Cell growth rate is a regulated process and a primary determinant of cell physiology. Continuous culturing using chemostats enables extrinsic control of cell growth rate by nutrient limitation facilitating the study of molecular networks that control cell growth and how those networks evolve to optimize cell growth.
Cells regulate their rate of growth in response to signals from the external world. As the cell grows, diverse cellular processes must be coordinated including macromolecular synthesis, metabolism and ultimately, commitment to the cell division cycle. The chemostat, a method of experimentally controlling cell growth rate, provides a powerful means of systematically studying how growth rate impacts cellular processes – including gene expression and metabolism – and the regulatory networks that control the rate of cell growth. When maintained for hundreds of generations chemostats can be used to study adaptive evolution of microbes in environmental conditions that limit cell growth. We describe the principle of chemostat cultures, demonstrate their operation and provide examples of their various applications. Following a period of disuse after their introduction in the middle of the twentieth century, the convergence of genome-scale methodologies with a renewed interest in the regulation of cell growth and the molecular basis of adaptive evolution is stimulating a renaissance in the use of chemostats in biological research.
The growth of cells is regulated by complex networks of interacting genetic and environmental factors1,2. The multifactorial regulation of cell growth necessitates a system-level approach to its study. However, the rigorous study of regulated cell growth is challenged by the difficulty of experimentally controlling the rate at which cells grow. Moreover, in even the simplest experiments extracellular conditions are frequently dynamic and complex as cells continuously alter their environment as they proliferate. A solution to these problems is provided by the chemostat: a method of culturing cells that enables experimental control of cell growth rates in defined, invariant and controlled environments.
The method of continuous culturing using a chemostat was independently described by Monod3 and Novick & Szilard4 in 1950. As originally conceived, cells are grown in a fixed volume of media that is continually diluted by addition of new media and simultaneous removal of old media and cells (Figure 1). Coupled ordinary differential equations (Figure 2) describe the rate of change in cell density (x) and the concentration of a growth-limiting nutrient (s) in the chemostat vessel. Importantly, this system of equations predicts a single (nonzero) stable steady-state (Figure 3) with the remarkable implication that at steady-state, the specific growth rate of the cells (i.e. the exponential growth rate constant) is equal to the rate at which the culture is diluted (D). By varying the dilution rate it is possible to establish steady-state populations of cells at different growth rates and under different conditions of nutrient limitation.
The experimental control of growth rate using chemostats was critical to the development of an understanding of how cell physiology changes with rates of growth5,6. However, this former mainstay of microbiological methods became increasingly obscure during the explosion in molecular biology research during the late twentieth century. Today, renewed interest in growth control in both microbes and multicellular organisms and the advent of genome-scale methods for systems-level analysis has renewed motivation for the use of chemostats. Here, we describe three applications that capitalize on the precise control of cell growth rates and the external environment that are uniquely possible using chemostats. First, we describe the use of chemostats to investigate how the abundance of thousands of biomolecules – such as transcripts and metabolites – are coordinately regulated with growth rate. Second, we describe how chemostats can be used to obtain precise estimates of growth-rate differences between different genotypes in nutrient-limited environments using competition experiments. Third, we describe how chemostats can be used to study adaptive evolution of cells growing in constant nutrient-poor environments. These examples exemplify the ways in which chemostats are enabling systems-level investigations of cell growth regulation, gene by environment interactions and adaptive evolution.
The principle of continuous culturing using a chemostat can be realized in a variety of implementations. In all chemostats it is essential to have 1) methods for maintaining sterility of all components, 2) a well-mixed culture, 3) appropriate aeration of the culture vessel and 4) a reliable means of media addition and culture removal. Here, we describe the use of a Sixfors bioreactor (Infors Inc) as a chemostat using methods that can be readily adapted to alternative setups.
1. Assembling the Chemostat Vessels
2. Preparing the Media
3. Calibrating dO2 Probes and Setting up Chemostat
4. Inoculation
5. Initiating Pumps and Attaining Steady State
6. Application 1: Studying Cells Growing at Different Rates in Steady-state Conditions
7. Application 2: Precise Measurement of Differences in Growth Rates Between Genotypes in Controlled Environments Using Flow Cytometry-based Competition Assays
8. Application 3: Experimental Evolution
A major advantage of chemostats is the ability to control the growth rate of cells experimentally by varying the dilution rate. In the budding yeast, Saccharomyces cerevisiae, the morphology of a cell is informative of its phase in the cell division cycle. Populations with higher growth rates contain a higher proportion of actively dividing cells as determined by measuring the fraction of unbudded cells (Figure 5A). Analyses of global mRNA expression in chemostat cultures has shown that the expression of many genes are differentially expressed as a function of growth rate (Figures 5B and Figure 5C).
