The supplementary motor area (SMA) is believed to contribute to higher-order aspects of motor control.To examine this contribution, we employed a novel cycling task and leveraged an emerging strategy: testing whether population trajectories possess properties necessary for a hypothesized class of computations. We found that, at the single-neuron level, SMA exhibited multiple response features absent in M1. We hypothesized that these diverse features might contribute, at the population level, to avoidance of 'population trajectory divergence' -ensuring that two trajectories never followed the same path before separating. Trajectory divergence was indeed avoided in SMA but not in M1. Network simulations confirmed that low trajectory divergence is necessary when guidance of future action depends upon internally tracking contextual factors. Furthermore, the empirical trajectory geometryhelical in SMA versus elliptical in M1 -was naturally reproduced by networks that did, versus did not, internally track context.
The supplementary motor area (SMA) is believed to contribute to higher-order aspects of motor control.To examine this contribution, we employed a novel cycling task and leveraged an emerging strategy: testing whether population trajectories possess properties necessary for a hypothesized class of computations. We found that, at the single-neuron level, SMA exhibited multiple response features absent in M1. We hypothesized that these diverse features might contribute, at the population level, to avoidance of 'population trajectory divergence' -ensuring that two trajectories never followed the same path before separating. Trajectory divergence was indeed avoided in SMA but not in M1. Network simulations confirmed that low trajectory divergence is necessary when guidance of future action depends upon internally tracking contextual factors. Furthermore, the empirical trajectory geometryhelical in SMA versus elliptical in M1 -was naturally reproduced by networks that did, versus did not, internally track context. 2Relative to primary motor cortex (M1), SMA activity is less coupled to actions of a specific body part 10-12 .3 Instead, SMA computations appear related to learned sensory-motor associations 11 , reward 4 anticipation 13 , internal initiation and guidance of movement 3,14 , movement timing 15,16 , and movement 5 sequencing 7,17,18 . Single-neuron responses in SMA reflect a variety of task-specific contingencies. For 6 example, in a sequence of three movements, a neuron may burst only when pulling precedes pushing. 7Another neuron might respond before the third movement regardless of the particular sequence 19 . 8 Different response features are observed in different tasks. Single SMA neurons exhibit a mixture of 9 ramping and rhythmic activity during an interval timing task 20 , and the SMA population exhibits 10 amplitude-modulated circular trajectories during rhythmic tapping 21 . A common thread linking prior 11 studies is that SMA computations are hypothesized to be critical when pending action depends upon 12 internal, abstract, and/or contextual factors. An important challenge is linking these high-level ideas to 13 network-level implementations. What general properties should activity exhibit in networks performing 14 the hypothesized class of computations? 15There exist many quantitative methods for relating population activity and computation (e.g., [22][23][24] ). 16These include decoding key hypothesized signals (e.g., via regression 25 ), or directly comparing empirical 17 and simulated population activity (e.g., via canonical correlation 26 ). An emerging strategy is to consider 18 the geometry of the population response: the arrangement of population states across conditions 23,27,28 19 and/or the shape traced by activity in neural state-space 15,26,[29][30][31][32][33][34][35][36] . A given geometry may be consistent 20 with some types of computation but not others 37 . An advantage of this approach is that it is sometimes 21 possible to measure geometric properties that are expected to hold f...
Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian input statistics. Interestingly, the speed, not the size, of synaptic fluctuations dictates the degree of sparsity in the model. In addition to simulations, we provide a mean-field analysis to illustrate the properties of these networks.
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