Boron neutron capture therapy of a murine mammary carcinoma using a lipophilic carboranyltetraphenylporphyrin

The first control of a malignant tumor in vivo by porphyrin- mediated boron neutron capture therapy (BNCT) is described. In mice bearing implanted EMT-6 mammary carcinomas, boron uptake using a single injection of either p-boronophenylalanine (BPA) or mercaptoundecahydrododecaborane (BSH) was compared with either a single injection or multiple injections of the carboranylporphyrin CuTCPH. The BSH and BPA doses used were comparable to the highest doses of these compounds previously administered in a single injection to rodents. For BNCT, boron concentrations averaged 85 microg (10)B/g in the tumor and 4 microg (10)B/g in blood 2 days after the last of six injections (over 32 h) that delivered a total of 190 microg CuTCPH/g body weight. During a single 15, 20, 25 or 30 MW-min exposure to the thermalized neutron beam of the Brookhaven Medical Research Reactor, a tumor received average absorbed doses of approximately 39, 52, 66 or 79 Gy, respectively. A long-term (>200 days) tumor control rate of 71% was achieved at a dose of 66 Gy with minimal damage to the leg. Equivalent long-term tumor control by a single exposure to 42 Gy X rays was achieved, but with greater damage to the irradiated leg.     

Multiplex relative risk and estimation of the number of loci underlying an inherited disease

Knowledge of the number of causative loci is necessary to estimate the power of mapping studies of complex diseases. In the present article, we reexamine a theory developed by Risch and its implications for estimating the number L of causative loci affecting a complex inherited disease. We first show that methods based on Risch's analysis can produce estimates of L that are inconsistent with the observed population prevalence of the disease. We demonstrate this point by showing that the maximum-likelihood estimate for L produced by the method of Farrall and Holder for cleft lip/cleft palate data is not consistent with the prevalence under the multiplicative model. We show how to incorporate disease prevalence and develop a maximum-likelihood method for estimating L that uses the entire distribution of numbers of affected individuals in families containing an affected individual. This method avoids the potential inconsistencies of the Risch method and has greater precision. We apply our method to data on cleft lip/cleft palate and schizophrenia.     

The average frequency of private alleles in a partially isolated population

An analytic model is developed to explore the relationship between gene flow, selection, and genetic drift. We assume that a single copy of a mutant allele appears in a finite, partially isolated population and allow for the effects of immigration, genic selection, and mutation on the frequency of the mutant. Our concern is with the distribution of the mutant's frequency before it either is lost from the population or emigrates. Before either of these events, the allele will be a “private allele” and would be found in only one of several populations in a larger collection. Slatkin [(1985) Evolution 39, 53–65] found several simple properties of private alleles in his simulations. We use the method developed by Karlin and Tavaré [(1980) Genet. Res. 37, 33–46; (1981a), Theor. Pop. Biol. 19, 187–214; (1981b) Theor. Pop. Biol. 19, 215–229] for a model similar to ours to obtain a diffusion equation with a “killing term” and obtain the mean and variance of the mutant's frequency and its expected frequency in samples of a specified size. There is only fair agreement between the analytic results from this model and those from Slatkin's (loc. cit.) simulations. The rescaling method used to obtain the results indicates that if emigration is relatively frequent, the distribution of rare alleles is governed largely by the balance between genetic drift and emigration, with selection, mutation, and immigration playing a lesser role.     

ISOLATION BY DISTANCE IN EQUILIBRIUM AND NON-EQUILIBRIUM POPULATIONS

It is shown that for allele frequency data a useful measure of the extent of gene flow between a pair of populations is , which is the estimated level of gene flow in an island model at equilibrium. For DNA sequence data, the same formula can be used if F_ST is replaced by N_ST. In a population with restricted dispersal, analytic theory shows that there is a simple relationship between M? and geographic distance in both equilibrium and non-equilibrium populations and that this relationship is approximately independent of mutation rate when the mutation rate is small. Simulation results show that with reasonable sample sizes, isolation by distance can indeed be detected and that, at least in some cases, non-equilibrium patterns can be distinguished. This approach to analyzing isolation by distance is used for two allozyme data sets, one from gulls and one from pocket gophers.     

