Syntactic sequencing in Hebbian cell assemblies

Hebbian cell assemblies provide a theoretical framework for the modeling of cognitive processes that grounds them in the underlying physiological neural circuits. Recently we have presented an extension of cell assemblies by operational components which allows to model aspects of language, rules, and complex behaviour. In the present work we study the generation of syntactic sequences using operational cell assemblies timed by unspecific trigger signals. Syntactic patterns are implemented in terms of hetero-associative transition graphs in attractor networks which cause a directed flow of activity through the neural state space. We provide regimes for parameters that enable an unspecific excitatory control signal to switch reliably between attractors in accordance with the implemented syntactic rules. If several target attractors are possible in a given state, noise in the system in conjunction with a winner-takes-all mechanism can randomly choose a target. Disambiguation can also be guided by context signals or specific additional external signals. Given a permanently elevated level of external excitation the model can enter an autonomous mode, where it generates temporal grammatical patterns continuously.     

Visual channels, Hebbian assemblies and the effect of Hebb's rule

 A model of sensory learning is proposed that is based upon Hebb's rule, where Hebb's rule has been generalised by introducing a stabilising function representing some feedback process within or at the adapting (cortical) neuron, preventing synaptic weights from increasing without limit. It will be shown that neurons adapting according to this stabilised Hebb rule will turn into a matched filter for that part of the stimulus pattern that covers the receptive field of a neuron. It follows that the presentation of a stimulus pattern may imply the formation of a set of neurons with overlapping receptive fields, where each neuron has adapted to a certain part of the stimulus. Making simplifying assumptions about the detection process, the model will be illustrated, fitting it to data from Meinhardt and Mortensen [Meinhardt G, Mortensen U (1998) Biol Cybern 79:413–425] which are not compatible with the classical matched filter model introduced by Hauske et al. [Hauske G, Wolf W, Lupp U (1976) Biol Cybern 22:181–188]. Received: 10 May 1999 / Accepted in revised form: 22 October 1999     

The formation of cell assemblies

A simple model is presented for the formation of functional groups in a random neural net. They show the following characteristics: 1. They can maintain autonomous activity which might serve as temporary memory traces. 2. Early in the process of formation they become resistant to contraction. 3. Later they become resistant to expansion. 4. Nearby groups inhibit one another. 5. Two groups may contain some cells in common.     

A review of cell assemblies

Since the cell assembly (CA) was hypothesised, it has gained substantial support and is believed to be the neural basis of psychological concepts. A CA is a relatively small set of connected neurons, that through neural firing can sustain activation without stimulus from outside the CA, and is formed by learning. Extensive evidence from multiple single unit recording and other techniques provides support for the existence of CAs that have these properties, and that their neurons also spike with some degree of synchrony. Since the evidence is so broad and deep, the review concludes that CAs are all but certain. A model of CAs is introduced that is informal, but is broad enough to include, e.g. synfire chains, without including, e.g. holographic reduced representation. CAs are found in most cortical areas and in some sub-cortical areas, they are involved in psychological tasks including categorisation, short-term memory and long-term memory, and are central to other tasks including working memory. There is currently insufficient evidence to conclude that CAs are the neural basis of all concepts. A range of models have been used to simulate CA behaviour including associative memory and more process- oriented tasks such as natural language parsing. Questions involving CAs, e.g. memory persistence, CAs’ complex interactions with brain waves and learning, remain unanswered. CA research involves a wide range of disciplines including biology and psychology, and this paper reviews literature directly related to the CA, providing a basis of discussion for this interdisciplinary community on this important topic. Hopefully, this discussion will lead to more formal and accurate models of CAs that are better linked to neuropsychological data.     

The effect of intracortical competition on the formation of topographic maps in models of Hebbian learning

Correlation-based learning (CBL) models and self-organizing maps (SOM) are two classes of Hebbian models that have both been proposed to explain the activity-driven formation of cortical maps. Both models differ significantly in the way lateral cortical interactions are treated, leading to different predictions for the formation of receptive fields. The linear CBL models predict that receptive field profiles are determined by the average values and the spatial correlations of the second order of the afferent activity patterns, wheras SOM models map stimulus features. Here, we investigate a class of models which are characterized by a variable degree of lateral competition and which have the CBL and SOM models as limit cases. We show that there exists a critical value for intracortical competition below which the model exhibits CBL properties and above which feature mapping sets in. The class of models is then analyzed with respect to the formation of topographic maps between two layers of neurons. For Gaussian input stimuli we find that localized receptive fields and topographic maps emerge above the critical value for intracortical competition, and we calculate this value as a function of the size of the input stimuli and the range of the lateral interaction function. Additionally, we show that the learning rule can be derived via the optimization of a global cost function in a framework of probabilistic output neurons which represent a set of input stimuli by a sparse code. Received: 23 June 1999 / Accepted in revised form: 05 November 1999     

