Neuromodulation of excitability and synaptic plasticity: an underestimated challenge for computational models

Neuroactive chemicals called neuromodulators organize the switch between different brain states changing the way networks process neural signals. Precise temporal and spatial control of brain states is required for changes associated with movement, attention, perception, motivation, or expectation. A well-known example occurs during the sleep-wake cycle. Neuronal population switches from active to oscillatory states. Zooming at the cellular level, thalamic neurons switch from tonic to burst [McCormick,1997]. From a computational point of view, neurons are commonly implemented using a conductance-based model (a formalism described by Hodgkin and Huxley) or using an integrate-and-fire model (reproducing the spiking activity).

In parallel, brains comprise well-defined circuits that are nonetheless modifiable by experience, a property critical for learning. This property is often attributed to the ability of neurons to modify their connections with other cells through a mechanism called synaptic plasticity. It exploits the correlation level in the activity of neighboring neurons. From a computational point of view, two categories of plasticity rules are established. The first category comprises phenomenological models reproducing spiking timing dependent plasticity (STDP) to drive the synaptic change [Pfister,2016; Graupner,2016]. The second category comprises biological models using calcium as the key signal. Synaptic potentiation or depression is activated when calcium crosses distinct thresholds. High (resp. intermediate) calcium levels cause a fast strengthening (resp. slow reduction) of the synaptic weight called potentiation (resp. depression) [Shouval,2002; Graupner,2012]. These rules rely on different properties of pre- and postsynaptic neuronal firing patterns making them susceptible to neuromodulation-induced changes in brain states.

Moreover, it has recently become more and more evident that synaptic plasticity rules themselves are also under the control of neuromodulators, by example the cholinergic, dopaminergic, noradrenergic, serotonergic, and histaminergic systems [Brzosko et al., 2019, Zhang, 2009]. From a computational point of view, neuromodulation is commonly implemented by tuning parameters of the diverse synaptic plasticity rules.

Now, neuromodulation of excitability and synaptic plasticity are often studied separately. It is partly due to the fact that most synaptic plasticity models consider simple spike time series as inputs for the plasticity rule [Babadi and Abbott, 2016], whereas neuromodulation of firing activity requires complex, quantitative neuron modeling. However, both effects often occur in concert.

In this project, we build a physiological circuit using neuron conductance-based models. The synaptic weight between neurons is driven either by a phenomenological rule or a calcium-based rule. We propose two simple experiments to study the interaction between neuromodulation of neuronal firing and synaptic plasticity. (i) We use two thalamocortical circuits that perform a neuromodulatory-induced transition from tonic to burst and we track the evolution of the synaptic weight. For a similar synchronous bursting pattern exhibited by the two circuits, we introduce a small variability affecting the causality between the pre- and the postsynaptic spike times inside the intra-burst period. This simple experiment illustrates a plausible situation since an endogenous synchronous burst does not lie on a synchronous spike timing. For the spike timing dependent plasticity rule, this small temporal perturbation leads to a contradictory result: the weight grows in one circuit and decreases to 0 in the other one. By contrast, a calcium-based rule is insensitive to this small timing change. (ii) We compare the evolution of the synaptic weight in two circuits distinct in the number of calcium channels - as found in real brains or by mimicking variability between individuals. Once again, this small difference results in contrasting outcomes. When this experiment is performed with a spike timing dependent rule, the synaptic weight evolution is not affected. While the calcium-based rule is fragile to this neuronal intrinsic perturbation.

To conclude, this work shows the lack of model compatibility between, on one side neuromodulation of excitability and on the other side neuromodulation of synaptic plasticity. The different plasticity rules are not consistent with (i) the impact of neuromodulatory-induced transition from tonic to burst and (ii) the neuromodulation of intrinsic parameters such as variation in calcium channel density. The experiments produce contradictory results depending on the chosen plasticity rule. It supports the importance of studying the interaction between these complex mechanisms and of building robust models rather than precisely tune mathematical rules.