Neuron numbers in the presubiculum, parasubiculum, and entorhinal area of the rat

Prenatal protein malnutrition decreases neuron numbers in the parahippocampal region but not prefrontal cortex in adult rats

OBJECTIVE

Prenatal protein malnutrition produces anatomical and functional changes in the developing brain that persist despite immediate postnatal nutritional rehabilitation. Brain networks of prenatally malnourished animals show diminished activation of prefrontal areas and an increased activation of hippocampal regions during an attentional task [1]. While a reduction in cell number has been documented in hippocampal subfield CA1, nothing is known about changes in neuron numbers in the prefrontal or parahippocampal cortices.

METHODS

In the present study, we used unbiased stereology to investigate the effect of prenatal protein malnutrition on the neuron numbers in the medial prefrontal cortex and the cortices of the parahippocampal region that comprise the larger functional network.

RESULTS

Results show that prenatal protein malnutrition does not cause changes in the neuronal population in the medial prefrontal cortex of adult rats, indicating that the decrease in functional activation during attentional tasks is not due to a reduction in the number of neurons. Results also show that prenatal protein malnutrition is associated with a reduction in neuron numbers in specific parahippocampal subregions: the medial entorhinal cortex and presubiculum.

DISCUSSION

The affected regions along with CA1 comprise a tightly interconnected circuit, suggesting that prenatal malnutrition confers a vulnerability to specific hippocampal circuits. These findings are consistent with the idea that prenatal protein malnutrition produces a reorganization of structural and functional networks, which may underlie observed alterations in attentional processes and capabilities.

Emerging many-to-one weighted mapping in hippocampus-amygdala network underlies memory formation

Memories are crucial for our daily lives, yet the network-level organizing principle that governs neural representations of our experiences remains to be determined. Employing dual-site electrophysiology recording in freely behaving mice, we discovered that hippocampal dorsal CA1 (dCA1) and basolateral amygdala (BLA) utilize distinct coding strategies to represent novel experiences. A small assembly of BLA neurons rapidly emerged during memory acquisition and remained active during subsequent consolidation, whereas the majority of dCA1 neurons engaged in the same processes. Machine learning decoding revealed that dCA1 population spikes predicted the BLA assembly firing rate. This suggests that most dCA1 neurons concurrently index an episodic event by rapidly establishing weighted communications with a specific BLA assembly, a process we call "many-to-one weighted mapping." Furthermore, we demonstrated that closed-loop optoinhibition of BLA activity triggered by dCA1 ripples after new learning resulted in impaired memory. These findings highlight a new principle of hippocampus-amygdala communication underlying memory formation and provide new insights into how the brain creates and stores memories.

Episodic Memory formation: A review of complex Hippocampus input pathways

Memories of everyday experiences involve the encoding of a rich and dynamic representation of present objects and their contextual features. Traditionally, the resulting mnemonic trace is referred to as Episodic Memory, i.e. the "what", "where" and "when" of a lived episode. The journey for such memory trace encoding begins with the perceptual data of an experienced episode handled in sensory brain regions. The information is then streamed to cortical areas located in the ventral Medio Temporal Lobe, which produces multi-modal representations concerning either the objects (in the Perirhinal cortex) or the spatial and contextual features (in the parahippocampal region) of the episode. Then, this high-level data is gated through the Entorhinal Cortex and forwarded to the Hippocampal Formation, where all the pieces get bound together. Eventually, the resulting encoded neural pattern is relayed back to the Neocortex for a stable consolidation. This review will detail these different stages and provide a systematic overview of the major cortical streams toward the Hippocampus relevant for Episodic Memory encoding.

Quantification of neuron types in the rodent hippocampal formation by data mining and numerical optimization

Quantifying the population sizes of distinct neuron types in different anatomical regions is an essential step towards establishing a brain cell census. Although estimates exist for the total neuronal populations in different species, the number and definition of each specific neuron type are still intensively investigated. Hippocampome.org is an open-source knowledge base with morphological, physiological and molecular information for 122 neuron types in the rodent hippocampal formation. While such framework identifies all known neuron types in this system, their relative abundances remain largely unknown. This work quantitatively estimates the counts of all Hippocampome.org neuron types by literature mining and numerical optimization. We report the number of neurons in each type identified by main neurotransmitter (glutamate or GABA) and axonal-dendritic patterns throughout 26 subregions and layers of the dentate gyrus, Ammon's horn, subiculum and entorhinal cortex. We produce by sensitivity analysis reliable numerical ranges for each type and summarize the amounts across broad neuronal families defined by biomarkers expression and firing dynamics. Study of density distributions indicates that the number of dendritic-targeting interneurons, but not of other neuronal classes, is independent of anatomical volumes. All extracted values, experimental evidence and related software code are released on Hippocampome.org.

Basic quantitative morphological methods applied to the central nervous system

Generating numbers has become an almost inevitable task associated with studies of the morphology of the nervous system. Numbers serve a desire for clarity and objectivity in the presentation of results and are a prerequisite for the statistical evaluation of experimental outcomes. Clarity, objectivity, and statistics make demands on the quality of the numbers that are not met by many methods. This review provides a refresher of problems associated with generating numbers that describe the nervous system in terms of the volumes, surfaces, lengths, and numbers of its components. An important aim is to provide comprehensible descriptions of the methods that address these problems. Collectively known as design-based stereology, these methods share two features critical to their application. First, they are firmly based in mathematics and its proofs. Second and critically underemphasized, an understanding of their mathematical background is not necessary for their informed and productive application. Understanding and applying estimators of volume, surface, length or number does not require more of an organizational mastermind than an immunohistochemical protocol. And when it comes to calculations, square roots are the gravest challenges to overcome. Sampling strategies that are combined with stereological probes are efficient and allow a rational assessment if the numbers that have been generated are "good enough." Much may be unfamiliar, but very little is difficult. These methods can no longer be scapegoats for discrepant results but faithfully produce numbers on the material that is assessed. They also faithfully reflect problems that associated with the histological material and the anatomically informed decisions needed to generate numbers that are not only valid in theory. It is within reach to generate practically useful numbers that must integrate with qualitative knowledge to understand the function of neural systems.

