Between Kepler and Newton: Hooke’s ‘principles of congruity and incongruity’ and the naturalization of mathematics

ABSTRACT

Robert Hooke’s development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke’s ‘Principles?…?of Congruity and Incongruity of bodies’ represent a uniquely powerful approach to the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke’s ‘Uniform Geometrical or Mechanical Method’ was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world.     

Type specimens of recent mammals in the Utah Museum of Natural History, University of Utah

A detailed list of holotypes of Recent mammals housed in the Utah Museum of Natural History is presented.     

How helpful are spatial effects in forecasting the growth of Chinese provinces?

In this paper, we make multi‐step forecasts of the annual growth rates of the real gross regional product (GRP) for each of the 31 Chinese provinces simultaneously. Beside the usual panel data models, we use panel models that explicitly account for spatial dependence between the GRP growth rates. In addition, the possibility of spatial effects being different for different groups of provinces (Interior and Coast) is allowed for. We find that both pooling and accounting for spatial effects help substantially to improve the forecast performance compared to the benchmark models estimated for each of the provinces separately. It is also shown that the effect of accounting for spatial dependence is even more pronounced at longer forecasting horizons (the forecast accuracy gain as measured by the root mean squared forecast error is about 8% at the 1‐year horizon and exceeds 25% at the 13‐ and 14‐year horizons). Copyright © 2010 John Wiley & Sons, Ltd.     

Signal sequence directs localized secretion of bacterial surface proteins

All living cells require specific mechanisms that target proteins to the cell surface. In eukaryotes, the first part of this process involves recognition in the endoplasmic reticulum of amino-terminal signal sequences and translocation through Sec translocons, whereas subsequent targeting to different surface locations is promoted by internal sorting signals. In bacteria, N-terminal signal sequences promote translocation across the cytoplasmic membrane, which surrounds the entire cell, but some proteins are nevertheless secreted in one part of the cell by poorly understood mechanisms. Here we analyse localized secretion in the Gram-positive pathogen Streptococcus pyogenes, and show that the signal sequences of two surface proteins, M protein and protein F (PrtF), direct secretion to different subcellular regions. The signal sequence of M protein promotes secretion at the division septum, whereas that of PrtF preferentially promotes secretion at the old pole. Our work therefore shows that a signal sequence may contain information that directs the secretion of a protein to one subcellular region, in addition to its classical role in promoting secretion. This finding identifies a new level of complexity in protein translocation and emphasizes the potential of bacterial systems for the analysis of fundamental cell-biological problems.     

Human immunodeficiency viruses: SIV infection in wild gorillas

Chimpanzees (Pan troglodytes troglodytes) from west central Africa are recognized as the reservoir of simian immunodeficiency viruses (SIVcpzPtt) that have crossed at least twice to humans: this resulted in the AIDS pandemic (from human immunodeficiency virus HIV-1 group M) in one instance and infection of just a few individuals in Cameroon (by HIV-1 group N) in another. A third HIV-1 lineage (group O) from west central Africa also falls within the SIVcpzPtt radiation, but the primate reservoir of this virus has not been identified. Here we report the discovery of HIV-1 group O-like viruses in wild gorillas.     

The type Ia supernova SNLS-03D3bb from a super-Chandrasekhar-mass white dwarf star

The accelerating expansion of the Universe, and the need for dark energy, were inferred from observations of type Ia supernovae. There is a consensus that type Ia supernovae are thermonuclear explosions that destroy carbon-oxygen white dwarf stars that have accreted matter from a companion star, although the nature of this companion remains uncertain. These supernovae are thought to be reliable distance indicators because they have a standard amount of fuel and a uniform trigger: they are predicted to explode when the mass of the white dwarf nears the Chandrasekhar mass of 1.4 solar masses (M(o)). Here we show that the high-redshift supernova SNLS-03D3bb has an exceptionally high luminosity and low kinetic energy that both imply a super-Chandrasekhar-mass progenitor. Super-Chandrasekhar-mass supernovae should occur preferentially in a young stellar population, so this may provide an explanation for the observed trend that overluminous type Ia supernovae occur only in 'young' environments. As this supernova does not obey the relations that allow type Ia supernovae to be calibrated as standard candles, and as no counterparts have been found at low redshift, future cosmology studies will have to consider possible contamination from such events.     