The relative fitness of different genotypes can be determined by conducting competition assays in chemostats using fluorescently labeled cells and flow cytometry analysis (Figure 6A). Figure 6B shows a representative result in which a mutant strain was competed against a fluorescently tagged wildtype strain. In this example, the mutant strain has a 40% growth rate advantage per generation. By comparison, an untagged wildtype strain competed against the fluorescently tagged wildtype strain does not differ in its rate of growth.
Chemostats provide a means of exerting a defined and continuous selective pressure on cells. Whole genome sequence analysis can be used to identify acquired mutations in cells with increased fitness. Adaptive evolution experiments in yeast cells in different nutrient limited chemostats have identified copy number variants as a frequent and repeated mechanism by which adaptive mutations are generated. For example, in independent adaptive evolution experiments performed in nitrogen-limited chemostats using different nitrogen sources, multiple copy number variants (CNVs) that include the GAP1 gene were identified 11 (Figure 7).
Chemostats pose some unique challenges that are not otherwise encountered in standard microbiological methods. Potential problems and solutions specific to chemostat experiments can be found in Table 1.
Figure 1. Diagram of a chemostat. The chemostat comprises a media reservoir, pump, a chemostat vessel, an effluent tube, and a collecting receptacle.
Figure 2. Mathematical model of the chemostat. Differential equation 1 describes the change in cell density (x) in the chemostat over time, which is the result of cell growth and cell removal by dilution (cell death is assumed to be negligible). Monod proposed 3 that cell growth (μ) depends on external nutrient concentration according to a Michaelis-Menten type relationship that includes the variables of maximal growth rate (μmax) and a half-maximal growth rate constant (Ks). The dilution rate (D) is determined by the rate of media addition and culture removal. Differential equation 2 describes the rate of change in the limiting nutrient concentration (s) in the chemostat vessel. The change in concentration of the limiting nutrient in the chemostat vessel is dependent on its concentration in the inflowing media (R), its dilution by outflow (D) and consumption by the cells, which is dependent on the cell parameters μmax, Ks and a yield constant, Y. For simplification, Y is assumed to be constant at different growth rates. The variables, and their typical units, in the coupled ordinary differential equations are x – cell density (cells/ml), s – limiting nutrient concentration (μM), μmax – maximal growth rate (hr-1), Ks – nutrient concentration at which the growth rate equals μmax/2 (μM), Y – yield (cells/ml/μM), D – dilution rate (hr-1), R – nutrient concentration in media reservoir (μM).
Figure 3. Approach to steady-state as predicted by the mathematical model. Nutrient concentration (red) and cell density (blue) attain non-zero steady states.
Figure 4. Establishing the limiting range of a nutrient. A haploid strain of Saccharomyces cerevisiae was grown at different concentrations of glucose and the final density determined. A linear relationship indicates that the nutrient concentration is in the limiting range.
Figure 5. Cell physiology varies with growth rate. The chemostat enables controlled studies of the relationship between growth rate and A) cell division as assayed on the basis of cell morphology (i.e. the fraction of budded cells). The abundance of ~25% of yeast mRNAs depends on growth rate: for example the gene B) UTR2 increases in expression as growth rate increases in both glucose- (o) and nitrogen-limited (Δ) chemostats and the gene C) ASM1 decreases in expression level as growth rate increases in glucose- (o) and nitrogen-limited (Δ) chemostats 10. Click here to view larger figure.
Figure 6. Strain competition assays in chemostats. A) Two strains that are differentially labeled by constitutively expressed fluorescent proteins are co-cultured in a single chemostat and the rate of change in the relative abundance of the two strains is determined every 2-4 generations using flow cytometry. B) The relative fitness of a strain is determined by linear regression of the natural log (ln) of the ratio of the two strains against time measured in generations. Click here to view larger figure.
