High concentration of IGF-I inhibited myogenic differentiation but enhanced proliferationIGF-I is essential for the proliferation and differentiation of L6 myoblasts. Studies have shown that muscle differentiation is inhibited at high IGF-I concentrations15. Thus, we examined proliferation and differentiation abilities in L6 myoblasts at high and low IGF-I concentrations. Confluent L6 myoblasts were differentiated into myotubes by exchanging Dulbecco’s modified Eagle medium (DMEM) supplemented with 10% fetal bovine serum (FBS) for DMEM with 2% FBS (differentiation medium) containing 0 or 100 ng/mL IGF-I. Two days after the induction of differentiation, the expression of the myogenic marker protein, MyHC (Myosin Heavy Chain), was induced in the differentiation medium that did not contain IGF-I. However, when 100 ng/mL IGF-I was added to the differentiation medium, MyHC expression was impaired (Fig. 1A), indicating that a high concentration of IGF-I inhibited myogenic differentiation. Expression levels of the myogenic master transcription factor, myogenin, were also impaired after the addition of 100 ng/mL IGF-I on the second day. Furthermore, the fusion index, which indicates the differentiation level of myoblasts into multinucleate myotube cells, was impaired after adding 100 ng/mL IGF-I (Fig. 1B,C). Next, their proliferative abilities under the same conditions were examined. [3H]-labeled thymidine was added to the medium for 4 h, whereafter the [3H] incorporated into DNA was measured as an indicator of proliferation ability. When L6 myoblasts were cultured in DMEM with 2% FBS containing 0, 1, or 10 ng/mL IGF-I, cell proliferation ability was weak. However, cell proliferation was enhanced when cultured in DMEM with 2% FBS containing 100 ng/mL IGF-I (Fig. 1D). Thus, the myoblast cell fate switched in the presence of different concentrations of IGF-I. To investigate the molecular mechanism by which IGF-I concentration switches the cell fate of L6 myoblasts, we analyzed whether the activation dynamics of IGF-I signaling were affected by differences in the IGF-I concentration.Fig. 1Effects of IGF-I concentration on IGF-I signaling pathway dynamics and bioactivity expression. (A) L6 myoblasts were incubated in a differentiation medium (DMEM with 2% fetal bovine serum (FBS)) supplemented with either 0 or 100 ng/mL insulin-like growth factor-I (IGF-I). Cell lysates were collected at 0, 1, or 2 days post-differentiation induction for immunoblotting analysis using the specified antibody. (B) L6 myoblasts were cultured in a differentiation medium. Cells were fixed with 4% paraformaldehyde at 0 and 4 days post-differentiation induction and subjected to immunostaining analysis using the MyHC antibody. Scale bar = 50 µm. (C) The fusion index was determined (n = 3). Data are presented as mean ± SEM. *P < 0.05, determined by Student’s t-test. (D) L6 myoblasts were cultured in a differentiation medium (DMEM with 2% FBS) supplemented with 0, 1, 10, or 100 ng/mL IGF-I. Forty-four hours later, [methyl-3H] thymidine was added, and after a 4-h incubation, the amount of [3H] incorporated into DNA was measured as an indicator of proliferation ability (n = 6). Data are presented as mean ± SEM. **P < 0.01, analyzed using one-way ANOVA followed by Tukey’s post hoc test.Mathematical model of IGF-I signalingWe constructed a mathematical model of IGF-I signaling. Recently, we reported a novel regulatory mechanism of the IGF-I signaling pathway in L6 myoblasts. Briefly, (1) IRS-1 interferes with IGF-I receptor internalization through competitively inhibiting AP2 function24. (2) IRS-1 protein levels are downregulated by active mTORC1 kinase23. As IGF-I signaling is known to be downregulated by IGF-I receptor internalization, high IRS-1 levels lead to their sustained activation. Thus, in this model, IRS-1 is not a mediator, but rather a regulator that