1.

Introduction

A characteristic property of invasive cancers is altered glucose metabolism.¹ Biochemical assays for measuring this important metabolic activity have given useful kinetic information in a variety of cancers. However, the precise regulatory dynamics of glucose metabolism in intact living cells is far from clear. Studies have indicated that there are short-term and long-term changes in pH in various organelles (cytosol, mitochondria, lysosomes, etc.) during substrate metabolism and apoptosis.^{2, 3} Living cells tightly regulate pH homeostasis in normal conditions as well as under stress. One of the biochemical hallmarks of tumors is up-regulation of glycolysis even in the presence of oxygen (aerobic glycolysis or Warburg effect), thereby leading to increased lactic acid production as compared to normal, untransformed cells.⁴ This led us to hypothesize that single-cell pH measurements during glucose metabolism may be valuable in assessing differences between normal and cancer cells.

In this paper, we have systematically characterized fluorescence intensity and lifetime kinetics of an improved version of cyan fluorescent protein⁵ (Cerulean) in mammary epithelial cells during glucose metabolism. We recently reported adaptation of a nonlinear dynamical scaling analysis in a single-cell imaging paradigm where we observed that liver cells displayed complex dynamics and scaling behavior in redox fluctuations and free radical fluctuations.^{6, 7} Here, we extend this novel application for gaining insight into the regulatory nature of glucose metabolism in normal and transformed (cancerous) mammary epithelial cell lines. For this scaling analysis, we have exploited the fact that fluorescent proteins exhibit fluorescence fluctuations of the order of milliseconds in a pH-dependent as well as conformation-dependent manner.⁸ Together, our data reveal complex dynamics in living cells manifested as regulatory time correlations in glucose metabolism. Initial theories for understanding glycolytic-flux control held the view that “rate-limiting enzymes” such as phosphofructokinase determine the entire metabolic flux; however, reevaluation by metabolic control analysis has confirmed that control is generally distributed, and effective physiological control of metabolic regulation can be shown to involve multiple sites simultaneously through action on a number of enzymes.⁹ These recent observations point to a more complex network for glucose metabolism rather than an apparently “linear” array of enzymes. Our long-term goal is to understand experimental manifestations of such network complexity at the level of single cells.

2.

Materials and Methods

2.3.

Time-Series Data Acquisition and Analysis

Time-series data for monitoring Cerulean fluorescence fluctuations in living cells were acquired as follows: A field of view with $\sim 4$ to 6 cells was chosen before measurements. For achieving high time resolution, a line scan was performed so that the chosen line spanned all the cells. Typically, time-series data were acquired for $N=8000$ time points ( $\sim 30\mathrm{ms}∕\mathrm{line}$ ; $\sim 58\mu \mathrm{s}∕\mathrm{pixel})$ . Every line scan samples the cell, yielding typically 100 to 300 individual time series depending on the region of interest. By averaging this set of time-series data, one. obtains a good statistical score of probing the spatiotemporal dynamics in single cells. In the present study, we are interested in asking how glucose metabolism in normal and cancer cells differs in different time scales (pixel time series: $\sim \mu \mathrm{s}$ ; lines scan time series: $\sim \mathrm{ms}$ ; and frame scan time series: $\sim \mathrm{s}$ to min). Scaling analysis is an elegant way to probe real-time regulatory dynamics by analyzing subtle signal fluctuations (fluorescence fluctuations in the present case) that attempts to look for time correlations between the signal (or process) at any instant and the same signal (or process) at some other instant. If there are no apparent correlations between various time windows, then the underlying process can be assumed to be a “random” process. Brownian diffusion is a classical example of a random process (Brownian noise) with no apparent long-range time correlations. On the other hand, a nonrandom scaling behavior may indicate positive regulatory correlations that control the cellular process. Toward this end, we applied an analytical method, namely, detrended fluctuation analysis (DFA), originally developed by C.-K. Peng, to quantify statistical correlations in a time-series signal.^{12, 13} The DFA approach is a modified root-mean-square fluctuation analysis of Random walk—to quantify statistical correlations in a nonstationary time series signal. Figure 1 describes a schematic of this analysis procedure. The original time series (of length $N$ ) is first integrated and then divided into boxes of equal size $\left(n\right)$ . In each box, the integrated profile is fit to a polynomial that gives a local trend in that box. Next this local trend is subtracted from the integrated profile in each box, which is termed “detrending.” Last, rms fluctuation $F\left(n\right)$ is calculated from the integrated and detrended signals in each box. These steps are repeated for different values of box size $\left(n\right)$ to generate $F\left(n\right)$ for a broad range of scale sizes $n$ . Intuitively, $F\left(n\right)$ will increase as $n$ increases, and for scale-invariant signals with power-law correlations, there is a scaling relationship $F\left(n\right)=n^{\alpha }$ . The scaling exponent $\alpha$ is a quantitative measure of the extent of correlations in the signal. $\alpha$ can characterize randomness ( $\alpha =0.5$ for white noise; $\alpha =1.5$ for Brownian noise) or correlations ( $\alpha <0.5$ for anticorrelations, and $0.5<\alpha <1.5$ for persistent power law–like correlations), regardless of the nature or source of the fluctuations. In other words, the scaling function is universal and can be used to analyze fluctuations in any time-series signal. Similar crossover in exponents has been noted in earlier studies of physiological signals. An important advantage of the DFA algorithm over other time-series analysis methods is that it can also be reliably used for nonstationary signals since local detrending eliminates the errors associated with nonstationary signals. Although this algorithm has been successfully used in quantifying correlations in physiological signals such as heartbeat dynamics and human gait dynamics, to the best of our knowledge, we were the first to carry out systematic application of this approach to understand single-cell dynamics in living cells. More details about this algorithm can be found in Ref. 6, and source code can be obtained from the webpage of the National Research source, at www.physionet.org.

