Surprisal analysis characterizes the free energy time course of cancer cells undergoing epithelial-to-mesenchymal transition

Significance

Epithelial-to-mesenchymal transition (EMT) has been investigated extensively in cancer progression. Tumor cells induced to undergo an EMT acquire mesenchymal, invasive properties. We apply methods developed in chemical reaction dynamics to characterize the changing transcriptional profile during an EMT and trace the temporal unfolding of the transition on a free energy landscape. The analysis identifies three EMT stages, including passage through an intermediate, low-energy maturation state. The uphill energy requirements during the ascent past maturation correlate with an increase in ATP production. A stable cell machinery whose performance remains unperturbed underlies the EMT.

Abstract

The epithelial-to-mesenchymal transition (EMT) initiates the invasive and metastatic behavior of many epithelial cancers. Mechanisms underlying EMT are not fully known. Surprisal analysis of mRNA time course data from lung and pancreatic cancer cells stimulated to undergo TGF-β1–induced EMT identifies two phenotypes. Examination of the time course for these phenotypes reveals that EMT reprogramming is a multistep process characterized by initiation, maturation, and stabilization stages that correlate with changes in cell metabolism. Surprisal analysis characterizes the free energy time course of the expression levels throughout the transition in terms of two state variables. The landscape of the free energy changes during the EMT for the lung cancer cells shows a stable intermediate state. Existing data suggest this is the previously proposed maturation stage. Using a single-cell ATP assay, we demonstrate that the TGF-β1–induced EMT for lung cancer cells, particularly during the maturation stage, coincides with a metabolic shift resulting in increased cytosolic ATP levels. Surprisal analysis also characterizes the absolute expression levels of the mRNAs and thereby examines the homeostasis of the transcription system during EMT.

The epithelial-to-mesenchymal transition (EMT) is a cellular transition critical for several normal biological events, including embryonic development and wound healing. EMT has been investigated most exhaustively in cancer progression. An evoked EMT in epithelial cancer cells induces gene expression changes that result in loss of adhesive properties and acquisition of mesenchymal cell traits associated with tumor progression and metastasis, e.g., increased cellular motility, migration, and invasion (1, 2).

Cultured epithelial tumor cells may be induced by several alternative stimuli to undergo an EMT, leading to acquisition of mesenchymal properties (3). Transforming growth factors (TGFs) are the most widely used EMT inducers. Microarray expression profiling enables identification of TGF-β1 EMT-induced molecular alterations and mechanisms (4).

Gene expression transcriptional profiling is a major tool in analyzing induced changes in cells, yet interpretation of microarray experiments is faced with challenges (5–7). Here we use an alternative approach, surprisal analysis (8), to better understand, characterize, and represent gene expression differences critical to the EMT (4, 9).

Surprisal analysis assumes that if a system can decrease its free energy, it will do so spontaneously unless constrained. If a system does not attain its minimal free energy state, surprisal analysis seeks to recognize the constraints that prevent a reduction in energy; surprisal analysis identifies the main constraints on a system that has the thermodynamic potential to change spontaneously but is restrained from doing so (10).

As in physics and chemistry (11, 12), surprisal analysis in biology (13–16) argues that the “stable state” of the system, the state of minimal free energy, must first be specified. Only then can we consider constraints responsible for deviations from this state. In principle, one should identify the stable state from first biophysical principles. However, for systems of such molecular complexity, we must apply computational abilities beyond what is currently available. We therefore identify the stable state by using available experimental data. We then have a baseline for our second task, examining deviations from the stable state.

We use the term “state” in the chemistry and physics sense, meaning everything we need to specify to predict how the system will change in response to a small modulation of its circumstances. By “state” here, we mean “thermodynamic state.” A 0.1-M, 100-mL aqueous saline solution at room temperature and pressure at rest is in a thermodynamic state. We can predict its osmotic pressure, but we cannot account for the Brownian motion of individual ions; a mechanical state is needed to specify the position and velocity of all the ions and water molecules. A thermodynamic description is much more parsimonious; many different mechanical states will give rise to essentially the same value for osmotic pressure. Here we describe the change in time of the thermodynamic state (state) of the transcription system during an EMT. We identify variables, analogous to the osmotic pressure, that characterize the transcription system state. The change in value of these variables describes the transition. By analogy to thermodynamics, we refer to these as the state variables.

