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THE NETWORK ARCHITECTURE OF
EMBRYO DEVELOPMENTAL REGULATION
Bradly Alicea1, Richard Gordon2
1 OpenWorm (http://www.openworm.org), [email protected]
2 Embryogenesis Center, Gulf Specimen Aquarium & Marine Laboratory, 222 Clark Drive Panacea, FL 32346 USA, [email protected]
We can learn new information about the cellular differentiation process by:
* transforming a lineage tree of Caenorhabditis elegans into an undirected complex
network [1].
* observing and measuring connectivity of that network using a distance-based
metric.
• adding three-dimensional (positional) information [2] to a model of cell lineage (a
five-dimensional data structure)
Provides both an alternative and a related method to lineage mapping and lineage
tree reconstruction [3].
Our approach is based on a multidimensional data structure:
Spatial position (x, y, z) and cell lineage (t, i) may provide complementary information, or
may reveal unique characteristics for certain groups of cells (sublineage, other functional
characteristics).
8 terminal cells (N = 15), C. elegans cell lineage, WormWeb.org
http://wormweb.org/celllineage#c=P0&z=1
Traditional lineage tree
Adapted from: http://courses.biology.utah.edu/
bastiani/3230/DB%20Lecture/Lectures/b12Worm.html
Traditional anatomical representation
5-layered tree
7-layered tree
8-layered tree
Magenta points are cells descended from the AB lineage, blue points are cells
descended from the P1 lineage.
Degree of spatial separability greatest in 5-layered tree, most overlap seen in 8-layered
tree.
The Worm and the Embryogenetic
Hairball
Complex networks are used in analyzing the
Caenorhabditis elegans connectome [4] and
Ciona intestinalis cell-cell contacts [5]:
3-D spatial information can be converted to a
series of Euclidean distances.
Examine this scalable and prunable
interactome (analogous to paracrine
signaling) at different spatial scales.
* exclude arcs that connect cell that are too
far away (scalable).
* exclude arcs that connect to cells that
possess or do not possess a given criterion
(e.g. size limit).
Distances can be used to establish “spheres of signaling influence” for a given cell.
Interactions [6] can be real (e.g. two cells alive at the same time) or virtual (e.g. two
cells that share an ancestor-descendent relationship, one of which no longer exists).
COURTESY: diagram in [7].
TOP LEFT: Maximum length (black), cell-cell distance (red).
BOTTOM LEFT: concentric radii from a single cell.
Step 1: find interactome amongst a subtree of cells. Plot out significant distances
in 3-D space.
In this case, we can see the undirected connections (adjacency measured in relative
Euclidean distances and angles) amongst 15 cells.
Embryonic cells in a virtual space centered
upon 0,0,0 and their relative 3-D position.
Connectivity (adjacency) between cells
in AB sublineage to a lineage depth of 4.
Connectivity (adjacency) amongst 224
nodes at a threshold of 0.95 (5% of
maximum distance in embryo structure)
Step 2: expand interactome-finding methodology to the entire tree. Below right is a
224-cell network with a distance threshold of 0.05 of the maximum distance coefficient.
5-dimensional Data Structure
A generalized parameter space based on
observations across embryos (x, y, z)
x (anterior-posterior axis)
y (left-right axis)
z (dorsal-ventral axis)
t (time – relative or absolute)
i (order of nodes at level t)
t
i
xy
z
A spatially-independent parameter space
ordered by some organizational criterion
(e.g. cell size, cell location)
AB P1
00 01 10 11
P0
4 level lineage tree: N=30.
AB subtree (blue), n=15;
P1 subtree (yellow), n=15.
Distance threshold of 0.75 (all
cells within 25% the maximum
distance in embryo structure).
Intra-subtree interaction
(AB, ABar)
Intra-subtree interaction
(P4, P2)
Inter-subtree interaction
(MSa, ABa)
AB
SubtreeP1
Subtree
COURTESY: Bhatla, N. Interactive C. elegans cell lineage. http://wormweb.org/celllineage#c=P0&z=1
What do distance-based interactions look like relative to the lineage tree?
