Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans.

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.     

Probing glycolytic and membrane potential oscillations in Saccharomyces cerevisiae

We have investigated glycolytic oscillations under semi-anaerobic conditions in Saccharomyces cerevisiae by means of NADH fluorescence, measurements of intracellular glucose concentration, and mitochondrial membrane potential. The glucose concentration was measured using an optical nanosensor, while mitochondrial membrane potential was measured using the fluorescent dye DiOC 2(3). The results show that, as opposed to NADH and other intermediates in glycolysis, intracellular glucose is not oscillating. Furthermore, oscillations in NADH and membrane potential are inhibited by the ATP/ADP antiporter inhibitor atractyloside and high concentrations of the ATPase inhibitor N, N'-dicyclohexylcarbodiimide, suggesting that there is a strong coupling between oscillations in mitochondrial membrane potential and oscillations in NADH mediated by the ATP/ADP antiporter and possibly also other respiratory components.     

Heterogeneous conditions in dissolved oxygen affect N-glycosylation but not productivity of a monoclonal antibody in hybridoma cultures

It is known that heterogeneous conditions exist in large-scale animal cell cultures. However, little is known about how heterogeneities affect cells, productivities, and product quality. To study the effect of non-constant dissolved oxygen tension (DOT), hybridomas were subjected to sinusoidal DOT oscillations in a one-compartment scale-down simulator. Oscillations were forced by manipulating the inlet oxygen partial pressure through a feedback control algorithm in a 220-mL bioreactor maintained at a constant agitation. Such temporal DOT oscillations simulate spatial DOT gradients that can occur in large scales. Different oscillation periods, in the range of 800 to 12,800 s (axis of 7% (air saturation) and amplitude of 7%), were tested and compared to constant DOT (10%) control cultures. Oscillating DOT decreased maximum cell concentrations, cell growth rates, and viability indexes. Cultures at oscillating DOT had an increased glycolytic metabolism that was evidenced by a decrease in yield of cells on glucose and an increase in lactate yield. DOT gradients, even several orders of magnitude higher than those expected under practical large-scale conditions, did not significantly affect the maximum concentration of an IgG(1) monoclonal antibody (MAb). The glycosylation profile of the MAb produced at a constant DOT of 10% was similar to that reported in the literature. However, MAb produced under oscillating culture conditions had a higher amount of triantennary and sialylated glycans, which can interfere with effector functions of the antibody. It was shown that transient excursions of hybridomas to limiting DOT, as occurs in deficiently mixed large-scale bioreactors, is important to culture performance as the oscillation period, and thus the time cells spent at low DOT, affected cell growth, metabolism, and the glycosylation pattern of MAb. Such results underline the importance of monitoring protein characteristics for the development of large-scale processes.     

Contribution of the endoplasmic reticulum to the glucose-induced [Ca(2+)](c) response in mouse pancreatic islets

Thapsigargin (TG), a blocker of Ca(2+) uptake by the endoplasmic reticulum (ER), was used to evaluate the contribution of the organelle to the oscillations of cytosolic Ca(2+) concentration ([Ca(2+)](c)) induced by repetitive Ca(2+) influx in mouse pancreatic beta-cells. Because TG depolarized the plasma membrane in the presence of glucose alone, extracellular K(+) was alternated between 10 and 30 mM in the presence of diazoxide to impose membrane potential (MP) oscillations. In control islets, pulses of K(+), mimicking regular MP oscillations elicited by 10 mM glucose, induced [Ca(2+)](c) oscillations whose nadir remained higher than basal [Ca(2+)](c). Increasing the depolarization phase of the pulses while keeping their frequency constant (to mimic the effects of a further rise of the glucose concentration on MP) caused an upward shift of the nadir of [Ca(2+)](c) oscillations that was reproduced by raising extracellular Ca(2+) (to increase Ca(2+) influx) without changing the pulse protocol. In TG-pretreated islets, the imposed [Ca(2+)](c) oscillations were of much larger amplitude than in control islets and occurred on basal levels. During intermittent trains of depolarizations, control islets displayed mixed [Ca(2+)](c) oscillations characterized by a summation of fast oscillations on top of slow ones, whereas no progressive summation of the fast oscillations was observed in TG-pretreated islets. In conclusion, the buffering capacity of the ER in pancreatic beta-cells limits the amplitude of [Ca(2+)](c) oscillations and may explain how the nadir between oscillations remains above baseline during regular oscillations or gradually increases during mixed [Ca(2+)](c) oscillations, two types of response observed during glucose stimulation.     