Linkage Disequilibrium in Growing and Stable Populations

Nonrandom associations between alleles at different loci can be tested for using Fisher's exact test. Extensive simulations show that there is a substantial probability of obtaining significant nonrandom associations between closely or completely linked polymorphic neutral loci in a population of constant size at equilibrium under mutation and genetic drift. In a rapidly growing population, however, there will be little chance of finding significant nonrandom associations even between completely linked loci if the growth has been sufficiently rapid. This result is illustrated by the analysis of mitochondrial DNA sequence data from humans. In comparing all pairs of informative sites, fewer than 5% of the pairs show significant disequilibrium in Sardinians, which have apparently undergone rapid population growth, while 20% to 30% in !Kung and Pygmies, which apparently have not undergone rapid growth, show significance. The extent of linkage disequilibrium in a population is closely related to the gene genealogies of the loci examined, with ``starlike' genealogies making significant linkage disequilibrium unlikely.     

Gene and Allelic Genealogies at a Gametophytic Self-Incompatibility Locus

The properties of gene and allelic genealogies at a gametophytic self-incompatibility locus in plants have been investigated analytically and checked against extensive numerical simulations. It is found that, as with overdominant loci, there are two genealogical processes with markedly different time scales. First, functionally distinct allelic lines diverge on an extremely long time scale which is inversely related to the mutation rate to new alleles. These alleles show a genealogical structure which is similar, after an appropriate rescaling of time, to that described by the coalescent process for genes at a neutral locus. Second, gene copies sampled within the same functional allelic line show genealogical relationships similar to neutral gene genealogies but on a much shorter time scale, which is on the same order of magnitude as the harmonic mean of the number of gene copies within an allelic line. These results are discussed in relation to data showing trans-specific polymorphisms for alleles at the gametophytic self-incompatibility locus in the Solanaceae. It is shown that population sizes on the order of 4 X 10(5) and a mutation rate per locus per generation as high as 10(-6) could account for estimated allelic divergence times in this family.     

Estimation of Levels of Gene Flow from DNA Sequence Data

We compare the utility of two methods for estimating the average levels of gene flow from DNA sequence data. One method is based on estimating FST from frequencies at polymorphic sites, treating each site as a separate locus. The other method is based on computing the minimum number of migration events consistent with the gene tree inferred from their sequences. We compared the performance of these two methods on data that were generated by a computer simulation program that assumed the infinite sites model of mutation and that assumed an island model of migration. We found that in general when there is no recombination, the cladistic method performed better than FST while the reverse was true for rates of recombination similar to those found in eukaryotic nuclear genes, although FST performed better for all recombination rates for very low levels of migration (Nm = 0.1).     

Finding confidence limits on population growth rates

Recent concern with the survival of endangered species has renewed interest in estimating the growth rates of natural populations. Estimates of population growth rate are subject to uncertainties because of both sampling and experimental errors incurred when estimating rates of fecundity and survivorship. In recent years, a variety of methods have been proposed for placing confidence limits on estimated growth rates. The commonly used analytical approximation assumes that errors are relatively small. There are several computer-intensive methods, including methods based on jackknife and bootsrap procedures, that test the robustness of that approximation. In addition, several computer simulations of hypothetical populations have led to some generalizations about the performance of different methods. In general, it is possible to find confidence intervals for estimates of population growth rates but the appropriate method for doing so depends on the kind of data available and on the magnitude and correlation structure of the errors.     

Boron neutron capture therapy of a murine melanoma with p-boronophenylalanine: dose-response analysis using a morbidity index

Boron-10 concentrations of 20 or 40 micrograms/g were attained in mouse B16 melanomas following one or two intragastric doses of p-boronophenylalanine (750 mg/kg body weight per dose), respectively. Tumor-to-normal-tissue (blood, muscle) boron concentration ratios were 4:1-6:1. The efficacy of boron neutron capture irradiation was monitored using the Wilcoxon two-sample test in conjunction with a system of ranking outcomes of different therapies that compared living mice and mice sacrificed because of excessive tumor growth concomitantly. Median survivals were extended progressively as radiation doses were increased up to 38.7 gray-equivalent (gray X relative biological effectiveness), with one of five and one of six tumors cured in each of the two highest dose groups, respectively. When comparable tumor inhibitory doses of 250-kVp X rays were used to treat these tumors, instead of the transient erythema and edema that resulted from boron neutron capture therapy, there resulted irreversible muscle necrosis in the irradiated zone and atrophy of the foot distal to the irradiated zone. The improvement in treatment outcome with boron neutron capture therapy is attributable to unprecedented tumor-to-normal-tissue radiation dose ratios of approximately 2.8 to 3.6.     

Pairwise Comparisons of Mitochondrial DNA Sequences in Stable and Exponentially Growing Populations

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.