Abstract
The tumor promoter, phorbol 12-myristate 13-acetate (PMA), affects the processing of fluid that enters a cell from the ambient medium. Previous work showed that marker accumulates to a higher level in PMA-treated than in untreated cells. Since PMA also affects the physical activity of the membrane and stimulates the normal process of taking up extracellular fluid, called endocytosis, it is important to learn whether the perturbations in fluid processing can be attributed entirely to a change in the cell’s limiting membrane. To this end, a model for fluid uptake and processing was developed and applied to experiments in which a marker for extracellular fluid was added to cells. From previous work on marker accumulation, it was deduced that there were at least two functional compartments involved in fluid movement. Compartment I is a rapidly filling and rapidly recycling compartment. Compartment II is a slowly filling and emptying compartment. Three routes of vesicle traffic must be considered, one mediating influx from the ambient medium into compartment I, a second, efflux from compartment I to the medium, and a third efflux from compartment I into compartment II. Using earlier models for processing, workers found it difficult to estimate rates of movement through either of the latter routes, as well as the volume of compartment I. The difficulty arises from the fact that only one kinetic constant can be estimated directly from data, namely the instantaneous uptake rate. The remaining data depend on measuring the total mass of marker in the cells. Since the concentration of marker in the cell changes continuously, it is advantageous to employ differential equations to simulate the tracer movement. By applying the model to experimental values, we found estimates for all three rates of fluid movement and the volume of compartment I. It is thought that the model will enable us to determine whether apparent alterations in the time course of uptake arise solely from altered properties of the limiting membrane.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bar-Sagi, D. and J. R. Feramisco (1986). Induction of membrane ruffling and fluid-phase pinocytosis in quiescent fibroblasts by ras proteins. Science 233, 1061–1068.
Berthiaume, E. P., C. Medina and J. A. Swanson (1995). Molecular size-fractionation during endocytosis in macrophages. J. Cell Biol. 129, 989–998.
Besterman, J. M., J. A. Airhart, R. C. Woodworth and R. B. Low (1981). Exocytosis of pinocytosed fluid in cultured cells: kinetic evidence for rapid turnover and compartmentation. J. Cell Biol. 91, 716–727.
Danowski, B. A. and A. K. Harris (1988). Changes in fibroblast contractility, morphology, and adhesion in response to a phorbol ester tumor promoter. Exp. Cell Res. 177, 47–59.
Downey, G. P., C. K. Chan, P. Lea, A. Takai and S. Grinstein (1992). Phorbol ester-induced actin assembly in neutrophils: role of protein kinase C. J. Cell Biol. 116, 695–706.
Exton, J. H. (1997). Phospholipase D: Enzymology, mechanisms of regulation, and function. Physiol. Rev. 77, 303–320.
Fletcher, R. (1987). Practical Methods of Optimization, 2nd edn, Wiley.
Grant, N. J. and D. Aunis (1990). Effects of phorbol esters on cytoskeletal proteins in cultured bovine chromaffin cells: induction of neurofilament phosphorylation and reorganization of actin. Eur. J. Cell Biol. 52, 36–46.
Hebbert, D. and E. H. Morgan (1985). Calmodulin antagonists inhibit and phorbol esters enhance transferrin endocytosis and iron uptake by immature erythroid cells. Blood 65, 758–763.
Heckman, C. A. and R. J. Jamasbi (1999). Describing shape dynamics in transformed cells through latent factors. Exp. Cell Res. 246, 69–82.
Heckman, C. A., K. I. Oravecz, D. Schwab and J. Ponten (1993). Ruffling and locomotion: role in cell resistance to growth factor-induced proliferation. J. Cell. Physiol. 154, 554–565.
Heckman, C. A., H. K. Plummer III and C. S. Runyeon (1996). Persistent effects of phorbol 12-myristate 13-acetate: Possible implication of vesicle traffic. J. Cell. Physiol. 166, 217–230.
Hodgkin, M. N., J. M. Clark, S. Rose, K. Saqib and M. J. Wakelam (1999). Characterization of the regulation of phospholipase D activity in the detergent-insoluble fraction of HL60 cells by protein kinase C and small G-proteins. Biochem. J. 339, 87–93.
Holm, P. K., P. Eker, K. Sandvig and B. van Deurs (1995). Phorbol myristate acetate selectively stimulates apical endocytosis via protein kinase C in polarized MDCK cells. Exp. Cell Res. 217, 157–168.
