Nanoscale mathematical modeling of synaptic transmission, calcium dynamics, transduction and cell sensing

# poster: Bursting versus spiking: Systematic investigation of how patterns of electrical activity control local Ca\textsuperscript{2+} and hormone release

speaker: Iulia Martina Bulai (Università di Padova)

abstract: In this work we focus our attention on how electrical activity of endocrine cells control hormone secretion, considering both spiking, the repetition of a brief electrical activity, and bursting, silent phases interspersed by active ones. In particular we study how the cell's electrical activity affects local Ca\textsuperscript{2+} dynamics and hormone release 1,2,3.

We are interested in how the dynamics of spiking and bursting influence Ca\textsuperscript{2+} dynamics and exocytosis. We consider three different types of spiking and bursting, which we call fast, medium and slow, respectively, characterized by the duration of the active and silent phases. Fast spiking is defined by 0.1 sec of active and silent phases, respectively. Medium spiking consist of 0.2 sec of active and silent phases, respectively, and the slow one has 0.1 sec of active phase and 0.5 sec or 0.9 sec of silent phase. The fast bursting is defined by 0.4 sec of active phase and 0.2 sec of silent phase, the medium one by 0.4 sec of active and silent phase, and the slow one by 0.4 sec of active phase and 0.6 sec of silent phase.

The softwares Matlab and CalC have been used for the simulations. We assume to work with a spherical cell of diameter 13 $$\mu$$m. Ca\textsuperscript{2+} diffusion and buffering are simulated in a conical region of the sphere. The channel is located at the center of the cone base on the surface of the sphere. We define the action potential $$V$$, and assume a stochastic dynamics of the channels.

The calcium current is computed with Matlab while CalC is used to compute the Ca\textsuperscript{2+} dynamics in time and space. Finally the exocytosis model introduced in 4 is used to simulate hormone release.

We found that fast bursting and fast spiking cause the largest influx of Ca\textsuperscript{2+} and thus exoytosis, followed by medium spiking and bursting and slow bursting and spiking respectively. To measure the efficiency of Ca\textsuperscript{2+} in triggering exocytosis, we plotted the cumulative number of fused granules ($$E$$) versus the integral of the measured Ca\textsuperscript{2+}-current ($$Q$$) at 5 different distances (30 nm, 100 nm, 200 nm, 300 nm and 500 nm) from the Ca\textsuperscript{2+} channel. We observed that close to the channel (30 nm) the $$E$$-vs-$$Q$$ curves for the different types of bursting and spiking are virtually superimposed, while further from the Ca\textsuperscript{2+} channel ($$\geq 200$$ nm) the curves deviate, and bursting has generally higher Ca\textsuperscript{2+}-efficiency than spiking.

References

1 A. Tagliavini, J. Tabak, R. Bertram, M.G. Pedersen, Is bursting more effective than spiking in evoking pituitary hormone secretion? A spatiotemporal simulation study of calcium and granule dynamics, American Journal of Physiology-Endocrinology and Metabolism, 310 (2016) E515-E525.

2 M.G. Pedersen, On depolarization-evoked exocytosis as a function of calcium entry: possibilities and pitfalls, Biophys J., 101(7) (2011) 793-802.

3 M. G. Pedersen, A. Tagliavini, G. Cortese, M. Riz, F. Montefusco, Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells, Mathematical Biosciences, 283 (2017) 60-70.

4 T. Voets, Dissection of three Ca\textsuperscript{2+} -dependent steps leading to secretion in chromaffin cells from mouse adrenal slices, Neuron, 28(2) (2000) 537-45.

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