Models at the single cell level

Abstract

Many cellular behaviors cannot be completely captured or appropriately described at the cell population level. Noise induced by stochastic chemical reactions, spatially polarized signaling networks and heterogeneous cell-cell communication are among the many phenomena that require fine-grained analysis. Accordingly, the mathematical models used to describe such systems must be capable of single cell or subcellular resolution. Here, we review techniques for modeling single cells, including models of stochastic chemical kinetics, spatially heterogeneous intracellular signaling, and spatial stochastic systems. We also briefly discuss applications of each type of model.

Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression

“…Cheong et al 2010;Shahrezaei and Swain 2008b) discussing the stochastic model (6), except for a special asymptotic case of fast mRNA degradation (Shahrezaei and Swain 2008a). The chemical kinetics description (1) for spontaneous gene expression is referred to as the two-stage model (Thattai and van Oudenaarden 2001;Shahrezaei and Swain 2008a), the stages being those of transcription and translation, as opposed to a more detailed three-stage model (Shahrezaei and Swain 2008a;Blake et al 2003;Raser and O'Shea 2004;Coulon et al 2010;Raj et al 2006), which includes an upstream mechanism of promoter transitioning between two or more states each associated with a distinct rate constant for transcription.…”

Systems approaches in osteoarthritis: Identifying routes to novel diagnostic and therapeutic strategies

“…More finely‐grained appreciation of cellular behavior, such as spatially restricted signaling, requires stochastic modelling at a single‐cell (or sub‐cellular) level 26. (C) Most network models are static and have not been validated.…”

“…Both studies have implications on our understanding of how chondrocytes may be manipulated (directed differentiation) in cell-based regenerative therapies for OA and the validity of current mechanistic models using established laboratory approaches. An obvious future approach would be the application of stochastic modeling techniques to quantify the biological variability and uncertainty in single cell measurements 25,26 ; failing to consider this may influence the interpretation of in vitro experiments.…”

“…More finely-grained appreciation of cellular behavior, such as spatially restricted signaling, requires stochastic modelling at a single-cell (or sub-cellular) level. 26 (C) Most network models are static and have not been validated. Dynamic models, using a series of ordinary differential equations, may be used to simulate a hypothetical regulatory mechanism (e.g., positive feedback), which may then inform in vitro validation studies; (D) Agent-based modelling is a "bottom-up" approach that uses the activity and interactions of autonomous "agents" (e.g., cells) to simulate and predict the observed complex behavior.…”

Strength in numbers: quantitative single‐molecule RNA detection assays

“…While originally restricted to bulk analysis, in recent years, these methods have become sensitive enough to detect virtually a single unique nucleic acid sequence within a sample . Single‐cell qRT‐PCR and RNA sequencing of various bacteria, yeast, and higher eukaryotic cells from cell culture, dissociated tissues, or from embryos have shown that there are gene expression differences of orders of magnitude between seemingly identical peers within a given population . With a few exceptions, these assays lack any subcellular and temporal resolving power: they cannot distinguish between physiological noise due to bursts of transcription, cell cycle, or developmental stage‐specific regulation of gene expression, or between functional mRNAs exported to the cytoplasm for translation and mRNAs targeted for intranuclear decay and other spatiotemporal events .…”