Grid Firing Research Articles

Impacts of changing fire weather conditions on reconstructed trends in U.S. wildland fire activity from 1979 to 2014

AbstractOne component of climate‐fire interactions is the relationship between weather conditions concurrent with burning (i.e., fire danger) and the magnitude of fire activity. Here daily environmental conditions are associated with daily observations of fire activity within ecoregions across the continental United States (CONUS) by aligning the latter 12 years of a 36 year gridded fire danger climatology with the Moderate Resolution Imaging Spectroradiometer fire products. Results reveal that although modern relationships (2003–2014) vary regionally, fires across the majority of CONUS are more likely to be present and burning more vigorously as fire danger increases. Applying modern relationships to the entire climatology (1979–2014) indicates that in the absence of other influences, changes in fire danger have significantly increased the number of days per year that fires are burning across 42–49% of CONUS (by area) while also significantly increasing daily fire growth and daily heat release across 37–45% of CONUS. Increases in the fire activity season length coupled with an intensification of daily burning characteristics resulted in a CONUS‐wide +0.02 Mha yr−1 trend in burned area, a 10.6 g m−2 yr−1 trend in the amount of fuel consumed per unit burned area, and ultimately a +0.51 Tg yr−1 trend in dry matter consumption. Overall, the results demonstrate regional variations in the response of fires to changes in fire danger and that weather conditions concurrent with burning have a three‐pronged impact on the magnitude of fire activity by affecting the seasonal duration, spatial extent, and combustion intensity.

Absence of Visual Input Results in the Disruption of Grid Cell Firing in the Mouse

SummaryGrid cells are spatially modulated neurons within the medial entorhinal cortex whose firing fields are arranged at the vertices of tessellating equilateral triangles [1]. The exquisite periodicity of their firing has led to the suggestion that they represent a path integration signal, tracking the organism’s position by integrating speed and direction of movement [2, 3, 4, 5, 6, 7, 8, 9, 10]. External sensory inputs are required to reset any errors that the path integrator would inevitably accumulate. Here we probe the nature of the external sensory inputs required to sustain grid firing, by recording grid cells as mice explore familiar environments in complete darkness. The absence of visual cues results in a significant disruption of grid cell firing patterns, even when the quality of the directional information provided by head direction cells is largely preserved. Darkness alters the expression of velocity signaling within the entorhinal cortex, with changes evident in grid cell firing rate and the local field potential theta frequency. Short-term (<1.5 s) spike timing relationships between grid cell pairs are preserved in the dark, indicating that network patterns of excitatory and inhibitory coupling between grid cells exist independently of visual input and of spatially periodic firing. However, we find no evidence of preserved hexagonal symmetry in the spatial firing of single grid cells at comparable short timescales. Taken together, these results demonstrate that visual input is required to sustain grid cell periodicity and stability in mice and suggest that grid cells in mice cannot perform accurate path integration in the absence of reliable visual cues.

Visual landmarks sharpen grid cell metric and confer context specificity to neurons of the medial entorhinal cortex.

Neurons of the medial entorhinal cortex (MEC) provide spatial representations critical for navigation. In this network, the periodic firing fields of grid cells act as a metric element for position. The location of the grid firing fields depends on interactions between self-motion information, geometrical properties of the environment and nonmetric contextual cues. Here, we test whether visual information, including nonmetric contextual cues, also regulates the firing rate of MEC neurons. Removal of visual landmarks caused a profound impairment in grid cell periodicity. Moreover, the speed code of MEC neurons changed in darkness and the activity of border cells became less confined to environmental boundaries. Half of the MEC neurons changed their firing rate in darkness. Manipulations of nonmetric visual cues that left the boundaries of a 1D environment in place caused rate changes in grid cells. These findings reveal context specificity in the rate code of MEC neurons.

Continuous attractor network models of grid cell firing based on excitatory-inhibitory interactions.

