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Intra-cluster percolation of calcium signals.

Solovey G, Dawson SP - PLoS ONE (2010)

Bottom Line: IP3R's areusually organized in clusters on the membrane of the endoplasmic reticulum and their spatial distribution has important effects on the resulting signal.The largest distance over which Ca2+-mediated coupling acts and the density of IP3-bound IP3R's of the cluster can also be estimated.The approach allows us to infer properties of the interactions among the channels of the cluster from statistical information on their emergent collective behavior.

View Article: PubMed Central - PubMed

Affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales-Universidad de Buenos Aires, Buenos Aires, Argentina. gsolovey@df.uba.ar

ABSTRACT
Calcium signals are involved in a large variety of physiological processes. Their versatility relies on the diversity of spatiotemporal behaviors that the calcium concentration can display. Calcium entry through inositol 1,4,5-trisphosphate (IP3) receptors (IP3R's) is a key component that participates in both local signals such as "puffs" and in global waves. IP3R's areusually organized in clusters on the membrane of the endoplasmic reticulum and their spatial distribution has important effects on the resulting signal. Recent high resolution observations of Ca2+ puffs offer a window to study intra-cluster organization. The experiments give the distribution of the number of IP3R's that open during each puff without much processing. Here we present a simple model with which we interpret the experimental distribution in terms of two stochastic processes: IP3 binding and unbinding and Ca2+-mediated inter-channel coupling. Depending on the parameters of the system, the distribution may be dominated by one or the other process. The transition between both extreme case sis similar to a percolation process. We show how, from an analysis of the experimental distribution, information can be obtained on the relative weight of the two processes. The largest distance over which Ca2+-mediated coupling acts and the density of IP3-bound IP3R's of the cluster can also be estimated. The approach allows us to infer properties of the interactions among the channels of the cluster from statistical information on their emergent collective behavior.

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Percolation transition: when all available channels open during a                            puff.A: Probability that all available IPR's become open, , as a function of the dimensionless radius of                            influence, , for  (circles),  (squares) and  (triangles). B:  (circles),  (squares) and  (triangles) as functions of . The values of  and  for the case with  are indicated in A with one and two asterisks,                            respectively.
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pone-0008997-g003: Percolation transition: when all available channels open during a puff.A: Probability that all available IPR's become open, , as a function of the dimensionless radius of influence, , for (circles), (squares) and (triangles). B: (circles), (squares) and (triangles) as functions of . The values of and for the case with are indicated in A with one and two asterisks, respectively.

Mentions: In the Ca limited behavior the number of open channels, , is small for most events, regardless of the value of . This implies for almost all events. In the IP-binding limited behavior all available IPR's become open ( in most cases). Therefore, in order to analyze the transition between the Ca-dominated to IP-binding dominated stochasticity, we study how often events occur for which all available IPR's become open. This happens trivially for events with . Here we are interested in situations with . To this end, we compute numerically the probability that all available IPR's, , become open, , which is a function of and of only one independent parameter, the dimensionless radius of influence, , (see Methods). We plot in Fig. 3 A as a function of , for (circles), (squares) and (triangles). As expected, is an increasing function of for each value of . We also observe that is an increasing (sigmoidal-like) function of that goes from 0 (i.e. in almost all cases, which corresponds to Ca-dominated stochasticity) to 1 (i.e. in almost all cases, which corresponds to IP-binding dominated stochasticity) and that such transition occurs over a smaller interval of values the larger is.


Intra-cluster percolation of calcium signals.

Solovey G, Dawson SP - PLoS ONE (2010)

Percolation transition: when all available channels open during a                            puff.A: Probability that all available IPR's become open, , as a function of the dimensionless radius of                            influence, , for  (circles),  (squares) and  (triangles). B:  (circles),  (squares) and  (triangles) as functions of . The values of  and  for the case with  are indicated in A with one and two asterisks,                            respectively.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2823777&req=5

pone-0008997-g003: Percolation transition: when all available channels open during a puff.A: Probability that all available IPR's become open, , as a function of the dimensionless radius of influence, , for (circles), (squares) and (triangles). B: (circles), (squares) and (triangles) as functions of . The values of and for the case with are indicated in A with one and two asterisks, respectively.
Mentions: In the Ca limited behavior the number of open channels, , is small for most events, regardless of the value of . This implies for almost all events. In the IP-binding limited behavior all available IPR's become open ( in most cases). Therefore, in order to analyze the transition between the Ca-dominated to IP-binding dominated stochasticity, we study how often events occur for which all available IPR's become open. This happens trivially for events with . Here we are interested in situations with . To this end, we compute numerically the probability that all available IPR's, , become open, , which is a function of and of only one independent parameter, the dimensionless radius of influence, , (see Methods). We plot in Fig. 3 A as a function of , for (circles), (squares) and (triangles). As expected, is an increasing function of for each value of . We also observe that is an increasing (sigmoidal-like) function of that goes from 0 (i.e. in almost all cases, which corresponds to Ca-dominated stochasticity) to 1 (i.e. in almost all cases, which corresponds to IP-binding dominated stochasticity) and that such transition occurs over a smaller interval of values the larger is.

Bottom Line: IP3R's areusually organized in clusters on the membrane of the endoplasmic reticulum and their spatial distribution has important effects on the resulting signal.The largest distance over which Ca2+-mediated coupling acts and the density of IP3-bound IP3R's of the cluster can also be estimated.The approach allows us to infer properties of the interactions among the channels of the cluster from statistical information on their emergent collective behavior.

View Article: PubMed Central - PubMed

Affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales-Universidad de Buenos Aires, Buenos Aires, Argentina. gsolovey@df.uba.ar

ABSTRACT
Calcium signals are involved in a large variety of physiological processes. Their versatility relies on the diversity of spatiotemporal behaviors that the calcium concentration can display. Calcium entry through inositol 1,4,5-trisphosphate (IP3) receptors (IP3R's) is a key component that participates in both local signals such as "puffs" and in global waves. IP3R's areusually organized in clusters on the membrane of the endoplasmic reticulum and their spatial distribution has important effects on the resulting signal. Recent high resolution observations of Ca2+ puffs offer a window to study intra-cluster organization. The experiments give the distribution of the number of IP3R's that open during each puff without much processing. Here we present a simple model with which we interpret the experimental distribution in terms of two stochastic processes: IP3 binding and unbinding and Ca2+-mediated inter-channel coupling. Depending on the parameters of the system, the distribution may be dominated by one or the other process. The transition between both extreme case sis similar to a percolation process. We show how, from an analysis of the experimental distribution, information can be obtained on the relative weight of the two processes. The largest distance over which Ca2+-mediated coupling acts and the density of IP3-bound IP3R's of the cluster can also be estimated. The approach allows us to infer properties of the interactions among the channels of the cluster from statistical information on their emergent collective behavior.

Show MeSH