We suggest that quantification of transcripts according to their free energy (rather than fold changes) has distinct value. Previously we considered the stability of the minimal free energy state during cellular processes (13). This thermodynamic consideration enables an approach that may be used to make statements about alternative cellular states and predictions about how targeted perturbations to a biological system might influence that system (17, 18).

Constraints for biological processes are not static; they may change in response to cellular and environmental perturbations (19). Stipulating the premise of minimal free energy subject to constraints, a change to the constraints will be followed by a move of the system toward a new constrained state. At any given time, a state of minimal free energy is unique and stable—stable in the technical sense that at that time, all other states that are consistent with the constraints will have a higher free energy. Surprisal analysis ascertains whether, at a given time, a state can be described as one of minimal free energy subject to constraint. If the description is appropriate, the state at that time is thermodynamically stable. We also want to characterize a state(s) that is kinetically stable. This presents a stronger requirement; states at nearby time points must have a higher free energy. For example, we show below that the (starting) epithelial state is stable both thermodynamically and kinetically.

When transcription system constraints change, the system may move to a new constrained state, one with a different free energy value. If the free energy increases, the constraints must do work on the transcription system; the process will not follow unless work is done to induce the change. With a constraint change, free energy also may decrease. The practical difference is that when free energy declines, the state change may occur spontaneously and the state is not kinetically stable.

At the molecular level, state changes are reflected in differential transcript abundance. Surprisal analysis characterizes biological transitions by considering independent phenotypes; each phenotype is a set of characteristic genes as well as a separate and independent constraint on the state. Each phenotype is a constraint that prevents the system from spontaneously decreasing in free energy.

The state change with time is described by the weight of the different phenotypes, where each weight changes with time in its own way. These time-dependent weights characterize the state; they are the state variables. Surprisal analysis of transcriptome data determines the time dependence of the state variables (20). Generally few in number, these variables identify the state at any time.

To provide a molecular-level interpretation, surprisal analysis shows how individual transcript levels are related to phenotypes: each phenotype is a set of transcripts. For any given phenotype, each transcript has a weight. This weight is time independent. Transcripts that constitute a phenotype all change with time in the same way; this common change is described by the state variable for that phenotype. The change in time for the expression levels of individual transcripts is represented as the sum over the contributions from the changes of the different phenotypes.

Results and Discussion

Surprisal analysis was applied as described previously (13–15, 21). The input expression level of mRNA i at time t, $X_i\left(t\right)$, is expressed as a sum of terms; here two, representing deviations from the balance state. Each deviation term (i.e., phenotype) is a product of a time-dependent weight of the phenotype; the state variable and the time-independent contribution of the transcript to that phenotype:

$$\underset{\begin{array}{c}\text{measured\hspace{0.17em}}\\ \text{expression\hspace{0.17em}level\hspace{0.17em}}\\ \text{of\hspace{0.17em}transcript\hspace{0.17em}}i\hspace{0.5em}\\ \text{at\hspace{0.17em}time\hspace{0.17em}}t\end{array}}{\underbrace{\mathrm{l}\mathrm{n}{X}_i\left(t\right)}}\hspace{0.5em}\hspace{1em}=\underset{\begin{array}{c}\hspace{0.17em}\text{balanced}\hspace{0.17em}\text{state}\\ \text{expression\hspace{0.17em}level\hspace{0.17em}}\\ \text{of\hspace{0.17em}transcript\hspace{0.17em}}i\end{array}}{\underbrace{\mathrm{l}\mathrm{n}{X}_i^o}}\hspace{0.17em}\hspace{0.5em}-\hspace{0.5em}\hspace{0.5em}\hspace{1em}\underset{\begin{array}{c}\text{the\hspace{0.17em}two\hspace{0.17em}deviation\hspace{0.17em}terms\hspace{0.17em}from\hspace{0.17em}the\hspace{0.17em}balanced\hspace{0.17em}state}\\ \text{of\hspace{0.17em}transcript\hspace{0.17em}}i\hspace{0.17em}\text{at}\hspace{0.17em}\text{time}\hspace{0.17em}t\end{array}}{\underbrace{\stackrel{\begin{array}{c}\text{state\hspace{0.17em}variable}\\ \text{of\hspace{0.17em}phenotype\hspace{0.17em}}1\\ \text{at\hspace{0.17em}time\hspace{0.17em}}t\end{array}}{\overbrace{{\lambda }_1\left(t\right)}}\stackrel{\begin{array}{c}\text{the\hspace{0.17em}contribution\hspace{0.17em}}\\ \text{of\hspace{0.17em}transcript\hspace{0.17em}}i\\ \text{to\hspace{0.17em}phenotype\hspace{0.17em}}1\end{array}}{\overbrace{G_{i1}}}\hspace{0.5em}+\stackrel{\begin{array}{c}\text{state\hspace{0.17em}variable}\\ \text{of\hspace{0.17em}phenotype\hspace{0.17em}}2\\ \text{at\hspace{0.17em}time\hspace{0.17em}}t\end{array}}{\overbrace{{\lambda }_2\left(t\right)}}\stackrel{\begin{array}{c}\text{the\hspace{0.17em}contribution\hspace{0.17em}}\\ \text{of\hspace{0.17em}transcript\hspace{0.17em}}i\\ \text{to\hspace{0.17em}phenotype\hspace{0.17em}}2\end{array}}{\overbrace{G_{i2}}}}}.$$

$X_i^o$ is the expression level of transcript i in the balance state. ${\lambda }_{\alpha }\left(t\right)$ is the state variable for phenotype $\alpha$ at time t. mRNA expression level during EMT is well described by the two state variables, α = 1,2. α = 1 is the leading term of the deviation. $G_{i\alpha }$ is the time-independent contribution of gene i to the phenotype $\alpha$ remaining the same throughout the transition.

An implication of the analysis is a correlation between the transcript’s thermodynamic stability and its expression level. This correlation is most reliable when deviations from the balanced state are not large. Then, $X_i\left(t\right)\approx X_i^o$. $X_i^o$ is the expression level at thermodynamic equilibrium—the balance state of minimal free energy. Therefore, the more stable the gene (i.e., the lower its free energy) the higher its expression level in the balance state. The surprisal itself at each point in time is defined as the (logarithmic) deviation from the balance state.

The Balance State During EMT for TGF-β1–Treated A549 Human Lung Cancer Cells.

Surprisal analysis was applied to the gene microarray expression profiles collected, in triplicates, at time points 0, 0.5, 1, 2, 4, 8, 16, 24, and 72 h during an EMT-initiated TGF-β1 stimulation of A549 cells (22). The first step in EMT surprisal analysis is to identify a balance state common to epithelial and mesenchymal states and throughout the transition. This balance state is the reference point at which all cellular processes are assumed balanced in forward and reverse directions and for which there is no net change in the surprisal system. It therefore is of central concern to demonstrate by analysis of expression data that the balance state is invariant throughout the transition.

The results for the A549 cell balance state at different times after TGF-β1 treatment are shown in Fig. 1. The expression level of transcript i in the balance state at time t after treatment is $X_i^o\left(t\right)=\mathrm{e}\mathrm{x}\mathrm{p}(-{\lambda }_0(t)\hspace{0.17em}{G}_{i0})$. We expect that the level in the balanced state will not depend on the time point, but this is not assumed in our procedure; analyses at different points in time validate this point of principle. ${\lambda }_0\left(t\right)G_{i0}$ is the free energy (in thermal energy units, RT) of transcript i. Consequently, transcripts with the lowest (i.e., most negative) free energy are those with the highest levels in the balance state. mRNAs identified with the lowest free energy, listed in Table S1, are those most correlated with cellular networks that regulate and maintain cellular homeostasis machinery. Our analysis illustrates the robustness of cellular homeostasis during EMT (13, 16).

