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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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Distribution of puff sizes: change of behavior with the radius of                            influence and comparison with observations.We show the probabiliy, , of having a puff with  open channels obtained with our model for , ,  and  (solid circles),  (open circles) and  (triangles). Each curve corresponds to 500                            realizations of the model. We observe a transition from a Ca-dominated to a IP-binding dominated stochasticity distribution as  increases. Superimposed with bars: experimental data                            taken from Fig. 4D                            of [1].
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pone-0008997-g002: Distribution of puff sizes: change of behavior with the radius of influence and comparison with observations.We show the probabiliy, , of having a puff with open channels obtained with our model for , , and (solid circles), (open circles) and (triangles). Each curve corresponds to 500 realizations of the model. We observe a transition from a Ca-dominated to a IP-binding dominated stochasticity distribution as increases. Superimposed with bars: experimental data taken from Fig. 4D of [1].

Mentions: A transition from Ca-dominated to IP-binding dominated stochasticity also occurs as is increased, while all other parameters are fixed. In this case, remains unchanged and so does the mean distance between available IPR's, . By changing it is possible to go from a situation in which is small for most events and is Ca-limited to a situation in which is large and is IP-binding limited. This is illustrated in Fig. 2 where we have plotted the distribution of event sizes that we obtain with our model for three different values of . For , the distribution is Ca-coupling limited and is concentrated around . As is increased, the relative frequency of events with small decreases. For , the distribution is IP-binding limited. In this example, is well approximated by a Poisson distribution of parameter (data not shown). The situation in between these extreme cases corresponds to and is able to reproduce reasonably well the experimental distribution of Fig. 4D of [1] (superimposed with bars in Fig. 2).


Intra-cluster percolation of calcium signals.

Solovey G, Dawson SP - PLoS ONE (2010)

Distribution of puff sizes: change of behavior with the radius of                            influence and comparison with observations.We show the probabiliy, , of having a puff with  open channels obtained with our model for , ,  and  (solid circles),  (open circles) and  (triangles). Each curve corresponds to 500                            realizations of the model. We observe a transition from a Ca-dominated to a IP-binding dominated stochasticity distribution as  increases. Superimposed with bars: experimental data                            taken from Fig. 4D                            of [1].
© Copyright Policy
Related In: Results  -  Collection

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

pone-0008997-g002: Distribution of puff sizes: change of behavior with the radius of influence and comparison with observations.We show the probabiliy, , of having a puff with open channels obtained with our model for , , and (solid circles), (open circles) and (triangles). Each curve corresponds to 500 realizations of the model. We observe a transition from a Ca-dominated to a IP-binding dominated stochasticity distribution as increases. Superimposed with bars: experimental data taken from Fig. 4D of [1].
Mentions: A transition from Ca-dominated to IP-binding dominated stochasticity also occurs as is increased, while all other parameters are fixed. In this case, remains unchanged and so does the mean distance between available IPR's, . By changing it is possible to go from a situation in which is small for most events and is Ca-limited to a situation in which is large and is IP-binding limited. This is illustrated in Fig. 2 where we have plotted the distribution of event sizes that we obtain with our model for three different values of . For , the distribution is Ca-coupling limited and is concentrated around . As is increased, the relative frequency of events with small decreases. For , the distribution is IP-binding limited. In this example, is well approximated by a Poisson distribution of parameter (data not shown). The situation in between these extreme cases corresponds to and is able to reproduce reasonably well the experimental distribution of Fig. 4D of [1] (superimposed with bars in Fig. 2).

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