Early expression of antiinsulin autoantibodies of humans and the NOD mouse: Evidence for early determination of subsequent diabetes

With the development of an insulin autoantibody (IAA) assay performed in 96-well filtration plates, we have evaluated prospectively the development of IAA in NOD mice (from 4 weeks of age) and children (from 7 to 10 months of age) at genetic risk for the development of type 1 diabetes. NOD mice had heterogeneous expression of IAA despite being inbred. IAA reached a peak between 8 and 16 weeks and then declined. IAA expression by NOD mice at 8 weeks of age was strongly associated with early development of diabetes, which occurred at 16–18 weeks of age (NOD mice IAA+ at 8 weeks: 83% (5/6) diabetic by 18 weeks versus 11% (1/9) of IAA negative at 8 weeks; P < .01). In man, IAA was frequently present as early as 9 months of age, the first sampling time. Of five children found to have persistent IAA before 1 year of age, four have progressed to diabetes (all before 3.5 years of age) and the fifth is currently less than age 2. Of the 929 children not expressing persistent IAA before age 1, only one has progressed to diabetes to date (age onset 3), and this child expressed IAA at his second visit (age 1.1). In new onset patients, the highest levels of IAA correlated with an earlier age of diabetes onset. Our data suggest that the program for developing diabetes of NOD mice and humans is relatively “fixed” early in life and, for NOD mice, a high risk of early development of diabetes is often determined by 8 weeks of age. With such early determination of high risk of progression to diabetes, immunologic therapies in humans may need to be tested in children before the development of IAA for maximal efficacy.

Measurement of genetic structure within populations using Moran's spatial autocorrelation statistics.

Spatial structure of genetic variation within populations, an important interacting influence on evolutionary and ecological processes, can be analyzed in detail by using spatial autocorrelation statistics. This paper characterizes the statistical properties of spatial autocorrelation statistics in this context and develops estimators of gene dispersal based on data on standing patterns of genetic variation. Large numbers of Monte Carlo simulations and a wide variety of sampling strategies are utilized. The results show that spatial autocorrelation statistics are highly predictable and informative. Thus, strong hypothesis tests for neutral theory can be formulated. Most strikingly, robust estimators of gene dispersal can be obtained with practical sample sizes. Details about optimal sampling strategies are also described.

Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Coalescent estimates of HIV-1 generation time in vivo

The generation time of HIV Type 1 (HIV-1) in vivo has previously been estimated using a mathematical model of viral dynamics and was found to be on the order of one to two days per generation. Here, we describe a new method based on coalescence theory that allows the estimate of generation times to be derived by using nucleotide sequence data and a reconstructed genealogy of sequences obtained over time. The method is applied to sequences obtained from a long-term nonprogressing individual at five sampling occasions. The estimate of viral generation time using the coalescent method is 1.2 days per generation and is close to that obtained by mathematical modeling (1.8 days per generation), thus strengthening confidence in estimates of a short viral generation time. Apart from the estimation of relevant parameters relating to viral dynamics, coalescent modeling also allows us to simulate the evolutionary behavior of samples of sequences obtained over time.

Visual constraints in foraging bumblebees: Flower size and color affect search time and flight behavior

In optimal foraging theory, search time is a key variable defining the value of a prey type. But the sensory-perceptual processes that constrain the search for food have rarely been considered. Here we evaluate the flight behavior of bumblebees (Bombus terrestris) searching for artificial flowers of various sizes and colors. When flowers were large, search times correlated well with the color contrast of the targets with their green foliage-type background, as predicted by a model of color opponent coding using inputs from the bees' UV, blue, and green receptors. Targets that made poor color contrast with their backdrop, such as white, UV-reflecting ones, or red flowers, took longest to detect, even though brightness contrast with the background was pronounced. When searching for small targets, bees changed their strategy in several ways. They flew significantly slower and closer to the ground, so increasing the minimum detectable area subtended by an object on the ground. In addition, they used a different neuronal channel for flower detection. Instead of color contrast, they used only the green receptor signal for detection. We relate these findings to temporal and spatial limitations of different neuronal channels involved in stimulus detection and recognition. Thus, foraging speed may not be limited only by factors such as prey density, flight energetics, and scramble competition. Our results show that understanding the behavioral ecology of foraging can substantially gain from knowledge about mechanisms of visual information processing.

