Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which we use work by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods.     

Crystal structures of catalytic and regulatory subunits of rat protein kinase CK2

Protein kinase CK2 consists of two catalytic subunits (CK2α) and two regulatory subunits (CK2β). Here, we report the crystal structures of rat CK2α mutant (rCK2α-△C, 1—335) and CK2β (rCK2β). The overall topology of rCK2α-△C and rCK2β are very similar to the human enzyme, although large structural differences could be observed in the N-terminal domain of rCK2α-△C. Our reported structure of rCK2α-△C is in the close conformation state while the counterpart hCK2α is in the open conformation state, indi- cating ...     

Parallel bacterial evolution within multiple patients identifies candidate pathogenicity genes

Bacterial pathogens evolve during the infection of their human host(1-8), but separating adaptive and neutral mutations remains challenging(9-11). Here we identify bacterial genes under adaptive evolution by tracking recurrent patterns of mutations in the same pathogenic strain during the infection of multiple individuals. We conducted a retrospective study of a Burkholderia dolosa outbreak among subjects with cystic fibrosis, sequencing the genomes of 112 isolates collected from 14 individuals over 16 years. We find that 17 bacterial genes acquired nonsynonymous mutations in multiple individuals, which indicates parallel adaptive evolution. Mutations in these genes affect important pathogenic phenotypes, including antibiotic resistance and bacterial membrane composition and implicate oxygen-dependent regulation as paramount in lung infections. Several genes have not previously been implicated in pathogenesis and may represent new therapeutic targets. The identification of parallel molecular evolution as a pathogen spreads among multiple individuals points to the key selection forces it experiences within human hosts.     

Identification of a functional transposon insertion in the maize domestication gene tb1

Genetic diversity created by transposable elements is an important source of functional variation upon which selection acts during evolution. Transposable elements are associated with adaptation to temperate climates in Drosophila, a SINE element is associated with the domestication of small dog breeds from the gray wolf and there is evidence that transposable elements were targets of selection during human evolution. Although the list of examples of transposable elements associated with host gene function continues to grow, proof that transposable elements are causative and not just correlated with functional variation is limited. Here we show that a transposable element (Hopscotch) inserted in a regulatory region of the maize domestication gene, teosinte branched1 (tb1), acts as an enhancer of gene expression and partially explains the increased apical dominance in maize compared to its progenitor, teosinte. Molecular dating indicates that the Hopscotch insertion predates maize domestication by at least 10,000 years, indicating that selection acted on standing variation rather than new mutation.     

Inverted genomic segments and complex triplication rearrangements are mediated by inverted repeats in the human genome

We identified complex genomic rearrangements consisting of intermixed duplications and triplications of genomic segments at the MECP2 and PLP1 loci. These complex rearrangements were characterized by a triplicated segment embedded within a duplication in 11 unrelated subjects. Notably, only two breakpoint junctions were generated during each rearrangement formation. All the complex rearrangement products share a common genomic organization, duplication-inverted triplication-duplication (DUP-TRP/INV-DUP), in which the triplicated segment is inverted and located between directly oriented duplicated genomic segments. We provide evidence that the DUP-TRP/INV-DUP structures are mediated by inverted repeats that can be separated by >300 kb, a genomic architecture that apparently leads to susceptibility to such complex rearrangements. A similar inverted repeat-mediated mechanism may underlie structural variation in many other regions of the human genome. We propose a mechanism that involves both homology-driven events, via inverted repeats, and microhomologous or nonhomologous events.     

MicroRNAs can generate thresholds in target gene expression

MicroRNAs (miRNAs) are short, highly conserved noncoding RNA molecules that repress gene expression in a sequence-dependent manner. We performed single-cell measurements using quantitative fluorescence microscopy and flow cytometry to monitor a target gene's protein expression in the presence and absence of regulation by miRNA. We find that although the average level of repression is modest, in agreement with previous population-based measurements, the repression among individual cells varies dramatically. In particular, we show that regulation by miRNAs establishes a threshold level of target mRNA below which protein production is highly repressed. Near this threshold, protein expression responds sensitively to target mRNA input, consistent with a mathematical model of molecular titration. These results show that miRNAs can act both as a switch and as a fine-tuner of gene expression.     

Alteration of the serine protease PRSS56 causes angle-closure glaucoma in mice and posterior microphthalmia in humans and mice

Angle-closure glaucoma (ACG) is a subset of glaucoma affecting 16 million people. Although 4 million people are bilaterally blind from ACG, the causative molecular mechanisms of ACG remain to be defined. High intraocular pressure induces glaucoma in ACG. High intraocular pressure traditionally was suggested to result from the iris blocking or closing the angle of the eye, thereby limiting aqueous humor drainage. Eyes from individuals with ACG often have a modestly decreased axial length, shallow anterior chamber and relatively large lens, features that predispose to angle closure. Here we show that genetic alteration of a previously unidentified serine protease (PRSS56) alters axial length and causes a mouse phenotype resembling ACG. Mutations affecting this protease also cause a severe decrease of axial length in individuals with posterior microphthalmia. Together, these data suggest that alterations of this serine protease may contribute to a spectrum of human ocular conditions including reduced ocular size and ACG.     

Genome-wide association study identifies susceptibility loci for IgA nephropathy

We carried out a genome-wide association study of IgA nephropathy, a major cause of kidney failure worldwide. We studied 1,194 cases and 902 controls of Chinese Han ancestry, with targeted follow up in Chinese and European cohorts comprising 1,950 cases and 1,920 controls. We identified three independent loci in the major histocompatibility complex, as well as a common deletion of CFHR1 and CFHR3 at chromosome 1q32 and a locus at chromosome 22q12 that each surpassed genome-wide significance (P values for association between 1.59 × 10?2? and 4.84 × 10?? and minor allele odds ratios of 0.63-0.80). These five loci explain 4-7% of the disease variance and up to a tenfold variation in interindividual risk. Many of the alleles that protect against IgA nephropathy impart increased risk for other autoimmune or infectious diseases, and IgA nephropathy risk allele frequencies closely parallel the variation in disease prevalence among Asian, European and African populations, suggesting complex selective pressures.     

Stopping RNA interference at the seed

MicroRNAs (miRNAs) regulate expression of more than one half of the genes in the human genome. A study now reports a new method for selectively silencing whole families of miRNAs, thus providing a new paradigm for disease therapy.