Neurons in the medial entorhinal cortex encode location through spatial firing fields that have a grid‐like organisation. The challenge of identifying mechanisms for grid firing has been addressed through experimental and theoretical investigations of medial entorhinal circuits. Here, we discuss evidence for continuous attractor network models that account for grid firing by synaptic interactions between excitatory and inhibitory cells. These models assume that grid‐like firing patterns are the result of computation of location from velocity inputs, with additional spatial input required to oppose drift in the attractor state. We focus on properties of continuous attractor networks that are revealed by explicitly considering excitatory and inhibitory neurons, their connectivity and their membrane potential dynamics. Models at this level of detail can account for theta‐nested gamma oscillations as well as grid firing, predict spatial firing of interneurons as well as excitatory cells, show how gamma oscillations can be modulated independently from spatial computations, reveal critical roles for neuronal noise, and demonstrate that only a subset of excitatory cells in a network need have grid‐like firing fields. Evaluating experimental data against predictions from detailed network models will be important for establishing the mechanisms mediating grid firing.

Grids from bands, or bands from grids? An examination of the effects of single unit contamination on grid cell firing fields.

Neural recording technology is improving rapidly, allowing for the detection of spikes from hundreds of cells simultaneously. The limiting step in multielectrode electrophysiology continues to be single cell isolation. However, this step is crucial to the interpretation of data from putative single neurons. We present here, in simulation, an illustration of possibly erroneous conclusions that may be reached when poorly isolated single cell data are analyzed. Grid cells are neurons recorded in rodents, and bats, that spike in equally spaced locations in a hexagonal pattern. One theory states that grid firing patterns arise from a combination of band firing patterns. However, we show here that summing the grid firing patterns of two poorly resolved neurons can result in spurious band-like patterns. Thus, evidence of neurons spiking in band patterns must undergo extreme scrutiny before it is accepted. Toward this aim, we discuss single cell isolation methods and metrics.

Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks.

Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength.

Grid cells form a global representation of connected environments

SummaryThe firing patterns of grid cells in medial entorhinal cortex (mEC) and associated brain areas form triangular arrays that tessellate the environment [1, 2] and maintain constant spatial offsets to each other between environments [3, 4]. These cells are thought to provide an efficient metric for navigation in large-scale space [5–8]. However, an accurate and universal metric requires grid cell firing patterns to uniformly cover the space to be navigated, in contrast to recent demonstrations that environmental features such as boundaries can distort [9–11] and fragment [12] grid patterns. To establish whether grid firing is determined by local environmental cues, or provides a coherent global representation, we recorded mEC grid cells in rats foraging in an environment containing two perceptually identical compartments connected via a corridor. During initial exposures to the multicompartment environment, grid firing patterns were dominated by local environmental cues, replicating between the two compartments. However, with prolonged experience, grid cell firing patterns formed a single, continuous representation that spanned both compartments. Thus, we provide the first evidence that in a complex environment, grid cell firing can form the coherent global pattern necessary for them to act as a metric capable of supporting large-scale spatial navigation.

Grid cell symmetry is shaped by environmental geometry.

Grid cells represent an animal's location by firing in multiple fields arranged in a striking hexagonal array. Such an impressive and constant regularity prompted suggestions that grid cells represent a universal and environmental-invariant metric for navigation. Originally the properties of grid patterns were believed to be independent of the shape of the environment and this notion has dominated almost all theoretical grid cell models. However, several studies indicate that environmental boundaries influence grid firing, though the strength, nature and longevity of this effect is unclear. Here we show that grid orientation, scale, symmetry and homogeneity are strongly and permanently affected by environmental geometry. We found that grid patterns orient to the walls of polarized enclosures such as squares, but not circles. Furthermore, the hexagonal grid symmetry is permanently broken in highly polarized environments such as trapezoids, the pattern being more elliptical and less homogeneous. Our results provide compelling evidence for the idea that environmental boundaries compete with the internal organization of the grid cell system to drive grid firing. Notably, grid cell activity is more local than previously thought and as a consequence cannot provide a universal spatial metric in all environments.

Ag contact properties according to the front grid width and firing temperature for silicon solar cells.