Generative models of rich clubs in Hebbian neuronal networks and large-scale human brain networks

Rich clubs arise when nodes that are ‘rich’ in connections also form an elite, densely connected ‘club’. In brain networks, rich clubs incur high physical connection costs but also appear to be especially valuable to brain function. However, little is known about the selection pressures that drive their formation. Here, we take two complementary approaches to this question: firstly we show, using generative modelling, that the emergence of rich clubs in large-scale human brain networks can be driven by an economic trade-off between connection costs and a second, competing topological term. Secondly we show, using simulated neural networks, that Hebbian learning rules also drive the emergence of rich clubs at the microscopic level, and that the prominence of these features increases with learning time. These results suggest that Hebbian learning may provide a neuronal mechanism for the selection of complex features such as rich clubs. The neural networks that we investigate are explicitly Hebbian, and we argue that the topological term in our model of large-scale brain connectivity may represent an analogous connection rule. This putative link between learning and rich clubs is also consistent with predictions that integrative aspects of brain network organization are especially important for adaptive behaviour.     

Assessing the reconstruction of macromolecular assemblies with toleranced models

We introduce toleranced models (TOMs), a generic and versatile framework meant to handle models of macromolecular assemblies featuring uncertainties on the shapes and the positions of proteins. A TOM being a continuum of nested shapes, the inner (resp. outer) ones representing high (low) confidence regions, we present topological and geometric statistics assessing features of this continuum at multiple scales. While the topological statistics qualify contacts between instances of protein types and complexes involving prescribed protein types, the geometric statistics scale the geometric accuracy of these complexes. We validate the TOM framework on recent average models of the entire nuclear pore complex (NPC) obtained from reconstruction by data integration, and confront our quantitative analysis against experimental findings related to complexes of the NPC, namely the Y-complex, the T-complex, and the Nsp1-Nup82-Nup159 complex. In the three cases, our analysis bridges the gap between global qualitative models of the entire NPC, and atomic resolution models or putative models of the aforementioned complexes. In a broader perspective, the quantitative assessments provided by the TOM framework should prove instrumental to implement a virtuous loop "model reconstruction-model selection", in the context of reconstruction by data integration.     

Computer models of a new deoxy-sickle cell hemoglobin fiber based on x-ray diffraction data.

A new x-ray fiber diffraction pattern from deoxygenated sickle cell erythrocytes has been observed. It displays 14 layer lines with a 109 A periodicity compared with the 64 A periodicity of the "classic" sickle cell hemoglobin (HbS) fiber. These data and association energy calculations serve as a basis for computer model building. Systematic searches over four-dimensional parameter space yielded twelve protofilament models that satisfy the following constraints: (a) two HbS molecules be related by twofold screw symmetry with a translational repeat of 109 A; (b) at least one of the substituted residues in HbS, val beta 6, should participate in intermolecular contacts; and (c) the energy of intermolecular interaction be less than -24 kcal/mol. Each of the protofilament models is a zigzag mono-strand that stands in contrast to the double-stranded protofilament of the "classic" fiber. Fiber models were constructed with each of the 12 protofilament models, pseudo-hexagonally packed. Searches of variable packing parameters showed four fiber models with minimal protofilament association energies and minimal differences between calculated transforms and observed data. The R-factor was less than 0.24 for each of these four models. In three of the fiber models the protofilament association energy is between -(93 and 130) kcal, and in a fourth, the energy is -64 kcal. One protofilament model constituted three distinct fiber models of the lower energy class, and a second protofilament model packed with a higher association energy into a fourth fiber model. The selection of a unique fiber model from among these four cannot be made because of the limited available data.(ABSTRACT TRUNCATED AT 250 WORDS)     

Age-dependent cell cycle models.

This paper presents age-dependent cell cycle models i.e., models where cell generation time is a random variable given by some distribution function, and the probability of cell division per unit time is a function only of cell age (not, for example, of cell mass). It is shown that there does not exist a stable mass distribution if the cells grow exponentially. In the case of linear growth, conditions for stability of the mass distribution are derived. To show these, the methods different from those considered up till now in the literature, are used. It is also shown that one can consider the cell mass growth as a linear dynamical system with a stochastic perturbation. The sister cell model as an improvement of the Transition Probability Model is derived. Statistical data are obtained for that model, and comparisons are made with some experimental data. As a verification tool, alpha and beta curves, are used.     

Dual-channel microfluorometer-photometer based on standard block assemblies and units

The principles of construction and methods of practical realizing of double-wave microfluorometers-photometers for investigation of molecular processes in cells and cell populations are considered.     