Real-time analysis of intracellular glucose and calcium in pancreatic beta cells by fluorescence microscopy

Glucose is the physiological stimulus for insulin secretion in pancreatic beta cells. The uptake and phosphorylation of glucose initiate and control downstream pathways, resulting in insulin secretion. However, the temporal coordination of these events in beta cells is not fully understood. The recent development of the FLII(12)Pglu-700μ-δ6 glucose nanosensor facilitates real-time analysis of intracellular glucose within a broad concentration range. Using this fluorescence-based technique, we show the shift in intracellular glucose concentration upon external supply and removal in primary mouse beta cells with high resolution. Glucose influx, efflux, and metabolism rates were calculated from the time-dependent plots. Comparison of insulin-producing cells with different expression levels of glucose transporters and phosphorylating enzymes showed that a high glucose influx rate correlated with GLUT2 expression, but was largely also sustainable by high GLUT1 expression. In contrast, in cells not expressing the glucose sensor enzyme glucokinase glucose metabolism was slow. We found no evidence of oscillations of the intracellular glucose concentration in beta cells. Concomitant real-time analysis of glucose and calcium dynamics using FLII(12)Pglu-700μ-δ6 and fura-2-acetoxymethyl-ester determined a glucose threshold of 4mM for the [Ca(2+)](i) increase in beta cells. Indeed, a glucose concentration of 7mM had to be reached to evoke large amplitude [Ca(2+)](i) oscillations. The K(ATP) channel closing agent glibenclamide was not able to induce large amplitude [Ca(2+)](i) oscillations in the absence of glucose. Our findings suggest that glucose has to reach a threshold to evoke the [Ca(2+)](i) increase and subsequently initiate [Ca(2+)](i) oscillations in a K(ATP) channel independent manner.     

Membrane potential dependent modulations of calcium oscillations in insulin-secreting INS-1 cells

This study was undertaken to examine the role of K(+) channels on cytosolic Ca(2+) ([Ca(2+)](i)) in insulin secreting cells. [Ca(2+)](i) was measured in single glucose-responsive INS-1 cells using the fluorescent Ca(2+) indicator Fura-2. Glucose, tolbutamide and forskolin elevated [Ca(2+)](i) and induced [Ca(2+)] oscillations. Whereas the glucose effect was delayed and observed in 60% and 93% of the cells, in a poorly and a highly glucose-responsive INS-1 cell clone, respectively, tolbutamide and forskolin increased [Ca(2+)](i) in all cells tested. In the latter clone, glucose induced [Ca(2+)](i) oscillations in 77% of the cells. In 16% of the cells a sustained rise of [Ca(2+)](i) was observed. The increase in [Ca(2+)](i) was reversed by verapamil, an L-type Ca(2+) channel inhibitor. Adrenaline decreased [Ca(2+)](i) in oscillating cells in the presence of low glucose and in cells stimulated by glucose alone or in combination with tolbutamide and forskolin. Adrenaline did not lower [Ca(2+)](i) in the presence of 30mM extracellular K(+), indicating that adrenaline does not exert a direct effect on Ca(2+) channels but increases K(+) channel activity. As for primary b-cells, [Ca(2+)](i) oscillations persisted in the presence of closed K(ATP) channels; these also persisted in the presence of thapsigargin, which blocks Ca(2+) uptake into Ca(2+) stores. In contrast, in voltage-clamped cells and in the presence of diazoxide (50mM), which hyperpolarizes the cells by opening K(ATP) channels, [Ca(2+)](i) oscillations were abolished. These results support the hypothesis that [Ca(2+)](i) oscillations depend on functional voltage-dependent Ca(2+) and K(+) channels and are interrupted by a hyperpolarization in insulin-secreting cells.     

Role of the Na+/K+/Cl- transporter in the positive inotropic effect of ouabain in cardiac myocytes