Fig. 1.

Stability of the balanced state of the mRNA expression in A549 cells during TGF-β1–induced EMT. (A) The heat map shows as the ordinate the logarithm of expression levels for the 20 most highly expressed transcripts of the EMT balance state. Each column is a transcript free energy at that time. (B) ${\lambda }_0\left(t\right)\hspace{0.17em}$vs. time, where $-\mathrm{l}\mathrm{n}{X}_i^o\left(t\right)={\lambda }_0\left(t\right)\hspace{0.17em}{G}_{i0}$. Fig. 1B is to be compared with Figs. 2B and 3B, which show variations of ${\lambda }_1\left(t\right)\hspace{0.17em}$and ${\lambda }_2\left(t\right)\hspace{0.17em}$with time. (C) Free energy of all of the transcripts in the balance state. The ordinate is the change in the free energy of that transcript during the EMT. (D) Stability of all transcripts of the balance state, and the free energy changes of all transcripts during EMT. All transcripts in the balance state are shown in red; free energy changes resulting from the EMT are shown in blue. The ordinate is the number of transcripts per bin. The width of the energy bins is 10 units of thermal energy, RT.

A graphical representation of free energy time variations for the most stable genes is shown in Fig. 1A. The heat map shows (negative) free energy for the 20 transcripts that have the highest weight in the balance state vs. time. The most stable transcripts are at the top, and they hardly vary with time. Fig. 1B shows the state variable of the stable state, ${\lambda }_0\left(t\right)\hspace{0.17em}$, vs. time. ${\lambda }_0\left(t\right)\hspace{0.17em}$variation with time is less than 0.1%, less than the SD of the state variable. Fig. 1B establishes the balance state time invariance during the EMT.

Of course, biochemical changes during an EMT may change the transcript free energies. To fully validate balance state stability, we therefore must show that EMT-induced changes are small compared with the transcript free energies of the stable state. Fig. 1C shows the individual transcript free energies (in thermal energy units) in the balance state (abscissa) vs. the change in the free energy of that transcript (ordinate) during the EMT. No transcript increases or decreases its free energy by more than 10 units; all balance-state transcripts are stable by more than −20 units. Consequently, for no transcript does its free energy become positive (i.e., fully destabilized) during the EMT. This conclusion is central; we show it in a different graphical representation in Fig. 1D, a free energy histogram. Transcript free energy distributions in the stable state are in red. Blue bins show transcript free energy changes due to the EMT. The red bars reiterate the point that there are no transcripts in the balance state whose free energy change becomes positive. About as many genes are stabilized (have a decrease in their free energy) further during EMT as are destabilized, illustrated by the two red bars of roughly the same height.

EMT-Specific Differential Gene Expression in A549 Cells During the EMT.

Each constraint identifies a transcript expression pattern unique to net ongoing biological processes in the system: a phenotype. The phenotypes are ranked such that the largest deviation from the balance state is $\alpha =1$. This phenotype has the largest value for its state variable, ${\lambda }_1\left(t\right)$; it is most responsible for the changes in free energy during the process.