Topographic Organization of Correlation Along the Longitudinal and Transverse Axes in Rat Hippocampal CA3 Due to Excitatory Afferents

The topographic organization of afferents to the hippocampal CA3 subfield are well-studied, but their role in influencing the spatiotemporal dynamics of population activity is not understood. Using a large-scale, computational neuronal network model of the entorhinal-dentate-CA3 system, the effects of the perforant path, mossy fibers, and associational system on the propagation and transformation of network spiking patterns were investigated. A correlation map was constructed to characterize the spatial structure and temporal evolution of pairwise correlations which underlie the emergent patterns found in the population activity. The topographic organization of the associational system gave rise to changes in the spatial correlation structure along the longitudinal and transverse axes of the CA3. The resulting gradients may provide a basis for the known functional organization observed in hippocampus.

Operations Research Methods for Estimating the Population Size of Neuron Types

Understanding brain computation requires assembling a complete catalog of its architectural components. Although the brain is organized into several anatomical and functional regions, it is ultimately the neurons in every region that are responsible for cognition and behavior. Thus, classifying neuron types throughout the brain and quantifying the population sizes of distinct classes in different regions is a key subject of research in the neuroscience community. The total number of neurons in the brain has been estimated for multiple species, but the definition and population size of each neuron type are still open questions even in common model organisms: the so called "cell census" problem. We propose a methodology that uses operations research principles to estimate the number of neurons in each type based on available information on their distinguishing properties. Thus, assuming a set of neuron type definitions, we provide a solution to the issue of assessing their relative proportions. Specifically, we present a three-step approach that includes literature search, equation generation, and numerical optimization. Solving computationally the set of equations generated by literature mining yields best estimates or most likely ranges for the number of neurons in each type. While this strategy can be applied towards any neural system, we illustrate its usage on the rodent hippocampus.

Cell numbers, distribution, shape, and regional variation throughout the murine hippocampal formation from the adult brain Allen Reference Atlas

Quantifying the distribution of cells in every brain region is fundamental to attaining a comprehensive census of distinct neuronal and glial types. Until recently, estimating neuron numbers involved time-consuming procedures that were practically limited to stereological sampling. Progress in open-source image recognition software, growth in computing power, and unprecedented neuroinformatics developments now offer the potentially paradigm-shifting alternative of comprehensive cell-by-cell analysis in an entire brain region. The Allen Brain Atlas provides free digital access to complete series of raw Nissl-stained histological section images along with regional delineations. Automated cell segmentation of these data enables reliable and reproducible high-throughput quantification of regional variations in cell count, density, size, and shape at whole-system scale. While this strategy is directly applicable to any regions of the mouse brain, we first deploy it here on the closed-loop circuit of the hippocampal formation: the medial and lateral entorhinal cortices; dentate gyrus (DG); areas Cornu Ammonis 3 (CA3), CA2, and CA1; and dorsal and ventral subiculum. Using two independent image processing pipelines and the adult mouse reference atlas, we report the first cellular-level soma segmentation in every sub-region and non-principal layer of the left hippocampal formation through the full rostral-caudal extent. It is important to note that our techniques excluded the layers with the largest number of cells, DG granular and CA pyramidal, due to dense packing. The numerical estimates for the remaining layers are corroborated by traditional stereological sampling on a data subset and well match sparse published reports.

Roles of K+ and cation channels in ORL-1 receptor-mediated depression of neuronal excitability and epileptic activities in the medial entorhinal cortex

Nociceptin (NOP) is an endogenous opioid-like peptide that selectively activates the opioid receptor-like (ORL-1) receptors. The entorhinal cortex (EC) is closely related to temporal lobe epilepsy and expresses high densities of ORL-1 receptors. However, the functions of NOP in the EC, especially in modulating the epileptiform activity in the EC, have not been determined. We demonstrated that activation of ORL-1 receptors remarkably inhibited the epileptiform activity in entorhinal slices induced by application of picrotoxin or by deprivation of extracellular Mg2+. NOP-mediated depression of epileptiform activity was independent of synaptic transmission in the EC, but mediated by inhibition of neuronal excitability in the EC. NOP hyperpolarized entorhinal neurons via activation of K+ channels and inhibition of cation channels. Whereas application of Ba2+ at 300 μM which is effective for the inward rectifier K+ (Kir) channels slightly inhibited NOP-induced hyperpolarization, the current-voltage (I-V) curve of the net currents induced by NOP was linear without showing inward rectification. However, a role of NOP-induced inhibition of cation channels was revealed after inhibition of Kir channels by Ba2+. Furthermore, NOP-mediated augmentation of membrane currents was differently affected by application of the blockers selective for distinct subfamilies of Kir channels. Whereas SCH23390 or ML133 blocked NOP-induced augmentation of membrane currents at negative potentials, application of tertiapin-Q exerted no actions on NOP-induced alteration of membrane currents. Our results demonstrated a novel cellular and molecular mechanism whereby activation of ORL-1 receptors depresses epilepsy.

