Multi-experiment nonlinear mixed effect modeling of single-cell translation kinetics after transfection

Recent advances, opportunities and challenges in cybergenetic identification and control of biomolecular networks

Cybergenetics is a new area of research aimed at developing digital and biological controllers for living systems. Synthetic biologists have begun exploiting cybergenetic tools and platforms to both accelerate the development of mathematical models and develop control strategies for complex biological phenomena. Here, we review the state of the art in cybergenetic identification and control. Our aim is to lower the entry barrier to this field and foster the adoption of methods and technologies that will accelerate the pace at which Synthetic Biology progresses toward applications.

Gene expression model inference from snapshot RNA data using Bayesian non-parametrics

Gene expression models, which are key towards understanding cellular regulatory response, underlie observations of single-cell transcriptional dynamics. Although RNA expression data encode information on gene expression models, existing computational frameworks do not perform simultaneous Bayesian inference of gene expression models and parameters from such data. Rather, gene expression models-composed of gene states, their connectivities and associated parameters-are currently deduced by pre-specifying gene state numbers and connectivity before learning associated rate parameters. Here we propose a method to learn full distributions over gene states, state connectivities and associated rate parameters, simultaneously and self-consistently from single-molecule RNA counts. We propagate noise from fluctuating RNA counts over models by treating models themselves as random variables. We achieve this within a Bayesian non-parametric paradigm. We demonstrate our method on the Escherichia coli lacZ pathway and the Saccharomyces cerevisiae STL1 pathway, and verify its robustness on synthetic data.

Resolving Crosstalk Between Signaling Pathways Using Mathematical Modeling and Time-Resolved Single Cell Data

Crosstalk between signaling pathways can modulate the cellular response to stimuli and is therefore an important part of signal transduction. For a comprehensive understanding of cellular responses, identifying points of interaction between the underlying molecular networks is essential. Here, we present an approach that allows the systematic prediction of such interactions by perturbing one pathway and quantifying the concomitant alterations in the response of a second pathway. As the observed alterations contain information about the crosstalk, we use an ordinary differential equation-based model to extract this information by linking altered dynamics to individual processes. Consequently, we can predict the interaction points between two pathways. As an example, we employed our approach to investigate the crosstalk between the NF-κB and p53 signaling pathway. We monitored the response of p53 to genotoxic stress using time-resolved single cell data and perturbed NF-κB signaling by inhibiting the kinase IKK2. Employing a subpopulation-based modeling approach enabled us to identify multiple interaction points that are simultaneously affected by perturbation of NF-κB signaling. Hence, our approach can be used to analyze crosstalk between two signaling pathways in a systematic manner.

Intercellular interaction mechanisms promote diversity in intracellular ATP concentration in Escherichia coli populations

In fluctuating environments, many microorganisms acquire phenotypic heterogeneity as a survival tactic to increase the likelihood of survival of the overall population. One example of this interindividual heterogeneity is the diversity of ATP concentration among members of Escherichia coli populations under glucose deprivation. Despite the importance of such environmentally driven phenotypic heterogeneity, how the differences in intracellular ATP concentration emerge among individual E. coli organisms is unknown. In this study, we focused on the mechanism through which individual E. coli achieve high intracellular ATP concentrations. First, we measured the ATP retained by E. coli over time when cultured at low (0.1 mM) and control (22.2 mM) concentrations of glucose and obtained the chronological change in ATP concentrations. Then, by comparing these chronological change of ATP concentrations and analyzing whether stochastic state transitions, periodic oscillations, cellular age, and intercellular communication-which have been reported as molecular biological mechanisms for generating interindividual heterogeneity-are involved, we showed that the appearance of high ATP-holding individuals observed among E. coli can be explained only by intercellular transmission. By performing metabolomic analysis of post-culture medium, we revealed a significant increase in the ATP, especially at low glucose, and that the number of E. coli that retain significantly higher ATP can be controlled by adding large amounts of ATP to the medium, even in populations cultured under control glucose concentrations. These results reveal for the first time that ATP-mediated intercellular transmission enables some individuals in E. coli populations grown at low glucose to retain large amounts of ATP.