modulates the duration of IGF-I signaling pathway activity (Fig. 2A).Fig. 2Mathematical model of the IGF-I signaling pathway. (A) Schematic illustration of the IGF-I signaling pathway model. Insulin receptor substrate-1 (IRS-1) inhibits AP2 function, thereby suppressing internalization of the active IGF-I receptor from the plasma membrane. Downstream signaling pathway activation induces the degradation of IRS-1. In this model, IRS-1 is not a mediator but rather a regulator of the IGF signaling pathway. (B) A mathematical model based on the IGF-I signaling pathway. (C,D) Simulation results of the IGF-I signaling pathway. C: k1 = 0.006. D: k1 = 0.06. (E) L6 myoblasts were serum-starved for 18 h, followed by stimulation with DMEM + 2% FBS containing 1 or 100 ng/mL IGF-I. Cell lysates were prepared from each sample, and the total cell lysate was used for immunoblotting analysis with anti-IRS-1, anti-pAkt, or anti-Akt antibodies. BSA bovine serum albumin, mTORC1 mechanistic target of rapamycin complex 1, PI3K phosphatidylinositol 3-kinase.We modeled the IGF-I signaling pathways using the form of ordinary differential equations (Fig. 2B):$$\frac{d{\varvec{x}}}{dt} = {\varvec{f}}\left({\varvec{x}}, {\varvec{k}}\right),$$
(1)
where x is a vector of substrates and k is a vector of the parameters. The ordinary differential equations for the three variables in the system are given as follows:$$\frac{d\left[pIGFIR\right]}{dt}={k}_{1}-{k}_{2}\left[pIGFIR\right]\left(1-\left[IRS1\right]\right),$$
(2)
$$\frac{d\left[IRS1\right]}{dt}={k}_{3}-{k}_{4}\left[IRS1\right]\left[pmTORC1\right],$$
(3)
$$\frac{d\left[pmTORC1\right]}{dt} ={k}_{5}\left[pIGFIR\right]-{k}_{6}\left[pmTORC1\right].$$
(4)
As shown below, the IGF-I signaling system has a unique equilibrium with nonnegative values:$$\left(\frac{\alpha \gamma + \beta }{\alpha \beta }, \frac{\alpha \gamma }{\alpha \gamma + \beta },\frac{\alpha \gamma + \beta }{\alpha \beta \gamma }\right),$$
(5)
where$$\alpha = \frac{{k}_{2}}{{k}_{1}}, \beta = \frac{{k}_{4}}{{k}_{3}}, \gamma = \frac{{k}_{6}}{{k}_{5}}.$$
(6)
We performed a linear stability analysis for this equilibrium point. That is, we analytically obtained the Jacobian matrix (J: linearized matrix) at the equilibrium point, and obtained the characteristic polynomial P.$$J = \left[\begin{array}{ccc}-{k}_{2}\left(1-\frac{\alpha \gamma }{\alpha \gamma +\beta }\right)& \frac{{k}_{1}\left(\alpha \gamma + \beta \right)}{\beta }& 0\\ 0& -\frac{{k}_{3}\left(\alpha \gamma + \beta \right)}{\alpha \gamma }& -\frac{{k}_{4}\alpha \gamma }{\alpha \gamma + \beta }\\ {k}_{5}& 0& -{k}_{6}\end{array}\right],$$
(7)
$$P ={\lambda }^{3}+ \left(\frac{{k}_{2}\beta }{\alpha \gamma + \beta }+\frac{{k}_{3}\left(\alpha \gamma + \beta \right)}{\alpha \gamma }+{k}_{6}\right){\lambda }^{2}+ \left(\frac{\alpha \gamma + \beta }{{k}_{2}\beta }+\frac{\alpha \gamma }{{k}_{3}\left(\alpha \gamma + \beta \right)}+\frac{1}{{k}_{6}}\right)\alpha \gamma \lambda +\alpha \gamma +\beta .$$
(8)
The stability of the equilibrium point is determined by the sign of the real part of the eigenvalues \(\lambda\) of the Jacobian matrix. The eigenvalues are given by the roots of the characteristic equation, P = 0. The equation has one negative real root (λ1) and two complex roots (λ2 and λ3). To examine the stability of the point, Hurwitz’s stability discriminant method was applied to P. The first and second Hurwitz determinants are always positive, and the third Hurwitz determinant given as:$${H}_{3}= \alpha \gamma + \beta – \left(\frac{{k}_{2}\beta }{\alpha \gamma + \beta } + \frac{{k}_{3}\left(\alpha \gamma + \beta \right)}{\alpha \gamma } + {k}_{6}\right)\left(\frac{\alpha \gamma + \beta }{{k}_{2}\beta }+\frac{\alpha \gamma }{{k}_{3}\left(\alpha \gamma + \beta \right)}+\frac{1}{{k}_{6}}\right)\alpha \gamma .$$
(9)
