Effects of random jumps on a very simple neuronal diffusion model

The effects of taking into account in a perfect integrate and fire model of neuronal activity the spatial localization of the synapses are studied by superposing to the diffusion a simple discrete jump component. Different criteria are employed to assess the role of excitatory and inhibitory discrete contributions. Comparisons are performed with respect to the case where contributions coming from synapses more distal from the trigger zone are summed up in a continuous model. A systematic study of the output frequency and of the inter spike interval coefficient of variation (CV) is performed by means of examples as the model parameters are varied.     

Mean-square displacement relationship in bioprotectant systems by elastic neutron scattering

Neutron intensity elastic scans on trehalose, maltose, and sucrose/H(2)O mixtures as a function of concentration, temperature, and exchanged wave vector are presented. The experimental findings show a crossover in molecular fluctuations between harmonic and anharmonic dynamical regimes. A new operative definition for the degree of fragility of glass-forming systems is furnished by using explicitly the connection between viscosity and mean-square displacement. The procedure is tested for the investigated mixtures and for a set of glass-forming systems. In this frame, the stronger character of trehalose/H(2)O mixture indicates a better attitude in respect to maltose and sucrose/H(2)O mixtures to encapsulate biostructures in a more rigid matrix.     

Smooth random effects distribution in a linear mixed model

A linear mixed model with a smooth random effects density is proposed. A similar approach to P-spline smoothing of Eilers and Marx (1996, Statistical Science 11, 89-121) is applied to yield a more flexible estimate of the random effects density. Our approach differs from theirs in that the B-spline basis functions are replaced by approximating Gaussian densities. Fitting the model involves maximizing a penalized marginal likelihood. The best penalty parameters minimize Akaike's Information Criterion employing Gray's (1992, Journal of the American Statistical Association 87, 942-951) results. Although our method is applicable to any dimensions of the random effects structure, in this article the two-dimensional case is explored. Our methodology is conceptually simple, and it is relatively easy to fit in practice and is applied to the cholesterol data first analyzed by Zhang and Davidian (2001, Biometrics 57, 795-802). A simulation study shows that our approach yields almost unbiased estimates of the regression and the smoothing parameters in small sample settings. Consistency of the estimates is shown in a particular case.     

Modeling random effects for censored data by a multivariate normal regression model

A normal distribution regression model with a frailty-like factor to account for statistical dependence between the observed survival times is introduced. This model, as opposed to standard hazard-based frailty models, has survival times that, conditional on the shared random effect, have an accelerated failure time representation. The dependence properties of this model are discussed and maximum likelihood estimation of the model's parameters is considered. A number of examples are considered to illustrate the approach. The estimated degree of dependence is comparable to other models, but the present approach has the advantage that the interpretation of the random effect is simpler than in the frailty model.     

Butterfly edge effects are predicted by a simple model in a complex landscape

Edge responses have been studied for decades and form a critical component of our understanding of how organisms respond to landscape structure and habitat fragmentation. Until recently, however, the lack of a general, conceptual framework has made it difficult to make sense of the patterns and variability reported in the edge literature. We present a test of an edge effects model which predicts that organisms should avoid edges with less-preferred habitat, show increased abundance near edges with preferred habitat or habitat containing complementary resources, and show no response to edges with similar-quality habitat that offers only supplementary resources. We tested the predictions of this model against observations of the edge responses of 15 butterfly species at 12 different edge types within a complex, desert riparian landscape. Observations matched model predictions more than would be expected by chance for the 211 species/edge combinations tested over 3 years of study. In cases where positive or negative edge responses were predicted, observed responses matched those predictions 70% of the time. While the model tends to underpredict neutral results, it was rare that an observed edge response contradicted that predicted by the model. This study also supported the two primary ecological mechanisms underlying the model, although not equally. We detected a positive relationship between habitat preferences and the slope of the observed edge response, suggesting that this basic life history trait underlies edge effects and influences their magnitude. Empirical evidence also suggested the presence of complementary resources underlies positive edge responses, but only when completely confined to the adjacent habitat. This multi-species test of a general edge effects model at multiple edge types shows that resource-based mechanisms can explain many edge responses and that a modest knowledge of life history attributes and resource availability is sufficient for predicting and understanding many edge responses in complex landscapes. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Modeling multivariate survival data by a semiparametric random effects proportional odds model

In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.     

Interpreting parameters in the logistic regression model with random effects

Logistic regression with random effects is used to study the relationship between explanatory variables and a binary outcome in cases with nonindependent outcomes. In this paper, we examine in detail the interpretation of both fixed effects and random effects parameters. As heterogeneity measures, the random effects parameters included in the model are not easily interpreted. We discuss different alternative measures of heterogeneity and suggest using a median odds ratio measure that is a function of the original random effects parameters. The measure allows a simple interpretation, in terms of well-known odds ratios, that greatly facilitates communication between the data analyst and the subject-matter researcher. Three examples from different subject areas, mainly taken from our own experience, serve to motivate and illustrate different aspects of parameter interpretation in these models.     

