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In order to forage for food, many animals regulate not only specific limb movements but the statistics of locomotor behavior, switching between long-range dispersal and local search depending on resource availability. How premotor circuits regulate locomotor statistics is not clear. Here, we analyze and model locomotor statistics and their modulation by attractive food odor in walkingDrosophila. Food odor evokes three motor regimes in flies: baseline walking, upwind running during odor, and search behavior following odor loss. During search, we find that flies adopt higher angular velocities and slower ground speeds and turn for longer periods in the same direction. We further find that flies adopt periods of different mean ground speed and that these state changes influence the length of odor-evoked runs. We next developed a simple model of neural locomotor control that suggests that contralateral inhibition plays a key role in regulating the statistical features of locomotion. As the fly connectome predicts decussating inhibitory neurons in the premotor lateral accessory lobe (LAL), we gained genetic access to a subset of these neurons and tested their effects on behavior. We identified one population whose activation induces all three signature of local search and that regulates angular velocity at odor offset. We identified a second population, including a single LAL neuron pair, that bidirectionally regulates ground speed. Together, our work develops a biologically plausible computational architecture that captures the statistical features of fly locomotion across behavioral states and identifies neural substrates of these computations. 

Neural activity in the cortex is highly variable in response to repeated stimuli. Population recordings across the cortex demonstrate that the variability of neuronal responses is shared among large groups of neurons and concentrates in a low dimensional space. However, the source of the population-wide shared variability is unknown. In this work, we analyzed the dynamical regimes of spatially distributed networks of excitatory and inhibitory neurons. We found chaotic spatiotemporal dynamics in networks with similar excitatory and inhibitory projection widths, an anatomical feature of the cortex. The chaotic solutions contain broadband frequency power in rate variability and have distance-dependent and low-dimensional correlations, in agreement with experimental findings. In addition, rate chaos can be induced by globally correlated noisy inputs. These results suggest that spatiotemporal chaos in cortical networks can explain the shared variability observed in neuronal population responses. 

We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviours that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase-locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.