When \({H}_{3}\) is positive, all roots of P = 0 have a negative real part, i.e., the equilibrium point is stable. By transforming \({H}_{3}\), we define our criteria of the stability F.$$F := \frac{\alpha \gamma + \beta }{\left(\frac{{k}_{2}\beta }{\alpha \gamma + \beta } + \frac{{k}_{3}\left(\alpha \gamma + \beta \right)}{\alpha \gamma } + {k}_{6}\right)\left(\frac{\alpha \gamma + \beta }{{k}_{2}\beta } + \frac{\alpha \gamma }{{k}_{3}\left(\alpha \gamma + \beta \right) }+ \frac{1}{{k}_{6}}\right)\alpha \gamma }.$$
(10)
Numerical calculations confirmed that at F = 1, signs of the real parts of λ2 and λ3 switch. The equilibrium point is stable if F > 1 but unstable when F ≦1. Therefore, in this system, Hopf bifurcation occurs at F = 1.As F is a function of k, the stability of the equilibrium switches as k varies (Fig. S1A). Each coefficient of this system was optimized by fitting the experimental results of IRS-1 protein levels and Akt activity (related to pmTORC1 activity) at various time points (0 min, 5 min, 30 min, 60 min, 3 h, 6 h, and 12 h) after stimulation with 100 ng/mL IGF-I (Fig. S2A). For fitting, Bayesian optimization was used. From this optimization process, k1–k6 coefficients, could be set, respectively, as shown in Fig. S2B. A comparison of the numerical calculations with optimized coefficient results with the actual values are shown in Fig. S2C. Evaluating the relationship between the k and F values predicted whether IGF-I signaling would oscillate or remain constant (Fig. S3). The values obtained by substituting the optimized coefficients into the F formula are indicated with a white cross symbol in each graph. Furthermore, we showed the change in the F value when coefficients on both axes were altered. In each graph, the F value is shown in the heatmap. A red color indicates that F > 1. For example, when k1 decreases, F decreases. As k1 is a value that depends on the IGF-I concentration, the IGF-I concentration is a bifurcation parameter that determines whether the IGF-I signaling pathway will oscillate or remain constant. This result can be predicted by referring to the following formula for F: the larger the k1 value, the larger the F value. Considering that F < 1 when k1 = 0, a high IGF-I concentration would stabilize the system with a large F value, whereas a low IGF-I concentration would destabilize the system with a small F value. The simulation results obtained through numerical calculations indicate that IGF-I signaling switches between constant and oscillatory signals depending on k1 (Fig. 2C,D). Interestingly, the simulation results indicate that the IGF-I signaling is constant when the optimized k1 value is used (k1 = 0.060; Fig. 2C). However, when the equivalent k1 value for the IGF-I concentration is set to one-tenth of the amount (k1 = 0.006), IGF-I signaling oscillates (Fig. 2D). As shown in Fig. 2C, the F value is greater than 1, whereas in Fig. 2D, it is less than 1. Bifurcation diagrams showing the relationship between the k1 value and amplitude of IRS-1 protein levels are shown in Fig. S1B.On the other hand, it is accepted by many researchers that IRS-1 is a critical mediator of the IGF-I signaling pathway and that activation of downstream kinase, mTORC1 leads to proteasomal degradation of IRS-1 resulting in suppression of IGF-I signaling activity. We also modeled this canonical IGF-I signaling pathway as differential equation (Fig. S4). This system has two different equilibria, E+, E−. Equilibrium point E− is unstable but exists in a region with negative [IRS1], [pIRS1], and [pmTORC1] coordinates. Thus, a state that is impossible in biological phenomena can be realized computationally. On the other hand, equilibrium point E+ is proved to be always stable under k > 0. These data strongly indicated that, in this canonical system, IGF-I signaling activity is always constant.IGF-I signaling dynamics in L6 myoblastsTo evaluate how the IGF-I signaling pathway was