exFINDER: identify external communication signals using single-cell transcriptomics data.

Cells make decisions through their communication with other cells and receiving signals from their environment. Using single-cell transcriptomics, computational tools have been developed to infer cell-cell communication through ligands and receptors. However, the existing methods only deal with signals sent by the measured cells in the data, the received signals from the external system are missing in the inference. Here, we present exFINDER, a method that identifies such external signals received by the cells in the single-cell transcriptomics datasets by utilizing the prior knowledge of signaling pathways. In particular, exFINDER can uncover external signals that activate the given target genes, infer the external signal-target signaling network (exSigNet), and perform quantitative analysis on exSigNets. The applications of exFINDER to scRNA-seq datasets from different species demonstrate the accuracy and robustness of identifying external signals, revealing critical transition-related signaling activities, inferring critical external signals and targets, clustering signal-target paths, and evaluating relevant biological events. Overall, exFINDER can be applied to scRNA-seq data to reveal the external signal-associated activities and maybe novel cells that send such signals.

Reaction-Diffusion Modeling of E. coli Colony Growth Based on Nutrient Distribution and Agar Dehydration.

The bacterial colony is a powerful experimental platform for broad biological research, and reaction-diffusion models are widely used to study the mechanisms of its formation process. However, there are still some crucial factors that drastically affect the colony growth but are not considered in the current models, such as the non-homogeneously distributed nutrient within the colony and the substantially decreasing expansion rate caused by agar dehydration. In our study, we propose two plausible reaction-diffusion models (the VN and MVN models) based on the above two factors and validate them against experimental data. Both models provide a plausible description of the non-homogeneously distributed nutrient within the colony and outperform the classical Fisher-Kolmogorov equation and its variation in better describing experimental data. Moreover, by accounting for agar dehydration, the MVN model captures how a colony's expansion slows down and the change of a colony's height profile over time. Furthermore, we demonstrate the existence of a traveling wave solution for the VN model.

Learning Biological Dynamics From Spatio-Temporal Data by Gaussian Processes.

Model discovery methods offer a promising way to understand biology from data. We propose a method to learn biological dynamics from spatio-temporal data by Gaussian processes. This approach is essentially "equation free" and hence avoids model derivation, which is often difficult due to high complexity of biological processes. By exploiting the local nature of biological processes, dynamics can be learned with data sparse in time. When the length scales (hyperparameters) of the squared exponential covariance function are tuned, they reveal key insights of the underlying process. The squared exponential covariance function also simplifies propagation of uncertainty in multi-step forecasting. After evaluating the performance of the method on synthetic data, we demonstrate a case study on real image data of E. coli colony.

Modularized Design and Construction of Tunable Microbial Consortia with Flexible Topologies.

Complex and fluid bacterial community compositions are critical to diversity, stability, and function. However, quantitative and mechanistic descriptions of the dynamics of such compositions are still lacking. Here, we develop a modularized design framework that allows for bottom-up construction and the study of synthetic bacterial consortia with different topologies. We showcase the microbial consortia design and building process by constructing amensalism and competition consortia using only genetic circuit modules to engineer different strains to form the community. Functions of modules and hosting strains are validated and quantified to calibrate dynamic parameters, which are then directly fed into a full mechanistic model to accurately predict consortia composition dynamics for both amensalism and competition without further fitting. More importantly, such quantitative understanding successfully identifies the experimental conditions to achieve coexistence composition dynamics. These results illustrate the process of both computationally and experimentally building up bacteria consortia complexity and hence achieve robust control of such fluid systems.

exFINDER: identify external communication signals using single-cell transcriptomics data.

Cells make decisions through their communication with other cells and receiving signals from their environment. Using single-cell transcriptomics, computational tools have been developed to infer cell-cell communication through ligands and receptors. However, the existing methods only deal with signals sent by the measured cells in the data, the received signals from the external system are missing in the inference. Here, we present exFINDER, a method that identifies such external signals received by the cells in the single-cell transcriptomics datasets by utilizing the prior knowledge of signaling pathways. In particular, exFINDER can uncover external signals that activate the given target genes, infer the external signal-target signaling network (exSigNet), and perform quantitative analysis on exSigNets. The applications of exFINDER to scRNA-seq datasets from different species demonstrate the accuracy and robustness of identifying external signals, revealing critical transition-related signaling activities, inferring critical external signals and targets, clustering signal-target paths, and evaluating relevant biological events. Overall, exFINDER can be applied to scRNA-seq data to reveal the external signal-associated activities and maybe novel cells that send such signals.

