Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Neurons of the Dentate Molecular Layer in the Rabbit Hippocampus

The molecular layer of the dentate gyrus appears as the main entrance gate for information into the hippocampus, i.e., where the perforant path axons from the entorhinal cortex synapse onto the spines and dendrites of granule cells. A few dispersed neuronal somata appear intermingled in between and probably control the flow of information in this area. In rabbits, the number of neurons in the molecular layer increases in the first week of postnatal life and then stabilizes to appear permanent and heterogeneous over the individuals’ life span, including old animals. By means of Golgi impregnations, NADPH histochemistry, immunocytochemical stainings and intracellular labelings (lucifer yellow and biocytin injections), eight neuronal morphological types have been detected in the molecular layer of developing adult and old rabbits. Six of them appear as interneurons displaying smooth dendrites and GABA immunoreactivity: those here called as globoid, vertical, small horizontal, large horizontal, inverted pyramidal and polymorphic. Additionally there are two GABA negative types: the sarmentous and ectopic granular neurons. The distribution of the somata and dendritic trees of these neurons shows preferences for a definite sublayer of the molecular layer: small horizontal, sarmentous and inverted pyramidal neurons are preferably found in the outer third of the molecular layer; vertical, globoid and polymorph neurons locate the intermediate third, while large horizontal and ectopic granular neurons occupy the inner third or the juxtagranular molecular layer. Our results reveal substantial differences in the morphology and electrophysiological behaviour between each neuronal archetype in the dentate molecular layer, allowing us to propose a new classification for this neural population

Fine-Tuning and the Stability of Recurrent Neural Networks

A central criticism of standard theoretical approaches to constructing stable, recurrent model networks is that the synaptic connection weights need to be finely-tuned. This criticism is severe because proposed rules for learning these weights have been shown to have various limitations to their biological plausibility. Hence it is unlikely that such rules are used to continuously fine-tune the network in vivo. We describe a learning rule that is able to tune synaptic weights in a biologically plausible manner. We demonstrate and test this rule in the context of the oculomotor integrator, showing that only known neural signals are needed to tune the weights. We demonstrate that the rule appropriately accounts for a wide variety of experimental results, and is robust under several kinds of perturbation. Furthermore, we show that the rule is able to achieve stability as good as or better than that provided by the linearly optimal weights often used in recurrent models of the integrator. Finally, we discuss how this rule can be generalized to tune a wide variety of recurrent attractor networks, such as those found in head direction and path integration systems, suggesting that it may be used to tune a wide variety of stable neural systems

Coexpression of vesicular glutamate transporters 1 and 2, glutamic acid decarboxylase and calretinin in rat entorhinal cortex

We studied the distribution and coexpression of vesicular glutamate transporters (VGluT1, VGluT2), glutamic acid decarboxylase (GAD) and calretinin (CR, calcium-binding protein) in rat entorhinal cortex, using immunofluorescence staining and multichannel confocal laser scanning microscopy. Images were computer processed and subjected to automated 3D object recognition, colocalization analysis and 3D reconstruction. Since the VGluTs (in contrast to CR and GAD) occurred in fibers and axon terminals only, we focused our attention on these neuronal processes. An intense, punctate VGluT1-staining occurred everywhere in the entorhinal cortex. Our computer program resolved these punctae as small 3D objects. Also VGluT2 showed a punctate immunostaining pattern, yet with half the number of 3D objects per tissue volume compared with VGluT1, and with statistically significantly larger 3D objects. Both VGluTs were distributed homogeneously across cortical layers, with in MEA VGluT1 slightly more densely distributed than in LEA. The distribution pattern and the size distribution of GAD 3D objects resembled that of VGluT2. CR-immunopositive fibers were abundant in all cortical layers. In double-stained sections we noted ample colocalization of CR and VGluT2, whereas coexpression of CR and VGluT1 was nearly absent. Also in triple-staining experiments (VGluT2, GAD and CR combined) we noted coexpression of VGluT2 and CR and, in addition, frequent coexpression of GAD and CR. Modest colocalization occurred of VGluT2 and GAD, and incidental colocalization of all three markers. We conclude that the CR-containing axon terminals in the entorhinal cortex belong to at least two subpopulations of CR-neurons: a glutamatergic excitatory and a GABAergic inhibitory

Hippocampal pyramidal cells: the reemergence of cortical lamination

The increasing resolution of tract-tracing studies has led to the definition of segments along the transverse axis of the hippocampal pyramidal cell layer, which may represent functionally defined elements. This review will summarize evidence for a morphological and functional differentiation of pyramidal cells along the radial (deep to superficial) axis of the cell layer. In many species, deep and superficial sublayers can be identified histologically throughout large parts of the septotemporal extent of the hippocampus. Neurons in these sublayers are generated during different periods of development. During development, deep and superficial cells express genes (Sox5, SatB2) that also specify the phenotypes of superficial and deep cells in the neocortex. Deep and superficial cells differ neurochemically (e.g. calbindin and zinc) and in their adult gene expression patterns. These markers also distinguish sublayers in the septal hippocampus, where they are not readily apparent histologically in rat or mouse. Deep and superficial pyramidal cells differ in septal, striatal, and neocortical efferent connections. Distributions of deep and superficial pyramidal cell dendrites and studies in reeler or sparsely GFP-expressing mice indicate that this also applies to afferent pathways. Histological, neurochemical, and connective differences between deep and superficial neurons may correlate with (patho-) physiological phenomena specific to pyramidal cells at different radial locations. We feel that an appreciation of radial subdivisions in the pyramidal cell layer reminiscent of lamination in other cortical areas may be critical in the interpretation of studies of hippocampal anatomy and function