Fig. 1

Schematic of detrended fluctuation analysis (DFA) of line scan time series data. (a) Representative intensity image where line scan time series were obtained. The $xt$ line spans typically 300 to 512 pixels, depending on the field of view, thereby rendering the same number of pixel time series; scale bar= $20\mu \mathrm{m}$ . (b) Representative time series data acquired with $30\mathrm{ms}∕\mathrm{line}$ scan and $N=8000$ total line scans. This renders probing the dynamics in the time scales of a few hundred microseconds (pixel dwell time) to a few hundred milliseconds (line scan duration) and eventually to few seconds (entire time series data). We employed DFA in obtaining scaling function from the raw time series. More details about this method are described in the text. In brief, DFA dissects the original time series data into many windows with progressively increasing scale size $\left(n\right)$ and calculates the rms fluctuations $F\left(n\right)$ for every scale size $\left(n\right)$ to yield a scaling function $F\left(n\right)=n^{\alpha }$ . The scaling exponent $\alpha$ is a quantitative measure of the extent of correlations in the signal. $\alpha$ can characterize randomness ( $\alpha =0.5$ for white noise; $\alpha =1.5$ for Brownian noise) or correlations ( $\alpha <0.5$ for anticorrelations, and $0.5<\alpha <1.5$ for persistent power law–like correlations), regardless of the nature or source of the fluctuations. (c) Representative scaling functions $F\left(n\right)=n^{\alpha }$ for normal and cancer cells with and without glycolytic inhibitor treatment. The inset shows an enlarged view of the fitted region $(0<\log n<2.0)$ where the scaling exponent $\alpha$ was calculated.

3.

Results

Although fluorescein-based ratiometric pH probes (e.g., BCECF) have a good dynamic range, we were interested in evaluating fluorescent protein-based pH probes, since these can be utilized in tumor models in vivo. Many fluorescent protein mutants have shown variable pH sensitivity, with maximum pH sensitivity being displayed by enhanced yellow fluorescent protein.³ In this paper, we have systematically characterized pH dependence of an improved version of enhanced cyan fluorescent protein, namely, Cerulean, reported by Rizzo .⁵ Normal and cancer phenotypes can be clearly distinguished by multilayer growth in the latter [Fig. 2a ]. Figure 2b shows the pH calibration curve for Cerulean stably expressed in parental MMuMG cells. It is seen that Cerulean lifetime displayed a good dynamic range of pH sensitivity: $\mathrm{\Delta }\tau =\pm 13\%$ $(\mathrm{\Delta }\tau \sim 17\%$ at pH 5, and $\mathrm{\Delta }\tau =13\%$ at pH 8) as compared to the lifetime at neutral pH. We carried out similar pH calibration experiments in cancerous NMuMG cells and obtained identical results (data not shown). This result is not surprising considering the fact that the pH calibration protocol required clamping of the buffer pH with nigericin. In order to test whether normal and cancer cells can show detectable differences in cytosolic pH during various perturbations that are known to alter cellular metabolism, we treated NMuMG and NMuMG-ST cells with mitochondrial complex inhibitors (rotenone and antimycin A) and apoptotic inducer staurosporine. As compared to control cells maintained at neutral pH 7, both normal and cancer cells show cytosolic acidification, as can been seen from the reduced lifetime of Cerulean [Fig. 2c]. Interestingly, cancer cells showed significantly larger acidification than the normal cells when mitochondrial electron transport was inhibited.