ABa x ABpl
(intra-subtree
interaction)
AB x ABa
(lineage-based
relationship)
ABp x EMS
(inter-subtree
interaction)
P1 x MS
(intra-subtree
interaction)MS x EMS
(lineage-based
relationship)
Levels between cells
in interaction (tree
depth)
Intra-subtree
interactions (AB)
Intra-subtree
Interactions (P1)
Inter-subtree
Interactions
0 57% 31% 12%
1 43% 35% 22%
2 27% 28% 45%
3-7 13% 13% 74%
What is the proportion of potential interactions within and between
subtrees?
Pairwise network that includes all
cells from Division Event 3 to
Division Event 8 in lineage tree (N =
224).
Distance threshold of 0.75 (all cells
within 25% the maximum distance in
embryo structure).
P1
subtree
AB
subtree
For all in
subtree [AB]
For all in
subtree [P1]
Observe different patterns of connectivity within subtrees, sort by lineage depth of cell:
Do the “intra-” patterns of connectivity have
any biological significance?
* no preferential hubs (as measured by
connectivity distribution, network statistics).
* scale-free network topology, with some
influence of ancestral cells.
No decrease in connectivity with lineage depth,
but some sublineages (MS, ABpr) yield
outliers.
Correcting topology for effects of cell lineage (factor in a two-dimensional
measure of distance). Factor of (t,i)
t
i
0 1
0 1 2 3
1
2
(1, 2.5)
Uncorrected topology (n=30),threshold of 0.85
Network of t,i only (n=30),threshold of 0.85
Network based on x,y,z,t,ionly (n=30), threshold of 0.85
0
Clique AnalysisABal ABar ABpl ABpr E MS C P3
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NUMBER OF CLIQUE NODES
FROM SUBTREE
A clique analysis was conducted to find subsets of
vertices where every node is fully connected with the
other nodes in that subset.
Clique analysis conducted on a network of 224 cells,
distance threshold of 0.95 (0.05 total length).
The optimal clique size was determined by balancing the
maximum number of cliques found with the largest
possible clique size itself.
117 cliques (out of 1530 total cell pairs) of size five (5)
were generated.
A heat map was constructed number of clique members
in a sublineage of any one cell in the 8-cell embryo (e.g.
ABal, ABar, ABpl, ABpr, E, MS, C, P3).
Generated cliques most often included more than one
cells from sublineages ABpr and C, least often included
cells from sublineage ABal.
A comparison between Caenorhabditis elegans and Mus
Musculus [8]
Sublineage
(AB, blue)
Sublineage
(P1, red)
Trophectoderm
(blue)
Inner Cell
Mass (red)
Model picks up geometry of
blastocoel, inner vs. outer
trophectoderm.
Model picks up geometry of axial
segregation of AB vs. non-AB
cells, cells on boundary.
REFERENCES:[1] Barabasi, A.L. and Oltvai, Z.N. (2004). Network biology: understanding the cell's functional organization. Nature ReviewsGenetics, 5, 101-113.
[2] Dataset: Bao et.al, Developmental Biology, 318(1), 65-72 (2008); Murray et.al, Genome Research, 22(7), 1282-1294(2012).
[3] Wasserstrom, A. et.al (2008). Reconstruction of Cell Lineage Trees in Mice. PLoS One, 3(4), e1939.
[4] Jabr, F. (2012). The Connectome Debate: Is Mapping the Mind of a Worm Worth It? Scientific American, October 2.
[5] Brozovic, M. et.al (2015). ANISEED 2015: a digital framework for the comparative developmental biology of ascidians.Nucleic Acids Research, 44(D1), D808-D818.
[6] Schnabel R. et.al (2006). Global cell sorting in the C. elegans embryo defines a new mechanism for pattern formation.Developmental Biology, 294(2), 418-431.
[7] Gonczy, P. and Rose, L.S. (2005). Asymmetric Cell Division. WormBook,http://www.wormbook.org/chapters/www_asymcelldiv/asymcelldiv.html
[8] Dataset: Strnad, P. et.al (2016). Inverted light-sheet microscope for imaging mouse pre-implantation development. NatureMethods, 13, 139-142.
ACKNOWLEDGMENTS:
Networks rendered in Gephi 0.8.2
Dr. Zhirong Bao and Dr. Stephen Larson (C. elegans embryo data)
Comments and Discussion
DevoWorm project:http://devoworm.weebly.com