Figure 7. Long-term selection in chemostats efficiently selects for mutants with increased fitness. Genome-scale analysis of mutants has identified frequent chromosomal rearrangements and copy number variation (CNV) in mutants with increased fitness. Independent adaptive evolution experiments in different nitrogen-limiting conditions results in selection for different CNV alleles at the GAP1 locus (demarked by gray dotted lines), which encodes the general amino acid permease. Each data point is the ratio of DNA copy number in the evolved strain compared with the ancestral strain measured using a DNA microarray that simultaneously analyzes every gene (black).
Table 1. Table of potential problem and solutions.
Problem | Solution |
Low pH in culture vessel. | pH can be monitored in real time and controlled by automated addition of acid/base. Alternatively, buffered media can be used. |
Flocculant cells and biofilms in culture vessel. | Keep culture well mixed by running impellor at > 400 rpm. |
Growth in media feed lines. | The use of filters at the inlet port reduces the potential for colonization of media feed lines. |
Cell synchronization and stable dO2 oscillations in carbon limited chemostats. | These can be avoided by using higher dilution rates and avoiding prolonged periods of starvation before initiation of culture dilution. |
Chemostats enable the cultivation of microbes in growth-controlled steady-state conditions. The cells grow continuously at a constant rate resulting in an invariant external environment. This is in contrast to batch culture methods in which the external environment is continuously changing and the rate of cell growth is determined by the complex interaction of environment and genotype. Thus, a major advantage of culturing microbes in chemostats over batch cultures is the ability to experimentally control the growth rate of cells.
The rate at which a cell grows is the result of interactions between myriad cellular processes including nutrient sensing, signal transduction, macromolecular synthesis and metabolism. Using chemostats in combination with global analytical methods allows investigation of how the rate of growth impacts fundamental processes in the cell and conversely how the cell regulates and coordinates cellular process with its rate of growth. Studies in wildtype cells have shown that cellular concentrations of RNA and protein are profoundly impacted by rates of cell growth6 and more recently it has been shown that transcriptome10,12,13 and metabolome8 are dramatically impacted by cell growth rates.
The study of mutant behavior in chemostats provides a potentially powerful means of studying the pathways that are important for growth rate regulation14. Using high throughput sequencing of molecular barcoded collections of thousands of mutants15 it is now feasible to multiplex these assays enabling systematic studies of the genetic requirements for growth in nutrient-limited environments. It should be noted, however, that one of the limitations of chemostats is that they do not address the underlying heterogeneity in individual cell growth rates that can be assessed using single cell microscopy methods16.
Chemostats also provide an ideal system for studying microbial evolution. Nutrient limitation is an ecologically relevant selective pressure and growth rate is a major component of microbial fitness. The chemostat provides a means of precisely controlling the selective pressure and studying how molecular networks evolve. Identifying the genetic loci that are targets of selection and proving their adaptive benefit in the same nutrient-limited environment11,17-20 holds the promise of understanding the functional basis of adaptive evolution.
Chemostats are increasingly being used in new areas of research including the study of transcriptional dynamics21,22 and metabolic oscillations23-26. Their application in ecology has proved useful in the study of predator-prey dynamics27. A renewed interest in mammalian cell growth regulation, and its impairment in human disease, may motivate a return to the study of mammalian cells in chemostats using cells that can be cultured in suspension28.
The authors have nothing to disclose.
This work was supported by start up funds form New York University. We thank Maitreya Dunham and Matt Brauer who initially developed the use of Sixfors bioreactors as chemostats.
