SC4: Computation in Neural Circuits


How do neural circuits generate interesting computations from the interaction of many components operating at the single neuron and network level? Despite the recent advancement in experimental techniques to record and manipulate neural circuits at unprecedented level, we still lack a unifying understanding of this process – computational approaches offer a unique insight because they allows us to study each of the interacting mechanisms and components one by one. In four lectures I will present mathematical and modelling approaches about how to formalize mathematical models of single neurons and synaptic connections, and how to study their interactions in large-scale circuits that generate interesting computations. I will first discuss computations performed by single neurons, such as adaptation and robustness, which can emerge from the joint action of ion channels acting on multiple timescales. Then, the course will discuss the functional implications of these single neurons in bigger neural networks where the intrinsic timescale in the neurons interact with synaptic timescales. We will formalize the concept of mean-field analysis and explain how to describe the dynamics of neural networks from averaging the behaviour of many of the single neurons in the network. At the level of circuits, we will study how different network states can be generated.

Throughout the course, we will constantly be working with models from real biological circuits. In particular, we will build models of networks in mammalian sensory cortex, during early and late postnatal development when many of the intrinsic and synaptic properties are changing. We will also give example from other circuits, for example in Drosophila, which also implement interesting computations important for the survival of the animal such as detection of motion vision and navigation through complex environments. If time permits, we will also discuss how neural circuits change (due to processes like synaptic plasticity) to shape emergent computations.


- Build models of single neurons and circuits
Study how intrinsic and synaptic properties interact to derive circuit dynamics
Apply models to relevant systems from neuroscience


W. Gerstner, W. M. Kistler, R. Naud and L. Paninski (2014). Neuronal Dynamics: From single neurons to networks and models of cognition. Cambridge University Press.

J. Gjorgjieva, G. Drion and E. Marder (2016). Computational implications of biophysical diversity and multiple timescales in neurons and synapses for circuit performance. Curr Opin Neurobiol 37:44-52.

J. Gjorgjieva, R. A. Mease, W. J. Moody and A. L. Fairhall (2014). Intrinsic neuronal properties govern information transmission in networks. PLoS Comp Biol 10(12): e1003962.

R. A. Mease, M. Famulare, J. Gjorgjieva, W. J. Moody and A. L. Fairhall (2013). Emergence of adaptive computation by single neurons in the developing cortex. J Neurosci 33:12154-12170.

Course location


Course requirements


Instructor information.

Julijana Gjorgijeva


Julijana Gjorgjieva is a Reseach Group Leader at the Max Planck Institute for Brain Research in Frankfurt and an Assistant Professor in Computational Neuroscience at the Technical University of Munich. She studied Mathematics at Harvey Mudd College in Claremont, California and obtained her PhD in 2011 at the University of Cambridge in the UK. After doing postdocs with Haim Sompolinsky and Markus Meister at Harvard University and Eve Marder at Brandeis University in the US, she started her group in Frankfurt in the summer of 2016. Julijana’s work is aimed at understanding the main principles governing the organization and computation in neural circuits, from sensory to motor. She addresses these questions using two types of methods: normative approaches, such as optimization of information transfer, to determine the emergence of cell type diversity, and bottom-up approaches to understand how neural computation arises from the interaction of different mechanisms acting at various levels, from single neurons to synaptic connections and circuits.