10.1 Synaptic Plasticity

Over the last 30 years, a large body of experimental results on synaptic plasticity has been accumulated. Many of these experiments are inspired by Hebb's postulate (Hebb, 1949) that describes how the connection from presynaptic neuron A to a postsynaptic neuron B should be modified:

**Figure 10.1:** The change at synapse w_ij depends on the state of the presynaptic neuron j and the postsynaptic neuron i and the present efficacy w_ij, but not on the state of other neurons k.
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Today, 50 years later, this famous postulate is often rephrased in the sense that modifications in the synaptic transmission efficacy are driven by correlations in the firing activity of pre- and postsynaptic neurons. Even though the idea of learning through correlations dates further back in the past (James, 1890), correlation-based learning is now generally called Hebbian learning.

Hebb formulated his principle on purely theoretical grounds. He realized that such a mechanism would help to stabilize specific neuronal activity patterns in the brain. If neuronal activity patterns correspond to behavior, then stabilization of specific patterns implies learning of specific types of behaviors (Hebb, 1949).

10.1.1 Long-Term Potentiation

When Hebb stated his principle in 1949, it was a mere postulate. More than 20 years later, long-lasting changes of synaptic efficacies were found experimentally (Bliss and Lomo, 1973; Bliss and Gardner-Medwin, 1973). These changes can be induced by the joint activity of presynaptic and postsynaptic neuron and resemble the mechanism that Hebb had in mind (Kelso et al., 1986). In this subsection we concentrate on long-term potentiation (LTP), viz., a persistent increase of synaptic efficacies. Long-term depression (LTD) is mentioned in passing.

The basic paradigm of LTP induction is, very schematically, the following (Bliss and Collingridge, 1993; Brown et al., 1989). A neuron is impaled by an intracellular electrode to record the membrane potential while presynaptic fibers are stimulated by means of a second extracellular electrode. Small pulses are applied to the presynaptic fibers in order measure the strength of the postsynaptic response (Fig. 10.2A). The amplitude of the test pulse is chosen so that the stimulation evokes a postsynaptic potential, but no action potentials.

**Figure 10.2:** Schematic drawing of a paradigm of LTP induction. A. A weak test pulse (left) evokes the postsynaptic response sketched on the right-hand side of the figure. B. A strong stimulation sequence (left) triggers postsynaptic firing (right, the peak of the action potential is out of bounds). C. A test pulse applied some time later evokes a larger postsynaptic response (right; solid line) than the initial response. The dashed line is a copy of the initial response in A (schematic figure).
$\vbox{ {\bf A} \vspace{20mm} \par {\bf B} \vspace{20mm} \par {\bf C} \vspace{-50... ...ce{30mm} \includegraphics[width=60mm]{Figs-ch-Hebbrules/Fig-Hebb-exper.eps} }}$

In a second step, the input fibers are strongly stimulated by a sequence of high frequency pulses so as to evoke postsynaptic firing (Fig. 10.2B). After that the strength of the postsynaptic response to small pulses is tested again and a significantly increased amplitude of postsynaptic potentials is found (Fig. 10.2C). This change in the synaptic strength persists over many hours and is thus called long-term potentiation.

What can be learned from such an experiment? Obviously, the result is consistent with Hebb's postulate because the joint activity of pre- and postsynaptic units has apparently lead to a strengthening of the synaptic efficacy. On the other hand, the above experiment would also be consistent with a purely postsynaptic explanation that claims that the strengthening is solely caused by postsynaptic spike activity. In order to exclude this possibility, a more complicated experiment has to be conducted (Bliss and Collingridge, 1993; Brown et al., 1989).

In an experiment as it is sketched in Fig. 10.3 a neuron is driven by two separate input pathways labeled S (strong) and W (weak), respectively. Each pathway projects to several synapses on the postsynaptic neuron i. Stimulating of the S pathway excites postsynaptic firing but stimulation of the W channel alone does not evoke spikes. The response to the W input is monitored in order to detect changes of the synaptic efficacy. A 100 Hz input over 600 ms at the W channel evokes no LTP at the W synapses. Similarly, a 100 Hz input (over 400 ms) at the S channel alone does not produce LTP at the W synapses (although it may evoke a change of the S synapses). However, if both stimulations occur simultaneously, then the W synapses are strengthened. This feature of LTP induction is known as cooperativity or associativity. It is consistent with the picture that both presynaptic and postsynaptic activity is required to induce LTP.