activated in cells, immunoblotting analysis was performed on the L6 myoblasts (Fig. 2E). L6 myoblasts were serum-starved for 18 h, followed by stimulation with 1, 10, or 100 ng/mL IGF-I for the indicated periods. The amount of IRS-1 protein, whose levels were altered in response to IGF-I stimulation, was measured. IRS-1 protein levels increased in all groups after 1 h of IGF-I stimulation. In groups stimulated with 1 ng/mL IGF-I, IRS-1 levels gradually increased for up to 18 h, decreased sharply at 24 h, and then recovered at 30 h. In the groups stimulated with 10 ng/mL IGF-I, IRS-1 levels decreased at 6 h, gradually increased again from 18 to 30 h, decreased at 36 h, and increased thrice at 48 h. Contrarily, in the 100 ng/mL IGF-I-stimulated group, IRS-1 levels decreased at 6 h, and little change was observed. These data indicated that the IGF-I signaling oscillated at a concentration of less than 100 ng/mL IGF-I, whereas the addition of 100 ng/mL IGF-I stabilized it. Contrastingly, activation of Akt, which is related to mTORC1 activity, did not oscillate in all test groups. Because prolonged incubation in serum-free medium is a unideal condition for cells, we performed similar experiments using medium containing 2% FBS. L6 myoblasts were serum-starved for 18 h and stimulated with DMEM 2% FBS containing 0, 1, or 100 ng/mL IGF-I. Stimulation with 2% FBS containing 0 or 1 ng/mL IGF-I made IGF signaling oscillate, but 100 ng/mL IGF-I addition did not (Fig. S5A). Moreover, in mouse C2C12 myoblasts, IRS-1 protein levels and phosphorylated Akt levels were oscillated by stimulation with DEME 2% FBS containing IGF-I (Fig. S5B). In addition, nuclear/cytoplasmic localization of FoxO1 in C2C12 cells under the 100 ng/mL IGF-I stimulation condition was oscillated (Fig. S5C). These experiments data strongly suggested that IGF-I signaling can be oscillated in myoblast under some conditions, and that a model in which IRS-1 is a regulator rather than a mediator (Fig. 2A) is more reliable than a canonical model in which IRS-1 is a mediator (Fig. S4).Cellular automaton simulation predicted that IRS-1 protein levels oscillate in phase through cell competition during myoblast differentiationWe previously reported that differential expression levels of the IRS-1 protein induce cell competition and that high-level IRS-1 cells are selectively eliminated from cell layers when surrounded by low-level IRS-1 cells25. Using cellular automaton analysis, IRS-1 protein levels during the progression of myoblast differentiation were simulated while considering cell competition (Fig. 3A). In this cellular automaton analysis, the cells were shown in a hexagon, and each cell was attached to six other cells. Within each cell, IRS-1 protein levels oscillated in different phases. When the target cell was surrounded by cells with lower levels of IRS-1 (the threshold for the difference in IRS-1 protein levels at which cell competition occurs is set at 0.136; 40% of the amplitude of the oscillation), the target cell was eliminated. The remaining space was then filled by the proliferation of neighboring cells. Detailed conditions under which the cells were eliminated are shown in Fig. 3A. At first, k1 value was fixed at 0.002, which is around the maximum amplitude of IRS-1 protein level oscillation (Fig. S1B). When the threshold for differences in IRS-1 protein levels at which cell competition occurs was varied, it was observed that lower thresholds resulted in the formation of cell populations with aligned IRS-1 levels (Fig. S6A). In the later analysis, IRS-1 level difference threshold is fixed at 0.136 (40% of amplitude of the oscillation), and the k1 value was fixed at 0.002. At time 0, each cell had a different IRS-1 protein level because IRS-1 oscillated at different phases (t = 0; Fig. 3B). Over time, some cell groups whose IRS-1 protein levels are the same