Learning exact enumeration and approximate estimation in deep neural network models

A system for approximate number discrimination has been shown to arise in at least two types of hierarchical neural network models-a generative Deep Belief Network (DBN) and a Hierarchical Convolutional Neural Network (HCNN) trained to classify natural objects. Here, we investigate whether the same two network architectures can learn to recognise exact numerosity. A clear difference in performance could be traced to the specificity of the unit responses that emerged in the last hidden layer of each network. In the DBN, the emergence of a layer of monotonic 'summation units' was sufficient to produce classification behaviour consistent with the behavioural signature of the approximate number system. In the HCNN, a layer of units uniquely tuned to the transition between particular numerosities effectively encoded a thermometer-like 'numerosity code' that ensured near-perfect classification accuracy. The results support the notion that parallel pattern-recognition mechanisms may give rise to exact and approximate number concepts, both of which may contribute to the learning of symbolic numbers and arithmetic.

Place cell rate remapping by CA3 recurrent collaterals

Episodic-like memory is thought to be supported by attractor dynamics in the hippocampus. A possible neural substrate for this memory mechanism is rate remapping, in which the spatial map of place cells encodes contextual information through firing rate variability. To test whether memories are stored as multimodal attractors in populations of place cells, recent experiments morphed one familiar context into another while observing the responses of CA3 cell ensembles. Average population activity in CA3 was reported to transition gradually rather than abruptly from one familiar context to the next, suggesting a lack of attractive forces associated with the two stored representations. On the other hand, individual CA3 cells showed a mix of gradual and abrupt transitions at different points along the morph sequence, and some displayed hysteresis which is a signature of attractor dynamics. To understand whether these seemingly conflicting results are commensurate with attractor network theory, we developed a neural network model of the CA3 with attractors for both position and discrete contexts. We found that for memories stored in overlapping neural ensembles within a single spatial map, position-dependent context attractors made transitions at different points along the morph sequence. Smooth transition curves arose from averaging across the population, while a heterogeneous set of responses was observed on the single unit level. In contrast, orthogonal memories led to abrupt and coherent transitions on both population and single unit levels as experimentally observed when remapping between two independent spatial maps. Strong recurrent feedback entailed a hysteretic effect on the network which diminished with the amount of overlap in the stored memories. These results suggest that context-dependent memory can be supported by overlapping local attractors within a spatial map of CA3 place cells. Similar mechanisms for context-dependent memory may also be found in other regions of the cerebral cortex.

The activity of ‘place cells’ in hippocampal area CA3 systematically changes as a function of the animal's position in an arena as well as contextual variables like the color or shape of enclosing walls. Large changes to the local environment, e.g. moving the animal to a different room, can induce a complete reorganization of place-cell firing locations. Such ‘global remapping’ reveals that memory for different environments is encoded as separate spatial maps. Smaller changes to features within an environment can induce a modulation of place cell firing rates without affecting their firing locations. This kind of ‘rate remapping’ is still poorly understood. In this paper we describe a computational model in which discrete memories for contextual features were stored locally within a spatial map of place cells. This network structure supports retrieval of both positional and contextual information from an arbitrary cue, as required by an episodic memory structure. The activity of the network qualitatively matches empirical data from rate remapping experiments, both on the population level and the level of single place cells. The results support the idea that CA3 rate remapping reflects content-addressable memories stored as multimodal attractor states in the hippocampus.

The entorhinal grid map is discretized

The medial entorhinal cortex (MEC) is part of the brain's circuit for dynamic representation of self-location. The metric of this representation is provided by grid cells, cells with spatial firing fields that tile environments in a periodic hexagonal pattern. Limited anatomical sampling has obscured whether the grid system operates as a unified system or a conglomerate of independent modules. Here we show with recordings from up to 186 grid cells in individual rats that grid cells cluster into a small number of layer-spanning anatomically overlapping modules with distinct scale, orientation, asymmetry and theta-frequency modulation. These modules can respond independently to changes in the geometry of the environment. The discrete topography of the grid-map, and the apparent autonomy of the modules, differ from the graded topography of maps for continuous variables in several sensory systems, raising the possibility that the modularity of the grid map is a product of local self-organizing network dynamics.