Fig. 2

Steady-state lifetime imaging in normal and cancer cells during metabolic perturbations. NMuMG and NMuMG-ST cells stably expressing Cerulean in cytosol were imaged in a custom-made two-photon imaging system, (a) Representative intensity images of cells either untreated (control) or treated with mitochondrial complex I inhibitor ( $10\mu \mathrm{M}$ rotenone; $4\mathrm{h}$ ; $37°\mathrm{C}$ ), complex III inhibitor ( $10\mu \mathrm{M}$ Antimycin A; $4\mathrm{h}$ ; $37°\mathrm{C}$ ), apoptosis inducer ( $1\mu \mathrm{M}$ staurosporine; $4\mathrm{h}$ ; $37°\mathrm{C}$ ), or glycolytic inhibitor ( $20\mathrm{mM}$ 2-deoxyglucose; $4\mathrm{h}$ ; $37°\mathrm{C}$ ); scale $\mathrm{bar}=20\mu \mathrm{m}$ . (b) pH calibration curve showing fluorescence lifetime versus pH for Cerulean. The cells were maintained in high ${\mathrm{K}}^{+}$ buffers at varying pH 5, 6, 7, and 8 at $37°\mathrm{C}$ for $30\min$ before imaging at room temperature. All the experiments at fixed pH were performed by clamping pH with $5\mu \mathrm{M}$ nigericin in the pH buffers. (c) Steady-state lifetime histograms (with corresponding pH scale shown in the right $y$ axis, as calculated from the pH calibration curve) of normal and cancer cells under representative metabolic perturbations. Data are shown as $\mathrm{mean}\pm \mathrm{SEM}$ , pooled from 3 to 5 experiments. Statistical significance in (c) was obtained from a one-way ANOVA test with $p<0.05$ .

Although this result does not conclusively demonstrate that the observed decrease in cytosolic pH is directly due to the effect of mitochondrial inhibitors, it is highly probable that the observed differences between normal and cancer cells (in the presence of mitochondrial electron transport inhibitors) are indicative of alterations in mitochondrial response as well as in cytosolic pH. Some earlier studies have used oxygen depletion (either by growing cells in nitrogen atmosphere or by chemical hypoxia) for modulating cytosolic pH. We carefully avoided this approach to eliminate possible artifacts in cancer cell discrimination since hypoxia is known to have dissimilar effects on glucose metabolism in normal and cancer cells. Next, we wanted to see whether we could monitor real-time lifetime modifications while the cells are metabolizing glucose. A single pulse of glucose transiently decreases Cerulean lifetime, but continuous monitoring of Cerulean lifetime after the glucose pulse showed that normal and cancer cells differ in the recovery of homeostasis (Fig. 3 ). Normal cells displayed an oscillatory lifetime profile indicative of approach to restore the pH equilibrium. However, the cancer cells displayed two larger reductions in Cerulean lifetime, clearly suggesting that normal and cancer cells are significantly different in their ability to metabolize glucose at the single-cell level. Even though we have not demonstrated a direct connection between glucose metabolism and pH changes, the only reasonable explanation of this observation can be attributed to hyperactivity of glucose metabolic machinery (either increased glucose transporters or increased glycolytic rate or both) in cancer cells.