**Figure 10.3:** Cooperativity in the induction of LTP. Synapses at the W channel are strengthened only if both the presynaptic site is stimulated via the W electrode and the postsynaptic neuron is active due to a simultaneous stimulation of the S pathway.
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Experiments as the one sketched in Figs. 10.2 and 10.3 have shown that synaptic weights change as a function of pre- and postsynaptic activity. Many other paradigms of LTP induction have been studied over the last twenty years. For example, the state of the postsynaptic neuron can be manipulated by depolarizing or hyperpolarizing currents; synaptic channels can be blocked or activated pharmacologically, etc. Nevertheless, the underlying subcellular processes that lead to LTP are still not fully understood.

10.1.2 Temporal Aspects

The essential aspect of the experiments described in the previous section is the AND condition that is at the heart of Hebb's postulate: Both pre- and postsynaptic neuron have to be active in order to induce a strengthening of the synapse. However, such a summary neglects the temporal requirements for weight changes. When are two neurons considered as being active together?

In the experiment sketched in Fig. 10.3 inputs can be switched on and off with some arbitrary timing. A large increase of the synaptic efficacy can be induced by stimulating the W and the S pathway simultaneously. If there is a certain delay in the stimulation of W and S then the synaptic efficacy is only slightly increased or even reduced. Stimulating W and S alternatively with a long interval in between does not result in any change at all (Debanne et al., 1994; Levy and Stewart, 1983; Gustafsson et al., 1987). With this setup, however, a precise measurement of the timing conditions for synaptic changes is difficult, because pre- and postsynaptic activity is generated by extracellular electrodes. With modern patch-clamp techniques it is possible to stimulate or record from one or several neurons intracellularly. Pairing experiments with multiple intracellular electrodes in synaptically coupled neurons have opened the possibility to study synaptic plasticity at an excellent spatial and temporal resolution (Zhang et al., 1998; Markram et al., 1997; Bi and Poo, 1998,1999; Debanne et al., 1998; Magee and Johnston, 1997); see Bi and Poo (2001) for a review.

**Figure 10.4:** Timing requirements between pre- and postsynaptic spikes. Synaptic changes $\Delta$ w_ij occur only if presynaptic firing at t_j^(f) and postsynaptic activity at t_i^(f) occur sufficiently close to each other. Experimentally measured weight changes (circles) as a function of t_j^(f) - t_i^(f) in milliseconds overlayed on a schematic two-phase learning window (solid line). A positive change (LTP) occurs if the presynaptic spike *precedes* the postsynaptic one; for a reversed timing, synaptic weights are decreased. Data points redrawn after the experiments of Bi and Poo (1998).
$\centerline{\includegraphics[width=55mm]{Figs-ch-Hebbrules/Fig-Bi3.eps} }$

Figure 10.4 illustrates a pairing experiment with cultured hippocampal neurons where the presynaptic neuron (j) and the postsynaptic neuron (i) are forced to fire spikes at time t_j^(f) and t_i^(f), respectively (Bi and Poo, 1998). The resulting change in the synaptic efficacy $\Delta$ w_ij after several repetitions of the experiment turns out to be a function of the spike time differences t_j^(f) - t_i^(f) (`spike-time dependent synaptic plasticity'). Most notably, the direction of the change depends critically, i.e., on a millisecond time-scale, on the relative timing of pre- and postsynaptic spikes. The synapse is strengthened if the presynaptic spike occurs shortly before the postsynaptic neuron fires, but the synapse is weakened if the sequence of spikes is reversed; cf. Fig. 10.4A. This observation is indeed in agreement with Hebb's postulate because presynaptic neurons that are active slightly before the postsynaptic neuron are those which `take part in firing it' whereas those that fire later obviously did not contribute to the postsynaptic action potential. An asymmetric learning window such as the one in Fig. 10.4, is thus an implementation of the causality requirement that is implicit in Hebb's principle.

Similar results on spike-time dependent synaptic plasticity have been found in various neuronal systems (Zhang et al., 1998; Markram et al., 1997; Egger et al., 1999; Bi and Poo, 1998,1999; Debanne et al., 1998), but there are also characteristic differences. Synapses between parallel fibers and `Purkinje-cells' in the cerebellar-like structure of electric fish, for example, show the opposite dependence on the relative timing of presynaptic input and the (so-called `broad') postsynaptic spike. In this case the synapse is weakened if the presynaptic input arrives shortly before the postsynaptic spike (anti-Hebbian plasticity). If the timing is the other way round then the synapse is strengthened. A change in the timing of less than 10 ms can change the effect from depression to potentiation (Bell et al., 1997b).