With the emergence of a ‘system-level’ focus in biology, there has been an increasing emphasis on characterizing gene expression and its regulation in a quantitative fashion (Bintu et al., 2005
; Golding et al., 2005
; Hasty et al., 2002
; Kaplan et al., 2008
; Kuhlman et al., 2007
). Quantitative and semi-quantitative studies have generated new concepts regarding the organization and the dynamic properties of gene regulatory networks, including, e.g., stability of control, robustness of the networks and stochastic heterogeneity of populations (Elowitz et al., 2002
; Rao et al., 2002
; Shen-Orr et al., 2002
), and have led to the design of synthetic genetic circuits (Andrianantoandro et al., 2006
; Atkinson et al., 2003
; Elowitz and Leibler, 2000
; Gardner et al., 2000
; Guido et al., 2006
). One complication in the quantitative studies of genetic circuits is that these circuits are always coupled to the physiological state of the cell, which, for example, affects the machinery of transcription and translation. As long as the state of the cell remains unchanged, this dependence does not affect the quantification of gene regulation. However, changes in gene expression often reflect changes in the environment, which also affect the state of the cell. In that case the coupling of gene expression to the global state of the cell cannot be ignored. We show in this study that this coupling generates an entire layer of physiologically important global effects on gene expression that has largely been overlooked in quantitative analysis so far. We focus on gene expression in bacteria in balanced exponential growth, for which the effects of environment on the state of the cell are reflected first and foremost by the growth rate.
The growth rate of bacteria can vary wildly, depending on the type or amount of nutrients available in the growth medium. For example, the doubling time of E. coli
in exponential batch culture growth ranges easily between ~20 min and several hours. Many parameters of the cells such as their macromolecular composition and the cell size are strongly dependent on the growth conditions (Maaløe, 1979
; Neidhardt et al., 1990
; Schaechter et al., 1958
). For E. coli
, in which this dependence has been quantitatively characterized, the results can be expressed miraculously as a dependence on growth rate
rather than on the specific growth media themselves: growth experiments with many different media have shown that media that support the same growth rate produce cells with the same macromolecular composition (Maaløe, 1979
; Neidhardt et al., 1990
; Schaechter et al., 1958
). Many parameters of the cell have therefore been characterized quantitatively as functions of the growth rate for E. coli
(Bremer and Dennis, 1996
), on which we focus in this study.
Many of these growth-rate dependent parameters, e.g. gene and plasmid copy numbers, the abundance of RNA polymerases and ribosomes (Bremer and Dennis, 1996
), are known to affect gene expression. Changes in gene expression, which are often accompanied by a change of the growth rate, thus result from a combination of gene regulation and intrinsic global effects due to growth rate. Any quantitative understanding of gene expression therefore requires an understanding of these global effects. Indeed, expression of a large number of proteins is known to exhibit different types of growth-rate dependences (Pedersen et al., 1978
). Growth-rate dependent regulation is most notable for the transcription of ribosomal RNA (Haugen et al., 2008
), but is also known for ribosomal proteins, where it relies largely on posttranscriptional regulation (Keener and Nomura, 1996
), as well as for several non-ribosomal proteins, where it is based on transcriptional mechanisms that appear to be different from the control of ribosomal RNA (Chiaramello and Zyskind, 1989
; Husnain and Thomas, 2008
). In contrast to these instances of specific growth-rate dependent regulation, the global effects addressed here are expected to affect all genes. Their interplay with specific mechanisms of gene regulation can lead to rather complex behaviors, and it is possible that they play a role in some of the known examples for specific growth-rate dependent regulation.
An obvious starting point to study global growth-rate dependent effects on gene expression is the growth-rate dependence of the expression of an unregulated (constitutively expressed) gene. Indeed, several studies have shown that the expression of a constitutively expressed gene is growth-rate dependent (Liang et al., 1999a
; Wanner et al., 1977
; Willumsen, 1975
). We will show that the observed dependence can be quantitatively explained by a simple model using the known growth rate dependencies of the key cellular parameters without invoking any adjustable free parameters.
We then expand our model to investigate the effect of growth rate on regulated genes and simple genetic circuits to address the following questions: How is the growth-rate dependence of gene expression affected by positive or negative regulation? How should a gene be regulated to exhibit a growth-rate-independent protein concentration? Is the qualitative behavior of a circuit the same at different growth rates? Answers to these questions may also help in the design on synthetic genetic circuits in order to obtain robust performance over a wide range of growth conditions. Experimental results are presented to validate key predictions of the model using simple synthetic genetic circuits.
Finally, we explore cases with global feedback mediated by growth-rate dependent effects: In these situations there is not only an effect of growth rate on gene expression, but the expression level of a protein also has an effect on the growth rate. Circuits of this type can lead to growth bistability. We discuss possible roles these effects may play in metabolic control, antibiotic resistance and tolerance (persistence).