General Analyses of Gene Expression Dependencies on Genetic Burden

Abstract

Over the last decade, the combining of newly developed molecular tools for DNA editing with engineering principles has allowed the creation of complex cellular devices, usually based on complex genetic circuits, for many different purposes. However, when the technological evolution of genetic circuitry is compared with previous technologies such as electronic circuitry, clear limitations regarding the technological scalability of genetic circuitry are observed due to the lack of predictability. To overcome this problem, it is necessary to create new theoretical frameworks for designing genetic circuits in a feasible and reliable manner, taking into account those limitations. Among a number of such limitations, the so-called genetic burden is one of the main constraints. Surprisingly, despite its relevance, little attention has been paid to genetic burden, and it is often not considered when designing genetic circuits. In this study, a new general mathematical formalism is presented, describing the effects of genetic burden on gene expression. The mathematical analysis shows that alterations in gene expression due to genetic burden can be qualitatively described independently of the specific genetic features of the system under consideration. The mathematical model was experimentally tested in different genetic circuits. The experimental evidence coincides with the expected behaviors described by the model in complex scenarios. For instance, observed modulations in the expression levels of constitutive genes in response to changes in the levels of external inducers of gene expression that do not directly modulate them, or the emergence of limitations in gene overexpression, can be understood in terms of genetic burden. The present mathematical formalism provides a useful general framework for gene circuit design that will help to advance synthetic biological systems.

Keywords: gene expression; genetic burden; gentic circuits; mathematical model; synthetic biological circuits.

FIGURE 1

Map of interactions associated with genetic burden. (A) Generic architecture of an inducible signal transduction system. The promoter and gene for the receptor protein R [Pc and gray (r) boxes, respectively] and the promoter and gene for the red fluorescent protein [Pr and red (rfp) boxes, respectively] are indicated. (B) Different mechanisms or modes of gene expression. Receptor protein R is constitutively produced (top row). RFP can be produced in three different ways: constitutively (second row); induction by a dimeric complex of the receptor protein R₂ (third row); or induction by a transcriptional complex formed by the dimeric R₂ combined with an external signal L (fourth row). All possible transcriptional and translational paths contribute to the total genetic burden with different weights (green arrows), Simultaneously, genetic burden generates a negative effect (dashed red line) on gene transcription and translation. mRFP, messenger RNA for R and RFP.

FIGURE 2

Experimental data and model fitting for constitutive gene expression. (A) Experimental measurement of relative promoter activity χ_p. RFP expression was monitored for each promoter. Promoter J23100 was chosen as a reference. (B) Change in the ratio of GFP levels in the absence (GFP₀) and upon RFP promoter activity increase (GFP_p). Orange dots, experimental data; solid line, model fitting. (C) Changes in GFP (green dots) and RFP (red dots) levels, indicated as arbitrary units (a.u.), upon increase in the number of RFP copies, Z. Solid line, GFP model fitting; dashed line, RFP model fitting. (D) GFP fold change versus increasing number of RFP copies Z.

FIGURE 3

Dependencies of gene expression in response to an external inducer. In all experiments, a construct (C17) from which GFP is constitutively expressed and RFP expression can be induced by C6 addition, was used. RFP levels (A) and GFP levels (B) were measured (a.u., arbitrary units) in response to different C6 concentrations. (C) Correlation between GFP fold change and RFP fold change. Dots are experimental values and the solid line is the model fitting. (D) Dependence of GFP fold change on the C6 concentration. Dots are experimental values and the solid line is the model fitting. This fitting combines the experimentally measured relationship between RFP and C6 with the relationship between GFP/GFP₀ and RFP described by equation (19).

FIGURE 4

A genetic construct with an inducible RFP and an inducible GFP gene. (A) RFP levels vs. the concentration of its inducer C6 at different arabinose concentrations. (B) GFP levels vs. the concentration of its inducer arabinose at different C6 concentrations. (C) RFP fold-change vs. GFP levels at different C6 concentrations upon different arabinose concentrations. The color code is as in (A). The solid line represents the model fitting. Error bars are the standard deviations of three independent experiments.

FIGURE 5

Gene overexpression limitation. RFP expression in a double system that combines constitutive and C6-dependent expression (blue dots) compared with that in a single system with only C6-inducible RFP expression (red dots).