Lindi M. Wahl

Perspectives on the basic reproductive ratio

The basic reproductive ratio, R0, is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R0 often serves as a threshold parameter that predicts whether an infection will spread. Related parameters which share this threshold behaviour, however, may or may not give the true value of R0. In this paper we give a brief overview of common methods of formulating R0 and surrogate threshold parameters from deterministic, non-structured models. We also review common means of estimating R0 from epidemiological data. Finally, we survey the recent use of R0 in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus.

Mutual information without the influence of phylogeny or entropy dramatically improves residue contact prediction

MOTIVATION Compensating alterations during the evolution of protein families give rise to coevolving positions that contain important structural and functional information. However, a high background composed of random noise and phylogenetic components interferes with the identification of coevolving positions. RESULTS We have developed a rapid, simple and general method based on information theory that accurately estimates the level of background mutual information for each pair of positions in a given protein family. Removal of this background results in a metric, MIp, that correctly identifies substantially more coevolving positions in protein families than any existing method. A significant fraction of these positions coevolve strongly with one or only a few positions. The vast majority of such position pairs are in contact in representative structures. The identification of strongly coevolving position pairs can be used to impose significant structural limitations and should be an important additional constraint for ab initio protein folding. AVAILABILITY Alignments and program files can be found in the Supplementary Information.

Using information theory to search for co-evolving residues in proteins

MOTIVATION Some functionally important protein residues are easily detected since they correspond to conserved columns in a multiple sequence alignment (MSA). However important residues may also mutate, with compensatory mutations occurring elsewhere in the protein, which serve to preserve or restore functionality. It is difficult to distinguish these co-evolving sites from other non-conserved sites. RESULTS We used Mutual Information (MI) to identify co-evolving positions. Using in silico evolved MSAs, we examined the effects of the number of sequences, the size of amino acid alphabet and the mutation rate on two sources of background MI: finite sample size effects and phylogenetic influence. We then assessed the performance of various normalizations of MI in enhancing detection of co-evolving positions and found that normalization by the pair entropy was optimal. Real protein alignments were analyzed and co-evolving isolated pairs were often found to be in contact with each other. AVAILABILITY All data and program files can be found at http://www.biochem.uwo.ca/cgi-bin/CDD/index.cgi

Reproducibility of Standardized Uptake Value Measurements Determined by 18F-FDG PET in Malignant Tumors

18F-FDG PET is increasingly being used to monitor the early response of malignant tumors to chemotherapy. Understanding the reproducibility of standardized uptake values (SUVs) is an important prerequisite in estimating what constitutes a significant change. Methods: Twenty-six patients were studied on 2 separate occasions (mean interval ± SD, 3 ± 2 d; range, 1–5 d). A static PET/CT scan was performed 94 ± 9 min after the intravenous injection of 383 ± 15 MBq of 18F-FDG. Mean and maximum SUVs (SUVmean and SUVmax, respectively) were determined for regions of interest drawn around the tumor on the first study and for the same regions of interest transferred to the second study. Results: SUVmean in tumors ranged from 1.49 to 17.48 and SUVmax ranged from 2.99 to 24.09. The correlation between SUVmean determined on the 2 separate visits was 0.99; the mean difference between the 2 measurements was 0.01 ± 0.27 SUV. The 95% confidence limits for the measurements were ±0.53. For SUVmax, the mean difference was −0.05 ± 1.14 SUV. Conclusion: Our study demonstrates that repeated measurements of SUVmean performed a few days apart are highly reproducible. A decrease of 0.5 in the SUV is statistically significant.

Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling

Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorders such as osteoporosis, osteoarthritis, and Pagets disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. The model predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Pagets disease. Parametric analysis demonstrated that the mode of dynamic behavior in the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor beta. Moreover, simulations demonstrated that nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process of remodeling in normal bone and in pathological conditions such as osteoporosis and Pagets disease.

Adherence and drug resistance: predictions for therapy outcome

We combine standard pharmacokinetics with an established model of viral replication to predict the outcome of therapy as a function of adherence to the drug regimen. We consider two types of treatment failure: failure to eliminate the wild–type virus, and the emergence of drug–resistant virus. Specifically, we determine the conditions under which resistance dominates as a result of imperfect adherence. We derive this result for both single– and triple–drug therapies, with attention to conditions which favour the emergence of viral strains that are resistant to one or more drugs in a cocktail. Our analysis provides quantitative estimates of the degree of adherence necessary to prevent resistance.We derive results specific to the treatment of human immunodeficiency virus infection, but emphasize that our method is applicable to a range of viral or other infections treated by chemotherapy.

