Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors
Considerable insight into intracellular Ca 2 + responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate ( IP 3 ) receptor Ca 2 + channel. However, a limitation of most whole cell...
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| Veröffentlicht in: | Journal of theoretical biology 2008-07, Vol.253 (1), p.170-188 |
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| creator | Williams, George S.B. Molinelli, Evan J. Smith, Gregory D. |
| description | Considerable insight into intracellular
Ca
2
+
responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate (
IP
3
) receptor
Ca
2
+
channel. However, a limitation of most whole cell models to date is the assumption that
IP
3
receptor
Ca
2
+
channels (
IP
3
R
s) are globally coupled by a “continuously stirred” bulk cytosolic [
Ca
2
+
], when in fact open
IP
3
R
s experience elevated “domain”
Ca
2
+
concentrations. Here we present a
2
N
+
2
-compartment whole cell model of local and global
Ca
2
+
responses mediated by
N
=
100
,
000
diffusely distributed
IP
3
R
s, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal
Ca
2
+
concentrations, and the remaining
2
N
compartments represent time-dependent cytosolic and luminal
Ca
2
+
domains associated with each
IP
3
R
. Using this Monte Carlo model as a starting point, we present an alternative formulation that solves a system of advection–reaction equations for the probability density of cytosolic and luminal domain [
Ca
2
+
] jointly distributed with
IP
3
R
state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [
Ca
2
+
], a realistic but minimal model of whole cell
Ca
2
+
dynamics is produced that accounts for the influence of local
Ca
2
+
signaling on channel gating and global
Ca
2
+
responses. The probability density approach is benchmarked and validated by comparison to Monte Carlo simulations, and the two methods are shown to agree when the number of
Ca
2
+
channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of
Ca
2
+
domain formation and collapse (both cytosolic and luminal) may influence global
Ca
2
+
oscillations, and we derive two reduced models of global
Ca
2
+
dynamics that account for the influence of local
Ca
2
+
signaling on global
Ca
2
+
dynamics when there is a separation of time scales between the stochastic gating of
IP
3
R
s and the dynamics of domain
Ca
2
+
. |
| doi_str_mv | 10.1016/j.jtbi.2008.02.040 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_69216034</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0022519308001136</els_id><sourcerecordid>20820824</sourcerecordid><originalsourceid>FETCH-LOGICAL-c385t-8aa2fc437a8c8c08845e7238306a6ffd0d1a45fcaa57a68ecb9206a1197a2d983</originalsourceid><addsrcrecordid>eNqFUcGKFDEQDaK44-oPeJCcPG23lXTSkwYvsuyqsLIXPYfqJL1myHTaJC3sdb_cNDPgTaFCFan3HtR7hLxl0DJg_YdDeyijbzmAaoG3IOAZ2TEYZKOkYM_JDoDzRrKhuyCvcj4AwCC6_iW5YEqAHDjsyNO3aF3w8wMN0WCgOFv6EOJYRz-XhMaFsAZMtC6NX480ubzEObtMj856LM7S8ZFaP01rdmGbckl-XLeFn2P2JQbKrsSVbOp_Xn7G-iqtChm3lJjya_JiwpDdm3O_JD9ub75ff2nu7j9_vf5015hOydIoRD4Z0e1RGWVAKSHdnneqgx77abJgGQo5GUS5x145M9YDe2Rs2CO3g-ouyfuT7pLir9Xloo8-b_fh7OKadT9w1kMn_gvkoLbagPwENCnmnNykl-SPmB41A71FpA96i0hvEWngukZUSe_O6utYLfxLOWdSAR9PAFfN-O1d0tl4N5tqd_WsaBv9v_T_AGpMpQc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>20820824</pqid></control><display><type>article</type><title>Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors</title><source>MEDLINE</source><source>Elsevier ScienceDirect Journals</source><creator>Williams, George S.B. ; Molinelli, Evan J. ; Smith, Gregory D.</creator><creatorcontrib>Williams, George S.B. ; Molinelli, Evan J. ; Smith, Gregory D.</creatorcontrib><description>Considerable insight into intracellular
Ca
2
+
responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate (
IP
3
) receptor
Ca
2
+