Structural basis of cell surface receptor recognition by botulinum neurotoxin B

Botulinum neurotoxins (BoNTs) are potent bacterial toxins that cause paralysis at femtomolar concentrations by blocking neurotransmitter release. A 'double receptor' model has been proposed in which BoNTs recognize nerve terminals via interactions with both gangliosides and protein receptors that mediate their entry. Of seven BoNTs (subtypes A-G), the putative receptors for BoNT/A, BoNT/B and BoNT/G have been identified, but the molecular details that govern recognition remain undefined. Here we report the crystal structure of full-length BoNT/B in complex with the synaptotagmin II (Syt-II) recognition domain at 2.6 A resolution. The structure of the complex reveals that Syt-II forms a short helix that binds to a hydrophobic groove within the binding domain of BoNT/B. In addition, mutagenesis of amino acid residues within this interface on Syt-II affects binding of BoNT/B. Structural and sequence analysis reveals that this hydrophobic groove is conserved in the BoNT/G and BoNT/B subtypes, but varies in other clostridial neurotoxins. Furthermore, molecular docking studies using the ganglioside G(T1b) indicate that its binding site is more extensive than previously proposed and might form contacts with both BoNT/B and synaptotagmin. The results provide structural insights into how BoNTs recognize protein receptors and reveal a promising target for blocking toxin-receptor recognition.     

Genetic evidence for complex speciation of humans and chimpanzees

The genetic divergence time between two species varies substantially across the genome, conveying important information about the timing and process of speciation. Here we develop a framework for studying this variation and apply it to about 20 million base pairs of aligned sequence from humans, chimpanzees, gorillas and more distantly related primates. Human-chimpanzee genetic divergence varies from less than 84% to more than 147% of the average, a range of more than 4 million years. Our analysis also shows that human-chimpanzee speciation occurred less than 6.3 million years ago and probably more recently, conflicting with some interpretations of ancient fossils. Most strikingly, chromosome X shows an extremely young genetic divergence time, close to the genome minimum along nearly its entire length. These unexpected features would be explained if the human and chimpanzee lineages initially diverged, then later exchanged genes before separating permanently.     

Graphene-based composite materials

Graphene sheets--one-atom-thick two-dimensional layers of sp2-bonded carbon--are predicted to have a range of unusual properties. Their thermal conductivity and mechanical stiffness may rival the remarkable in-plane values for graphite (approximately 3,000 W m(-1) K(-1) and 1,060 GPa, respectively); their fracture strength should be comparable to that of carbon nanotubes for similar types of defects; and recent studies have shown that individual graphene sheets have extraordinary electronic transport properties. One possible route to harnessing these properties for applications would be to incorporate graphene sheets in a composite material. The manufacturing of such composites requires not only that graphene sheets be produced on a sufficient scale but that they also be incorporated, and homogeneously distributed, into various matrices. Graphite, inexpensive and available in large quantity, unfortunately does not readily exfoliate to yield individual graphene sheets. Here we present a general approach for the preparation of graphene-polymer composites via complete exfoliation of graphite and molecular-level dispersion of individual, chemically modified graphene sheets within polymer hosts. A polystyrene-graphene composite formed by this route exhibits a percolation threshold of approximately 0.1 volume per cent for room-temperature electrical conductivity, the lowest reported value for any carbon-based composite except for those involving carbon nanotubes; at only 1 volume per cent, this composite has a conductivity of approximately 0.1 S m(-1), sufficient for many electrical applications. Our bottom-up chemical approach of tuning the graphene sheet properties provides a path to a broad new class of graphene-based materials and their use in a variety of applications.     

Chromosomal landscape of nucleosome-dependent gene expression and silencing in yeast

Eukaryotic genomes are packaged into nucleosomes, which are thought to repress gene expression generally. Repression is particularly evident at yeast telomeres, where genes within the telomeric heterochromatin appear to be silenced by the histone-binding silent information regulator (SIR) complex (Sir2, Sir3, Sir4) and Rap1 (refs 4-10). Here, to investigate how nucleosomes and silencing factors influence global gene expression, we use high-density arrays to study the effects of depleting nucleosomal histones and silencing factors in yeast. Reducing nucleosome content by depleting histone H4 caused increased expression of 15% of genes and reduced expression of 10% of genes, but it had little effect on expression of the majority (75%) of yeast genes. Telomere-proximal genes were found to be de-repressed over regions extending 20 kilobases from the telomeres, well beyond the extent of Sir protein binding and the effects of loss of Sir function. These results indicate that histones make Sir-independent contributions to telomeric silencing, and that the role of histones located elsewhere in chromosomes is gene specific rather than generally repressive.