The Library
Geometry of gene regulatory dynamics
Tools
Tools
Tools
Rand, David A., Raju, Archishman, Sáez, Meritxell, Corson, Francis and Siggia, Eric D. (2021) Geometry of gene regulatory dynamics. Proceedings of the National Academy of Sciences of the United States of America, 118 (38). e2109729118. doi:10.1073/pnas.2109729118 ISSN 0027-8424.
|
PDF
WRAP-geometry-gene-regulatory-dynamics-Rand-2021.pdf - Accepted Version - Requires a PDF viewer. Download (4Mb) | Preview |
Official URL: http://dx.doi.org/10.1073/pnas.2109729118
Abstract
Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all three-way cellular decisions realizable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs. model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form (i.e., as topographic elevation). Turing systems appear nonpotential, yet in suitable variables the dynamics are low dimensional and potential. A time-independent embedding recovers the original variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the Drosophila eye appears as relaxation in a bistable potential. Geometric reasoning provides intuitive dynamic models for development that are well adapted to fit time-lapse data.
| Item Type: | Journal Article | ||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QH Natural history > QH301 Biology |
||||||||||||||||||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Computational biology, Cellular signal transduction -- Mathematical models, Mathematical physics, Systems biology -- Mathematical models, Differential equations, Biological models, Morse theory, Genetics -- Data processing | ||||||||||||||||||||||||||||||||||||
| Journal or Publication Title: | Proceedings of the National Academy of Sciences of the United States of America | ||||||||||||||||||||||||||||||||||||
| Publisher: | National Academy of Sciences | ||||||||||||||||||||||||||||||||||||
| ISSN: | 0027-8424 | ||||||||||||||||||||||||||||||||||||
| Official Date: | 13 September 2021 | ||||||||||||||||||||||||||||||||||||
| Dates: |
|
||||||||||||||||||||||||||||||||||||
| Volume: | 118 | ||||||||||||||||||||||||||||||||||||
| Number: | 38 | ||||||||||||||||||||||||||||||||||||
| Article Number: | e2109729118 | ||||||||||||||||||||||||||||||||||||
| DOI: | 10.1073/pnas.2109729118 | ||||||||||||||||||||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||||||||||||||||||||
| Date of first compliant deposit: | 28 September 2021 | ||||||||||||||||||||||||||||||||||||
| Date of first compliant Open Access: | 13 March 2022 | ||||||||||||||||||||||||||||||||||||
| RIOXX Funder/Project Grant: |
|
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
