Spatial heterogeneity tunes the behavior of bacterial genetic circuits

Deterministic ordinary differential equation (ODE) models of genetic circuits, commonly assume a well-mixed ensemble of species inside the cell. However, intracellular spatial heterogeneity is frequently observed experimentally, with a circuits DNA location and volume occupied by the chromosome (excluded volume effects) as two primary variables. Here, we derive a reduced ODE model that captures spatial effects, yet has the same structure as commonly used "well-mixed" models. Specifically, the only difference with respect to a well-mixed model, is that the association rate constant of binding reactions is multiplied by a coefficient, which we refer to as the binding correction factor (BCF). The BCF depends on the size of interacting molecular species and on their location (poles versus chromosome) if fixed in space. In particular, the effective association rate constant between genes and RNAP (or transcription factors) is lower for genes near mid-cell than for those in the cell poles and thus the transcription rate of genes is less (more) effectively regulated for genes near mid-cell (cell poles). The effective ribosome binding strength (RBS) is always greater relative to a well-mixed model and thus our proposed model predicts higher translation rate. Therefore, location of DNA and transcription factor size determine the behavior of genetic circuits. As an example, we show that for a circuit that produces sustained oscillations according to a well-mixed model may instead result in no oscillations according to our model that accounts for spatial heterogeneity. Our model has broad validity as we derived it from a general reaction-diffusion partial differential equation (PDE) model by only using time scale separation between diffusion and chemical reactions. Since our reduced model is an ODE with the same dimension as a well-mixed model, it is computationally advantageous with respect to PDE also for computational studies. Therefore, this work provides an analysis tool that easily incorporates intracellular heterogeneity in gene network models and also an engineering method to exploit spatial effects in the design of genetic circuits. Highlights O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=120 SRC="FIGDIR/small/886473v1_ufig1.gif" ALT="Figure 1"> View larger version (24K): org.highwire.dtl.DTLVardef@1db1b38org.highwire.dtl.DTLVardef@1d8131aorg.highwire.dtl.DTLVardef@ce2465org.highwire.dtl.DTLVardef@1b79176_HPS_FORMAT_FIGEXP M_FIG C_FIG O_LIIntracellular spatial heterogeneity modulates the effective association constant of binding reactions C_LIO_LIA well-mixed model can be appropriate despite spatial heterogeneity C_LIO_LIChromosome genes are less effectively regulated than pole-localized plasmid genes and this difference increases with regulator size C_LIO_LIIntracellular spatial heterogeneity affects genetic circuit dynamics C_LI Statement of significanceWe derive a general and simple ordinary differential equation model that captures spatial heterogeneity in the dynamics of gene networks. This model accounts for freely diffusing species inside bacteria are pushed out of the tightly packed chromosome and localize at the cells poles (excluded volume effects). We discover that transcription and its regulation is less effective for genes in the chromosome than is for genes in pole-localized plasmids. Furthermore, the rate at which two freely diffusing molecules bind (e.g, mRNA-ribosome) increases with molecule size. These results indicate that the size of diffusing regulators and the location of regulated genes are important parameters that affect genetic circuit behavior. We illustrate that the operation of well-known genetic circuits is dramatically impacted by these parameters.