The ability of the nervous system to adapt and change to a new functional and structural state in response to intrinsic or extrinsic factors can be broadly de- fined as ‘Neural Plasticity’. Neural plasticity is manifested from the micro scale at the level of neurons and synaptic modifications to a macroscale as changes in spatiotemporal patterns at different brain regions. The concept of neural plas- ticity is not a new idea. The early conceptualisation of neural plasticity can be traced back to 1913 to Ramon y Cajal, who put forward the idea that changes in synaptic connections could be the foundation for memory [66].
Activity-dependent plasticity is a form of neural plasticity, both functional and structural, as a result of personal experiences and cognitive functions [67] and is believed to constitute the cellular basis of learning and memory [68]. Activity dependent modifications of neural connections provide a powerful mechanism to describe development and shaping of neural responses to neural inputs. Co- ordinated development and shaping of neural responses at network level can give arise to interesting stimulus-specific responses, which at a higher level may be manifested as higher level cognitive activity such as learning and memory.
The seminal idea on neural plasticity, proposed by Donald Hebb [69], which later was became known as Hebb’s rule, attempted to relate neural activity with synaptic plasticity. Hebb boldly postulated:
“When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased”(p.62) [69]
Essentially Hebb proposed that repetitive correlated activation of pre- and postsynaptic neural activity gives rise to longer lasting changes in or between these neurons involved, which can be simplified as,“when one neuron drives an- other neuron to fire repeatedly, the connection between the two is potentiated’ or ’Neurons that fire together wire together’ [69]. Although Hebb’s formulation wasn’t well received when first formulated, subsequent advances in neurophysi- ological technology allowed for accumulating neurophysiological data that con- firms Hebb’s postulate. The instances of Hebb’s synapse was later reported in
an induced long term potentiation experiment by Bliss and Tomo in 1973, which showed evidence of synaptic change based on pre- and post-synaptic neuron’s ac- tivity [70], and kindling [71]. Theoretical studies have indicated that along with Hebbian like potentiation, depression between two neurons that are not active, is also equally necessary [72,73]. Depression is necessary to prevent saturation of all the synapses to maximum output which affects the stimulus selectivity prop- erties, and to prevent a runway positive feedback loop between network activity and synaptic weights [74].
In 1973, a study of the neural pathway in rabbit hippocampus by Bliss and Tomo [70] discovered that rapidly and repeatedly activating the synapses resulted in a long lasting increment in the synaptic strength, which is defined as long term potentiation; a reverse phenomenon, first observed in rabbit cerebellar cortex in 1982 [75], also exists in which the synaptic strengths weaken with repeated acti- vation of synapses. This is called, long term depression. Long-term potentiation (LTP) and long-term depression(LTD) are important phenomenon in the study of neural plasticity. Both LTP and LTD have long been regarded as potential mechanisms for memory and learning. Induction of LTP includes depolarisation of the postsynaptic neuron and activation of N -methyl-D-aspartate (NMDA) re- ceptors by release of glutamate, which causes an increase in intracellular Ca++, which in turn increases the amount of functional α amino-3-hydroxy-5-methyl-4- isoxazolepropionic acid (AMPA) receptors in the membrane, increasing the ex- citability of the postsynaptic cell [20].
3.2.1
From Hebbian rule to spike-timing dependent plas-
ticity
The Hebbian learning framework has been refined into a temporally asymmetric learning rule induced by temporal correlation between spikes of pre- and post- synaptic neurons. One such form of Hebbian learning is called Spike-timing Dependent Plasticity (STDP) , and is relevant to neuronal network dynamics. STDP can be considered as a spike-based adaptation of the Hebbian learning rule where repeated arrival of a presynaptic spike just a few milliseconds before the postsynaptic spike leads to strongly potentiated synaptic weights (LTP) and
Figure 3.1: STDP function schematic that shows the change of synaptic weight change as a function of the relative timing of pre- and post-synaptic spikes. [76]
arrival of a presynaptic spike a few milliseconds after the postsynaptic spike lead to strongly depressed synaptic weights (LTD). The repeated controlled firing of pre- and post-synaptic neurons induces a change in the amplitude of a single ex- citatory post-synaptic potential (EPSP) . Figure3.1 shows synaptic potentiation and depression plotted against the spike time difference ∆t = tpost− tpre. The de- gree of synaptic change to the relative timing of spikes suggests that information transfer may be encoded as temporal coding in the range of milliseconds.
The early experiments with precisely timed pre- and post-synaptic spikes at milliseconds resolution was conducted by [77,78]. Even earlier investigations can be traced back to 1983 by Levy and Stuart, although Levy and Stuart’s ex- periments used lower temporal resolution and bursts of spike rather than single spikes [79]. Further works by [80–82], paved a path as a precursor for model STDP investigations. Bi and Poo [82] demonstrated that in cultures of rat hip-
pocampal neurons, correlated spiking of pre- and postsynaptic neurons induces persistent potentiation and depression of glutamatergic synapses. The strength of potentiation and depression was dependent on the timing of postsynaptic spike before or after presynaptic firing, demonstrating dependence on spike timing. Mathematically, a basic STDP model can be expressed with a small number of simple expressions as follows.
Consider two neurons, a presynaptic neuron j and postsynaptic neuron i. The synaptic weight change ∆wij from presynaptic neuron j is dependent on the relative spike timing between presynaptic spike arrival and the postsynaptic spike generated. Let’s describe the presynaptic spike arrival times at synapse j by tfj where f = 1, 2, 3, ..., which is the spike count. Similarly, tni with n = 1, 2, 3, ... indicates the firing times of the postsynaptic neuron. According to [83], the total synaptic weight change induced by stimulation can be expressed as,
∆wij = N X f =1 N X n=1 W (tni − tfj) (3.1)
where W (x) denotes the learning window function illustrated in Figure 3.1
which can be further expressed as,
W (x) = A+exp(−x/τ+) f or x > 0 (3.2)
W (x) = −A−exp(x/τ−) f or x < 0 (3.3) The parameters A+ and A− may depend on the current values of the synaptic weight wij; τ+ and τ− are time constants which are of the order of 10ms. x > 0 indicates postsynaptic spike after presynaptic spike, leading to potentiation and x < 0 indicates postsynaptic spiking before presynaptic spiking, leading to depression. These STDP models have been used to fit experimental data [81] and also on simulation models [84].