Funneled potential and flux landscapes dictate the stabilities of both the states and the flow: Fission yeast cell cycle

Uncovering underlying physical principles and driving forces of cell differentiation and reprogramming from single-cell transcriptomics

Recent advances in single-cell sequencing technology have revolutionized our ability to acquire whole transcriptome data. However, uncovering the underlying transcriptional drivers and nonequilibrium driving forces of cell function directly from these data remains challenging. We address this by learning cell state vector fields from discrete single-cell RNA velocity to quantify the single-cell global nonequilibrium driving forces as landscape and flux. From single-cell data, we quantified the Waddington landscape, showing that optimal paths for differentiation and reprogramming deviate from the naively expected landscape gradient paths and may not pass through landscape saddles at finite fluctuations, challenging conventional transition state estimation of kinetic rate for cell fate decisions due to the presence of the flux. A key insight from our study is that stem/progenitor cells necessitate greater energy dissipation for rapid cell cycles and self-renewal, maintaining pluripotency. We predict optimal developmental pathways and elucidate the nucleation mechanism of cell fate decisions, with transition states as nucleation sites and pioneer genes as nucleation seeds. The concept of loop flux quantifies the contributions of each cycle flux to cell state transitions, facilitating the understanding of cell dynamics and thermodynamic cost, and providing insights into optimizing biological functions. We also infer cell-cell interactions and cell-type-specific gene regulatory networks, encompassing feedback mechanisms and interaction intensities, predicting genetic perturbation effects on cell fate decisions from single-cell omics data. Essentially, our methodology validates the landscape and flux theory, along with its associated quantifications, offering a framework for exploring the physical principles underlying cellular differentiation and reprogramming and broader biological processes through high-throughput single-cell sequencing experiments.

Quantifying Dynamic Phenotypic Heterogeneity in Resistant Escherichia coli under Translation-Inhibiting Antibiotics

Understanding the phenotypic heterogeneity of antibiotic-resistant bacteria following treatment and the transitions between different phenotypes is crucial for developing effective infection control strategies. The study expands upon previous work by explicating chloramphenicol-induced phenotypic heterogeneities in growth rate, gene expression, and morphology of resistant Escherichia coli using time-lapse microscopy. Correlating the bacterial growth rate and cspC expression, four interchangeable phenotypic subpopulations across varying antibiotic concentrations are identified, surpassing the previously described growth rate bistability. Notably, bacterial cells exhibiting either fast or slow growth rates can concurrently harbor subpopulations characterized by high and low gene expression levels, respectively. To elucidate the mechanisms behind this enhanced heterogeneity, a concise gene expression network model is proposed and the biological significance of the four phenotypes is further explored. Additionally, by employing Hidden Markov Model fitting and integrating the non-equilibrium landscape and flux theory, the real-time data encompassing diverse bacterial traits are analyzed. This approach reveals dynamic changes and switching kinetics in different cell fates, facilitating the quantification of observable behaviors and the non-equilibrium dynamics and thermodynamics at play. The results highlight the multi-dimensional heterogeneous behaviors of antibiotic-resistant bacteria under antibiotic stress, providing new insights into the compromised antibiotic efficacy, microbial response, and associated evolution processes.

Quantifying cancer cell plasticity with gene regulatory networks and single-cell dynamics

Phenotypic plasticity of cancer cells can lead to complex cell state dynamics during tumor progression and acquired resistance. Highly plastic stem-like states may be inherently drug-resistant. Moreover, cell state dynamics in response to therapy allow a tumor to evade treatment. In both scenarios, quantifying plasticity is essential for identifying high-plasticity states or elucidating transition paths between states. Currently, methods to quantify plasticity tend to focus on 1) quantification of quasi-potential based on the underlying gene regulatory network dynamics of the system; or 2) inference of cell potency based on trajectory inference or lineage tracing in single-cell dynamics. Here, we explore both of these approaches and associated computational tools. We then discuss implications of each approach to plasticity metrics, and relevance to cancer treatment strategies.

Quantifying nonequilibrium dynamics and thermodynamics of cell fate decision making in yeast under pheromone induction

Cellular responses to pheromone in yeast can range from gene expression to morphological and physiological changes. While signaling pathways are well studied, the cell fate decision-making during cellular polar growth is still unclear. Quantifying these cellular behaviors and revealing the underlying physical mechanism remain a significant challenge. Here, we employed a hidden Markov chain model to quantify the dynamics of cellular morphological systems based on our experimentally observed time series. The resulting statistics generated a stability landscape for state attractors. By quantifying rotational fluxes as the non-equilibrium driving force that tends to disrupt the current attractor state, the dynamical origin of non-equilibrium phase transition from four cell morphological fates to a single dominant fate was identified. We revealed that higher chemical voltage differences induced by a high dose of pheromone resulted in higher chemical currents, which will trigger a greater net input and, thus, more degrees of the detailed balance breaking. By quantifying the thermodynamic cost of maintaining morphological state stability, we demonstrated that the flux-related entropy production rate provides a thermodynamic origin for the phase transition in non-equilibrium morphologies. Furthermore, we confirmed that the time irreversibility in time series provides a practical way to predict the non-equilibrium phase transition.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