In this study we have characterized the bumetanide-sensitive K+/Na+/Cl- cotransport in cultured rat cardiac myocytes. 1) It carries about 10% of the total K+ influx. 2) It is sensitive to furosemide (Ki0.5 = 10(-6)M) and bumetanide (Ki0.5 = 10(-7)M). 3) It is strongly dependent on the extracellular concentrations of Na+ and Cl-. 4) It carries out influx of both ions, K+ and Na+. A therapeutic concentration of ouabain (10(-7) M) stimulated the bumetanide-sensitive K+ influx (as measured by 86Rb+), in the cultured myocytes, with no effect on the bumetanide-resistant K+ influx, which was mediated mostly by the Na+/K+ pump. Stimulation of the bumetanide-sensitive Rb+ influx by a low ouabain concentration was strongly dependent on Na+ and Cl- in the extracellular medium. A low concentration of ouabain (10(-7) M) was found to increase the steady-state level of cytosolic Na+ by 15%. This increase was abolished by the addition of bumetanide or furosemide. These findings suggest that ouabain, at a low (10(-7) M) concentration, induced its positive inotropic effect in rat cardiac myocytes by increasing Na+ influx into the cells through the bumetanide-sensitive Na+/K+/Cl- cotransporter. In order to examine this hypothesis, we measured the effect of bumetanide on the increased amplitude of systolic cell motion induced by ouabain. Bumetanide or furosemide, added to cultured cardiac myocytes, inhibited the increased amplitude of systolic cell motion induced by ouabain. Neither bumetanide nor furosemide alone has any significant effect on the basal amplitude of systolic cell motion. We propose that stimulation of bumetanide-sensitive Na+ influx plays an essential role in the positive inotropic effect in rat cardiac myocytes induced by low concentration of ouabain.     

The effect of oscillating dissolved oxygen concentrations on the metabolism of a Spodoptera frugiperda IPLB-Sf21-AE clonal isolate

The effect of oscillating dissolved oxygen (DO) concentration on the metabolism of a clonal isolate of the Spodoptera frugiperda IPLB-Sf21-AE insect cell line was investigated. Specifically, the effect on cell growth, re- combinant protein synthesis, glucose and glutamine consumption, and lactate accumulation was determined. Prior to conducting the oscillating DO experiments, it was found that the DO concentration could be reduced to 15% air saturation without adversely affecting the growth rate. Under these conditions, glucose and glutamine became depleted as the maximum cell density was reached. The introduction of DO oscillations, that is, cycles consisting of 30 min at 15% DO followed by 30 min of anoxia, significantly altered cell metabolism, including inhibition of cell growth and recombinant protein synthesis. The effect of DO oscillations on glucose consumption was dependent on the experimental conditions. Glucose exhaustion occurred when the DO oscillations contained either an "apparent" anoxia period (nitrogen sparging discontinued upon reaching 0% DO) without pH control or a "true" anoxia period (nitrogen sparging continued throughout anoxia period) with pH control. Glucose consumption was significantly decreased, however, when the cells were exposed to a "true" anoxia period without pH control, that is, low pH inhibited glucose utilization. Glutamine uptake was not significantly affected by DO oscillations. Lactate only accumulated in the oscillating DO runs, a finding consistent with previous results demonstrating that significant lactate accumulation only occurs under DO-limited conditions. (c) 1995 John Wiley & Sons, Inc.     

Oscillations of Ca++ concentration during the cell differentiation of Dictyostelium discoideum: their relation to oscillations in cyclic AMP and other components

Periodic cyclic-AMP pulses control the cell aggregation and differentiation of Dictyostelium discoideum. Another component required for the aggregation and differentiation of these cells appears to be extracellular Ca+ +. Oscillations in extracellular Ca+ + concentration were investigated in suspensions of differentiating cells. We observed spike-shaped and sinusoidal Ca+ + oscillations. In the course of differentiation, spike-shaped Ca+ + oscillations preceded sinusoidal oscillations, and no phase change occurred at the transition from spike-shaped to sinusoidal Ca+ + oscillations. Spike-shaped and sinusoidal Ca+ + oscillations were related to oscillations in (1) the cyclic-AMP and cyclic-GMP content of cells, (2) the light-scattering properties of cells, and (3) the extracellular pH. Spikeshaped Ca+ + oscillations were observed together with cyclic-AMP oscillations. The minima of the extracellular Ca+ + concentration trailed the maxima of the cyclic-AMP concentration by about 30 s. Sinusoidal Ca+ + oscillations were not accompanied by measurable cyclic-AMP oscillations. The amplitudes of the sinusoidal Ca+ + oscillations were smaller than those of the spike-shaped Ca+ + oscillations. A Ca+ + oscillation of small amplitude (instead of a spike-shaped oscillation) was observed when one cyclic-AMP spike was skipped. Our results provide evidence for the existence of a sinusoidal cyclic-AMP-independent Ca+ + oscillation of small amplitude, and they also suggest that spike-shaped Ca+ + oscillations may be superimposed on such small-amplitude oscillations. When D. discoideum cells produce cyclic-AMP spikes, the uptake of additional Ca+ + is induced, resulting in Ca+ + oscillations of a large amplitude.     

