History of the Lenz-Ising Model 1920–1950: From Ferromagnetic to Cooperative Phenomena

I chart the considerable changes in the status and conception of the Lenz-Ising model from 1920 to 1950 in terms of three phases: In the early 1920s, Lenz and Ising introduced the model in the field of ferromagnetism. Based on an exact derivation, Ising concluded that it is incapable of displaying ferromagnetic behavior, a result he erroneously extended to three dimensions. In the next phase, Lenz and Isings contemporaries rejected the model as a representation of ferromagnetic materials because of its conflict with the new quantum mechanics. In the third phase, from the early 1930s to the early 1940s, the model was revived as a model of cooperative phenomena. I provide more detail on this history than the earlier accounts of Brush (1967) and Hoddeson, Schubert, Heims, and Baym (1992) and question some of their conclusions. Moreover, my account differs from these in its focus on the development of the model in its capacity as a model. It examines three aspects of this development: (1) the attitudes on the degree of physical realism of the Lenz-Ising model in its representation of physical phenomena; (2) the various reasons for studying and using it; and (3) the effect of the change in its theoretical basis during the transition from the old to the new quantum mechanics. A major theme of my study is that even though the Lenz-Ising model is not fully realistic, it is more useful than more realistic models because of its mathematical tractability. I argue that this point of view, important for the modern conception of the model, is novel and that its emergence, while perhaps not a consequence of its study, is coincident with the third phase of its development.     

TRPC6 is a glomerular slit diaphragm-associated channel required for normal renal function

Progressive kidney failure is a genetically and clinically heterogeneous group of disorders. Podocyte foot processes and the interposed glomerular slit diaphragm are essential components of the permeability barrier in the kidney. Mutations in genes encoding structural proteins of the podocyte lead to the development of proteinuria, resulting in progressive kidney failure and focal segmental glomerulosclerosis. Here, we show that the canonical transient receptor potential 6 (TRPC6) ion channel is expressed in podocytes and is a component of the glomerular slit diaphragm. We identified five families with autosomal dominant focal segmental glomerulosclerosis in which disease segregated with mutations in the gene TRPC6 on chromosome 11q. Two of the TRPC6 mutants had increased current amplitudes. These data show that TRPC6 channel activity at the slit diaphragm is essential for proper regulation of podocyte structure and function.     

Myosin IXB variant increases the risk of celiac disease and points toward a primary intestinal barrier defect

Celiac disease is probably the best-understood immune-related disorder. The disease presents in the small intestine and results from the interplay between multiple genes and gluten, the triggering environmental factor. Although HLA class II genes explain 40% of the heritable risk, non-HLA genes accounting for most of the familial clustering have not yet been identified. Here we report significant and replicable association (P = 2.1 x 10(-6)) to a common variant located in intron 28 of the gene myosin IXB (MYO9B), which encodes an unconventional myosin molecule that has a role in actin remodeling of epithelial enterocytes. Individuals homozygous with respect to the at-risk allele have a 2.3-times higher risk of celiac disease (P = 1.55 x 10(-5)). This result is suggestive of a primary impairment of the intestinal barrier in the etiology of celiac disease, which may explain why immunogenic gluten peptides are able to pass through the epithelial barrier.     

Identification of a new gene mutated in Fraser syndrome and mouse myelencephalic blebs

Fraser syndrome is a recessive, multisystem disorder presenting with cryptophthalmos, syndactyly and renal defects and associated with loss-of-function mutations of the extracellular matrix protein FRAS1. Fras1 mutant mice have a blebbed phenotype characterized by intrauterine epithelial fragility generating serous and, later, hemorrhagic blisters. The myelencephalic blebs (my) strain has a similar phenotype. We mapped my to Frem2, a gene related to Fras1 and Frem1, and showed that a Frem2 gene-trap mutation was allelic to my. Expression of Frem2 in adult kidneys correlated with cyst formation in my homozygotes, indicating that the gene is required for maintaining the differentiated state of renal epithelia. Two individuals with Fraser syndrome were homozygous with respect to the same missense mutation of FREM2, confirming genetic heterogeneity. This is the only missense mutation reported in any blebbing mutant or individual with Fraser syndrome, suggesting that calcium binding in the CALXbeta-cadherin motif is important for normal functioning of FREM2.     

