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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).
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Fig. 1. Evolution of the time delays after the Andronov-Hopf bifurcation in a 3-cell network of leech heart neurons
Some of these synchronization patterns of individual neurons are related with some undesirable neurologic diseases, and they are believed to play a crucial role in the emergence of pathological rhythmic brain activity in different diseases, like Parkinson's disease. We show how, with a suitable combination of short and weak global inhibitory and excitatory stimuli over the network, we can switch between different stable bursting patterns in small neuron networks (in our case a 3-neuron network). We have developed a systematic study (Lozano et al., 2016) showing and explaining the effects of applying the pulses at different moments. Moreover, we apply the technique on a completely symmetric network and on a slightly perturbed one (a more realistic situation). The approach of using global stimuli, as in the case of applying a current or a chemical substance to all the network, allows one to avoid undesirable synchronization patterns with nonaggressive stimuli. In Fig. 2 we show the result of the use of the global stimuli to the symmetric network.
Fig. 2. Different synchronization patterns and the result of the application of the control strategy to the network
The control technique takes advantage of the information given by detailed biparametric "roadmaps" (Barrio & Shilnikov, 2011; Barrio et al., 2014). Such a roadmap provides an exhaustive information (Wojcik et al., 2014) about the dynamics of a single neuron that one must have in order to build small neuron networks and to study rhythmogenesis in central pattern generators (CPG).
Acknowledgements
R.B., M.R. and S.S. have been supported during this research by the Spanish Research projects MTM2012-31883 and MTM2015-64095-P, the University of Zaragoza/CUD project UZCUD2015-CIE-05 and by the European Social Fund and Diputacion General de Aragon (Grant E48). A.L. has been supported during this research by the Spanish Research project MTM2013-46337-C2-2-P, the University of Zaragoza/CUD project UZCUD2015-CIE-05 and by the European Social Fund and Diputacion General de Aragon (Grant E15). A.S. acknowledges the support from RFFI 11-01-00001, RSF grant 14-41-00044 at the Lobachevsky University of Nizhny Novgorod, and the grant in the agreement of Aug. 27, 2013 N 02.B.49.21.0003 between The Ministry of Education and Science of the Russian Federation and Lobachevsky State University of Nizhni Novgorod (Sections 2-4), as well as NSF grant IOS-1455527.
References
1. WOJCIK J, SCHWABEDAL J., CLEWLEY R. & SHILNIKOV A. (2014): Key bifurcations of bursting polyrhythms in 3-cell central pattern generators, PloS ONE, 9 (4), e92918.
2. LOZANO A., RODRIGUEZ M. & BARRIO R. (2016): Control strategies of 3-cell Central Pattern Generator via global stimuli, Scientific Reports, in press.
3. BARRIO R. & SHILNIKOV A. (2011): Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of the Hindmarsh-Rose model, J Mathematical Neuroscience, 1 (6), 1-22.
4. BARRIO R., MARTINEZ MA., SERRANO S. & SHILNIKOV A. (2014): Macro and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons. Chaos, 24 (2), 023128.
5. BARRIO R., RODRIGUEZ S., SERRANO S. & SHILNIKOV A. (2015): Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network, EPL, 112 (3), 38002.
Frequency and Hemispheric Specialization of Brain Activity in Convergent and Divergent Thinking: the Intelligence Effect
O.M. Razumnikova1,2 *, K.D. Krivonogova1, A.A. Yashanina1,2
1 Novosibirsk State Technical University, Novosibirsk, Russia;
2 State Research Institute of Physiology and Basic Medicine, Novosibirsk, Russia. * Presenting e-mail: razoum@mail.ru
The actual problem of current research in cognitive activity is the study of the organization of different forms of thinking. J. P. Guilford introduced the concepts of convergent and divergent thinking, representing a fundamentally different form of solution to the problem: in the first case, the goal is to find the only correct solution to the problem, while the second - generation of set of alternative ideas [2]. A quantitative measure of the success of convergent thinking (CT) can be considered as the level of intelligence, since it used the criterion of measuring the only answer; the effectiveness of divergent thinking (DT) can estimate the parameters of creativity: fluency generation of ideas and originality. Transition from convergent to divergent thinking in creative problem solving, as well as different points of view on the relationship of intelligence and creativity [4, 7] induce the question about the causes of these differences, which can be resolved at the neurophysiological level. In this regard, the aim of the work was to study the relation of intelligence and changes of bioelectrical activity of the cerebral cortex in convergent and divergent thinking.
The study involved 46 students of NSTU. Verbal, figurative and arithmetic components of intelligence were determined by Amthauer's test. To register 19-channell EEG, the program "Mitsar EEG-201" (St. Petersburg, Russia) was used. EEG was recorded in three functional states: baseline, in situations of CT (sequential addition in the mind of the prime numbers) and DT (decision of heuristic problem). Throughout all experimental conditions (resting, CT, and DT) participants had their eyes closed. Data processing was based on 30 artifact-free EEG signals with Han windowed epochs of 2 s. The averaged spectral power density for the six frequency ranges from delta to beta 2 using fast Fourier transformation was calculated.
CT-induced EEG changes were found in the delta and theta range with increased power delta rhythm, significant for left-hemispheric activity and theta rhythm - the right hemisphere. Delta oscillations during DT increased in both the left and right hemisphere, another EEG correlate of DT was to strengthen the right-hemispheric alpha 2oscillations. The analysis of regional effects showed that the increase of CT associated delta rhythm was represented in the frontal areas, whereas DT - covering widespread cortical areas. The right hemispheric increase of alpha2 rhythm during DT was presented in posterior cortex whereas the left hemispheric effect as compared to the CT was generalized. Given that the change in the power of delta rhythm is associated with "internal" attention while enhancing cognitive load [3], we can conclude that the solution of the heuristic task requires the use of large brain resources, combining the functions of both hemispheres, and changes in the theta rhythm in the CT can be explained by increased support attention needed to perform arithmetic operations and preservation in the working memory of intermediate summation results [6]. DT related changes of alpha2 activity are consistent with the concepts of "defocused" or internal attention required finding an original idea [1,5].
It was found significant positive relationship between the arithmetic intelligence and the success of CT (calculated amount) (see Figure), and between verbal or figurative and spatial components of the intelligence and efficiency of DT (originality of ideas).
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