Disparate forms of heterogeneities and interactions among them drive channel decorrelation in the dentate gyrus: Degeneracy and dominance

The ability of a neuronal population to effectuate channel decorrelation, which is one form of response decorrelation, has been identified as an essential prelude to efficient neural encoding. To what extent are diverse forms of local and afferent heterogeneities essential in accomplishing channel decorrelation in the dentate gyrus (DG)? Here, we incrementally incorporated four distinct forms of biological heterogeneities into conductance-based network models of the DG and systematically delineate their relative contributions to channel decorrelation. First, to effectively incorporate intrinsic heterogeneities, we built physiologically validated heterogeneous populations of granule (GC) and basket cells (BC) through independent stochastic search algorithms spanning exhaustive parametric spaces. These stochastic search algorithms, which were independently constrained by experimentally determined ion channels and by neurophysiological signatures, revealed cellular-scale degeneracy in the DG. Specifically, in GC and BC populations, disparate parametric combinations yielded similar physiological signatures, with underlying parameters exhibiting significant variability and weak pair-wise correlations. Second, we introduced synaptic heterogeneities through randomization of local synaptic strengths. Third, in including adult neurogenesis, we subjected the valid model populations to randomized structural plasticity and matched neuronal excitability to electrophysiological data. We assessed networks comprising different combinations of these three local heterogeneities with identical or heterogeneous afferent inputs from the entorhinal cortex. We found that the three forms of local heterogeneities were independently and synergistically capable of mediating significant channel decorrelation when the network was driven by identical afferent inputs. However, when we incorporated afferent heterogeneities into the network to account for the divergence in DG afferent connectivity, the impact of all three forms of local heterogeneities was significantly suppressed by the dominant role of afferent heterogeneities in mediating channel decorrelation. Our results unveil a unique convergence of cellular- and network-scale degeneracy in the emergence of channel decorrelation in the DG, whereby disparate forms of local and afferent heterogeneities could synergistically drive input discriminability.

Stereological analysis of the rhesus monkey entorhinal cortex

The entorhinal cortex is a prominent structure of the medial temporal lobe, which plays a pivotal role in the interaction between the neocortex and the hippocampal formation in support of declarative and spatial memory functions. We implemented design-based stereological techniques to provide estimates of neuron numbers, neuronal soma size, and volume of different layers and subdivisions of the entorhinal cortex in adult rhesus monkeys (Macaca mulatta; 5-9 years of age). These data corroborate the structural differences between different subdivisions of the entorhinal cortex, which were shown in previous connectional and cytoarchitectonic studies. In particular, differences in the number of neurons contributing to distinct afferent and efferent hippocampal pathways suggest not only that different types of information may be more or less segregated between caudal and rostral subdivisions, but also, and perhaps most importantly, that the nature of the interaction between the entorhinal cortex and the rest of the hippocampal formation may vary between different subdivisions. We compare our quantitative data in monkeys with previously published stereological data for the rat and human, in order to provide a perspective on the relative development and structural organization of the main subdivisions of the entorhinal cortex in two model organisms widely used to decipher the basic functional principles of the human medial temporal lobe memory system. Altogether, these data provide fundamental information on the number of functional units that comprise the entorhinal-hippocampal circuits and should be considered in order to build realistic models of the medial temporal lobe memory system.

A unified hierarchical oscillatory network model of head direction cells, spatially periodic cells, and place cells

Spatial cells in the hippocampal complex play a pivotal role in the navigation of an animal. Exact neural principles behind these spatial cell responses have not been completely unraveled yet. Here we present two models for spatial cells, namely the Velocity Driven Oscillatory Network (VDON) and Locomotor Driven Oscillatory Network. Both models have basically three stages in common such as direction encoding stage, path integration (PI) stage, and a stage of unsupervised learning of PI values. In the first model, the following three stages are implemented: head direction layer, frequency modulation by a layer of oscillatory neurons, and an unsupervised stage that extracts the principal components from the oscillator outputs. In the second model, a refined version of the first model, the stages are extraction of velocity representation from the locomotor input, frequency modulation by a layer of oscillators, and two cascaded unsupervised stages consisting of the lateral anti-hebbian network. The principal component stage of VDON exhibits grid cell-like spatially periodic responses including hexagonal firing fields. Locomotor Driven Oscillatory Network shows the emergence of spatially periodic grid cells and periodically active border-like cells in its lower layer; place cell responses are found in its higher layer. This model shows the inheritance of phase precession from grid cell to place cell in both one- and two-dimensional spaces. It also shows a novel result on the influence of locomotion rhythms on the grid cell activity. The study thus presents a comprehensive, unifying hierarchical model for hippocampal spatial cells.

Structural modularity and grid activity in the medial entorhinal cortex

Following the groundbreaking discovery of grid cells, the medial entorhinal cortex (MEC) has become the focus of intense anatomical, physiological, and computational investigations. Whether and how grid activity maps onto cell types and cortical architecture is still an open question. Fundamental similarities in microcircuits, function, and connectivity suggest a homology between rodent MEC and human posteromedial entorhinal cortex. Both are specialized for spatial processing and display similar cellular organization, consisting of layer 2 pyramidal/calbindin cell patches superimposed on scattered stellate neurons. Recent data indicate the existence of a further nonoverlapping modular system (zinc patches) within the superficial MEC layers. Zinc and calbindin patches have been shown to receive largely segregated inputs from the presubiculum and parasubiculum. Grid cells are also clustered in the MEC, and we discuss possible structure-function schemes on how grid activity could map onto cortical patch systems. We hypothesize that in the superficial layers of the MEC, anatomical location can be predictive of function; thus relating functional properties and neuronal morphologies to the cortical modules will be necessary for resolving how grid activity maps onto cortical architecture. Imaging or cell identification approaches in freely moving animals will be required for testing this hypothesis.

