Algorithms for Finding Small Attractors in Boolean Networks

A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]     

Fibulin 5 Forms a Compact Dimer in Physiological Solutions

Fibulin 5 is a 52-kDa calcium-binding epidermal growth factor (cbEGF)-rich extracellular matrix protein that is essential for the formation of elastic tissues. Missense mutations in fibulin 5 cause the elastin disorder cutis laxa and have been associated with age-related macular degeneration, a leading cause of blindness. We investigated the structure, hydrodynamics, and oligomerization of fibulin 5 using small angle x-ray scattering, EM, light scattering, circular dichroism, and sedimentation. Compact structures for the monomer were determined by small angle x-ray scattering and EM, and are supported by close agreement between the theoretical sedimentation of the structures and the experimental sedimentation of the monomer in solution. EM showed that monomers associate around a central cavity to form a dimer. Light scattering and equilibrium sedimentation demonstrated that the equilibrium between the monomer and the dimer is dependent upon NaCl and Ca²⁺ concentrations and that the dimer is dominant under physiological conditions. The dimerization of fragments containing just the cbEGF domains suggests that intermolecular interactions between cbEGFs cause dimerization of fibulin 5. It is possible that fibulin 5 functions as a dimer during elastinogenesis or that dimerization may provide a method for limiting interactions with binding partners such as tropoelastin.Fibulins are a family of seven extracellular matrix glycoproteins, some of which associate with elastic fibers and basement membranes (1, 2). They are involved in the assembly, organization, and stabilization of macromolecular complexes (3). Fibulins contain arrays of cbEGF²-like domains and a fibulin-type C-terminal (Fc) module (4). Fibulins 3–5 have a modified N-terminal cbEGF domain, followed by five cbEGF domains (4).Fibulin 5 (supplemental Fig. S1) is highly expressed in developing arteries with a low expression in adult vessels that is up-regulated following vascular injury and in atherosclerosis (5, 6). Expression has been detected in other elastin-rich tissues, including aorta, skin, uterus, lung, heart, ovary, and colon (5, 6). The extensibility of such tissues is provided by elastic fibers (7), and aging is associated with a loss of elasticity (8). Fibulin 5 is essential for elastinogenesis. The fibulin 5 knock-out mouse exhibits disorganized elastic fibers resulting in severe elastinopathies, with loose skin, vascular abnormalities, and emphysematous lungs. Similar changes are seen in an aged phenotype (9, 10). Mutations in fibulin 5 lead to the elastin disorder cutis laxa (11–13) and have been associated with age-related macular degeneration (14, 15).It has been shown that fibulin 5 binds elastic fibers (16) and interacts with tropoelastin (10), fibrillin 1 (17), lysyl oxidase-like protein 1 (18), -2, and -4 (19), latent transforming growth factor-β-binding protein 2 (19), emilin 1 (20), apolipoprotein (a) (21), and superoxide dismutase (22). Through an RGD motif fibulin 5 interacts with integrins (6, 9, 23).The assembly of elastic fibers is a complex hierarchical process. A model proposes that fibulin 5 associates with microfibrils via interactions with fibrillin 1; tropoelastin molecules bind fibulin 5 and coacervate, and lysyl oxidase-like protein 1 enzymes cross-link tropoelastin to form mature elastin (7, 16). Data that support this model indicate that fibulin 5 potentially increases the coacervation of tropoelastin, enhancing elastic fiber formation (24). However, other data suggest that fibulin 5 slows the maturation of elastin assemblies (25).Rotary-shadowing EM has suggested that fibulin 5 exists as a short rod with a globular domain at one end (26). We used size-exclusion column multiangle laser light scattering (SEC-MALLS), small angle x-ray scattering (SAXS), EM single particle analysis, analytical ultracentrifugation (AUC), CD, and isoelectric focusing to investigate the structures of fibulin 5 in monomeric and dimeric form, and the equilibrium between the two forms.     

Analysis of Free Energy Signals Arising from Nucleotide Hybridization Between rRNA and mRNA Sequences during Translation in Eubacteria

A decoding algorithm is tested that mechanistically models the progressive alignments that arise as the mRNA moves past the rRNA tail during translation elongation. Each of these alignments provides an opportunity for hybridization between the single-stranded, -terminal nucleotides of the 16S rRNA and the spatially accessible window of mRNA sequence, from which a free energy value can be calculated. Using this algorithm we show that a periodic, energetic pattern of frequency 1/3 is revealed. This periodic signal exists in the majority of coding regions of eubacterial genes, but not in the non-coding regions encoding the 16S and 23S rRNAs. Signal analysis reveals that the population of coding regions of each bacterial species has a mean phase that is correlated in a statistically significant way with species () content. These results suggest that the periodic signal could function as a synchronization signal for the maintenance of reading frame and that codon usage provides a mechanism for manipulation of signal phase.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]