Protein denaturant binding polynomials

We show how moments of the denaturant binding distribution function can be extracted from experimental data on the denaturation of a protein as a function of the concentration of denaturant and how in turn these moments can be used to construct the denaturant binding distribution function. This approach is similar to our recent work on using the maximum-entropy method to construct ligand-binding distributions from moments obtained from titration curves for nucleic acids and proteins. As an example we take literature data on the denaturation of ferro- and ferricytochrome c by guanidine hydrochloride and from it construct the denaturant binding polynomial and binding distribution function for the unfolded protein.     

Significance testing for QTL mapping by marker difference regression

Marker difference regression, also known as joint mapping or simple marker regression, regresses differences of means for marker classes (’marker differences’) on their expected value, which is a function of the QTL effect and position. The genome is scanned by a likelihood ratio statistic, which conditionally on the QTL position follows a chi-squared distribution. The unconditional distribution is a chi-squared process. This paper proposes a quick method for controlling the genome-wise Type-I error rate. The method is shown by simulation to work satisfactorily for a number of settings.     

Sex chromatin frequency in buccal mucosal tissue: The distribution of single,double and triple sex chromatin bodies

Summary A method of recording sex chromatin scores with a reproducibility of ±3% at two standard deviations is used to investigate the incidence of sex chromatin bodies in normal and polysomic-X individuals. The distribution of sex chromatin bodies in nuclei from both groups may be expressed by a single simple distribution function. The form of the function suggests that the condensation of all X chromosomes (normal and abnormal nuclei) is a random process occurring within a limited period of the cell cycle.Supported by a postgraduate research grant from the Science Research Council. This work forms part of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, University of Sheffield.     

A dosimetry method in the transverse plane of HDR Ir-192 brachytherapy source using gafchromic EBT2 film

Radiochromic film dosimetry is increasingly used in brachytherapy applications for its higher resolution ability as compared to other experimental methods. The present study was aimed to assess the accuracy and suitability of use of the improved radiochromic film model, Gafchromic EBT2, to evaluate the dose distribution in the transverse plane of microselectron HDR ¹⁹²Ir source.A specially designed and locally fabricated Polymethyl methacrylate (PMMA) phantom was used in this work for the experimental measurement of dose distribution around the source in its transverse plane. The AAPM TG-43U1 recommended radial dose function, g (r), and dose rate constant, Λ, for the source were measured using Gafchromic EBT2 film and thermoluminescent dosimeters (TLD). The EBT2 film measured dosimetric quantities were validated against their values obtained from the TLD measurements and previously published values for the same source available in literature.The dose rate constant and radial dose function for microselectron HDR ¹⁹²Ir source obtained from Gafchromic EBT2 film measurements are in agreement with their TLD measured results within 3.9% and 2.8% respectively. They also agree within the accepted range of uncertainty with their experimental and Monte Carlo calculated results reported in literature.This work demonstrates the suitability of using Gafchromic EBT2 film dosimetry in characterization of dose distribution in the transverse plane of HDR Ir-192 source. This is a more efficient method than TLD dosimetry at discrete and distant positions. Relative to TLD dosimetry, it is found to be better reproducible, easy to use and a less expensive method of dosimetry.     

Ultimate Use of Two-Photon Fluorescence Microscopy to Map Orientational Behavior of Fluorophores

The orientational distribution of fluorophores is an important reporter of the structure and function of their molecular environment. Although this distribution affects the fluorescence signal under polarized-light excitation, its retrieval is limited to a small number of parameters. Because of this limitation, the need for a geometrical model (cone, Gaussian, etc.) to effect such retrieval is often invoked. In this work, using a symmetry decomposition of the distribution function of the fluorescent molecules, we show that polarized two-photon fluorescence based on tunable linear dichroism allows for the retrieval of this distribution with reasonable fidelity and without invoking either an a priori knowledge of the system to be investigated or a geometrical model. We establish the optimal level of detail to which any distribution can be retrieved using this technique. As applied to artificial lipid vesicles and cell membranes, the ability of this method to identify and quantify specific structural properties that complement the more traditional molecular-order information is demonstrated. In particular, we analyze situations that give access to the sharpness of the angular constraint, and to the evidence of an isotropic population of fluorophores within the focal volume encompassing the membrane. Moreover, this technique has the potential to address complex situations such as the distribution of a tethered membrane protein label in an ordered environment.     

Ultimate Use of Two-Photon Fluorescence Microscopy to Map Orientational Behavior of Fluorophores

The orientational distribution of fluorophores is an important reporter of the structure and function of their molecular environment. Although this distribution affects the fluorescence signal under polarized-light excitation, its retrieval is limited to a small number of parameters. Because of this limitation, the need for a geometrical model (cone, Gaussian, etc.) to effect such retrieval is often invoked. In this work, using a symmetry decomposition of the distribution function of the fluorescent molecules, we show that polarized two-photon fluorescence based on tunable linear dichroism allows for the retrieval of this distribution with reasonable fidelity and without invoking either an a priori knowledge of the system to be investigated or a geometrical model. We establish the optimal level of detail to which any distribution can be retrieved using this technique. As applied to artificial lipid vesicles and cell membranes, the ability of this method to identify and quantify specific structural properties that complement the more traditional molecular-order information is demonstrated. In particular, we analyze situations that give access to the sharpness of the angular constraint, and to the evidence of an isotropic population of fluorophores within the focal volume encompassing the membrane. Moreover, this technique has the potential to address complex situations such as the distribution of a tethered membrane protein label in an ordered environment.     

