Fine temporal control of the medium gas content and acidity and on-chip generation of series of oxygen concentrations for cell cultures

Abstract

We describe the design, operation, and applications of two microfluidic devices that generate series of concentrations of oxygen, [O₂], by on-chip gas mixing. Both devices are made of polydimethylsiloxane (PDMS) and have two layers of channels, the flow layer and the gas layer. By using in-situ measurements of [O₂] with an oxygen-sensitive fluorescent dye, we show that gas diffusion through PDMS leads to equilibration of [O₂] in an aqueous solution in the flow layer with [O₂] in a gas injected into the gas layer on a time scale of ∼1 sec. Injection of carbon dioxide into the gas layer causes the pH in the flow layer to drop within ∼0.5 sec. Gas-mixing channel networks of both devices generate series of 9 gas mixtures with different [O₂] from two gases fed to the inlets, thus creating regions with 9 different [O₂] in the flow layer. The first device generates nitrogen-oxygen mixtures with [O₂] varying linearly between 0 and 100%. The second device generates nitrogen-air mixtures with [O₂] varying exponentially between 0 and 20.9%. The flow layers of the devices are designed for culturing bacteria in semi-permeable microchambers, and the second device is used to measure growth curves of E. coli colonies at 9 different [O₂] in a single experiment. The cell division rates at [O₂] of 0, 0.2, and 0.5% are found to be significantly different, further validating the capacity of the device to set [O₂] in the flow layer with high precision and resolution. The degree of control of [O₂] achieved in the devices and the robustness with respect to oxygen consumption due to respiration would be difficult to match in a traditional large-scale culture. The proposed devices and technology can be used in research on bacteria and yeast under microaerobic conditions and on mammalian cells under hypoxia.

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Introduction

Live cells can be exquisitely sensitive to the gas content of the medium, as they depend on consuming oxygen and other gases for survival and appropriate function. Therefore, to avoid misregulation of cell homeostasis, growth, and death due to low oxygen content in the medium (hypoxia) in cultures of mammalian cells and aerobic bacteria, it is important to continually replenish oxygen and to maintain its concentration in the medium at a sufficiently high level. In contrast, the presence of oxygen in the medium can be harmful or even lethal for anaerobic organisms. Appropriate maintenance of a cell culture may also require provisions for evacuation of gases produced as a result of cell metabolism or for maintaining an elevated level of CO₂ in the medium. Mammalian cells, for instance, are often cultured in media saturated with a mixture of air and 5% CO₂ in specialized incubators.

There is wide variation in the adaptation of organisms to different concentrations of oxygen, [O₂], found in terrestrial environments. In addition to obligate aerobes and anaerobes, there are microaerophilic organisms, which are most comfortable at [O₂] lower than the 21% found in the atmosphere. Moreover, many life forms, including two of the commonly used single cell model organisms, Escherichia coli and Baker's yeast, Saccharomyces cerevisiae, are facultative anaerobes. They can switch between aerobic and anaerobic metabolism depending on the nutrient concentrations (i.e., the presence of carbon sources in the medium) and [O₂] in the cell microenvironment. Aerobic respiration is generally more efficient, but requires the more extensive metabolic apparatus of the Krebs cycle, and is thus more ‘costly’ for the cell. The switch between aerobic and anaerobic modes of metabolism is therefore tightly controlled. High-throughput studies of gene expression profiles indicated that the expression of dozens of E. colioperons is switched on or off by the aerobic shift.¹ The extensive re-wiring of the gene regulation network implies that the global regulators sense oxygen levels independently and that the sensing can lead to a cell decision that precisely evaluates the cost to benefit ratio of the potential metabolic and gene transcription switch.² These precise sensing capabilities, potentially coupled with sensing of other medium conditions, can allow cells to perform complex ‘computation’ of its gene expression profile and ensuing functional response.³

Because of the multitude of regulators and sensing mechanisms involved, the transition between aerobic and anaerobic metabolism and gene expression patterns in facultative anaerobes is likely to occur over an extended range of [O₂]. Therefore, a detailed quantitative study of the transition would require setting a desired [O₂] in the medium and maintaining it with a sufficient degree of accuracy. By Henry's law, when a liquid is in equilibrium with a gas mixture, the concentrations of gases in the liquid is proportional to their partial pressures (and molar concentrations) in the mixture. Therefore, a standard method of setting the gas content of a growth medium is the perfusion (bubbling) of the medium with a gas mixture of the desired composition. The bubbling is often combined with agitation of the medium to ensure its efficient exposure to gas in the mixture.

This simple method is appropriate for culturing cells in well-aerated ([O₂] = 20.9% as in the air) or anaerobic conditions ([O₂] = 0), with the medium bubbled through with atmospheric air or a non-reactive gas (e.g., argon or nitrogen), respectively. However, the preparation of customized gas mixtures with different [O₂] and accurate monitoring of [O₂] in them, as required for a study of the aerobic-anaerobic transition, is a more difficult task. Whereas certified O₂/N₂ mixtures with a broad range of [O₂] are available commercially, low levels of [O₂] (< 1%), at which some components of the anaerobic machinery may be activated, present an additional technical challenge. The actual [O₂] in the medium is always lower than [O₂] in the gas mixture because cellular respiration leads to consumption of oxygen in the medium. If the target value of [O₂] is low, the respiration may lead to rapid depletion of oxygen in the medium, thus making the difference between [O₂] in the gas and medium unacceptably large. In theory, a nearly uniform [O₂] in the medium can be achieved by sufficiently fast bubbling and agitation. For practical cell cultures in a chemostat or a flask, however, high rates of gas bubbling may be costly, excessive rates of agitation may cause cell rupture, and the local levels of [O₂] may be difficult to monitor. Therefore, it is difficult to ensure that [O₂] is sufficiently uniform everywhere, especially near walls and in the corners, where the agitating flow is relatively slow and where cells may accumulate, reaching particularly high density.

Microfluidic devices made of polydimethylsiloxane (PDMS) were applied previously to culturing bacteria and yeast under thermostatic and chemostatic (constant medium content) conditions.^4,5 The microfluidic chemostat did not have any specific provisions for efficiently supplying oxygen to growing cell colonies or for monitoring of [O₂] in the medium and relied on the high porosity and gas permeability of PDMS.⁴ The diffusivity of O₂ in PDMS was reported at 3.4 × 10⁻⁵cm²/s vs. 2 × 10⁻⁵cm²/s in water,⁶ and the O₂ solubility in PDMS (effective porosity of PDMS) was reported at 0.18. Therefore, when at equilibrium with pure oxygen at 1 atm, the concentration of O₂ in PDMS is 0.18/22.4 M = 8.04 mM, which is ∼6 times higher that the concentration of O₂ in water at the same conditions (1.3 mM at 25 °C). The efficiency of the diffusive gas exchange through a PDMS layer increases as the layer becomes thinner. Gas-permeable PDMS membranes have been used to study the rate of respiration of E. coli⁷ and to build fuel cells⁸ and an oxygen sensor.⁹ Thin PDMS membranes can be easily incorporated in monolith PDMS devices with two layers of microchannels.¹⁰ Two-layer PDMS devices have been used for exchanging the gas content of an aqueous solution in one layer by flow of a gas through the other layer.¹¹ Multi-layer PDMS devices with some of the channel layers perfused by oxygen have been applied for culturing hepatocytes.¹²

