Critical transport properties of random metals in large magnetic fields

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se)2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

A universal scaling law between gray matter and white matter of cerebral cortex

Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4/3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.

Predicting species diversity in tropical forests

A fundamental question in ecology is how many species occur within a given area. Despite the complexity and diversity of different ecosystems, there exists a surprisingly simple, approximate answer: the number of species is proportional to the size of the area raised to some exponent. The exponent often turns out to be roughly 1/4. This power law can be derived from assumptions about the relative abundances of species or from notions of self-similarity. Here we analyze the largest existing data set of location-mapped species: over one million, individually identified trees from five tropical forests on three continents. Although the power law is a reasonable, zeroth-order approximation of our data, we find consistent deviations from it on all spatial scales. Furthermore, tropical forests are not self-similar at areas ≤50 hectares. We develop an extended model of the species-area relationship, which enables us to predict large-scale species diversity from small-scale data samples more accurately than any other available method.

PartsList: a web-based system for dynamically ranking protein folds based on disparate attributes, including whole-genome expression and interaction information

As the number of protein folds is quite limited, a mode of analysis that will be increasingly common in the future, especially with the advent of structural genomics, is to survey and re-survey the finite parts list of folds from an expanding number of perspectives. We have developed a new resource, called PartsList, that lets one dynamically perform these comparative fold surveys. It is available on the web at http://bioinfo.mbb.yale.edu/partslist and http://www.partslist.org. The system is based on the existing fold classifications and functions as a form of companion annotation for them, providing ‘global views’ of many already completed fold surveys. The central idea in the system is that of comparison through ranking; PartsList will rank the approximately 420 folds based on more than 180 attributes. These include: (i) occurrence in a number of completely sequenced genomes (e.g. it will show the most common folds in the worm versus yeast); (ii) occurrence in the structure databank (e.g. most common folds in the PDB); (iii) both absolute and relative gene expression information (e.g. most changing folds in expression over the cell cycle); (iv) protein–protein interactions, based on experimental data in yeast and comprehensive PDB surveys (e.g. most interacting fold); (v) sensitivity to inserted transposons; (vi) the number of functions associated with the fold (e.g. most multi-functional folds); (vii) amino acid composition (e.g. most Cys-rich folds); (viii) protein motions (e.g. most mobile folds); and (ix) the level of similarity based on a comprehensive set of structural alignments (e.g. most structurally variable folds). The integration of whole-genome expression and protein–protein interaction data with structural information is a particularly novel feature of our system. We provide three ways of visualizing the rankings: a profiler emphasizing the progression of high and low ranks across many pre-selected attributes, a dynamic comparer for custom comparisons and a numerical rankings correlator. These allow one to directly compare very different attributes of a fold (e.g. expression level, genome occurrence and maximum motion) in the uniform numerical format of ranks. This uniform framework, in turn, highlights the way that the frequency of many of the attributes falls off with approximate power-law behavior (i.e. according to V–b, for attribute value V and constant exponent b), with a few folds having large values and most having small values.

A power law for cells

Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.

Bioenergetic scaling: metabolic design and body-size constraints in mammals.

The cytosolic phosphorylation ratio ([ATP]/[ADP][P(i)]) in the mammalian heart was found to be inversely related to body mass with an exponent of -0.30 (r = 0.999). This exponent is similar to -0.25 calculated for the mass-specific O2 consumption. The inverse of cytosolic free [ADP], the Gibbs energy of ATP hydrolysis (delta G'ATP), and the efficiency of ATP production (energy captured in forming 3 mol of ATP per cycle along the mitochondrial respiratory chain from NADH to 1/2 O2) were all found to scale with body mass with a negative exponent. On the basis of scaling of the phosphorylation ratio and free cytosolic [ADP], we propose that the myocardium and other tissues of small mammals represent a metabolic system with a higher driving potential (a higher delta G'ATP from the higher [ATP]/[ADP][P(i)]) and a higher kinetic gain [(delta V/Vmax)/delta [ADP]] where small changes in free [ADP] produce large changes in steady-state rates of O2 consumption. From the inverse relationship between mitochondrial efficiency and body size we calculate that tissues of small mammals are more efficient than those of large mammals in converting energy from the oxidation of foodstuffs to the bond energy of ATP. A higher efficiency also indicates that mitochondrial electron transport is not the major site for higher heat production in small mammals. We further propose that the lower limit of about 2 g for adult endotherm body size (bumblebee-bat, Estrucan shrew, and hummingbird) may be set by the thermodynamics of the electron transport chain. The upper limit for body size (100,000-kg adult blue whale) may relate to a minimum delta G'ATP of approximately 55 kJ/mol for a cytoplasmic phosphorylation ratio of 12,000 M-1.