The mass, but not the frequency, of insulin secretory bursts in isolated human islets is entrained by oscillatory glucose exposure

Insulin is secreted in discrete insulin secretory bursts. Regulation of insulin release is accomplished almost exclusively by modulation of insulin pulse mass, whereas the insulin pulse interval remains stable at approximately 4 min. It has been reported that in vivo insulin pulses can be entrained to a pulse interval of approximately 10 min by infused glucose oscillations. If oscillations in glucose concentration play an important role in the regulation of pulsatile insulin secretion, abnormal or absent glucose oscillations, which have been described in type 2 diabetes, might contribute to the defective insulin secretion. Using perifused human islets exposed to oscillatory vs. constant glucose, we questioned 1) whether the interval of insulin pulses released by human islets is entrained to infused glucose oscillations and 2) whether the exposure of islets to oscillating vs. constant glucose confers an increased signal for insulin secretion. We report that oscillatory glucose exposure does not entrain insulin pulse frequency, but it amplifies the mass of insulin secretory bursts that coincide with glucose oscillations (P < 0.001). Dose-response analyses showed that the mode of glucose drive does not influence total insulin secretion (P = not significant). The apparent entrainment of pulsatile insulin to infused glucose oscillations in nondiabetic humans in vivo might reflect the amplification of underlying insulin secretory bursts that are detected as entrained pulses at the peripheral sampling site, but without changes in the underlying pacemaker activity.     

Oscillations in cell morphology and redox state

Fluctuations in the intensity of light scattered and absorbed by cells in suspension have been analysed by smoothing, periodogram and power spectrum methods to reveal oscillations attributed to changes in cell morphology and the redox state of NADH and FAD (periods 10 s to 30 min). The rhythms are themselves periodically modulated in amplitude at a similar frequency and exhibit burst characteristics. The low frequency scatter dynamics are provisionally attributed to oscillations in gross morphology and the high frequency variation to changes at the cell surface. Agents, such as insulin and transferrin, affect the dynamics. The scatter results suggest that rhythmic changes in cell morphology associated with locomotion are largely inherent in the cell and not due to periodic attachment and detachment from a surface.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

Propagation of cytoplasmic Ca2+ oscillations in clusters of pancreatic beta-cells exposed to glucose

Digital image analysis was employed for resolving the temporal and spatial variations of the cytoplasmic Ca2+ concentration ([Ca2+]i) in pancreatic beta-cells loaded with the Ca(2+)-indicator Fura-2. Glucose-stimulated individual beta-cells exhibited large amplitude oscillations of [Ca2+]i with a mean frequency of 0.33 min-1. When Ca2+ diffusion was restricted by increasing the Ca2+ buffering capacity, the sugar-induced rise of [Ca2+]i preferentially affected the peripheral cytoplasm. When glucagon was present glucose also caused less prominent oscillations with about a 10-fold higher frequency superimposed on an elevated [Ca2+]i. In small clusters of 6-14 cells the average frequency of the large amplitude oscillations increased to 0.60 min-1. The clusters were found to contain micro-domains of electrically coupled cells with synchronized oscillations. After increasing the glucose concentration, adjacent domains became functionally coupled. The oscillations originated from different cells in the cluster. Also the fast glucagon-dependent oscillations were synchronized between cells and had different origins. The results indicate that coupling of beta-cells leads to an increased frequency of the large amplitude oscillations, and that the oscillatory characteristics are determined collectively among electrically coupled beta-cells rather than by particular pacemaker cells. In the light of these data it is necessary to reconsider the previous ideas that glucose-induced oscillations of membrane potential and [Ca2+]i require coupling between many beta-cells, and that the peak [Ca2+]i values reached during oscillations should increase with the size of the coupled cluster.     

Glucose sensing of individual pancreatic beta-cells involves transitions between steady-state and oscillatory cytoplasmic Ca2+.

