Network motifs in cellular neurophysiology
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Cited by 3 publications
References 126 publications
Dichotomous impact of afferent sensory noise on grid-patterned firing and path integration in a continuous attractor network model
Background: The continuous attractor network (CAN) model has been effective in explaining grid-patterned firing in the rodent medial entorhinal cortex, with strong lines of experimental evidence and widespread utilities in understanding spatial navigation and path integration. A surprising lacuna in CAN analyses is the paucity of quantitative studies on the impact of afferent sensory noise on path integration. Here, we evaluate the impact of afferent sensory noise on grid-patterned firing and on the accuracy of position estimates derived from network pattern flow velocity. Motivated by the ability of border cells to act as an error-correction mechanism, we also assess the impact of interaction between afferent noise and border cell inputs on CAN performance.Methodology: We used an established 2D CAN model that received velocity inputs from a virtual animal traversing a 2D arena to generate grid-patterned firing. We estimated network pattern flow velocity from network activity and used that to compute an activity-based position estimate at each time step. We tracked the difference between the real and the estimated positions as a function of time and called it the deviation in integrated path (DIP). We defined afferent sensory noise to be additive Gaussian, with different noise levels achieved by changing the variance. We introduced north and east border cells and connected them to grid cells based on co-activity patterns. For different levels of noise, we computed DIP and metrics for grid-patterned activity in the presence vs. absence of border cells. Importantly, to avoid potential bias owing to the use of a single trajectory in computing these measurements, we performed all simulations across 50 different trajectories.Results: The computed grid scores and position accuracy (as DIP) showed pronounced trajectory-to-trajectory variability, even in a noise-free network. With the introduction of sensory noise, the variability prevailed and unveiled a dichotomous impact of afferent sensory noise on position accuracyvs. grid-patterned activity. Specifically, low levels of sensory noise improved position estimation accuracy without altering the ability of the network to generate grid-patterned activity. In contrast, high levels of sensory noise impaired position estimates as well as grid-patterned activity, although position estimates were more sensitive to sensory noise compared to grid-patterned activity. The stochastic resonance observed in the relationship between position accuracy and sensory noise level was partially explained by the interaction of noisy inputs with the rectification nonlinearity in the neural transfer function. Finally, across noise levels, pronounced trajectory-to-trajectory variability in grid-score and position accuracy was observed with the addition of border inputs. Across the population of trajectories, addition of border inputs yielded modest changes in both measurements across noise levels.Implications: Our analyses demonstrate that the robustness of grid-patterned activity in CAN models to noise does not extend to other functions of the CAN model. Stochastic resonance with reference to position estimation and sensory noise implies that biological CANs could evolve to yield optimal performance (path integration) in the presence of noise in biological sensory systems. An important methodological implication that emerges from our observations is the critical need to account for trajectory-to-trajectory variability in position estimates and path integration. Given the pronounced nature of trajectory-to-trajectory variability, conclusions based on a single trajectory are bound to be erroneous thereby warranting analyses with multiple trajectories. Together, our analyses unveil important roles for sensory noise in improving position estimates obtained from activity in CAN models.
