Synaptic modification and entrained phase are phase dependent in STDP

Synapse strength can be modified in an activity dependent manner, in which the temporal relationship between preand post-synaptic spikes plays a major role. This spike timing dependent plasticity (STDP) has profound implications in neural coding, computation and functionality, and this line of research is booming in recent years. Many functional roles of STDP have been put forward. Because the STDP learning curve is strongly nonlinear, initial state may have great impacts on the eventual state of the system. However, this feature has not been explored before. This paper proposes two possible functional roles of STDP by considering the influence of initial state in modeling studies. First, STDP could lead to phase-dependent synaptic modification that have been reported in experiments[1, 2]. Second, rather than leading to a fixed phase relation between preand post-synaptic neurons, STDP that includes suppression between the effects of spike pairs [3] lead to a distributed entrained phase which also depend on the initial relative phase. This simple mechanism is proposed here to have the ability to organize temporal firing pattern into dynamic cell assemblies in a probabilistic manner and cause cell assemblies to update in a deterministic manner. It has been demonstrated that olfactory system in locust, and even other sensory systems, adopts the strategy of combining probabilistic cell assemblies with their deterministic update to encode information. These results suggest that STDP rule is a potentially powerful mechanism by which higher network functions emerge. Since the discovery of spike-timing dependent plasticity (STDP) [4-6], in which a synapse is depressed or potentiated according to the time of preand post-synaptic spikes, the functional role of STDP has been an intensive field of research. Recent findings, both theoretical and experimental, on fundamental questions include facilitation of dual coding[7, 8], bringing about competition between different synapse[9, 10], converging a neural network to a stable state[11, 12], enhancing synchronization of neuron and neural networks[13-19], shaping the selectivity of neuron or neural circuits [20-24] and mediating sensory experience-dependent circuit refinement in the developing nervous system[25, 26]. Other results have also been reported, such as bridging the gap between time scales of behavioral tasks and neuron firing[27], generating great memory capacity[28], eliminating location dependence of synapses and enabling democratic plasticity[29], reducing variability of neural response[30], leading to reinforcement learning[31, 32], leading to slowness learning required for recognizing objects in variable context[33] and solving the distal reward problem[34]. Here I present two possible consequences of STDP : initial relative phase dependent probabilistic frequency synchronization (entrainment), which could result in phase-dependent LTP/LTD, and initial relative phase dependent entrained phase, which could lead to formation of probabilistic cell assemblies and cause deterministic updates between them. Neural synchronization is believed to underlie many important functional aspects of neural systems, such as perception, learning, memory and attention [35, 36]. Mechanisms that lead to neural synchronization have been widely discussed in the literature. As demonstrated in [13] and [19], STDP facilitates frequency synchronization (entrainment) to a great extent if potentiation and depression is well balanced. However, since the modification of synapse conductance in STDP is bi-directional and the corresponding learning curve is strongly nonlinear, little difference in initial state may cause great difference in the ultimate fate of the system, e.g. success or failure of entrainment, just as initial value does in a deterministic chaotic system. Moreover, the interactions between the effects of spike pairs [3] further complicate the dynamics of the synapse by introducing suppressions between them, therefore allowing more possibilities for initial state to play. To consider the effects of initial state in STDP and synchronization is not trivial, since it has been reported experimentally that phase sensitive synaptic modifications is present both in θ (7Hz)[1, 37-40] and β-γ (20-60Hz) [2]oscillation in vitro. And it has also been demonstrated that STDP is involved in olfactory information flow in locusts to ensure precise synchronization [15]. Furthermore, it has been demonstrated earlier that olfactory information in locust is encoded by both transient cell assembly, in which the firing of a specific neuron is probabilistic, and the precise temporal sequence in which cell assemblies are updated [41]. It is natural to conjecture that the update sequence of cell assemblies is determined by the initial state of neurons in consequent cell assemblies. Therefore, it is reasonable and meaningful to ask whether and, if yes, how, initial state of a STDP system would have great impacts on the eventual state of the system. This paper presents an effort to study the influence of initial state in STDP, by numerically investigating a simple system which consists of an excitatory STDP synapse and two repetitive firing neurons with different autonomous period. Detailed numerical studies strongly support that initial state is a major determinant to the eventual state of the system. Specifically, the probability of successful entrainment is largely determined by the initial relative phase of the system. Moreover, the synaptic conductance evolves to a stable value if successful entrainment is established and, decreases to zero if not. Therefore, this mechanism may be able to account for the phase sensitivity of synaptic modification [1, 2, 37-40], a phenomenon that has been reported experimentally. Furthermore, if STDP with suppression[3] is considered, the stable entrained phase is no longer fixed to a unified value. In stead, the entrained phase is dependent on the initial relative phase and distributed in a wide range. Thus STDP with suppression provides a natural mechanism to organize post-synaptic neurons’ temporal firing pattern according to their initial state and allow probabilistic cell assemblies to update in a determinant manner.