The small depth of microchannels and relatively high diffusivity of O₂ in water result in short diffusive mixing times (∼1 s for 50 µm deep channels), making [O₂] nearly uniform along the vertical direction. Therefore, the local level of [O₂] can be accurately measured using a film of an oxygen-sensitive luminescent dye at the bottom of the channels¹¹ or a fluorescent dye dissolved in the liquid in the channels.^13,14 The fluorescence of ruthenium tris(2,2′-bipyridil) dichloride hexahydrate (RTDP) is quenched by oxygen, such that the intensity of fluorescence decreases as [O₂] increases. Consequently, it was used to monitor the rate of respiration of cells in culture.¹⁴

The laminar character of flow and small channel diameters in microfluidic devices combined with the high diffusivity of molecules in the gas phase (four orders of magnitude higher for oxygen in air than in water) make it possible to mix gases in a controlled and efficient way and to create [O₂] gradients in the gas phase.¹⁵ The techniques of microfluidic mixing in liquid phase enable on-chip generation of solutions with concentrations following linear, polynomial,¹⁶ or exponential series.¹⁷ The series and gradients of concentrations have been applied to culturing cells under different medium conditions on the same chip¹⁸ and to studies of chemotaxis.^19,20

Here we present two microfluidic devices (Fig. 1), each of which is made of two layers of PDMS and has two layers of channels, the flow layer and the gas layer. In each device, the flow layer channel network is a modification of the microfluidic chemostat,⁴ and the gas layer has a gas-mixing channel network generating a series of nine O₂/N₂ mixtures. The values of [O₂] in the mixtures vary linearly in device 1 and exponentially in device 2. Molecular diffusion across thin PDMS membranes separating the two layers equilibrates the O₂ content of aqueous solutions in the flow layer (monitored in-situ by measuring the fluorescence of RTDP) with the on-chip generated gas mixtures in the gas layer. We use device 2 to study cultures of E. coli in microchambers with [O₂] varying exponentially between 0% (pure N₂) and 20.9% (air) at room temperature. We find that the dependence of the E. coli division rate on [O₂] has a sigmoidal shape. Importantly, we observe a significant difference in the growth rates between colonies at [O₂] = 0, 0.2%, and 0.5%. We argue that in addition to its capacities to generate a range of gas mixtures and to enable testing cellular behavior in a range of [O₂] in a single experiment, the proposed technology offers a degree of control of [O₂] that would be difficult to match in a flask or conventional chemostat. We also show that the same devices can be used to change the O₂ content of an aqueous solution in a flow channel on a scale of 0.8 sec and to reduce the pH of a buffered solution by 2.5 points within ∼0.5 sec by injecting CO₂ into the gas channels.

Fig. 1 Microfluidic devices. (a) and (b) Drawings of the devices 1 and 2, respectively. Flow channels are shown in black and gas channels are shown in semi-transparent gray. The functional region of a device is the area where the flow and gas channels overlap. The gas test channels are numbered the same as their outlets, 1–9 from top to bottom. Three stages of the gas mixing networks are labeled 1–3 in italic. (c) A micrograph of a fragment of the functional region of the device, showing gas test channel 1 with three sets of growth chambers under it (three nodes of the growth chamber grid with 100 × 100 and 100 × 50 µm chambers, both 6 µm deep), each flanked by two 25 µm wide, 6 µm deep flow-through channels. 0.7 µm deep capillaries connect the chambers and channels. The dashed line indicates the line along which the distribution of fluorescence in a flow-through channel was measured (cf.Fig. 3 and ESI Fig. S-1†). (d) Schematic drawing of a fragment of the xz-cross-section of the functional region of a device, showing channels in the two layers of the device. (x- and z-directions, as well as the depths of flow and gas channels are not to scale).

Experimental

Design and fabrication of microfluidic devices

The two microfluidic devices used in the project share the same general layout (Fig. 1). They are made of two layers of PDMS and have two layers of channels: a flow layer for liquids and cell cultures and a gas layer for gas mixtures. The flow channel network is the same in devices 1 and 2, whereas the gas channel networks are different and are designed to generate a linear and an exponential series of O₂ concentrations, respectively. The flow channel network is a modified version of the microfluidic chemostat introduced in Ref. 4. It has an inlet, an outlet, a vent, and channels of two depths, 6 and 0.7 µm (Fig. 1). The vent, which is connected to the inlet by low resistance channels, was added for fast exchange of solution in the inlet well and was normally blocked. The functional region of the flow channel network is an area where it overlaps with the gas channel network. It is an array of 32 parallel 25 µm wide flow-through channels (vertical strips in Fig. 1a–c) and 288 growth chambers (Fig. 1c). The channels and growth chambers are 6 µm deep. The growth chambers are arranged in a 16 × 9 grid in the xy-plane with 240 and 1200 µm steps along the x- and y-directions, respectively, (Fig. 1a–c) with a 100 × 100 µm and a 100 × 50 µm chamber (x × y dimensions) in each node of the grid (Fig. 1c). Each of the 16 rows of chambers along the y-axis is flanked by two dedicated flow-through channels, and each of the 9 rows along the x-axis is situated under a specific gas test channel (Fig. 1a–d). The gas test channels are all 600 µm wide with 600 µm wide partitions (Fig. 1), and the edges of the growth chambers are at distances of >200 µm from the edges of the gas test channels (Fig. 1c). The gas channels are separated from the flow channels by a 50 µm thick layer of PDMS (Fig. 1d).

The growth chambers are connected to the flow-through channels by 0.7 µm deep 25 × 25 µm capillaries (two and one on each side of the 100 × 100 and 100 × 50 µm chambers, respectively; Fig. 1c,d) that are normally impassable for E. colicells but enable efficient diffusive exchange of nutrients and metabolites between the channels and growth chambers.⁴ Therefore, continuous perfusion of the flow-through channels with fresh medium, which is fed into the inlet and drawn off from the outlet, maintains the medium in the chambers nearly identical to the medium in the channels.⁴ To load E. colicells into the chambers, pressure at both the inlet and outlet is raised causing the capillaries to bulge up and their depth to increase to >1.5 µm and making them passable for cells.⁴

The gas channel network of each of the devices has 150 µm deep channels with two inlets (gas inlets 1 and 2 in Fig. 1a, b) and 9 outlets and consists of two parts, a gas-mixing network and an array of 9 parallel gas test channels (also called “gas channels” further in the text) in the functional area of the device. The purpose of the gas-mixing network is to generate a series of 9 different gas mixtures from two gases fed to the gas inlets and to direct these mixtures to the gas test channels (Fig. 1a, b). The gas-mixing networks of both devices are of the type introduced in Ref. 17 (called “gradient-making network” in Ref. 17) and consist of long serpentine channels (intended for mixing of gases by diffusion) and wide redistribution channels (called horizontal channels in Ref. 17), which are arranged in three separate stages of mixing (labeled in italic as 1–3 in Fig. 1a, b). Mixing stages 1, 2, and 3 have, respectively, 3, 5, and 9 serpentine channels of non-equal lengths. The serpentine channels of stages 2 and 3 are 100 µm wide, and the serpentine channels of stage 1 are 150 µm wide. The lengths of the shortest serpentine channels of the three stages are chosen to provide nearly equal ratios of the gas residence times (channel length divided by the gas flow velocity) to the diffusive mixing times (channel width squared divided by the gas diffusivity).