Dichotomous impact of afferent sensory noise on grid-patterned firing and path integration in a continuous attractor network model
Background: The continuous attractor network (CAN) model has been effective in explaining grid-patterned firing in the rodent medial entorhinal cortex, with strong lines of experimental evidence and widespread utilities in understanding spatial navigation and path integration. A surprising lacuna in CAN analyses is the paucity of quantitative studies on the impact of afferent sensory noise on path integration. Here, we evaluate the impact of afferent sensory noise on grid-patterned firing and on the accuracy of position estimates derived from network pattern flow velocity. Motivated by the ability of border cells to act as an error-correction mechanism, we also assess the impact of interaction between afferent noise and border cell inputs on CAN performance.Methodology: We used an established 2D CAN model that received velocity inputs from a virtual animal traversing a 2D arena to generate grid-patterned firing. We estimated network pattern flow velocity from network activity and used that to compute an activity-based position estimate at each time step. We tracked the difference between the real and the estimated positions as a function of time and called it the deviation in integrated path (DIP). We defined afferent sensory noise to be additive Gaussian, with different noise levels achieved by changing the variance. We introduced north and east border cells and connected them to grid cells based on co-activity patterns. For different levels of noise, we computed DIP and metrics for grid-patterned activity in the presence vs. absence of border cells. Importantly, to avoid potential bias owing to the use of a single trajectory in computing these measurements, we performed all simulations across 50 different trajectories.Results: The computed grid scores and position accuracy (as DIP) showed pronounced trajectory-to-trajectory variability, even in a noise-free network. With the introduction of sensory noise, the variability prevailed and unveiled a dichotomous impact of afferent sensory noise on position accuracyvs. grid-patterned activity. Specifically, low levels of sensory noise improved position estimation accuracy without altering the ability of the network to generate grid-patterned activity. In contrast, high levels of sensory noise impaired position estimates as well as grid-patterned activity, although position estimates were more sensitive to sensory noise compared to grid-patterned activity. The stochastic resonance observed in the relationship between position accuracy and sensory noise level was partially explained by the interaction of noisy inputs with the rectification nonlinearity in the neural transfer function. Finally, across noise levels, pronounced trajectory-to-trajectory variability in grid-score and position accuracy was observed with the addition of border inputs. Across the population of trajectories, addition of border inputs yielded modest changes in both measurements across noise levels.Implications: Our analyses demonstrate that the robustness of grid-patterned activity in CAN models to noise does not extend to other functions of the CAN model. Stochastic resonance with reference to position estimation and sensory noise implies that biological CANs could evolve to yield optimal performance (path integration) in the presence of noise in biological sensory systems. An important methodological implication that emerges from our observations is the critical need to account for trajectory-to-trajectory variability in position estimates and path integration. Given the pronounced nature of trajectory-to-trajectory variability, conclusions based on a single trajectory are bound to be erroneous thereby warranting analyses with multiple trajectories. Together, our analyses unveil important roles for sensory noise in improving position estimates obtained from activity in CAN models.
Ion-channel degeneracy and heterogeneities in the emergence of signature physiological characteristics of dentate gyrus granule cells
Complex systems are neither fully determined nor completely random. Biological complex systems, including single neurons, manifest intermediate regimes of randomness that recruit integration of specific combinations of functionally segregated subsystems. Such emergence of biological function provides the substrate for the expression of degeneracy, the ability of disparate combinations of subsystems to yield similar function. Here, we present evidence for the expression of degeneracy in morphologically realistic models of dentate gyrus granule cells (GC) through functional integration of disparate ion-channel combinations. We performed a 45-parameter randomized search spanning 16 active and passive ion channels, each biophysically constrained by their gating kinetics and localization profiles, to search for valid GC models. Valid models were those that satisfied 17 sub- and supra-threshold cellular-scale electrophysiological measurements from rat GCs. A vast majority (>99%) of the 15,000 random models were not electrophysiologically valid, demonstrating that arbitrarily random ion-channel combinations wouldn't yield GC functions. The 141 valid models (0.94% of 15,000) manifested heterogeneities in and cross-dependencies across local and propagating electrophysiological measurements, which matched with their respective biological counterparts. Importantly, these valid models were widespread throughout the parametric space and manifested weak cross-dependencies across different parameters. These observations together showed that GC physiology could neither be obtained by entirely random ion-channel combinations nor is there an entirely determined single parametric combination that satisfied all constraints. The complexity, the heterogeneities in measurement and parametric spaces, and degeneracy associated with GC physiology should be rigorously accounted for, while assessing GCs and their robustness under physiological and pathological conditions.
The Brain's Best Kept Secret Is Its Degenerate Structure
Degeneracy is defined as multiple sets of solutions that can produce very similar system performance. Degeneracy is seen across phylogenetic scales, in all kinds of organisms. In neuroscience, degeneracy can be seen in the constellation of biophysical properties that produce a neuron's characteristic intrinsic properties and/or the constellation of mechanisms that determine circuit outputs or behavior. Here, we present examples of degeneracy at multiple levels of organization, from single-cell behavior, small circuits, large circuits, and, in cognition, drawing conclusions from work ranging from bacteria to human cognition. Degeneracy allows the individual-to-individual variability within a population that creates potential for evolution.
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