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Theoretical Types of Embryo/Developmental Networks

Publications and Presentations

Euler Cycles for Life Abstract

Embryo Networks as Generative Divergent Integration Abstract

Work from the DevoWorm group:

Papers

Alicea, B. and Gordon R. (2018). Cell Differentiation Processes as Spatial Networks: identifying four-dimensional structure in embryogenesis. BioSystems, 173, 235-246.

Alicea, B. (2017). The Emergent Connectome in Caenorhabditis elegans Embryogenesis. BioSystems, 173, 247-255.

Presentation

Embryo Networks as Generative Divergent Integration . Networks 2021.

Euler Cycles for Life: developing biological structure using multi-cell networks. TopoNets (satellite of Networks 2021 conference).

Open Datasets

Alicea, B., Gordon, R., and Banerjee, A. (2018). Embryo networks and connectomes in Caenorhabditis elegans. doi:10.17605/OSF.IO/Q9JVB.

Connectome Datasets, Orthogonal Research and Education Laboratory.

Synthetic and Pseudo-data

Network Emergent Connectivity using TSP and Euler Paths Github repo, talk

Basic Network Concepts and Similar Work (see also bibiography):

  1. Network Primer from NetSciEd

  2. Anatomical Networks Approach

  3. Embryogenetic Connectome data from DevoWorm

  4. Matthew D.B. Jackson and the Bassell Lab, University of Birmingham (UK)

Conventional Types of Complex Network:

  1. Random Network

  2. Scale-free Network

  3. Small-world Network

These types are based on degree distribution and the global patterns of connectivity. These types do not account for connectivity based on geometric or spatial constraints.

Experimental Control Networks:

In Hilgetag and Goulas (2020, Figure 4), three types of experimental control networks are used to compare and contrast with a circular network layout of the primate visual system. The networks used have the following connectivity patterns on a circular layout: most sequential, randomized, and most distributed.

Hilgetag, C.C. and Goulas, A. (2020). ‘Hierarchy’ in the organization of brain networks. Philisophical Transactions of the Royal Society B, 375, 20190319.

Types of Spatial Networks:

  1. Hyperbolic Geometric Graph

  2. Random Geometric Graph

  3. Planar Graph

These types do account for connectivity based on geometric or spatial constraints, and provide a means to model phenomena that are dependent on spatial structure.

Types of Node and Edge Construction:

  1. Barabási–Albert model (preferential attachment)

  2. Erdos–Renyi model (equiprobable edges)

  3. Fitness model

These models account for the probability of all connections between nodes. In the equiprobable case, any one node can be connected to any other node with equal probability. In other models, there is bias for certain nodes given active processes (selection, decision-making bias).

Types of Topological Minimization:

  1. Steiner Tree/Voronoi Trees

  2. Dependency Network

  3. Interdependent Network

These types are defined by their ability to capture and reproduce geometric features and spatial dependencies. However, these are no clear relationships between spatial connectivity and scaling laws, particularly as they relate to biological processes.

In vivo:

We find a number of global patterns in embryo networks that do not conform with a typical mathematical model of connectivity. Some of these features have to do with differentiation, while others have to do with polarity and the geometry of the emerging phenotpye:

  1. spatial segregation by sublineage a few rounds of division after the founder cells appear for major sublineages.

  2. spatial diversification of sublineages over time.

  3. spatial re-segregation of cells as tissues begin to form.

In embryo networks, so-called nodes are cells that are both small and have many immediate neighbors.

See examples from various species in repository, and check out work on Zebrafish embryo for Zygote and Cleavage stages.

Criticality in the Embryo and Developing Nervous System:

Avalanche model:

Vollmer, J., Casares, F., and Iber, D. (2017). Growth and size control during development. Open Biology, 7, 170190.

Dhar, D., and Sadhu, T. (2013). A sandpile model for proportionate growth. Journal of Statistical Mechanics: Theory and Experiment, P11006.

Jamming transition:

Mongera, A., Serwane, F., Rowghanian, P., Gustafson, H.J., Shelton, E., Kealhofer, D.A., Carn, E.K., Serwane, F., Lucio, A.A., Giammona, J., and Campas, O. (2018). A fluid-to-solid jamming transition underlies vertebrate body axis elongation. Nature, 561, 401-405.

Sadati, M., Qazvini, N.T., Krishnan, R., Park, C.Y., Fredberg, J.J. (2013). Collective migration and cell jamming. Differentiation, 86(3), 121-125.

