Understanding the Dynamics and Function of Networks of Spiking Neurons

Peter Stratton

Project 1: In Vivo Spike Shape Analysis – collaboration with Francois Windels.

Spikes have been recorded from single neurons in awake, behaving animals. Some of the neurons were also subjected to pharmacological manipulation to, for example, increase excitability of the neural membrane or block inhibition. This is a unique dataset that enables characterisation of spiking dynamics in awake, behaving animals rather than in anesthetised animals or in slice preparations. Analysis of this dataset has shown strong dependence of spike amplitude on spiking rate for the majority of cells (see Figure 1) as well as spike shape changes for some cells.

Figure 1: Spike amplitude is inversely correlated with firing rate. Top-left: Firing rate (green) and spike amplitude (red) shown over 130 s of recording. Bottom-left: Spike amplitude plotted against firing rate shows a clear inverse correlation (line of best fit – green; mean and std dev. – red). Top-right: Spike rise time (blue), fall time (green) and half width (red) in milliseconds, plotted against firing rate, show no significant change. Bottom-right: Average spike shapes plotted for low firing rates to high firing rates in five steps (blue, green, red, cyan and magenta) shows falling spike amplitude for higher firing rates.

The dataset is also unique because each recording clearly identifies a single recorded cell, allowing comparisons to be drawn between spike shapes of different neurons. The similarity of the spike shapes recorded from different neurons and the high level of noise that is typically present in neural recordings mean that spikes from different cells are likely to be misclassified (i.e. attributed to incorrect neurons) when doing normal multi-neuron recordings using single electrodes. We have calculated, for any given signal-to-noise ratio (SNR) and any given neural density, how likely misclassification is to occur. We have shown that neural recordings using single electrodes are highly likely to give erroneous results, with misclassification rates above 99% for many brain regions.

Project 2: Spike Timing Dependent Plasticity and Oscillations in Networks of Spiking Neurons

Complex activity in the brain is hypothesised to underlie its flexibility and sophisticated processing capability (i.e. higher cognitive function). This is particularly evident during periods of quiet relaxation when 10 Hz alpha waves are seen in many brain regions. This activity is associated with memory retrieval, planning, problem solving and day dreaming. Until now, it has not been possible to reproduce this sort of activity in a model of the brain; this is what we have been able to do. We are now investigating how modification of the synapses connecting the neurons (using Spike Timing Dependent Plasticity (STDP)) changes the network dynamics and how learning of spatiotemporal patterns of network activity can be achieved. Understanding how patterns can be stored in a network of spiking neurons is critical to understanding learning and memory in the brain.

Figure 2: Patterns of activity can be learned in a network of spiking neurons. The network contains 1250 neurons (Y axis) and was simulated for 30 seconds (X axis). For the first 5 seconds of simulation the network operated in a random activity regime with no external input, after which a fixed activity pattern was held for 10 seconds through input provided by external connections. When the external input was released at 15 seconds time, the observed pattern is partially reproduced in the ongoing network activity from 15 to 30 seconds.

Project 3: Calibration of Head Direction Networks on Robots

Neurons have been discovered in the brains of mammals that are active only when the animal is in a certain place in its environment, and others when the animal is facing a certain direction, effectively providing a brain-based map and compass. Understanding how such specific functions arise and are controlled in the brain can assist in revealing how the brain functions in general and how these functions can go awry in cases of brain injury and disease. We have modelled the brain network that contains the neurons that represent head direction in the mammalian brain (see Figure 3), and have shown how this network can be calibrated on a mobile robot, through feedback from the world, when the robot follows specific movements that many infant mammals perform. This work advances our understanding of the neural systems involved in motion tracking and the representation of space, links these systems to specific developmental behaviours and motor deficits, and further demonstrates how biological processes can afford practical solutions to engineering problems.

Figure 3: Head direction network. Head direction (HD) cells excite their close neighbours strongly and more distant neighbours less strongly, and this self-excitation creates the HD activity. These excitatory connections are calibrated to allow the HD system to accurately represent head direction as the animal or robot moves. The HD cells are also inhibited by the asymmetric Angular Head Velocity (AHV); the overall efficacy of this inhibition is also calibrated. DTN: Dorsal tegmental nucleus, LMN: Lateral mammillary nucleus.