Free energy changes during the EMT for genes whose free energies undergo the greatest deviation (both up and down) from their balance state values are shown in Fig. 2A. Genes that dominate this phenotype for the 549-cell EMT are listed in Table S2 in order of their contribution to free energy change. Some are highly up-regulated, and some are very down-regulated. These genes and their weights are time independent but are associated with the first time-dependent state variable, ${\lambda }_1\left(t\right)$ (Fig. 2B); all these genes vary with time in the same way. Genes up-regulated during the first few hours following TGF-β1 treatment in A549 cells are down-regulated during the subsequent time, ending in the mesenchymal state at ∼24 h. These data demonstrate that the first constraint provides a signature that distinguishes the two EMT end states; the phenotype that corresponds to this largest deviation distinguishes the epithelial and mesenchymal cellular states. Because of this first constraint, the mesenchymal free energy state is higher than for the epithelial state. Note that most transcripts have a negligible contribution to this phenotype (Fig. S1).

Fig. 2.

The EMT-specific gene signature distinguishes epithelial and mesenchymal states in A549 cells. (A) Logarithm of expression levels for the 20 uppermost and 20 most down-regulated transcripts of the first phenotype, $\alpha =1$. (B) The first state variable, ${\lambda }_1\left(t\right)$, during the EMT. The ${\lambda }_1\left(t\right)$ sign change identifies the time (∼8 h) when the transition from the epithelial to the mesenchymal state occurs. This sign change is correlated with the minimum in free energy in A.

On Transcript Regulation.

The state variables determine the direction of deviation of the process from the balance state. When the state variables change sign, transcripts that were overexpressed with reference to the balance state become underexpressed, and vice versa. To avoid unambiguity, we rank the transcripts according to their time-independent weights, the $G_{i\alpha }\text{s}$ (see phenotypes $\alpha =0,1,2$ in SI Appendix).

From a biological perspective, surprisal analysis weighs the impact of individual genes differently from the ranking of genes by fold change in expression. For example, the down-regulated anterior gradient-2 (AGR2) gene, a transcript that decreases in abundance, tops the EMT-specific surprisal A549-cell gene signature list (Table S2), whereas in fold-change microarray analysis, AGR2 levels do not vary significantly. However, AGR2 has the greatest free energy contribution to the first deviation from the balance state. Note also that AGR2 has been implicated as a major player in other studies when observed in proteomic data (23). Near the bottom of the list of phenotype 1 is an up-regulated gene by fold-increase analysis, serine protease inhibitor 2/protease-nexin 1 (SERPINE2) (Table S2, opposite column). AGR2 and the plasminogen activator SERPINE1 illustrate the resolving power of surprisal analysis compared with purely statistical methods. SERPINE2 is known to greatly enhance the local invasiveness of pancreatic tumors, accompanied by a massive increase in ECM production in the invasive tumors (24).

The list of genes shown in Table S2 is representative of phenotype 1, the phenotype that distinguishes the epithelial and mesenchymal states. The state variable sign change of this phenotype can be seen in Fig. 2B.

TGF-β1–Stimulated A549-Cell EMT Proceeds Through a Maturation Stage.

Surprisal analysis of TGF-β1 EMT-induced changes in A549 mRNA levels shows a second leading deviation from the balance state (Fig. 3A). The time dependence of the second state variable, ${\lambda }_2\left(t\right)$, exhibits a change in sign (Fig. 3B) that coincides with the epithelial state transitioning (at about 2 h) to what we call, following ref. 9, a “maturation state.” This state is a state of low free energy. The maturation state is followed by a second change (at about 24 h) out of the maturation stage and into the mesenchymal state (Fig. 3B and Fig. S2). Transition from the maturation stage is costly in free energy and might possibly offer a target for inhibiting the EMT.

Fig. 3.

Surprisal analysis reveals an intermediate maturation stage during TGF-β1–induced EMT in A549 cells. (A) Free energy for the 20 uppermost and 20 most down-regulated transcripts of the second phenotype, $\alpha =2$. Between ∼2 and 24 h, the free energy switches signs. We identify this interval with a maturation stage (16). (B) During this maturation stage, the second state variable, ${\lambda }_2\left(t\right)$, has a sign that differs from that before or after entering the maturation stage; the first sign change coincides with the epithelial state entering the maturation stage, the second sign change coincides with the exit from the maturation stage into the mesenchymal state.

