faced by the (macrobial) ecology community, in which systematic calibration approaches are often employed to improve quantitative predictions from computational models. Here, we review single-cell observation techniques that are being applied to study microbial communities and the calibration strategies that are being employed for accompanying spatiotemporal models. To facilitate future calibration efforts, we have compiled a list of summary statistics relevant for quantifying spatiotemporal patterns in microbial communities. Finally, we highlight some recently developed techniques that hold promise for improved model calibration, including algorithmic guidance of summary statistic selection and machine learning approaches for efficient model simulation.

Predictive Modeling of a Batch Filter Mating Process.

Quantitative characterizations of horizontal gene transfer are needed to accurately describe gene transfer processes in natural and engineered systems. A number of approaches to the quantitative description of plasmid conjugation have appeared in the literature. In this study, we seek to extend that work, motivated by the question of whether a mathematical model can accurately predict growth and conjugation dynamics in a batch process. We used flow cytometry to make time-point observations of a filter-associated mating between two E. coli strains, and fit ordinary differential equation models to the data. A model comparison analysis identified the model formulation that is best supported by the data. Identifiability analysis revealed that the parameters were estimated with acceptable accuracy. The predictive power of the model was assessed by comparison with test data that demanded extrapolation from the training experiments. This study represents the first attempt to assess the quality of model predictions for plasmid conjugation. Our successful application of this approach lays a foundation for predictive modeling that can be used both in the study of natural plasmid transmission and in model-based design of engineering approaches that employ conjugation, such as plasmid-mediated bioaugmentation.

Exploiting stoichiometric redundancies for computational efficiency and network reduction.

Analysis of metabolic networks typically begins with construction of the stoichiometry matrix, which characterizes the network topology. This matrix provides, via the balance equation, a description of the potential steady-state flow distribution. This paper begins with the observation that the balance equation depends only on the structure of linear redundancies in the network, and so can be stated in a succinct manner, leading to computational efficiencies in steady-state analysis. This alternative description of steady-state behaviour is then used to provide a novel method for network reduction, which complements existing algorithms for describing intracellular networks in terms of input-output macro-reactions (to facilitate bioprocess optimization and control). Finally, it is demonstrated that this novel reduction method can be used to address elementary mode analysis of large networks: the modes supported by a reduced network can capture the input-output modes of a metabolic module with significantly reduced computational effort.

A quantitative model of the initiation of DNA replication in Saccharomyces cerevisiae predicts the effects of system perturbations.

BACKGROUND: Eukaryotic cell proliferation involves DNA replication, a tightly regulated process mediated by a multitude of protein factors. In budding yeast, the initiation of replication is facilitated by the heterohexameric origin recognition complex (ORC). ORC binds to specific origins of replication and then serves as a scaffold for the recruitment of other factors such as Cdt1, Cdc6, the Mcm2-7 complex, Cdc45 and the Dbf4-Cdc7 kinase complex. While many of the mechanisms controlling these associations are well documented, mathematical models are needed to explore the network's dynamic behaviour. We have developed an ordinary differential equation-based model of the protein-protein interaction network describing replication initiation. RESULTS: The model was validated against quantified levels of protein factors over a range of cell cycle timepoints. Using chromatin extracts from synchronized Saccharomyces cerevisiae cell cultures, we were able to monitor the in vivo fluctuations of several of the aforementioned proteins, with additional data obtained from the literature. The model behaviour conforms to perturbation trials previously reported in the literature, and accurately predicts the results of our own knockdown experiments. Furthermore, we successfully incorporated our replication initiation model into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes. CONCLUSIONS: This study establishes a robust model of the processes driving DNA replication initiation. The model was validated against observed cell concentrations of the driving factors, and characterizes the interactions between factors implicated in eukaryotic DNA replication. Finally, this model can serve as a guide in efforts to generate a comprehensive model of the mammalian cell cycle in order to explore cancer-related phenotypes.

Differential chromatin proteomics of the MMS-induced DNA damage response in yeast.

BACKGROUND: Protein enrichment by sub-cellular fractionation was combined with differential-in-gel-electrophoresis (DIGE) to address the detection of the low abundance chromatin proteins in the budding yeast proteome. Comparisons of whole-cell extracts and chromatin fractions were used to provide a measure of the degree of chromatin association for individual proteins, which could be compared across sample treatments. The method was applied to analyze the effect of the DNA damaging agent methyl methanesulfonate (MMS) on levels of chromatin-associated proteins. RESULTS: Up-regulation of several previously characterized DNA damage checkpoint-regulated proteins, such as Rnr4, Rpa1 and Rpa2, was observed. In addition, several novel DNA damage responsive proteins were identified and assessed for genotoxic sensitivity using either DAmP (decreased abundance by mRNA perturbation) or knockout strains, including Acf2, Arp3, Bmh1, Hsp31, Lsp1, Pst2, Rnr4, Rpa1, Rpa2, Ste4, Ycp4 and Yrb1. A strain in which the expression of the Ran-GTPase binding protein Yrb1 was reduced was found to be hypersensitive to genotoxic stress. CONCLUSION: The described method was effective at unveiling chromatin-associated proteins that are less likely to be detected in the absence of fractionation. Several novel proteins with altered chromatin abundance were identified including Yrb1, pointing to a role for this nuclear import associated protein in DNA damage response.