Device 1 used pure N₂ and pure O₂ fed to gas inlets 1 and 2, respectively, to generate a series of O₂/N₂ mixtures with [O₂] varying linearly between 0 to 100% in the gas test channels 1–9. The viscosity of O₂ is ∼16% higher than the viscosity of N₂, and the viscosity of O₂/N₂ mixtures is a linear function of [O₂].²¹ Therefore, to account for the variations in viscosity between O₂/N₂ mixtures, the design rules stated in Ref. 17 were modified for both gas-mixing networks by dividing the calculated lengths of the serpentine channels by factors of 1 + 0.16[O₂]/100%, where [O₂] are the intended concentrations of O₂ in the respective channels. The gas-mixing network of device 2 was designed to generate an exponential series of [O₂],^17,20 with the fraction of O₂ in the gas mixtures varying by a factor of 3^½ between consecutive test channels and spanning a range from 1 to 81 in relative units, when [O₂] in gas inlet 2 was 81 times higher than in gas inlet 1. In practice, however, gas inlet 1 was fed with pure N₂ ([O₂] = 0), thus shifting the exponential series of concentrations by 1 in the relative units, with [O₂] = 0 in test channel 1 and [O₂] in channeln equal to (3^{(n − 1)/2} − 1)/(81 − 1) parts of [O₂] in the gas fed to gas inlet 2. (Because (3^{(9 − 1)/2} − 1)/(81 − 1) = 1, [O₂] in gas test channel 9 is always the same as in gas inlet 2.) The gas-mixing network in device 2 was specifically designed to be fed with N₂ and air, generating gas mixtures with [O₂] = 0, 0.2, 0.5, 1.1, 2.1, 3.8, 6.8, 12.1, and 20.9% in the gas test channels 1–9, respectively. Importantly, because of the non-linear variation of [O₂] with the gas test channel number in device 2, the step in [O₂] was substantially reduced near 0, enabling an increased resolution in the microaerobic regime.

The devices were fabricated using two separate master molds, silicon wafers with rectangular relief on them made by SU8 photolithography, as described in detail elsewhere.⁴ The mold with the flow channel relief was spin-coated with a 50 µm layer of PDMS pre-polymer (13:1 mixture of base and curing agent of Sylgard 184 by Dow Corning), which was partially cured by 30 min baking in an 80 °C oven. The gas layer mold was used to cast ∼4 mm thick chips of PDMS (7:1 mixture of Sylgard 184, partially cured by 30 min baking in an 80 °C oven). After the inlet and outlet holes were punched in the chips (circles in Fig. 1a, b), the chips were placed on top of the 50 µm layer of PDMS on the flow layer mold in alignment with the flow channels. The two PDMS layers were bonded and fully cured by 3 hours baking in the oven. The monolith two-layer chips were separated from the mold, and the flow layer port holes were punched in the chips. To complete the microfluidic devices, the chips were reversibly bonded to #1.5 microscope cover glasses by overnight baking in an 80 °C oven.

Reagents and cells

Ruthenium tris(2,2′-bipyridil) dichloride hexahydrate (RTDP), Tween20, and fluorescein-isothiocyanate were obtained from Sigma. The E. coli strain used in the study was described elsewhere.²² In brief, a truncated quorum sensingluxoperon from V.fischeri was expressed in E.coli to track the multigenerational colony growth. An EcoRI-KpnI fragment containing luxR, the luxbox, and luxI promoter region was inserted into the MCS of pPROBE′-gfp-tagless vector to create pJWP01S. This construct was used to transform E.coli strain MG1655. The culture (growth) medium both in test tubes and microfluidic devices was LB broth with 50 µg/ml kanamycin and 10 nM of V. fischeri specific autoinducer, N-3-oxo-hexanoyl homoserine lactone (HSL). The addition of 10 nM of autoinducer to the growth medium causes overexpression of the gfp-tagless reporter.²³ Before the on-chip experiments, the E.coli strain was cultured overnight at 35 °C to an OD₆₀₀ of 1.0–1.5.

Setup and procedure

The liquids fed into and drawn off from the flow inlet and flow outlet of a device were kept in modified 1 cc plastic syringes attached to stages sliding on a vertical rail. The flow through the device was driven by a combination of hydrostatic pressure (due to differences in the syringe elevations) and regulated pressure of compressed air.⁴ To fill the growth chambers of the device with a liquid, the flow-through channels were filled with a 0.5% solution of Tween20 (fed from the inlet), and the inlet and outlet were both pressurized at ∼0.7 psi. After no air was left in the chambers, the device was perfused for 15 min with 0.1% solution of BSA in a phosphate buffer to purge Tween20 and to make the surfaces non-sticky for cells. To load E. colicells into the growth chambers, the device was filled from the outlet with an E. coli culture grown overnight, and the inlet and outlet were both pressurized at ∼1.5 psi (with somewhat higher pressure at the outlet) to make the capillaries passable for cells. Once there were enough cells in chambers, the outlet was depressurized and cells were purged from the flow-through channels by 15 min perfusion from the inlet driven by a pressure of 0.7 psi. After that, a syringe with the growth medium was connected to the outlet, with the level of the medium set at ∼2″ above the device level. The inlet syringe was raised to a higher level to provide a differential pressure of 0.5 psi for continuous perfusion of the flow-through channels with fresh growth medium.

The pressure of compressed air, oxygen, and nitrogen, fed to the gas inlets of the devices, was adjusted by two Porter pressure regulators (8310ANBF10, range 0–10 psi) and measured by a Heise digital pressure indicator with an accuracy of 0.015 psi. To prevent the clogging of gas channels with dust, inline gas filters were placed upstream of the pressure regulators. [O₂] in gas mixtures emerging from the gas outlets (Fig. 1a,b) was sampled off-chip (one outlet at a time) using a commercial oxygen analyzer, MAXO₂ by Maxtec, with a nominal precision of 1% of [O₂]. Because of the low volumetric flow rate of the incoming gas mixtures (∼2 mL/min), to ensure reliable [O₂] measurements with a minimal response time, the oxygen sensor of the analyzer (MAX-250E by Maxtec) was equipped with a specially made receptacle that had a low internal volume (0.5 mL) and effectively isolated the sensor from the ambient air. The sensor was connected to the gas outlets through a ∼10 cm line of Tygon tubing (ID = 1/16″) and a short piece of hypodermic tubing, which was inserted into the gas outlets.

The experiments with E. coli and measurements of fluorescence in the microchannels were done on a Nikon TE300 inverted fluorescence microscope. For measurements of RTDP and FITC fluorescence, we used Sony XCD-X900 and Basler A102f IEEE 1394 cameras. GFP fluorescence of E. coli was recorded with a CoolSnap HQ cooled camera. For stable fluorescence illumination, we used a modified Nikon mercury lamphouse with the mercury lamp replaced by an LED mounted on a small cooling fan. The LEDs used for measurements of fluorescence of RTDP and FITC were Luxeon V royal-blue and Luxeon V cyan (LXHL-LR5C and LXHL-LE5C by Lumiled), respectively, with the central wave lengths of 455 and 505 nm, respectively, and with maximal light powers of 700 mW and 160 lumens (at a current of 700 mA). Both LEDs were powered by a stabilized HP power supply, and the current through both LEDs was set at 650 mA and continuously monitored with a 6.5 digit multimeter, Fluke 8500A. By directing the light from the royal-blue LED onto the CCD array of a 10 bit digital camera, we found that the power of light emitted by the LED varies by <0.1% within 20 min. The filter cube used for RTDP fluorescence contained a 450/50 nm excitation filter, a 490 nm dichroic splitter and a 530 nm long-pass filter as the emission filter. The filter cube used for FITC fluorescence contained a 500/20 nm excitation filter, 520 nm dichroic splitter, and 550/50 nm emission filter. For the visualization of E. coli GFP fluorescence, we used the royal-blue LED and a standard GFP filter cube.

