Table 1.
Neuron parameters as used in [35].
Fig 1.
Schematic of the STN-GPe network.
The connection probability, synaptic strength and delay for each connection is shown in red, blue and green, respectively. The number in parentheses (1000, 2000) represent the number of neurons in STN and GPe, respectively. The connection with arrowhead are excitatory and those with filled circle are inhibitory. The F-I curves for the neuron model with different spike burst lengths is plotted in S1 Fig. The inter spike interval within the burst is kept constant.
Table 2.
Network parameters as used in [35] The median, 25% and 75% quartiles of the distributions are reported in brackets.
Fig 2.
Effect of STN and GPe firing rates on β band oscillations.
(A) Average firing rate of GPe neurons as a function of different input rates to the STN and GPe. (B) Same as in A but for STN neurons. (C) Strength of oscillations in the GPe population (quantified using spectral entropy, see Methods). (B) Same as in C but for STN neurons. (E) The effect of the STN and GPe firing rates (as in A and B) on spectral entropy (as in C and D). These results show that β band oscillations in the STN-GPe network depend on the STN firing rate but not on the GPe firing rates. All the values (firing rate and spectral entropy) were averaged over 5 trials. A scatter plot for spectral entropy against the STN and GPe firing rates for all the 5 trials is shown in S4 Fig.
Fig 3.
State dependent effect of spike bursting on the strength of β band oscillations.
(A) Spectral entropy as a function of input to the STN and GPe neurons. This panel is same as the Fig 2C with three regimes of network activity marked as, 1: oscillatory, 2: transition regime, 3: non-oscillatory regime. (B): Top GPe (left) and STN (right) firing rates as a function of the fraction of bursting neurons in the STN (x-axis) and GPe (y-axis), in the oscillatory regime 1. (B): Bottom GPe (left) and STN (right) spectral entropy as a function of the fraction of bursting neurons in the STN (x-axis) and GPe (y-axis), in the oscillatory regime (i.e. state 1 in the panel A). Spike bursting has no effect on the network activity dynamics in this regime. (C) Same as in the panel (B) but when the network was operating in the transition regime (marked as state 2 in the panel A). In this regime, spike bursting affects the network activity state: increase in the fraction of bursting neurons in GPe induces oscillations whereas an optimal fraction of bursting neurons in STN can quench oscillations. (D) Same as in the panel (B) but when the network was operating in a non-oscillatory regime (marked as 3 in panel A). Addition of BS neurons did not affect a strong non-oscillatory regime.
Fig 4.
Non-monotonic effect of STN spike bursting on network oscillations when the network operates in the transition regime.
Here the fraction of bursting neurons in the GPe was fixed to 40% of GPe neurons and the fraction of bursting neurons in the STN (FBSTN) was increased systematically (as marked on different subplots). 40% of GPe neurons were made to elicit spike bursts from time point 1500 ms. This resulted in emergence of oscillations. A fraction of STN neurons (FBSTN marked on each subplot) were made to burst, starting at time 3500ms. For small to moderate FBSTN, oscillations disappeared. But when FBSTN was larger oscillations reappeared albeit at a lower frequency. The spectrograms shown here were averaged over 5 trials of the network with different random seeds.
Fig 5.
Comparison of firing rate changes induced by the input drive and spike bursting.
The pale background (same as in Fig 2E) illustrates the effect of GPe and STN firing rates on oscillations. This is used to compare the effects of firing rates and spike bursting. The inset shows the 6 network states chosen for the comparison: two oscillatory (1 and 1′), two border (2 and 2′) and two non-oscillatory (3 and 3′). In each of the chosen states, we varied the fraction of bursting neurons in both STN and GPe populations from 0 to 100%. For each combination of the fraction of spike bursting neurons we estimated the firing rate of STN and GPe neurons and their corresponding spectral entropy. Then firing rates and spectral entropy are plotted to create the six manifolds. The size of manifolds is much smaller than the background indicating that the changes in firing rates induced solely by spike bursting is rather small.
Fig 6.
Effect of spike bursting on beta-band oscillation bursts.
(A) An example of the amplitude envelope of the beta band (15-20 Hz) oscillations (blue trace). Beta oscillation burst threshold (red dashed line) was determined by averaging the maximum of beta band amplitude envelop for a Poisson process (orange trace) with the same firing rate as the neuron in the STN-GPe network. The averaging was done over Poissonian firing rates corresponding to all GPe and STN spike bursting ratios and 5 trials per STN-GPe bursty ratio combination. (B) Low pass filtered (15-20 Hz band) trace of population firing rate in the STN population in the beta band (15-20Hz). The orange trace shows the population firing rate of the Poisson process with same average firing rate as the STN activity. (C) Beta oscillation burst length as a function of the fraction of spike bursting neurons in the GPe and the STN. (D) Beta oscillation burst amplitude as a function of the fraction of spike bursting neurons in the GPe and the STN. (E,F,G) Correlation between β oscillation burst length and amplitude for three different combinations of FBSTN and FBGPe(marked with cyan, orange and green colors in the pane C. Cyan marker shows beta oscillation burst length and amplitude for 10% of spike bursting neurons in GPe and 20% in STN—this combination of spike bursting neurons gives an average oscillation burst length of 0.24 s which is comparable to experimentally measured values. In panels E-F the p-values are listed to 4 places after decimal point.
Fig 7.
Effect of spike bursting on the excitation-inhibition balance in different network activity regimes.
E-I balance was characterized by estimating the total effective excitation and inhibition received by a GPe neuron (see Methods). E-I balance for oscillatory and non-oscillatory network states for 100% non-bursting neurons. Each filled circle shows E-I balance for different external inputs to STN and GPe neurons shown in Figs 2 and 3. The effect of spike bursting on E-I balance is shown for the three exemplary network activity regimes: 1-Oscillatory regime, 2-Transition regime, 3-Non-oscillatory regime (see Fig 3 for details). Different colored stars and filled circles show how the E-I balance varied as function of change in the fraction of spike bursting neurons in the GPe (warmer colors indicate higher % of spike bursting neurons). The trajectory from the star (STN spike bursting ratio = 0%) to the filled circle shows change in the E-I balance as the fraction of spike bursting in STN is varied from 0% to 100%. In all the states spike bursting tends to make the network activity more oscillatory, however, the amount by which spike bursting is able to push the network towards oscillatory regime depends on the network activity regime itself.
Fig 8.
Summary of the effect of firing rate and spike bursting on network state.
The background image (same as Fig 7) show the oscillatory and non-oscillatory regimes of STN-GPe network as a function of effective excitation and inhibition. The arrows schematically show the change in EI-balances as we increase spike bursting in the STN or GPe. The STN-GPe network oscillations are more sensitive to the STN firing rate. The balance of STN and GPe firing rates determines the global state of network activity. Spike bursting in GPe always increases both effective inhibition and effective excitation. Small increases in spike bursting in STN results in a decrease in both effective excitation and effective inhibition and thereby, reduces oscillations. By contrast, a large increase in the fraction of spike bursting neurons in the STN increases both effective inhibition and effective excitation and thereby, enhances oscillations. However, this effect is smaller and therefore, spike bursting is effective in altering the network oscillations only when the network is operating close to the border of oscillatory and non-oscillatory states.