Theory of cell fate

Primer

Michael J. Casey, Patrick S. Stumpf, Ben D. MacArthur

Published Online: Dec 12 2019

DOI: 10.1002/wsbm.1471

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Abstract Cell fate decisions are controlled by complex intracellular molecular regulatory networks. Studies increasingly reveal the scale of this complexity: not only do cell fate regulatory networks contain numerous positive and negative feedback loops, they also involve a range of different kinds of nonlinear protein–protein and protein–DNA interactions. This inherent complexity and nonlinearity makes cell fate decisions hard to understand using experiment and intuition alone. In this primer, we will outline how tools from mathematics can be used to understand cell fate dynamics. We will briefly introduce some notions from dynamical systems theory, and discuss how they offer a framework within which to build a rigorous understanding of what we mean by a cell “fate”, and how cells change fate. We will also outline how modern experiments, particularly high‐throughput single‐cell experiments, are enabling us to test and explore the limits of these ideas, and build a better understanding of cellular identities. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Biological Mechanisms > Cell Fates Models of Systems Properties and Processes > Cellular Models

Mapping molecular states to cell fates. An individual cell can be described both in terms of its molecular state, and its fate. Each point in the molecular state box is a complete descriptor of the molecular constitution of a cell. The mapping between states and fates is many‐to‐one: different subsets of expression state space may map to the same fates. Here, three different fates A, B, and C, are illustrated, colored blue, red, and gray. Furthermore, similar molecular expression states may map to different fates. Two such states, marked i and ii are illustrated

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Analysis of single‐cell RNA‐Seq profiling of a human bone marrow sample. Each point is an individual cell. (Left) Data are projected into two dimensions using t‐distributed stochastic neighbor embedding (t‐SNE) and clustered using the Louvain method. (Right) Known cell fates can be mapped to clusters by examining localization of characteristic markers. Clusters correspond to (1) myeloblasts, (2) monoblasts, (3) lymphoid cells (4) stem and progenitors, and (5) erythroblasts

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Cell fate trajectories envisaged as a path of steepest descent over a Waddington‐like landscape. The distance from molecular state A to point molecular state B over the landscape is not the same as the Euclidean distance between them in the expression space

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The cell as a dynamical system. Functional associations between molecular components in the cell give rise to a complex intracellular regulatory network. This network encodes the architecture of a complex dynamical system that may admit numerous attractors, each of which may be identified with a distinct cell “fate”. The basins of attraction of the attractors partition the state space into discrete pieces. The cell's intracelluar molecular dynamics may admit many different kinds of attractor including various different kinds of fixed‐point such as (Upper‐Left) stable nodes and (Right) stable spirals, as well as (Lower‐Left) limit cycles, and (Lower‐Centre) more exotic structures such as limit tori (shown) or even strange attractors

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