Fig. 3

Glucose-induced lifetime changes in NMuMG and NMuMG-ST cells. (a) Representative 2p-fluorescence images of normal and cancer cells expressing Cerulean pre- and post-glucose stimulus. $20\mathrm{mM}$ glucose was added during kinetic experiments, and images were collected subsequently to analyze the glucose-induced fluorescence decay curves; scale $\mathrm{bar}=20\mu \mathrm{m}$ . (b) Representative lifetime kinetic profiles in NMuMG and NMuMG-ST cells with a single $20\mathrm{mM}$ glucose pulse as indicated by an arrow. All experiments were performed at room temperature $(25°\mathrm{C})$ . Typically, 20 to 30 cells were imaged per experiment, and the displayed results are representative of $n=4$ experiments in the case of pH kinetics and $n=6$ experiments in the case of scaling measurements. A typical data acquisition time was $\sim 3\min$ per line scan per imaging chamber ( $n=4$ cells; scaling measurements) and $\sim 20\min$ per imaging chamber ( $n=6$ cells; pH kinetics).

We next addressed the issue of regulatory dynamics of intracellular glucose metabolic machinery. We recently reported long-range time correlations in fluorescence fluctuations characteristic of subcellular regulatory dynamics.⁶ By analyzing scaling parameters in time-series data from intact living cells, we observed that mitochondrial redox fluctuations and free radical signal fluctuations displayed nonrandom correlations.^{6, 7} Figures 1a and 1b demonstrate the schematic of the scaling analysis procedure in intact living cells, and the figure caption describes the premise of the scaling analysis procedure. Earlier studies, including our recent reports, have pointed out that regulatory correlations may decrease during aging and in diseases.^{14, 15}

With this rationale, we wanted to test whether scaling analysis of Cerulean fluorescence fluctuations can yield additional information on the regulatory nature of glucose metabolism in normal and cancer cells. We acquired an extensive set of time-series data from living cells (normal and cancer) where we monitored Cerulean fluorescence fluctuations before and during glucose stimulus. Figure 1c shows representative scaling functions $F\left(n\right)=n^{\alpha }$ calculated from the Cerulean time series in NMuMG and NMuMG-ST cells. The insets show a magnified view of the fitted regions where the scaling exponent $\alpha$ was determined. Since cancer cells are expected to show more sensitive dependence on glycolysis than the normal cells, we also obtained scaling exponents under the conditions of glycolytic inhibition (2-deoxyglucose). As can be seen from these figures, the normal cells are more robust in maintaining regulatory time correlations than cancer cells. In the latter, glycolytic inhibition almost completely suppresses the nonrandom scaling behavior, thereby reducing the scaling exponent $\alpha$ from 0.63 to 0.54.

It is worth mentioning here that this difference is highly significant since the exponent appears as the power of window size as in the scaling relationship: $F\left(n\right)=n^{\alpha }$ . Fluorescence intensity measurements of Cerulean, although are not indicative of pH status in living cells, can provide useful kinetic information. Figure 4a shows kinetic profiles of Cerulean fluorescence emission in normal and cancer cells when stimulated by a single glucose pulse. As can be seen from the kinetic profiles, normal and cancer cells differ in their instantaneous fluorescence decay rates. Normal cells have a faster decay rate probably due to an innate adaptive response to glycolytic inhibition. However, the cancer cells show a dramatic difference in glucose metabolism rate after glycolytic inhibition, indicating that glycolytic dependence is still preserved in these cells. Figure 4b shows a time course of scaling exponent $\alpha$ during glucose metabolism in normal and cancer cells. Prior to glycolytic inhibition, it can be seen that both normal and cancer cells displayed nonrandom $(\alpha >0.5)$ correlations in Cerulean fluorescence fluctuations, indicating that-there is a regulatory network operative in these epithelial cells. Since the primary goal of this paper is to test whether single cells exhibit regulatory network correlations rather than identifying the individual members of the network, we would like to treat the observed scaling response in normal and cancer cells as a global response of the entire glucose processing machinery. With this in mind, it is intriguing to note that cancer cells have a significantly higher value of scaling exponent during glucose metabolism. This will be further discussed in the next section. In line with the kinetic profiles, we carried out scaling analysis in normal and cancer cells under glycolytic inhibition conditions as well. Figure 4b shows that normal cells indeed maintain the regulatory correlations even after preconditioning with glycolytic inhibitor, whereas the cancer cells show a significant reduction in scaling exponent upon 2dG treatment. In fact, the kinetic profile of scaling exponent after 2dG treatment looks similar to that when the cells were stimulated with Hanks’ balanced salt solution (HBSS) buffer as a negative control.

