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Section DYNAMICS IN LIFE SCIENCES, NEUROSCIENCE APPLICATIONS WORKSHOP
Quantification of Fast Presynaptic Ca2+ Kinetics Using Non-Stationary Single Compartment Model
Y. Timofeeva1,2 *, D.A. Rusakov3, K.E. Volynski3
1 Department of Computer Science ,
2 Centre for Complexity Science, University of Warwick, Coventry, UK;
3 UCL Institute of Neurology, London, UK.
* Presenting e-mail: Y.Timofeeva@warwick.ac.uk
Fluorescence imaging is an important tool in examining Ca2+ -dependent machinery of synaptic transmission. Classically, deriving the kinetics of free Ca2+ from the fluorescence recorded inside small cellular structures has relied on singe-compartment models of Ca2+ entry, buffering and removal. In many cases, steady-state approximation of Ca2+ binding reactions in such a model allows elegant analytical solutions for the Ca2+ kinetics in question1-3. However, the fast rate of action potential driven Ca2+ influx can be comparable with the rate of Ca2+ buffering inside the synaptic terminal. In this case, computations that reflect non-stationary changes in the system might be required for obtaining essential information about rapid transients of intracellular free Ca2+ refs4-6. Based on the experimental data we propose an improved procedure to evaluate the underlying presynaptic Ca2+ kinetics. We show that in most cases the non-stationary single compartment model provides accurate estimates of action-potential evoked presynaptic Ca2+ concentration transients, similar to that obtained with the full 3D diffusion model. Based on this we develop a computational tool aimed at stochastic optimisation and cross-validation of the kinetic parameters based on a single set of experimental conditions. The proposed methodology provides robust estimation of Ca2+ kinetics even when a priori information about endogenous Ca2+ buffering is limited.
References
1. Rozov et al. J. Physiol. (2001).
2. Maravall et al. Biophys. J. (2000).
3. Helmchen et al. Biophys. J. (1997).
4. Scott & Rusakov J. Neurosci. (2006).
5. Ermolyuk et al. PLoS Biol. (2012).
6. Ermolyuk et al. Nat. Neurosci. (2013).
Bursting Synchronization, Pattern Bifurcations and Control Strategies of Central Pattern Generators
Roberto Barrio1 *, Alvaro Lozano2, Marcos Rodríguez2, Sergio Serrano1, Andrey Shilnikov3
1 University of Zaragoza, Zaragoza, Spain;
2 Centro Universitario de la Defensa, Zaragoza, Spain;
3 Georgia State University, Atlanta, USA. * Presenting e-mail: rbarrio@unizar.es
The study of the synchronization patterns of small neuron networks that control several biological processes has become an interesting growing discipline (Wojcik et al., 2014). The development of new methods to help in the visualization and location of these synchronization patterns is currently a quite important task. A direct approach to study bursting rhythmic patterns of small neuron networks (see (Wojcik et al., 2014)) is the analysis of fixed points (FPs) and invariant cycles (ICs) in the Poincare return map for phase lags between neurons. That is, in a 3-cell network, we take one cell as the reference one and we study the phase lags q>_21, q>_31. With these data for several initial phase lags, we can generate a bidimensional picture with the evolution of the delays showing the convergence to different rhythmic patterns. Using the combination of these techniques we are able to aggregate big data to parametrically continue FPs and ICs of the maps and to fully disclose their bifurcation unfoldings as the network configuration is varied (Barrio et al., 2015). In Fig. 1 we show how the use of these techniques may reveal (Barrio et al., 2015) the existence of heteroclinic cycles (it is shown the previous limit cycle before the bifurcation giving rise to the heteroclinic cycle) between saddle fixed points (FP) and invariant circles (IC) in a 3-cell Central Pattern Generator (CPG) network of leech heart neurons. Such a cycle underlies a robust "jiggling" behavior in bursting synchronization (Barrio et al., 2015).
38 Opera Med Physiol 2016 Vol. 2 (S1)
