A novel assay based on fluorescence microscopy and image processing for determining phenotypic distributions of rod-shaped bacteria

Estimation methods for heterogeneous cell population models in systems biology

Heterogeneity among individual cells is a characteristic and relevant feature of living systems. A range of experimental techniques to investigate this heterogeneity is available, and multiple modelling frameworks have been developed to describe and simulate the dynamics of heterogeneous populations. Measurement data are used to adjust computational models, which results in parameter and state estimation problems. Methods to solve these estimation problems need to take the specific properties of data and models into account. The aim of this review is to give an overview on the state of the art in estimation methods for heterogeneous cell population data and models. The focus is on models based on the population balance equation, but stochastic and individual-based models are also discussed. It starts with a brief discussion of common experimental approaches and types of measurement data that can be obtained in this context. The second part describes computational modelling frameworks for heterogeneous populations and the types of estimation problems occurring for these models. The third part starts with a discussion of observability and identifiability properties, after which the computational methods to solve the various estimation problems are described.

Contributions of cell growth and biochemical reactions to nongenetic variability of cells

Cell-to-cell variability in the molecular composition of isogenic, steady-state growing cells arises spontaneously from the inherent stochasticity of intracellular biochemical reactions and cell growth. Here, we present a general decomposition of the total variance in the copy number per cell of a particular molecule. It quantifies the individual contributions made by processes associated with cell growth, biochemical reactions, and their control. We decompose the growth contribution further into variance contributions of random partitioning of molecules at cell division, mother-cell heterogeneity, and variation in cell-cycle progression. The contribution made by biochemical reactions is expressed in variance generated by molecule synthesis, degradation, and their regulation. We use this theory to study the influence of different growth and reaction-related processes, such as DNA replication, variable molecule-partitioning probability, and synthesis bursts, on stochastic cell-to-cell variability. Using simulations, we characterize the impact of noise in the generation-time on cell-to-cell variability. This article offers a widely-applicable theory on the influence of biochemical reactions and cellular growth on the phenotypic variability of growing, isogenic cells. The theory aids the design and interpretation of experiments involving single-molecule counting or real-time imaging of fluorescent reporter constructs.

Coarse-grained analysis of stochastically simulated cell populations with a positive feedback genetic network architecture

Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and efficient study of their long-time behaviour over a wide range of parameter values, the performance of solely direct temporal simulations requires significantly high computational time. In addition, when the dynamics of the cell populations exhibit non-trivial bistable behaviour, such an analysis becomes a prohibitive task, since a large ensemble of initial states need to be tested for the quest of possibly co-existing steady state solutions. In this work, we study cell populations which carry the lac operon network exhibiting solution multiplicity over a wide range of extracellular conditions (inducer concentration). By adopting ideas from the so-called "equation-free" methodology, we perform systems-level analysis, which includes numerical tasks such as the computation of coarse steady state solutions, coarse bifurcation analysis, as well as coarse stability analysis. Dynamically stable and unstable macroscopic (population level) steady state solutions are computed by means of bifurcation analysis utilising short bursts of fine-scale simulations, and the range of bistability is determined for different sizes of cell populations. The results are compared with the deterministic cell population balance model, which is valid for large populations, and we demonstrate the increased effect of stochasticity in small size populations with asymmetric partitioning mechanisms.

Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.