channel. However, a limitation of most whole cell models to date is the assumption that
IP
3
receptor
Ca
2
+
channels (
IP
3
R
s) are globally coupled by a “continuously stirred” bulk cytosolic [
Ca
2
+
], when in fact open
IP
3
R
s experience elevated “domain”
Ca
2
+
concentrations. Here we present a
2
N
+
2
-compartment whole cell model of local and global
Ca
2
+
responses mediated by
N
=
100
,
000
diffusely distributed
IP
3
R
s, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal
Ca
2
+
concentrations, and the remaining
2
N
compartments represent time-dependent cytosolic and luminal
Ca
2
+
domains associated with each
IP
3
R
. Using this Monte Carlo model as a starting point, we present an alternative formulation that solves a system of advection–reaction equations for the probability density of cytosolic and luminal domain [
Ca
2
+
] jointly distributed with
IP
3
R
state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [
Ca
2
+
], a realistic but minimal model of whole cell
Ca
2
+
dynamics is produced that accounts for the influence of local
Ca
2
+
signaling on channel gating and global
Ca
2
+
responses. The probability density approach is benchmarked and validated by comparison to Monte Carlo simulations, and the two methods are shown to agree when the number of
Ca
2
+
channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of
Ca
2
+
domain formation and collapse (both cytosolic and luminal) may influence global
Ca
2
+
oscillations, and we derive two reduced models of global
Ca
2
+
dynamics that account for the influence of local
Ca
2
+
signaling on global
Ca
2
+
dynamics when there is a separation of time scales between the stochastic gating of
IP
3
R
s and the dynamics of domain
Ca
2
+
.</description><identifier>ISSN: 0022-5193</identifier><identifier>EISSN: 1095-8541</identifier><identifier>DOI: 10.1016/j.jtbi.2008.02.040</identifier><identifier>PMID: 18405920</identifier><language>eng</language><publisher>England: Elsevier Ltd</publisher><subject>Animals ; Calcium - metabolism ; Calcium Channels - metabolism ; Calcium domain ; Calcium oscillations ; Calcium Signaling ; Computer Simulation ; Cytosol - metabolism ; Inositol 1,4,5-Trisphosphate - metabolism ; Inositol 1,4,5-Trisphosphate Receptors - metabolism ; Ion Channel Gating ; Local calcium signaling ; Markov chain ; Markov Chains ; Models, Biological ; Models, Chemical ; Monte Carlo Method ; Probability density ; Stochastic gating ; Whole cell model</subject><ispartof>Journal of theoretical biology, 2008-07, Vol.253 (1), p.170-188</ispartof><rights>2008 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c385t-8aa2fc437a8c8c08845e7238306a6ffd0d1a45fcaa57a68ecb9206a1197a2d983</citedby><cites>FETCH-LOGICAL-c385t-8aa2fc437a8c8c08845e7238306a6ffd0d1a45fcaa57a68ecb9206a1197a2d983</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0022519308001136$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65534</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/18405920$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Williams, George S.B.</creatorcontrib><creatorcontrib>Molinelli, Evan J.</creatorcontrib><creatorcontrib>Smith, Gregory D.</creatorcontrib><title>Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors</title><title>Journal of theoretical biology</title><addtitle>J Theor Biol</addtitle><description>Considerable insight into intracellular
Ca
2
+
responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate (
IP
3
) receptor
Ca
2
+
channel. However, a limitation of most whole cell models to date is the assumption that
IP
3
receptor
Ca
2
+
channels (
IP
3
R
s) are globally coupled by a “continuously stirred” bulk cytosolic [
Ca
2
+
], when in fact open
IP
3
R
s experience elevated “domain”
Ca
2
+
concentrations. Here we present a
2
N
+
2
-compartment whole cell model of local and global
Ca
2
+