Ongoing Collaborative Research

  • Collaborated with Michael Milford and Gordon Wyeth: Calibrating spiking head direction networks on robots with long-term deployments, for example in factory and warehouse delivery tasks, where on-going calibration is required due to mechanical wear and damage accrued over long timeframes.
  • Collaborated with Francois Windels and Allen Cheung: Continued analysis of the unique neural recording datasets from awake, behaving animals.
  • Collaborated with David Ball and Chris Nolan: Controlling Braitenberg vehicles with spiking neural networks – how do the temporal dynamics of spiking networks assist in the temporal organisation of embodied behaviour?
  • Collaborating with Bryan Mowry on the potential role of synaptic homeostasis in schizophrenia. Paper in preparation: Complex cortical activity mediated by homeostatic mechanisms at the synapse; hypothesised Homeostatic Plasticity Deficit-type schizophrenia (HPDS)

Publications

  • Stratton, P., Cheung, A., Wiles, J., Kiyatkin, E., Sah, P., Windels, F. Action potential waveform variability limits multi-unit separation in freely behaving rats. (submitted)
  • Stratton, P., Milford, M., Wyeth, G.F., Wiles, J. (2011) Using strategic movement to calibrate a neural compass: a spiking network for tracking head direction in rats and robots. PLoS ONE, vol.6(10)
  • Stratton, P., Wiles, J. (2010) Self-sustained non-periodic activity in a network of spiking neurons: The contribution of local and long-range connections and dynamic synapses. NeuroImage 52: 1070-1079. (PDF File 1,934 KB)
  • Stratton, P., Wyeth, G.F. and Wiles, J. (2010) Calibration of the Head Direction Network: a role for Symmetric Angular Head Velocity cells. Journal of Computational Neuroscience 28: 527-538. (PDF File 485 KB)
  • Wiles, J., Ball, D., Heath, S., Nolan, C., Stratton, P. (2010) Spike-time robotics: a rapid response circuit for a robot that seeks temporally varying stimuli. To appear In Australian Journal of Intelligent Information Processing Systems. (PDF File 718 KB)
  • Stratton, P., Wiles, J. (2010) Complex Spiking Models: A Role for Diffuse Thalamic Projections in Complex Cortical Activity. To appear In Springer LNCS. (PDF File 599 KB)
  • Stratton, P., Milford, M., Wiles, J., Wyeth, G.F. (2009) Automatic Calibration of a Spiking Head-Direction Network for Representing Robot Orientation. In Proceedings of the Australasian Conference on Robotics and Automation, Sydney, Australia. 8 pages. (PDF File 2,071 KB)
  • Stratton, P., Wiles, J. (2008) Comparing Kurtosis Score to Traditional Statistical Metrics for Characterizing the Structure in Neural Ensemble Activity. In M. Marinaro et al., editors, Dynamic Brain – from Neural Spikes to Behaviors, Springer LNCS V 5286, 115-122. (PDF File 135 KB)

Conference Abstracts or Posters

  • Stratton, P., Cheung, A., Wiles, J., Kiyatkin, E., Sah, P., Windels, F. (2012) Action potential waveform separability in awake unrestrained rats. Australian Neuroscience Society 32nd annual meeting, Gold Coast, Australia, January
  • Stratton, P., Milford, M., Wyeth, G.F., Wiles, J. (2011) Computation in spiking neural networks - from complex dynamics to navigation. Thinking Systems Symposium, Powerhouse Museum, Sydney, Australia, Dec 8-9
  • Stratton, P., Wiles, J. (2011) Complex Dynamics in a Critical Regime – Spontaneous, Autonomous Transition to and from Seizure. Fifth International Workshop on Seizure Prediction, Dresden, Germany, September
  • Stratton, P., Wiles, J. A role for symmetric head-angular-velocity cells: Tuning the head-direction network. Frontiers in Systems Neuroscience, 2009 (COSYNE’09)
  • Stratton, P. Poster presentation at Complex (2007) (Complex Systems conference), Gold Coast, Australia, July 2-5, 2007

Related Activities

  • Invited to talk at the Dynamic Brain: From Neural Spikes to Behaviour workshop, Sicily, Italy, Dec 5-12, 2007
  • Co-organiser of the “Summer of Spikes” summer school on Computation in Spiking Neural Networks, Dec 2009 – Feb 2010
  • Invited to talk at the Fifth International Workshop on Seizure Prediction, Dresden, Germany, September 2011
  • Invited to talk at Brain Corporation, San Diego, USA, December 2011

International Links

Presented at University College London, December 2007. Comparing Kurtosis Score to Traditional Statistical Metrics for Characterizing the Structure in Neural Ensemble Activity.

Presented at the Salk Institute, San Diego, USA, February 2011 – Complex Spiking Models: Network properties governing emergent complex dynamics.

Presented at Brain Corporation, San Diego, USA, December 2011 – Computation in spiking neural networks – active vision, complex dynamics, spontaneous sequence replay and head movement calibration.

Where to Next?

Leading on from the collaborative work I have done with the Sah lab at the Queensland Brain Institute, I am now employed in this laboratory to analyse neural recording data being obtained from human patients undergoing electrode implantation for deep brain stimulation (DBS) therapy. DBS has been shown to be an effective treatment for many disorders including Parkinson’s disease, essential tremor, dystonia, chronic and phantom pain, depression, epilepsy, Tourette’s syndrome and obsessive-compulsive disorder. However its mechanism of action is poorly understood. Recent developments have produced electrodes that can be used to record brain activity, providing a unique opportunity to investigate brain function before and after long-term stimulation. A primary goal of this research is to improve electrode placement to induce the optimal clinical outcome for patients.