Nonequilibrium Thermodynamics in Cell Biology: Extending Equilibrium Formalism to Cover Living Systems

We discuss new developments in the nonequilibrium dynamics and thermodynamics of living systems, giving a few examples to demonstrate the importance of nonequilibrium thermodynamics for understanding biological dynamics and functions. We study single-molecule enzyme dynamics, in which the nonequilibrium thermodynamic and dynamic driving forces of chemical potential and flux are crucial for the emergence of non-Michaelis-Menten kinetics. We explore single-gene expression dynamics, in which nonequilibrium dissipation can suppress fluctuations. We investigate the cell cycle and identify the nutrition supply as the energy input that sustains the stability, speed, and coherence of cell cycle oscillation, from which the different vital phases of the cell cycle emerge. We examine neural decision-making processes and find the trade-offs among speed, accuracy, and thermodynamic costs that are important for neural function. Lastly, we consider the thermodynamic cost for specificity in cellular signaling and adaptation.

Role of noise and parametric variation in the dynamics of gene regulatory circuits

Stochasticity in gene expression impacts the dynamics and functions of gene regulatory circuits. Intrinsic noises, including those that are caused by low copy number of molecules and transcriptional bursting, are usually studied by stochastic simulations. However, the role of extrinsic factors, such as cell-to-cell variability and heterogeneity in the microenvironment, is still elusive. To evaluate the effects of both the intrinsic and extrinsic noises, we develop a method, named sRACIPE, by integrating stochastic analysis with random circuit perturbation (RACIPE) method. RACIPE uniquely generates and analyzes an ensemble of models with random kinetic parameters. Previously, we have shown that the gene expression from random models form robust and functionally related clusters. In sRACIPE we further develop two stochastic simulation schemes, aiming to reduce the computational cost without sacrificing the convergence of statistics. One scheme uses constant noise to capture the basins of attraction, and the other one uses simulated annealing to detect the stability of states. By testing the methods on several synthetic gene regulatory circuits and an epithelial-mesenchymal transition network in squamous cell carcinoma, we demonstrate that sRACIPE can interpret the experimental observations from single-cell gene expression data. We observe that parametric variation (the spread of parameters around a median value) increases the spread of the gene expression clusters, whereas high noise merges the states. Our approach quantifies the robustness of a gene circuit in the presence of noise and sheds light on a new mechanism of noise-induced hybrid states. We have implemented sRACIPE as an R package.

Cell cycle time series gene expression data encoded as cyclic attractors in Hopfield systems

Modern time series gene expression and other omics data sets have enabled unprecedented resolution of the dynamics of cellular processes such as cell cycle and response to pharmaceutical compounds. In anticipation of the proliferation of time series data sets in the near future, we use the Hopfield model, a recurrent neural network based on spin glasses, to model the dynamics of cell cycle in HeLa (human cervical cancer) and S. cerevisiae cells. We study some of the rich dynamical properties of these cyclic Hopfield systems, including the ability of populations of simulated cells to recreate experimental expression data and the effects of noise on the dynamics. Next, we use a genetic algorithm to identify sets of genes which, when selectively inhibited by local external fields representing gene silencing compounds such as kinase inhibitors, disrupt the encoded cell cycle. We find, for example, that inhibiting the set of four kinases AURKB, NEK1, TTK, and WEE1 causes simulated HeLa cells to accumulate in the M phase. Finally, we suggest possible improvements and extensions to our model.

Cell cycle—the process in which a parent cell replicates its DNA and divides into two daughter cells—is an upregulated process in many forms of cancer. Identifying gene inhibition targets to regulate cell cycle is important to the development of effective therapies. Although modern high throughput techniques offer unprecedented resolution of the molecular details of biological processes like cell cycle, analyzing the vast quantities of the resulting experimental data and extracting actionable information remains a formidable task. Here, we create a dynamical model of the process of cell cycle using the Hopfield model (a type of recurrent neural network) and gene expression data from human cervical cancer cells and yeast cells. We find that the model recreates the oscillations observed in experimental data. Tuning the level of noise (representing the inherent randomness in gene expression and regulation) to the “edge of chaos” is crucial for the proper behavior of the system. We then use this model to identify potential gene targets for disrupting the process of cell cycle. This method could be applied to other time series data sets and used to predict the effects of untested targeted perturbations.