A simple model describing the elastic properties of human umbilical arterial smooth muscle

Elastic properties of cylindrical segments of 71 normal double and 4 single human umbilical arteries were studied. This specimen is rich in vascular smooth muscle in comparison with other great arteries. Outer diameter versus intraluminal pressure characteristic curves were taken with decreasing pressures in vitro in different contraction states. Tangential force and circumferential incremental elastic modulus were computed. A sum of 222 curves was analysed. The investigations showed that if we take tangential force and outer radius values measured at the same pressure levels but in different contraction states, then a similar proportional change in tangential force will induce a similar proportional passive change in the outer radius, to some extent independently of the degree of active tangential shortening of the segment. For example to induce a 10% passive decrease of the outer radius from values measured at 100 mm Hg intraluminal pressure, tangential force had to be decreased by 76.7 +/- 9.9% in single relaxed arteries, and by 79.6 +/- 0.8% in normal double relaxed segments. These values corresponded to intraluminal pressure levels of 26.4 +/- 4.9 mm Hg and 23.1 +/- 0.9 mm Hg, respectively. In 30% active spontaneous shortening to reach the same 10% passive decrease in outer radius from the value measured at 100 mm Hg, tangential force had to be decreased by 75.2 +/- 1.9% which corresponded to 29.6 +/- 20 mm Hg. The same values in 5-HT induced contraction, 30% active shortening were 76.7 +/- 2.0% and 28.4 +/- 2.6 mm Hg, respectively. In addition to the similarity of relative changes in tangential force, the pressure levels were to some extent also similar. These data suggest that elastic elements in the human umbilical arterial smooth muscle may be organized in such a way as to ensure similar prestretch of similar elastic elements at similar pressures independently of the degree of active shortening of the circumference.     

Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.     

Determination of the elastic constants of collagen by Brillouin light scattering

The high-frequency elastic properties of rat-tail tendon collagen have been investigated by means of Brillouin (inelastic) light scattering. Longitudinally and transversely polarised elastic waves of frequency about 10¹⁰ Hz have been observed propagating at various angles to the fibre axis of stretched, partially dried tendon. Assuming that the elastic properties of tendon are transversely isotropic, these measurements enable the five elastic constants for such a system to be determined. In particular the ratio of the Young's modulus for strain parallel to the axis to that for strain perpendicular to the axis ($\text{E}{}_{\mathrm{\parallel }}\text{E}{}_{\mathrm{\perp }}$) is found to be 1.43 and the ratio of the shear modulus to E_∥ is 0.28. In wet collagen only the longitudinal branch has been observed and in this case the ratio $\text{E}{}_{\mathrm{\parallel }}\text{E}{}_{\mathrm{\perp }}$ increases to 1.82. The absolute value for E_∥ in dry collagen is 11.9 GN m^?2 reducing to 5.1 GN m^?2 in wet collagen. An interpretation of these results in terms of the expected vibrations of the collagen molecular assembly is given. Possible applications to the determination of the mechanical properties of collagen composite materials such as bone are discussed as well as some measurements on silk and α- and β-keratins, which are fibrous proteins of different molecular conformation to collagen.     

Measurement of particle sizes by elastic and quasi-elastic light scattering.

A method of measuring an average particle radius in a highly polydisperse dispersion using the wavelength dependence of turbidity is described. For particles which are no larger than 0.3 of the wavelength of light used, a polynomial representation of the scattering cross-section can be used. For larger particles, more extensive numerical calculations are required. The use of the method is illustrated by determining the average particle radius of casein micelles by both elastic and quasi-elastic light scattering techniques. A polydisperse homogeneous sphere model is found to be a reasonably accurate representation of casein micelles. Several modifications of the model which would improve the agreement between the two techniques are mentioned briefly.     

Interpretation of the X-ray scattering profiles of chromatin at various NaCl concentrations by a simple chain model.

In order to interpret the change in the X-ray scattering profiles from rat thymus chromatin, extensive model calculation was carried out. Chromatin is modelled as a string of subunits (nucleosomes) in which disorder is introduced into the positions of adjacent subunits. Disposition parameters characterizing the arrangement of subunits were estimated for various states of chromatin, so that the main feature of the scattering profiles is described. The result indicated that the structure of chromatin changes, as the NaCl concentration increases, from the extended "beads-on-a string" structure to the condensed helical structure. The latter has an outer diameter of about 26 nm with 3-4 nucleosomes per turn. In the intermediate state, it has a loose helical structure. The estimation of disorder suggested that the arrangement of subunits is appreciably disordered even in the condensed helical filament at 50 mM NaCl. Our model for chromatin condensation seems to support models of the "crossed linker" type.     

Effective protein folding in simple random search

Here I show the following facts using a simple random search model without including any sophisticated energy term. As the size of elements exponentially affects the efficiency of folding, it can be remarkably enhanced by dividing the elements into small blocks. As the folding of the blocks is completely independent, the total folding time can be reduced to the folding time of the single hardest block. This result gives the simplest and most straightforward answer to the Levinthal paradox.     

A simple method to test condoms for penetration by viruses.

A method by which virus penetration through condoms can be tested with simple, inexpensive equipment is described. The method uses chi X174 bacteriophage as the challenge virus and physiologically relevant pressure. Penetration by 0.1 microliters (or less) of challenge suspension can be readily detected. As examples, latex and natural-membrane condoms were examined.