The extrapolation problem and how population modeling can help

We argue that population modeling can add value to ecological risk assessment by reducing uncertainty when extrapolating from ecotoxicological observations to relevant ecological effects. We review other methods of extrapolation, ranging from application factors to species sensitivity distributions to suborganismal (biomarker and "-omics'') responses to quantitative structure activity relationships and model ecosystems, drawing attention to the limitations of each. We suggest a simple classification of population models and critically examine each model in an extrapolation context. We conclude that population models have the potential for adding value to ecological risk assessment by incorporating better understanding of the links between individual responses and population size and structure and by incorporating greater levels of ecological complexity. A number of issues, however, need to be addressed before such models are likely to become more widely used. In a science context, these involve challenges in parameterization, questions about appropriate levels of complexity, issues concerning how specific or general the models need to be, and the extent to which interactions through competition and trophic relationships can be easily incorporated.

Modeling cumulative evidence for freedom from disease with applications to BSE surveillance trials

This investigation deals with the question of when a particular population can be considered to be disease-free. The motivation is the case of BSE where specific birth cohorts may present distinct disease-free subpopulations. The specific objective is to develop a statistical approach suitable for documenting freedom of disease, in particular, freedom from BSE in birth cohorts. The approach is based upon a geometric waiting time distribution for the occurrence of positive surveillance results and formalizes the relationship between design prevalence, cumulative sample size and statistical power. The simple geometric waiting time model is further modified to account for the diagnostic sensitivity and specificity associated with the detection of disease. This is exemplified for BSE using two different models for the diagnostic sensitivity. The model is furthermore modified in such a way that a set of different values for the design prevalence in the surveillance streams can be accommodated (prevalence heterogeneity) and a general expression for the power function is developed. For illustration, numerical results for BSE suggest that currently (data status September 2004) a birth cohort of Danish cattle born after March 1999 is free from BSE with probability (power) of 0.8746 or 0.8509, depending on the choice of a model for the diagnostic sensitivity.

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favorability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB)versus Thr(HB)-Asn(nHB). Significantly (p < or = 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi1 rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi1 conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi1 and chi2 conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favorability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http://www.rubic.rdg.ac.uk/betapairprefsparallel/).

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favourability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB) versus Thr(HB)-Asn(nHB). Significantly (p <= 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi(1) rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi(1) conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi(1) and chi(2) conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favourability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http:// www.rubic.rdg.ac.uk/betapairprefsparallel/). (c) 2005 Elsevier Ltd. All rights reserved.