Network plasticity

Network plasticity

To induce neuronal assemblies, a subset of N_p excitatory neurons in the network are perturbed (the perturbed ensemble). The perturbation pattern consists of n_s alternating pulses (ON/OFF); each pulse stays ON (s_ON=s₀+δ_s) for T_ON and turns off (s_OFF=s₀) for T_OFF. s₀ describes the input to the neurons before perturbations, and δ_s denotes the strength of perturbation (e.g. corresponding to laser intensity in optogenetic stimulations (16)). The total duration of perturbation is therefore T_ON+T_OFF, with the duty cycle of T_ON/(T_ON+T_OFF) Assuming T_p=T_ON=T_OFF, the stimulation frequency is f_p=1/T_p. 

Following perturbations, synaptic plasticity is assumed to change the initial weight matrix as a result of network activity. The change in the weight w_ij is given as a function of the activity of pre- and post-synaptic neurons:

where r_j and r_i describe the firing rate of pre- and postsynaptic neurons, respectively, η is the learning rate, and <. > denotes the temporal average which is evaluated during perturbations. r⁰ denotes the average firing rate of individual neurons in their baseline state, obtained from network simulations before perturbations. We refer to this rule as covariance-based Hebbian learning, where covariance of the activity of pre- and postsynaptic neurons drives the plasticity. Two other versions of the rule are also tested, where response changes in only pre- or postsynaptic sources are considered, while the other term (post or pre, respectively) is still contributing to plasticity in absolute terms:

pre:       

post:      

At each weight update, the weights of synapses are updated according to: 

After each update, we calculate the largest eigenvalue of the updated weight matrix (spectral radius; λ₀). Weight update continues until the spectral radius is smaller than a threshold (λ₀ < λ_th=0.8); after that, the update stops and the last value of the weight matrix before passing the threshold is taken. The learning rate (η) is chosen such that the growth is not too fast or too slow. Learning rates are specified for different synapse types in Table 1 for different stimulations and figures; when the learning rate is zero or not specified for a synapse type, it means that the respective connections are static.

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