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  • Review Article
  • Published:

Quantitative approaches in developmental biology

Nature Reviews Genetics volume 10, pages 517–530 (2009)Cite this article

Key Points

  • Understanding complex systems such as developing embryos requires quantitative approaches.

  • Mathematical models of developmental processes have provided insight into mechanisms and suggested new experimental directions. Quantitative data are required to precisely define the developing system and to test mathematical models.

  • Dynamic, quantitative imaging of embryonic development is an important source of data, which are now available through developments in microscopy and image analysis.

  • The formation of an exponential morphogen gradient across a tissue can be understood through mathematical models in terms of three fundamental processes: the flux of morphogen from the source, the diffusion coefficient of the morphogen and the degradation rate of the morphogen.

  • The precision with which gradients can specify positional information is not yet understood; secondary responses from the patterned tissue may be required.

  • Cells not only exert forces on their environment, but are also able to respond to mechanical stimuli from their environment and to translate these stimuli into biochemical signals controlling cell fate specification, proliferation and survival.

  • The relationship between the bulk material properties of the tissue and the individual properties of the cells is not well understood; different tissues may have different contributions from these properties.

  • The rhythmic patterning of somitogenesis can be understood through mathematical models as the coordinated output of coupled cellular oscillators.

  • The origin of the oscillatory instability and the spatial control of the oscillators' arrest are not yet understood.

  • Progress in quantitative developmental biology will depend on collaboration between experimentalists and theorists with contributions from biology, physics, engineering and computer science.

Abstract

The tissues of a developing embryo are simultaneously patterned, moved and differentiated according to an exchange of information between their constituent cells. We argue that these complex self-organizing phenomena can only be fully understood with quantitative mathematical frameworks that allow specific hypotheses to be formulated and tested. The quantitative and dynamic imaging of growing embryos at the molecular, cellular and tissue level is the key experimental advance required to achieve this interaction between theory and experiment. Here we describe how mathematical modelling has become an invaluable method to integrate quantitative biological information across temporal and spatial scales, serving to connect the activity of regulatory molecules with the morphological development of organisms.

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Figure 1: Precision of morphogen gradients.
Figure 2: Mechanical cues in cell fate specification.
Figure 3: Tensile forces acting on germ layer organization.
Figure 4: Cell rearrangements and cell shape changes drive morphogenesis.
Figure 5: Somitogenesis and the segmentation clock.

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Acknowledgements

We thank A. Martinez-Arias for discussion and feedback during the preparation of this work, and members of our laboratories for comments and helpful discussion. We are grateful to J. de Navacsués for discussion and help with Box 2, J. Lewis, R. Kageyama, I. Riedel-Kruse, C. Eugster and D. Roellig for comments on an earlier version of the manuscript, and J.-L. Maitre for discussion. We also thank E. Farge and P.-A. Pouille for providing the images used in Fig. 4c.

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Authors and Affiliations

  1. Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, D-01307, Germany

    Andrew C. Oates & Carl-Philipp Heisenberg

  2. Department of Genetics, University of Cambridge, Cambridge, CB2 3EH, UK

    Nicole Gorfinkiel

  3. Department of Biochemistry, University of Geneva, Geneva, 1211, Switzerland

    Marcos González-Gaitán

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  1. Andrew C. Oates
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  2. Nicole Gorfinkiel
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  3. Marcos González-Gaitán
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  4. Carl-Philipp Heisenberg
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Correspondence to Andrew C. Oates or Carl-Philipp Heisenberg.

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Nature Reviews Genetics Series on Modelling

Glossary

Morphogen gradient

The morphogen gradient model proposes that undifferentiated cells in a developing tissue acquire information about their position in the field by reading the concentration of a substance (a morphogen), which is distributed in a spatial gradient of concentration.

Planar cell polarity

The polarization of many epithelial cells in the plane of the tissue.

Imaginal disc

Epithelial infoldings in the larvae of insects that are determined during the embryonic stage; they grow during the larval stage and finally develop into adult appendages during metamorphosis.

Phyllotaxis

The arrangement of leaves on the stem of a plant. Basic patterns are alternate, opposite, whorled and spiral.

Cell autonomous

A genetic trait in multicellular organisms in which only genotypically mutant cells exhibit the mutant phenotype.

