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A1: Stochastic models for neural dynamics in recurrent cortical networks

A1: Stochastic models for neural dynamics in recurrent cortical networks

Stefan RotterB and Jens TimmerC,M

B = Bernstein Center for Computational Neuroscience;
C = Department of Physics;
M = Center for Data Analysis and Modeling (FDM) .

Scientific background

Recently, numerical studies of large cortical networks based on biologically realistic model neurons yielded new insight into the interplay between the dynamics of neuronal activity and the structure of the underlying network. Stochastic processes were employed to successfully racterize network dynamics and pin down its structural determinants. New methods of statistical data analysis were also derived and successfully applied to problems within and outside the neurosciences. Recent progress in random graph theory provides a suitable theoretical framework to extend the analysis of cortical dynamics to biologically realistic networks.


Activity dynamics in large recurrent networks of spiking neurons will be tackled using probabilistic models. Applying the resulting tools complements numerical simulations and experimental data analysis performed in this and other projects. We will characterize cooperative network dynamics on different temporal and spatial scales, identify its structural determinants, and try to understand its underlying biophysical mechanisms in the brain. The following specific issues in recurrent networks will be addressed: the role of nonlinear properties of neurons, the emergence and scale of correlations, the geometry of synaptic connectivity, and its effect on the graph underlying the network and the dynamics supported by it. The results of this study will greatly aid the interpretation of physiological data (e.g. multiple single-neuron recordings and local field potentials) and provide a better understanding of the structure-function relation of cortical networks.

Associated Postdoc-Project: "Detection of synchronized neuronal groups in population spike trains" (Dr. Benjamin Staude)

The cell assembly hypothesis postulates dynamically interacting groups of neurons as building blocks of cortical information processing (Hebb, 1949). Synchronized spiking across large neuronal groups was later suggested as a potential signature for active assemblies (Gerstein et al., 1989), and analysis methods for assembly detection focused on the estimation of higherorder correlations among simultaneously recorded neurons (Martignon et al., 1995; Nakahara & Amari, 2002). However, the number of parameters in presently available techniques grows exponentially with the number of recorded neurons, which requires vast sample sizes (Martignon et al., 2000). As a consequence, most attempts to detect active cell assemblies resort to pairwise interactions (Vaadia et al., 1995; Gray et al., 1989; Riehle et al., 1997). These, however, do not allow to infer on large synchronized neuronal pools, and are insensitive for sparse synchronous events (Schneidman et al., 2006). The advent of the multi-electrode array provides the technical possibility to record increasing number of neurons simultaneously. Testing the assembly hypothesis in such massively parallel spike train recordings however hinges on the inapplicability of the available analysis techniques (Brown et al., 2004).

List of project-related publications

1. Schelter B, Winterhalder M, Eichler M, Peifer M, Hellwig B, Guschlbauer B, Lücking CH, Dahlhaus R, Timmer J. Testing for directed influences among neural signals using partial directed coherence. Journal of Neuroscience Methods 152: 210-219, 2006.

2. Shin S-L, Rotter S, Aertsen A, De Schutter E. Stochastic description of complex and simple spike firing in cerebellar Purkinje cells. European Journal of Neuroscience 25: 785-794, 2007.

3. Voges N, Aertsen A, Rotter S. Statistical analysis of spatially embedded networks: From grid to random node positions. Neurocomputing 70: 1833-1837, 2007.

4. Nawrot MP, Boucsein C, Rodriguez Molina V, Aertsen A, Grün S, Rotter S. Serial interval statistics of spontaneous activity in cortical neurons. Neurocomputing 70: 1717-1722, 2007.

5. Kremkow J, Kumar A, Rotter S, Aertsen A. Population synchrony in a layered network model of the cat visual cortex. Neurocomputing 70: 2069-2073, 2007.

6. Kumar A, Schrader S, Aertsen A, Rotter S. The high-conductance state of cortical networks. Neural Computation 20(1): 1-43, 2008.

7. Staude B, Rotter S, Grün S. Can spike coordination be differentiated from rate covariation? Neural Computation 20: 1973-1999, 2008.

8. Tetzlaff T, Rotter S, Stark E, Abeles M, Aertsen A, Diesmann M. Dependence of neuronal correlations on filter characteristics and marginal spike-train statistics. Neural Computation 20: 2133-2184, 2008.

9. Nawrot MP, Boucsein C, Rodriguez Molina V, Riehle A, Aertsen A, Rotter S. Measurement of variability dynamics in cortical spike trains. Journal of Neuroscience Methods 169: 374-390, 2008.

10. Ehm W, Staude B, Rotter S. Decomposition of neuronal assembly activity via empirical de-Poissonization. Electronic Journal of Statistics 1: 473-495, 2007.

11. Kriener B, Tetzlaff T, Aertsen A, Diesmann M, Rotter S. Correlations and population dynamics in cortical networks. Neural Computation 20: 2185-2226, 2008.

12. Kumar A, Rotter S, Aertsen A. Conditions for Propagating Synchronous Spiking and Asynchronous Firing Rates in a Cortical Network Model. The Journal of Neuroscience 28(20): 5268-5280, 2008.

13. Winterhalder M, Schelter B, Timmer J. Detecting coupling directions in multivariate oscillatory systems. International Journal of Bifurcations and Chaos 17: 3735-3739, 2007.

14. Henschel K, Hellwig B, Amtage F, Jachan M, Lücking CH, Timmer J, Schelter B. Multivariate analyis of dynamical processes: Point processes and time series. The European Physical Journal, Special Topics 165: 25-34, 2008.

15. Schelter B, Timmer J, Eichler M. Assessing the strength of directed influences among neural signals using renormalized partial directed coherence. Journal of Neuroscience Methods 179: 121-130, 2009.

16. Kriener B, Helias M, Aertsen A, Rotter S. Correlations in spiking neuronal networks with distance dependent connections. Journal of Computational Neuroscience 27(2): 177-200, 2009

17. Voges N, Guijarro C, Aertsen A, Rotter S. Models of cortical networks with long-range patchy projections. Journal of Computational Neuroscience 28(1): 137-154, 2010 (online 2009).

18. Staude B, Rotter S, Grün S. CuBIC: cumulant based inference of higher-order correlations in massively parallel spike trains. Journal of Computational Neuroscience, in press (online 2009).

19. Cardanobile S, Rotter S. Multiplicatively interacting point processes and applications to neural modeling. Journal of Computational Neuroscience, in press (online 2009).

20. Rickert J, Riehle A, Aertsen A, Rotter S, Nawrot MP. Dynamic encoding of movement direction in motor cortical neurons. The Journal of Neuroscience 29(44): 13870-13882, 2009.

Complementary poster abstracts

P1. Reimer ICG, Staude B, Rotter S. Detecting assembly activity in massively parallel spike trains. Proc. Eighth Göttingen Meeting of the German Neuroscience Society 2009, T26-8C.

P2. Muthmann O, Cardanobile S, Rotter S. Count variability in doubly stochastic point processes. Proc. Eighth Göttingen Meeting of the German Neuroscience Society 2009, T26-13C.

P3. Deger M, Cardanobile S, Helias M, Rotter S. The Poisson process with dead time captures important statistical features of neural activity. Proc. Eighteenth Annual Computational Neuroscience Meeting CNS*2009, P110.

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