Spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) is a biological process that adjusts the strength of connections between neurons in the brain. The process adjusts the connection strengths based on the relative timing of a particular neuron's output and input action potentials (or spikes). The STDP process partially explains the activity-dependent development of nervous systems, especially with regard to long-term potentiation and long-term depression.

Process

Under the STDP process, if an input spike to a neuron tends, on average, to occur immediately before that neuron's output spike, then that particular input is made somewhat stronger. If an input spike tends, on average, to occur immediately after an output spike, then that particular input is made somewhat weaker hence: "spike-timing-dependent plasticity". Thus, inputs that might be the cause of the post-synaptic neuron's excitation are made even more likely to contribute in the future, whereas inputs that are not the cause of the post-synaptic spike are made less likely to contribute in the future. The process continues until a subset of the initial set of connections remain, while the influence of all others is reduced to 0. Since a neuron produces an output spike when many of its inputs occur within a brief period, the subset of inputs that remain are those that tended to be correlated in time. In addition, since the inputs that occur before the output are strengthened, the inputs that provide the earliest indication of correlation will eventually become the final input to the neuron.

History

In 1973, M. M. Taylor[1] suggested that if synapses were strengthened for which a presynaptic spike occurred just before a postsynaptic spike more often than the reverse (Hebbian learning), while with the opposite timing or in the absence of a closely timed presynaptic spike, synapses were weakened (anti-Hebbian learning), the result would be an informationally efficient recoding of input patterns. This proposal apparently passed unnoticed in the neuroscientific community, and subsequent experimentation was conceived independently of these early suggestions.

Early experiments on associative plasticity were carried out by W. B. Levy and O. Steward in 1983[2] and examined the effect of relative timing of pre- and postsynaptic action potentials at millisecond level on plasticity. Bruce McNaughton contributed much to this area, too. In studies on neuromuscular synapses carried out by Y. Dan and Mu-ming Poo in 1992,[3] and on the hippocampus by D. Debanne, B. Gähwiler, and S. Thompson in 1994,[4] showed that asynchronous pairing of postsynaptic and synaptic activity induced long-term synaptic depression. However, STDP was more definitively demonstrated by Henry Markram in his postdoc period till 1993 in Bert Sakmann's lab (SFN and Phys Soc abstracts in 1994–1995) which was only published in 1997.[5] C. Bell and co-workers also found a form of STDP in the cerebellum. Henry Markram used dual patch clamping techniques to repetitively activate pre-synaptic neurons 10 milliseconds before activating the post-synaptic target neurons, and found the strength of the synapse increased. When the activation order was reversed so that the pre-synaptic neuron was activated 10 milliseconds after its post-synaptic target neuron, the strength of the pre-to-post synaptic connection decreased. Further work, by Guoqiang Bi, Li Zhang, and Huizhong Tao in Mu-Ming Poo's lab in 1998,[6] continued the mapping of the entire time course relating pre- and post-synaptic activity and synaptic change, to show that in their preparation synapses that are activated within 5-20 ms before a postsynaptic spike are strengthened, and those that are activated within a similar time window after the spike are weakened. This phenomenon has been observed in various other preparations, with some variation in the time-window relevant for plasticity. Several reasons for timing-dependent plasticity have been suggested. For example, STDP might provide a substrate for Hebbian learning during development,[7][8] or, as suggested by Taylor[1] in 1973, the associated Hebbian and anti-Hebbian learning rules might create informationally efficient coding in bundles of related neurons. Works from Y. Dan's lab advanced to study STDP in in vivo systems.[9]

Mechanisms

Postsynaptic NMDA receptors are highly sensitive to the membrane potential (see coincidence detection in neurobiology). Due to their high permeability for calcium, they generate a local chemical signal that is largest when the back-propagating action potential in the dendrite arrives shortly after the synapse was active (pre-post spiking). Large postsynaptic calcium transients are known to trigger synaptic potentiation (Long-term potentiation). The mechanism for spike-timing-dependent depression is less well understood, but often involves either postsynaptic voltage-dependent calcium entry/mGluR activation, or retrograde endocannabinoids and presynaptic NMDARs.

From Hebbian rule to STDP

According to the Hebbian rule, synapses increase their efficiency if the synapse persistently takes part in firing the postsynaptic target neuron. An often-used simplification is those who fire together, wire together, but if two neurons fire exactly at the same time, then one cannot have caused, or taken part in firing the other. Instead, to take part in firing the postsynaptic neuron, the presynaptic neuron needs to fire just before the postsynaptic neuron. Experiments that stimulated two connected neurons with varying interstimulus asynchrony confirmed the importance of temporal precedence implicit in Hebb's principle: the presynaptic neuron has to fire just before the postsynaptic neuron for the synapse to be potentiated.[10] In addition, it has become evident that the presynaptic neural firing needs to consistently predict the postsynaptic firing for synaptic plasticity to occur robustly,[11] mirroring at a synaptic level what is known about the importance of contingency in classical conditioning, where zero contingency procedures prevent the association between two stimuli.