Total Number Is Important: Using the Disector Method in Design-Based Stereology to Understand the Structure of the Rodent Brain

The advantages of using design-based stereology in the collection of quantitative data, have been highlighted, in numerous publications, since the description of the disector method by Sterio (1984). This review article discusses the importance of total number derived with the disector method, as a key variable that must continue to be used to understand the rodent brain and that such data can be used to develop quantitative networks of the brain. The review article will highlight the huge impact total number has had on our understanding of the rodent brain and it will suggest that neuroscientists need to be aware of the increasing number of studies where density, not total number, is the quantitative measure used. It will emphasize that density can result in data that is misleading, most often in an unknown direction, and that we run the risk of this type of data being accepted into the collective neuroscience knowledge database. It will also suggest that design-based stereology using the disector method, can be used alongside recent developments in electron microscopy, such as serial block-face scanning electron microscopy (SEM), to obtain total number data very efficiently at the ultrastructural level. Throughout the article total number is discussed as a key parameter in understanding the micro-networks of the rodent brain as they can be represented as both anatomical and quantitative networks.

Paradox of pattern separation and adult neurogenesis: A dual role for new neurons balancing memory resolution and robustness

Hippocampal adult neurogenesis is thought to subserve pattern separation, the process by which similar patterns of neuronal inputs are transformed into distinct neuronal representations, permitting the discrimination of highly similar stimuli in hippocampus-dependent tasks. However, the mechanism by which immature adult-born dentate granule neurons cells (abDGCs) perform this function remains unknown. Two theories of abDGC function, one by which abDGCs modulate and sparsify activity in the dentate gyrus and one by which abDGCs act as autonomous coding units, are generally suggested to be mutually exclusive. This review suggests that these two mechanisms work in tandem to dynamically regulate memory resolution while avoiding memory interference and maintaining memory robustness.

A principle of economy predicts the functional architecture of grid cells

Grid cells in the brain respond when an animal occupies a periodic lattice of ‘grid fields’ during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths.

DOI:http://dx.doi.org/10.7554/eLife.08362.001

In the 1930s, neuroscientists studying how rodents find their way through a maze proposed that the animals could construct an internal map of the maze inside their heads. The map was thought to enable the animals to navigate between familiar locations and also to identify shortcuts and alternative routes whenever familiar ones were blocked.

In the 1960s, recordings of electrical activity in the rat brain provided the first clues as to which nerve cells form this spatial map. In a region of the brain called the hippocampus, nerve cells called ‘place cells’ are active whenever the rat finds itself in a specific location. However, place cells alone are not able to support all types of navigation. Some spatial tasks also require cells in a region of the brain called the medial entorhinal cortex (MEC), which supplies most of the information that the hippocampus receives.

Cells in the MEC called ‘grid cells’ represent two-dimensional space as a repeating grid of triangles. A given grid cell is activated if the animal is located at a particular distance and angle away from the center of any of these triangles. The size of the triangles in these grids varies systematically throughout the MEC. Individual grid cells at one end of the structure encode space in finer detail than grid cells at the opposite end.

Wei et al. have now used mathematical modeling to explore how grid cells are organized. The model assumes that the brain seeks to encode space at whatever resolution an animal requires using as few nerve cells as possible. The model successfully reproduces several known features of grid cells, including the triangular shape of the grid, and the fact that the size of the triangles increases in steps of a specific size across the MEC.

In addition to providing a mathematical basis for the way that grid cells are organized in the brain, the model makes a number of testable predictions. These include predictions of the number of grid cells in the rat brain, as well as the pattern that grid cells adopt in three-dimensions: a question that is currently being studied in bats. Wei et al.'s findings suggest that the code used by the grid to represent space is an analog of a decimal number system—except that space is not subdivided by factors of 10 to form decimal ‘digits’, but by a quantity related to a famous constant in the field of mathematics called Euler's number.

DOI:http://dx.doi.org/10.7554/eLife.08362.002

Stereological estimation of neuron number and plaque load in the hippocampal region of a transgenic rat model of Alzheimer's disease

The main hallmarks of Alzheimer's disease (AD) are senile plaques, neurofibrillary tangles and neuronal death. The McGill-R-Thy1-APP rat is one of the few transgenic rat models of AD that displays progressive amyloid pathology. This study aimed to further characterise this rat model, focusing on the pathological changes in the hippocampal formation and the parahippocampal region. These structures, that are important for episodic memory and spatial navigation, are affected in the early stages of the disease. This study used unbiased stereology to investigate possible neuronal loss in the CA1, subiculum and entorhinal cortex of 18-month-old homozygous McGill-R-Thy1-APP rats, and also quantified the plaque load in all the areas of the hippocampal formation and parahippocampal region from 9 to 18 months old. A significant reduction of neurons at 18 months was only seen in the subiculum. The first plaque pathology was seen at 9 months in the subiculum. Although the quantified plaque load was variable between animals, the pattern of spatiotemporal progression was similar for all animals. The spread of plaque pathology mainly affected anatomically connected regions. Overall, the plaque pathology observed in the transgenic rats was similar to the early phases of amyloid beta (Aβ)-deposition described in human patients. The findings here thus indicate that the McGill-R-Thy1-APP rat could be a good model of the Aβ pathology in AD, but less so with respect to neuron loss.

