Bulletin of Mathematical Biology

, Volume 80, Issue 10, pp 2669–2697 | Cite as

Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans

  • J. M. Wentz
  • A. R. Mendenhall
  • D. M. BortzEmail author
Original Article


Aging in Caenorhabditis elegans is controlled, in part, by the insulin-like signaling and heat shock response pathways. Following thermal stress, expression levels of small heat shock protein-16.2 show a spatial patterning across the 20 intestinal cells that reside along the length of the worm. Here, we present a hypothesized mechanism that could lead to this patterned response and develop a mathematical model of this system to test our hypothesis. We propose that the patterned expression of heat shock protein is caused by a diffusion-driven instability within the pseudocoelom, or fluid-filled cavity, that borders the intestinal cells in C. elegans. This instability is due to the interactions between two classes of insulin-like peptides that serve antagonistic roles. We examine output from the developed model and compare it to experimental data on heat shock protein expression. Given biologically bounded parameters, the model presented is capable of producing patterns similar to what is observed experimentally and provides a first step in mathematically modeling aging-related mechanisms in C. elegans.


Aging Diffusion-driven instability Insulin-like signaling Reaction diffusion model 



JMW is supported in part by an NSF GRFP and in part by the Interdisciplinary Quantitative Biology (IQ Biology) program at the BioFrontiers Institute, University of Colorado, Boulder. IQ Biology is generously supported by NSF IGERT Grant Number 1144807. ARM is supported by the National Institute on Aging at the National Institutes of Health by Grant 4R00AG045341. The authors would also like to thank T.E. Johnson (University of Colorado, Boulder) for insightful discussions and suggestions concerning this work.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Interdisciplinary Quantitative Biology Graduate Program and Department of Applied MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Department of PathologyUniversity of WashingtonSeattleUSA
  3. 3.Department of Applied MathematicsUniversity of ColoradoBoulderUSA

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