Results

To obtain the local values of [O₂] in the flow channels of a device, we filled it with a solution of RTDP and measured its fluorescence. Oxygen is a quencher of RTDP fluorescence. The intensity of fluorescence of RTDP molecules in the presence of oxygen, I, is reduced compared to the intensity without oxygen, I₀, according to the Stern–Volmer equation, I₀/I = 1 + K_q[O₂], where K_q is a quenching constant. To avoid possible confusion with the intensity of fluorescence recorded by our microscopy setup, in what follows, the molecular fluorescence intensities entering the Stern–Volmer equation will be called fluorescent yields. According to the Stern–Volmer equation, [O₂] can be evaluated from measurements of the fluorescent yields as [O₂] = (I₀/I − 1)/K_q. The value of K_q can be obtained by comparing the fluorescence of the RTDP solution when it is saturated with a chemically inert gas, such as N₂, and when it is saturated with O₂ (in equilibrium with pure O₂). Because our measurements were always performed at atmospheric pressure and room temperature, with [O₂] in a saturated solution remaining nearly constant (at ∼1.3 mM), it was convenient to normalize [O₂] to its saturation value. With this normalization, the quenching constant, K_q, became dimensionless and was obtained as K_q = I₀/I₁₀₀ − 1, where I₁₀₀ is the fluorescent yield in a solution saturated with O₂. We note, however, that K_q defined this way was temperature dependent and was expected to decrease by ∼2% per 1 °C near room temperature, because the solubility of O₂ in water decreases by ∼2% when the temperature increases by 1 °C. In addition, because of variability of the values of K_q for RTDP reported in the literature^14,24,25 and because of possible dependence of the fluorescence lifetime and K_q on pH, temperature and on the concentration of ions in the solution,²⁶ the value of K_q for the system had to be found experimentally. The task of our first set of experiments was to check whether the oxygen content of the medium in flow channels is at equilibrium with the gas flowing through gas channels.

Equilibration between the O₂ content in gas and flow channels

To test the equilibrium between the O₂ content in the RTDP solution in flow channels and the gas in the gas channels, each of the gas inlets in device 1 was connected to a source of compressed N₂ and a source of compressed O₂, both set at a pressure of 5.00 psi, through a 3-way solenoid valve that was controlled by a home-made driver. The valves were switched between three different states: (1) ON/ON, with both gas inlets fed with O₂ (thus flooding the entire gas channel network with O₂); (2) OFF/OFF, with both gas inlets fed with N₂ (N₂ in the entire gas channel network); and (3) OFF/ON, with the gas composition in the gas channels varying from pure O₂ to pure N₂ along the positive y-axis direction (Fig. 1a). We determined the rates of flow through the gas outlets in state 3 by measuring the rate of displacement of water from a graduated cylinder. The flow rates were all ∼30 µL/s, corresponding to a flow rate of Q ≈ 135 µL/s through each of the inlets. The flow rate through the central serpentine channel of the 1^stmixing stage (56 mm long with 150 × 150 µm cross-section), was estimated as ∼110 µL/s, corresponding to a mean velocity of ∼5 m/s and a passage time of ∼11 ms. This passage time was ∼10 time longer than the diffusive mixing time, w²/D = 1.1 ms (D ≈ 0.2cm²/s is the diffusion coefficient for N₂/O₂ mixture and w is the channel width), indicating that N₂ and O₂ were completely mixed after passing through this channel as well as through other serpentine channels of the gas-mixing network.¹⁷

The Reynolds number in the gas flow was calculated as Re = Qρ/(h_gη), where ρ = 1.25 kg/m³ and η = 1.8 × 10⁻⁵ Pa s are the density and viscosity of N₂, and h_g = 150 µm is the channel height. Re had its highest value of ∼60 in the 100 × 150 µm channels connected to the inlets. At this relatively low value of Re, the flow was expected to be laminar and stable, except for possible Dean vortices in curved segments of the channels. The volume of the gas between a solenoid valve and the test area of the device was <20 µL (most of it in the valve and the tubing connecting the valve with the device inlet). Therefore, the characteristic time of exchange of the gas content in the test area was expected to be <0.15 s.

The flow channels of the device were filled with a 250 ppm (by weight) solution of RTDP in a pH 7.5 10 mM phosphate buffer. The solution was driven through the flow channels of the device by applying various differential pressures between the inlet and outlet. The maximal flow velocity in 25 µm wide flow-through channels, which was measured by tracking fluorescent beads, had a linear dependence on the applied differential pressure (not shown) with a slope of 460 µm/s per 1 psi, corresponding a slope of 260 µm/s per 1 psi in mean flow velocity. The intensity of fluorescence of RTDP in the flow channels was measured using an epi-fluorescence video microscopy setup. Therefore, in addition to the fluorescence yield, I, the signal recorded by the camera in the setup was proportional to the local depth of the flow channels. Because the flow channels of the device were separated from the gas channels by a relatively thin layer of PDMS (50 µm), the depth of the flow channels was sensitive to variations in pressure in the gas and flow layers. To minimize the measurement errors resulting from uncontrolled variations of the flow channel depths, the fluorescence was measured in 25 µm wide flow-through channels, whose depth had substantially smaller pressure sensitivity than that of the 100 µm wide chambers. The local intensity of fluorescence of RTDP was calculated by averaging the values of pixels corresponding to the central ∼10 µm of the channel width and subtracting the background, which was sampled at ∼50 µm from the channel in an area without microchannels or sources of fluorescence.

When the two solenoid valves were simultaneously switched off or on, changing the gas fed to both inlets from O₂ to N₂ or back (both at 5.00 psi), the intensity of fluorescence averaged over a 200 µm long internal region (y-axis extension) of a flow-through channel under gas test channel 1 changed by a factor of 3.37 within ∼4 sec (Fig. 2a). Because the flow-through channel depth was expected to remain unchanged, it was assumed that the ratio of fluorescence yields of RTDP, I/I₀, was the same as the measured ratio of fluorescent intensities. Following the Stern–Volmer equation [O₂] = (I₀/I − 1)/K_q, we plotted the dependences of I₀/I − 1 on time, t, after the switching from O₂ to N₂ and from N₂ to O₂ (Fig. 2b). The two dependences were well fitted by functions a exp(−(t − t₁)/τ) and a[1 − exp(−(t − t₂)/τ)], respectively, with a = 2.37 (putative value for K_q) and τ = 0.79 sec, indicating that the oxygen exchange occurred as an exponential decay with a characteristic time τ = 0.79 sec. (The value of K_q is somewhat higher than the values of ∼2.25 measured in most other tests, most likely because of a relatively low temperature in the room during this test.)

Fig. 2 Dynamics of changes in the fluorescence of RTDP in a 25 µm wide flow-through channel under gas test channel 1 during switching of the gas fed to the gas inlets from O₂ to N₂ and back. The fluorescence was recorded at 15 frames per second with a Sony XCD-X700 camera. (a) Intensity of fluorescence as a function of time. The intensity is normalized to its level with N₂ fed to the gas channels. The gas was switched from O₂ to N₂ at ∼0.5 sec and back at ∼10.5 sec. (b) I₀/I − 1 (symbols) as a function of time, t, where I is the fluorescence intensity at a given moment, and I₀ is the intensity with N₂ fed to the gas channels. The dependences at 0.5 < t < 6.5sec and 10.5 < t < 16.5 sec are fitted by exponential functions (continuous lines) aexp(−(t − t₁)/τ) and a[1 − exp(−(t − t₂)/τ)], respectively, with a = 2.37, τ = 0.79 sec, t₁ = 0.40 sec and t₂ = 10.67 sec.

