Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Theory of Precise Timing in Spiking Neural Networks


Patterns of precisely timed and spatially distributed spikes have been experimentally observed in different neuronal systems [1]. These spike patterns correlate with external stimuli (events) and are thus considered key features of neural computation [2]. Their dynamical origin, however, is unclear. One possible explanation for their occurrence is the existence of excitatorily coupled feed-forward structures, synfire chains [3] which are embedded in a network of otherwise random connectivity and receive a large number of random external inputs. In complementary theoretical modeling studies we investigate whether precise spike timing and temporal locking can naturally arise in the nonlinear dynamics of recurrent neural networks that contain no additionally embedded feed-forward structures. In particular, we study how strongly heterogeneous networks of complicated connectivity can still coordinate the timing of spikes of different neurons, possibly even if they are not directly linked by a synapse. We are addressing different groups of phenomena:


Speed Limits to Coordinating Spike Times - Revealed by Random Matrix Theory (in collaboration with F. Wolf and T. Geisel, Dept. Nonlinear Dynamics). In large networks of spiking neurons, we uncovered a topology-induced speed limit to coordinating spike times [4] and explained both the speed and its limit via random matrix theory. The mechanism underlying the coordinating barrier points to a cooperative effect of the existence of a minimum time a neuron needs to generate subsequent spikes, the temporally discrete communication between neurons and their complex interaction network [5].



Network Design: Heterogeneous Networks with Specific Dynamics. Under which conditions can spiking neural networks exhibit certain predefined patterns of precisely timed spikes? For a broad class of model networks (that include, among other features, strong heterogeneities, complicated connectivity and distributed delays) we analytically determined the subset of all networks (parameterized by features of single neurons and their interactions) which exhibit an arbitrary predefined pattern [6]. This provides a novel method to find potential network structures, for instance by modifying the synaptic interaction strengths that generate a desired, e.g. experimentally observed dynamics. In particular, the method enables us to find stable as well as unstable patterns, which might both be computationally relevant, cf. [7]. In a first application, we combined this network design with additional requirements on the resulting network, for instance realizing networks with a given type of coupling (e.g., only inhibitory) and a given type of connectivity (e.g., with exponentially distributed number synapses per neuron) which simultaneously exhibits a desired spike pattern. In a second application, we identified networks that exhibit a predefined pattern, but simultaneously optimize structural features, e.g. minimize wiring costs [8]. Recent experimental results [9] obtained by the group of W. Singer, Max Planck Institute for Brain Research, Frankfurt, strongly indicate the importance of the precise timing of spikes in unprecedented detail. This initiated a further intense investigation of the origin of precise timing in recurrent networks. Furthermore, in collaboration with the BCCN Berlin and the RIKEN Brain Science Institute, we recently developed a novel method for detecting precise timing dependencies between spiking activity and the coarser signal of local field potentials [M. Denker et al., in prep.]. Application of the method to activity recorded from motor cortex of awake behaving monkeys revealed that during a movement preparation task spikes tend to keep a fixed phase relationship to the LFP, largely independent of the LFP amplitude [10].

How Chaotic is the Balanced State? Highly irregular dynamics is a prominent feature of multi-dimensional complex systems and often attributed to chaos. In particular, sparsely coupled networks of spiking neurons exhibit a balanced state [11] with very irregular dynamics. Here excitatory and inhibitory inputs to each neuron balance on average and only the fluctuations create spikes at irregular, seemingly random points in time. Mean field theory shows that such balanced activity occurs in networks with excitatory and inhibitory recurrent feedback as well as in networks that receive external excitatory inputs and exhibit recurrent inhibition only. Going beyond mean field theory, our studies on the microscopic dynamics of the latter networks reveals that the dynamics in fact is not chaotic but rather dynamically stable [12], a fact that comes as a surprise to many theoreticians, not only in the neurosciences.



[1] M. Abeles et al. (1993) J Neurophysiol 70(4):1629-1638; Y. Ikegaya et al. (2004) Science 304:559-564

[2] M. Abeles (2004) Science 304:523-524

[3] M. Diesmann, M.-O. Gewaltig, and A. Aertsen (1999) Nature 402:529-533; Y. Aviel, C. Mehring, M. Abeles, and D. Horn (2003) Neural Comput 15:1321-1340

[4] M. Timme, F. Wolf, and T. Geisel (2004) Phys Rev Lett 92:074101

[5] M. Timme, T. Geisel, and F. Wolf (2006) Chaos 16:015108

[6] R.-M. Memmesheimer, M. Timme, and T. Geisel (2005) In: Verhandl. DPG (VI) 40, 2/2005, DY 22.6, pg 202; R.-M. Memmesheimer and M. Timme (2006) Phys Rev Lett 97:188101

[7] P. Ashwin and M. Timme (2005) Nonlinearity 18:2035-2060 and (2005) Nature 436:36-37

[8] R.-M. Memmesheimer and M. Timme (2006) Physica D 224:182-201

[9] K. Gansel and W. Singer (2005) Soc Neurosci Abstr 276.8

[10] M. Denker, S. Roux, M. Timme, A. Riehle, S. Grün (2007) Neurocomputing 70:2096

[11] C. van Vreeswijk and H. Sompolinsky (1996) Science 274:1724

[12] S. Jahnke R.-M. Memmesheimer, and M. Timme  Phys Rev Lett 100:048102 (2008).


