Spike patterns are among the most common electrophysiological descriptors of neuron types. Surprisingly, it is not clear how the diversity in firing patterns of the neurons in a network affects its activity dynamics. Here, we introduce the state-dependent stochastic bursting neuron model allowing for a change in its firing patterns independent of changes in its input-output firing rate relationship. Using this model, we show that the effect of single neuron spiking on the network dynamics is contingent on the network activity state. While spike bursting can both generate and disrupt oscillations, these patterns are ineffective in large regions of the network state space in changing the network activity qualitatively. Finally, we show that when single-neuron properties are made dependent on the population activity, a hysteresis like dynamics emerges. This novel phenomenon has important implications for determining the network response to time-varying inputs and for the network sensitivity at different operating points.

The excess of 15-30 Hz (β-band) oscillations in the basal ganglia is one of the key signatures of Parkinson's disease (PD). The STN-GPe network is integral to generation and modulation of β band oscillations in basal ganglia. However, the role of changes in the firing rates and spike bursting of STN and GPe neurons in shaping these oscillations has remained unclear. In order to uncouple their effects, we studied the dynamics of STN-GPe network using numerical simulations. In particular, we used a neuron model, in which firing rates and spike bursting can be independently controlled. Using this model, we found that while STN firing rate is predictive of oscillations, GPe firing rate is not. The effect of spike bursting in STN and GPe neurons was state-dependent. That is, only when the network was operating in a state close to the border of oscillatory and non-oscillatory regimes, spike bursting had a qualitative effect on the β band oscillations. In these network states, an increase in GPe bursting enhanced the oscillations whereas an equivalent proportion of spike bursting in STN suppressed the oscillations. These results provide new insights into the mechanisms underlying the transient β bursts and how duration and power of β band oscillations may be controlled by an interplay of GPe and STN firing rates and spike bursts.

Spike patterns are among the most common electrophysiological descriptors of neuron types. Surprisingly, it is not clear how the diversity in firing patterns of the neurons in a network affects its activity dynamics. Here, we introduce the state-dependent stochastic bursting neuron model allowing for a change in its firing patterns independent of changes in its input-output firing rate relationship. Using this model, we show that the effect of single neuron spiking on the network dynamics is contingent on the network activity state. While spike bursting can both generate and disrupt oscillations, these patterns are ineffective in large regions of the network state space in changing the network activity qualitatively. Finally, we show that when single-neuron properties are made dependent on the population activity, a hysteresis like dynamics emerges. This novel phenomenon has important implications for determining the network response to time-varying inputs and for the network sensitivity at different operating points.Neurons express a large diversity in terms of their biochemical, morphological and electrophysiological properties 1-4 . However, it is not clear if and under which conditions such diversity plays a functional role. It has been shown that selective stimulation of neurons of a given type expressing specific bio-markers can modulate different aspects of brain function 5 . For instance, selective stimulation of neurons changes the excitation/inhibition balance 6 , network dynamics 7,8 and computations performed by the network 9 , thereby leading to an altered animal behaviour. Moreover, noise introduced by intrinsic properties of neurons/synapses can have several effects. It can render the dynamics more robust to perturbations 10 and can improve the encoding and decoding of neuronal activity by reducing correlations 11 . These experiments provide strong support to the 'neuron doctrine' and motivate the search for novel bio-markers and specific functions of different classes of neurons 4,12 . However, experiments also suggest that stimulation of a certain neuron type may not cause any discernible change in the population activity and animal behaviour 13 . Moreover, detailed models of single neurons 14 and networks 15 have shown that multiple combinations of neuron and synapse parameters can lead to similar activity states 16 ; suggesting that exact neuronal properties are not crucial to obtain a specific dynamical network state and, hence, a specific function.These conflicting studies make it important to identify: (1) Changes in neuron properties that can affect network dynamics. (2) Dynamical states in which the network activity is susceptible to changes in a certain neuronal property. Here we focus on the effect of spike bursting on the network activity dynamics and vice versa. Spike bursting is a common electrophysiological descriptor of a neuron type 17,18 . The fraction of bursting neurons depends on the brain region 19 , and even in a given brain region the firing rate of spike bursts may change ...

12The excess of 15-30 Hz (β-band) oscillations in the basal ganglia is one of the key 13 signatures of Parkinson's disease (PD). The STN-GPe network is integral to generation 14 and modulation of β band oscillations in basal ganglia. However, the role of changes in 15 the firing rates and spike bursting of STN and GPe neurons in shaping these oscillations 16 has remained unclear. In order to uncouple their effects, we studied the dynamics of 17 STN-GPe network using numerical simulations. In particular, we used a neuron model, 18 in which firing rates and spike bursting can be independently controlled. Using this 19 model, we found that while STN firing rate is predictive of oscillations but GPe firing 20 rate is not. The effect of spike bursting in STN and GPe neurons was state-dependent . 21 That is, only when the network was operating in a state close to the border of 22 oscillatory and non-oscillatory regimes, spike bursting had a qualitative effect on the β 23 band oscillations. In these network states, an increase in GPe bursting enhanced the 24 oscillations whereas an equivalent proportion of spike bursting in STN suppressed the 25 oscillations. These results provide new insights into the mechanisms underlying the 26 transient β bursts and how duration and power of β band oscillations may be controlled 27 by an interplay of GPe and STN firing rates and spike bursts. 28Author summary 29The STN-GPe network undergoes a change in firing rates as well as increased bursting 30 during excessive β band oscillations during Parkinson's disease. In this work we 31 uncouple their effects by using a novel neuron model and show that presence of 32 oscillations is contingent on the increase in STN firing rates, however the effect of spike 33 bursting on oscillations depends on the network state. In a network state on the border 34 of oscillatory and non-oscillatory regime, GPe spike bursting strengthens oscillations. 35The effect of spike bursting in the STN depends on the proportion of GPe neurons 36 bursting. These results suggest a mechanism underlying a transient β band oscillation 37 bursts often seen in experimental data. 38 Introduction 39Parkinson's disease (PD) is a progressive neurodegenerative brain disease caused by the 40 depletion of dopamine neurons in the substantia nigra pars compacta (SNc) [1]. Loss of 41 March 4, 2020 1/36 dopamine causes a host of cognitive and motor impairments. The dopaminergic cells 42 death can be attributed many causes e.g. genetic mutations [1], pathogen that affects 43 the gut microbome and travels to the central nervous systems [2, 3], excitotoxicity [4], 44 and mitichondrial dysfunction [5] etc. [6]. While the etiology of PD is still debated, the 45 behavioral symptoms of PD are accompanied by various changes in the neuronal 46 activity in Basal Ganglia (BG): e.g, increased firing rate of D2 type dopamine receptors 47 expressing striatal neurons [7-9]; increase in spike bursts in striatum, globus pallidus 48 externa (GPe), globus pallidus interna (GPi) and subthalamic nucle...