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.     

From Carlquist’s ecological wood anatomy to Carlquist’s Law: why comparative anatomy is crucial for functional xylem biology

All students of xylem structure–function relations need to be familiar with the work of Sherwin Carlquist. He studies xylem through the lens of the comparative method, which uses the appearance of similar anatomical features under similar conditions of natural selection to infer function. “Function” in biology implies adaptation; maximally supported adaptation inferences require experimental and comparative xylem scientists to work with one another. Engaging with comparative inferences of xylem function will, more likely sooner rather than later, bring one to the work of Sherwin Carlquist. To mark his 90th birthday, I highlight just a few examples of his extraordinarily perceptive and general comparative insights. One is “Carlquist’s Law”, the pervasive tendency for vessels to be solitary when background cells are conductive. I cover his pioneering of “ecological” wood anatomy, viewing xylem variation as reflecting the effects of selection across climate and habit variation. Another is the embolism vulnerability–conduit diameter relationship, one of the most widely invoked structure–function relationships in xylem biology. I discuss the inferential richness within the notion of Carlquistian paedomorphosis, including detailed functional inferences regarding ray cell orientation. My final example comes from his very recent work offering the first satisfactory hypothesis accounting for the geographical and histological distribution of scalariform perforation plates as an adaptation, including “Carlquist’s Ratchet”, why scalariform plates are adaptive but do not re-evolve once lost. This extraordinarily rich production over six decades is filled with comparative inferences that should keep students of xylem function busy testing for decades to come.     

Computation of the Full Likelihood Function for Estimating Variance at a Quantitative Trait Locus

The proportion of alleles identical by descent (IBD) determines the genetic covariance between relatives, and thus is crucial in estimating genetic variances of quantitative trait loci (QTL). However, IBD proportions at QTL are unobservable and must be inferred from marker information. The conventional method of QTL variance analysis maximizes the likelihood function by replacing the missing IBDs by their conditional expectations (the expectation method), while in fact the full likelihood function should take into account the conditional distribution of IBDs (the distribution method). The distribution method for families of more than two sibs has not been obvious because there are n(n - 1)/2 IBD variables in a family of size n, forming an n X n symmetrical matrix. In this paper, I use four binary variables, where each indicates the event that an allele from one of the four grandparents has passed to the individual. The IBD proportion between any two sibs is then expressed as a function of the indicators. Subsequently, the joint distribution of the IBD matrix is derived from the distribution of the indicator variables. Given the joint distribution of the unknown IBDs, a method to compute the full likelihood function is developed for families of arbitrary sizes.     

Quantitative biomechanical workplace exposure measures: Distribution centers

Physical work exposure characteristics assessed in most previous epidemiologic studies have been described mostly in gross categorical terms (e.g. heavy work, lifting and forceful movements, etc.) and have resulted in relatively moderate associations with low back pain risk. We hypothesized that it was necessary to characterize work demands in a much more quantitative fashion so that the precise biomechanically meaningful measures of exposure were available for risk analysis. In this study, we used sophisticated instrumentation to continuously document 390 physical exposures during lifting (in four types of distribution centers) throughout work. This study profiles these exposures and shows how these exposures vary as a function of the type of distribution center and compares the exposures to (previously documented) manufacturing exposures. Static load and load moment measures were found to greatly under-represent true (dynamic) load and load moment exposures to workers. Lift durations averaged 11–12% of the cycle time in distribution environments. This study indicates that distribution workers are commonly exposed to greater extreme loads and move much more rapidly than manufacturing employees. The information provided here can serve as a basis for low back pain risk assessments.     

Nonparametric estimation of 1-dimensional continuous distribution density functions using the continuous LOLINREG approximation

A nonparametric method for estimation of one-dimensional continuous probability distribution functions is presented. Procedures for calculation of estimation of the unknown distribution function and the distribution density will be discussed in their application. 2 items are what type of weight function may be chosen for the proposed local-linear continuous approximation of the empirical distribution function by the least squares method (LOLINREG), and upon what value of bandwidth- or smoothing parameter one optimally should settle. The latter problem is practically very important with respect to the quality of the estimation results. Examples of simulated measurements which come from a standardized normal distribution as random numbers serve to demonstrate the mode of working, the advantages as well as the limits of the presented continuous LOLINREG-approximation.     

