Abstract
Multicellularity, the coordinated collective behavior of cell populations, gives rise to the emergence of self-organized phenomena at many different spatio-temporal scales. At the genetic scale, oscillators are ubiquitous in regulation of multicellular systems, including during their development and regeneration. Synthetic biologists have successfully created simple synthetic genetic circuits that produce oscillations in single cells. Studying and engineering synthetic oscillators in a multicellular chassis can therefore give us valuable insights into how simple genetic circuits can encode complex multicellular behaviors at different scales. Here we develop a study of the coupling between the repressilator synthetic genetic ring oscillator and constraints on cell growth in colonies. We show in silico how mechanical constraints generate characteristic patterns of growth rate inhomogeneity in growing cell colonies. Next, we develop a simple one-dimensional model which predicts that coupling the repressilator to this pattern of growth rate via protein dilution generates traveling waves of gene expression. We show that the dynamics of these spatio-temporal patterns are determined by two parameters; the protein degradation and maximum expression rates of the repressors. We derive simple relations between these parameters and the key characteristics of the traveling wave patterns: firstly, wave speed is determined by protein degradation and secondly, wavelength is determined by maximum gene expression rate. Our analytical predictions and numerical results were in close quantitative agreement with detailed individual based simulations of growing cell colonies. Confirming published experimental results we also found that static ring patterns occur when protein stability is high. Our results show that this pattern can be induced simply by growth rate dilution and does not require transition to stationary phase as previously suggested. Our method generalizes easily to other genetic circuit architectures thus providing a framework for multi-scale rational design of spatio-temporal patterns from genetic circuits. We use this method to generate testable predictions for the synthetic biology design-build-test-learn cycle.
Highlights
Multicellularity and collective cell behavior exemplify the emergence of complex patterns and structures across scales in living systems
We consider the case of Escherichia coli, the cellular chassis for which the repressilator (Figure 1) was designed, FIGURE 1 | Repressilator genetic oscillator circuit. (A) Network representation of the repressilator, in the schematic 1 represses 2, 2 represses 3, and 3 represses 1. (B) Genetic circuit diagram of a plasmid encoding the repressilator. (C) Oscillating repressor concentrations over time computed by solving Equation (11) with fixed growth rate
By coupling the repressilator (Potvin-Trottier et al, 2016) to a heterogeneous growth rate pattern via protein dilution we generated emergent traveling waves of gene expression. These traveling waves can be characterized by two properties; the wavelength and the wave speed
Summary
Multicellularity and collective cell behavior exemplify the emergence of complex patterns and structures across scales in living systems When cells interact they can generate higher order patterns of gene expression (differentiation) as well as patterns of mechanical stresses and strains (Chan et al, 2017; Vining and Mooney, 2017). This process takes place in natural phenomena such as embryonic development, tumor formation, wound healing, among others (Velardo et al, 2004; Aboobaker et al, 2005; Khain and Sander, 2006; Gjorevski and Nelson, 2010; Santos-Moreno and Schaerli, 2019). These synthetic circuits simplify biological systems reproducing a specific function (Xie and Fussenegger, 2018) such as toggle switches (Gardner et al, 2000; Yeung et al, 2017), oscillators (Elowitz and Leibler, 2000; Stricker et al, 2008; Danino et al, 2010; Potvin-Trottier et al, 2016), logic gates (Tamsir et al, 2011; Nielsen et al, 2016; Green et al, 2017; Kim et al, 2018), and arithmetic operators (Wong et al, 2015; Ausländer et al, 2018)
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