Proteomics analysis of chinese hamster ovary cells undergoing apoptosis during prolonged cultivation.

The degradation of environmental conditions, such as nutrient depletion and accumulation of toxic waste products over time, often lead to premature apoptotic cell death in mammalian cell cultures and suboptimal protein yield. Although apoptosis has been extensively researched, the changes in the whole cell proteome during prolonged cultivation, where apoptosis is a major mode of cell death, have not been examined. To our knowledge, the work presented here is the first whole cell proteome analysis of non-induced apoptosis in mammalian cells. Flow cytometry analyses of various activated caspases demonstrated the onset of apoptosis in Chinese hamster ovary cells during prolonged cultivation was primarily through the intrinsic pathway. Differential in gel electrophoresis proteomic study comparing protein samples collected during cultivation resulted in the identification of 40 differentially expressed proteins, including four cytoskeletal proteins, ten chaperone and folding proteins, seven metabolic enzymes and seven other proteins of varied functions. The induction of seven ER chaperones and foldases is a solid indication of the onset of the unfolded protein response, which is triggered by cellular and ER stresses, many of which occur during prolonged batch cultures. In addition, the upregulation of six glycolytic enzymes and another metabolic protein emphasizes that a change in the energy metabolism likely occurred as culture conditions degraded and apoptosis advanced. By identifying the intracellular changes during cultivation, this study provides a foundation for optimizing cell line-specific cultivation processes, prolonging longevity and maximizing protein production.

Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network.

It has long been known to control theorists and engineers that integral feedback control leads to, and is necessary for, "perfect" adaptation to step input perturbations in most systems. Consequently, implementation of this robust control strategy in a synthetic gene network is an attractive prospect. However, the nature of genetic regulatory networks (density-dependent kinetics and molecular signals that easily reach saturation) implies that the design and construction of such a device is not straightforward. In this study, we propose a generic two-promoter genetic regulatory network for the purpose of exhibiting perfect adaptation; our treatment highlights the challenges inherent in the implementation of a genetic integral controller. We also present a numerical case study for a specific realization of this two-promoter network, "constructed" using commonly available parts from the bacterium Escherichia coli. We illustrate the possibility of optimizing this network's transient response via analogy to a linear, free-damped harmonic oscillator. Finally, we discuss extensions of this two-promoter network to a proportional-integral controller and to a three-promoter network capable of perfect adaptation under conditions where first-order protein removal effects would otherwise disrupt the adaptation.

Estimating the stochastic bifurcation structure of cellular networks.

High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. Since cellular networks are inherently noisy, we generalize the traditional bifurcation diagram of deterministic systems theory to stochastic dynamical systems. We demonstrate how statistical methods for density estimation, in particular, mixture density and conditional mixture density estimators, can be employed to establish empirical bifurcation diagrams describing the bistable genetic switch network controlling galactose utilization in yeast Saccharomyces cerevisiae. These approaches allow us to make novel qualitative and quantitative observations about the switching behavior of the galactose network, and provide a framework that might be useful to extract information needed for the development of quantitative network models.

Sequential activation of metabolic pathways: a dynamic optimization approach.

The regulation of cellular metabolism facilitates robust cellular operation in the face of changing external conditions. The cellular response to this varying environment may include the activation or inactivation of appropriate metabolic pathways. Experimental and numerical observations of sequential timing in pathway activation have been reported in the literature. It has been argued that such patterns can be rationalized by means of an underlying optimal metabolic design. In this paper we pose a dynamic optimization problem that accounts for time-resource minimization in pathway activation under constrained total enzyme abundance. The optimized variables are time-dependent enzyme concentrations that drive the pathway to a steady state characterized by a prescribed metabolic flux. The problem formulation addresses unbranched pathways with irreversible kinetics. Neither specific reaction kinetics nor fixed pathway length are assumed.In the optimal solution, each enzyme follows a switching profile between zero and maximum concentration, following a temporal sequence that matches the pathway topology. This result provides an analytic justification of the sequential activation previously described in the literature. In contrast with the existent numerical approaches, the activation sequence is proven to be optimal for a generic class of monomolecular kinetics. This class includes, but is not limited to, Mass Action, Michaelis-Menten, Hill, and some Power-law models. This suggests that sequential enzyme expression may be a common feature of metabolic regulation, as it is a robust property of optimal pathway activation.

Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories.

A sensitivity analysis of general stoichiometric networks is considered. The results are presented as a generalization of Metabolic Control Analysis, which has been concerned primarily with system sensitivities at steady state. An expression for time-varying sensitivity coefficients is given and the Summation and Connectivity Theorems are generalized. The results are compared to previous treatments. The analysis is accompanied by a discussion of the computation of the sensitivity coefficients and an application to a model of phototransduction.