Parametric Anatomical Modeling: a method for modeling the anatomical layout of neurons and their projections

Computational models of neural networks can be based on a variety of different parameters. These parameters include, for example, the 3d shape of neuron layers, the neurons' spatial projection patterns, spiking dynamics and neurotransmitter systems. While many well-developed approaches are available to model, for example, the spiking dynamics, there is a lack of approaches for modeling the anatomical layout of neurons and their projections. We present a new method, called Parametric Anatomical Modeling (PAM), to fill this gap. PAM can be used to derive network connectivities and conduction delays from anatomical data, such as the position and shape of the neuronal layers and the dendritic and axonal projection patterns. Within the PAM framework, several mapping techniques between layers can account for a large variety of connection properties between pre- and post-synaptic neuron layers. PAM is implemented as a Python tool and integrated in the 3d modeling software Blender. We demonstrate on a 3d model of the hippocampal formation how PAM can help reveal complex properties of the synaptic connectivity and conduction delays, properties that might be relevant to uncover the function of the hippocampus. Based on these analyses, two experimentally testable predictions arose: (i) the number of neurons and the spread of connections is heterogeneously distributed across the main anatomical axes, (ii) the distribution of connection lengths in CA3-CA1 differ qualitatively from those between DG-CA3 and CA3-CA3. Models created by PAM can also serve as an educational tool to visualize the 3d connectivity of brain regions. The low-dimensional, but yet biologically plausible, parameter space renders PAM suitable to analyse allometric and evolutionary factors in networks and to model the complexity of real networks with comparatively little effort.

Quantitative assessment of CA1 local circuits: knowledge base for interneuron-pyramidal cell connectivity

In this work, through a detailed literature review, data-mining, and extensive calculations, we provide a current, quantitative estimate of the cellular and synaptic constituents of the CA1 region of the rat hippocampus. Beyond estimating the cell numbers of GABAergic interneuron types, we calculate their convergence onto CA1 pyramidal cells and compare it with the known input synapses on CA1 pyramidal cells. The convergence calculation and comparison are also made for excitatory inputs to CA1 pyramidal cells. In addition, we provide a summary of the excitatory and inhibitory convergence onto interneurons. The quantitative knowledge base assembled and synthesized here forms the basis for data-driven, large-scale computational modeling efforts. Additionally, this work highlights specific instances where the available data are incomplete, which should inspire targeted experimental projects toward a more complete quantification of the CA1 neurons and their connectivity.

Optimal population codes for space: grid cells outperform place cells

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial "tuning curves" for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

Implementation of topographically constrained connectivity for a large-scale biologically realistic model of the hippocampus

In order to understand how memory works in the brain, the hippocampus is highly studied because of its role in the encoding of long-term memories. We have identified four characteristics that would contribute to the encoding process: the morphology of the neurons, their biophysics, synaptic plasticity, and the topography connecting the input to and the neurons within the hippocampus. To investigate how long-term memory is encoded, we are constructing a large-scale biologically realistic model of the rat hippocampus. This work focuses on how topography contributes to the output of the hippocampus. Generally, the brain is structured with topography such that the synaptic connections formed by an input neuron population are organized spatially across the receiving population. The first step in our model was to construct how entorhinal cortex inputs connect to the dentate gyrus of the hippocampus. We have derived realistic constraints from topographical data to connect the two cell populations. The details on how these constraints were applied are presented. We demonstrate that the spatial connectivity has a major impact on the output of the simulation, and the results emphasize the importance of carefully defining spatial connectivity in neural network models of the brain in order to generate relevant spatiotemporal patterns.

Disambiguating the similar: the dentate gyrus and pattern separation

The human hippocampus supports the formation of episodic memory without confusing new memories with old ones. To accomplish this, the brain must disambiguate memories (i.e., accentuate the differences between experiences). There is convergent evidence linking pattern separation to the dentate gyrus. Damage to the dentate gyrus reduces an organism's ability to differentiate between similar objects. The dentate gyrus has tenfold more principle cells than its cortical input, allowing for a divergence in information flow. Dentate gyrus granule neurons also show a very different pattern of representing the environment than "classic" place cells in CA1 and CA3, or grid cells in the entorhinal cortex. More recently immediate early genes have been used to "timestamp" activity of individual cells throughout the dentate gyrus. These data indicate that the dentate gyrus robustly differentiates similar situations. The degree of differentiation is non-linear, with even small changes in input inducing a near maximal response in the dentate. Furthermore this differentiation occurs throughout the dentate gyrus longitudinal (dorsal-ventral) axis. Conversely, the data point to a divergence in information processing between the dentate gyrus suprapyramidal and infrapyramidal blades possibly related to differences in organization within these regions. The accumulated evidence from different approaches converges to support a role for the dentate gyrus in pattern separation. There are however inconsistencies that may require incorporation of neurogenesis and hippocampal microcircuits into the currents models. They also suggest different roles for the dentate gyrus suprapyramidal and infrapyramidal blades, and the responsiveness of CA3 to dentate input.

Could adult hippocampal neurogenesis be relevant for human behavior?

