A semiparametric estimate of treatment effects with censored data

A semiparametric estimate of an average regression effect with right-censored failure time data has recently been proposed under the Cox-type model where the regression effect beta(t) is allowed to vary with time. In this article, we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in k-sample transformation models when the random error belongs to the G(rho) family of Harrington and Fleming (1982, Biometrika 69, 553-566), the latter being equivalent to the conditional regression effect in a gamma frailty model. The models considered here are suitable for the attenuating hazard ratios that often arise in practice. The results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards. The algebraic relationship provides a simple estimator under the transformation model. We develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods. When there is truncation in the right tail of the failure times, we propose a method of bias correction to improve the coverage properties of the confidence intervals. The estimate, its estimated variance, and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression.     

Estimating the Location and Time Course of Synaptic Input from Multi-Site Potential Recordings

A method is introduced that permits accurate and robust extraction of the location and time course of synaptic conductance from potentials recorded on either side of, and perhaps at some distance from, the synapse in question. It is shown that such data permits one to fully overcome the problems typically associated with lack of spaceclamp. The method does not presume anything about the nature of the time course and yet is applicable to branched, active cells receiving simultaneous input from a number of synapses.     

Evaluation of surface hydrophobicity of immobilized protein with a surface plasmon resonance sensor

Immobilization is widely used to isolate agglutinative and associative proteins with large hydrophobic surfaces. Surface hydrophobicities of immobilized proteins were quantified by measuring the adsorption amounts of Triton X-100 as a hydrophobic probe with a biosensor that utilizes the phenomena of surface plasmon resonance (SPR). We measured SPR signal changes derived from adsorption of Triton X-100 to five kinds proteins and calculated the monolayer adsorption capacity using the Brunauer-Emmett-Teller equation, partly modified with a term for correcting an influence of the net charge of immobilized protein. SPR signal changes obtained by this method correlated with the values of surface hydrophobicities obtained by conventional assay using a hydrophobic probe. Thus this measuring method using an SPR sensor and Triton X-100 is expected to be a tool for quantifying surface hydrophobicities of immobilized proteins.     

Evaluation of viscosities of aqueous two-phase systems containing protein

The dynamic viscosities of aqueous polyethylene glycol, aqueous bovine serum albumin, and polyethylene glycol-bovine serum albumin-water solutions were measured at temperatures of 15, 20, 25, 30 and 35 degree C. To estimate the viscosity values of polyethylene glycol-bovine serum albumin-water solutions, a one parameter Grunberg-like model which was satisfactorily used earlier by the present author for polyethylene glycol-dextran-water solutions was employed. The disposable parameter a for our temperature range was estimated as 3.71. The relative errors varying from 0.29 to 18.98 in absolute value indicates that the Grunberg-like model works perfectly for polymer-protein solutions as well.     

Electrostatic interactions in a peptide--RNA complex

Parallel experimental measurements and theoretical calculations have been used to investigate the energetics of electrostatic interactions in the complex formed between a 22 residue, alpha-helical peptide from the N protein of phage lambda and its cognate 19 nucleotide box B RNA hairpin. Salt-dependent free energies were measured for both peptide folding from coil to helix and peptide binding to RNA, and from these the salt-dependence of binding pre-folded, helical peptide to RNA was determined ( partial differential (DeltaG degrees (dock))/ partial differential log[KCl]=5.98(+/-0.21)kcal/mol). (A folding transition taking place in the RNA hairpin loop was shown to have a negligible dependence on salt concentration.) The non-linear Poisson-Boltzmann equation was used to calculate the same salt dependence of the binding free energy as 5.87(+/-0.22)kcal/mol, in excellent agreement with the measured value. Close agreement between experimental measurements and calculations was also obtained for two variant peptides in which either a basic or acidic residue was replaced with an uncharged residue, and for an RNA variant with a deletion of a single loop nucleotide. The calculations suggest that the strength of electrostatic interactions between a peptide residue and RNA varies considerably with environment, but that all 12 positive and negative N peptide charges contribute significantly to the electrostatic free energy of RNA binding, even at distances up to 11A from backbone phosphate groups. Calculations also show that the net release of ions that accompanies complex formation originates from rearrangements of both peptide and RNA ion atmospheres, and includes accumulation of ions in some regions of the complex as well as displacement of cations and anions from the ion atmospheres of the RNA and peptide, respectively.     

Power-law versus exponential distributions of animal group sizes

There has been some confusion concerning the animal group size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; as power-law decay with exponent 3/2 was proposed in physical analogy to aerosol condensation. Here I show that the animal group-size distribution follows a power-law decay with exponent 1, and is truncated at a cut-off size which is the expected size of the groups an arbitrary individual engages in. An elementary model of animal aggregation based on binary splitting and coalescing on contingent encounter is presented. The model predicted size distribution holds for various data from pelagic fishes and mammalian herbivores in the wild.     

A study of prey-predator relations for mammals

In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore, the predator will be attracted towards that area where prey are less in number. A new physical constant has been introduced into the radiation-type condition on that part of the boundary where interaction between prey and predator takes place. This constant allows us to efficiently model group defence capabilities of the herds and its numerical values have to be determined for different pairs of prey-predator species from field observations. A way of measuring the constants involved in the model is suggested. Numerical results are provided and thoroughly discussed for a habitat of circular shape. The obtained results show that in the region away from the protected area, the density of large-size prey species is higher than that of small-size prey species, a fact that is in accordance with observations.     

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect

We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the speed of migration in the second one can depend on the population density. Mathematically, this model consists of a non-linear partial differential equation of advection-diffusion-reaction type. Using an appropriate change of variables, we obtain an exact solution of the equation describing propagation of travelling population fronts. We show that, depending on parameter values and thus on the relative intensity of density-dependent and density-independent factors, the direction of the propagation can be different thus describing either species invasion or species retreat.     

Effect of channel geometry on the electrostatic potential in acetylcholine channels

We study the effect of channel geometry on the potential barrier encountered by ions as they permeate the acetylcholine receptor channel. Among the various channel geometries which have been used to represent the acetylcholine receptor channel include the cylinder and the toroidal catenary. The main reasons for those choices appear to be the facilitation of separation of the Poisson equation, rather than biological considerations. We consider a novel and realistic acetylcholine channel geometry, and calculate the electrostatic potential profiles within it, and compare our results with results from other channel geometries.     

A mathematical model of quorum sensing in a growing bacterial biofilm

In a process called quorum sensing, bacteria monitor their population density via extracellular signaling molecules and modulate gene expression accordingly. This paper describes a one-dimensional model of a growing Pseudomonas aeruginosa biofilm. Quorum sensing has been included in the model by the addition of equations describing the production, degradation, and diffusion of acyl-homoserine lactones in the biofilm. In order for quorum sensing to initiate near the substratum, in accordance with experimental observations, model results suggest that cells in oxygen-deficient regions of the biofilm must still be synthesizing the signal compound. This result highlights the importance of careful study of the relationship between metabolic activity of the bacterium and signal synthesis. Received 11 March 2002/ Accepted in revised form 01 August 2002