Fractals in the Neurosciences, Part I: General Principles and Basic Neurosciences.

The natural complexity of the brain, its hierarchical structure, and the sophisticated topological architecture of the neurons organized in micronetworks and macronetworks are all factors contributing to the limits of the application of Euclidean geometry and linear dynamics to the neurosciences. The introduction of fractal geometry for the quantitative analysis and description of the geometric complexity of natural systems has been a major paradigm shift in the last decades. Nowadays, modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at various levels of observation, from the microscale to the macroscale, in molecular, anatomic, functional, and pathological perspectives.

Molecular epigenetics, chromatin, and NeuroAIDS/HIV: translational implications.

We describe current research that applies epigenetics to a novel understanding of the immuno-neuropathogenesis of HIV-1 viral infection and NeuroAIDS. We propose the hypothesis that HIV-1 alters the structure-function relationship of chromatin, coding DNA and non-coding DNA, including RNA transcribed from these regions resulting in pathogenesis in AIDS, drug abuse, and NeuroAIDS. We discuss the general implications of molecular epigenetics with special emphasis on drug abuse, bar-codes, pyknons, and miRNAs for translational and clinical research.

Molecular epigenetics, chromatin, and NeuroAIDS/HIV: immunopathological implications.

Epigenetics studies factors related to the organism and environment that modulate inheritance from generation to generation. Molecular epigenetics examines non-coding DNA (ncdDNA) vs. coding DNA (cdDNA), and pertains to every domain of physiology, including immune and brain function.

The principle of recursive genome function.

Responding to an open request, the principle of recursive genome function (PRGF) is put forward, effectively reversing two axioms of genomics as we used to know it, prior to the Encyclopedia of DNA Elements Project (ENCODE). The PRGF is based on the reversal of the interlocking but demonstrably invalid central dogma and "Junk DNA" conjectures that slowed down the advance of sound theory of genome function, as far as information science is concerned, for half a century. PRGF illustrates the utility of the class of recursive algorithms as the intrinsic mathematics of post-ENCODE genomics.

Genomics, morphogenesis and biophysics: triangulation of Purkinje cell development.

The cerebellar Purkinje cells (P-cells) comprise an organelle that is suitable for combined analysis by morphology and genomics, using biophysical tools. In some unknown way, genomic information specifies the development of P-cells. One of us (AJP) has previously proposed that fractal processes associated with DNA are in a causal relation to the fractal properties of organelles such as P-cells (FractoGene, 2002, patent pending).