Using single-cell models to predict the functionality of synthetic circuits at the population scale

Feedback between stochastic gene networks and population dynamics enables cellular decision-making

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging-like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

A local polynomial moment approximation for compartmentalized biochemical systems

Compartmentalized biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyze mathematically - especially in the presence of stochasticity. We have recently proposed an effective moment equation approach to study the statistical properties of compartmentalized biochemical systems. So far, however, this approach is limited to polynomial rate laws and moreover, it relies on suitable moment closure approximations, which can be difficult to find in practice. In this work we propose a systematic method to derive closed moment dynamics for compartmentalized biochemical systems. We show that for the considered class of systems, the moment equations involve expectations over functions that factorize into two parts, one depending on the molecular content of the compartments and one depending on the compartment number distribution. Our method exploits this structure and approximates each function with suitable polynomial expansions, leading to a closed system of moment equations. We demonstrate the method using three systems inspired by cell populations and organelle networks and study its accuracy across different dynamical regimes.

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Stochastic chemical kinetics is a widely used formalism for studying stochasticity of chemical reactions inside single cells. Experimental studies of reaction networks are generally performed with cells that are part of a growing population, yet the population context is rarely taken into account when models are developed. Models that neglect the population context lose their validity whenever the studied system influences traits of cells that can be selected in the population, a property that naturally arises in the complex interplay between single-cell and population dynamics of cell fate decision systems. Here, we represent such systems as absorbing continuous-time Markov chains. We show that conditioning on non-absorption allows one to derive a modified master equation that tracks the time evolution of the expected population composition within a growing population. This allows us to derive consistent population dynamics models from a specification of the single-cell process. We use this approach to classify cell fate decision systems into two types that lead to different characteristic phases in emerging population dynamics. Subsequently, we deploy the gained insights to experimentally study a recurrent problem in biology: how to link plasmid copy number fluctuations and plasmid loss events inside single cells to growth of cell populations in dynamically changing environments.

Advances in automated and reactive flow cytometry for synthetic biotechnology

Automated flow cytometry (FC) has been initially considered for bioprocess monitoring and optimization. More recently, new physical and software interfaces have been made available, facilitating the access to this technology for labs and industries. It also comes with new capabilities, such as being able to act on the cultivation conditions based on population data. This approach, known as reactive FC, extended the range of applications of automated FC to bioprocess control and the stabilization of cocultures, but also to the broad field of synthetic and systems biology for the characterization of gene circuits. However, several issues must be addressed before automated and reactive FC can be considered standard and modular technologies.

Maximizing protein production by keeping cells at optimal secretory stress levels using real-time control approaches

Optimizing the production of recombinant proteins is a problem of major industrial and pharmaceutical importance. Secretion of the protein by the host cell considerably simplifies downstream purification processes. However, for many proteins, this is also the limiting production step. Current solutions involve extensive engineering of the chassis cell to facilitate protein trafficking and limit protein degradation triggered by excessive secretion-associated stress. Here, we propose instead a regulation-based strategy in which induction is dynamically adjusted to an optimal strength based on the current stress level of the cells. Using a small collection of hard-to-secrete proteins, a bioreactor-based platform with automated cytometry measurements, and a systematic assay to quantify secreted protein levels, we demonstrate that the secretion sweet spot is indicated by the appearance of a subpopulation of cells that accumulate high amounts of proteins, decrease growth, and face significant stress, that is, experience a secretion burnout. In these cells, adaptations capabilities are overwhelmed by a too strong production. Using these notions, we show for a single-chain antibody variable fragment that secretion levels can be improved by 70% by dynamically keeping the cell population at optimal stress levels using real-time closed-loop control.

Constrained disorder principle-based variability is fundamental for biological processes: Beyond biological relativity and physiological regulatory networks

The constrained disorder principle (CDP) defines systems based on their degree of disorder bounded by dynamic boundaries. The principle explains stochasticity in living and non-living systems. Denis Noble described the importance of stochasticity in biology, emphasizing stochastic processes at molecular, cellular, and higher levels in organisms as having a role beyond simple noise. The CDP and Noble's theories (NT) claim that biological systems use stochasticity. This paper presents the CDP and NT, discussing common notions and differences between the two theories. The paper presents the CDP-based concept of taking the disorder beyond its role in nature to correct malfunctions of systems and improve the efficiency of biological systems. The use of CDP-based algorithms embedded in second-generation artificial intelligence platforms is described. In summary, noise is inherent to complex systems and has a functional role. The CDP provides the option of using noise to improve functionality.

