Variability Measures of Positive Random Variables

During the stationary part of neuronal spiking response, the stimulus can be encoded in the firing rate, but also in the statistical structure of the interspike intervals. We propose and discuss two information-based measures of statistical dispersion of the interspike interval distribution, the entropy-based dispersion and Fisher information-based dispersion. The measures are compared with the frequently used concept of standard deviation. It is shown, that standard deviation is not well suited to quantify some aspects of dispersion that are often expected intuitively, such as the degree of randomness. The proposed dispersion measures are not entirely independent, although each describes the interspike intervals from a different point of view. The new methods are applied to common models of neuronal firing and to both simulated and experimental data

The Secrets of a Functional Synapse – From a Computational and Experimental Viewpoint

BACKGROUND: Neuronal communication is tightly regulated in time and in space. The neuronal transmission takes place in the nerve terminal, at a specialized structure called the synapse. Following neuronal activation, an electrical signal triggers neurotransmitter (NT) release at the active zone. The process starts by the signal reaching the synapse followed by a fusion of the synaptic vesicle and diffusion of the released NT in the synaptic cleft; the NT then binds to the appropriate receptor, and as a result, a potential change at the target cell membrane is induced. The entire process lasts for only a fraction of a millisecond. An essential property of the synapse is its capacity to undergo biochemical and morphological changes, a phenomenon that is referred to as synaptic plasticity. RESULTS: In this survey, we consider the mammalian brain synapse as our model. We take a cell biological and a molecular perspective to present fundamental properties of the synapse:(i) the accurate and efficient delivery of organelles and material to and from the synapse; (ii) the coordination of gene expression that underlies a particular NT phenotype; (iii) the induction of local protein expression in a subset of stimulated synapses. We describe the computational facet and the formulation of the problem for each of these topics. CONCLUSION: Predicting the behavior of a synapse under changing conditions must incorporate genomics and proteomics information with new approaches in computational biology

A Multi-Component Model of the Developing Retinocollicular Pathway Incorporating Axonal and Synaptic Growth

During development, neurons extend axons to different brain areas and produce stereotypical patterns of connections. The mechanisms underlying this process have been intensively studied in the visual system, where retinal neurons form retinotopic maps in the thalamus and superior colliculus. The mechanisms active in map formation include molecular guidance cues, trophic factor release, spontaneous neural activity, spike-timing dependent plasticity (STDP), synapse creation and retraction, and axon growth, branching and retraction. To investigate how these mechanisms interact, a multi-component model of the developing retinocollicular pathway was produced based on phenomenological approximations of each of these mechanisms. Core assumptions of the model were that the probabilities of axonal branching and synaptic growth are highest where the combined influences of chemoaffinity and trophic factor cues are highest, and that activity-dependent release of trophic factors acts to stabilize synapses. Based on these behaviors, model axons produced morphologically realistic growth patterns and projected to retinotopically correct locations in the colliculus. Findings of the model include that STDP, gradient detection by axonal growth cones and lateral connectivity among collicular neurons were not necessary for refinement, and that the instructive cues for axonal growth appear to be mediated first by molecular guidance and then by neural activity. Although complex, the model appears to be insensitive to variations in how the component developmental mechanisms are implemented. Activity, molecular guidance and the growth and retraction of axons and synapses are common features of neural development, and the findings of this study may have relevance beyond organization in the retinocollicular pathway

Recurrent, Robust and Scalable Patterns Underlie Human Approach and Avoidance

BACKGROUND. Approach and avoidance behavior provide a means for assessing the rewarding or aversive value of stimuli, and can be quantified by a keypress procedure whereby subjects work to increase (approach), decrease (avoid), or do nothing about time of exposure to a rewarding/aversive stimulus. To investigate whether approach/avoidance behavior might be governed by quantitative principles that meet engineering criteria for lawfulness and that encode known features of reward/aversion function, we evaluated whether keypress responses toward pictures with potential motivational value produced any regular patterns, such as a trade-off between approach and avoidance, or recurrent lawful patterns as observed with prospect theory. METHODOLOGY/PRINCIPAL FINDINGS. Three sets of experiments employed this task with beautiful face images, a standardized set of affective photographs, and pictures of food during controlled states of hunger and satiety. An iterative modeling approach to data identified multiple law-like patterns, based on variables grounded in the individual. These patterns were consistent across stimulus types, robust to noise, describable by a simple power law, and scalable between individuals and groups. Patterns included: (i) a preference trade-off counterbalancing approach and avoidance, (ii) a value function linking preference intensity to uncertainty about preference, and (iii) a saturation function linking preference intensity to its standard deviation, thereby setting limits to both. CONCLUSIONS/SIGNIFICANCE. These law-like patterns were compatible with critical features of prospect theory, the matching law, and alliesthesia. Furthermore, they appeared consistent with both mean-variance and expected utility approaches to the assessment of risk. Ordering of responses across categories of stimuli demonstrated three properties thought to be relevant for preference-based choice, suggesting these patterns might be grouped together as a relative preference theory. Since variables in these patterns have been associated with reward circuitry structure and function, they may provide a method for quantitative phenotyping of normative and pathological function (e.g., psychiatric illness).National Institute on Drug Abuse (14118, 026002, 026104, DABK39-03-0098, DABK39-03-C-0098); The MGH Phenotype Genotype Project in Addiction and Mood Disorder from the Office of National Drug Control Policy - Counterdrug Technology Assessment Center; MGH Department of Radiology; the National Center for Research Resources (P41RR14075); National Institute of Neurological Disorders and Stroke (34189, 05236