Spiking Hippocampal Models for Learning and Recall of Places and Paths

Christopher Nolan

Summary

Navigation is a foundational skill for animals. From insects to birds to mammals, many animals have developed various strategies to search for that which they require, remember its location, then safely return home. Discovering some of the techniques these animals use has yielded unique solutions for the navigational problems of artificial autonomous systems. Yet many questions remain unanswered regarding the navigational abilities that so many animals appear to possess.

One such ability is path planning – learning a set of places in an environment and the connectivity between those places, then using the resulting graph or map for myriad goals. Empirical data collected over the past century indicates that some animals, and specifically rodents, are capable of behaviours difficult to reconcile using alternative explanations. In more recent decades, since the discovery of spatially sensitive ‘place cells’ in the rat brain, it has become clear that the hippocampus plays a significant role in map-based navigation. Simultaneously developing in the field of mobile autonomous systems have been algorithmic techniques to solve a similar map-based navigation problem, termed Simultaneous Localisation and Mapping (SLAM), which highlight the information-theoretical principles involved. The goal of this work has been to explore, using spiking neural modelling techniques, how the electrophysiological and anatomical properties of the rodent hippocampus can satisfy these theoretical requirements of an online path planning system.

Spike timing and novelty detection

Recognition of novelty is a key element of any memory system. Existing studies have demonstrated both learning mechanisms capable of developing appropriate unique memories, and corresponding recall mechanisms capable of ignoring random variance in the input. These features are necessary for navigational memory from a theoretical perspective, and also provide a good fit for some electrophysiological data. However these studies have neglected to address the issue of when each process, learning and recall, should occur. As one element of the current work, we extended the existing models of the hippocampal network, incorporating the timing of individual spikes, and using this extra dimension to provide an internal novelty signal. More specifically, we implemented a network that matches known hippocampal anatomy, and demonstrated how such a network could instigate a race between a teaching signal and recall signal, with the teaching signal winning the race only in the case of a novel input (see Figure 1). Using this novelty signal, what constitutes a novel input can itself be modified dynamically, without destabilising the system.

A role for place cells in path encoding

In a navigational context, individual memories can be likened to place, and sequences of such memories to paths. The predominant interpretation of the spatial selectivity of place cells is that these cells are 'coding for' the location of the animal at the time of their firing. Beyond this pure spatial selectivity, evidence demonstrates that during traversal of a cell's place field, its firing processes with respect to the local theta oscillation - an effect termed 'theta phase precession' - and this precession is correlated with relative progression through the place field. One common interpretation of this precession effect is that it provides a greater degree of locational specificity. Within this project we explored an alternative hypothesis that place fields and theta phase precession are evidence of a path encoding and recall mechanism (Figure 2). We developed a mechanism based on the known anatomy of hippocampal subregion CA3 that is consistent with many dynamical properties of the region and can explain known variations in spatial selectivity across the CA3 network. The proposed mechanism suggests that CA3 performing path encoding and recall over complete foraging ranges could be the functional justification for anatomical and dynamical variation across the region.

Figure 1. Response timing distinguishes learned from novel inputs: Initially the input (green dots) is novel, and although the input is directly connected to the output cells (blue dots), the output cells are slow to activate, not responding until the input activates the teaching signal (red dots) (highlighted for stimulus 2 in b). After repeated presentations, output cells start responding faster, activated directly by the recall signal and eventually respond before the arrival of the teaching signal (highlighted for stimulus 2 in c).

Figure 2. Diagrammatic characterisation of theta-phase and position interpreted using the traditional theory of place fields vs. the theory proposed in the current work. By definition a place field is the region of the environment that the cell fires. The traditional interpretation is that the perimeter of a place field is delimited by the onset and offset of a cell's firing irrespective of the trajectory through the field (left). This interpretation of position is a consequence of place field sizes being minimised during analysis. The theory proposed in the current work states that spatially-sensitive cells respond both directly and indirectly to the location in the environment (right). The subset of these regions of the environment that cause a direct response are termed “anchor fields” (right, green dot). In practice, these anchor fields could be determined by examining the location when the cell fires at maximum theta precession. When an animal's path will potentially pass through the anchor field, the cell fires with a delay proportional to the length of the path to the anchor field. When an animal's path does not pass through the anchor field, the cell never reaches its maximal phase precession.

Publications

  • Nolan, C.R., Wyeth, G.F., Milford, M.J., Wiles, J. (2010) “The Race to Learn: Spike Timing and STDP Can Coordinate Learning and Recall in CA3”, Hippocampus. DOI: 10.1002/hipo.20777 (PDF File 980 KB)
  • Wiles, J., Ball, D., Heath, S., Nolan, C.R., Stratton, P. (2010) Spike-time robotics: a rapid response circuit for a robot that seeks temporally varying stimuli. Australian Journal of Intelligent Information Processing Systems, 11(1)

Conference Abstracts

Nolan, C.R., Wyeth, G.F., Milford, M.J., Wiles, J. (2010) A neural microcircuit using spike timing for novelty detection. Computational and systems neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00099.