Iyer, S. S. and D. J. Kusner (1999). Association of phospholipase D activity with the detergent-insoluble cytoskeleton of U937 promonocytic leukocytes. J. Biol. Chem. 274, 2350–2359.
Keller, H. U. (1990). Diacylglycerols and PMA are particularly effective stimulators of fluid pinocytosis in human neutrophils. J. Cell. Physiol. 145, 465–471.
Keller, H. U. and V. Niggli (1994). Selective effects of the PKC inhibitors Ro 31-8220 and CGP 41 251 on PMN locomotion, cell polarity, and pinocytosis. J. Cell. Physiol. 161, 526–536.
Kellie, S., T. C. Holme and M. J. Bissell (1985). Interaction of tumour promoters with epithelial cells in culture-an immunofluorescence study. Exp. Cell Res. 160, 259–274.
Kiss, Z. (1996). Regulation of phospholipase D by protein kinase C. Chemistry and Physics of Lipids 80, 81–102.
Majumdar, S., M. W. Rossi, T. Fujiki, W. A. Phillips, S. Disa, C. F. Queen, R. B. Johnston, O. M. Rosen, B. E. Corkey and H. M. Korchak (1991). Protein kinase C isotypes and signaling in neutrophils. Differential substrate specificities of a translocatable calcium-dependent and phospholipid-dependent beta-protein kinase C and a novel calcium-independent and phospholipid-dependent protein kinase which is inhibited by long chain fatty acyl coenzyme-A. J. Biol. Chem. 266, 9285–9294.
Masson-Gadais, B., P. Salers, P. Bongrand and J.-C. Lissitzky (1997). PKC regulation of microfilament network organization in keratinocytes defined by a pharmacological study with PKC activators and inhibitors. Exp. Cell Res. 236, 238–247.
Meacci, E., V. Vasta, J. P. Moorman, D. A. Bobak, P. Bruni, J. Moss and M. Vaughan (1999). Effect of Rho and ADP-ribosylation factor GTPases on phospholipase D activity in intact human adenocarcinoma A549 cells. J. Biol. Chem. 274, 18605–18612.
Myrdal, S. E. and N. Auersperg (1986). An agent or agents produced by virus-transformed cells cause unregulated ruffling in untransformed cells. J. Cell Biol. 102, 1224–1229.
Pratten, M. K., K. E. Williams and J. B. Lloyd (1977). A quantitative study of pinocytosis and intracellular proteolysis in rat peritoneal macrophages. Biochem. J. 168, 365–372.
Rosen, A., K. F. Keenan, M. Thelen, A. C. Nairn and A. Aderem (1990). Activation of protein kinase C results in the displacement of its myristoylated, alanine-rich substrate from punctate structures in macrophoge filopodia. J. Exp. Med. 172, 1211–1215.
Simon, J. P., I. E. Ivanov, M. Adesnik and D. D. Sabatini (1996). The production of post-Golgi vesicles requires a protein kinase C-like molecule, but not its phosphorylating activity. J. Cell Biol. 135, 355–370.
Steinman, R. M., S. E. Brodie and Z. A. Cohn (1976). Membrane flow during pinocytosis. A stereological analysis. J. Cell Biol. 68, 665–687.
Swanson, J. A. (1989). Phorbol esters stimulate macropinocytosis and solute flow through macrophages. J. Cell Sci. 94, 135–142.
Swanson, J. A., B. D. Yirinec and S. C. Silverstein (1985). Phorbol esters and horseradish peroxidase stimulate pinocytosis and redirect the flow of pinocytosed fluid in macrophages. J. Cell Biol. 100, 851–859.
Thelen, M., A. Rosen, A. C. Nairn and A. Aderem (1991). Regulation by phosphorylation of reversible association of a myristoylated protein kinase C substrate with the plasma membrane. Nature 351, 320–322.
Vitale, M. L., A. Rodriguezn Del Castillo and J. M. Trifaro (1992). Protein kinase C activation by phorbol esters induces chromaffin cell cortical filamentous actin disassembly and increases the initial rate of exocytosis in response to nicotinic receptor stimulation. Neuroscience 51, 463–474.
Author information
Authors and Affiliations
Additional information
This revised version submitted December, 2000. Research supported in part by a grant from the National Institutes of Health, R15 CA78322-01.
Rights and permissions
About this article
Cite this article
Heckman, C.A., Runyeon, C.S., Wade, J.G. et al. Mathematical modeling of marker influx and efflux in cells. Bull. Math. Biol. 63, 431–449 (2001). https://doi.org/10.1006/bulm.2001.0216
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1006/bulm.2001.0216