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1.  A Biologically Plausible Transform for Visual Recognition that is Invariant to Translation, Scale, and Rotation 
Visual object recognition occurs easily despite differences in position, size, and rotation of the object, but the neural mechanisms responsible for this invariance are not known. We have found a set of transforms that achieve invariance in a neurally plausible way. We find that a transform based on local spatial frequency analysis of oriented segments and on logarithmic mapping, when applied twice in an iterative fashion, produces an output image that is unique to the object and that remains constant as the input image is shifted, scaled, or rotated.
doi:10.3389/fncom.2011.00053
PMCID: PMC3222220  PMID: 22125522
biological classifier; cortico-striatal; hybrid model; reinforcement; unsupervised; hierarchical
2.  The Effects of NR2 Subunit-Dependent NMDA Receptor Kinetics on Synaptic Transmission and CaMKII Activation 
PLoS Computational Biology  2008;4(10):e1000208.
N-Methyl-d-aspartic acid (NMDA) receptors are widely expressed in the brain and are critical for many forms of synaptic plasticity. Subtypes of the NMDA receptor NR2 subunit are differentially expressed during development; in the forebrain, the NR2B receptor is dominant early in development, and later both NR2A and NR2B are expressed. In heterologous expression systems, NR2A-containing receptors open more reliably and show much faster opening and closing kinetics than do NR2B-containing receptors. However, conflicting data, showing similar open probabilities, exist for receptors expressed in neurons. Similarly, studies of synaptic plasticity have produced divergent results, with some showing that only NR2A-containing receptors can drive long-term potentiation and others showing that either subtype is capable of driving potentiation. In order to address these conflicting results as well as open questions about the number and location of functional receptors in the synapse, we constructed a Monte Carlo model of glutamate release, diffusion, and binding to NMDA receptors and of receptor opening and closing as well as a model of the activation of calcium-calmodulin kinase II, an enzyme critical for induction of synaptic plasticity, by NMDA receptor-mediated calcium influx. Our results suggest that the conflicting data concerning receptor open probabilities can be resolved, with NR2A- and NR2B-containing receptors having very different opening probabilities. They also support the conclusion that receptors containing either subtype can drive long-term potentiation. We also are able to estimate the number of functional receptors at a synapse from experimental data. Finally, in our models, the opening of NR2B-containing receptors is highly dependent on the location of the receptor relative to the site of glutamate release whereas the opening of NR2A-containing receptors is not. These results help to clarify the previous findings and suggest future experiments to address open questions concerning NMDA receptor function.
Author Summary
Information processing in the brain is carried out by networks of neurons connected by synapses. Synapses can change strength, allowing these networks to adapt and learn, in a process known as synaptic plasticity. At a synapse, an electrical signal in one neuron is converted into a chemical signal, carried by a neurotransmitter, which is in turn converted into electrical and chemical signals in another neuron by specialized proteins called receptors. One such protein, the N-methyl-d-aspartic acid (NMDA) receptor, is particularly important for plasticity, due to its ability to detect the voltage of the cell receiving the neurotransmitter signal and to the fact that it allows calcium, an important signaling molecule, to enter the cell. Here we use computational modeling to investigate the role of one part of the NMDA receptor: the NR2 subunit. The subunit has various forms, and which of these forms are present in the NMDA receptor can strongly affect the kinetics and other properties of the receptor. We show that, along with changing the kinetics of the receptor, changing the NR2 subunit affects the reliability of the receptor, its ability to respond to large stimuli, and its spatial response properties. These results have implications for synaptic transmission and plasticity.
doi:10.1371/journal.pcbi.1000208
PMCID: PMC2563690  PMID: 18974824
3.  Learning to Control a Brain–Machine Interface for Reaching and Grasping by Primates 
PLoS Biology  2003;1(2):e42.
Reaching and grasping in primates depend on the coordination of neural activity in large frontoparietal ensembles. Here we demonstrate that primates can learn to reach and grasp virtual objects by controlling a robot arm through a closed-loop brain–machine interface (BMIc) that uses multiple mathematical models to extract several motor parameters (i.e., hand position, velocity, gripping force, and the EMGs of multiple arm muscles) from the electrical activity of frontoparietal neuronal ensembles. As single neurons typically contribute to the encoding of several motor parameters, we observed that high BMIc accuracy required recording from large neuronal ensembles. Continuous BMIc operation by monkeys led to significant improvements in both model predictions and behavioral performance. Using visual feedback, monkeys succeeded in producing robot reach-and-grasp movements even when their arms did not move. Learning to operate the BMIc was paralleled by functional reorganization in multiple cortical areas, suggesting that the dynamic properties of the BMIc were incorporated into motor and sensory cortical representations.
With visual feedback, macaque monkeys learn to control a robot arm through a neural interface which records activity from multiple cortical areas
doi:10.1371/journal.pbio.0000042
PMCID: PMC261882  PMID: 14624244

Results 1-3 (3)