bioRxiv preprint doi: https://doi.org/10.1101/137984; this version posted November 7, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. Noname manuscript No. (will be inserted by the editor) Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity Tomasz G´orski 1,2,* · Romain Veltz 3 · Mathieu Galtier 1 · H´elissande Fragnaud 1 · Jennifer S. Goldman 1,2 · Bartosz Tele´nczuk 1,2 · Alain Destexhe 1,2 Received: date / Accepted: date Abstract Many neurons possess dendrites enriched with integration is played by dendritic spikes: regenerative sodium channels and are capable of generating action currents through Na+, Ca2+ or NMDAr channels. The potentials. However, the role of dendritic sodium spikes first evidence of dendritic spikes came from field record- remain unclear. Here, we study computational mod- ings [1{5], corroborated by the intracellular recordings els of neurons to investigate the functional effects of [6{8]. The repertoire of techniques was further enlarged dendritic spikes. In agreement with previous studies, by patch clamp [9{13] and optical methods. Calcium we found that point neurons or neurons with passive imaging allowed for the direct observation of calcium dendrites increase their somatic firing rate in response spikes [14{18], and glutamate uncaging and voltage sen- to the correlation of synaptic bombardment for a wide sitive dyes led to the discovery of NMDA spikes [19,20]. range of input conditions, i.e. input firing rates, synap- Dendritic spikes allow for more subtle integration tic conductances or refractory periods. However, neu- of synaptic input than in a passive dendrite. A sin- rons with active dendrites show the opposite behav- gle dendritic branch can act as a coincidence detector, ior: for a wide range of conditions the firing rate de- generating a spike when exposed to synchronized in- creases as a function of correlation. We found this prop- put [20{22]. The propagation of dendritic spikes gener- erty in three types of models of dendritic excitability: ated in the distal part of dendritic tree can be gated a Hodgkin-Huxley model of dendritic spikes, a model by synaptic input in the proximal region, as was shown with integrate-and-fire dendrites, and a discrete-state for hippocampal CA1 pyramidal neurons [23], and L5 dendritic model. We conclude that neurons equipped pyramidal neurons [24]. After the initiation of a den- with with fast dendritic spikes confer much broader dritic spike, sodium channels inactivate and the branch computational properties to neurons, sometimes oppo- switches into a refractory state which crucially affects site to that of point neurons. integration [25]. Backpropagating action potentials also Keywords Dendritic integration · Synaptic input play an essential role in spike time-dependent plasticity correlations [26{28], and the participation of local dendritic spikes has been implicated in long-term potentiation [29,30]. 1 Introduction Sodium spikes can propagate in many cell types: neocortical pyramidal cells [9,31{34], hippocampal CA1 Increasing evidence shows that nonlinear integration and CA3 pyramidal cells [35{39], interneurons [40] or of synaptic inputs in dendrites is crucial for the com- thalamic neurons [41]. Models predicted that, in vivo, putational properties of neurons. A major role in the the presence of synaptic background activity should greatly enhance the initiation and propagation of den- * [email protected] dritic spikes [42, 43]. This suggests that there can be a 1 Unit´ede Neurosciences, Information et Complexit´e,Centre National de la Recherche Scientifique, Gif-sur-Yvette, France heavy traffic of dendritic spikes, as indeed found in re- 2 European Institute for Theoretical Neuroscience Paris, cent dendritic recordings in awake animals [44]. There- France fore interactions between dendritic spikes likely play an 3 Inria, Sophia Antipolis, France important role in dendritic integration. bioRxiv preprint doi: https://doi.org/10.1101/137984; this version posted November 7, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 2 Tomasz G´orski 1,2,* et al. These interactions can be conveyed by the refrac- To generate such locally and globally correlated synap- tory period which follows each spike [45], and can pre- tic inputs, we used a previously proposed algorithm vent initiations of subsequent spikes, or can result in a [54]. From a global spike train G obtained from Pois- collision and annihilation of spikes [46]. Here, compar- son process, we draw random spikes with probability ing different types of computational models, we show rG. The spike train Lk thus obtained corresponds to all that interactions between dendritic spikes can change synapses