are formed (t = 20–140; Fig. 3B). These simulation results indicate that cell competition gradually aligns the IRS-1 levels of neighboring cells, forming cell populations that oscillate during the same phase.Fig. 3Synchronization of IGF-I signaling oscillations. (A) Cellular automaton-based algorithm considering cell competition. When the target cell is surrounded by low-level IRS-1 cells, target cells are eliminated, and the empty space is replaced by the proliferation of neighboring cells. (B) Cellular automaton simulation results. The IRS-1 level in each cell is shown as a heatmap, and the dead space is in black. At time 0, each cell had different IRS-1 protein levels because IRS-1 oscillation was not synchronized. Over time, IRS-1 protein levels gradually synchronized between neighboring cells. (C) L6 myoblasts were serum-starved for 18 h, followed by stimulation with 100 ng/mL IGF-I for the indicated time. Afterward, cells were fixed and immunostained with anti-IRS-1 antibody. (D) L6 myoblasts were differentiated into myotubes in a differentiation medium. On days 0, 1, or 2 after induction of differentiation, cells were fixed and immunostained with anti-IRS-1 antibody. The green color shows IRS-1, and the blue color indicates the nuclei stained with Hoechst 33342. Scale bar = 20 µm; applicable to all images in each panel. (E) The diversity index was calculated from the data of photographs immunostained with IRS-1 and shown as a graph (n = 4). Results are presented as mean ± SEM. *P < 0.05. One-way ANOVA and Tukey’s post hoc test were performed for assessment.Immunofluorescent analysis revealed synchronized IRS-1 protein oscillations in differentiated myotubesTo confirm this prediction, IRS-1 protein levels in each cell were assessed using immunostaining with an anti-IRS-1 antibody during the progression of myoblast differentiation. Initially, L6 myoblasts were serum-starved for 18 h, stimulated with 100 ng/mL IGF-1, and stained with an anti-IRS-1 antibody (Fig. 3C). Under serum-starved conditions, the fluorescence level of IRS-1 was high, and IRS-1 was mainly localized in nuclei. One hour after IGF-I stimulation, the fluorescence intensity decreased, and the IRS-1 proteins were localized throughout the cell. IRS-1 proteins were exported from nuclei 6 h later and localized mainly in the cytosol. It has been reported that IRS-1 localization was changed in response to IGF-I, but the underlying mechanism remains unknown. Although the relationship between the difference in IRS-1 localization and oscillations of IRS-1 protein level is unclear, these results show that the status of IGF-I signaling activity can be identified by immunostaining of IRS-1. Thus, three types of IRS-1 staining patterns (Type A, B, and C) were identified (Fig. 3C). L6 myoblasts were differentiated into myotubes by culturing in a differentiation medium. Cells were then immunostained with an anti-IRS-1 antibody at 0, 1, or 2 days after the induction of differentiation (Fig. 3D,E). Before induction of differentiation, the staining pattern of IRS-1 was random. Two days after the induction of differentiation, IRS-1 immunostaining patterns aligned with each other. As mentioned in the “Materials and methods” section, we defined the diversity index as a synchronization parameter and calculated it at 0, 1, and 2 days after the induction of differentiation. Two days after the induction of differentiation, the diversity index decreased significantly, suggesting that the IRS-1 protein oscillation was synchronized after the induction of differentiation.Synchronization of IGF-I signaling oscillation was critical for myogenic cell fusion to form multinucleate myotubesTo evaluate the biological significance of IGF-I signaling synchronization, cell competition was inhibited by adding an apoptotic inhibitor, Z-VAD-FMK, to the differentiation medium. Addition of Z-VAD-FMK