Optimal control of bioproduction in the presence of population heterogeneity

Cell-to-cell variability, born of stochastic chemical kinetics, persists even in large isogenic populations. In the study of single-cell dynamics this is typically accounted for. However, on the population level this source of heterogeneity is often sidelined to avoid the inevitable complexity it introduces. The homogeneous models used instead are more tractable but risk disagreeing with their heterogeneous counterparts and may thus lead to severely suboptimal control of bioproduction. In this work, we introduce a comprehensive mathematical framework for solving bioproduction optimal control problems in the presence of heterogeneity. We study population-level models in which such heterogeneity is retained, and propose order-reduction approximation techniques. The reduced-order models take forms typical of homogeneous bioproduction models, making them a useful benchmark by which to study the importance of heterogeneity. Moreover, the derivation from the heterogeneous setting sheds light on parameter selection in ways a direct homogeneous outlook cannot, and reveals the source of approximation error. With view to optimally controlling bioproduction in microbial communities, we ask the question: when does optimising the reduced-order models produce strategies that work well in the presence of population heterogeneity? We show that, in some cases, homogeneous approximations provide remarkably accurate surrogate models. Nevertheless, we also demonstrate that this is not uniformly true: overlooking the heterogeneity can lead to significantly suboptimal control strategies. In these cases, the heterogeneous tools and perspective are crucial to optimise bioproduction.

Platforms for Optogenetic Stimulation and Feedback Control

Harnessing the potential of optogenetics in biology requires methodologies from different disciplines ranging from biology, to mechatronics engineering, to control engineering. Light stimulation of a synthetic optogenetic construct in a given biological species can only be achieved via a suitable light stimulation platform. Emerging optogenetic applications entail a consistent, reproducible, and regulated delivery of light adapted to the application requirement. In this review, we explore the evolution of light-induction hardware-software platforms from simple illumination set-ups to sophisticated microscopy, microtiter plate and bioreactor designs, and discuss their respective advantages and disadvantages. Here, we examine design approaches followed in performing optogenetic experiments spanning different cell types and culture volumes, with induction capabilities ranging from single cell stimulation to entire cell culture illumination. The development of automated measurement and stimulation schemes on these platforms has enabled researchers to implement various in silico feedback control strategies to achieve computer-controlled living systems—a theme we briefly discuss in the last part of this review.

Revisiting moment-closure methods with heterogeneous multiscale population models

Stochastic chemical kinetics at the single-cell level give rise to heterogeneous populations of cells even when all individuals are genetically identical. This heterogeneity can lead to nonuniform behaviour within populations, including different growth characteristics, cell-fate dynamics, and response to stimuli. Ultimately, these diverse behaviours lead to intricate population dynamics that are inherently multiscale: the population composition evolves based on population-level processes that interact with stochastically distributed single-cell states. Therefore, descriptions that account for this heterogeneity are essential to accurately model and control chemical processes. However, for real-world systems such models are computationally expensive to simulate, which can make optimisation problems, such as optimal control or parameter inference, prohibitively challenging. Here, we consider a class of multiscale population models that incorporate population-level mechanisms while remaining faithful to the underlying stochasticity at the single-cell level and the interplay between these two scales. To address the complexity, we study an order-reduction approximations based on the distribution moments. Since previous moment-closure work has focused on the single-cell kinetics, extending these techniques to populations models prompts us to revisit old observations as well as tackle new challenges. In this extended multiscale context, we encounter the previously established observation that the simplest closure techniques can lead to non-physical system trajectories. Despite their poor performance in some systems, we provide an example where these simple closures outperform more sophisticated closure methods in accurately, efficiently, and robustly solving the problem of optimal control of bioproduction in a microbial consortium model.