Computational RSM Modeling of Neuromorphofunctional Relations of Dentate Nuclear Neurons and Dentatostriate Inter-Cluster Mapping with the Dentatostriate Neural Network Reconstruction: RLSR/PCR Regression and Canonical Correlation Analysis

Aim: The aim of this study is to find relational connections (interdependence) between the two most general categorical aspects of a neuron, i.e., between the form (morphology) and its function, using as a model for this task dentate nucleus neurons. Furthermore, the configuration of the dentatostriate nucleotopic inter-cluster mapping of the dentatostriate neural network is investigated in order to determine mutual, inter-neuronal, neuromorphofunctional remote influence, i.e. the neuromorphofunctional relations at the level of a neural network.Materials and methods: (Semi) virtual dentate and neostriate adult human neuronal samples were used. Neuromorphological parameters of each neuron have been directly measured, i.e. experimentally determined, whereas the corresponding neurofunctional parameters have been theoretically obtained. The neuromorphological parameters determine the following properties of a neuron: neuron shape, compartmental length and size/ surface, dendritic branching, complexity and organization of neuronal morphology. The group of neurofunctional parameters determines functional aspects of action potential (AV/AP), as well as neurofunctional properties of the perikaryodendritic compartment of a neuron. Data analysis is performed using response surface (RSM) modeling, along with partial least-squares (PLSR) and principal component regression analysis (PCR), accompanied by canonical and Pearson correlation analysis. A stepwise algorithm formulates the complete data analysis.Results: Obtained RSM models represent response-predictor relations, where a neuromorphological/functional response parameter is expressed as a function in terms of parameters of other category (morphology/function). Additionally, RSM modeling is also used to decipher the symmetry of the dentatostriate inter-cluster neural network by the corresponding inter-cluster inter-nuclear mapping, using so-called integral parameters/variables, obtained on a computational, theoretical manner. The obtained network is a fully connected, symmetric, Hopfield neural network.Conclusion: Neuronal morphology and function are definitely interrelated and depend on each other. By intensity, however, this interconnectedness can be treated as mild to moderate. It is determined by elementary neuromorphofunctional relations, observed at the macroscopic, phenomenological level, i.e. only through measured parameters as their observable and explicit manifestation without considering the microscopic, molecular causality of them. These relations are the strongest when acting upon a single neuron and their mutual remote influence on each other weakens in neural circuits and networks up to 10% of deterministic relational interconnection strength observed at the level of single neuron relations.