Compensatory variability in network parameters enhances memory performance in the Drosophila mushroom body

Neural circuits use homeostatic compensation to achieve consistent behavior despite variability in underlying intrinsic and network parameters. However, it remains unclear how compensation regulates variability across a population of the same type of neurons within an individual and what computational benefits might result from such compensation. We address these questions in the Drosophila mushroom body, the fly’s olfactory memory center. In a computational model, we show that under sparse coding conditions, memory performance is degraded when the mushroom body’s principal neurons, Kenyon cells (KCs), vary realistically in key parameters governing their excitability. However, memory performance is rescued while maintaining realistic variability if parameters compensate for each other to equalize KC average activity. Such compensation can be achieved through both activity-dependent and activity-independent mechanisms. Finally, we show that correlations predicted by our model’s compensatory mechanisms appear in the Drosophila hemibrain connectome. These findings reveal compensatory variability in the mushroom body and describe its computational benefits for associative memory.

Noise and variability are inevitable features of biological systems. Neural circuits achieve consistent activity patterns despite this variability using homeostatic plasticity; because neural activity is governed by multiple intrinsic and network parameters, variability in one parameter can compensate for variability in another to achieve the same circuit behavior (1–5). This phenomenon of compensatory variability has typically been addressed from the perspective of consistency of neural activity across individual animals (6, 7) or over an animal’s lifetime, in the face of circuit perturbations (8–11). However, less attention has been paid to potential benefits of maintaining consistent neuronal properties across a population of neurons within an individual circuit.Indeed, previous work has emphasized the benefits of neuronal variability/heterogeneity rather than neuronal homogeneity (12–14). (Here, we follow ref. 5 in using “heterogeneity” to refer to qualitative differences [e.g., between cell types] and “variability” to refer to quantitative differences in parameter values.) Of course, different neuronal classes encode different information (e.g., visual vs. auditory neurons or ON vs. OFF cells). Yet, even in populations that ostensibly encode the same kind of stimulus, like olfactory mitral cells, variability of neuronal excitability can increase the information content of their population activity (15–17). In addition, variability in neuronal timescales can improve learning in neural networks (18, 19). In what contexts and in what senses might the opposite be true (i.e., when does neuronal similarity provide computational benefits over neuronal variability)? Additionally, what mechanisms could enforce neuronal similarity in the face of interneuronal variability?Here, we address these questions using olfactory associative memory in the mushroom body of the fruit fly Drosophila. Flies learn to associate specific odors with salient events (e.g., food or danger). These olfactory associative memories are stored in the principal neurons of the mushroom body, called Kenyon cells (KCs), as modifications in KCs’ output synapses (20–22) (reviewed in ref. 23). Because learning occurs at the single output layer, the nature of the odor representation in the KC population is crucial to the fly’s ability to learn to form distinct associative memories for different odors. In particular, the fact that KCs respond sparsely to incoming odors (≈ 10% per odor) (24) allows different odors to activate unique, nonoverlapping subsets of KCs and thereby enhances flies’ learned discrimination of similar odors (25).A potential problem for this sparse coding arises from variability between KCs. KCs receive inputs from second-order olfactory neurons called projection neurons (PNs), with an average of approximately six PN inputs per KC, and typically require simultaneous activation of multiple input channels in order to spike (26), thanks to high spiking thresholds and feedback inhibition (25, 27). However, there is substantial variation across KCs in the key parameters controlling their activity, such as the number of PN inputs per KC (28), the strength of PN–KC synapses, and KC spiking thresholds (27). Intuitively, such variation could lead to a situation where some KCs with low spiking thresholds and many or strong excitatory inputs fire indiscriminately to many different odors, while other KCs with high spiking thresholds and few or weak excitatory inputs never fire; KCs at both extremes are effectively useless for learning to classify odors, even if overall only 10% of KCs respond to each odor. However, it remains unclear whether biologically realistic inter-KC variability would affect the mushroom body’s memory performance and what potential strategies might counter the effects of inter-KC variability.Here, we show in a rate-coding model of the mushroom body that introducing experimentally derived inter-KC variability into the model substantially impairs its memory performance. This impairment arises from increased variability in average activity among KCs, which means fewer KCs have sparse-enough activity to be specific to rewarded vs. punished odors. However, memory performance can be rescued by compensating away variability in KC activity while preserving the experimentally observed variation in the underlying parameters. This can occur through activity-dependent homeostatic plasticity or direct correlations between key parameters like number vs. strength of inputs. Finally, we analyze the hemibrain connectome to show that, indeed, the number of PN inputs per KC is inversely correlated with the strength of each input, while the strength of inhibitory inputs is correlated with the total strength of excitatory inputs. Thus, we show both the existence and computational benefit of compensatory variability in mushroom body network parameters.