Skip to main content

A theory of mechanical stress-induced H2O2 signaling waveforms in Planta


Recent progress in nanotechnology-enabled sensors that can be placed inside of living plants has shown that it is possible to relay and record real-time chemical signaling stimulated by various abiotic and biotic stresses. The mathematical form of the resulting local reactive oxygen species (ROS) wave released upon mechanical perturbation of plant leaves appears to be conserved across a large number of species, and produces a distinct waveform from other stresses including light, heat and pathogen-associated molecular pattern (PAMP)-induced stresses. Herein, we develop a quantitative theory of the local ROS signaling waveform resulting from mechanical stress in planta. We show that nonlinear, autocatalytic production and Fickian diffusion of H2O2 followed by first order decay well describes the spatial and temporal properties of the waveform. The reaction–diffusion system is analyzed in terms of a new approximate solution that we introduce for such problems based on a single term logistic function ansatz. The theory is able to describe experimental ROS waveforms and degradation dynamics such that species-dependent dimensionless wave velocities are revealed, corresponding to subtle changes in higher moments of the waveform through an apparently conserved signaling mechanism overall. This theory has utility in potentially decoding other stress signaling waveforms for light, heat and PAMP-induced stresses that are similarly under investigation. The approximate solution may also find use in applied agricultural sensing, facilitating the connection between measured waveform and plant physiology.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Data availability

All data generated or analyzed during this study are included in this published article and its supplementary information files.


Download references


The mathematical and analytical work is supported by Nanotechnology for Agricultural and Food Systems (A1511) [Grant No. 2021-67021-33999/Project Accession No. 1025638] from the USDA National Institute of Food and Agriculture. The extension of the theory to plant signaling data was supported by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program. The Disruptive & Sustainable Technology for Agricultural Precision (DiSTAP) is an interdisciplinary research group of the Singapore MIT Alliance for Research and Technology (SMART) Centre. DJL and TKP are grateful for support from the National Science Foundation Graduate Research Fellowship Program under Grant No. 1745302. TTSL acknowledges a graduate fellowship by the Agency of Science, Research and Technology, Singapore. KSS was supported by the Department of Energy Computational Science Graduate Fellowship program under Grant DE-FG02-97ER25308. Professor Per-Olof Persson is acknowledged for helpful insights during the development of the approximate solutions.

Author information

Authors and Affiliations



TKP: Data Curation, Formal analysis, Methodology, Software, Visualization, Writing—Original Draft (main text), Writing—Review & Editing. MNH: Formal analysis, Methodology, Software, Writing—Original Draft (Supplementary Information), Writing—Review & Editing. DJL: Formal analysis, Methodology, Writing—Review & Editing. AMB: Formal analysis, Methodology, Writing—Review & Editing. TTSL: Data Curation, Formal analysis, Investigation, Methodology, Software, Writing—Review & Editing. KSS: Formal analysis, Methodology, Software, Writing—Review & Editing. VBK: Formal analysis, Methodology, Writing—Review & Editing. MCYA: Investigation, Validation, Writing—Review & Editing. DTK: Investigation, Validation, Writing—Review & Editing. GPS: Conceptualization, Funding acquisition, Supervision, Writing—Review & Editing. JWS: Conceptualization, Formal analysis, Methodology, Supervision. RS: Conceptualization, Funding acquisition, Supervision, Writing—Reviewing & Editing. NHC: Conceptualization, Funding acquisition, Supervision, Writing—Review & Editing. MSS: Conceptualization, Formal analysis, Funding acquisition, Methodology, Supervision, Writing—Review & Editing.

Corresponding author

Correspondence to Michael S. Strano.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

This paper is dedicated, with appreciation, to our colleague and co-author Professor James W. Swan, who died suddenly on Nov. 5th, 2021.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 108 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Porter, T.K., Heinz, M.N., Lundberg, D.J. et al. A theory of mechanical stress-induced H2O2 signaling waveforms in Planta. J. Math. Biol. 86, 11 (2023).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI:


  • Plant systemic stress signaling
  • Plant wounding response
  • ROS wave
  • Reaction–diffusion
  • Solitons

Mathematics Subject Classification

  • 35
  • 92