Although the function of adult neurogenesis is still unclear, tools for directly studying the behavioral role of new hippocampal neurons now exist in rodents. Since similar studies are impossible to do in humans, it is important to assess whether the role of new neurons in rodents is likely to be similar to that in humans. One feature of adult neurogenesis that varies tremendously across species is the number of neurons that are generated, so a key question is whether there are enough neurons generated in humans to impact function. In this review we examine neuroanatomy and circuit function in the hippocampus to ask how many granule neurons are needed to impact hippocampal function and then discuss what is known about numbers of new neurons produced in adult rats and humans. We conclude that relatively small numbers of neurons could affect hippocampal circuits and that the magnitude of adult neurogenesis in adult rats and humans is probably larger than generally believed.

Number estimates of neuronal phenotypes in layer II of the medial entorhinal cortex of rat and mouse

Modelling entorhinal function or evaluating the consequences of neuronal losses which accompany neurodegenerative disorders requires detailed information on the quantitative cellular composition of the normal entorhinal cortex. Using design-based stereological methods, we estimated the numbers, proportions, densities and sectional areas of layer II cells in the medial entorhinal area (MEA), and its constituent caudal entorhinal (CE) and medial entorhinal (ME) fields, in the rat and mouse. We estimated layer II of the MEA to contain approximately 58,000 neurons in the rat and approximately 24,000 neurons in the mouse. Field CE accounted for more than three-quarters of the total neuron population in both species. In the rat, layer II of the MEA is comprised of 38% ovoid stellate cells, 29% polygonal stellate cells and 17% pyramidal cells. The remainder is comprised of much smaller populations of horizontal bipolar, tripolar, oblique pyramidal and small round cells. In the mouse, MEA layer II is comprised of 52% ovoid stellate cells, 22% polygonal stellate cells and 14% pyramidal cells. Significant species differences in the proportions of ovoid and polygonal stellate cells suggest differences in physiological and functional properties. The majority of MEA layer II cells contribute to the entorhinal-hippocampal pathways. The degree of divergence from MEA layer II cells to the dentate granule cells was similar in the rat and mouse. In both rat and mouse, the only dorsoventral difference we observed is a gradient in polygonal stellate cell sectional area, which may relate to the dorsoventral increase in the size and spacing of individual neuronal firing fields. In summary, we found species-specific cellular compositions of MEA layer II, while, within a species, quantitative parameters other than cell size are stable along the dorsoventral and mediolateral axis of the MEA.

Grid cells: the position code, neural network models of activity, and the problem of learning

We review progress on the modeling and theoretical fronts in the quest to unravel the computational properties of the grid cell code and to explain the mechanisms underlying grid cell dynamics. The goals of the review are to outline a coherent framework for understanding the dynamics of grid cells and their representation of space; to critically present and draw contrasts between recurrent network models of grid cells based on continuous attractor dynamics and independent-neuron models based on temporal interference; and to suggest open questions for experiment and theory.

Accurate path integration in continuous attractor network models of grid cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

Even in the absence of external sensory cues, foraging rodents maintain an estimate of their position, allowing them to return home in a roughly straight line. This computation is known as dead reckoning or path integration. A discovery made three years ago in rats focused attention on the dorsolateral medial entorhinal cortex (dMEC) as a location in the rat's brain where this computation might be performed. In this area, so-called grid cells fire whenever the rat is on any vertex of a triangular grid that tiles the plane. Here we propose a model that could generate grid-cell-like responses in a neural network. The inputs to the model network convey information about the rat's velocity and heading, consistent with known inputs projecting into the dMEC. The network effectively integrates these inputs to produce a response that depends on the rat's absolute position. We show that such a neural network can integrate position accurately and can reproduce grid-cell-like responses similar to those observed experimentally. We then suggest a set of experiments that could help identify whether our suggested mechanism is responsible for the emergence of grid cells and for path integration in the rat's brain.

Additive neurogenesis as a strategy for avoiding interference in a sparsely-coding dentate gyrus

Recently we presented a model of additive neurogenesis in a linear, feedforward neural network that performed an encoding-decoding memory task in a changing input environment. Growing the neural network over time allowed the network to adapt to changes in input statistics without disrupting retrieval properties, and we proposed that adult neurogenesis might fulfil a similar computational role in the dentate gyrus of the hippocampus. Here we explicitly evaluate this hypothesis by examining additive neurogenesis in a simplified hippocampal memory model. The model incorporates a divergence in unit number from the entorhinal cortex to the dentate gyrus and sparse coding in the dentate gyrus, both notable features of hippocampal processing. We evaluate two distinct adaptation strategies; neuronal turnover, where the network is of fixed size but units may be deleted and new ones added, and additive neurogenesis, where the network grows over time, and quantify the performance of the network across the full range of adaptation levels from zero in a fixed network to one in a fully adapting network. We find that additive neurogenesis is always superior to neuronal turnover as it permits the network to be responsive to changes in input statistics while at the same time preserving representations of earlier environments.

Loss of synapses in the entorhinal-dentate gyrus pathway following repeated induction of electroshock seizures in the rat

The goal of this study was to answer the question of whether repeated administration of electroconvulsive shock (ECS) seizures causes structural changes in the entorhinal-dentate projection system, whose neurons are known to be particularly vulnerable to seizure activity. Adult rats were administered six ECS seizures, the first five of which were spaced by 24-hr intervals, whereas the last two were only 2 hr apart. Stereological approaches were employed to compare the total neuronal and synaptic numbers in sham- and ECS-treated rats. Golgi-stained material was used to analyze dendritic arborizations of the dentate gyrus granule cells. Treatment with ECS produced loss of neurons in the entorhinal layer III and in the hilus of the dentate gyrus. The number of neurons in the entorhinal layer II, which provides the major source of dentate afferents, and in the granular layer of the dentate gyrus, known to receive entorhinal projections, remained unchanged. Despite this, the number of synapses established between the entorhinal layer II neurons and their targets, dentate granule cells, was reduced in ECS-treated rats. In addition, administration of ECS seizures produced atrophic changes in the dendritic arbors of dentate granule cells. The total volumes of entorhinal layers II, III, and V-VI were also found to be reduced in ECS-treated rats. By showing that treatment with ECS leads to partial disconnection of the entorhinal cortex and dentate gyrus, these findings shed new light on cellular processes that may underlie structural and functional brain changes induced by brief, generalized seizures.