Time Course of Early Response to Chemotherapy in Non–Small Cell Lung Cancer Patients with 18F-FDG PET/CT

PET and 18F-FDG have the potential to follow the early metabolic response to chemotherapy in patients with non–small cell lung cancer and to predict success or failure of the therapy. Methods: We studied 16 patients with non–small cell lung cancer as they followed 2 courses of docetaxel and carboplatin. Each patient was studied weekly for 7 wk, and tissue activity was assessed by the amount of radioactivity retained 90 min after the intravenous injection of 18F-FDG. In a prospective analysis, the linear least-squares method was used to evaluate the time course of metabolic activity in tumor and liver, bone marrow, and unaffected lung tissues; a metabolic response was defined as a response in which the slope of the regression was negative and significantly different from zero. Our hypothesis was that patients who exhibited a tumor metabolic response would survive longer than those who did not. In a retrospective examination of our data, we grouped our patients into those who survived <6 mo and those who survived longer and calculated the difference in the standardized uptake value (SUV) between day 7 and subsequent time points to determine the most appropriate timing of 2 PET studies in predicting response to therapy. Results: Fifteen of 16 patients completed the study. In the prospective study, 8 patients were classified as nonresponders as the slope of the regression of tumor SUV versus time was not different from zero; they all died within 35 wk of the end of their study. Seven patients were classified as responders; 5 survived and 2 died, one at 25 wk and the other at 76 wk. In the retrospective study, a decrease of 0.5 SUV between studies performed at 1 and 3 wk after the initiation of chemotherapy was predictive of those patients who survived >6 mo and in whom chemotherapy was presumably successful. Conclusion: Patients with non–small cell lung cancer who had a positive outcome, as exhibited by prolonged survival, were those who showed a tumor metabolic response assessed using weekly 18F-FDG PET studies. 18F-FDG PET studies performed at 1 and 3 wk after the initiation of chemotherapy allowed prediction of the response to therapy.

The fixation probability of beneficial mutations

The fixation probability, the probability that the frequency of a particular allele in a population will ultimately reach unity, is one of the cornerstones of population genetics. In this review, we give a brief historical overview of mathematical approaches used to estimate the fixation probability of beneficial alleles. We then focus on more recent work that has relaxed some of the key assumptions in these early papers, providing estimates that have wider applicability to both natural and laboratory settings. In the final section, we address the possibility of future work that might bridge the gap between theoretical results to date and results that might realistically be applied to the experimental evolution of microbial populations. Our aim is to highlight the concrete, testable predictions that have arisen from the theoretical literature, with the intention of further motivating the invaluable interplay between theory and experiment.

THE PROBABILITY THAT BENEFICIAL MUTATIONS ARE LOST IN POPULATIONS WITH PERIODIC BOTTLENECKS

Abstract Population bottlenecks affect the dynamics of evolution, increasing the probability that beneficial mutations will be lost. Recent protocols for the experimental study of evolution involve repeated bottlenecks–when fresh media are inoculated during serial transfer or when chemostat tubes are changed. Unlike population reductions caused by stochastic environmental factors, these bottlenecks occur at known, regular intervals and with a fixed dilution ratio. We derive the ultimate probability of extinction for a beneficial mutation in a periodically bottlenecked population, using both discrete and continuous approaches. We show that both approaches yield the same approximation for extinction probability. From this, we derive an approximate expression for an effective population size.

The Distribution and Kinetics of [18F]6-Fluoro-3-O-methyl-L-dopa in the Human Brain

The analysis of positron tomographic studies of 3,4-dihydroxyphenylethylamine (dopamine) metabolism in which [18F]6-fluoro-l-3,4-dihydroxyphenylalanine (F-dopa) is used as a tracer is confounded by the presence of [18F]6-fluoro-3-O-methyl-l-3,4-dihydroxyphenylalanine (OMFD). This labeled molecule, formed by the action of peripheral cathechol-O-methyltransferase on F-dopa, crosses the blood–brain barrier and contributes to the radioactivity measured by the tomograph. Corrections for this radioactivity in the brain have been proposed. They rely upon the assumption that regional variations in the handling of this molecule by the brain are negligible. Although this assumption is pivotal for the proper quantification of dopamine metabolism using F-dopa, the distribution and kinetics of OMFD have never been studied in humans. We present results in humans that show that there is little selective regional 18F accumulation in the brain, that the distribution volume of OMFD is close to unity, and that a single, reversible compartment is adequate to model the measured time course of radioactivity after an OMFD injection. Analysis of plasma samples for labeled metabolites showed that more than 95% of the radioactivity was associated with OMFD at all times. Our results for OMFD kinetics are in accord with published results obtained in nonhuman primates and for the bidirectional transport of large neutral amino acids across the blood-brain barrier measured using a synthetic amino acid. However, our results also indicate that there are small but significant differences in OMFD kinetics in different parts of the brain that may prevent inferences about the handling of OMFD in one part of the brain from being extended to other parts of the brain.