responses mediated by
N
=
100
,
000
diffusely distributed
IP
3
R
s, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal
Ca
2
+
concentrations, and the remaining
2
N
compartments represent time-dependent cytosolic and luminal
Ca
2
+
domains associated with each
IP
3
R
. Using this Monte Carlo model as a starting point, we present an alternative formulation that solves a system of advection–reaction equations for the probability density of cytosolic and luminal domain [
Ca
2
+
] jointly distributed with
IP
3
R
state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [
Ca
2
+
], a realistic but minimal model of whole cell
Ca
2
+
dynamics is produced that accounts for the influence of local
Ca
2
+
signaling on channel gating and global
Ca
2
+
responses. The probability density approach is benchmarked and validated by comparison to Monte Carlo simulations, and the two methods are shown to agree when the number of
Ca
2
+
channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of
Ca
2
+
domain formation and collapse (both cytosolic and luminal) may influence global
Ca
2
+
oscillations, and we derive two reduced models of global
Ca
2
+
dynamics that account for the influence of local
Ca
2
+
signaling on global
Ca
2
+
dynamics when there is a separation of time scales between the stochastic gating of
IP
3
R
s and the dynamics of domain
Ca
2
+
.</description><subject>Animals</subject><subject>Calcium - metabolism</subject><subject>Calcium Channels - metabolism</subject><subject>Calcium domain</subject><subject>Calcium oscillations</subject><subject>Calcium Signaling</subject><subject>Computer Simulation</subject><subject>Cytosol - metabolism</subject><subject>Inositol 1,4,5-Trisphosphate - metabolism</subject><subject>Inositol 1,4,5-Trisphosphate Receptors - metabolism</subject><subject>Ion Channel Gating</subject><subject>Local calcium signaling</subject><subject>Markov chain</subject><subject>Markov Chains</subject><subject>Models, Biological</subject><subject>Models, Chemical</subject><subject>Monte Carlo Method</subject><subject>Probability density</subject><subject>Stochastic gating</subject><subject>Whole cell model</subject><issn>0022-5193</issn><issn>1095-8541</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFUcGKFDEQDaK44-oPeJCcPG23lXTSkwYvsuyqsLIXPYfqJL1myHTaJC3sdb_cNDPgTaFCFan3HtR7hLxl0DJg_YdDeyijbzmAaoG3IOAZ2TEYZKOkYM_JDoDzRrKhuyCvcj4AwCC6_iW5YEqAHDjsyNO3aF3w8wMN0WCgOFv6EOJYRz-XhMaFsAZMtC6NX480ubzEObtMj856LM7S8ZFaP01rdmGbckl-XLeFn2P2JQbKrsSVbOp_Xn7G-iqtChm3lJjya_JiwpDdm3O_JD9ub75ff2nu7j9_vf5015hOydIoRD4Z0e1RGWVAKSHdnneqgx77abJgGQo5GUS5x145M9YDe2Rs2CO3g-ouyfuT7pLir9Xloo8-b_fh7OKadT9w1kMn_gvkoLbagPwENCnmnNykl-SPmB41A71FpA96i0hvEWngukZUSe_O6utYLfxLOWdSAR9PAFfN-O1d0tl4N5tqd_WsaBv9v_T_AGpMpQc</recordid><startdate>20080707</startdate><enddate>20080707</enddate><creator>Williams, George S.B.</creator><creator>Molinelli, Evan J.</creator><creator>Smith, Gregory D.</creator><general>Elsevier Ltd</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QP</scope><scope>7X8</scope></search><sort><creationdate>20080707</creationdate><title>Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors</title><author>Williams, George S.B. ; Molinelli, Evan J. ; Smith, Gregory D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c385t-8aa2fc437a8c8c08845e7238306a6ffd0d1a45fcaa57a68ecb9206a1197a2d983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Animals</topic><topic>Calcium - metabolism</topic><topic>Calcium Channels - metabolism</topic><topic>Calcium domain</topic><topic>Calcium oscillations</topic><topic>Calcium Signaling</topic><topic>Computer Simulation</topic><topic>Cytosol - metabolism</topic><topic>Inositol 1,4,5-Trisphosphate - metabolism</topic><topic>Inositol 1,4,5-Trisphosphate Receptors - metabolism</topic><topic>Ion Channel Gating</topic><topic>Local calcium signaling</topic><topic>Markov chain</topic><topic>Markov Chains</topic><topic>Models, Biological</topic><topic>Models, Chemical</topic><topic>Monte Carlo Method</topic><topic>Probability density</topic><topic>Stochastic gating</topic><topic>Whole cell model</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Williams, George S.B.