Fig. 4

Glucose-induced modifications in scaling exponent. (a) Two-photon fluorescence intensity kinetic profiles in normal and cancer cells with and without glycolytic inhibitor, 2-deoxyglucose (2dG). A single glucose pulse $\left(20\mathrm{mM}\right)$ transiently increases Cerulean intensity, probably due to the cytosolic pH buffering, and the decay curves display dramatic difference between normal and cancer cells. In line with these intensity kinetics, the kinetic profiles of scaling exponents (b) reveal that normal cells are robust under glycolytic inhibition treatment (control: $\alpha =0.55$ ; 2dG: $\alpha =0.55$ ), whereas cancer cells completely lose regulatory correlations (control: $\alpha =0.63$ ; 2dG: $\alpha =0.53$ ), indicating that cancer cells acutely depend on glycolysis more than the normal cells.

4.

Discussion

In this paper, we have carefully exploited the fluctuation regime dynamics of fluorescent protein Cerulean and explored a novel possibility for applying the scaling analysis as a tool in understanding the regulatory nature of glucose metabolism in living cells. Cerulean is a recent addition to the gamut of fluorescent protein variants. For the first time, we have systematically explored the pH dependence of this protein in living cells. Cerulean lifetime displayed a robust pH-sensitive response of $\mathrm{\Delta }\tau =\pm 13\%$ above and below neutral pH. Metabolic perturbations such as staurosporine (protein kinase inhibitor and apoptosis inducer) and mitochondrial complex inhibitors (that will alter glycolytic rates) consistently showed cytosolic acidification [Fig. 2c]. Cancer cells displayed significantly higher acidification owing to the fact that they usually display more glycolytic dependence. Our data are in agreement with earlier reports where these treatments are known to acidify cytosol and/or mitochondria.³ Further, glucose stimulus transiently increased the fluorescence emission of Cerulean (time scale $\sim 60\mathrm{s}$ ), possibly due to the transient buffering capacity of acidified cytosol. Kinetic measurements of fluorescence lifetime revealed an interesting discrimination between normal and cancer cells (Fig. 3). While normal cells have a tight oscillatory lifetime curve after the glucose stimulus indicative of pH homeostasis, the cancer cells are less efficient in restoring pH balance after glucose stimulus, as displayed by large reductions in Cerulean lifetime. Earlier reports have pointed out that cancer cells have increased expression of glucose transporter proteins (GLUTs). Since we did not measure the levels of GLUTs in normal and cancer cells, we cannot rule out the possibility that the difference in acidification can arise due to the difference in GLUT activity in cancer cells.

Thus, in step with the literature, it is possible that NMuMG-ST cells have an upregulated glycolytic pathway, thereby making these cells distinct from the normal cell phenotype. This assumption was further confirmed by the scaling analysis of fluorescence fluctuations in these cells, which revealed interesting features. First, the effect of glycolytic inhibition is less severe on normal cells, probably due to the fact that both mitochondrial and glycolytic machinery operate in concert in these cells. On the other hand, glycolytic up-regulation in cancer cells seems to be not merely a sufficient condition for increased energy consumption but a necessary condition for cell proliferation and survival as displayed by the acute dependence on glycolysis. Second, scaling exponents offer a more reproducible way of distinguishing normal and cancer cells rather than fluorescence intensity alone since the latter can be affected by concentration and spectral artifacts. We have observed that scaling exponents are not affected by differences in absolute fluorescence intensity but are dependent only on the fluctuation dynamics (data not shown). This implies that scaling analysis might be a rapid diagnostic measure of altered glucose metabolism in in vivo tumors. It is to be noted that all our experiments were performed at $25°\mathrm{C}$ . Although the temperature per se does not affect the glucose metabolism kinetics (the intensity kinetic profiles as shown in Fig. 1a were identical at $25°$ and $37°\mathrm{C}$ ) in our in vitro experiments, we cannot completely discard the possibility that these in vitro results may not be identical to real physiological metabolic status in vivo. Since we have not undertaken any in vivo experiments, it is difficult for us to predict the extent of differences. However, we can certainly speculate that if there are differences between our in vitro and future in vivo experiments, they may arise from other sources of physiological complexity in the animal models rather than just temperature dependence of pH and/or the scaling exponents.

