Preston R. Aldrich

Genetic Structure of the Invasive Tree Ailanthus altissima in Eastern United States Cities

Ailanthus altissima is an invasive tree from Asia. It now occurs in most US states, and although primarily an urban weed, it has become a problem in forested areas especially in the eastern states. Little is known about its genetic structure. We explore its naturalized gene pool from 28 populations, mostly of the eastern US where infestations are especially severe. Five microsatellite markers were used to examine presumed neutral genetic variation. Results show a gene pool that is moderately diverse and sexually active and has significant but small genetic differences among populations and little correspondence between geographic and genetic distance. These findings are consistent with a model of multiple introductions followed by high rates of gene exchange between cities and regions. We propose movement along road and railway systems as the chief mode of range expansion.

Fractal Topology of Gene Promoter Networks at Phase Transitions

Much is known regarding the structure and logic of genetic regulatory networks. Less understood is the contextual organization of promoter signals used during transcription initiation, the most pivotal stage during gene expression. Here we show that promoter networks organize spontaneously at a dimension between the 1-dimension of the DNA and 3-dimension of the cell. Network methods were used to visualize the global structure of E. coli sigma (σ) recognition footprints using published promoter sequences (RegulonDB). Footprints were rendered as networks with weighted edges representing bp-sharing between promoters (nodes). Serial thresholding revealed phase transitions at positions predicted by percolation theory, and nuclei denoting short steps through promoter space with geometrically constrained linkages. The network nuclei are fractals, a power-law organization not yet described for promoters. Genome-wide promoter abundance also scaled as a power-law. We propose a general model for the development of a fractal nucleus in a transcriptional grammar.

Symmetry in the Language of Gene Expression: A Survey of Gene Promoter Networks in Multiple Bacterial Species and Non-σ Regulons

The language of gene expression displays topological symmetry. An important step during gene expression is the binding of transcriptional proteins to DNA promoters adjacent to a gene. Some proteins bind to many promoters in a genome, defining a regulon of genes wherein each promoter might vary in DNA sequence relative to the average consensus. Here we examine the linguistic organization of gene promoter networks, wherein each node in the network represents a promoter and links between nodes represent the extent of base pair-sharing. Prior work revealed a fractal nucleus in several σ-factor regulons from Escherichia coli. We extend these findings to show fractal nuclei in gene promoter networks from three bacterial species, E. coli, Bacillus subtilis, and Pseudomonas aeruginosa. We surveyed several non-σ transcription factors from these species and found that many contain a nucleus that is both visually and numerically fractal. Promoter footprint size scaled as a negative power-law with both information entropy and fractal dimension, while the latter two parameters scaled positively and linearly. The fractal dimension of the diffuse networks (dB = ~1.7) was close to that expected of a diffusion limited aggregation process, confirming prior predictions as to a possible mechanism for development of this structure.

The curriculum prerequisite network: Modeling the curriculum as a complex system

This article advances the prerequisite network as a means to visualize the hidden structure in an academic curriculum. Networks have been used to represent a variety of complex systems ranging from social systems to biochemical pathways and protein interactions. Here, I treat the academic curriculum as a complex system with nodes representing courses and links between nodes the course prerequisites as readily obtained from a course catalogue. I show that the catalogue data can be rendered as a directed acyclic graph, which has certain desirable analytical features. Using metrics developed in mathematical graph theory, I characterize the overall structure of the undergraduate curriculum of Benedictine University along with that of its Biochemistry and Molecular Biology program. The latter program is shown to contain hidden community structure that crosses disciplinary boundaries. The overall curriculum is seen as partitioned into numerous isolated course groupings, the size of the groups varying considerably. Individual courses serve different roles in the organization, such as information sources, hubs, and bridges. The curriculum prerequisite network represents the intrinsic, hard‐wired constraints on the flow of information in a curriculum, and is the organizational context within which learning occurs. I explore some applications for advising and curriculum reform.

Hybridization network for the system of woody plant gene pools in the United States

Abstract Hybridization generates similarities among gene pools. This structure can be visualized and analyzed at the systems level using networks. Here we construct a network of the 315 woody plant species native or naturalized in the United States using data compiled by the Forest Service of the US Department of Agriculture (USFS). Each species is represented by a node in the network whose size is proportional to a recent census for live stems in the continental United States. Each of the 416 links between node pairs represents evidence for hybridization compiled from the USFS manual Silvics of North America. The total network resolved into 100 separate connected components or clusters (mean size, 3.15 species), with 44% of species linked to at least one other. Betula had the largest component (18 species) following by the separate Quercus clusters (17 red oaks and 16 white oaks); Q. velutina was the most genetically connected woody plant in the continental US. The number of species held together per component (i.e. size) scaled as a power–law albeit a slightly truncated one. The truncation suggests there are fewer than expected hybridizing species within the large woody genera of plants in the US.