Name of the reagent | Company | Catalogue number | Comments (optional) |
Infors-HT Sixfors Chemostat | Appropriate Technical Resources, Inc. | ||
Glass Bottle 9.5 L | Fisher Scientific | 02-887-1 | For Media Vessel and Hosing |
Pinchcock | Fisher Scientific | 05-867 | For Media Vessel and Hosing |
Stopper, Size 12, Green Neoprene | Cole-Palmer | EW-62991-42 | For Media Vessel and Hosing |
Straight Connector | Cole-Palmer | EW-30703-02 | For Media Vessel and Hosing |
General purpose ties 4 in | Fisher Scientific | NC9557052 | For Media Vessel and Hosing |
Tubing, Silicone Rubber | Small Parts | B000FMWTDE | For Media Vessel and Hosing |
Tubing, Silicone, 3/8 in OD | Fisher Scientific | 02-587-1Q | For Media Vessel and Hosing |
Tubing, Silicone, 7/32 in OD | Fisher Scientific | 02-587-1E | For Media Vessel and Hosing |
Tubing, Stainless Steel, 3/16 in OD | McMaster-Carr | 6100K164 | For Media Vessel and Hosing |
Tubing, Stainless Steel, 3/8 in OD | McMaster-Carr | 6100K161 | For Media Vessel and Hosing |
Hook Connectors | Fisher Scientific | 14-66-18Q | For Media Vessel and Hosing |
Ratchet Clamp | Cole-Palmer | EW-06403-11 | For Media Vessel and Hosing |
Luer, Female | Cole-Palmer | EW-45512-34 | For Media Vessel and Hosing |
Luer, Male | Cole-Palmer | EW-45513-04 | For Media Vessel and Hosing |
Millipore Aervent MTGR05010 62 mm Filter, 0.2 μm | Fisher Scientific | MTGR05010 | For Media Vessel and Hosing |
PTFE Acrodisc CR 13 mm filters, 0.2 μm | Fisher Scientific | NC9131037 | For Media Vessel and Hosing |
Direct-Reading Flowtube for Air | Cole-Palmer | EW-32047-77 | For Nitrogen Gas Setup |
Direct-Reading Flowtube for Nitrogen | Cole-Palmer | EW-32048-63 | For Nitrogen Gas Setup |
Gas Proportioner Multitube Frames | Cole-Palmer | EW-03218-50 | For Nitrogen Gas Setup |
Regulator, Two-Stage Analytical | Airgas | Y12-N145D580 | For Nitrogen Gas Setup |
Hose Adaptor, Stainless Steel | Airgas | Y99-26450 | For Nitrogen Gas Setup |
Hose Male Adaptor | Airgas | WES544 | For Nitrogen Gas Setup |
Norprene Tubing | US Plastics | 57280 | For Nitrogen Gas Setup |
Tripod Base | Cole-Palmer | EW-03218-58 | For Nitrogen Gas Setup |
Valve Cartridges | Cole-Palmer | EW-03217-92 | For Nitrogen Gas Setup |
Carboy 10 L | Fisher Scientific | 02-963-2A | For Media Preperation |
Steritop Sterile Vacuum Bottle-Top Filters, 1,000 ml, PES membrane; for 45 mm neck size | Fisher Scientific | SCGP-T10-RE | For Media Preperation |
Media Bottle 100 ml, 45 mm neck size | Fisher Scientific | FB-800-100 | For Media Preperation |
calcium chloride·2H2O | Fisher Scientific | C79-500 | Media Reagents |
sodium chloride | Fisher Scientific | BP358-1 | Media Reagents |
magnesium sulfate·7H2O | Sigma Aldrich | 230391 | Media Reagents |
potassium phosphate monobasic | Fisher Scientific | AC424205000 | Media Reagents |
ammonium sulfate | Fisher Scientific | AC423400010 | Media Reagents |
potassium chloride | Sigma Aldrich | P9541 | Media Reagents |
boric acid | Sigma Aldrich | B6768 | Media Reagents |
copper sulfate·5H2O | Sigma Aldrich | 209198 | Media Reagents |
potassium iodide | Sigma Aldrich | 60400 | Media Reagents |
ferric chloride·6H2O | Fisher Scientific | I88-100 | Media Reagents |
manganese sulfate·H2O | Sigma Aldrich | 230391 | Media Reagents |
sodium molybdate·2H2O | Sigma Aldrich | M7634 | Media Reagents |
zinc sulfate·7H2O | Fisher Scientific | Z68-500 | Media Reagents |
biotin | Fisher Scientific | BP232-1 | Media Reagents |
calcium pantothenate | Fisher Scientific | AC24330-1000 | Media Reagents |
folic acid | Sigma Aldrich | F7876 | Media Reagents |
inositol (aka myo-inositol) | Fisher Scientific | AC12226-1000 | Media Reagents |
niacin (aka nicotinic acid) | Sigma Aldrich | N4126 | Media Reagents |
p-aminobenzoic acid | Fisher Scientific | AC14621-2500 | Media Reagents |
pyridoxine HCl | Sigma Aldrich | P9755 | Media Reagents |
riboflavin | Sigma Aldrich | R4500-25G | Media Reagents |
thiamine HCl | Fisher Scientific | BP892-100 | Media Reagents |
Leucine | Sigma Aldrich | L8000-100G | Media Reagents |
Uracil | Sigma Aldrich | U0750 | Media Reagents |
Dextrose | Fisher Scientific | DF0155-08-5 | Media Reagents |