impaired the decrease observed in the diversity index (Fig. 4A), indicating that the synchronization of oscillating IRS-1 levels was inhibited. Z-VAD-FMK addition did not inhibit the expression of MyHC but significantly decreased the fusion index (Fig. 4B). Myomaker plays an important role in myogenic cell fusion28, and the addition of Z-VAD-FMK was found to decrease its mRNA levels (Fig. 4C). These results indicated that apoptotic inhibitors impeded myogenic cell fusion to form multinucleate myotubes.Fig. 4Synchronization of IRS-1 oscillation is critical for cell fusion. (A) L6 myoblast differentiation was induced in the differentiation medium containing Dimethyl sulfoxide (DMSO) or Z-VAD-FMK. At 0 or 4 days after induction of differentiation, cells were fixed and immunostained with an anti-IRS-1 antibody. The green color shows IRS-1, and the blue color indicates the nuclei stained with Hoechst 33342. Scale bar = 50 µm; applicable to all images in each panel. The diversity index was calculated and shown in the graph (n = 4). Results are presented as mean ± SEM. *P < 0.05. One-way ANOVA and Tukey’s post hoc test were performed for assessment. (B) L6 myoblasts were differentiated in the differentiation medium for 4 days. Cells were fixed and immunostained with an anti-MyHC antibody. Scale bar = 20. The fusion index was calculated and shown in the graphs (n = 3). Results are presented as mean ± SEM. *P < 0.05. Student’s t-test was performed for assessment. (C) L6 myoblasts were differentiated in the differentiation medium for 3 days. Myomaker mRNA levels in L6 myoblasts were measured via qPCR (n = 3). Results are presented as mean ± SEM. *P < 0.05. One-way ANOVA and Tukey’s post hoc test were performed for assessment. (D) L6 myoblasts were directly differentiated by exchanging the culture medium from DMEM + 10% FBS to DMEM + 2% FBS (normal). L6 myoblasts were serum-starved for 1 day, followed by differentiation induction in DMEM + 2% FBS. Total cell lysates were prepared for immunoblotting analysis using the indicated antibodies.Next, we examined whether synchronization of IGF-I signaling oscillations was sufficient for myogenic differentiation. L6 myoblasts were serum-starved for 1 day to synchronize IGF-I signaling oscillation in advance, whereafter differentiation was induced (Fig. 4D). Serum removal before the induction of differentiation clearly accelerated MyHC expression. Interestingly, caspase-3 activation did not enhance after one day under serum-starved conditions. These data strongly suggested that differentiation was accelerated by the pre-synchronization of IGF-I signaling following serum removal.Synchronization of IGF-I signaling oscillation possibly occurs only under limited IGF concentrationsThe relationship between the k1 value and amplitude of IRS-1 protein oscillation is shown in Figs. S1B and S6B. The k1 value at which the oscillation and stability switch occurred was approximately 0.0077 (Hopf branch [HB]; Fig. S6B). The amplitude of the IRS-1 protein levels was low when k1 was close to the HB. Furthermore, as k1 approached zero, the amplitude of IRS-1 also decreased. Thus, the signaling amplitude was extremely small at IGF-I concentrations near the HB or zero. IGF-I concentrations at which IGF-I signaling oscillated were in the single-digit range, indicating that signaling oscillated only at very limited concentrations. Results of the cellular automaton analysis at various k1 values are shown in Fig. S6B. When the amplitude of the IRS-1 level is large (when k1 is between 0.002 and 0.005; very limited concentrations of IGF-I), the amount of IRS-1 in cells becomes synchronized; however, above or below that amount, no synchronization occurs because of the low amplitude of IRS-1 levels.
IGF-I concentration determines cell fate by converting signaling dynamics as a bifurcation parameter in L6 myoblasts
