Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding

Key Points

  • One of the central problems in neuroscience is the characterization and understanding of the neural code. In 1968 Perkel and Bullock defined four key functions for a candidate neural code: stimulus representation, interpretation, transformation and transmission. Although the first three have been studied extensively, surprisingly, the fourth has been largely ignored in experiments. Yet, signal transmission is a vital functions for a neural code in ensuring communication among highly specialized brain regions.

  • Feedforward networks with convergent or divergent connections between subsequent groups of neurons have been the model system of choice in the study of spiking-activity propagation. The simple feedforward topology captures key features of the modular architecture of the brain. Moreover, from a functional perspective, certain classes of recurrent networks can be treated as feedforward networks.

  • Theoretical studies have identified two dominant modes for propagating spiking activity in feedforward networks: the aynchronous rate mode, in which the average spike count is propagated across the sub-networks; and the synchronous event mode, in which only synchronous volleys of spikes are propagated.

  • Various properties of individual neurons and the structure of feedforward networks can amplify even weak correlations in spiking-activity propagation. Such amplification rapidly degenerates the fidelity of an asynchronous rate code. Thus, only feedforward networks with weak shared connectivity are suitable for propagating asynchronous firing rates. Large, shared connectivity favours the propagation of a synchrony code.

  • Structural properties of feedforward networks, in particular connection probability and synaptic strengths, have a crucial role in determining whether asynchronous firing rates or synchronous spikes are propagated. Thus, appropriate architecture of the FFN may support stable propagation of asynchronous and synchronous neural codes simultaneously.

  • Indirect experimental evidence suggests that neural networks in vivo may indeed induce synchrony in their propagating activity. However, a direct testing of theoretical predictions is currently lacking. Controlled stimulation of appropriately selected neural networks in vivo to generate activity patterns mimicking either asynchronous or synchronous input and monitoring of their temporal evolution downstream could provide an effective paradigm for testing these predicitions.


The brain is a highly modular structure. To exploit modularity, it is necessary that spiking activity can propagate from one module to another while preserving the information it carries. Therefore, reliable propagation is one of the key properties of a candidate neural code. Surprisingly, the conditions under which spiking activity can be propagated have received comparatively little attention in the experimental literature. By contrast, several computational studies in the last decade have addressed this issue. Using feedforward networks (FFNs) as a generic network model, they have identified two dynamical activity modes that support the propagation of either asynchronous (rate code) or synchronous (temporal code) spiking. Here, we review the dichotomy of asynchronous and synchronous propagation in FFNs, propose their integration into a single extended conceptual framework and suggest experimental strategies to test our hypothesis.

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Figure 1: The feedforward network as a model of information processing in the brain.
Figure 2: Cascaded neural assemblies.
Figure 3: Transmission of asynchronous firing rate in an FFN.
Figure 4: Propagation of a pulse packet in an FFN.
Figure 5: Coexistence of firing rate propagation and synchrony propagation.


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We thank J. Kremkow and T. Vogels for helpful discussions, G. Grah for preparing some of the graphical illustrations and U. Froriep for proofreading the manuscript. We also thank the editorial staff at the Nature Reviews Neuroscience for their continuous help in organizing the manuscript. This work was supported by the German Federal Ministry of Education and Research (grant 01GQ0420 to the Bernstein Center for Computational Neuroscience, Freiburg), the EU (grant no. 15,879-FACETS) and the German Research Foundation (Collaborative Research Center 780).

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Correspondence to Arvind Kumar.

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Supplementary information

Supplementary information S1 (box)

Network model (PDF 269 kb)

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A. Aertsen, C. Boucsein and A. Kumar's Brainworks homepage

The Bernstein Center Freiburg homepage


Convergent–divergent connection

A connectivity scheme in which neurons in a group receive inputs from many neurons in a previous group (convergent connections) and at the same time project to many neurons in subsequent groups (divergent connections).

Unreliable synapses

Synapses may fail to induce a postsynaptic potential in the target neuron despite stimulation owing to the probabilistic nature of synaptic vesicle release.

Read-out problem

The problem of how the neural activity of a single neuron or group of neurons received and transformed ('decoded') by a postsynaptic group of neurons, to result in, for example, a decision, perception or motor act.

Embedding recurrent network

A large recurrent network typically composed of excitatory and inhibitory neurons that contain feedforward networks as subnetworks.

In- and out-degree

In-degree refers to the number of input synapses that a neuron receives. Out-degree refers to the number of synapses a neuron makes.


A network state characterized by irregular firing of individual neurons (measured by the coefficient of variation of the inter-spike-interval distribution) and by asynchronous population activity (measured by pairwise correlation or fano factor) (Box 2).

Fixed point

If the system arrives at this point in its state-space, it remains there permanently in the absence of disturbances (a steady state). Fixed points can be stable or unstable.


A fixed point in the state-space that attracts all of the system trajectories passing through its neighbourhood.

Saddle node

A fixed point that attracts some nearby trajectories but repels others.


A multi-dimensional space defined by variables that characterize the system state. If there are N such variables, each state is represented by a point in an N-dimensional state-space.

Rank-order coding

A spatiotemporal pattern of spikes in which the temporal rank of spikes carries information about a stimulus or cognitive state.

Sparse code

A coding scheme in which strong activation of a relatively small set of available neurons is used for information representation.

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Kumar, A., Rotter, S. & Aertsen, A. Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding. Nat Rev Neurosci 11, 615–627 (2010). https://doi.org/10.1038/nrn2886

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