This second phenotype identified by surprisal analysis reveals that EMT cellular reprogramming is a multistep process that includes an intermediate low free energy state. The free energy changes reflected in the sign changes for the state variable suggest that this multistep process is correlated with changes in cell metabolism as the external source of energy. The corresponding gene signature (Table S3) for this second phenotype indeed includes an increased contribution of metabolic genes.

The EMT Free Energy Landscape.

At any time t during an EMT, the work done to bring the system to its current state can be computed from the surprisal analysis (10, 19). Two important constraints for the A549 TGF-β1–induced EMT have been identified; therefore, there are two variables in a plot of the free energy change during the EMT. We chose as the two variables the state variables ${\lambda }_1\left(t\right)$ and ${\lambda }_2\left(t\right)$ (Fig. 4). After exiting the epithelial state, the system dissipates energy as it moves to a lower minimal energy, the maturation state. However, work must be done to drive the system from the maturation state into the mesenchymal state.

Fig. 4.

The free energy landscape for the TGF-β1–induced EMT in A549 cells. At every point in time, the energetic state of the cell undergoing the EMT may be characterized by two time-dependent state variables, ${\lambda }_1\left(t\right)\hspace{0.5em}$and ${\lambda }_2\left(t\right)$. The path of the transition is along the orange arrows and proceeds through a stable intermediate, the maturation point. Energy is released in transition from the epithelial state to the maturation point and consumed from the maturation point to the higher-in-energy mesenchymal state.

Surprisal analysis shows that this EMT proceeds through a low-energy, intermediate maturation state. It is not the case that a trough invariably must be traversed between two states; a path also might exist in which energy is first required and subsequently released. Careful examination of Fig. 4 shows that here, too, there are barriers to cross. Transition from the epithelial state is over a small barrier, showing that the epithelial state is stable not only at a given time but also for small changes in time. Similarly, the transition into the mesenchymal state also crosses a small barrier. In summary, the EMT involves three states—the epithelial, maturation, and mesenchymal states—that not only are thermodynamically stable but also are kinetically stable, that is, stable against small changes in time. As in traditional chemical kinetics, there is a barrier between any two connected, kinetically stable states.

Error Analysis: Additional Constraints.

The TGF-β1–induced EMT A549 microarray study (www.ncbi.nlm.nih.gov/sites/GDSbrowser?acc=GDS3710) was conducted in triplicate, permitting evaluation of error bars on the state variables (21). The balance state is robust; error bars are negligible (Fig. 1B). Error bars on the potential ${\lambda }_1\left(t\right)$ of the first constraint also are small (Fig. 2B). Error bars on the potential ${\lambda }_2\left(t\right)$ of the second constraint are more significant (Fig. 3B). Surprisal analysis for this experiment determines a third constraint and a corresponding state variable ${\lambda }_3\left(t\right)$ (Fig. S3). However, error bars for $\delta \hspace{0.17em}{\lambda }_3\left(t\right)$ are large; the error bars are comparable to the value of the variable itself, i.e., $\delta \hspace{0.17em}{\lambda }_3\left(t\right)\approx {\lambda }_3\left(t\right)$ at all time points. Consequently, the value zero is within the range of possibility for ${\lambda }_3\left(t\right)$. The state variable measures the importance of the constraint as judged by the search for a minimal free energy state. When $\delta \hspace{0.17em}{\lambda }_3\left(t\right)\approx {\lambda }_3\left(t\right)$, we arrive at the same state, regardless of whether the third constraint is included in the search for this minimum. In such cases, the imposition of a third (or any higher) constraint is not supported.

EMT Time Scales.