The optimal measure of allelic association

Allelic association between pairs of loci is derived in terms of the association probability ρ as a function of recombination θ, effective population size N, linear systematic pressure v, and time t, predicting both ρrt, the decrease of association from founders and ρct, the increase by genetic drift, with ρt = ρrt + ρct. These results conform to the Malecot equation, with time replaced by distance on the genetic map, or on the physical map if recombination in the region is uniform. Earlier evidence suggested that ρ is less sensitive to variations in marker allele frequencies than alternative metrics for which there is no probability theory. This robustness is confirmed for six alternatives in eight samples. In none of these 48 tests was the residual variance as small as for ρ. Overall, efficiency was less than 80% for all alternatives, and less than 30% for two of them. Efficiency of alternatives did not increase when information was estimated simultaneously. The swept radius within which substantial values of ρ are conserved lies between 385 and 893 kb, but deviation of parameters between measures is enormously significant. The large effort now being devoted to allelic association has little value unless the ρ metric with the strongest theoretical basis and least sensitivity to marker allele frequencies is used for mapping of marker association and localization of disease loci.

Effects of sampling standardization on estimates of Phanerozoic marine diversification

Global diversity curves reflect more than just the number of taxa that have existed through time: they also mirror variation in the nature of the fossil record and the way the record is reported. These sampling effects are best quantified by assembling and analyzing large numbers of locality-specific biotic inventories. Here, we introduce a new database of this kind for the Phanerozoic fossil record of marine invertebrates. We apply four substantially distinct analytical methods that estimate taxonomic diversity by quantifying and correcting for variation through time in the number and nature of inventories. Variation introduced by the use of two dramatically different counting protocols also is explored. We present sampling-standardized diversity estimates for two long intervals that sum to 300 Myr (Middle Ordovician-Carboniferous; Late Jurassic-Paleogene). Our new curves differ considerably from traditional, synoptic curves. For example, some of them imply unexpectedly low late Cretaceous and early Tertiary diversity levels. However, such factors as the current emphasis in the database on North America and Europe still obscure our view of the global history of marine biodiversity. These limitations will be addressed as the database and methods are refined.

A general additive distance with time-reversibility and rate variation among nucleotide sites.

As additivity is a very useful property for a distance measure, a general additive distance is proposed under the stationary time-reversible (SR) model of nucleotide substitution or, more generally, under the stationary, time-reversible, and rate variable (SRV) model, which allows rate variation among nucleotide sites. A method for estimating the mean distance and the sampling variance is developed. In addition, a method is developed for estimating the variance-covariance matrix of distances, which is useful for the statistical test of phylogenies and molecular clocks. Computer simulation shows (i) if the sequences are longer than, say, 1000 bp, the SR method is preferable to simpler methods; (ii) the SR method is robust against deviations from time-reversibility; (iii) when the rate varies among sites, the SRV method is much better than the SR method because the distance is seriously underestimated by the SR method; and (iv) our method for estimating the sampling variance is accurate for sequences longer than 500 bp. Finally, a test is constructed for testing whether DNA evolution follows a general Markovian model.

Enhanced conformational sampling in Monte Carlo simulations of proteins: application to a constrained peptide.

A Monte Carlo simulation method for globular proteins, called extended-scaled-collective-variable (ESCV) Monte Carlo, is proposed. This method combines two Monte Carlo algorithms known as entropy-sampling and scaled-collective-variable algorithms. Entropy-sampling Monte Carlo is able to sample a large configurational space even in a disordered system that has a large number of potential barriers. In contrast, scaled-collective-variable Monte Carlo provides an efficient sampling for a system whose dynamics is highly cooperative. Because a globular protein is a disordered system whose dynamics is characterized by collective motions, a combination of these two algorithms could provide an optimal Monte Carlo simulation for a globular protein. As a test case, we have carried out an ESCV Monte Carlo simulation for a cell adhesive Arg-Gly-Asp-containing peptide, Lys-Arg-Cys-Arg-Gly-Asp-Cys-Met-Asp, and determined the conformational distribution at 300 K. The peptide contains a disulfide bridge between the two cysteine residues. This bond mimics the strong geometrical constraints that result from a protein's globular nature and give rise to highly cooperative dynamics. Computation results show that the ESCV Monte Carlo was not trapped at any local minimum and that the canonical distribution was correctly determined.

Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.

A sampling problem in molecular dynamics simulations of macromolecules.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.