Exploring the information transmission properties of noise-induced dynamics: application to glioma differentiation

Abstract

Background: Cells operate in an uncertain environment, where critical cell decisions must be enacted in the presence of biochemical noise. Information theory can measure the extent to which such noise perturbs normal cellular function, in which cells must perceive environmental cues and relay signals accurately to make timely and informed decisions. Using multivariate response data can greatly improve estimates of the latent information content underlying important cell fates, like differentiation.

Results: We undertake an information theoretic analysis of two stochastic models concerning glioma differentiation therapy, an alternative cancer treatment modality whose underlying intracellular mechanisms remain poorly understood. Discernible changes in response dynamics, as captured by summary measures, were observed at low noise levels. Mitigating certain feedback mechanisms present in the signaling network improved information transmission overall, as did targeted subsampling and clustering of response dynamics.

Conclusion: Computing the channel capacity of noisy signaling pathways present great probative value in uncovering the prevalent trends in noise-induced dynamics. Areas of high dynamical variation can provide concise snapshots of informative system behavior that may otherwise be overlooked. Through this approach, we can examine the delicate interplay between noise and information, from signal to response, through the observed behavior of relevant system components.

Keywords: Channel capacity; Chemical langevin equation; Glioma differentiation; Information theory; Mutual information; Stochastic modeling; k-means clustering; k-nearest neighbors.

Fig. 1

Glioma differentiation signaling network. Cholera toxin (purple) acts as a principal input to the system, inducing glioma cell differentiation via multiple pathways, the PKA/CREB [13], P13K/AKT/pGSK3 β/cyclin D1 [14], and IL6/JAK2/STAT3 [15] pathways. GFAP (pink) serves as the differentiation marker, measuring the extent to which glioma cells differentiate into normal glia-like cells

Fig. 2

CLE response dynamics. Time courses of GFAP level are shown, corresponding to 500 simulated cells exposed to different signals composed of CT dose and noise (intrinsic & extrinsic noise). Dark blue lines represent average GFAP level, with shaded areas indicating 95% confidence intervals. Noise levels are defined in Table 1

Fig. 3

Heatmaps for summary descriptors of CLE model. Average maximum response (left), maximum fold change (center), and area under the curve (right) values were calculated for the simulated cell population exposed to each signal. Noise levels are defined in Table 1

Fig. 4

Information transmission for static and dynamic response data. Channel capacity values were calculated for static summary descriptors (left) and multivariate vectors representing GFAP dynamics (right), for all target models. Vector channel capacity values were calculated for both original (Raw) dataset, and fold-transformed (Fold) dataset. Results represent mean and standard deviation of 10 replications

Fig. 5

Information transmission for different multivariate vector sampling strategies with the CLE model. The default symmetric sampling method was compared against balanced (uniform sampling of maximum dynamical variation across time course) and greedy (non-uniform sampling) asymmetric methods. Results represent mean and standard deviation of 10 replications

Fig. 6

CLE response dynamics arranged by cluster. Time courses of GFAP level are shown, corresponding to 500 simulated cells exposed to different signals composed of CT dose and noise (intrinsic & extrinsic noise). Dynamics are colored by cluster membership

Fig. 7

Information transmission for original and modified response data with CLE model. Channel capacity values were calculated for original (Raw) dataset, dataset with cells that reached differentiation threshold at end of simulation (Final Differentiated), and datasets representing distinct dynamical clusters (C1, C2, and C3). Results represent mean and standard deviation of 10 replications