Because the solubility of O₂ in PDMS is ∼6 times higher than in water (at room temperature),⁶ the O₂ content of a saturated solution in a 6 µm deep flow channel is equivalent to that of an ∼1 µm thick layer of PDMS. Given the diffusion coefficient of O₂ in water, D_w = 2 × 10⁻⁵ cm²/s, the time of diffusive mixing of O₂ in a channel with a depth h = 6 µm is estimated as h²/(2D_w) = 9 msec. Hence, the measured exchange time τ = 0.79 sec is almost entirely due to the exchange of O₂ content in the 50 µm thick PDMS membrane between the gas channel and flow channel. We used FemLab to perform a numerical simulation of the PDMS layer as a slab with a thickness d = 50 µm that is initially filled with a substance with a diffusion coefficient D_p = 3.4 × 10⁻⁵ cm²/s,⁶ with boundary conditions of zero concentration at the top (gas channel with a flow of N₂) and zero diffusion at the bottom (cover glass). The concentration at the bottom of the slab was decaying exponentially with a characteristic time of τ = 0.30 sec, whereas the experimentally measured decay time of 0.79 sec corresponded to a diffusion coefficient of D_p = 1.3 × 10⁻⁵ cm²/s inside PDMS. We note that a simple estimate of the time of diffusive exchange, d²/(2D_p) = 0.96 sec, is in good agreement with the simulation. A likely reason for the discrepancy between the experiment and simulation is reduced gas permeability of the 50 µm thick PDMS layer near its surfaces that reduces the rate of gas exchange through it.¹⁴ Another source of the discrepancy is a finite exchange time of the gas in the gas channel, which is estimated as ∼0.1 sec.

The time dependences in Fig. 2 indicate that there is a fast transport of O₂ between the flow and gas channels and that the O₂ content of liquid in the flow channels reaches a steady state in ∼4 sec after switching the gas fed to the gas channel network. The O₂ content in the liquid might still be out of equilibrium with that in the gas channel because of the presence of two competing gas transport mechanisms: the diffusion in the plane of the device (xy-plane, Fig. 1) and the flow of the liquid that causes downstream (y-direction) transport of O₂ dissolved in the liquid. The diffusion of O₂ in the x-direction (Fig. 1) is not likely to cause any net transport, because the gas test channels extend over a distance of 6 mm in this direction, practically precluding any gradients of O₂ in the x-direction. On the other hand, the width (y-axis extension) of the gas test channels is relatively small (600 µm), and large gradients of O₂ in the y-direction are expected near the channel edges.

To test whether the y-direction transport of O₂ by the diffusion and flow has an effect on the O₂ concentration in flow channels under a gas test channel, we measured distributions of fluorescence intensities in a 25 µm wide flow channel when both gas inlets are fed with N₂ or O₂. The measurements were done at three differential pressures between the flow inlet and outlet (0.25, 0.5, and 1 psi) corresponding to mean flow velocities of 65, 130, and 260 µm/s. The fluorescence micrographs were taken at least 30 sec after the gas supply was switched to allow the gas content to reach a steady state (cf.Fig. 2). The ratio of fluorescence intensities under N₂ and O₂ as a function of a position in the y-direction is shown in Fig. 3 for a region under the gas test channel 1 and immediately upstream of it. (We note that with an appropriate subtraction of the background, the ratio of fluorescence intensities is not sensitive to non-uniformity of the channel depth and of fluorescence illumination and light collection.)

Fig. 3 The ratio of fluorescent intensities between the states when the gas inlets are fed with N₂ and with O₂ (both at 5 psi) as a function of position, y, along a flow-through channel at three differential pressures between the flow inlet and outlet. The three curves are marked by the values of the differential pressure, ΔP, in psi, 0.25, 0.5, and 1. The position y = 0 corresponds to the upstream edge of gas test channel 1. Inset: the ratio of fluorescence intensities under the internal region of gas test channel 1 between the states when the gas inlets are fed with N₂ and with O₂ as a function of pressure at the gas inlets, P_g. The flow of liquid was driven at ΔP = 0.5 psi.

The three curves in Fig. 3 have two main features in common. First, the fluorescence ratio at large distances upstream of the gas channel always approaches unity, indicating that the switching of the gas has little effect on the O₂ content in these far upstream areas. This result is expected. At large distances, the gas channel is an inefficient source or sink of O₂, because the diffusion of O₂ occurs in two dimensions in the yz-plane (whereas the gas channel is only 150 µm deep) and the characteristic time of diffusive exchange increases as the distance squared. Because of the slow rate of the diffusive exchange, the shapes of the curves upstream of the gas channel (y > 0) differed and depended on the long-time history of the content of the gas channel. Second, in the range of y corresponding to an internal region of the gas channel starting 200 µm from the channel edge (y < −200µm), where all growth chambers are situated, the fluorescence ratios for all three curves have plateaus with mean values that are within 0.5% of 3.25. (The measurement error in this experiment was estimated as 0.5–1%, with two major sources being the uncertainty in the background level and the variation of the channel depth with the pressure in the flow layer.) The experimental results indicate that in this internal region under the gas channel there are no gradients of [O₂] along the y-direction and no dependence of [O₂] on the liquid flow rate, when either N₂ or O₂ flow in the gas channel.

The absence of [O₂] gradients along the y-direction precludes any net diffusive transport in this direction. Together with the absence of the dependence of [O₂] on the liquid flow rate, it indicates that [O₂] in the flow-through channels and growth chambers under the internal region of the gas channel is at equilibrium with [O₂] in the gas channel. As an additional control, we measured the N₂/O₂ ratios of fluorescence intensities in segments of 8 different flow channels that were all in the internal region under gas channel 5. The ratios had a mean value of 3.25 with a coefficient of variation of 0.5%, indicating that, as expected, [O₂] is constant under a given gas channel.

The composition of gas flowing through the gas channels is expected to vary on the way from the inlets to the test region due to diffusive exchange through the channel walls with the gas dissolved in the PDMS chip (which is air in the beginning of the experiments). This variation in gas composition is expected to depend on the gas flow rate, becoming strong at low flow rates. Therefore, to test the magnitude of this effect, we repeated the experiments described above with the gas flow driven by pressures, P_g, from 0.25 to 5 psi (always the same pressure for N₂ and O₂). The flow rate through the gas outlets was a linear function of P_g (not shown). The fluorescence intensity ratio under gas channel 1 (inset in Fig. 3) steeply increased with P_g up to P_g of 1 psi but was largely leveled off at P_g >1 psi. When both gas inlets were fed with O₂, sampling of the gas emerging from gas outlet 1 gave [O₂] = 88.9% at a P_g = 0.25 psi, [O₂] = 96.0% at P_g = 0.5 psi, and [O₂] saturated at 100% at P_g > 1.2 psi, in qualitative agreement with the on-chip fluorescence tests. These results indicated that at a gas pressure of 5 psi, the gas exchange through the channel walls did not have appreciable effect on the composition of gas in test area. Therefore, the measured ratio of fluorescence intensities under the gas channel with N₂ and O₂ corresponds to the ratio of fluorescent yields I₀/I₁₀₀ between RTDP fluorescence without quenching and with quenching by a saturated solution of O₂.

To test for possible cross-talk between adjacent gas channels, we measured the fluorescence intensity in device 1 under gas channel 1 when the gas inlet 1 is fed with N₂ and gas inlet 2 is fed with O₂. Under these conditions, the gas in channel 1 is pure N₂ as in the previous test, whereas the gas in channel 2 is 87.5% N₂ and 12.5% O₂ (see Fig. 4a below) instead of pure N₂ in the previous test. When divided by the fluorescence intensity profile with pure O₂ in all gas channels (not shown), the measured profile was similar to the curves in Fig. 3 with an unchanged ratio of 3.25 under the gas channel 1, indicating that there was no cross-talk between the gas channels 1 and 2. To test for evaporation of water from the flow channels, a 3 ppm solution of FITC in a 10 mM phosphate buffer was perfused through the device at a differential pressure of 0.5 psi (same as used in experiments with E. coli below). The evaporation would raise the concentration of FITC and thus the intensity of fluorescence in the flow channels. The fluorescence was measured under gas channel 9 (at the most downstream growth chambers) with and without flow of dry air through the gas channel network and was found to be unchanged to within 0.5%, indicating that the flow of air caused practically no evaporation of water from the flow channels.