The effect of peak firing temperature and grid width on the contact properties between Ag metal and silicon (n+ emitter) was investigated for screen-printed silicon solar cells. We confirmed the factors that control the specific contact resistance as follows: (1) the Ag coverage fraction on the silicon surface, d(2) the thickness of the glass layer and (3) the etching depth on the n+ emitter region. The lowest specific contact resistance (8.27 mΩ x cm2) was obtained at the optimum firing temperature (720 degrees C). We also found that the grid width affected the contact quality of Ag paste because the contact width related to the absorbed heat of samples in RTP system. For this reason, when the grid width was further reduced, meaning more heat absorption, more Ag crystallites grew and the glass layer thickened. Light I-V results of a 6-inch silicon solar cell with minimum busbar width were similar to the PC1D simulation results. The efficiency was improved by 0.2% with the reduction of the busbar width.

Fire severity, size, and climate associations diverge from historical precedent along an ecological gradient in the Pinaleño Mountains, Arizona, USA

In recent decades fire size and severity have been increasing in high elevation forests of the American Southwest. Ecological outcomes of these increases are difficult to gauge without an historical context for the role of fire in these systems prior to interruption by Euro-American land uses. Across the gradient of forest types in the Pinaleño Mountains, a Sky Island system in southeast Arizona that experienced two relatively large high-severity fires in the last two decades, we compared fire characteristics and climate associations before and after the onset of fire exclusion to determine the degree of similarity between past and recent fires. We use a gridded fire scar and demography sampling network to reconstruct spatially explicit estimates of fire extent and burn severity, as well as climate associations of fires from individual site to landscape scales from 1640 to 2008 C.E. We found that patterns of fire frequency, size, and severity were relatively stable for at least several centuries prior to 1880. A combination of livestock grazing and active fire suppression after circa 1880 led to (1) a significant reduction in fire spread but not fire ignition, (2) a conversion of more than 80% of the landscape from a frequent, low to mixed-severity fire regime to an infrequent mixed to high-severity fire regime, and (3) an increase in fuel continuity within a mid-elevation zone of dry mixed-conifer forest, resulting in increased opportunities for surface and crown fire spread into higher elevation mesic forests. The two most recent fires affecting mesic forests were associated with drought and temperature conditions that were not exceptional in the historical record but that resulted in a relative proportion of high burn severity up to four times that of previous large fires. The ecological effects of these recent fires appear to be more severe than any fire in the reconstructed period, casting uncertainty upon the recovery of historical species composition in high-severity burn patches. Significant changes to the spatial pattern, frequency, and climate associations of spreading fires after 1880 suggest that limits to fuel loading and fuel connectivity sustained by frequent fire have been removed. Coinciding factors of high fuel continuity and fuel loading, projected lengthening of the fire season, and increased variability in seasonal precipitation suggest that large high-severity fires, especially in mixed-conifer forests, will become the predominant fire type without aggressive actions to reduce fuel continuity and restore fire-resilient forest structure and species composition.

Controlling phase noise in oscillatory interference models of grid cell firing.

Oscillatory interference models account for the spatial firing properties of grid cells in terms of neuronal oscillators with frequencies modulated by the animal's movement velocity. The phase of such a "velocity-controlled oscillator" (VCO) relative to a baseline (theta-band) oscillation tracks displacement along a preferred direction. Input from multiple VCOs with appropriate preferred directions causes a grid cell's grid-like firing pattern. However, accumulating phase noise causes the firing pattern to drift and become corrupted. Here we show how multiple redundant VCOs can automatically compensate for phase noise. By entraining the baseline frequency to the mean VCO frequency, VCO phases remain consistent, ensuring a coherent grid pattern and reducing its spatial drift. We show how the spatial stability of grid firing depends on the variability in VCO phases, e.g., a phase SD of 3 ms per 125 ms cycle results in stable grids for 1 min. Finally, coupling N VCOs with similar preferred directions as a ring attractor, so that their relative phases remain constant, produces grid cells with consistently offset grids, and reduces VCO phase variability of the order square root of N. The results suggest a viable functional organization of the grid cell network, and highlight the benefit of integrating displacement along multiple redundant directions for the purpose of path integration.

Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales, attention and oscillations

A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps (SOMs). The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. The model's parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same SOM mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus (HC) may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to HC ('neural relativity'). The model clarifies how top-down HC-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta and gamma oscillations. The article also compares the three main types of grid cell models in the light of recent data.