A columnar model of somatosensory reorganizational plasticity based on Hebbian and non-Hebbian learning rules

Topographical and functional aspects of neuronal plasticity were studied in the primary somatosensory cortex of adult rats in acute electrophysiological experiments. Under these experimental conditions, we observed short-term reversible reorganization induced by intracortical microstimulation or by an associative pairing of peripheral tactile stimulation. Both types of stimulation generate large-scale and reversible changes of the representational topography and of single cell functional properties. We present a model to simulate the spatial and functional reorganizational aspects of this type of short-term and reversible plasticity. The columnar structure of the network architecture is described and discussed from a biological point of view. The simulated architecture contains three main levels of information processing. The first one is a sensor array corresponding to the sensory surface of the hind paw. The second level, a pre-cortical relay cell array, represents the thalamo-cortical projection with different levels of excitatory and inhibitory relay cells and inhibitory nuclei. The array of cortical columns, the third level, represents stellate, double bouquet, basket and pyramidal cell interactions. The dynamics of the network are ruled by two integro-differential equations of the lateral-inhibition type. In order to implement neuronal plasticity, synaptic weight parameters in those equations are variables. The learning rules are motivated by the original concept of Hebb, but include a combination of both Hebbian and non-Hebbian rules, which modifies different intra- and inter-columnar interactions. We discuss the implications of neuronal plasticity from a behavioral point of view in terms of information processing and computational resources.     

From high-resolution AFM topographs to atomic models of supramolecular assemblies

Atomic force microscopy (AFM) has developed into a powerful tool in membrane biology. AFM features an outstanding signal-to-noise ratio that allows substructures on individual macromolecules to be visualized. Most recently, AFM topographs have shown the supramolecular assembly of the bacterial photosynthetic complexes in native membranes. Here, we have determined the translational and rotational degrees of freedom of the complexes in AFM images of multi-protein assemblies, in order to build realistic atomic models of supramolecular assemblies by docking high-resolution structures into the topographs. Membrane protein assemblies of megadalton size comprising several hundreds of polypeptide chains and pigments were built with Angstrom precision.     

Rigid-cluster models of conformational transitions in macromolecular machines and assemblies

We present a rigid-body-based technique (called rigid-cluster elastic network interpolation) to generate feasible transition pathways between two distinct conformations of a macromolecular assembly. Many biological molecules and assemblies consist of domains which act more or less as rigid bodies during large conformational changes. These collective motions are thought to be strongly related with the functions of a system. This fact encourages us to simply model a macromolecule or assembly as a set of rigid bodies which are interconnected with distance constraints. In previous articles, we developed coarse-grained elastic network interpolation (ENI) in which, for example, only Calpha atoms are selected as representatives in each residue of a protein. We interpolate distance differences of two conformations in ENI by using a simple quadratic cost function, and the feasible conformations are generated without steric conflicts. Rigid-cluster interpolation is an extension of the ENI method with rigid-clusters replacing point masses. Now the intermediate conformations in an anharmonic pathway can be determined by the translational and rotational displacements of large clusters in such a way that distance constraints are observed. We present the derivation of the rigid-cluster model and apply it to a variety of macromolecular assemblies. Rigid-cluster ENI is then modified for a hybrid model represented by a mixture of rigid clusters and point masses. Simulation results show that both rigid-cluster and hybrid ENI methods generate sterically feasible pathways of large systems in a very short time. For example, the HK97 virus capsid is an icosahedral symmetric assembly composed of 60 identical asymmetric units. Its original Hessian matrix size for a Calpha coarse-grained model is >(300,000)(2). However, it reduces to (84)(2) when we apply the rigid-cluster model with icosahedral symmetry constraints. The computational cost of the interpolation no longer scales heavily with the size of structures; instead, it depends strongly on the minimal number of rigid clusters into which the system can be decomposed.     

Macromolecular assemblies based on coupled inclusion complex and electrostatic interactions

Macromolecular assemblies are elaborated by mixing beta-cyclodextrin-containing polymer (polybetaCD), dextran sulfate polyanion (NaDxS), and cationic amphiphiles which are adamantane derivatives (Ada1 or Ada2) in aqueous medium. These components are assembled via coupled inclusion complex interactions (adamantyl group with cyclodextrin cavity) and electrostatic attractive interactions (positive charges of Ada with negative charge of NaDxS). The structural properties are studied by viscometry and small angle neutron scattering. Ternary aggregates with larger size and lower compacities are observed as the cation concentration is increased, until phase separation occurs. The results are in good agreement with a core-shell association mechanism, the core being made of one polybetaCD chain, the shell of NaDxS chains, and the Ada amphiphiles being distributed more or less homogeneously inside the cyclodextrin cavities. The nature of the Ada counterions has a strong influence on the association as Ada1 with I(-) counterions give smaller and less compact aggregates than Ada2 with Br(-) counterions.