{"id":{"repo_id":"auckland-ms","oai_identifier":"oai:researchspace.auckland.ac.nz:2292/20068"},"canonical_url":"https://search.dev.ndltd.org/etd/auckland-ms/oai:researchspace.auckland.ac.nz:2292/20068","repository":{"repo_id":"auckland-ms","name":"University of Auckland","base_url":"https://researchspace.auckland.ac.nz/server/oai/request"},"display":{"title":"A mathematical study of the role of calcium in the regulation of saliva secretion","abstract":"Xerostomia is estimated to affect 30% of adults over the age of 65. The condition is characterised by a lack of saliva secretion, resulting in a range of health problems. A rise in the concentration of free cytosolic calcium (Ca²⁺) is essential to initiate saliva secretion. We construct mathematical models of saliva secretion and Ca²⁺ dynamics in salivary acinar and duct cells. We investigate how the distribution of K⁺ channels affects the rate of primary saliva secretion. Maximum saliva secretion is hypothesised to occur when a small amount of K⁺ conductance is located in the apical membrane, with the majority in the basolateral membrane. Apical K⁺ channels have since been experimentally located. For a range of applied agonist, the concentration of Ca²⁺ in salivary cells is seen experimentally to oscillate and to travel in waves across the cytosol. We construct a model of Ca2+ oscillations in parotid acinar cells that requires paired oscillations of IP₃. This ODE model reproduces a number of experimentally observed phenomena. The model is later spatially extended. An inhomogeneous distribution of Ca²⁺ channels is shown to produce apical to basal Ca²⁺ waves, as seen experimentally. We investigate how Ca²⁺ wave properties affect the rate of saliva secretion. Mean Ca²⁺ concentration is found to be the most significant property in regulating secretion. Wave speed was found to encode a range of secretion rates. Ca²⁺ oscillation frequency and amplitude had little effect on the fluid secretion rate. Recent experimental results show coupled oscillations of Ca²⁺ and IP3 in HSY cells, a duct cell line. We present a mathematical model of HSY cells in which IP₃ oscillations are not required for the generation of Ca²⁺ oscillations. The inclusion of passive IP₃ oscillations is shown to increase the Ca²⁺ oscillation frequency range and be consistent with the experimental data. These single-cell models provide insight into the regulation of saliva secretion by themselves. They also suggest what is important to include, and what can be simplified in constructing a whole-organ model. With a greater understanding of the regulation of saliva secretion, and the role Ca²⁺ plays, it is hoped that we might learn how salivary gland dysfunction occurs.","abstract_html":"Xerostomia is estimated to affect 30% of adults over the age of 65. The condition is characterised by a lack of saliva secretion, resulting in a range of health problems. A rise in the concentration of free cytosolic calcium (Ca²⁺) is essential to initiate saliva secretion. We construct mathematical models of saliva secretion and Ca²⁺ dynamics in salivary acinar and duct cells. We investigate how the distribution of K⁺ channels affects the rate of primary saliva secretion. Maximum saliva secretion is hypothesised to occur when a small amount of K⁺ conductance is located in the apical membrane, with the majority in the basolateral membrane. Apical K⁺ channels have since been experimentally located. For a range of applied agonist, the concentration of Ca²⁺ in salivary cells is seen experimentally to oscillate and to travel in waves across the cytosol. We construct a model of Ca2+ oscillations in parotid acinar cells that requires paired oscillations of IP₃. This ODE model reproduces a number of experimentally observed phenomena. The model is later spatially extended. An inhomogeneous distribution of Ca²⁺ channels is shown to produce apical to basal Ca²⁺ waves, as seen experimentally. We investigate how Ca²⁺ wave properties affect the rate of saliva secretion. Mean Ca²⁺ concentration is found to be the most significant property in regulating secretion. Wave speed was found to encode a range of secretion rates. Ca²⁺ oscillation frequency and amplitude had little effect on the fluid secretion rate. Recent experimental results show coupled oscillations of Ca²⁺ and IP3 in HSY cells, a duct cell line. We present a mathematical model of HSY cells in which IP₃ oscillations are not required for the generation of Ca²⁺ oscillations. The inclusion of passive IP₃ oscillations is shown to increase the Ca²⁺ oscillation frequency range and be consistent with the experimental data. These single-cell models provide insight into the regulation of saliva secretion by themselves. They also suggest what is important to include, and what can be simplified in constructing a whole-organ model. With a greater understanding of the regulation of saliva secretion, and the role Ca²⁺ plays, it is hoped that we might learn how salivary gland dysfunction occurs.","abstract_has_math":false,"creators":["Palk, Laurence"],"institution":"ResearchSpace@Auckland","degree_name":"PhD","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Sneyd, J","Crampin, E"],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-24T01:04:15Z","subjects":[],"languages":[],"rights":["Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. 