What Are Autapses Good for?
Hazem Toutounji1
1

Department of Psychology, University of Sheffield, United KingdomSummary. I develop a simple model of an autaptic neuron and analyse its neurocomputational
properties. I show that the model can capture diverse experimental observations and demonstrate
how autapses can provide a novel biologically plausible route to chaos in cortical pyramidal cells.

An autapse is a synapse connecting the neuron to itself. Previous anatomical studies suggest thatAutapses in excitatory cortical neurons known as pyramidal cells are rare, irrelevant errors in neuronalwiring. However, a recent electrophysiological study challenges this view by showing that autapses are acommon phenomenon, specifically in layer 5 pyramidal cells of the prefrontal cortex, that are alsofunctionally relevant to neural computation [1]. Among other findings, Yin and colleagues [1] observedthat autapses enhance bursting in pyramidal cells, which may suggest a role in boosting neural informationtransmission. Furthermore, previous studies on a genus of marine invertebrates called aplysia demonstratethat autapses in aplysia’s motor neurons facilitate persistent activity (necessary for memory) in the absenceof sufficiently strong input [2], a phenomenon that was not observed in layer 5 pyramidal cells according
to Yin and colleagues.
The first aim of this work is to reconcile these disparate experimental observations within a single
theoretical framework, namely, dynamical systems theory [3]. I augmented a simple, biophysical neuralmodel with autaptic excitation. Simulations show that, for different parameter choices, the presence of anautapse either enhances bursting, as in layer 5 autaptic prefrontal pyramidal cells (Figure 1, left) or leads topersistent activity in absence of strong external excitation, as in autaptic motor neurons in the aplysia(Figure 1, right). As I will show, the fact these results conform to two different experimental observations
is not surprising when taking a dynamical-systems perspective, and it reflects the nonarbitrary choice ofparameters, which is based on known biophysical properties of the modelled neuronal structures. This

Figure 1. Left, model simulations showing the neuron membrane potential without (middle) and with(bottom) an autpase given layer 5 pyramidal cell biophysical parameters. Without an autapse, theneuron shows regular firing. With an autapse, the neuron shows an initial burst of action potentials (orspikes), in strong agreement with experimental observations in [1]. Right, same as (left) for aplysia
motor-neuron parameters, showing persistent activity due to the presence of an autapse in the absenceof a strong stimulation current, consistent with experimental observations in [2]. Top panels show thestimulation current in each case.

suggests that this autaptic neuron model can support diverse modes of operation that correspond to different
neuro-computational properties of functionally specific cell types.
The second aim is to present a novel, biologically plausible route to chaos in single neuron models.
While previous studies discovered parameter regimes within which single neuron models act as chaotic
dynamical systems [4], these parameter regimes were outside the ranges that can be observed naturally.
Chaos in single neurons remained therefore a subject of mathematical curiosity, rather than a biologicallyplausible phenomenon. On the other hand, it is very easy to induce chaos in a dynamical system byincorporating delays. Indeed, chaos [5,6] and delays [7,8] are two important ingredients for richer neuraldynamics that can support complex computations. Interestingly, staying within a biologically plausible
layer 5 parameters in the current model, adding a delay to the autaptic current as it arrives to the soma, andapplying a strong stimulation current give rise to chaos (Figure 2). This suggests delayed autaptic pyramidalcells may provide another source for neural variability, expanding the dynamic range of these neurons andallowing for complex neural and neuro-inspired computations. This opens the door for further studies
investigating the computational properties of spiking neural networks with autaptic connections and for
future development of neuromorphic hardware that incorporates delayed autapses into its architecture.

Figure 2. Chaotic first return map (comparing successive inter-spike intervals, or ISIs) for a delayed
autaptic current (left), compared to period-5 oscillation for instantaneous autaptic current (middle).
Right, a delayed autapse shows high sensitivity to initial conditions, a sign of chaos: perturbing themembrane potential by 2 millivolts resulted in an exponential divergence in membrane potential
trajectory and a completely different spiking behaviour.

References[1] Yin, L., Zheng, R., Ke, W., He, Q., Zhang, Y., Li, J… Shu, Y. (2018). Autapses enhance bursting andcoincidence detection in neocortical pyramidal cells. Nat Commun, 9(4890).
[2] Saada, R., Miller, N., Hurwitz, I., & Susswein, A. J. (2009). Autaptic Excitation Elicits Persistent Activity and aPlateau Potential in a Neuron of Known Behavioral Function. Curr Biol, 19(6), 479–484.
[3] Izhikevich, Eugene M. Dynamical systems in neuroscience. MIT press, 2007.
[4] Nobukawa, S., Nishimura, H., & Yamanishi, T. (2017). Chaotic Resonance in Typical Routes to Chaos in theIzhikevich Neuron Model. Sci Rep, 7(1331).
[5] Sussillo, D., & Abbott, L. F. (2009). Generating Coherent Patterns of Activity from Chaotic Neural Networks.
Neuron, 63(4), 544–557.
[6] Shim, Y., & Husbands, P. (2012). Chaotic Exploration and Learning of Locomotion Behaviors. Neural Comput,24(8), 2185–2222.
[7] Brunner, D., Soriano, M. C., Mirasso, C. R., & Fischer, I. (2013). Parallel photonic information processing at
gigabyte per second data rates using transient states. Nat Comm, 4(1), 1364.
[8] Toutounji, H., Schumacher, J., & Pipa, G. (2015). Homeostatic Plasticity for Single Node Delay-Coupled
Reservoir Computing. Neural Comput, 27(6), 1159–1185.