Identifiability analysis for models of the translation kinetics after mRNA transfection

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. That is, whether parameters can be uniquely determined from perfect or realistic data in theory and practice. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

Personalized computational model quantifies heterogeneity in postprandial responses to oral glucose challenge

Plasma glucose and insulin responses following an oral glucose challenge are representative of glucose tolerance and insulin resistance, key indicators of type 2 diabetes mellitus pathophysiology. A large heterogeneity in individuals' challenge test responses has been shown to underlie the effectiveness of lifestyle intervention. Currently, this heterogeneity is overlooked due to a lack of methods to quantify the interconnected dynamics in the glucose and insulin time-courses. Here, a physiology-based mathematical model of the human glucose-insulin system is personalized to elucidate the heterogeneity in individuals' responses using a large population of overweight/obese individuals (n = 738) from the DIOGenes study. The personalized models are derived from population level models through a systematic parameter selection pipeline that may be generalized to other biological systems. The resulting personalized models showed a 4-5 fold decrease in discrepancy between measurements and model simulation compared to population level. The estimated model parameters capture relevant features of individuals' metabolic health such as gastric emptying, endogenous insulin secretion and insulin dependent glucose disposal into tissues, with the latter also showing a significant association with the Insulinogenic index and the Matsuda insulin sensitivity index, respectively.

Strategies for simultaneous and successive delivery of RNA

Advanced non-viral gene delivery experiments often require co-delivery of multiple nucleic acids. Therefore, the availability of reliable and robust co-transfection methods and defined selection criteria for their use in, e.g., expression of multimeric proteins or mixed RNA/DNA delivery is of utmost importance. Here, we investigated different co- and successive transfection approaches, with particular focus on in vitro transcribed messenger RNA (IVT-mRNA). Expression levels and patterns of two fluorescent protein reporters were determined, using different IVT-mRNA doses, carriers, and cell types. Quantitative parameters determining the efficiency of co-delivery were analyzed for IVT-mRNAs premixed before nanocarrier formation (integrated co-transfection) and when simultaneously transfecting cells with separately formed nanocarriers (parallel co-transfection), which resulted in a much higher level of expression heterogeneity for the two reporters. Successive delivery of mRNA revealed a lower transfection efficiency in the second transfection round. All these differences proved to be more pronounced for low mRNA doses. Concurrent delivery of siRNA with mRNA also indicated the highest co-transfection efficiency for integrated method. However, the maximum efficacy was shown for successive delivery, due to the kinetically different peak output for the two discretely operating entities. Our findings provide guidance for selection of the co-delivery method best suited to accommodate experimental requirements, highlighting in particular the nucleic acid dose-response dependence on co-delivery on the single-cell level.

Fine-Tuning of Energy Levels Regulates SUC2 via a SNF1-Dependent Feedback Loop

Nutrient sensing pathways are playing an important role in cellular response to different energy levels. In budding yeast, Saccharomyces cerevisiae, the sucrose non-fermenting protein kinase complex SNF1 is a master regulator of energy homeostasis. It is affected by multiple inputs, among which energy levels is the most prominent. Cells which are exposed to a switch in carbon source availability display a change in the gene expression machinery. It has been shown that the magnitude of the change varies from cell to cell. In a glucose rich environment Snf1/Mig1 pathway represses the expression of its downstream target, such as SUC2. However, upon glucose depletion SNF1 is activated which leads to an increase in SUC2 expression. Our single cell experiments indicate that upon starvation, gene expression pattern of SUC2 shows rapid increase followed by a decrease to initial state with high cell-to-cell variability. The mechanism behind this behavior is currently unknown. In this work we study the long-term behavior of the Snf1/Mig1 pathway upon glucose starvation with a microfluidics and non-linear mixed effect modeling approach. We show a negative feedback mechanism, involving Snf1 and Reg1, which reduces SUC2 expression after the initial strong activation. Snf1 kinase activity plays a key role in this feedback mechanism. Our systems biology approach proposes a negative feedback mechanism that works through the SNF1 complex and is controlled by energy levels. We further show that Reg1 likely is involved in the negative feedback mechanism.