Representation of Geometric Borders in the Entorhinal Cortex

We report the existence of an entorhinal cell type that fires when an animal is close to the borders of the proximal environment. The orientation-specific edge-apposing activity of these “border cells” is maintained when the environment is stretched and during testing in enclosures of different size and shape in different rooms. Border cells are relatively sparse, making up less than 10% of the local cell population, but can be found in all layers of the medial entorhinal cortex as well as the adjacent parasubiculum, often intermingled with head-direction cells and grid cells. Border cells may be instrumental in planning trajectories and anchoring grid fields and place fields to a geometric reference frame.

From grid cells to place cells: a mathematical model

Anatomical connectivity and recent neurophysiological results imply that grid cells in the medial entorhinal cortex are the principal cortical inputs to place cells in the hippocampus. The authors propose a model in which place fields of hippocampal pyramidal cells are formed by linear summation of appropriately weighted inputs from entorhinal grid cells. Single confined place fields could be formed by summing input from a modest number (10-50) of grid cells with relatively similar grid phases, diverse grid orientations, and a biologically plausible range of grid spacings. When the spatial phase variation in the grid-cell input was higher, multiple, and irregularly spaced firing fields were formed. These observations point to a number of possible constraints in the organization of functional connections between grid cells and place cells.

Algal toxins as guidance to identify phosphoproteins with key roles in apoptotic cell death

The protein phosphatase inhibiting toxins microcystin and nodularin act rapidly to induce apoptotic cell death. Their inhibitory effect on protein phosphatases 1 and 2A can be utilized as tools to understand the phosphorylation-dependent regulatory mechanism underlying the early stage of apoptosis. The incubation of freshly isolated hepatocytes with these toxins results in a rapid hyperphosphorylation of cellular proteins before any morphological signs of apoptosis appears [Fladmark, K. E., Brustugun, O. T., Hovland, R., Boe, R., Gjertsen, B. T., Zhivotovsky, B. and Doskeland, S. O. (1999) Cell Death Differ. 6, 1099-108]. Proteins subjected to phosphorylation in this early phase of apoptosis may play key roles in this cellular process and become valuable targets for drug development. The ultra-rapid apoptosis-induction by microcystin and nodularin provides a unique amount of synchronized apoptotic cells with "large" amounts of mainly serine/threonine phosphorylated proteins. This ultra-rapid toxin-induced up-concentration of phosphorylated proteins reduces the material needed as well as simplifies our effort in order to obtain enough phosphoproteins for mass spectrometric identification and characterization. We will here give an overview of our strategy for identification of low-abundance phosphoproteins involved in algal toxin-induced apoptosis and most likely also in a general apoptotic pathway.

Microheterogeneity of recombinant human phenylalanine hydroxylase as a result of nonenzymatic deamidations of labile amide containing amino acids. Effects on catalytic and stability properties

The microheterogeneity of recombinant human phenylalanine hydroxylase (hPAH) was investigated by isoelectric focusing and 2D electrophoresis. When expressed in Escherichia coli four main components (denoted hPAH I-IV) of approximately 50 kDa were observed on long-term induction at 28-37 degrees C with isopropyl thio-beta-D-galactoside (IPTG), differing in pI by about 0.1 pH unit. A similar type of microheterogeneity was observed when the enzyme was expressed (1 h at 37 degrees C) in an in vitro transcription-translation system, including both its nonphosphorylated and phosphorylated forms which were separated on the basis of a difference in mobility on SDS/PAGE. Experimental evidence is presented that the microheterogeneity is the result of nonenzymatic deamidations of labile amide containing amino acids. When expressed in E. coli at 28 degrees C, the percentage of the acidic forms of the enzyme subunit increased as a function of the induction time with IPTG, representing about 50% on 8 h induction. When the enzyme obtained after 2 h induction (containing mainly hPAH I) was incubated in vitro, its conversion to the acidic components (hPAH II-IV) revealed a pH and temperature dependence characteristic of a nonenzymatic deamidation of asparagine residues in proteins, with the release of ammonia. Comparing the microheterogeneity of the wild-type and a truncated form of the enzyme expressed in E. coli, it is concluded that the labile amide groups are located in the catalytic domain as defined by crystal structure analysis [Erlandsen, H., Fusetti, F., Martínez, A., Hough, E., Flatmark, T. & Stevens, R. C. (1997) Nat. Struct. Biol. 4, 995-1000]. It is further demonstrated that the progressive deamidations which occur in E. coli results in a threefold increase in the catalytic efficiency (Vmax/[S]0.5) of the enzyme and an increased susceptibility to limited tryptic proteolysis, characteristic of a partly activated enzyme. The results also suggest that deamidation may play a role in the long term regulation of the catalytic activity and the cellular turnover of this enzyme.