GAP-43 mRNA and protein expression in the hippocampal and parahippocampal region during the course of epileptogenesis in rats

In order to reveal axonal rewiring in the hippocampal and parahippocampal regions after status epilepticus, we investigated the temporal evolution of growth-associated protein-43 (GAP-43) mRNA and protein expression in two rat models of mesial temporal lobe epilepsy (MTLE). Status epilepticus (SE) was induced by electrical stimulation of the angular bundle or by intraperitoneal kainic acid (KA) injections. Despite increased GAP-43 mRNA expression in dentate granule cells at 24 h after SE, GAP-43 protein expression in the inner molecular layer (IML) of the dentate gyrus decreased progressively after 24 h after SE in both models. Nevertheless robust mossy fiber sprouting (MFS) was evident in the IML of chronic epileptic rats. Remaining GAP-43 protein expression in the IML in chronic epileptic rats did not correlate with the extent of MFS, but with the number of surviving hilar neurons. In the parahippocampal region, GAP-43 mRNA expression was decreased in layer III of the medial entorhinal area (MEAIII) in parallel with extensive neuronal loss in this layer. There was a tendency of GAP-43 mRNA up-regulation in the presubiculum, a region that projects to MEAIII. With regard to this parahippocampal region, however, changes in GAP-43 mRNA expression were not followed by protein changes. The presence of the presynaptic protein GAP-43 in a neurodegenerated MEAIII indicates that fibers still project to this layer. Whether reorganization of fibers has occurred in this region after SE needs to be investigated with tools other than GAP-43.

Life-long stability of neurons: a century of research on neurogenesis, neuronal death and neuron quantification in adult CNS

In this chapter we provide an extensive review of 100 years of research on the stability of neurons in the mammalian brain, with special emphasis on humans. Although Cajal formulated the Neuronal Doctrine, he was wrong in his beliefs that adult neurogenesis did not occur and adult neurons are dying throughout life. These two beliefs became accepted "common knowledge" and have shaped much of neuroscience research and provided much of the basis for clinical treatment of age-related brain diseases. In this review, we consider adult neurogenesis from a historical and evolutionary perspective. It is concluded, that while adult neurogenesis is a factor in the dynamics of the dentate gyrus and olfactory bulb, it is probably not a major factor during the life-span in most brain areas. Likewise, the acceptance of neuronal death as an explanation for normal age-related senility is challenged with evidence collected over the last fifty years. Much of the problem in changing this common belief of dying neurons was the inadequacies of neuronal counting methods. In this review we discuss in detail implications of recent improvements in neuronal quantification. We conclude: First, age-related neuronal atrophy is the major factor in functional deterioration of existing neurons and could be slowed down, or even reversed by various pharmacological interventions. Second, in most cases neuronal degeneration during aging is a pathology that in principle may be avoided. Third, loss of myelin and of the white matter is more frequent and important than the limited neuronal death in normal aging.

Conservation of neuronal number and size in the entorhinal cortex of behaviorally characterized aged rats

Despite abundant evidence of behavioral and electrophysiological dysfunction of the rodent hippocampal formation with aging, the structural basis of age-related cognitive decline remains unclear. Recently, unbiased stereological studies of the mammalian hippocampus have found little evidence to support the dogma that cellular loss accompanies hippocampal aging, thereby supporting an alternative hypothesis that aging is marked by widespread conservation of neuronal number. However, to date, the effects of aging have not been reported in another key component of memory systems in the rodent brain, the entorhinal cortex. In the present study, we stereologically estimated total neuronal number and size (cross-sectional area and cell volume) in the subdivisions and cellular layers of the rat entorhinal cortex, using the optical fractionator and nucleator, respectively. Comparisons were made among Fischer 344 rats that were young, aged-impaired, and aged-unimpaired (based on functional analysis in the Morris water maze). No significant differences in cell number or size were observed in any of the entorhinal subdivisions or laminae examined in each group. Thus, aging is associated with widespread conservation of neuronal number, despite varying degrees of cognitive decline, in all memory-related systems examined to date. These data suggest that mechanisms of age-related cognitive decline are to be found in parameters other than neuronal number or size in the cortex of the mammalian brain.

Adult neurogenesis produces a large pool of new granule cells in the dentate gyrus

Knowing the rate of addition of new granule cells to the adult dentate gyrus is critical to understanding the function of adult neurogenesis. Despite the large number of studies of neurogenesis in the adult dentate gyrus, basic questions about the magnitude of this phenomenon have never been addressed. The S-phase marker bromodeoxyuridine (BrdU) has been extensively used in recent studies of adult neurogenesis, but it has been carefully tested only in the embryonic brain. Here, we show that a high dose of BrdU (300 mg/kg) is a specific, quantitative, and nontoxic marker of dividing cells in the adult rat dentate gyrus, whereas lower doses label only a fraction of the S-phase cells. By using this high dose of BrdU along with a second S-phase marker, [(3)H]thymidine, we found that young adult rats have 9,400 dividing cells proliferating with a cell cycle time of 25 hours, which would generate 9,000 new cells each day, or more than 250,000 per month. Within 5-12 days of BrdU injection, a substantial pool of immature granule neurons, 50% of all BrdU-labeled cells in the dentate gyrus, could be identified with neuron-specific antibodies TuJ1 and TUC-4. This number of new granule neurons generated each month is 6% of the total size of the granule cell population and 30-60% of the size of the afferent and efferent populations (West et al. [1991] Anat Rec 231:482-497; Mulders et al. [1997] J Comp Neurol 385:83-94). The large number of the adult-generated granule cells supports the idea that these new neurons play an important role in hippocampal function.

