This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Our goal in this research is to design a statistical model and an algorithm that generates realistic dendritic morphologies of hippocampal principal neurons: CA pyramidal and dentate granule cells. These results can then be related to underlying biophysical mechanisms with implications for developmental theories. We currently have relatively good results including models and algorithms implemented in Matlab (see References). Our present task to be solved on the supercomputer is to optimize parameters of algorithms that generate virtual cells. This task is the final step in a long sequence of efforts that Dr. Ascoli and I started in 2000. At this stage we are not planning to modify the algorithms. Moreover, finding the absolute optimum may not be an option, given the time constraint (about 1 month). In essence, our approach to generating a virtual morphology is based on two steps of sampling. (1) Using a statistical model of a population of cells, we sample parameters of a statistical model of an individual cell. (2) Using the latter, we sample the individual cell morphology. The optimization task therefore consists in finding the optimal parameters of the population model (which is used at step 1). The measure of fitness in our case could be a statistical measure of consistency (e.g., the Wilcoxon test P-value) between the population of real reconstructed neurons and a population of virtual neurons generated by the algorithm. A typical given reconstructed population consists of 24 cells (some populations have up to 40 cells). Therefore, this could be also the size of the virtual population. Because sampled individual cells may vary dramatically from one instance to another, it could take about a hundred (plus-minus an order of magnitude) of sampled virtual populations to measure the fitness function with an acceptable accuracy. This gives us about 10e3 - 10e4 virtual cells in total (per one fitness evaluation). Our statistical model of the population has the order of 10e2 parameters. Therefore, to evaluate the direction of the gradient in this space of parameters, we would need an order of 10e2 sampling points, which gives us the total of 10e6 virtual cells per one gradient evaluation. All this could be an estimate for one iteration step in a classical steepest-descent optimization setup. Assuming that we would need at least a 10e2 steps of minimization for convergence (or, if not convergence, then any significant improvement with respect to the starting point), this gives us the total of 10e8 virtual cells. Currently, the time to generate one virtual cell on a 2.2 GHz AMD Athlon is about 0.1 seconds (without any emergent parameter calculation), which means that it could take about 10e7 seconds to solve the task on the PC. Given that we need to do this several times, for different populations of cells (our database currently includes a dozen of reconstructed populations) and (possibly) trying different versions of the implementation, it appears absolutely necessary to use a supercomputer in order to sole this task. References: Samsonovich AV, Ascoli GA. (2005) Algorithmic description of hippocampal granule cell dendritic morphology. Neurocomputing, 65-66: 253-260. Samsonovich AV, Ascoli GA (2004) Statistical determinants of dendritic morphology in hippocampal pyramidal neurons: A hidden Markov model. Hippocampus, 15 (2): 166-183. Samsonovich AV, Ascoli GA. (2003) Statistical morphological analysis of hippocampal principal neurons indicates cell-specific repulsion of dendrites from their own cell. Journal of Neuroscience Research 71 (2): 173-187.
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