Fig. 4 Concentrations of oxygen, [O₂], (in % of pure oxygen) generated in the 9 gas test channels, as measured by the fluorescence of RTDP in flow-through channels under the gas test channels (open circles) and by the off-chip gas sampling (solid squares). Solid lines show the values of [O₂], which the device is designed to generate. (a) Device 1 built to generate a linear dependence of [O₂] on the channel number, n, [O₂] = 12.5% × (n − 1). (b) Device 2 built to generate an exponential dependence of [O₂] on n, [O₂] = 20.9% × (3^{(n − 1)/2} − 1)/80.

To obtain an alternative estimate of the difference in [O₂] between gas channel 1 and the flow channels under it, we used FemLab (COMSOL) to perform a time-dependent two-dimensional simulation of a fragment of the yz-cross-section of the device (see ESI and Fig. S-1 for details†). The distribution of [O₂] under gas channel 1 found in the simulation (ESI Fig. S-1b†) had a shape similar to the experimentally obtained distributions of the N₂/O₂ fluorescence ratio in Fig. 3. In particular, in a 200 µm wide internal region (y from −400 to −200 µm) corresponding to the area of growth chambers in the device, [O₂] was above 99.9%, which is within 0.01% of [O₂] in the gas channel. Therefore, the results of the simulations agree with the experimental findings and indicate that [O₂] in the growth chambers very closely matches [O₂] in the gas channels above the growth chambers.

Generation of linear and exponential series of O₂ concentration

To generate a linear series of [O₂] spanning from 0 to 100%, gas inlets 1 and 2 of device 1 were fed by N₂ and O₂, respectively, both pressurized at 5.0 psi. The flow channels were filled by a 250 ppm (by weight) solution of RTDP, as before, with ΔP = 0.5 psi applied between the flow inlet and outlet. [O₂] under the gas test channels 1–9 was calculated based on the intensity of fluorescence, I, measured in a 25 µm flow-through channel under the internal region of the gas channel (>100 µm from the edges) as [O₂] = (I₀/I − 1)/(I₀/I₁₀₀ − 1), where I₀ and I₁₀₀were the intensities of fluorescence measured when both gas inlets were fed with N₂ and O₂, respectively (open symbols in Fig. 4a). In parallel, [O₂] in the gas mixtures coming out of the gas outlets was measured by the off-chip oxygen analyzer (solid symbols in Fig. 4a). The [O₂] values evaluated from the fluorescence and off-chip sampling both closely followed the linear series of [O₂] that the device was designed to generate (solid line in Fig. 4a). The root-mean-square (RMS) of the differences between the target and actual values of [O₂] as measured by the fluorescence intensity and off-chip analyses were 0.6% and 0.8%, respectively. The RMS of the differences between the results of [O₂] measurements by the two methods was 0.8%, which was within the 1% accuracy of the oxygen analyzer as stated by the manufacturer.

To generate an exponential series of [O₂] spanning from 0 to 20.9%, gas inlets 1 and 2 of device 2 were fed by N₂ and air, respectively. The inlet pressures were set at ∼5 psi and subsequently adjusted to bring [O₂] at the gas outlet 5 to its target value of 2.1%. (The final pressure values, 4.84 psi and 4.65 psi, for N₂ and air, respectively, were somewhat different from each other, which was most likely due to imperfections in the device fabrication.) As in the previous experiment, [O₂] was measured in parallel from the fluorescence and off-chip sampling (Fig. 4b). The values of [O₂] from both types of measurements closely followed the exponential dependence on the number of the gas outlet, n, that the device was designed to produce, [O₂] = 20.9% × (3^{(n − 1)/2} − 1)/80 = 20.9% × {exp[k(n − 1)] − 1}/80, where k = ln(3)/2 (solid line in Fig. 4b). The RMS of the differences between the expected and measured values of [O₂] was 0.17% and 0.13% of [O₂] for the measurements by fluorescence and off-chip sampling, respectively, and the RMS of the differences between the measurements by the two methods was 0.20% of [O₂]. In particular, for gas channels 2–4 with the expected [O₂] of 0.19, 0.52, and 1.10%, [O₂] was measured at 0.14, 0.53, and 1.04%, respectively. This range of [O₂] corresponded to 1 ≤ I₀/I < 1.025, and the accuracy of measurements of I₀/I was improved to ∼0.001–0.002 (limited by the variations of the channel depth and the fluctuations of the light source), corresponding to 0.05–0.1% in [O₂].

Changing pH in flow channels by injection of CO₂ into gas channels

To test the equilibration between the flow channels and gas channels for a gas other than O₂, we used the setup with the two solenoid valves to switch the gas fed to the two gas inlets from air to CO₂ and back to air. The diffusion of CO₂ through porous polypropylene membranes sandwiched between channels machined in PMMA was used before to create gradients of pH in the channels.²⁷ Indeed, when dissolved in water, CO₂ produces carbonic acid and bicarbonate, thus reducing the pH of the solution. Therefore, [CO₂] in the solution was monitored by the intensity of fluorescence of FITC, which is an increasing function of pH with a strong dependence near pH 7. Device 1 was filled with a 3 ppm solution of FITC in a pH 7 10 mM phosphate buffer and its flow through the device was driven by a differential pressure of 0.5 psi. The pressure of both air and CO₂ was set at 5 psi, as before. After the gas fed to the gas inlets was switched from air to CO₂, the intensity of fluorescence of FITC under gas test channel 1 decreased by a factor of ∼20 within 0.47 sec based on 90–10% criterion (Fig. 5). The initial fluorescence intensity was recovered, after the gas fed to the gas channel network was switched back to air. The transition back was much slower, however, ∼10 sec based on 90–10% criterion (Fig. 5). We note that based on the value reported for the diffusion coefficient of CO₂ in PDMS (2.2 × 10⁻⁵ cm²/s or 1.5 times lower than for O₂),⁶ the CO₂ exchange was expected to have an exponential relaxation time of ∼1.2 sec (cf.Fig. 2b).

Fig. 5 Time dependence of fluorescence (in arbitrary units) of a 3 ppm solution of FITC in a phosphate buffer (with pH = 7.0 when exposed to air) measured in a flow-through channel under gas test channel 1. The gas supplied to the two gas inlets was switched from air to pure CO₂ at 1.8 sec and back to air at 12 sec.

To estimate the change in pH in the flow channels caused by CO₂ of the gas channels, we measured the pH of the FITC solution in a test tube after it was saturated with CO₂ (by bubbling pure CO₂ through it) and found it at 4.5. A 3 ppm solution of FITC in a buffer with pH 4.5 was then prepared, and the intensity of its fluorescence in the same flow-through channel was measured (with air in the gas channel above it). The fluorescence was ∼1.6 in the units of Fig. 5, which was, within the experimental uncertainly, identical to the value measured in the previous experiment with CO₂ in the gas channel. This result was consistent with equilibrium between [CO₂] in the gas and flow channel and also indicated that the flow of CO₂ in the gas channel reduced pH of the buffer solution by 2.5 points, from 7.0 to 4.5. The relatively large change in pH explains the strong asymmetry between the transition curves from air to CO₂ and back from CO₂ to air. Because H₂CO₃ is a weak acid, the number of protons per dissolved molecule of CO₂ decreases as pH is reduced. Moreover, pH itself is a logarithmic function of the concentration of protons in the solution, making pH and the reduction in pH-dependent fluorescence of FITC a strongly non-linear, saturating function of [CO₂]. Therefore, when the same FITC solution was bubbled through with 5% CO₂ in air, its pH decreased from 7.0 to 5.8, about a half of the reduction measured for 100% CO₂. In other words, a major reduction in pH and FITC fluorescence occurs after [CO₂] in the solution is increased from zero to a few percent a short time after the gas is switched from air to [CO₂], and the initial level of fluorescence is not recovered until the last few percent of [CO₂] diffuse out of the solution, after the gas is switched back to air. In terms of practical applications, injection of [CO₂] into the gas channels proved to be an efficient way to rapidly reduce the pH of the solution in the flow channels.