Contact:  Marc Timme 

Members working within this Project:

 Marc Timme 
 Francesca Schönsberg 
 Christian Tetzlaff 
 Diemut Regel 

Former Members:

 Christoph Kirst 
 Raoul Martin Memmesheimer 
 Hinrich Arnoldt 
 Fabio Schittler Neves 
 Birgit Kriener 
 Andreas Sorge 
 Annette Witt 

Selected Publications:

F. Faraci (2015).
The 60th anniversary of the Hodgkin-Huxley model: a critical assessment from a historical and modeller’s viewpoint
Masters thesis, Mathematical Institute of Leiden University. download file

H. Arnoldt, S. Chang, S. Jahnke, B. Urmersbach, H. Taschenberger, and M. Timme (2015).
When Less Is More: Non-monotonic Spike Sequence Processing in Neurons
PLoS Comput. Biol. 11(2):e1004002. download file

S. Jahnke, M. Timme, and R.M. Memmesheimer (2015).
A Unified Dynamic Model for Learning, Replay, and Sharp-Wave/Ripples
J. Neurosci. 35(49):16236. download file

D. Breuer, M. Timme, and R.M. Memmesheimer (2014).
Statistical Physics of Neural Systems with Nonadditive Dendritic Coupling
Phys. Rev. X 4(1):011053. download file

S. Jahnke, R.M. Memmesheimer, and M. Timme (2014).
Hub-activated signal transmission in complex networks
Phys. Rev. E (Rapid) 89:030701. download file

S. Jahnke, R.M. Memmesheimer, and M. Timme (2014).
Oscillation-Induced Signal Transmission and Gating in Neural Circuits
PLoS Comput. Biol. 10(12):1003940. download file

A. Witt, A. Palmigiano, A. Neef, A. El Hady, F. Wolf, and D. Battaglia (2013).
Controlling the oscillation phase through precisely timed closed-loop optogenetic stimulation: a computational study
Frontiers in Neural Circuits 7.

C. Tetzlaff, C. Kolodziejski, M. Timme, M. Tsodyks, and F. Woergoetter (2013).
Synaptic Scaling Enables Dynamically Distinct Short- and Long-Term Memory Formation
PLoS Comput. Biol. 9:e1003307. download file

S. Jahnke, R.M. Memmesheimer, and M. Timme (2013).
Propagating Synchrony in Feed-Forward Networks
Frontiers Comput. Neurosci. 7:153. download file

F.S. Neves, and M. Timme (2012).
Computation by Switching in Complex Networks of States
Phys. Rev. Lett. 109:018701. download file

R.M. Memmesheimer, and M. Timme (2012).
Non-Additive Coupling Enables Propagation of Synchronous Spiking Activity in Purely Random Networks
PLoS Comput. Biol. 8:e1002384.

S. Jahnke, M. Timme, and R.M. Memmesheimer (2012).
Guiding Synchrony through Random Networks
Phys. Rev. X 2:041016. download file

F. van Bussel, B. Kriener, and M. Timme (2011).
Inferring synaptic connectivity from spatio-temporal spike patterns
Frontiers Comput. Neurosci. 5:3. download file

H. Kielblock, C. Kirst, and M. Timme (2011).
Breakdown of order preservation in symmetric oscillator networks with pulse-coupling
Chaos 21:025113. download file

C. Kirst, and M. Timme (2010).
Partial Reset in Pulse-coupled Oscillators
SIAM J. Appl. Math. 70:2119--2149. download file

R.M. Memmesheimer, and M. Timme (2010).
Stable and unstable periodic orbits in complex networks of spiking neurons with delays
Discr. Cont. Dyn. Syst. 28:1555 - 1588. download file

R.M. Memmesheimer, and M. Timme (2010).
Synchrony and Precise Timing in Complex Neural Networks
In: Handbook on Biological Networks, edited by Stefano Boccaletti, Vito Latora and Yamir Moreno. World Scientific, Singapore, chapter 13, pages 279-304. download file

S. Steingrube, M. Timme, F. Wörgötter, and P. Manoonpong (2010).
Self-organized adaptation of a simple neural circuit enables complex robot behaviour
Nature Physics 6:224-230. download file

C. Bick, and M. Rabinovich (2009).
Dynamical Origin of the Effective Storage Capacity in the Brain’s Working Memory
Phys. Rev. Lett. 103:218101. download file

C. Kirst, and M. Timme (2009).
How precise is the timing of action potentials?
Frontiers in Neurosci. 3:2. download file

C. Kirst, T. Geisel, and M. Timme (2009).
Sequential Desynchronization in Networks of Spiking Neurons with Partial Reset
Phys. Rev. Lett. 102:068101. download file

F.S. Neves, and M. Timme (2009).
Controlled perturbation-induced switching in pulse-coupled oscillator networks
J. Phys. A: Math. Theor. 42:345103. download file

J. Klingmayr, C. Bettstetter, and M. Timme (2009).
Globally Stable Synchronization by Inhibitory Pulse Coupling
Proc. IEEE Intern. Symp. Appl. Sci. in Biomedical and Communication Technologies (ISABEL), Bratislava, Slovak Republic. download file

S. Jahnke, R.M. Memmesheimer, and M. Timme (2009).
How chaotic is the balanced State?
Frontiers Comput. Neurosci. 3:13. download file

S. Jahnke, R.M. Memmesheimer, and M. Timme (2008).
Stable Irregular Dynamics in Complex Neural Networks
Phys. Rev. Lett. 100:048102. download file

M. Timme, T. Geisel, and F. Wolf (2006).
Speed of synchronization in complex networks of neural oscillators: Analytic results based on Random Matrix Theory
Chaos 16:015108.

R.-. Memmesheimer, and M. Timme (2006).
Designing the Dynamics of Spiking Neural Networks
Phys. Rev. Lett. 97:188101.

R.M. Memmesheimer, and M. Timme (2006).
Designing complex networks
Physica D 224:182-201.

M. Timme, F. Wolf, and T. Geisel (2004).
Topological Speed Limits to Network Synchronization
Phys. Rev. Lett. 92:074101.