Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Inhibition of nociceptors by TRPV1-mediated entry of impermeant sodium channel blockers

Most local anaesthetics used clinically are relatively hydrophobic molecules that gain access to their blocking site on the sodium channel by diffusing into or through the cell membrane. These anaesthetics block sodium channels and thereby the excitability of all neurons, not just sensory neurons. We tested the possibility of selectively blocking the excitability of primary sensory nociceptor (pain-sensing) neurons by introducing the charged, membrane-impermeant lidocaine derivative QX-314 through the pore of the noxious-heat-sensitive TRPV1 channel. Here we show that charged sodium-channel blockers can be targeted into nociceptors by the application of TRPV1 agonists to produce a pain-specific local anaesthesia. QX-314 applied externally had no effect on the activity of sodium channels in small sensory neurons when applied alone, but when applied in the presence of the TRPV1 agonist capsaicin, QX-314 blocked sodium channels and inhibited excitability. Inhibition by co-applied QX-314 and capsaicin was restricted to neurons expressing TRPV1. Injection of QX-314 together with capsaicin into rat hindpaws produced a long-lasting (more than 2 h) increase in mechanical and thermal nociceptive thresholds. Long-lasting decreases in pain sensitivity were also seen with regional injection of QX-314 and capsaicin near the sciatic nerve; however, in contrast to the effect of lidocaine, the application of QX-314 and capsaicin together was not accompanied by motor or tactile deficits.     

A reversible wet/dry adhesive inspired by mussels and geckos

The adhesive strategy of the gecko relies on foot pads composed of specialized keratinous foot-hairs called setae, which are subdivided into terminal spatulae of approximately 200 nm (ref. 1). Contact between the gecko foot and an opposing surface generates adhesive forces that are sufficient to allow the gecko to cling onto vertical and even inverted surfaces. Although strong, the adhesion is temporary, permitting rapid detachment and reattachment of the gecko foot during locomotion. Researchers have attempted to capture these properties of gecko adhesive in synthetic mimics with nanoscale surface features reminiscent of setae; however, maintenance of adhesive performance over many cycles has been elusive, and gecko adhesion is greatly diminished upon full immersion in water. Here we report a hybrid biologically inspired adhesive consisting of an array of nanofabricated polymer pillars coated with a thin layer of a synthetic polymer that mimics the wet adhesive proteins found in mussel holdfasts. Wet adhesion of the nanostructured polymer pillar arrays increased nearly 15-fold when coated with mussel-mimetic polymer. The system maintains its adhesive performance for over a thousand contact cycles in both dry and wet environments. This hybrid adhesive, which combines the salient design elements of both gecko and mussel adhesives, should be useful for reversible attachment to a variety of surfaces in any environment.     

Dynamics of human adipose lipid turnover in health and metabolic disease

Adipose tissue mass is determined by the storage and removal of triglycerides in adipocytes. Little is known, however, about adipose lipid turnover in humans in health and pathology. To study this in vivo, here we determined lipid age by measuring (14)C derived from above ground nuclear bomb tests in adipocyte lipids. We report that during the average ten-year lifespan of human adipocytes, triglycerides are renewed six times. Lipid age is independent of adipocyte size, is very stable across a wide range of adult ages and does not differ between genders. Adipocyte lipid turnover, however, is strongly related to conditions with disturbed lipid metabolism. In obesity, triglyceride removal rate (lipolysis followed by oxidation) is decreased and the amount of triglycerides stored each year is increased. In contrast, both lipid removal and storage rates are decreased in non-obese patients diagnosed with the most common hereditary form of dyslipidaemia, familial combined hyperlipidaemia. Lipid removal rate is positively correlated with the capacity of adipocytes to break down triglycerides, as assessed through lipolysis, and is inversely related to insulin resistance. Our data support a mechanism in which adipocyte lipid storage and removal have different roles in health and pathology. High storage but low triglyceride removal promotes fat tissue accumulation and obesity. Reduction of both triglyceride storage and removal decreases lipid shunting through adipose tissue and thus promotes dyslipidaemia. We identify adipocyte lipid turnover as a novel target for prevention and treatment of metabolic disease.     

Common variants at TRAF3IP2 are associated with susceptibility to psoriatic arthritis and psoriasis

Psoriatic arthritis (PsA) is an inflammatory joint disease that is distinct from other chronic arthritides and which is frequently accompanied by psoriasis vulgaris (PsV) and seronegativity for rheumatoid factor. We conducted a genome-wide association study in 609 German individuals with PsA (cases) and 990 controls with replication in 6 European cohorts including a total of 5,488 individuals. We replicated PsA associations at HLA-C and IL12B and identified a new association at TRAF3IP2 (rs13190932, P = 8.56 × 10?1?). TRAF3IP2 was also associated with PsV in a German cohort including 2,040 individuals (rs13190932, P = 1.95 × 10?3). Sequencing of the exons of TRAF3IP2 identified a coding variant (p.Asp10Asn, rs33980500) as the most significantly associated SNP (P = 1.13 × 10?2?, odds ratio = 1.95). Functional assays showed reduced binding of this TRAF3IP2 variant to TRAF6, suggesting altered modulation of immunoregulatory signals through altered TRAF interactions as a new and shared pathway for PsA and PsV.     

On Cowania and its intergeneric hybrids in Arizona

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HIV-1 superinfection despite broad CD8+ T-cell responses containing replication of the primary virus

Early treatment of acute HIV-1 infection followed by treatment interruptions has shown promise for enhancing immune control of infection. A subsequent loss of control, however, allows the correlates of protective immunity to be assessed. Here we show that sudden breakthrough of plasma viraemia occurred after prolonged immune containment in an individual infected with HIV-1 at a time when 25 distinct CD8+ T-cell epitopes in the viral proteins Gag, RT, Integrase, Env, Nef, Vpr, Vif and Rev were being targeted. Sequencing of the virus in plasma and cells showed that superinfection with a second clade-B virus was coincident with the loss of immune control. This sudden increase in viraemia was associated with a decline in half of the CD8+ T-cell responses. The declining CD8+ T-cell responses were coupled with sequence changes relative to the initial virus that resulted in impaired recognition. Our data show that HIV-1 superinfection can occur in the setting of a strong and broadly directed virus-specific CD8+ T-cell response. The lack of cross-protective immunity for closely related HIV-1 strains, despite persistent recognition of multiple CD8 epitopes, has important implications for public health and vaccine development.     

Sequence of Plasmodium falciparum chromosomes 2, 10, 11 and 14

The mosquito-borne malaria parasite Plasmodium falciparum kills an estimated 0.7-2.7 million people every year, primarily children in sub-Saharan Africa. Without effective interventions, a variety of factors-including the spread of parasites resistant to antimalarial drugs and the increasing insecticide resistance of mosquitoes-may cause the number of malaria cases to double over the next two decades. To stimulate basic research and facilitate the development of new drugs and vaccines, the genome of Plasmodium falciparum clone 3D7 has been sequenced using a chromosome-by-chromosome shotgun strategy. We report here the nucleotide sequences of chromosomes 10, 11 and 14, and a re-analysis of the chromosome 2 sequence. These chromosomes represent about 35% of the 23-megabase P. falciparum genome.