# 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 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 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, and on the hippocampus by D. Debanne, B. Gähwiler, and S. Thompson in 1994, 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. 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, 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 transiently weakened. It has since been shown that the initially highly asymmetric STDP window turns into a more symmetric "LTP only" window three days after induction. Spike-timing-dependent plasticity is thought to be a substrate for Hebbian learning during development. As suggested by Taylor in 1973, Hebbian learning rules might create informationally efficient coding in bundles of related neurons. While STDP was first discovered in cultured neurons and brain slice preparations, it has also been demonstrated by sensory stimulation of intact animals.

## Biological mechanisms

Postsynaptic NMDA receptors (NMDARs) 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), when NMDA and AMPA receptors are still bound to glutamate. 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. Similarly, the efficiency of synapses decreases when the firing of their presynaptic targets is persistently independent of firing their postsynaptic ones. These principles are often simplified in the mnemonics: those who fire together, wire together; and those who fire out of sync, lose their link. However, 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 relation implicit in Hebb's principle: for the synapse to be potentiated or depressed, the presynaptic neuron has to fire just before or just after the postsynaptic neuron, respectively. In addition, it has become evident that the presynaptic neural firing needs to consistently predict the postsynaptic firing for synaptic plasticity to occur robustly, 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.

## Role in hippocampal learning

For the most efficient STDP, the presynaptic and postsynaptic signal has to be separated by approximately a dozen milliseconds. However, events happening within a couple of minutes can typically be linked together by the hippocampus as episodic memories. To resolve this contradiction, a mechanism relying on the theta waves and the phase precession has been proposed: Representations of different memory entities (such as a place, face, person etc.) are repeated on each theta cycle at a given theta phase during the episode to be remembered. Expected, ongoing, and completed entities have early, intermediate and late theta phases, respectively. In the CA3 region of the hippocampus, the recurrent network turns entities with neighboring theta phases into coincident ones thereby allowing STDP to link them together. Experimentally detectable memory sequences are created this way by reinforcing the connection between subsequent (neighboring) representations.

## Computational models and applications
### Training spiking neural networks

The principles of STDP can be utilized in the training of artificial spiking neural networks. Using this approach the weight of a connection between two neurons is increased if the time at which a presynaptic spike ($t_{pre}$) occurs is shortly before the time of a post synaptic spike($t_{post}$), ie. $t=t_{post}-t_{pre}$ and $t>0$. The size of the weight increase is dependent on the value of $t$ and decreases exponentially as the value of $t$ increases given by the equation:
$A_{+}\exp {\left({\frac {-t}{\tau _{+}}}\right)}$
where $A_{+}$ is the maximum possible change and $\tau _{+}$ is the time constant.
If the opposite scenario occurs ie a post synaptic spike occurs before a presynaptic spike then the weight is instead reduced according to the equation:
$A_{-}\exp {\left({\frac {-t}{\tau _{-}}}\right)}$
Where $A_{-}$and $\tau _{-}$ serve the same function of defining the maximum possible change and time constant as before respectively.
The parameters that define the decay profile ($A_{+}$,$A_{-}$, etc.) do not necessarily have to be fixed across the entire network and different synapses may have different shapes associated with them.
Biological evidence suggests that this pairwise STDP approach cannot give a complete description of a biological neuron and more advanced approaches which look at symmetric triplets of spikes (pre-post-pre, post-pre-post) have been developed and these are believed to be more biologically plausible.