The time course of the TGF-β1–elicited A549-cell EMT is shown through the time dependence of the state variables ${\lambda }_1\left(t\right)$ and ${\lambda }_2\left(t\right)$ (Figs. 2B and 3B). The TGF-β1–induced progression from the epithelial to the mesenchymal state lasts ∼24 h. At ∼8 h, the switch from the epithelial to the mesenchymal state occurs [shown by the sign change for ${\lambda }_1\left(t\right)$, Fig. 2B and Fig. S1]. Somewhat earlier, at ∼4 h, the maturation phase begins [as shown in the first sign change for ${\lambda }_2\left(t\right)$ (Fig. 3B)]. The energy release along the transition to maturation occurs rapidly and quite early; in contrast, the energy buildup from the maturation point to the mesenchymal end state is far slower [${\lambda }_2\left(t\right)$, Fig. 3B], extending beyond the 24-h time point. The energy buildup is complete by 72 h; without mRNA expression level data between 24–72 h, it is not possible to conclude when the transition to the mesenchymal state is finished.

An Increase in Cytosolic ATP Levels Correlates with the Maturation Stage of the TGF-β1–Induced A549-Cell EMT.

TGF-β1 A549 treatment induces mesenchymal-like protrusions and filopodia at 4 and 8 h (Fig. 5A). The TGF-β1 maturation stage of this EMT begins when the second state variable, ${\lambda }_2\left(t\right)$, is positive (Fig. 3B). A single-cell enhanced-acceptor fluorescence (EAF)-based ATP biosensor (25, 26) demonstrates that individual cell ATP levels in the mesenchymal state appear higher than in cells in the epithelial state (Fig. 5B), consistent with the idea that the energy required to bring the cells from the maturation point to the mesenchymal state is greater than that for the epithelial state (Fig. 3B and Fig. S1).

Fig. 5.

Cytosolic ATP levels during the EMT. (A) EMT is induced in A549 cells with TGF-β1. At the times indicated, cells were collected for analysis. (B) At the times shown, the cells were imaged by phase contrast microscopy (20×). Cellular fasciculation is present within 4 h; an increase in filopodia migratory protrusions occurs in 8 h. (C) EAF-based single-cell ATP biosensor analysis of A549 cells following TGF-β1 treatment. (Upper) Donor fluorescence was monitored (GFP, pseudocolored red for better contrast). (Lower) Fluorescence images are overlaid on bright-field images. n = 4 across three independent cultures. (D) Quantification of EAF-based ATP biosensor donor signal. GFP fluorescence was monitored in individual cells at the times shown (n = 5, three cells per field); data are means ± SEM of five independent experiments. *P < 0.05, **P < 0.01, using Student t test. (E) Whole-cell ATP levels were monitored with a modified luciferin/luciferase-based ATP assay at the time points shown (n = 5, three cells per field); data are means ± SEM of five independent experiments. *P < 0.05, **P < 0.01, using Student t test.

The data (Figs. 2–4 and Fig. S1) suggest that the minimum free energy change in the TGF-β1–driven EMT, the maturation point, occurs ∼8 h after TGF-β1 application, and that work input is required to drive an energetically dependent transition from the maturation point to the mesenchymal state. By using both single-cell (Fig. 5C) and bulk-cell ATP measurements (Fig. 5D), increased cytosolic ATP levels are observed at 8 h. Transition from the maturation state to the mesenchymal state occurs at ∼20 h (Fig. 3B); elevated ATP levels are observed at 20 h (Fig. 5 C and D), when cells have left the maturation state and entered the mesenchymal state. The data suggest that ATP levels reflect, and possibly may drive, the maturation process.

The Balance State During EMT for TGF-β1–Treated Pancreatic Cancer Cells.

Surprisal analysis also was applied to microarray data for cultured Panc-1 epithelial cells 48 h after TGF-β1 treatment, when the cells attained a mesenchymal state (27). The balance state of Panc-1 cells, like that of A549 cells, was unaffected by TGF-β1 treatment (Fig. S2A). Like A549 cells, ribosomal genes and structural proteins for Panc-1 cells have the greatest negative free energy (Table S1). When free energy changes for the most up- and down-regulated genes in the epithelial and mesenchymal states, relative to the balance state, are evaluated, a definitive “switch” is observed (Fig. S4B).

