The goal of this project is to define and analyze segments of protein and nucleotide sequences showing compositional bias and to understand their structural, functional and evolutionary significance, and their pathology. These sequences include local low complexity regions or domains, including conformationally mobile or intrinsically unstructured regions of proteins, tandemly-repeated sequences, and also more generally distributed amino acid content bias. The latter can reflect directional mutation pressures at the genomic level and constraints specific to protein or domain function. Low complexity regions comprise a large proportion of the genome-encoded amino acids, and may contain homopolymeric tracts or mosaics of a few amino acids, or repeated patterns, frequently subtle, including those typical of many non-globular domains. New mathematical definitions and algorithms are being developed to identify regions of compositional bias, and to discover and analyze properties of these regions relevant to their structures, interactions, biological functions, and evolution. Strong background bias is shown by proteins encoded by very AT-rich or GC-rich genomes, which include those of several important infectious disease organisms: these raise problems for sequence alignment algorithms which are being addressed. Local regions of low complexity and tandemly repeated amino acid sequences occur in many proteins involved in cellular differentiation and embryonic development, RNA processing, transcriptional regulation, signal transduction and aspects of cellular and extracellular structural integrity. Experimental data indicate that low complexity segments of proteins are generally non-globular, intrinsically unstructured, or conformationally mobile: however, knowledge of the molecular structures and dynamics of these domains is still very limited. They are generally relatively intractable to investigation by crystallography and NMR, and they account for less than 1% of the residues in current structural databases. Hence, mathematically rigorous sequence analysis and ab initio quantum chemical methods, together with some relevant high-resolution structural data, are methods of choice for gaining insights into these regions of proteins and for raising questions to be investigated expermentally. These methods are also valuable, for both nucleotide and amino acid sequences, in detecting and eliminating some artifacts in sequence database searches and alignment analysis.