Culturing E. coli in chambers with different O₂ concentrations

To demonstrate an application of the proposed technology of on-chip generation of series of [O₂] to live cell experimentation, we cultured E. coli in the chambers of microfluidic device 2, measured their growth curves, and tested the dependence of the growth curves on [O₂]. Our goal was to perform a feasibility study only. Therefore, the experiments were done at room temperature (instead of 35 °C as is optimal for E. coli) and the numbers of sampled colonies and cells were relatively small. In all experiments, the cell culture medium was perfused through the device at a differential pressure of 0.5 psi.

As in the previous study,⁴ the size of an E. coli colony in a growth chamber was evaluated by measuring the total power of fluorescence in the chamber under the assumption that the power of GFP fluorescence per cell is constant. This is a reasonable assumption in a logarithmic growth phase, when the rate of cell growth and division is constant, and a dynamic equilibrium is expected to exist between the synthesis and folding of GFP on one hand and its degradation and dilution due to cell growth and division on the other hand. In addition, whenever possible, particularly in small colonies, the number of cells was also assessed by direct counting. In our preliminary experiments, we noticed that in colonies under gas channel 1, which were exposed to completely anaerobic conditions (pure N₂), the number of cells remained nearly constant for hours, whereas the total power of fluorescence gradually increased and nearly doubled after several hours. This was likely because the transition from an aerobic culture in the test tube to the anaerobic growth chambers led to a change in the relationship between the rates of GFP production, degradation, and dilution due to cell division. The cells eventually reached a steady level of fluorescence, but it required many hours, apparently because of a reduced rate of intracellular processes in the N₂ atmosphere at room temperature.

Therefore, to avoid the long term adaptation processes during the measurement of growth curves, cells were loaded into the chambers in the evening and incubated overnight in an N₂ atmosphere by feeding N₂ to both gas inlets. In the morning, the gas supplied to gas inlet 2 was switched to air, exposing cells under gas channels 1–9 to different graded levels of O₂ (Fig. 4b). The growth curve measurements were started 3–4 hours later to allow the cells to accommodate to the new conditions and to reach a steady level of fluorescence per cell. Two or three separate growth chambers were selected under each of the gas test channels, and the images of GFP fluorescence in the chambers were periodically taken (Fig. 6). When the imaging was started, the number of cells per chamber varied between 5 and 50.

Fig. 6 Fluorescence micrographs of three growth chambers with E. coli colonies at different time points. The chambers were situated under the gas test channels with [O₂] of 0% (left column), 0.5% (central column), and 12% (right column). The photographs were taken at 0, 150, 270, and 390 min from the point at which the growth curve measurements were started. Dashed lines show the boundaries of the growth chambers, 100 × 50 µm in size. The micrographs were taken with a 60×/1.2 WI objective and a CoolSnap HQ camera, under illumination with the royal-blue LED using a GFP filter cube.

The time dependence of the integral fluorescence in the growth chambers showed that, as expected, cells grew faster at higher [O₂] (Fig. 7a) and the largest increase in the colony growth rates occurred at [O₂] near zero, when the conditions changed from completely anaerobic to microaerobic. The division rate leveled off at ∼0.55 hr⁻¹ or 110 min per division, when [O₂] increased to ∼7%. Somewhat unexpectedly, however, we repeatedly found by direct cell counting and measurements of fluorescence that cells exposed to pure N₂ ([O₂] = 0) did not divide at all and the integral fluorescence of colonies exposed to pure N₂ remained unchanged within the experimental error. On the other hand, the addition of as little as 0.2% of O₂ (1% of air in the air/N₂ mixture) led to a slow but measurable growth with a division time of ∼6 hours (evaluated by the total power of fluorescence and confirmed by the direct cell counting), and at [O₂] = 0.5% the division rate reached about a half of its saturated level (Fig. 7b). A t-test indicated that the growth rate at [O₂] = 0.2% was significantly higher than at [O₂] = 0 (p < 0.01) and the growth rate at [O₂] = 0.5% was significantly higher than at [O₂] = 0.2% (p < 0.025).

Fig. 7 Growth of E. coli colonies at various concentrations of oxygen, [O₂]. (a) Growth curves (in semi-logarithmic coordinates) in chambers with [O₂] = 0, 0.2, 0.5, and 12% are shown by gray circles, black circles, gray squares, and black squares, respectively. [O₂] = 100% corresponds to the medium in equilibrium with pure O₂ at 1 atm. The colony growth is measured by the total power of fluorescence recorded from the area of the growth chamber, and the fluorescence is normalized to its value at time zero. Each growth curve shows an average of data from two growth chambers. All curves were obtained from a single experiment. (b) The rate of cell division (in inverse hours) as a function of [O₂] in semi-logarithmic coordinates. The time between cell divisions was calculated as the doubling time of the total power of fluorescence in the growth chamber. Each data point represents an average of growth exponents obtained from growth curves in an average of 5 separate chambers in two different experiments. Error bars are SEM.

When cells were cultured in the same room and in the same medium in a 15 mL test tube, which was covered by a loose cap and placed on a shaker rotating at 240 rpm, their growth rate was ∼0.48 hr⁻¹ (as measured by OD₆₀₀ between 0.11 and 0.42). This growth rate was consistent with the growth rates measured on the chip, especially taking into account that without active air bubbling, the aeration of the test tube culture was not perfect. In another experiment, cells were cultured in a sealed 15 mL test tube, which was equipped with a gas inlet and outlet (again, at the same room temperature, in the same medium and with 240 rpm shaking), and the medium was bubbled with N₂ at 0.6 mL/sec. The OD₆₀₀ increased from 0.16 to 0.49 within 19 hr, corresponding to a growth rate of 0.085 hr⁻¹ and division time of ∼12 hr. This growth rate was substantially lower than the growth rate measured on the chip at [O₂] = 0.2%, but unlike the on-chip cultures exposed to pure N₂, the test tube culture bubbled with N₂ showed measurable growth. A possible reason for the difference in the growth rates is that the bubbling of the test tube culture with N₂ was not as efficient in setting a pure N₂ atmosphere in the medium as the positioning of the microfluidic growth chambers under a gas test channel ventilated with N₂ (see a more detailed discussion below).

Discussion and conclusions

The proposed technology and devices have three major capacities: on-chip generation of series of mixtures with different gas content out of two gases fed to the device; setting the gas content of liquid in microchannels in the flow layer by a flow of a designed gas mixture through channels in the gas layer; fast variation of the gas content of the liquid in the flow channels. To generate gas mixtures with linearly and exponentially varying concentrations of O₂, the gas channel layers of the devices had gas-mixing networks of a type used before for mixing liquids.¹⁷ The original networks were modified to account for a much higher diffusivity in the gas phase (0.2 cm²/s for N₂/O₂ mixture vs. ∼10⁻⁵ cm²/s for small molecules in an aqueous solution) and relatively large volumetric flow rate required to minimize the unwanted changes in the gas composition caused by the diffusive exchange with the gas contained in the porous PDMS chip (inset in Fig. 3). The on-chip gas-mixing network in device 2 made it possible to generate 7 customized N₂/O₂ mixtures out of air and N₂ fed to the device and to use these two readily available gases and two gas supply lines to study the growth of E. coli colonies at 9 different O₂ concentrations in a single chip.