Parameter-free testing of the shape of a probability distribution

The Kolmogorov-Smirnov test determines the consistency of empirical data with a particular probability distribution. Often, parameters in the distribution are unknown, and have to be estimated from the data. In this case, the Kolmogorov-Smirnov test depends on the form of the particular probability distribution under consideration, even when the estimated parameter-values are used within the distribution. In the present work, we address a less specific problem: to determine the consistency of data with a given functional form of a probability distribution (for example the normal distribution), without enquiring into values of unknown parameters in the distribution. For a wide class of distributions, we present a direct method for determining whether empirical data are consistent with a given functional form of the probability distribution. This utilizes a transformation of the data. If the data are from the class of distributions considered here, the transformation leads to an empirical distribution with no unknown parameters, and hence is susceptible to a standard Kolmogorov-Smirnov test. We give some general analytical results for some of the distributions from the class of distributions considered here. The significance level and power of the tests introduced in this work are estimated from simulations. Some biological applications of the method are given.     

Ligand binding distributions in nucleic acids

We illustrate a new method for the determination of the complete binding polynomial for nucleic acids based on experimental titration data with respect to ligand concentration. From the binding polynomial, one can then calculate the distribution function for the number of ligands bound at any ligand concentration. The method is based on the use of a finite set of moments of the binding distribution function, which are obtained from the titration curve. Using the maximum-entropy method, the moments are then used to construct good approximations to the binding distribution function. Given the distribution functions at different ligand concentrations, one can calculate all of the coefficients in the binding polynomial no matter how many binding sites a molecule has. Knowledge of the complete binding polynomial in turn yields the thermodynamics of binding. This method gives all of the information that can be obtained from binding isotherms without the assumption of any specific molecular model for the nature of the binding. Examples are given for the binding of Mn(2+) and Mg(2+) to t-RNA and for the binding of Mg(2+) and I(6) to poly-C using literature data.     

Assigning functional linkages to proteins using phylogenetic profiles and continuous phenotypes

MOTIVATION: A class of non-homology-based methods for protein function prediction relies on the assumption that genes linked to a phenotypic trait are preferentially conserved among organisms that share the trait. These methods typically compare pairs of binary strings, where one string encodes the phylogenetic distribution of a trait and the other of a protein. In this work, we extended the approach to automatically deal with continuous phenotypes. RESULTS: Rather than use a priori rules, which can be very subjective, to construct binary profiles from continuous phenotypes, we propose to systematically explore thresholds which can meaningfully separate the phenotype values. We illustrate our method by analyzing optimal growth temperatures, and demonstrate its usefulness by automatically retrieving genes which have been associated with thermophilic growth. We also apply the general approach, for the first time, to optimal growth pH, and make novel predictions. Finally, we show that our method can also be applied to other properties which may not be classically considered as phenotypes. Specifically, we studied correlations between genome size and the distribution of genes.     

Estimating marginal and incremental effects on health outcomes using flexible link and variance function models

We propose an extension to the estimating equations in generalized linear models to estimate parameters in the link function and variance structure simultaneously with regression coefficients. Rather than focusing on the regression coefficients, the purpose of these models is inference about the mean of the outcome as a function of a set of covariates, and various functionals of the mean function used to measure the effects of the covariates. A commonly used functional in econometrics, referred to as the marginal effect, is the partial derivative of the mean function with respect to any covariate, averaged over the empirical distribution of covariates in the model. We define an analogous parameter for discrete covariates. The proposed estimation method not only helps to identify an appropriate link function and to suggest an underlying distribution for a specific application but also serves as a robust estimator when no specific distribution for the outcome measure can be identified. Using Monte Carlo simulations, we show that the resulting parameter estimators are consistent. The method is illustrated with an analysis of inpatient expenditure data from a study of hospitalists.     

General Time-Reversible Distances with Unequal Rates across Sites: Mixing Γ and Inverse Gaussian Distributions with Invariant Sites

A series of new results useful to the study of DNA sequences using Markov models of substitution are presented with proofs. General time-reversible distances can be extended to accommodate any fixed distribution of rates across sites by replacing the logarithmic function of a matrix with the inverse of a moment generating function. Estimators are presented assuming a gamma distribution, the inverse Gaussian distribution, or a mixture of either of these with invariant sites. Also considered are the different ways invariant sites may be removed and how these differences may affect estimated distances. Through collaboration, we implemented these distances into PAUP* in 1994. The variance of these new distances is approximated via the delta method. It is also shown how to predict the divergence expected for a pair of sequences given a rate matrix and a distribution of rates across sites, allowing iterated ML estimates of distances under any reversible model. A simple test of whether a rate matrix is time reversible is also presented. These new methods are used to estimate the divergence time of humans and chimps from mtDNA sequence data. These analyses support suggestions that the human lineage has an enhanced transition rate relative to other hominoids. These studies also show that transversion distances differ substantially from the overall distances which are dominated by transitions. Transversions alone apparently suggest a very recent divergence time for humans versus chimps and/or a very old (>16 myr) divergence time for humans versus organgutans. This work illustrates graphically ways to interpret the reliability of distance-based transformations, using the corrected transition to transversion ratio returned for pairs of sequences which are successively more diverged.