Conservation of neuron number and size in entorhinal cortex layers II, III, and V/VI of aged primates

Past dogma asserted that extensive loss of cortical neurons accompanies normal aging. However, recent stereologic studies in humans, monkeys, and rodents have found little evidence of age-related neuronal loss in several cortical regions, including the neocortex and hippocampus. Yet to date, a complete investigation of age-related neuronal loss or size change has not been undertaken in the entorhinal cortex, a retrohippocampal structure essential for learning and memory. The aged rhesus macaque monkey (Macaca mulatta), a species that develops beta-amyloid plaques and exhibits cognitive deficits with age, is considered the best commonly available model of aging in humans. In the present study, we examined changes in total neuron number and size in layers II, III, and V/VI of the intermediate division of the entorhinal cortex in aged vs. nonaged rhesus monkeys by using unbiased stereologic methods. Total neuron number was conserved in aged primates when compared with nonaged adults in entorhinal cortex layer II (aged = 56,500 +/- 12,100, nonaged adult = 48,500 +/- 10,900; P = 0.37), layer III (aged = 205, 600 +/- 50,700, nonaged adult = 187,600 +/- 60,300; P = 0.66), and layers V/VI (aged = 246,400 +/- 76,700, nonaged adult = 236,800 +/- 69,600; P = 0.87). In each of the layers examined, neuronal area and volume were also conserved with aging. This lack of morphologically evident neurodegeneration in primate entorhinal cortex with aging further supports the concept that fundamental differences exist between the processes of normal "healthy" aging and pathologic age-related neurodegenerative disorders such as Alzheimer's disease.

Stereological methods for estimating the total number of neurons and synapses: issues of precision and bias

The emergence of a new generation of stereological techniques for counting objects in histological sections has prompted a debate about whether or not these methods are better than previously available techniques when they are used to make estimates of the total numbers of neurons and synapses in a neural structure. During this debate, the concepts of an unbiased estimate and that of a precise estimate have often been confused. A full understanding of the distinction between these two separate aspects of an estimate is required in order to be able to appreciate the virtues of these new counting methods and to apply them correctly. This review intends to make the fundamental issues of this debate more clear, and describes (1) the fundamental differences between the newer design-based counting techniques and previously available assumption-based techniques, and (2) the distinction between an unbiased estimate and a precise estimate.

Total number of neurons in the layers of the human entorhinal cortex

The total number of neurons in the major laminae of the human entorhinal cortex were estimated with a design-based stereological technique, the optical fractionator. Detailed descriptions of the laminar organization and the cortical limits of the region required for the analysis are provided, along with detailed descriptions of the sampling scheme employed. The individual, mean values, and variances for estimates made in layers II, III, V, and VI are presented and discussed in terms of the precision of the estimation procedure and the results of other studies. Neuron numbers were estimated to be about 1 million layer II cells, 5 million layer III cells, 2 million layer V cells, and 4 million layer VI cells, for a total of slightly more that 13 million neurons in the entorhinal cortex. Combined with data from a similar study carried out in the human hippocampus, the data presented represent the first rigorous stereological evidence of the divergence of entorhinal projections to the hippocampus. The data presented also indicate that projections from layer II of the entorhinal cortex to the dentate gyrus and CA2/3 and projections from layer III of the entorhinal cortex to CA1 differ in the degrees of their divergence.

Differential vulnerability of the subiculum and entorhinal cortex of the adult rat to prolonged protein deprivation

Protein deprivation experienced in adult life leads to deficits in the number of hippocampal granule and CA3-CA1 pyramidal cells and to changes in the dendritic domain of granule cells and CA3 pyramids. To obtain a more complete insight into the effects of malnutrition on the limbic system of the adult rat we have analyzed the subiculum and the entorhinal cortex (neuronal layers II, III, and V-VI) in groups of 8-month-old rats fed with a low-protein diet (8% casein) since the age of 2 months and in age-matched control rats. Stereological methods were employed to estimate the total number of neurons in the subiculum and layers II, III, and V-VI of the entorhinal cortex and the volume of the respective cell layers. Moreover, to evaluate whether protein deprivation affects the dendritic domains of the neurons from these regions we have analyzed, in Golgi-impregnated material, the dendritic trees of the pyramidal cells of the subiculum and of the stellate neurons of the entorhinal cortex layer II applying quantitative and metric methods. The volume of the subiculum and the total number of its neurons were reduced in malnourished animals. In these animals we also found marked regressive changes in the apical and basal dendritic trees of the pyramidal subicular neurons. However, the spine density was increased in malnourished rats. No differences in the volume of the neuronal layers of the entorhinal cortex or in the total number of their neurons were found between protein-deprived and control rats, and no alterations were depicted in the dendritic trees of the stellate neurons of layer II. We can thus conclude that the effects of long-term protein deprivation are region specific and that the resulting structural alterations are confined to the three-layered components of the hippocampal region.