The firing rate of speed cells, a dedicated subpopulation of neurons in the medial entorhinal cortex (MEC), is correlated with running speed. This correlation has been interpreted as a speed code used in various computational models for path integration. These models consider firing rate to be linearly tuned by running speed in real-time. However, estimation of firing rates requires integration of spiking events over time, setting constraints on the temporal accuracy of the proposed speed code. We therefore tested whether the proposed speed code by firing rate is accurate at short time scales using data obtained from open-field recordings in male rats and mice. We applied a novel filtering approach differentiating between speed codes at multiple time scales ranging from deciseconds to minutes. In addition, we determined the optimal integration time window for firing-rate estimation using a general likelihood framework and calculated the integration time window that maximizes the correlation between firing rate and running speed. Data show that these time windows are on the order of seconds, setting constraints on real-time speed coding by firing rate. We further show that optogenetic inhibition of either cholinergic, GABAergic, or glutamatergic neurons in the medial septum/diagonal band of Broca does not affect modulation of firing rates by running speed at each time scale tested. These results are relevant for models of path integration and for our understanding of how behavioral activity states may modulate firing rates and likely information processing in the MEC.

Neuronal representations of spatial location and movement speed in the medial entorhinal cortex during the ‘active’ theta state of the brain are important for memory-guided navigation and rely on visual inputs. However, little is known about how visual inputs change neural dynamics as a function of running speed and time. By manipulating visual inputs in mice, we demonstrate that changes in spatial stability of grid cell firing correlate with changes in a proposed speed signal by local field potential theta frequency. In contrast, visual inputs do not alter the running speed-dependent gain in neuronal firing rates. Moreover, we provide evidence that sensory inputs other than visual inputs can support grid cell firing, though less accurately, in complete darkness. Finally, changes in spatial accuracy of grid cell firing on a 10 s time scale suggest that grid cell firing is a function of velocity signals integrated over past time.

11Neuronal representations of spatial location and movement speed are important for a broad 12 range of cognitive functions, including spatial self-localization and memory-guided navigation. 13Two possible speed signals, by theta frequency or by firing rate, have been hypothesized to 14 provide the velocity signal needed for generating the spatially periodic grid cell firing pattern. 15However, which of these speed signals is utilized by the brain remains unknown. By 16 manipulating visual inputs and analyzing the time-courses of evoked changes, we demonstrate 17 that changes in spatial stability of grid cell firing correlate in time with changes in speed coding 18 by local field potential theta frequency. In contrast, visual inputs do not affect speed coding by 19 firing rate even if baseline firing rates are changed. Moreover, grid cells maintain a spatially 20 periodic firing pattern, though less stable, in complete darkness. These data suggest that mice 21 use an oscillatory speed signal to perform path integration. 22 23 ( Supplementary Fig. 1B & C). 126 127Local field potential activity in the MEC primarily reflects the summed activity of synaptic inputs 128 to the MEC, which is likely to be correlated with firing patterns of MEC neurons. Many neurons 129 in the MEC show a theta rhythmic firing pattern and-similarly to the LFP theta frequency-the 130 frequency of theta rhythmic firing increases with running speed (Hinman et al., 2016). In our 131 data set, we identified a total of n = 342 neurons from 14 mice as theta modulated based on 132 their autocorrelograms. We asked if and how theta rhythmic firing in these theta modulated 133 MEC neurons is affected by removing and reinstating all visual inputs. Towards that aim we 134 used an MLE approach (Climer et al., 2015) to fit a model of theta spiking rhythmicity to the 135 observed spike train autocorrelations and identify the frequency and magnitude of theta 136

No abstract

Conductance-based models of neurons are used extensively in computational neuroscience. Working with these models can be challenging due to their high dimensionality and large number of parameters. Here, we present a neuron and network simulator built on a novel automatic type system that binds object-oriented code written in C++ to objects in MATLAB. Our approach builds on the tradition of uniting the speed of languages like C++ with the ease-of-use and feature-set of scientific programming languages like MATLAB. Xolotl allows for the creation and manipulation of hierarchical models with components that are named and searchable, permitting intuitive high-level programmatic control over all parts of the model. The simulator's architecture allows for the interactive manipulation of any parameter in any model, and for visualizing the effects of changing that parameter immediately. Xolotl is fully featured with hundreds of ion channel models from the electrophysiological literature, and can be extended to include arbitrary conductances, synapses, and mechanisms. Several core features like bookmarking of parameters and automatic hashing of source code facilitate reproducible and auditable research. Its ease of use and rich visualization capabilities make it an attractive option in teaching environments. Finally, xolotl is written in a modular fashion, includes detailed tutorials and worked examples, and is freely available at https://github.com/sg-s/xolotl, enabling seamless integration into the workflows of other researchers.