Glucose stimulation of individual pancreatic beta-cells is associated with a rise of the cytoplasmic Ca2+ concentration ([Ca2+]i) manifested either as large amplitude oscillations (0.2-0.5/min) or as a sustained increase. Determinants for the transitions between the basal and the two stimulated states have now been studied using dual-wavelength fluorometric measurements on individual ob/ob mouse beta-cells loaded with the Ca2+ indicator Fura-2. The transition from the basal state to large amplitude oscillations was induced by raising the glucose concentration to 7 mM or above. The frequencies and shapes of the [Ca2+]i cycles remained largely unaffected when raising glucose as high as 40 mM. However, in some cells the oscillatory pattern was transformed into a sustained increase of [Ca2+]i at high glucose concentrations. Although the peak values for the oscillations exceeded the steady-state increase, the time average [Ca2+]i was higher during the latter phase. Both types of glucose-induced transitions were facilitated by the presence of 1-100 nM glucagon. Protein kinase C activation by 10 nM of the phorbol ester TPA resulted in a transformation of the glucose-induced oscillations into a sustained increase of [Ca2+]i but the levels reached were considerably lower than obtained with glucose alone. It is concluded that the glucose sensing of the individual beta-cell is based on sudden transitions between steady-state and oscillating cytoplasmic Ca2+. It is these transitions rather than alterations of the oscillatory characteristics which determine the average [Ca2+]i regulating insulin release.     

The oscillatory behavior of pancreatic islets from mice with mitochondrial glycerol-3-phosphate dehydrogenase knockout

Glucose stimulation of pancreatic beta cells induces oscillations of the membrane potential, cytosolic Ca(2+) ([Ca(2+)](i)), and insulin secretion. Each of these events depends on glucose metabolism. Both intrinsic oscillations of metabolism and repetitive activation of mitochondrial dehydrogenases by Ca(2+) have been suggested to be decisive for this oscillatory behavior. Among these dehydrogenases, mitochondrial glycerol-3-phosphate dehydrogenase (mGPDH), the key enzyme of the glycerol phosphate NADH shuttle, is activated by cytosolic [Ca(2+)](i). In the present study, we compared different types of oscillations in beta cells from wild-type and mGPDH(-/-) mice. In clusters of 5-30 islet cells and in intact islets, 15 mM glucose induced an initial drop of [Ca(2+)](i), followed by an increase in three phases: a marked initial rise, a partial decrease with rapid oscillations and eventually large and slow oscillations. These changes, in particular the frequency of the oscillations and the magnitude of the [Ca(2+)] rise, were similar in wild-type and mGPDH(-/-) mice. Glucose-induced electrical activity (oscillations of the membrane potential with bursts of action potentials) was not altered in mGPDH(-/-) beta cells. In single islets from either type of mouse, insulin secretion strictly followed the changes in [Ca(2+)](i) during imposed oscillations induced by pulses of high K(+) or glucose and during the biphasic elevation induced by sustained stimulation with glucose. An imposed and controlled rise of [Ca(2+)](i) in beta cells similarly increased NAD(P)H fluorescence in control and mGDPH(-/-) islets. Inhibition of the malate-aspartate NADH shuttle with aminooxyacetate only had minor effects in control islets but abolished the electrical, [Ca(2+)](i) and secretory responses in mGPDH(-/-) islets. The results show that the two distinct NADH shuttles play an important but at least partially redundant role in glucose-induced insulin secretion. The oscillatory behavior of beta cells does not depend on the functioning of mGPDH and on metabolic oscillations that would be generated by cyclic activation of this enzyme by Ca(2+).     

D-arabinose countertransport in Bakers' yeast

The initial rate of the glucose-induced countertransport of d-arabinose was measured at several concentrations of extracellular glucose. These data permit the calculation of the intracellular concentration of free glucose, and, if the rate of glucose metabolism is known, the maximal rate of glucose transport can be estimated. Since the maximal transport rate remained essentially constant when the extracellular glucose concentration was increased from 2 to 100 mm, the results are consistent with the hypothesis that, during glucose metabolism, glucose is transported across the yeast cell membrane by a symmetrical carrier system which functions independently of metabolism.     

Dynamics of plasmid maintenance in a CSTR upon square-wave perturbations in the dilution rate

The effects of forced oscillations in the dilution rate on a population of Escherichia coli K12 harboring the plasmid pBR322 in a chemostat with a nonselective medium were studied. In the constant dilution rate control experiments, the percentage of plasmid-containing cells decreased after a long lag time. Eventually, the culture approached a population consisting of 100% plasmid-free ells. However, under forced perturbations of the dilution rate, the culture maintained a mixed population of plasmid-free and plasmid-carrying cells for a longer period of ime. An unstructured model was developed to describe the above observations. Our results indicate that transient conditions created by dilution-rate perturbations provide a favorable environment for the plasmid-carrying population. In addition, experiments with different cycling frequencies suggest that adaptation by the culture to these transient conditions will reduce or totally eliminate such an advantage.