A systematic approach to decipher crosstalk in the p53 signaling pathway using single cell dynamics

The transcription factors NF-κB and p53 are key regulators in the genotoxic stress response and are critical for tumor development. Although there is ample evidence for interactions between both networks, a comprehensive understanding of the crosstalk is lacking. Here, we developed a systematic approach to identify potential interactions between the pathways. We perturbed NF-κB signaling by inhibiting IKK2, a critical regulator of NF-κB activity, and monitored the altered response of p53 to genotoxic stress using single cell time lapse microscopy. Fitting subpopulation-specific computational p53 models to this time-resolved single cell data allowed to reproduce in a quantitative manner signaling dynamics and cellular heterogeneity for the unperturbed and perturbed conditions. The approach enabled us to untangle the integrated effects of IKK/ NF-κB perturbation on p53 dynamics and thereby derive potential interactions between both networks. Intriguingly, we find that a simultaneous perturbation of multiple processes is necessary to explain the observed changes in the p53 response. Specifically, we show interference with the activation and degradation of p53 as well as the degradation of Mdm2. Our results highlight the importance of the crosstalk and its potential implications in p53-dependent cellular functions.

Cells can respond to external and internal inputs by transducing information to the nucleus where transcription factors initiate corresponding cellular responses. Cellular signaling is mediated by several pathways; molecular networks that can interact with each other, which alters signal processing and modulates cellular responses. As deregulated signaling can lead to the development of tumors it is important to understand not only how signaling pathways function but also the contribution of their interaction on the signaling dynamics. Here, we analyzed the interplay of the IKK/ NF-κB and p53 pathway, which are both critical for the cellular response to DNA damage and have been implicated in tumor development. To systematically identify interaction points between both pathways, we perturbed IKK/ NF-κB signaling and tracked the changes in the response of p53 to DNA damage. Using computational methods, we show that several reactions in the p53 pathway are simultaneously affected by NF-κB signaling and that this combined action is necessary to explain altered behaviour of the p53 pathway. Hence, our results provide new insights into the interplay between the NF-κB and p53 pathway and help to gain a more comprehensive understanding of the crosstalk.

Inheritance and variability of kinetic gene expression parameters in microbial cells: modeling and inference from lineage tree data

Motivation

Modern experimental technologies enable monitoring of gene expression dynamics in individual cells and quantification of its variability in isogenic microbial populations. Among the sources of this variability is the randomness that affects inheritance of gene expression factors at cell division. Known parental relationships among individually observed cells provide invaluable information for the characterization of this extrinsic source of gene expression noise. Despite this fact, most existing methods to infer stochastic gene expression models from single-cell data dedicate little attention to the reconstruction of mother–daughter inheritance dynamics.

Results

Starting from a transcription and translation model of gene expression, we propose a stochastic model for the evolution of gene expression dynamics in a population of dividing cells. Based on this model, we develop a method for the direct quantification of inheritance and variability of kinetic gene expression parameters from single-cell gene expression and lineage data. We demonstrate that our approach provides unbiased estimates of mother–daughter inheritance parameters, whereas indirect approaches using lineage information only in the post-processing of individual-cell parameters underestimate inheritance. Finally, we show on yeast osmotic shock response data that daughter cell parameters are largely determined by the mother, thus confirming the relevance of our method for the correct assessment of the onset of gene expression variability and the study of the transmission of regulatory factors.

Availability and implementation

Software code is available at https://github.com/almarguet/IdentificationWithARME. Lineage tree data is available upon request.

Supplementary information

Supplementary material is available at Bioinformatics online.