Gene Ontogeny Analysis of the Two Major Phenotypes for A549 Cells During the EMT.

In SI Appendix, we outline and apply a synergistic procedure for analysis of microarray data. Gene ontogeny (GO) analysis (28) is applied separately to each of the phenotypes that surprisal analysis identifies as relevant for the transition and to the gene list of the balance state (Figs. S5–S7). GO analysis of the second constraint suggests that the critical cellular functions that dominate this phenotypic state are functions involved in receptor binding mechanisms (Fig. S7). We suggest that this phenotype integrates information from the cell environment, through receptors and subsequent ligand-dependent signaling pathways, into its cellular decision-making processes. It is expected that during an EMT, the ability of cells to assimilate environmental cues is critical as they take on a mesenchymal-like state and acquire migratory properties (29, 30).

In conclusion, we applied surprisal analysis to characterize and elucidate gene expression behavior responsible for an EMT. We identified an intermediate state in the process and observed a correlation of metabolic shifts with progress through the EMT. Surprisal analysis can monitor cell phenotype-specific thermodynamic behavior, trace the change of state with time on a free energy landscape, and provide an increased understanding of cell transitions and cellular state-dependent processes. Surprisal analysis also begins to provide fundamental insights into the mechanisms that regulate the unbalanced processes—by identification of “process-specifying” genes. Surprisal analysis thus suggests that the state variables are potential drug targets.

Experimental Procedures

EMT in Lung Adenocarcinoma Cells.

Expression profiles are available publically at www.ncbi.nlm.nih.gov/sites/GDSbrowser?acc=GDS3710 and ref. 22. Human A549 lung adenocarcinoma cells were treated with 5 ng/mL TGF-β for 0, 0.5, 1, 2, 4, 8, 16, 24, and 72 h to induce EMT. The experiment was performed in triplicate. Samples were assayed using Affymetrix HG_U133_plus_2 arrays with 54,675 probe sets, following standard techniques.

EMT in Pancreatic Adenocarcinoma Cells.

Expression profiles are publically available at www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE23952 by Zadran et al. (26), who treated human Panc-1 pancreatic adenocarcinoma cells with 5 ng/mL TGF-β for 0 and 48 h to induce EMT. The experiment was performed in triplicate. Samples were assayed using Affymetrix HG_U133_plus_2 arrays.

ATP Imaging and Measurement.

A549 cells, from D. Shackelford, UCLA, Los Angeles CA, were cultured and maintained as adherent monolayers in DMEM (Cellgro) supplemented with 5% (vol/vol) FBS (Omega Scientific) and 100 U/mL penicillin and streptomycin (Gibco) in 5% (vol/vol) CO₂ at 37 °C.

Single-Cell ATP Imaging.

An EAF-based single-cell ATP biosensor was generated as described previously (24, 25). A549 cells were plated on laminin-coated glass-bottom dishes and transfected with FuGENE6 transfection reagent (Roche Diagnostics) and the EAF-based ATP biosensor. Cells were subjected to confocal imaging 2–3 d after transfection. Wide-field observations used a Nikon TE2000-PFS inverted microscope (Nikon Instruments); cells were maintained at 37 °C with a continuous supply of a 95% air and 5% carbon dioxide mixture, by using a stage-top incubator. Untreated A549 cells expressing the EAF-based ATP biosensor initially were monitored via confocal microscopy for donor (GFP) and acceptor (YFP) emission. After TGF-β1 (5 ng/mL) treatment, EAF behavior in single cells was monitored over 72 h. The experiment was repeated in triplicate across three independent cultures. Image analysis used ImageJ.

Luciferase-Based ATP Analysis.

Cellular ATP also was monitored with a modified luciferase/luciferin-based assay (24).

GO Enrichment Analysis.

GO analysis was conducted as described previously (ref. 27 and http://cbl-gorilla.cs.technion.ac.il). Threshold P value was 10⁻¹¹.