Metastability and dynamics of stem cells: from direct observations to inference at the single cell level

Organismal development, homeostasis, and pathology are rooted in inherently probabilistic events. From gene expression to cellular differentiation, rates and likelihoods shape the form and function of biology. Processes ranging from growth to cancer homeostasis to reprogramming of stem cells all require transitions between distinct phenotypic states, and these occur at defined rates. Therefore, measuring the fidelity and dynamics with which such transitions occur is central to understanding natural biological phenomena and is critical for therapeutic interventions.

While these processes may produce robust population-level behaviors, decisions are made by individual cells. In certain circumstances, these minuscule computing units effectively roll dice to determine their fate. And while the 'omics' era has provided vast amounts of data on what these populations are doing en masse, the behaviors of the underlying units of these processes get washed out in averages.

Therefore, in order to understand the behavior of a sample of cells, it is critical to reveal how its underlying components, or mixture of cells in distinct states, each contribute to the overall phenotype. As such, we must first define what states exist in the population, determine what controls the stability of these states, and measure in high dimensionality the dynamics with which these cells transition between states.

To address a specific example of this general problem, we investigate the heterogeneity and dynamics of mouse embryonic stem cells (mESCs). While a number of reports have identified particular genes in ES cells that switch between 'high' and 'low' metastable expression states in culture, it remains unclear how levels of many of these regulators combine to form states in transcriptional space. Using a method called single molecule mRNA fluorescent in situ hybridization (smFISH), we quantitatively measure and fit distributions of core pluripotency regulators in single cells, identifying a wide range of variabilities between genes, but each explained by a simple model of bursty transcription. From this data, we also observed that strongly bimodal genes appear to be co-expressed, effectively limiting the occupancy of transcriptional space to two primary states across genes studied here. However, these states also appear punctuated by the conditional expression of the most highly variable genes, potentially defining smaller substates of pluripotency.

Having defined the transcriptional states, we next asked what might control their stability or persistence. Surprisingly, we found that DNA methylation, a mark normally associated with irreversible developmental progression, was itself differentially regulated between these two primary states. Furthermore, both acute or chronic inhibition of DNA methyltransferase activity led to reduced heterogeneity among the population, suggesting that metastability can be modulated by this strong epigenetic mark.

Finally, because understanding the dynamics of state transitions is fundamental to a variety of biological problems, we sought to develop a high-throughput method for the identification of cellular trajectories without the need for cell-line engineering. We achieved this by combining cell-lineage information gathered from time-lapse microscopy with endpoint smFISH for measurements of final expression states. Applying a simple mathematical framework to these lineage-tree associated expression states enables the inference of dynamic transitions. We apply our novel approach in order to infer temporal sequences of events, quantitative switching rates, and network topology among a set of ESC states.

Taken together, we identify distinct expression states in ES cells, gain fundamental insight into how a strong epigenetic modifier enforces the stability of these states, and develop and apply a new method for the identification of cellular trajectories using scalable in situ readouts of cellular state.

Real-time load-side control of electric power systems

Two trends are emerging from modern electric power systems: the growth of renewable (e.g., solar and wind) generation, and the integration of information technologies and advanced power electronics. The former introduces large, rapid, and random fluctuations in power supply, demand, frequency, and voltage, which become a major challenge for real-time operation of power systems. The latter creates a tremendous number of controllable intelligent endpoints such as smart buildings and appliances, electric vehicles, energy storage devices, and power electronic devices that can sense, compute, communicate, and actuate. Most of these endpoints are distributed on the load side of power systems, in contrast to traditional control resources such as centralized bulk generators. This thesis focuses on controlling power systems in real time, using these load side resources. Specifically, it studies two problems.

(1) Distributed load-side frequency control: We establish a mathematical framework to design distributed frequency control algorithms for flexible electric loads. In this framework, we formulate a category of optimization problems, called optimal load control (OLC), to incorporate the goals of frequency control, such as balancing power supply and demand, restoring frequency to its nominal value, restoring inter-area power flows, etc., in a way that minimizes total disutility for the loads to participate in frequency control by deviating from their nominal power usage. By exploiting distributed algorithms to solve OLC and analyzing convergence of these algorithms, we design distributed load-side controllers and prove stability of closed-loop power systems governed by these controllers. This general framework is adapted and applied to different types of power systems described by different models, or to achieve different levels of control goals under different operation scenarios. We first consider a dynamically coherent power system which can be equivalently modeled with a single synchronous machine. We then extend our framework to a multi-machine power network, where we consider primary and secondary frequency controls, linear and nonlinear power flow models, and the interactions between generator dynamics and load control.

(2) Two-timescale voltage control: The voltage of a power distribution system must be maintained closely around its nominal value in real time, even in the presence of highly volatile power supply or demand. For this purpose, we jointly control two types of reactive power sources: a capacitor operating at a slow timescale, and a power electronic device, such as a smart inverter or a D-STATCOM, operating at a fast timescale. Their control actions are solved from optimal power flow problems at two timescales. Specifically, the slow-timescale problem is a chance-constrained optimization, which minimizes power loss and regulates the voltage at the current time instant while limiting the probability of future voltage violations due to stochastic changes in power supply or demand. This control framework forms the basis of an optimal sizing problem, which determines the installation capacities of the control devices by minimizing the sum of power loss and capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments show that the proposed sizing and control schemes significantly improve the reliability of voltage control with a moderate increase in cost.