Uses in artificial neural networks

The concept of STDP has been shown to be a proven learning algorithm for forward-connected artificial neural networks in pattern recognition. Recognising traffic,[12] sound or movement using Dynamic Vision Sensor (DVS) cameras has been a recent area of research.[13][14] Correct classifications with a high degree of accuracy with only minimal learning time has been shown. It was shown that a spiking neuron trained with STDP learns a linear model of a dynamic system with minimal least square error.[15]

A general approach, replicated from the core biological principles, is to apply a window function (Δw) to each synapse in a network. The window function will increase the weight (and therefore the connection) of a synapse when the parent neuron fires just before the child neuron, but will decrease otherwise.

Several variations of the window function have been proposed to allow for a range of learning speeds and classification accuracy.

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See also

References
  1. Taylor MM (1973). "The Problem of Stimulus Structure in the Behavioural Theory of Perception". South African Journal of Psychology. 3: 23–45.
  2. Levy WB, Steward O (April 1983). "Temporal contiguity requirements for long-term associative potentiation/depression in the hippocampus". Neuroscience. 8 (4): 791–7. CiteSeerX 10.1.1.365.5814. doi:10.1016/0306-4522(83)90010-6. PMID 6306504.
  3. Dan Y, Poo MM (1992). "Hebbian depression of isolated neuromuscular synapses in vitro". Science. 256 (5063): 1570–73. Bibcode:1992Sci...256.1570D. doi:10.1126/science.1317971. PMID 1317971.
  4. Debanne D, Gähwiler B, Thompson S (1994). "Asynchronous pre- and postsynaptic activity induces associative long-term depression in area CA1 of the rat hippocampus in vitro". Proceedings of the National Academy of Sciences of the United States of America. 91 (3): 1148–52. Bibcode:1994PNAS...91.1148D. doi:10.1073/pnas.91.3.1148. PMC 521471. PMID 7905631.
  5. Markram H, Lübke J, Frotscher M, Sakmann B (January 1997). "Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs" (PDF). Science. 275 (5297): 213–5. doi:10.1126/science.275.5297.213. PMID 8985014.
  6. Bi GQ, Poo MM (15 December 1998). "Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type". Journal of Neuroscience. 18 (24): 10464–72. doi:10.1523/JNEUROSCI.18-24-10464.1998. PMC 6793365. PMID 9852584.
  7. Gerstner W, Kempter R, van Hemmen JL, Wagner H (September 1996). "A neuronal learning rule for sub-millisecond temporal coding". Nature. 383 (6595): 76–78. Bibcode:1996Natur.383...76G. doi:10.1038/383076a0. PMID 8779718.
  8. Song S, Miller KD, Abbott LF (September 2000). "Competitive Hebbian learning through spike-timing-dependent synaptic plasticity". Nature Neuroscience. 3 (9): 919–26. doi:10.1038/78829. PMID 10966623.
  9. Meliza CD, Dan Y (2006), "Receptive-field modification in rat visual cortex induced by paired visual stimulation and single-cell spiking", Neuron, 49 (2): 183–189, doi:10.1016/j.neuron.2005.12.009, PMID 16423693
  10. Caporale N.; Dan Y. (2008). "Spike timing-dependent plasticity: a Hebbian learning rule". Annual Review of Neuroscience. 31: 25–46. doi:10.1146/annurev.neuro.31.060407.125639. PMID 18275283.
  11. Bauer E. P.; LeDoux J. E.; Nader K. (2001). "Fear conditioning and LTP in the lateral amygdala are sensitive to the same stimulus contingencies". Nature Neuroscience. 4 (7): 687–688. doi:10.1038/89465. PMID 11426221.
  12. Bichler, Olivier; Querlioz, Damien; Thorpe, Simon J.; Bourgoin, Jean-Philippe; Gamrat, Christian (22 Feb 2012). "Extraction of temporally correlated features from dynamic vision sensors with spike-timing-dependent plasticity". Neural Networks. 32: 339–348. doi:10.1016/j.neunet.2012.02.022. PMID 22386501.
  13. Thorpe, Simon J. (2012). Fusiello, Andrea; Murino, Vittorio; Cucchiara, Rita (eds.). Spike-Based Image Processing: Can We Reproduce Biological Vision in Hardware?. Computer Vision – ECCV 2012. Workshops and Demonstrations. Lecture Notes in Computer Science. 7583. Springer Berlin Heidelberg. pp. 516–521. CiteSeerX 10.1.1.460.4473. doi:10.1007/978-3-642-33863-2_53. ISBN 978-3-642-33862-5.
  14. O'Connor, Peter; Neil, Daniel; Liu, Shih-Chii; Delbruck, Tobi; Pfeiffer, Michael (2013). "Real-time classification and sensor fusion with a spiking deep belief network". Frontiers in Neuroscience. 7: 178. doi:10.3389/fnins.2013.00178. PMC 3792559. PMID 24115919.
  15. Suri, Roland E. (2004). "A computational framework for cortical learning" (PDF). Biological Cybernetics. 90 (6): 400–9. doi:10.1007/s00422-004-0487-1. hdl:20.500.11850/64482. ISSN 0340-1200. PMID 15316786.

Further reading
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