Noise-induced properties of active dendrites

Dendrites play an essential role in the integration of highly fluctuating input in vivo into neurons across all nervous systems. Yet, they are often studied under conditions where inputs to dendrites are sparse. The dynamic properties of active dendrites facing in vivo–like fluctuating input thus remain elusive. In this paper, we uncover dynamics in a canonical model of a dendritic compartment with active calcium channels, receiving in vivo–like fluctuating input. In a single-compartment model of the active dendrite with fast calcium activation, we show noise-induced nonmonotonic behavior in the relationship of the membrane potential output, and mean input emerges. In contrast, noise can induce bistability in the input–output relation in the system with slowly activating calcium channels. Both phenomena are absent in a noiseless condition. Furthermore, we show that timescales of the emerging stochastic bistable dynamics extend far beyond a deterministic system due to stochastic switching between the solutions. A numerical simulation of a multicompartment model neuron shows that in the presence of in vivo–like synaptic input, the bistability uncovered in our analysis persists. Our results reveal that realistic synaptic input contributes to sustained dendritic nonlinearities, and synaptic noise is a significant component of dendritic input integration.

Neuronal interactions are mediated via synapses primarily located on large, tree-like dendritic structures. These dendritic trees integrate synaptic inputs and determine the extent of the neuron’s spiking output (1). Dendrites contribute substantially to neuronal plasticity and function (2–4). Their active calcium dynamics can induce nonlinear regenerative events, such as dendritic spikes, both in vitro (5) and in vivo (6). Dendritic spikes also serve a functional role in in vivo cortical visual processing, where a typical pyramidal neuron receives massive amounts of intensely fluctuating synaptic input from excitatory and inhibitory presynaptic neurons in the circuit (7). Although dendrites’ importance in integrating relevant signals in vivo is evident (3), how a dendritic tree transfers its input into output in noisy conditions is essentially unknown. Synaptic noise is commonly assumed to be a nuisance, and nervous systems develop strategies to filter it. However, noise can also induce new organized behaviors in systems that lack in deterministic conditions (8). Examples of noise leading to spontaneous order in biological and physical systems include stochastic resonance (9), noise-induced phase transitions (10), and noise-induced bistability (11). To investigate whether in vivo–like fluctuating input induces novel dynamic states in active dendrites, we analytically study a canonical model of a dendritic compartment with voltage-gated calcium channels.Various types of voltage-gated calcium channels in the dendrite have been studied (12, 13). In spinal motoneurons, where input is sparse, dendritic calcium channels can mediate a persistent depolarizing drive underlying their bistable dendritic properties (14). Despite the diversity of dendritic calcium channels in central nervous system neurons, no in vitro experiments have reported calcium channels that directly induce bistability. However, the experimental evidence suggests long-lasting dendritic elevated responses to a brief input in vivo, known as dendritic plateau potentials (15–17). Dendritic plateau potentials play an essential role in enhancing localized learning and information storage capacity at a specific dendritic branch (15). In this paper, we study whether the interaction of nonlinear calcium dynamics and in vivo–like fluctuation contributes to dendritic plateau potentials in the central nervous system.We study a canonical single-compartment model of an active dendrite to understand how the realistic in vivo input interacts with dendritic calcium channels. Our results indicate that stochastic phenomena emerge in dendritic dynamics with in vivo–like fluctuating input that is entirely absent in the deterministic condition. We observe that in vivo–like noise induces nonmonotonic or bistable dynamics in the input–output relation of a single-compartment dendritic model, depending on the timescales of calcium-gating variables. To investigate the relevance of these results for spatially extended neurons, we further numerically study a multicompartmental model neuron receiving realistic synaptic inputs across the dendritic branches. Our paper reveals that the interaction between in vivo–like input fluctuations and dendritic voltage-gated calcium channels could lead to dendritic plateau potentials.