Skip to main content
  • Poster presentation
  • Open access
  • Published:

Interaction between memories in an abstract mathematical model based on the Hebbian cell assembly hypothesis

Learning and memory are essential properties of adaptive neural circuits. Thereby, the general hypothesis (Synaptic-Plasticity-and-Memory hypothesis; [1, 2]) is that the adaptive process of synaptic plasticity induces changes at the synapses connecting the neurons. These changes lead to the formation of strongly interconnected subgroups of neurons, so-called cell assemblies [3]. It has been suggested that such cell assemblies represent the learned memory items. However, as known from everyday life, after learning, humans and animals show the remarkable ability to connect, generalize, and discriminate old and new memories. How these memory interactions are realized on a neuronal level based on the idea of cell assemblies is still unknown.

In this work, we use a network model dependent on the interaction between synaptic plasticity and synaptic scaling [4, 5]. Amongst others, this interaction yields the formation of cell assemblies showing dynamics comparable to human memories [6]. For simplicity, here, we further abstract this complex network model by the methods of mean-field theory. Thereby, the dynamics of each cell assembly in the network are reduced to two differential equations; one for the average neuronal activity and one for the average synaptic weight. Given this simplified model, we show that, in contrast to loosely connected groups of neurons, the formation of cell assemblies lets the activity of the neuronal population follow a hysteresis which creates complex network dynamics, which depend on the initial conditions. Given this hysteresis, in the next step, we connect two such assemblies with each other by plastic connections also adapted by the interaction between synaptic plasticity and scaling. Amongst others, we analyzed under which circumstances the dynamics of this two-cell-assembly system are comparable to the above mentioned dynamics of human and animal memories and how different parameters of the system (e.g., cell assembly size) influence them.

In summary, this work is one of the first using a mathematical model to relate the dynamics of memories on a psychological scale to the hypothesized dynamics of cell assemblies on a neuronal scale.


  1. Eichenbaum H: The cognitive neuroscience of memory: An introduction. 2012, Oxford University Press

    Google Scholar 

  2. Martin SJ, Grimwood PD, Morris RGM: Synaptic plasticity and memory: An evaluation of the hypothesis. Annual Review Neuroscience. 2000, 23: 649-711.

    Article  CAS  Google Scholar 

  3. Hebb DO: The Organization of Behaviour. 1949, Wiley, New York

    Google Scholar 

  4. Tetzlaff C, Kolodziejski C, Timme M, Wörgötter F: Synaptic scaling in combination with many generic plasticity mechanisms stabilizes circuit connectivity. Frontiers in Computational Neuroscience. 2011, 5: 47-

    Article  PubMed  PubMed Central  Google Scholar 

  5. Turrigiano GG, Leslie KR, Desai NS, Rutherford LC, Nelson SB: Activity-dependent scaling of quantal amplitude in neocortical neurons. Nature. 1998, 391: 892-896.

    Article  PubMed  CAS  Google Scholar 

  6. Tetzlaff C, Kolodziejski C, Timme M, Tsodyks M, Wörgötter F: Synaptic scaling enables dynamically distinct short- and long-term memory formation. PLoS Computational Biology. 2013, 9 (10): e1003307-

    Article  PubMed  PubMed Central  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Juliane Herpich.

Rights and permissions

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Herpich, J., Wörgötter, F. & Tetzlaff, C. Interaction between memories in an abstract mathematical model based on the Hebbian cell assembly hypothesis. BMC Neurosci 16 (Suppl 1), P253 (2015).

Download citation

  • Published:

  • DOI: