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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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Change of behavior with event size.A:  for data obtained with our model using , ,  and  (solid circles). Complementary cumulative Poisson                            distributions, , for  (inverted triangles),  (triangles),  (squares),  (rhombes). B: Error of approximating  by the various  for  (see text for definition) as a function of . Symbols are the same as in A. From this figure we                            choose  as the one that provides the best fit to the tail of . The error in the  case is larger than 0.02 in most cases and falls                            outside the region displayed in the figure. C:  for the four values of  that we tested. We see that .
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pone-0008997-g004: Change of behavior with event size.A: for data obtained with our model using , , and (solid circles). Complementary cumulative Poisson distributions, , for (inverted triangles), (triangles), (squares), (rhombes). B: Error of approximating by the various for (see text for definition) as a function of . Symbols are the same as in A. From this figure we choose as the one that provides the best fit to the tail of . The error in the case is larger than 0.02 in most cases and falls outside the region displayed in the figure. C: for the four values of that we tested. We see that .

Mentions: The procedure is illustrated in Fig. 4 where the “experimental” distribution comes from a simulation of our model with , , and . In this case, . We show in Fig. 4 A the complementary cumulative distribution functions and in Fig. 4 B the errors for the values of that we have considered: (inverted triangles), (triangles), (squares) and (rhombes). Larger values of give very bad approximations and are not shown. We show in Fig. 4 C the values, , obtained for each using the threshold, (shown with a horizontal line in Fig. 4 B). In this example, the best value is for which . We estimate the density of IP-bound IPR's at which the departure between the experimental and the Poisson distribution occurs as , where we have used . Using the relationship displayed in Fig. 3 B, we estimate from which we get . This provides an estimate of the radius of influence which compares very well with the value that was used to generate the data, . Using the same procedure, we analyzed the data presented in Fig. 4D of [1] and obtained assuming .


Intra-cluster percolation of calcium signals.

Solovey G, Dawson SP - PLoS ONE (2010)

Change of behavior with event size.A:  for data obtained with our model using , ,  and  (solid circles). Complementary cumulative Poisson                            distributions, , for  (inverted triangles),  (triangles),  (squares),  (rhombes). B: Error of approximating  by the various  for  (see text for definition) as a function of . Symbols are the same as in A. From this figure we                            choose  as the one that provides the best fit to the tail of . The error in the  case is larger than 0.02 in most cases and falls                            outside the region displayed in the figure. C:  for the four values of  that we tested. We see that .
© Copyright Policy
Related In: Results  -  Collection

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

pone-0008997-g004: Change of behavior with event size.A: for data obtained with our model using , , and (solid circles). Complementary cumulative Poisson distributions, , for (inverted triangles), (triangles), (squares), (rhombes). B: Error of approximating by the various for (see text for definition) as a function of . Symbols are the same as in A. From this figure we choose as the one that provides the best fit to the tail of . The error in the case is larger than 0.02 in most cases and falls outside the region displayed in the figure. C: for the four values of that we tested. We see that .
Mentions: The procedure is illustrated in Fig. 4 where the “experimental” distribution comes from a simulation of our model with , , and . In this case, . We show in Fig. 4 A the complementary cumulative distribution functions and in Fig. 4 B the errors for the values of that we have considered: (inverted triangles), (triangles), (squares) and (rhombes). Larger values of give very bad approximations and are not shown. We show in Fig. 4 C the values, , obtained for each using the threshold, (shown with a horizontal line in Fig. 4 B). In this example, the best value is for which . We estimate the density of IP-bound IPR's at which the departure between the experimental and the Poisson distribution occurs as , where we have used . Using the relationship displayed in Fig. 3 B, we estimate from which we get . This provides an estimate of the radius of influence which compares very well with the value that was used to generate the data, . Using the same procedure, we analyzed the data presented in Fig. 4D of [1] and obtained assuming .

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