Miguel A. Andrade

Proteinotopic feature maps

Abstract In this paper a system based on Kohonens SOM (Self-Organizing Map) for protein classification according to Circular Dichroism (CD) spectra is described. As a result, proteins with different secondary structures are clearly separated through a completely unsupervised training process. The algorithm is able to extract features from a high-dimensional vector (CD spectra) and map it to a 2-dimensional network. A new measure, called distortion, has been introduced to test SOM performance. Distortion can be used to fine tune and optimize some of the parameters of the SOM algorithm.

A model of an autocatalytic network formed by error-prone self-replicative species

A generalized model ofn catalytically-coupled self-replicative molecules witherror-prone replication is presented. A generalized mathematical formulation of this model and the outline of its asymptotic behaviour have been developed. Due to the complexity of the model, only in simple situations is it possible to draw general conclusions from the standard analysis. Some complex situations are illustrated by means of numerical integration of particular examples.

Complex dynamics of a catalytic network having faulty replication into error-species

Abstract We examine the dynamics of catalytic networks when error is introduced through faulty self-replication into a mutant molecular species. The model consists of n species that individually self-replicate through noncatalytic and catalytic action, and catalyze the replication of other species. Faulty replication produces error mutants which are assumed to be kinetically indistinguishable from one another. This aggregate error-species (error-tail) undergoes noncatalyzed self-replication, but has no effect on the catalytic species. A constant-population criterion produces competition among all reactants. The time evolution of the catalytic species can be expressed by a set of ordinary differential equations. We provide a detailed parametric analysis of the dynamics in a computationally tractable reduced model. Kinetic constants K ji controlling the enzymatic reactions can be used as bifurcation parameters to generate a rich repertoire of periodic and complex chaotic dynamics. Except for changes in the parametric position of bifurcation points, system dynamics is stable in response to changes in the quality of replication Q , where 1- Q is the mutation rate, and in the amplification constant A for the catalytic species. At low values of Q , the system falls out of chaotic regimes and into a “random-replication” state at which there are no catalytic species present. There is a similar insensitivity to changes in the amplification factor for the error species, A e , except for A = 0, at which the chaotic regimes remain stable throughout the full range of Q . We discuss the behavior of our model against one in which error is handled by means of mutual intermulation between the catalytic species. Complex behavior in this intermutation model is extremely sensitive to the mutation rate. Because the error-tail is expressed only in terms of the catalytic species themselves rather than in variables representing the error-species, the error-tail model may provide a useful method with which to examine models of error-utilization in neuronal and other biological systems involving competitive interactions among their constituent parts.

Simulation of plasticity in the adult visual cortex

Abstract. Retinal plasticity has been shown in the adult visual nervous system in mammals. Following a retinal lesion (scotoma) there is a reorganization of the cortical receptive field distribution: cortical neurons selective to visual stimuli in the area of the visual field corresponding to the retinal lesion, become selective to other parts of the visual field. In this work, we study this effect with a self-organizing neural network. In a first stage, the network reaches a pattern of connectivity that represents normal development of neuronal selectivity. The scotoma is simulated by perturbing accordingly the properties of a region of the input layer representing the retina. The system evolves to a new receptive field distribution mainly by means of the reorganization of the intra cortical connectivity. No major change of the geniculo cortical connectivity is detected. This may explain the surprisingly short time scale of the event.

Non-uniformities and superimposed competition in a model of an autocatalytic network formed by error-prone self-replicative species

The particular dynamics of the previously proposed model of a catalytic network formed byn error-prone self-replicative species without and with superimposed competition is analysed. In the first case, two situations are studied in detail: a uniform network in which all the species are inter-coordinated in the same way, and a network with a species differentiated in its catalytic relation with the remaining elements. In the second case, the superimposed competition is introduced at two levels: first, as an asymmetry in one of the network species amplification factor considering a null self-catalytic vector, and secondly, as a non-null self-catalytic vector with no asymmetry in the other propertics of the species. This kind of system does not present complex behaviour and can be adequately deseribed by performing a standard linear analysis, which gives direct information on the asymptotic behaviour of the sytem. Finally, the biological implications of this analysis within the framework of biological evolution are discussed.

Receptive field map development by anti-Hebbian learning

Neurons selective to oriented visual stimuli participate in the early steps of visual signal processes in higher mammals. A highly ordered neural connectivity responds to such a selectivity. The information necessary to establish this connectivity is too large to be contained in a genome. Moreover, neurophysiological experiments show that the alteration of small parts of the developing visual neural system affects the normal development of the whole system. Self-organizing processes able to produce local order from general properties have already been proposed as the driving force of these development stages. In order to model these self-organizing processes we study a two layer neural network based on simple organizational rules such as (1) diffusion of neural signal in the same layer, (2) Hebbian and anti-Hebbian learning, and (3) individual restrictions to the growth of each neuronal connection. We simulate the development of neurons selective to orientation and size organized in a map, underscoring the importance of anti-Hebbian learning for normal neural visual system development. Copyright 1997 Elsevier Science Ltd.

Application of Vector Quantization Algorithms to Protein Classification and Secondary Structure Computation

In this paper a feature-map based system for protein classification according to circular dichroism spectra is described. The training algorithm has been developed from Kohonen LVQ (Learning Vector Quantization) optimized to get maximum efficiency. As a result, proteins with different secondary structure are clearly separated through a completely unsupervised training process. The algorithm is able to extract features from a high-dimensional vector (CD spectra) and map it to a 2-dimensional network. A new tool has been developed to test LVQ performance, which can be used to fine tune some of LVQ algorithm parameters. Secondary structure for unknown proteins can also be computed, giving better results than classical methods. A 3D solid representation has been introduced to represent 3D feature maps.

A Model for the Development of Neurons Selective to Visual Stimulus Size

In this work, a neural network model for the development of variable sized receptive fields is presented. The system self-organizes under simple rules such as correlation of activity, signal diffusion, and competitive synaptic growth. The network model has one input and one output layer. They are fully connected by an excitatory weight matrix. In addition, the neurons of the output layer are interconnected by inhibitory weights. The set of differential equations for the time evolution of the system is calculated. Numerical integration shows that according to the set of network parameters the system reaches either a non-organized steady state, where all the connections have the same value, or any of two organized states, one of them having connections that represent mexican hat shaped receptive fields of variable size.