Impact of noise on theta-nested gamma oscillations in a spiking continuous attractor model of grid cells

Grid cells in the medial entorhinal cortex (MEC) encode location through firing fields that form grid-like maps of the environment. At the same time network activity in the MEC is dominated by oscillations in the theta (4-12 Hz) and gamma (30-100 Hz) bands. Our recent experimental data established that feedback inhibition between excitatory stellate cells and inhibitory fast spiking interneurons dominates the synaptic connectivity in layer II of the MEC, and that continuous attractor models derived from these properties are sufficient to explain both the network oscillations and grid firing fields [1]. Here we use a spiking continuous attractor network model of layer II stellate cells and fast spiking interneurons to examine the effect of intrinsic noise on the emergence of theta nested-gamma oscillations. In this model, stellate cells connect exclusively to interneurons, while interneurons contact only stellate cells. When driven with a theta (8 Hz) modulated external input, we observed network synchronization in the gamma range during the trough of the theta signal, which depended on the amount of intrinsic Gaussian noise generated independently at each neuron. Without noise, the network exhibited aberrant hyper-synchronous firing of a subpopulation of stellate cells at the beginning of each theta cycle. The stellate cell firing resulted in a strong feedback inhibitory postsynaptic currents from fast spiking interneurons that had an additional synchronizing effect. The strong inhibitory feedback abolished nested gamma oscillations. With increasing noise, the network entered an intermediate state in which we observed theta nested-gamma oscillations [1]. When noise level was set even higher, the nested gamma oscillations disappeared without increasing the amount of inhibitory coupling. We also present the impact of noise on bump attractor formation and gridness score of the grid-like receptive fields. Together, these results show that the presence of noise may have profound implications on the stability of theta-nested gamma oscillations in attractor neural circuits with feedback inhibition.

Spiking neurons in a hierarchical self-organizing map model can learn to develop spatial and temporal properties of entorhinal grid cells and hippocampal place cells.

Medial entorhinal grid cells and hippocampal place cells provide neural correlates of spatial representation in the brain. A place cell typically fires whenever an animal is present in one or more spatial regions, or places, of an environment. A grid cell typically fires in multiple spatial regions that form a regular hexagonal grid structure extending throughout the environment. Different grid and place cells prefer spatially offset regions, with their firing fields increasing in size along the dorsoventral axes of the medial entorhinal cortex and hippocampus. The spacing between neighboring fields for a grid cell also increases along the dorsoventral axis. This article presents a neural model whose spiking neurons operate in a hierarchy of self-organizing maps, each obeying the same laws. This spiking GridPlaceMap model simulates how grid cells and place cells may develop. It responds to realistic rat navigational trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with one or more firing fields that match neurophysiological data about these cells and their development in juvenile rats. The place cells represent much larger spaces than the grid cells, which enable them to support navigational behaviors. Both self-organizing maps amplify and learn to categorize the most frequent and energetic co-occurrences of their inputs. The current results build upon a previous rate-based model of grid and place cell learning, and thus illustrate a general method for converting rate-based adaptive neural models, without the loss of any of their analog properties, into models whose cells obey spiking dynamics. New properties of the spiking GridPlaceMap model include the appearance of theta band modulation. The spiking model also opens a path for implementation in brain-emulating nanochips comprised of networks of noisy spiking neurons with multiple-level adaptive weights for controlling autonomous adaptive robots capable of spatial navigation.

Grid cells on the ball

What sort of grid cells do we expect to see in rodents who have spent their developmental period inside a large spherical cage? Or, in a different experimental paradigm, toddling on a revolving ball, with virtual reality simulating a coherently revolving surround? We consider a simple model of grid firing map formation, based on firing rate adaptation, that we have earlier analyzed when playing out on a flat environment. The model predicts that whether experienced on the outside or inside, a spherical environment induces one of a succession of grid maps realized as combinations of spherical harmonics, depending on the relation of the radius to the preferred grid spacing, itself related to the parameters of firing rate adaptation. Numerical simulations concur with analytical predictions.

