Stochastic modeling suggests that noise reduces differentiation efficiency by inducing a heterogeneous drug response in glioma differentiation therapy

Abstract

Background: Glioma differentiation therapy is a novel strategy that has been used to induce glioma cells to differentiate into glia-like cells. Although some advances in experimental methods for exploring the molecular mechanisms involved in differentiation therapy have been made, a model-based comprehensive analysis is still needed to understand these differentiation mechanisms and improve the effects of anti-cancer therapeutics. This type of analysis becomes necessary in stochastic cases for two main reasons: stochastic noise inherently exists in signal transduction and phenotypic regulation during targeted therapy and chemotherapy, and the relationship between this noise and drug efficacy in differentiation therapy is largely unknown.

Results: In this study, we developed both an additive noise model and a Chemical-Langenvin-Equation model for the signaling pathways involved in glioma differentiation therapy to investigate the functional role of noise in the drug response. Our model analysis revealed an ultrasensitive mechanism of cyclin D1 degradation that controls the glioma differentiation induced by the cAMP inducer cholera toxin (CT). The role of cyclin D1 degradation in human glioblastoma cell differentiation was then experimentally verified. Our stochastic simulation demonstrated that noise not only renders some glioma cells insensitive to cyclin D1 degradation during drug treatment but also induce heterogeneous differentiation responses among individual glioma cells by modulating the ultrasensitive response of cyclin D1. As such, the noise can reduce the differentiation efficiency in drug-treated glioma cells, which was verified by the decreased evolution of differentiation potential, which quantified the impact of noise on the dynamics of the drug-treated glioma cell population.

Conclusion: Our results demonstrated that targeting the noise-induced dynamics of cyclin D1 during glioma differentiation therapy can increase anti-glioma effects, implying that noise is a considerable factor in assessing and optimizing anti-cancer drug interventions.

Keywords: Differentiation efficiency; Drug resistance; Glioma differentiation therapy; Noise; Stochastic modeling; Ultrasensitivity.

Fig. 1

Signaling network of drug-induced glioma differentiation. Signaling pathways involved in the regulation of glioma differentiation during glioma differentiation. Elevation of cAMP level by cholera toxin (CT), can induce glioma cell differentiation, which is mediated by CREB phosphorylation at Ser-133 in a PKA dependent manner [2]. cAMP/PKA signaling can also inhibit the PI3K/AKT pathway, leading to activation of the downstream molecule GSK-3β and subsequent degradation of cyclin D1 [3]. Additionally, the IL-6/JAK2/STAT3 pathway, which is activated by increased cAMP levels, is also involved in glioma cell differentiation [4]. Glial fibrillary acidic protein (GFAP) is used as a reliable marker for evaluating the differentiation of glioma cells

Fig. 2

Ultrasensitive response of cyclin D1 controls the phenotypic transition of drug-induced glioma differentiation. a The sensitivity analysis revealed that cyclin D1 critically regulates glioma differentiation. b Activation levels of cyclin D1 and GFAP under treatment with increasing doses of CT for 48 h. Lines represent simulations (green - cyclin D1; red - GFAP), and dots are experimental data (blue - cyclin D1; brown - GFAP). The apparent Hill coefficients (n _H) of the simulated dose-response curves of cyclin D1 and GFAP are 40 and 43, respectively, indicating an ultrasensitive response of glioma differentiation to drug treatment. c Time-courses of cyclin D1 (green) and GFAP (red) following drug treatment (CT = 10 ng/ml)

Fig. 3

Heterogeneous response of cyclin D1 and GFAP in glioma cells simulated using the ANM model. The simulated cells were subjected to continuous stimulation with CT (10 ng/ml) for 48 h. The stochastic evolution of cyclin D1 and GFAP activity was simulated with different noise intensities (0.1 % (a, b), 1 % (c, d), 5 % (e, f) and 10 % (g, h), respectively) of signal variation

Fig. 4

Stochastic cellular responses of glioma cells to differentiation therapy simulated using the ANM model with different noise intensities. The noise intensity was set at 0.1, 1, 5 or 10 %. The upper panel a, b, c, d shows the probabilistic distribution of GFAP at 48 h during drug treatment (CT = 10 ng/ml) at different noise intensities. The lower panel e, f, g, h shows the stochastic temporal evolution of the differentiation potential of the glioma cell population at different noise intensities

Fig. 5

Effects of intrinsic and extrinsic noises on the molecular and cellular responses simulated using the CLE model. a-d Control group: the intrinsic noise has a standard deviation of $1/\sqrt{V}$ =0.001, and the extrinsic noise has a standard deviation of λ = 0.001; e-f increasing strength of intrinsic noise ($1/\sqrt{V}$ =0.01); i-l increasing strength of extrinsic noise (λ = 0.01). The stochastic temporal responses of cyclin D1 and GFAP, the distribution of GFAP levels and the differentiation potential of glioma cells evaluated at 48 h were simulated

Fig. 6

Differentiation potential simulated using the CLE model with a wide range of intrinsic and extrinsic noise strengths. The combined intrinsic and extrinsic noise strength in the range of 10^-3 to 10^-1 was examined. a The differentiation potential of CT-treated glioma cells. b The differentiation potential of glioma cells treated with CT combined with inhibition of cyclin D1 feedback. The results were evaluated at 48 h. The inhibition of cyclin D1 feedback was simulated by increasing the value of the Michaelis constant (K _6a) of the cyclin D1 feedback loop by 10-fold in the CLE model