Linear models for endocytic transformations from live cell imaging

John A. Belward, Kevin Burrage, Rohan D. Teasdale, Nicholas A. Hamilton


Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

  • Y. Mosesson, G. B. Mills, Y. Yarden. Derailed endocytosis: an emerging feature of cancer. Nature Reviews Cancer 2008 Nov; 8(11):835--50. doi:10.1038/nrc2521
  • L. R. Prost, S. Sanowar, S. I. Miller. Salmonella sensing of anti-microbial mechanisms to promote survival within macrophages. Immunological Reviews 2007; 219:55--65. doi:10.1111/j.1600-065X.2007.00557.x
  • M. C. Kerr, T. Wang, N. A. Castro, N. Hamilton, L. Town, D. L. Brown, F. A. Meunier, N. F. Brown, J. Stow and R. D. Teasdale.Inhibition of the PtdIns(5) kinase PIKfyve disrupts intracellular replication of Salmonella. EMBO 29:1331--1347, 2010. doi:10.1038/emboj.2010.28
  • D. J. Wilkinson Stochastic Modelling for Systems Biology Chapman and Hall. 2006.
  • P. J. Cullen, G. E. Cozier, G. Banting, H. Mellor. Modular phosphoinositide-binding domains---their role in signalling and membrane trafficking. Current Biology Volume 11, Issue 21, 30 October 2001, Pages R882--R893. doi:10.1016/S0960-9822(01)00523-1


differential equation, parameter fitting, chemical reaction, endocytosis, video-microscopy

Full Text:



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.