Bottom-up modelling

A modelling approach wherein the microscopic dynamics of the individual constituents of a developing system is described as a function of the properties of each constituent and its relevant interactions with other constituents. Higher-level attributes of the system (emergent properties) are calculated from these interactions over time.

Markov chain model

A stochastic process such that, with the present state known, future states are independent of the past states. At each time step, the potential transition to the next state is drawn from a probability distribution.

Top-down modelling

A modelling approach wherein an empirical relationship between observable parameters is defined by starting with the higher-level properties of the developing system that may have a collective or statistical character, for example, differentiated cell states, tissue deformation or oscillation period. A top-down model does not require detailed knowledge of lower-level processes, such as gene expression or function.

Primordia

An organ or tissue in its earliest recognizable stage of development. The leaf and flower primordia arise from the shoot apical meristem in a process that is regulated by the hormone auxin.

Apical meristem

The tissue that is found at the growth tip of plants. It consists of completely undifferentiated cells, and is equivalent to stem cells in animals.

Elastic mechanics

The physical theory that deals with materials deforming under stress and returning to their original shape when the stress is removed, as typified by a spring.

Multiscale modelling

The integration of interactions between multiple levels of spatial or temporal organization, each with its own model substructure.

Genetic regulatory network

A common type of bottom-up model in which the emphasis is on rates of production of mRNA and proteins from genes in response to regulatory signals, leading to altered states of the network.

Cytoneme

A long, thin and polarized actin-based cytoplasmic extension with a diameter of approximately 0.2 μm that projects from a cell.

Focal adhesions

Large, dynamic protein complexes at the cell cortex through which the actin cytoskeleton of a cell connects to the extracellular matrix and transmits force. It is typically coordinated by the binding of cellular integrin transmembrane proteins to the matrix, which also act as integrin-regulated signalling centres.

Adherens junctions

Protein complexes at cell–cell junctions in epithelial tissues that link the actin cytoskeleton across the tissue and transmit force. They are mediated by cadherin transmembrane protein binding to cadherins at an opposing adherens junction on a neighbouring epithelial cell, and can act as cadherin-regulated signalling centres.

Tensegrity

Describes structures that stabilize their shape by continuous tension, and includes pre-stressed and geodesic classes. In the pre-stressed class, a pre-existing tensile stress or isometric tension distributed among embedded compressive elements holds the joints in position. In the geodesic class, structural members are triangulated and oriented along minimal paths to geometrically constrain movement. For a cell, the internal pre-stressed cytoskeleton interconnects at the cell periphery with a highly elastic, geodesic cytoskeletal network directly beneath the plasma membrane.

Cell cortex

A network of crosslinked actin filaments that is attached to the inner face of the plasma membrane and is able to contract through the action of myosin molecular motors.

Anisotropies

Differences in the value of a physical property of a material when measured along different axes.

Finite-element modelling

A numerical tool, widely used in engineering design and analysis, used to solve partial differential equations. It requires the subdivision of the system into discrete elements, which are analyzed separately in terms of the loads and displacements at the nodes.

Germ band extension

The morphogenetic process that occurs shortly after gastrulation in long germ band insects, in which the body axis is elongated through extensive cell intercalation in the epidermal epithelium.

Somites

Bilaterally symmetrical blocks of cells that are arranged in serial rows along the embryo. They give rise to the reiterated axial skeleton and associated musculature of the adult organism.

Mean field

An approximation from physics in which interactions between many components are replaced by interactions with a single component. Technically, all the components contribute to the generation of a mean field across the system, which in turn feeds back to each component to regulate its behaviour.

Selective plane illumination microscopy

An approach that combines two-dimensional laser illumination with orthogonal camera-based detection, thereby obtaining high-resolution, optical sectioning throughout an entire embryo. Advantages include minimal phototoxicity and speeds capable of capturing dynamic phenomena.

Two photon laser scanning microscopy

A fluorescence imaging technique that uses the simultaneous absorption of two low-energy photons to excite a fluorophore. The use of long wavelength excitation photons reduces scattering in biological material, allowing deeper tissue penetration. Additional advantages over conventional confocal microscopy are efficient light detection and reduced phototoxicity.

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Oates, A., Gorfinkiel, N., González-Gaitán, M. et al. Quantitative approaches in developmental biology. Nat Rev Genet 10, 517–530 (2009). https://doi.org/10.1038/nrg2548

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