The fast switching of the gas composition utilizes a special feature of PDMS, its high permeability to low-molecular gases. When the composition of the gas fed to the gas inlets of the device is switched, [O₂] in the flow channels changes with a characteristic delay time (exponential decay time) of 0.8 sec (Fig. 2), with a similar response time of ∼1 sec found for [CO₂] (Fig. 5). These relatively short gas exchange times make the technique a promising tool for testing real-time responses of live cells to the changes in [O₂] and pH in terms of changes in the cell shape, motility, intracellular distribution of soluble proteins, and conformations of proteins and protein complexes. For the last two tasks, fluorescently labeled proteins could be used. Importantly, the switching of the gas content is accomplished by molecular diffusion and, with an appropriate balance of gas pressures, does not cause any flow of liquid or other mechanical perturbation in the flow channels. In addition, it does not change the concentrations of nutrients, ions, macromolecular factors, or any other non-volatile components of the liquid, except for products of chemical reactions between components of the gas mixture and liquid, such as bicarbonate for CO₂ and water. Numerical simulations indicate that the gas exchange time is proportional to the square of the thickness of the membrane between the gas and flow channel. Therefore, decreasing the membrane thickness below the current value of 50 µm is expected to reduce the gas exchange time to <0.8 sec.

The results of experiments with O₂, N₂, and the RTDP solution indicated that, within the experimental precision, the composition of gas dissolved in an aqueous solution under the internal region of a gas channel is identical to the composition of gas in the gas channel (Fig. 3 and 4). (The experimental error was ∼1% near 100% [O₂] and ∼0.1% at 0–1% [O₂].) Numerical simulations (ESI Fig. S-1†) further showed that the matching between [O₂] in the flow channels and gas channels can be as close as 0.01%. These findings from measurements with a fluorescent dye and numerical simulations were corroborated by the experiments on culturing E. coli in growth chambers of the device. We consistently found no detectable colony growth in chambers exposed to pure N₂ and significant growth of colonies in chambers exposed to air/N₂ mixtures with [O₂] as little as 0.2% (Fig. 7).

It is instructive to estimate how the consumption of O₂ by growing bacteria may influence [O₂] in the growth chambers. The O₂ consumption of E. coli was reported to increase linearly with the division rate,^28,29 reaching 20 mmol per hour per 1 g of dry mass (20 mmol/hr/g) at a growth rate of ∼1 division per hour. At the growth rate of 0.2 divisions per hour measured in the microfluidic device at [O₂] = 0.2% (Fig. 7), the O₂ consumption was reported at ∼6 mmol/hr/g. With the E. colicell footprint of ∼2 µm² and its dry mass of ∼0.3 × 10⁻¹² g (taken to be 27% of the live cell mass³⁰), a tightly packed monolayer of E. coli corresponds to a dry mass density of 0.15 g/m². The O₂ consumption of the monolayer at [O₂] = 0.2% is then expected to be 0.9 mmol/m²/hr or 0.25 µmol/m²/s. This consumption requires a supply equivalent to a flux of pure O₂ (44.6 mol/m³ of gas at 1 atm) at a rate J = 5.6 × 10⁻⁹ m³/m²/s = 5.6 × 10⁻⁹ m/s. Given the PDMS thickness d = 5 × 10⁻⁵ m, O₂ solubility in PDMS b = 0.18, and O₂ diffusion coefficient D_p = 1.3 × 10⁻⁹ m²/s, the difference in [O₂] across the PDMS layer, Δ[O₂], required to provide this flux (which is diffusion driven) can be found as Δ[O₂] = Jd/(bD_p) = 1.2 × 10⁻³ or 0.12% of pure O₂.

If the practical goal is to limit Δ[O₂] to 0.01%, which is 1/20 of the [O₂] = 0.2% that device 2 is designed to impose in growth chambers under gas channel 2 (Fig. 4), cell densities of up to 1/12 of a tightly packed monolayer can be allowed in these growth chambers. For the 50 × 100 µm chambers used in the experiments, this cell density amounts to ∼200 cells per chamber, which is 3–5 times higher that the cell numbers typically reached by the end of our experiments (Figs. 6 and 7). Cell colonies in chambers at [O₂] > 6% reached substantially larger sizes and had ∼3 times higher growth rate that was expected to lead to the O₂ consumption at rates of ∼15 mmol/hr/g.^28,29 Nevertheless, for [O₂] = 6%, the condition Δ[O₂] = 1/20 [O₂] is satisfied at Δ[O₂] equal to 0.3%. At this value of Δ[O₂] the flux of oxygen is expected to be J = Δ[O₂]bD_p/d = 1.4 × 10⁻⁸ m/s (equivalent to 2.3 mmol/m²/hr), which is expected to suffice for a very large colony of up to 2500 cells (close to a tightly packed monolayer or 1/6 of the chamber volume). The estimates for the O₂ supply also indicate that the device should efficiently evacuate from the culture chambers the gases generated as a result of cell metabolism and respiration, if these gases have good solubility and high diffusivity in PDMS, as is the case for CO₂.

The capacity of the proposed device to maintain bacterial colonies at well-defined low levels of [O₂] (such as 0.2% maintained within 0.01%) in spite of the continuous consumption of O₂ by the cells could prove useful for detailed studies of cell cultures at microaerobic conditions ([O₂] << 21%). To compare the device with a large-scale culture in a test tube, flask, or a chemostat, we note that the time of equilibration of [O₂] between a growth chamber and the gas test channel above it can be estimated as τ' = dh/(6D_p) ≈ 38 msec (see ESI for a detailed discussion†). This equilibration time corresponds to the time of O₂ diffusion through a water layer of thickness . Therefore, a large-scale culture with conditions similar to those on the chip would have to involve intensive bubbling with a gas mixture of a desired [O₂] in combination with vigorous agitation that would homogenize [O₂] on scales down to 12 µm within ∼38 msec (with the homogenization on scales below 12 µm occurring by molecular diffusion). Such conditions would be very difficult to implement in large-scale cultures.

The techniques and devices for generating series of different gas mixtures and for culturing cells in media with well-defined [O₂] can have numerous potential applications in microbiology and cell biology. They can be used to study the levels of expression of various genes associated with anaerobic and aerobic metabolism of E. coli and other microorganisms at high throughput and with [O₂] controlled with a resolution and accuracy that are difficult to achieve with conventional tools. The devices and techniques introduced in this paper can also be used to study gene expression and cell division rates under conditions when [O₂] changes in time along a prescribed pattern with switching times as short as 1–2 sec. The devices could provide a convenient platform to study the dependence of metabolism and gene expression on the concentration of other gases, in particular CO₂,³¹ and be applied to culturing anaerobic organisms. With some modifications, the devices can also potentially be used for detailed analyses of responses of higher eukaryotes, including mammalian cells, to various steady levels and temporal patterns of [O₂] (hypoxia, normoxia, oxidative stress), mimicking diverse cell microenvironments in a variety of pathological and physiological conditions.³²

Acknowledgements

We thank Terry Hwa, Dalai Yan, Sydney Kustu, and Rob Gunsalus for helpful discussions and Virginia VanDelinder for useful suggestions. The work was partially funded by DARPA and by NSF NIRT Grant No. 0608863.

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Footnotes

† Electronic supplementary information (ESI) available: Time-dependent two-dimensional numerical simulation of oxygen concentration, [O₂], in a fragment of cross-section of device 1 in the yz-plane (Fig. S-1). See DOI: 10.1039/b816191g

‡ The authors contributed equally to this work.

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