Propagation Criticality

Cota, W., Odor, G., and Ferreira, S.C. (2018). Griffiths phases in infinite-dimensional, non-hierarchical modular networks. Scientific Reports, 8, 9144. doi:10.1038/s41598-018-27506-x.

Symmetry-breaking in development:

Durston, A.J. (2013). Dislocation is a developmental mechanism in Dictyostelium and vertebrates. PNAS, 110(49), 19826-19831.

Grimes, D.T. (2019). Making and breaking symmetry in development, growth and disease. Development, 146(16), dev170985.

Wiring Minimization (Efficiency of Wiring):

Chklovskii, D.B., Schikorski, T., Stevens, C.F. (2002). Wiring Optimization in Cortical Circuits. Neuron, 34, 341–347.

Raj, A., Chen, Y-H. (2011). The Wiring Economy Principle: Connectivity Determines Anatomy in the Human Brain. PLoS One, 6(9), e14832.

Sporns, O. (2011). The non-random brain: efficiency, economy, and complex dynamics. Frontiers in Computational Neuroscience, doi:10.3389/fncom.2011.00005.

Avena-Koenigsberger, A., Yan, X., Kolchinsky, A., van den Heuvel, M.P., Hagmann, P., Sporns, O. (2019). A spectrum of routing strategies for brain networks. PLoS Computational Biology, 15(3), e1006833.

Kaiser, M. and Hilgetag, C.C. (2006). Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems. PLoS Computational Biology, 2(7), e95.

Network Structure:

Azulay, A., Itskovits, E., and Zaslaver, A. (2016). The C. elegans Connectome Consists of Homogenous Circuits with Defined Functional Roles. PLoS Computational Biology, 12(9), e1005021.

Bassett, D.S. and Bullmore, E.T. (2017). Small-World Brain Networks Revisited. The Neuroscientist, 23(5), 499–516.

Hilgetag, C.C. and Goulas, A. (2016). Is the brain really a small-world network? Brain Structure and Function, 221, 2361–2366. doi:10.1007/s00429-015-1035-6

Holme, P. (2019). Rare and everywhere: Perspectives on scale-free networks. Nature Communications, doi:10.1038/s41467-019-09038-8.

Majhi, S., Bera, B.K., Ghosh, D., Perc, M. (2018). Chimera states in neuronal networks: A review. Physics of Life Reviews, doi:10.1016/j.plrev.2018.09.003.

Muldoon, S.F., Bridgeford, E.W., & Bassett, D.S. (2016). Small-World Propensity and Weighted Brain Networks. Scientific Reports, 6, 22057.

Papo, D., Zanin, M., Martinez, J.H., and Buldu, J.M. (2016). Beware of the Small-World Neuroscientist! Frontiers in Human Neuroscience, doi:10.3389/fnhum.2016.00096.

Wig, G.S. (2017). Segregated Systems of Human Brain Networks. Trends in Cognitive Science, 21(12), 981-996. doi:10.1016/j.tics.2017.09.006

Watts, D.J. and Strogatz, S.H. (1998). Collective dynamics of small-world networks. Nature, 393, 440-442.

Standards:

INCF SIG: Standard Representations of Network Structures.

Bibliography:

Alicea, B. and Gordon R. (2018). Cell Differentiation Processes as Spatial Networks: identifying four-dimensional structure in embryogenesis. BioSystems, 173, 235-246. doi:10.1016/j.biosystems.2018.09.009.

Esteve-Altava B, Marugán-Lobón J, Botella H, and Rasskin-Gutman D. (2011). Network models in anatomical systems. Journal of Anthropological Sciences, 89, 175-184. doi:10.4436/jass.89016.

Esteve-Altava, B., Marugán-Lobon, J., Botella, H. (2013). Structural Constraints in the Evolution of the Tetrapod Skull Complexity: Williston’s Law Revisited Using Network Models. Evolutionary Biology, 40, 209. doi:10.1007/s11692-012-9200-9.

Jackson, M.D.B., Duran-Nebreda, S., and Bassel, G.W. (2017). Network-based approaches to quantify multicellular development. Journal of the Royal Society Interface, 14(135), 20170484. doi:10.1098/rsif.2017.0484.

Jackson, M.D.B., Xu, H., Duran-Nebreda, S., Stamm, P., Bassel, G.W. (2017). Topological analysis of multicellular complexity in the plant hypocotyl. eLife, 6, e26023. doi:10.7554/eLife.26023.