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Revealing non-trivial information structures in aneural biological tissues via functional connectivity.
Blackiston D
,
Dromiack H
,
Grasso C
,
Varley TF
,
Moore DG
,
Srinivasan KK
,
Sporns O
,
Bongard J
,
Levin M
,
Walker SI
.
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A central challenge in the progression of a variety of open questions in biology, such as morphogenesis, wound healing, and development, is learning from empirical data how information is integrated to support tissue-level function and behavior. Information-theoretic approaches provide a quantitative framework for extracting patterns from data, but so far have been predominantly applied to neuronal systems at the tissue-level. Here, we demonstrate how time series of Ca2+ dynamics can be used to identify the structure and information dynamics of other biological tissues. To this end, we expressed the calcium reporter GCaMP6s in an organoid system of explanted amphibian epidermis derived from the African clawed frog Xenopus laevis, and imaged calcium activity pre- and post- a puncture injury, for six replicate organoids. We constructed functional connectivity networks by computing mutual information between cells from time series derived using medical imaging techniques to track intracellular Ca2+. We analyzed network properties including degree distribution, spatial embedding, and modular structure. We find organoid networks exhibit potential evidence for more connectivity than null models, with our models displaying high degree hubs and mesoscale community structure with spatial clustering. Utilizing functional connectivity networks, our model suggests the tissue retains non-random features after injury, displays long range correlations and structure, and non-trivial clustering that is not necessarily spatially dependent. In the context of this reconstruction method our results suggest increased integration after injury, possible cellular coordination in response to injury, and some type of generative structure of the anatomy. While we study Ca2+ in Xenopus epidermal cells, our computational approach and analyses highlight how methods developed to analyze functional connectivity in neuronal tissues can be generalized to any tissue and fluorescent signal type. We discuss expanded methods of analyses to improve models of non-neuronal information processing highlighting the potential of our framework to provide a bridge between neuroscience and more basal modes of information processing.
Fig 1. Long-term calcium transience in vertebrate epithelium in the basal state and following injury.A: 4-cell stage of embryonic development, B: animal cap excised after 24 hours, C: spheroid tissue after another 24 hours, and D: compressed spheroid tissue into disk. 7 days post-fertilization calcium imaging was performed, E: Individual frame of calcium intensity, F: average intensity of stacked frames, G and H: Cell identification. I and J: experimental setup where the tissue is punctured with a glass capillary. K: Kymograph analysis was performed on the explant outside the conventional timescale (on the order of milliseconds), because it is only when the timescale is on the order of thousands of seconds when new structures are observed within the tissue. What these structures represent requires further investigations beyond the scope of kymograph analysis. Calcium transience within these tissues displays more diverse structures when longer timescales are observed.
Fig 2. FC inference pipeline as observed in organoid 4.A: Average pixel intensity over time, observed signal peaks at the time of puncture (t = 0 s) and then remains unstable for a period post puncture. Frames at the time of puncture are removed, producing two distinct videos: pre- puncture (blue) and post- puncture (red). B: Calcium transience throughout the observation time frame. Orientation of the organoid changes due to impact from the needle at t = 0 s. C: Cell segmentation as determined by Cellpose pre- puncture. D: Raw calcium signal intensity time series for a random sample of nine segmented cells (a–k) pre- puncture. E: The same time series after post-processing with global signal regression and transformation into feature [57] (a–k). F: FC networks are generated by computing mutual information between all pairs of cells’ processed signal intensity time series. Nodes of the network (blue dots) represent segmented cells in the organoid. Edges of the network (gray lines) represent non-zero mutual information between a given pair of nodes. G–J: Same as C–F but for the post- puncture video and displayed in red.
Fig 3. Edge time series, computed as the element-wise product of two z-scored calcium time series, measures instantaneous co-fluctuation between pairs of nodes pre- (left) and post- (right) damage for each organoid (top row in quadruplet).Co-fluctuations are plotted by the magnitude away from the mean; where red signifies results above the mean, and blue below: these are interpreted as how strongly the cells are connected within the functional connectivity network. Root sum squared (RSS) amplitude shows the points in time where many cells collectively co-fluctuate (bottom row in quadruplet). In pre- puncture networks there is no clear pattern in co-fluctuations across the organoids, though in post- puncture networks there is a general decrease from strong co-fluctuations and amplitudes to some baseline levels.
Fig 4. Degree distributions.Empirical networks (black) have heavier tails and higher maximum degrees than expected by random networks (red). The null network model used is the average of 100 Erdős Rènyi graphs with the same number of nodes and edges as the corresponding empirically derived network.
Fig 5. FC is negatively correlated with distance between nodes.A: Spatially closer nodes in organoid 4 tend to have a higher functional connectivity, represented by higher density on the plot in yellow, pre- (left) and post- (right) puncture. Organoid 4 has a Spearman correlation coefficient of − 0 . 22 (p = 0 . 00) before damage and -0.18 (p = 0 . 00) after damage. B: Spearman correlation coefficients pre- and post- puncture for all N = 6 organoids.
Fig 6. Network modularity.A: FC matrix reordered by modular structure for organoid 4 pre- puncture with the three largest communities highlighted (blue, green, orange, largest to smallest). B: Physical location of nodes composing the three largest modules painted by color in organoid 4 pre- puncture at t = − 1220s. Modular structure can be clustered locally in space, distributed across the spatial extent of the organoid, or have a combination of the two. C: FC network visualization with nodes placed by physical location and painted by corresponding module color (gray represents all other nodes not in the three largest modules). Nodes within a module have more connections to other nodes within the same module than to nodes outside the module. D: Within- and between- module distance distributions pre- and post- puncture, normalized by the size of the network for N = 6 organoids. E: Neighborhood modular diversity, measured as the number of distinct modules a given node’s neighbors are members of, post- puncture networks showed significantly higher diversity then pre- puncture networks (Mann-Whitney U test, U = 2004296, N = 6, p < 0 . 001).
S1 Fig. General network characteristic.
Number of Nodes, Edges, and Network Density for each video.
https://doi.org/10.1371/journal.pcbi.1012149.s001
