A model for the spatio-temporal design of gene regulatory circuits

Abstract

The design of increasingly complex gene regulatory networks relies upon mathematical modelling to link the gap that goes from conceptualisation to implementation.An overarching challenge is to update modelling abstractions and assumptions as new mechanistic information arises. Although models of bacterial gene regulation are often based on the assumption that the role played by intracellular physical distances between genetic elements is negligible, it has been shown that bacteria are highly ordered organisms, compartmentalizing their vital functions in both time and space. Here, we analysed the dynamical properties of regulatory interactions by explicitly modelling spatial constraints. Key to the model is the combined search by a regulator for its target promoter via 1D sliding along the chromosome and 3D diffusion through the cytoplasm. Moreover, this search was coupled to gene expression dynamics, with special attention to transcription factor-promoter interplay. As a result, promoter activity within the model depends on its physical separation from the regulator source. Simulations showed that by modulating the distance between DNA components in the chromosome, output levels changed accordingly. Finally, previous experimental results with engineered bacteria in which this distance was minimized or enlarged were successfully reproduced by the model. This suggests that the spatial specification of the

Effects of spatial heterogeneity on bacterial genetic circuits

“…Simulations confirm that total mRNA levels are higher for pole localized genes than those near mid-cell and that the discrepancy increases with the size of RNAP relative to r * . The agreement between the full PDE model ((59) in SI Section 2.6) and the reduced ODE model (15) provides numerical validation of the model reduction results. In the SI Section 2.6, we show in Figure 9 the transient response corresponding to Figure 5, for which the full-PDE and reduced models agree.…”

“…We set r s /r * = 1 × 10 −3 , such that θ S ≈ 1 and thus the result is independent of the spatial location where the gene is expressed. We refer to the well-mixed model as (15) with (16) given by θ * S = 1 and θ * R = 1. The parameter values and full simulation details are provided in SI Section 2.6…”

“…where Figure 11: Ribosome and mRNA steady state spatial profiles and space averaged transients For the following we refer to the well-mixed model as (15) with (16) given by θ s = 1 and θ r = 1. Here time is nondimensionalized with the time scale associated with dilution.…”

“…Note as the size of the mRNA increases, it is further excluded from the chromosome. (C) The temporal space averaged concentration of ribosomes normalized by the steady state of the well-mixed model for the reduced ODE model (15) and the PDE model (59) when r m /r * = r R /r * = 1.8. (D)The temporal space averaged concentration of mRNA normalized by the steady state of the well-mixed model for the reduced ODE model (15) and the PDE model (59) when r m /r * = r R /r * = 1.8.…”

“…We assume that the total concentration of D is conserved, so that D T (x) = D(t, x) + c 2 (t, x). The reaction diffusion equations corresponding to (65) are Figure 15: 10 ribosomes binding to a strand of mRNA For the following we refer to the well-mixed model as (15) (for the transcriptional dynamicsc s ,S, andD) and (63) with θ * s = 1 and θ R,p = 1. To model 10 ribosome binding to a single mRNA we set p = 10 in (62).…”