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Maximum saliva secretion is hypothesised to occur when a small amount of K⁺ conductance is located in the apical membrane, with the majority in the basolateral membrane. Apical K⁺ channels have since been experimentally located. For a range of applied agonist, the concentration of Ca²⁺ in salivary cells is seen experimentally to oscillate and to travel in waves across the cytosol. We construct a model of Ca2+ oscillations in parotid acinar cells that requires paired oscillations of IP₃. This ODE model reproduces a number of experimentally observed phenomena. The model is later spatially extended. An inhomogeneous distribution of Ca²⁺ channels is shown to produce apical to basal Ca²⁺ waves, as seen experimentally. We investigate how Ca²⁺ wave properties affect the rate of saliva secretion. Mean Ca²⁺ concentration is found to be the most significant property in regulating secretion. Wave speed was found to encode a range of secretion rates. Ca²⁺ oscillation frequency and amplitude had little effect on the fluid secretion rate. Recent experimental results show coupled oscillations of Ca²⁺ and IP3 in HSY cells, a duct cell line. We present a mathematical model of HSY cells in which IP₃ oscillations are not required for the generation of Ca²⁺ oscillations. The inclusion of passive IP₃ oscillations is shown to increase the Ca²⁺ oscillation frequency range and be consistent with the experimental data. These single-cell models provide insight into the regulation of saliva secretion by themselves. They also suggest what is important to include, and what can be simplified in constructing a whole-organ model. With a greater understanding of the regulation of saliva secretion, and the role Ca²⁺ plays, it is hoped that we might learn how salivary gland dysfunction occurs."]},{"key":"dc:title","label":"Title","values":["A mathematical study of the role of calcium in the regulation of saliva secretion"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sneyd, J","Crampin, E"],"dc:creator":["Palk, Laurence"],"dc:date.accessioned":["2013-02-27T20:04:52Z"],"dc:date.issued":["2012"],"dc:description.abstract":["Xerostomia is estimated to affect 30% of adults over the age of 65. The condition is characterised by a lack of saliva secretion, resulting in a range of health problems. A rise in the concentration of free cytosolic calcium (Ca²⁺) is essential to initiate saliva secretion. We construct mathematical models of saliva secretion and Ca²⁺ dynamics in salivary acinar and duct cells. We investigate how the distribution of K⁺ channels affects the rate of primary saliva secretion. Maximum saliva secretion is hypothesised to occur when a small amount of K⁺ conductance is located in the apical membrane, with the majority in the basolateral membrane. Apical K⁺ channels have since been experimentally located. For a range of applied agonist, the concentration of Ca²⁺ in salivary cells is seen experimentally to oscillate and to travel in waves across the cytosol. We construct a model of Ca2+ oscillations in parotid acinar cells that requires paired oscillations of IP₃. This ODE model reproduces a number of experimentally observed phenomena. The model is later spatially extended. An inhomogeneous distribution of Ca²⁺ channels is shown to produce apical to basal Ca²⁺ waves, as seen experimentally. We investigate how Ca²⁺ wave properties affect the rate of saliva secretion. Mean Ca²⁺ concentration is found to be the most significant property in regulating secretion. Wave speed was found to encode a range of secretion rates. Ca²⁺ oscillation frequency and amplitude had little effect on the fluid secretion rate. Recent experimental results show coupled oscillations of Ca²⁺ and IP3 in HSY cells, a duct cell line. We present a mathematical model of HSY cells in which IP₃ oscillations are not required for the generation of Ca²⁺ oscillations. The inclusion of passive IP₃ oscillations is shown to increase the Ca²⁺ oscillation frequency range and be consistent with the experimental data. These single-cell models provide insight into the regulation of saliva secretion by themselves. They also suggest what is important to include, and what can be simplified in constructing a whole-organ model. With a greater understanding of the regulation of saliva secretion, and the role Ca²⁺ plays, it is hoped that we might learn how salivary gland dysfunction occurs."],"dc:identifier.uri":["https://hdl.handle.net/2292/20068"],"dc:publisher":["ResearchSpace@Auckland"],"dc:rights":["Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher."],"dc:rights.uri":["https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm"],"dc:title":["A mathematical study of the role of calcium in the regulation of saliva secretion"],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["PhD"],"thesis:institution_name":["The University of Auckland"]},"updated_at":"2026-07-24T01:04:15Z"}