Dynamics and growth rate implications of ribosomes and mRNAs interaction in E. coli.

Understanding how cells grow and adapt under various nutrient conditions is pivotal in the study of biological stoichiometry. Recent studies provide empirical evidence that cells use multiple strategies to maintain an optimal protein production rate under different nutrient conditions. Mathematical models can provide a solid theoretical foundation that can explain experimental observations and generate testable hypotheses to further our understanding of the growth process. In this study, we generalize a modeling framework that centers on the translation process and study its asymptotic behaviors to validate algebraic manipulations involving the steady states. Using experimental results on the growth of E. coli under C-, N-, and P-limited environments, we simulate the expected quantitative measurements to show the feasibility of using the model to explain empirical evidence. Our results support the findings that cells employ multiple strategies to maintain a similar protein production rate across different nutrient limitations. Moreover, we find that the previous study underestimates the significance of certain biological rates, such as the binding rate of ribosomes to mRNA and the transition rate between different ribosomal stages. Furthermore, our simulation shows that the strategies used by cells under C- and P-limitations result in a faster overall growth dynamics than under N-limitation. In conclusion, the general modeling framework provides a valuable platform to study cell growth under different nutrient supply conditions, which also allows straightforward extensions to the coupling of transcription, translation, and energetics to deepen our understanding of the growth process.

A Predictive Reaction-diffusion Based Model of E.coli Colony Growth Control.

Bacterial colony formations exhibit diverse morphologies and dynamics. A mechanistic understanding of this process has broad implications to ecology and medicine. However, many control factors and their impacts on colony formation remain underexplored. Here we propose a reaction-diffusion based dynamic model to quantitatively describe cell division and colony expansion, where control factors of colony spreading take the form of nonlinear density-dependent function and the intercellular impacts take the form of density-dependent hill function. We validate the model using experimental E. coli colony growth data and our results show that the model is capable of predicting the whole colony expansion process in both time and space under different conditions. Furthermore, the nonlinear control factors can predict colony morphology at both center and edge of the colony.

Emergent Damped Oscillation Induced by Nutrient-Modulating Growth Feedback.

Growth feedback, the inherent coupling between the synthetic gene circuit and the host cell growth, could significantly change the circuit behaviors. Previously, a diverse array of emergent behaviors, such as growth bistability, enhanced ultrasensitivity, and topology-dependent memory loss, were reported to be induced by growth feedback. However, the influence of the growth feedback on the circuit functions remains underexplored. Here, we reported an unexpected damped oscillatory behavior of a self-activation gene circuit induced by nutrient-modulating growth feedback. Specifically, after dilution of the activated self-activation switch into the fresh medium with moderate nutrients, its gene expression first decreases as the cell grows and then shows a significant overshoot before it reaches the steady state, leading to damped oscillation dynamics. Fitting the data with a coarse-grained model suggests a nonmonotonic growth-rate regulation on gene production rate. The underlying mechanism of the oscillation was demonstrated by a molecular mathematical model, which includes the ribosome allocation toward gene production, cell growth, and cell maintenance. Interestingly, the model predicted a counterintuitive dependence of oscillation amplitude on the nutrition level, where the highest peak was found in the medium with moderate nutrients, but was not observed in rich nutrients. We experimentally verified this prediction by tuning the nutrient level in the culture medium. We did not observe significant oscillatory behavior for the toggle switch, suggesting that the emergence of damped oscillatory behavior depends on circuit network topology. Our results demonstrated a new nonlinear emergent behavior mediated by growth feedback, which depends on the ribosome allocation between gene circuit and cell growth.

Dynamics and implications of models for intermittent androgen suppression therapy.

In this paper, we formulate a three cell population model of intermittent androgen suppression therapy for cancer patients to study the treatment resistance development. We compare it with other models that have different underlying cell population structure using patient prostate specific antigen (PSA) and androgen data sets. Our results show that in the absence of extensive data, a two cell population structure performs slightly better in replicating and forecasting the dynamics observed in clinical PSA data. We also observe that at least one absorbing state should be present in the cell population structure of a plausible model for it to produce treatment resistance under continuous hormonal therapy. This suggests that the heterogeneity of prostate cancer cell population can be represented by two types of cells differentiated by their level of dependence on androgen, where the two types are linked via an irreversible transformation.