</creatorcontrib><creatorcontrib>Molinelli, Evan J.</creatorcontrib><creatorcontrib>Smith, Gregory D.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>MEDLINE - Academic</collection><jtitle>Journal of theoretical biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Williams, George S.B.</au><au>Molinelli, Evan J.</au><au>Smith, Gregory D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors</atitle><jtitle>Journal of theoretical biology</jtitle><addtitle>J Theor Biol</addtitle><date>2008-07-07</date><risdate>2008</risdate><volume>253</volume><issue>1</issue><spage>170</spage><epage>188</epage><pages>170-188</pages><issn>0022-5193</issn><eissn>1095-8541</eissn><abstract>Considerable insight into intracellular
Ca
2
+
responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate (
IP
3
) receptor
Ca
2
+
channel. However, a limitation of most whole cell models to date is the assumption that
IP
3
receptor
Ca
2
+
channels (
IP
3
R
s) are globally coupled by a “continuously stirred” bulk cytosolic [
Ca
2
+
], when in fact open
IP
3
R
s experience elevated “domain”
Ca
2
+
concentrations. Here we present a
2
N
+
2
-compartment whole cell model of local and global
Ca
2
+
responses mediated by
N
=
100
,
000
diffusely distributed
IP
3
R
s, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal
Ca
2
+
concentrations, and the remaining
2
N
compartments represent time-dependent cytosolic and luminal
Ca
2
+
domains associated with each
IP
3
R
. Using this Monte Carlo model as a starting point, we present an alternative formulation that solves a system of advection–reaction equations for the probability density of cytosolic and luminal domain [
Ca
2
+
] jointly distributed with
IP
3
R
state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [
Ca
2
+
], a realistic but minimal model of whole cell
Ca
2
+
dynamics is produced that accounts for the influence of local
Ca
2
+
signaling on channel gating and global
Ca
2
+
responses. The probability density approach is benchmarked and validated by comparison to Monte Carlo simulations, and the two methods are shown to agree when the number of
Ca
2
+
channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of
Ca
2
+
domain formation and collapse (both cytosolic and luminal) may influence global
Ca
2
+
oscillations, and we derive two reduced models of global
Ca
2
+
dynamics that account for the influence of local
Ca
2
+
signaling on global
Ca
2
+
dynamics when there is a separation of time scales between the stochastic gating of
IP
3
R
s and the dynamics of domain
Ca
2
+
.</abstract><cop>England</cop><pub>Elsevier Ltd</pub><pmid>18405920</pmid><doi>10.1016/j.jtbi.2008.02.040</doi><tpages>19</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-5193 |
| ispartof | Journal of theoretical biology, 2008-07, Vol.253 (1), p.170-188 |
| issn | 0022-5193 1095-8541 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_69216034 |
| source | MEDLINE; Elsevier ScienceDirect Journals |
| subjects | Animals Calcium - metabolism Calcium Channels - metabolism Calcium domain Calcium oscillations Calcium Signaling Computer Simulation Cytosol - metabolism Inositol 1,4,5-Trisphosphate - metabolism Inositol 1,4,5-Trisphosphate Receptors - metabolism Ion Channel Gating Local calcium signaling Markov chain Markov Chains Models, Biological Models, Chemical Monte Carlo Method Probability density Stochastic gating Whole cell model |
| title | Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors |
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