McMillen P et al. (2022), Information Theory as an Experimental Tool for ...

XB-ART-59317

Int J Mol Sci 2022 Aug 24;2317:. doi: 10.3390/ijms23179580.

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Information Theory as an Experimental Tool for Integrating Disparate Biophysical Signaling Modules.

McMillen P , Walker SI , Levin M .

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There is a growing appreciation in the fields of cell biology and developmental biology that cells collectively process information in time and space. While many powerful molecular tools exist to observe biophysical dynamics, biologists must find ways to quantitatively understand these phenomena at the systems level. Here, we present a guide for the application of well-established information theory metrics to biological datasets and explain these metrics using examples from cell, developmental and regenerative biology. We introduce a novel computational tool named after its intended purpose, calcium imaging, (CAIM) for simple, rigorous application of these metrics to time series datasets. Finally, we use CAIM to study calcium and cytoskeletal actin information flow patterns between Xenopus laevis embryonic animal cap stem cells. The tools that we present here should enable biologists to apply information theory to develop a systems-level understanding of information processing across a diverse array of experimental systems.

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Species referenced: Xenopus laevis
Genes referenced: clock

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	Figure 1. Secondary messengers as primary nodes: (A) Cell signaling is often conceptualized as pathways between signals and target genes with secondary messengers as intermediates; (B) because the same secondary messengers are used in many different pathways, it may be more appropriate to think of them as primary nodes integrating diverse signaling regimes.
	Figure 2. Information metric flowchart. Suggested workflow for deciding which information theory metrics to apply based on qualitative observations of a system.
	Figure 3. Information: Information is a formally defined value (A) that increases as variables spend more time in multiple states (B). Signals that frequently shift between âactiveâ and âinactiveâ states (green) contain more Information than signals that are either always on (blue) or always off (red) (C).
	Figure 4. Mutual Information: (A) Mutual information measures the information that knowing the state of one variable provides about a second variable; (B) mutual information can be used to detect novel communication channels, as in the case of contralateral bioelectric injury signals. Redrawn with permission after [26]; 2018, The Company of Biologists Ltd.
	Figure 5. Delayed mutual information and transfer entropy: (A) Delayed mutual information measures the predictive power of one variable to another variableâs future, allowing for detection of causal interactions, whereas, transfer entropy is a more powerful approach that considers predictive power of the receiving variableâs own history, and thus, avoids inferring causation from time delayed correlative interactions; (B) the vertebrate segmentation clock is a biological example of the incorrect interpretations that can arise from failing to account for a cellâs history. Waves of gene expression appear to migrate posterior to anterior in the growing tail, but will form even when the apparent âsendingâ cells are ablated, indicating that they result from intrinsic oscillations within the cells.
	Figure 6. Active information storage: (A) Active information storage measures how well a variableâs past predicts its current state; (B) a healthy heart should have relatively high active information storage, while an unhealthy heart in which periodicity is pathologically perturbed show have lower AIS.
	Figure 7. Effective information: (A) Effective information measures the predictive power of interventions over a system; (B) when âinstructor cellsâ are set to a particular state, the state of the system can be well predicted, and thus, these cells have high effective information with the system, setting the state of non-instructor cells, however, does not well predict the state of the system, indicating low effective information between the cell and the system; (C) an approach similar to effective information is used in reverse genetic screens in which each candidate gene (variable) is set to a specific state via mutation and the predictive power of this mutation over a trait is calculated.
	Figure 8. CAIM: A tool for applying information theory metrics to time series data: (A) CAIM provides users a GUI to select regions of interest (demarcated by consistent colors throughout the analysis) from which it will extract timeseries data (B) that can then be binarized (C); (DâF) then AIS, ME, and TE, respectively, can be calculated between each ROI and displayed in tables with statistically significant values indicated in blue.
	Figure 9. Information metrics within each signal. Representative frame of: (A) LifeAct-mcherry; (B) jGCaMP8S; (C) an overlay of two channels from one of the explants imaged; (D) AIS is significantly higher in real vs. randomized datasets for both the actin and calcium signals, and AIS for the actin signal is significantly higher than for the calcium signal; (E) mutual information between ROIs within the same time series is higher than for the randomized datasets, and MI is higher between ROIs for the calcium signal than for the actin signal. The calcium signal, but not the actin signal, demonstrates significantly higher TE than any of the randomized datasets (F). The real actin signal data demonstrates significantly less TE than the randomized actin does with itself. The real calcium signal also demonstrates significantly greater TE than the actin signal. *** = p > 0.0001, MannâWhitney test.
	Figure 10. Information metrics between the calcium and actin signals. MI between the actin signal of nearby ROIs, between the calcium signal of nearby ROI, and between actin and calcium signal of nearby ROIs is significantly higher than MI between the randomized actin signal and calcium or the randomized calcium signal to actin. (A) The highest MI is observed between nearby ROIs within the calcium signal, with MI between nearby ROIs for the actin signal being significantly higher than MI between the two signals; (B) within nearby ROIs, both the actin and calcium signals have significant TE to the calcium signal as compared with randomized controls, with the actin and calcium TE to calcium being statistically insignificant, neither has significant TE to the actin signal; (C) within a single ROI, the actin and calcium signals have significant MI, but while the calcium has significant TE to calcium the reverse is not true. From these data we propose a model in which actin establishes boundaries through which calcium signals flow (D). *** = p > 0.0001, MannâWhitney test.

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