Recurrent inhibitory circuitry as a mechanism for grid formation

Grid cells in layer II of the medial entorhinal cortex form a principal component of the mammalian neural representation of space. The firing pattern of a single grid cell has been hypothesized to be generated through attractor dynamics in a network with a specific local connectivity including both excitatory and inhibitory connections. However, experimental evidence supporting the presence of such connectivity among grid cells in layer II is limited. Here we report recordings from more than 600 neuron pairs in rat entorhinal slices, demonstrating that stellate cells, the principal cell type in the layer II grid network, are mainly interconnected via inhibitory interneurons. Using a model attractor network, we demonstrate that stable grid firing can emerge from a simple recurrent inhibitory network. Our findings thus suggest that the observed inhibitory microcircuitry between stellate cells is sufficient to generate grid-cell firing patterns in layer II of the medial entorhinal cortex.

Feedback Inhibition Enables Theta-Nested Gamma Oscillations and Grid Firing Fields

Cortical circuits are thought to multiplex firing rate codes with temporal codes that rely on oscillatory network activity, but the circuit mechanisms that combine these coding schemes are unclear. We establish with optogenetic activation of layer II of the medial entorhinal cortex that theta frequency drive to this circuit is sufficient to generate nested gamma frequency oscillations in synaptic activity. These nested gamma oscillations closely resemble activity during spatial exploration, are generated by local feedback inhibition without recurrent excitation, and have clock-like features suitable as reference signals for multiplexing temporal codes within rate-coded grid firing fields. In network models deduced from our data, feedback inhibition supports coexistence of theta-nested gamma oscillations with attractor states that generate grid firing fields. These results indicate that grid cells communicate primarily via inhibitory interneurons. This circuit mechanism enables multiplexing of oscillation-based temporal codes with rate-coded attractor states.

How reduction of theta rhythm by medial septum inactivation may covary with disruption of entorhinal grid cell responses due to reduced cholinergic transmission

Oscillations in the coordinated firing of brain neurons have been proposed to play important roles in perception, cognition, attention, learning, navigation, and sensory-motor control. The network theta rhythm has been associated with properties of spatial navigation, as has the firing of entorhinal grid cells and hippocampal place cells. Two recent studies reduced the theta rhythm by inactivating the medial septum (MS) and demonstrated a correlated reduction in the characteristic hexagonal spatial firing patterns of grid cells. These results, along with properties of intrinsic membrane potential oscillations (MPOs) in slice preparations of medial entorhinal cortex (MEC), have been interpreted to support oscillatory interference models of grid cell firing. The current article shows that an alternative self-organizing map (SOM) model of grid cells can explain these data about intrinsic and network oscillations without invoking oscillatory interference. In particular, the adverse effects of MS inactivation on grid cells can be understood in terms of how the concomitant reduction in cholinergic inputs may increase the conductances of leak potassium (K+) and slow and medium after-hyperpolarization (sAHP and mAHP) channels. This alternative model can also explain data that are problematic for oscillatory interference models, including how knockout of the HCN1 gene in mice, which flattens the dorsoventral gradient in MPO frequency and resonance frequency, does not affect the development of the grid cell dorsoventral gradient of spatial scales, and how hexagonal grid firing fields in bats can occur even in the absence of theta band modulation. These results demonstrate how models of grid cell self-organization can provide new insights into the relationship between brain learning and oscillatory dynamics.

How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.

From A to Z: a potential role for grid cells in spatial navigation

Since their discovery, the strikingly regular and spatially stable firing of entorhinal grid cells has attracted the attention of experimentalists and theoreticians alike. The bulk of this work has focused either on the assumption that the principal role of grid cells is to support path integration or the extent to which their multiple firing locations can drive the sparse activity of hippocampal place cells. Here, we propose that grid cells are best understood as part of a network that combines self-motion and environmental cues to accurately track an animal’s location in space. Furthermore, that grid cells - more so than place cells - efficiently encode self-location in allocentric coordinates. Finally, that the regular structure of grid firing fields represents information about the relative structure of space and, as such, may be used to guide goal directed navigation.