Estimating single-channel kinetic parameters from idealized patch-clamp data containing missed events.

We present here a maximal likelihood algorithm for estimating single-channel kinetic parameters from idealized patch-clamp data. The algorithm takes into account missed events caused by limited time resolution of the recording system. Assuming a fixed dead time, we derive an explicit expression for the corrected transition rate matrix by generalizing the theory of Roux and Sauve (1985, Biophys. J. 48:149-158) to the case of multiple conductance levels. We use a variable metric optimizer with analytical derivatives for rapidly maximizing the likelihood. The algorithm is applicable to data containing substates and multiple identical or nonidentical channels. It allows multiple data sets obtained under different experimental conditions, e.g., concentration, voltage, and force, to be fit simultaneously. It also permits a variety of constraints on rate constants and provides standard errors for all estimates of model parameters. The algorithm has been tested extensively on a variety of kinetic models with both simulated and experimental data. It is very efficient and robust; rate constants for a multistate model can often be extracted in a processing time of approximately 1 min, largely independent of the starting values.     

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. A simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rock lobsters to assess the possible seasonal effect on growth.     

Estimating kinetic constants from single channel data.

The process underlying the opening and closing of ionic channels in biological or artificial lipid membranes can be modeled kinetically as a time-homogeneous Markov chain. The elements of the chain are kinetic states that can be either open or closed. A maximum likelihood procedure is described for estimating the transition rates between these states from single channel data. The method has been implemented for linear kinetic schemes of fewer than six states, and is suitable for nonstationary data in which one or more independent channels are functioning simultaneously. It also provides standard errors for all estimates of rate constants and permits testing of smoothly parameterized subhypotheses of a general model. We have illustrated our approach by analysis of single channel data simulated on a computer and have described a procedure for analysis of experimental data.     

Estimating transfer parameters in the absence of data

The calculation of transfer of radionuclides from the abiotic to the biotic environment is a well-established practice in radiological assessments. Concentration ratios provide simple means to estimate radionuclide activity in biota, from measured (or estimated) radionuclide concentrations in either a food source or an abiotic component such as soil or water. They are typically reported by element, and data compilations may include information such as soil type (e.g., sand, loam, clay) and species. The data may be for multiple species at a single location, single species at multiple locations, or represent compilations from multiple sources. Recently published guidance suggests that estimates are best made using data from the same ecosystem. This paper examines this recent guidance, in the context of using measured data from within a single ecosystem and comparing results to more generic values. Results suggest that generic values may be an adequate substitute for site-specific information. It illustrates how ionic potential may be used as an alternative to group chemical properties in estimating transfer factors. Lastly, limited evidence is found to support the concept of allometric scaling functions for elemental concentrations in plants.     

Estimating quantitative genetic parameters using sibships reconstructed from marker data

Previous techniques for estimating quantitative genetic parameters, such as heritability in populations where exact relationships are unknown but are instead inferred from marker genotypes, have used data from individuals on a pairwise level only. At this level, families are weighted according to the number of pairs within which each family appears, hence by size rather than information content, and information from multiple relationships is lost. Estimates of parameters are therefore not the most efficient achievable. Here, Markov chain Monte Carlo techniques have been used to partition the population into complete sibships, including, if known, prior knowledge of the distribution of family sizes. These pedigrees have then been used with restricted maximum likelihood under an animal model to estimate quantitative genetic parameters. Simulations to compare the properties of parameter estimates with those of existing techniques indicate that the use of sibship reconstruction is superior to earlier methods, having lower mean square errors and showing nonsignificant downward bias. In addition, sibship reconstruction allows the estimation of population allele frequencies that account for the relationships within the sample, so prior knowledge of allele frequencies need not be assumed. Extensions to these techniques allow reconstruction of half sibships when some or all of the maternal genotypes are known.     

Estimating negative binomial parameters from occurrence data with detection times

The negative binomial distribution is a common model for the analysis of count data in biology and ecology. In many applications, we may not observe the complete frequency count in a quadrat but only that a species occurred in the quadrat. If only occurrence data are available then the two parameters of the negative binomial distribution, the aggregation index and the mean, are not identifiable. This can be overcome by data augmentation or through modeling the dependence between quadrat occupancies. Here, we propose to record the (first) detection time while collecting occurrence data in a quadrat. We show that under what we call proportionate sampling, where the time to survey a region is proportional to the area of the region, that both negative binomial parameters are estimable. When the mean parameter is larger than two, our proposed approach is more efficient than the data augmentation method developed by Solow and Smith ( 2010 , Am. Nat. 176 , 96–98), and in general is cheaper to conduct. We also investigate the effect of misidentification when collecting negative binomially distributed data, and conclude that, in general, the effect can be simply adjusted for provided that the mean and variance of misidentification probabilities are known. The results are demonstrated in a simulation study and illustrated in several real examples.     

Comparison of three kinetic models of HIV-1 infection: implications for optimization of treatment

Clinical markers in the peripheral blood guide the treatment of human immunodeficiency virus type 1 (HIV-1). Likewise, many of the theoretical models developed to simulate infection only incorporate variables in the blood. To test the suitability of blood-only models, three distinct models of HIV infection kinetics are compared: "full model" including latently and actively infected cells and virus in the peripheral blood and lymphoid tissue (LT); "reduced model", including peripheral blood and LT without latent cells; and "blood model" including only actively infected cells and virus in the peripheral blood. Using the same parameter values for all three, qualitative differences are demonstrated between the blood model and its more inclusive counterparts. Additionally, optimization studies show that the reduced and blood models generate progressively lower optimal treatment levels relative to the full model when constant-level treatment is considered. These findings indicate that including the lymphoid tissue and latently infected cells into kinetic models may lead to differing conclusions with regard to optimal treatment and could be useful in guiding therapy even when plasma viral levels are below detectable limits.     