There are two aspects to the observed scaling behavior that need attention: first, the photophysical nature of fluorescent protein (Cerulean) fluctuations, and second, the biological mechanism that gives rise to scaling phenomenon during glucose metabolism in living cells. Fluorescence correlation spectroscopic studies have revealed that the initial excited state process in green fluorescent protein (GFP) involves a proton transfer reaction and that fluorescence blinking of anionic GFP mutants is known to take place on a time scale of 45 to $300\mathrm{ms}$ , depending on pH.¹⁶ A more recent time-resolved fluorescence/anisotropy study reported the structural basis of fluorescence fluctuation dynamics of GFPs in acidic environments.⁸ These authors provided experimental evidence that the total fluorescence of the excited neutral state of GFP displayed a strong correlation between the fluorescence lifetime, structural conformation, and pH. Biexponential anisotropy decay analysis further suggested a segmental mobility of the chromophore associated with conformational changes of the protein, and this segmental motion became faster with an enhanced amplitude as the pH is reduced.

Thus, fluorescence fluctuations of GFP mutants including Cerulean as in this work can be rationalized by a subtle interplay of intracellular, pH dynamics and excited state dynamics of the fluorophore itself. More recent x-ray studies of Cerulean have revealed intriguing features such as shift in absorbance band in acidic pH (7 to 5) without significant modulation of fluorescence emission.¹⁷ It was further suggested that acidification may be accompanied by a slow chromophore ionization from trans to cis form, and we speculate that Cerulean fluorescence fluctuations reported in this paper arise predominantly from excited state dynamics rather than conformational changes since these authors did not find evidence for multiple conformations of the protein.¹⁷ As far as the biological mechanism behind the glucose-induced scaling behavior in normal and cancer cells, the observations are consistent with a tight regulatory network that encompasses glycolytic and mitochondrial OxPhos pathways. In this paper, we have attempted to correlate transient pH changes (as measured through lifetime imaging) and scaling behavior in intensity fluctuations (as measured through fluorescence intensity imaging). Although we have demonstrated a clear correlation between these two independent assays in discriminating normal from cancer cells, it will be certainly intriguing and worthwhile to directly probe scaling behavior in fluorescence lifetime fluctuations. The major impediment lies in the vast difference in data acquisition time in intensity and lifetime imaging approaches. For statistical robustness, it is imperative to sample many pixels (i.e, line scan) and to collect at least 6000 to 8000 time points. This condition implies that a line-scan time series ( $\mathrm{N}\sim 8000$ time points) could be obtained in $\sim 200\mathrm{s}$ in the intensity imaging approach. On the other hand, the current lifetime imaging platform in our laboratory would require typically $40\min$ to obtain a line-scan time series. This prolonged data acquisition would defeat the purpose of monitoring fast, transient phenomena in the biological system under question. Furthermore, it is highly probable that the scaling exponents from such lifetime fluctuation measurements may not reflect the “true” nonlinear dynamical features but only some averaged, macroscopic behavior of the system.

In summary, we have reported a hitherto unknown scaling behavior in normal and cancer cells during glucose metabolism. To the best of our knowledge, this is the first demonstration of nonlinear dynamics in the glucose metabolizing network in living cells. Understanding tumor metabolism is the first step in designing efficient therapeutic intervention. Since tumors have higher probability for glycolytic up-regulation, targeting this evolutionarily conserved pathway can be a realistic approach for early detection of tumors in vivo as well as for targeting drugs for therapy. Since clinical modalities such as positron emission tomography (PET) already utilize preferential glucose uptake by tumors as a means to achieve imaging contrast, the scaling analysis reported in this paper might serve as a complementary tool in augmenting diagnostic information in vivo. Although we have no sufficient data to prove that scaling analysis is effective in vivo, we speculate that the present study is the first step in achieving that goal.