Genetic dissection and prognostic modeling of overt stroke in sickle cell anemia

Sickle cell anemia (SCA) is a paradigmatic single gene disorder caused by homozygosity with respect to a unique mutation at the beta-globin locus. SCA is phenotypically complex, with different clinical courses ranging from early childhood mortality to a virtually unrecognized condition. Overt stroke is a severe complication affecting 6-8% of individuals with SCA. Modifier genes might interact to determine the susceptibility to stroke, but such genes have not yet been identified. Using Bayesian networks, we analyzed 108 SNPs in 39 candidate genes in 1,398 individuals with SCA. We found that 31 SNPs in 12 genes interact with fetal hemoglobin to modulate the risk of stroke. This network of interactions includes three genes in the TGF-beta pathway and SELP, which is associated with stroke in the general population. We validated this model in a different population by predicting the occurrence of stroke in 114 individuals with 98.2% accuracy.     

Population structure, differential bias and genomic control in a large-scale, case-control association study

The main problems in drawing causal inferences from epidemiological case-control studies are confounding by unmeasured extraneous factors, selection bias and differential misclassification of exposure. In genetics the first of these, in the form of population structure, has dominated recent debate. Population structure explained part of the significant +11.2% inflation of test statistics we observed in an analysis of 6,322 nonsynonymous SNPs in 816 cases of type 1 diabetes and 877 population-based controls from Great Britain. The remainder of the inflation resulted from differential bias in genotype scoring between case and control DNA samples, which originated from two laboratories, causing false-positive associations. To avoid excluding SNPs and losing valuable information, we extended the genomic control method by applying a variable downweighting to each SNP.     

Topological versus chemical ordering in network glasses at intermediate and extended length scales

Atomic ordering in network glasses on length scales longer than nearest-neighbour length scales has long been a source of controversy. Detailed experimental information is therefore necessary to understand both the network properties and the fundamentals of glass formation. Here we address the problem by investigating topological and chemical ordering in structurally disordered AX2 systems by applying the method of isotopic substitution in neutron diffraction to glassy ZnCl2. This system may be regarded as a prototypical ionic network forming glass, provided that ion polarization effects are taken into account, and has thus been the focus of much attention. By experiment, we show that both the topological and chemical ordering are described by two length scales at distances greater than nearest-neighbour length scales. One of these is associated with the intermediate range, as manifested by the appearance in the measured diffraction patterns of a first sharp diffraction peak at 1.09(3) A(-1); the other is associated with an extended range, which shows ordering in the glass out to 62(4) A. We also find that these general features are characteristic of glassy GeSe2, a prototypical covalently bonded network material. The results therefore offer structural insight into those length scales that determine many important aspects of supercooled liquid and glass phenomenology.     

Neon isotopes constrain convection and volatile origin in the Earth's mantle

Identifying the origin of primordial volatiles in the Earth's mantle provides a critical test between models that advocate magma-ocean equilibration with an early massive solar-nebula atmosphere and those that require subduction of volatiles implanted in late accreting material. Here we show that neon isotopes in the convecting mantle, resolved in magmatic CO2 well gases, are consistent with a volatile source related to solar corpuscular irradiation of accreting material. This contrasts with recent results that indicated a solar-nebula origin for neon in mantle plume material, which is thought to be sampling the deep mantle. Neon isotope heterogeneity in different mantle sources suggests that models in which the plume source supplies the convecting mantle with its volatile inventory require revision. Although higher than accepted noble gas concentrations in the convecting mantle may reduce the need for a deep mantle volatile flux, any such flux must be dominated by the neon (and helium) isotopic signature of late accreting material.