Estimating the distribution of selection coefficients from phylogenetic data using sitewise mutation-selection models

Estimation of the distribution of selection coefficients of mutations is a long-standing issue in molecular evolution. In addition to population-based methods, the distribution can be estimated from DNA sequence data by phylogenetic-based models. Previous models have generally found unimodal distributions where the probability mass is concentrated between mildly deleterious and nearly neutral mutations. Here we use a sitewise mutation-selection phylogenetic model to estimate the distribution of selection coefficients among novel and fixed mutations (substitutions) in a data set of 244 mammalian mitochondrial genomes and a set of 401 PB2 proteins from influenza. We find a bimodal distribution of selection coefficients for novel mutations in both the mitochondrial data set and for the influenza protein evolving in its natural reservoir, birds. Most of the mutations are strongly deleterious with the rest of the probability mass concentrated around mildly deleterious to neutral mutations. The distribution of the coefficients among substitutions is unimodal and symmetrical around nearly neutral substitutions for both data sets at adaptive equilibrium. About 0.5% of the nonsynonymous mutations and 14% of the nonsynonymous substitutions in the mitochondrial proteins are advantageous, with 0.5% and 24% observed for the influenza protein. Following a host shift of influenza from birds to humans, however, we find among novel mutations in PB2 a trimodal distribution with a small mode of advantageous mutations.     

Estimating recombinational parameters in Streptococcus pneumoniae from multilocus sequence typing data

Multilocus sequence typing (MLST) is a highly discriminatory molecular typing method that defines isolates of bacterial pathogens using the sequences of approximately 450-bp internal fragments of seven housekeeping genes. This technique has been applied to 575 isolates of Streptococcus pneumoniae and identifies a number of discrete clonal complexes. These clonal complexes are typically represented by a single group of isolates sharing identical alleles at all seven loci, plus single-locus variants that differ from this group at only one out of the seven loci. As MLST is highly discriminatory, the members of each clonal complex can be assumed to have a recent common ancestor, and the molecular events that give rise to the single-locus variants can be used to estimate the relative contributions of recombination and mutation to clonal divergence. By comparing the sequences of the variant alleles within each clonal complex with the allele typically found within that clonal complex, we estimate that recombination has generated new alleles at a frequency approximately 10-fold higher than mutation, and that a single nucleotide site is approximately 50 times more likely to change through recombination than mutation. We also demonstrate how to estimate the average length of recombinational replacements from MLST data.     

Estimating vaccine effects on transmission of infection from household outbreak data

This article is concerned with a method for making inferences about various measures of vaccine efficacy. These measures describe reductions in susceptibility and in the potential to transmit infection. The method uses data on household outbreaks; it is based on a model that allows for transmission of infection both from within a household and from the outside. The use of household data is motivated by the hope that these are informative about vaccine-induced reduction of the potential to transmit infection, as household outbreaks contain some information about the possible source of infection. For illustration, the method is applied to observed data on household outbreaks of smallpox. These data are of the form needed and the number of households is of a size that can be managed in a vaccine trial. It is found that vaccine effects, such as the mean reduction in susceptibility and the mean reduction in the potential to infect others, per infectious contact, can be estimated with precision. However, a more specific parameter reflecting the reduction in infectivity for individuals partially responding to vaccination is not estimated well in the application. An evaluation of the method using artificial data shows that this parameter can be estimated with greater precision when we have outbreak data on a large number of small households.     

Estimating trees from filtered data: Identifiability of models for morphological phylogenetics

As an alternative to parsimony analyses, stochastic models have been proposed ( [Lewis, 2001] and [Nylander et al., 2004]) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A key feature of these models is that they account for ascertainment bias, in that only varying, or parsimony-informative characters are observed. However, statistical consistency of such model-based inference requires that the model parameters be identifiable from the joint distribution they entail, and this issue has not been addressed.Here we prove that parameters for several such models, with finite state spaces of arbitrary size, are identifiable, provided the tree has at least eight leaves. If the tree topology is already known, then seven leaves suffice for identifiability of the numerical parameters. The method of proof involves first inferring a full distribution of both parsimony-informative and non-informative pattern joint probabilities from the parsimony-informative ones, using phylogenetic invariants. The failure of identifiability of the tree parameter for four-taxon trees is also investigated.     

Estimating the size of the HIV epidemic by using mortality data

Evidence that more people are dying as a result of HIV infection than is reflected by the number of deaths among reported cases meeting the WHO definition of AIDS is derived from mortality data. Ninety-five causes of death likely to be associated with HIV infection were selected. Standardized mortality ratios due to these causes increased for single men aged 15-54 years from 100 in 1984 to 118 in 1987. The age, sex, marital status, temporal and geographic distribution of these excess deaths suggest that they are HIV-associated. It is estimated that 58% of excess deaths due to HIV-related causes were among cases reported to the CDSC AIDS Surveillance Programme in 1987. Some of these deaths may have been among HIV-positive people who did not meet the WHO definition at the time of death. There is a need for surveillance to be extended to include HIV-positive people who die before meeting the WHO definition if the full extent of the HIV epidemic is to be identified.