on a single dendritic compartment. Finally, i the way the correlation of synaptic input affects the the spike train Sk for a synapse i situated on compart- firing rate of the cell. For single-compartment neurons ment k is built by drawing spikes from Lk with local and neurons with passive dendrites an increase of cor- probability rL [Fig. 1]. relation of synaptic input is known to cause an increase In this model, the ratio of shared spikes between of firing rate [47{50], while this relation can be reversed synapses situated on the same compartment is equal to only for high input intensities. We show that neurons cL = rL and the ratio of spikes shared by synapses situ- with active dendrites behave the opposite way: for wide ated on different compartments is equal to cG = rLrG. range of input conditions, the firing rate varies inversely Note that cL is always greater than or equal to cG. At proportionally to the level of correlation. We discuss the end, we added a jitter to each spike time to obtain possible consequences of this property at the network desynchronized input. The jitter is drawn from expo- level. nential distribution with a standard deviation τj with equal probability for positive and negative values. To obtain the time-dependent synaptic conductances, we 2 Results convolve the resulting spike trains with an exponential function reflecting the change of synaptic conductance We first show the phenomenon of inverse correlation due to a single spike. processing using a multi-compartment Hodgkin-Huxley model with active dendrites. Next, we investigate the impact of the refractory period duration on inverse pro- 2.2 Response to correlated synaptic activity in cessing using a multi-compartment integrate-and-fire biophysical dendritic models model. Finally, we show that this phenomenon is also present in simplified discrete-state dendritic models. We first apply this model of correlation processing to Hodgkin-Huxley model of neuron with a dendrite (see Methods). In our model the dendritic spikes can be one 2.1 Model of correlated synaptic activity order of magnitude more frequent than somatic spikes (Fig. 2), value similar to that observed in vivo [44]. In In all models studied here, we considered neurons sub- Fig. 3, we show how dendritic sodium spikes propagate ject to in vivo{like synaptic activity. In particular, we and collide in the model. We investigate how interac- aimed at investigating the effects of synaptic noise cor- tions between dendritic spikes can affect the response of relations on the firing of the cell. The synapses were lo- a neuron to correlated synaptic activity. We run simu- cated on the somatic and dendritic compartments and lations of the model under correlated synaptic activity. were of two types: excitatory AMPA synapses (with re- For each run, we measured the firing rate of somatic versal potential Ee = 0 mV) and inhibitory GABAA spikes and asked how this quantity is affected by the synapses (Ei = −75 mV), with five times more excita- ratio of shared spikes (Fig.4). For each ratio we per- tory than inhibitory synapses [51]. formed 20 runs with a duration of 20 s. With increasing We considered the case where the pre-synaptic spikes density of active channels in the dendrite, the somatic triggering the excitatory inputs are correlated. There firing response changes to become inverse, i.e. we ob- might be two biological sources of such correlation. First serve a decrease of somatic firing rate with the correla- of all, in cortical networks neurons are known to share tion of synaptic input (Fig.4a). To adequately compare some of their synaptic inputs which inevitably makes the multicompartment neuron with a point neuron, we their spikes correlated. Since this type of correlation have scaled the synaptic conductances in the point neu- is common to larger populations of neurons, we call it ron to emulate filtering of EPSPs by the dendrite. The the global correlation [52]. In addition, a single axon inverse response of a neuron with dendrite can be en- can create several synapses on close-by segments of the hanced by the increase of input firing rate and the in- dendrite activating them at the same time [53], so that crease of synaptic weights (Fig.4a,b). In contrast, in the the correlation of the input spikes within the same den- point neuron model, the firing rate response generally dritic segments (local correlation) can be higher than increased with correlation, as found previously [47,48]. the global correlation. It could also remain approximately constant for high bioRxiv preprint doi: https://doi.org/10.1101/137984; this version posted November 7, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.