Neutral behavior of shared polymorphism

Several cases have been described in the literature where genetic polymorphism appears to be shared between a pair of species. Here we examine the distribution of times to random loss of shared polymorphism in the context of the neutral Wright–Fisher model. Order statistics are used to obtain the distribution of times to loss of a shared polymorphism based on Kimura’s solution to the diffusion approximation of the Wright–Fisher model. In a single species, the expected absorption time for a neutral allele having an initial allele frequency of ½ is 2.77 N generations. If two species initially share a polymorphism, that shared polymorphism is lost as soon as either of two species undergoes fixation. The loss of a shared polymorphism thus occurs sooner than loss of polymorphism in a single species and has an expected time of 1.7 N generations. Molecular sequences of genes with shared polymorphism may be characterized by the count of the number of sites that segregate in both species for the same nucleotides (or amino acids). The distribution of the expected numbers of these shared polymorphic sites also is obtained. Shared polymorphism appears to be more likely at genetic loci that have an unusually large number of segregating alleles, and the neutral coalescent proves to be very useful in determining the probability of shared allelic lineages expected by chance. These results are related to examples of shared polymorphism in the literature.

Ciliary neurotrophic factor protects striatal output neurons in an animal model of Huntington disease.

Huntington disease is a dominantly inherited, untreatable neurological disorder featuring a progressive loss of striatal output neurons that results in dyskinesia, cognitive decline, and, ultimately, death. Neurotrophic factors have recently been shown to be protective in several animal models of neurodegenerative disease, raising the possibility that such substances might also sustain the survival of compromised striatal output neurons. We determined whether intracerebral administration of brain-derived neurotrophic factor, nerve growth factor, neurotrophin-3, or ciliary neurotrophic factor could protect striatal output neurons in a rodent model of Huntington disease. Whereas treatment with brain-derived neurotrophic factor, nerve growth factor, or neurotrophin-3 provided no protection of striatal output neurons from death induced by intrastriatal injection of quinolinic acid, an N-methyl-D-aspartate glutamate receptor agonist, treatment with ciliary neurotrophic factor afforded marked protection against this neurodegenerative insult.

A model-based approach for assessing in vivo combination therapy interactions

We present an approach for evaluating the efficacy of combination antitumor agent schedules that accounts for order and timing of drug administration. Our model-based approach compares in vivo tumor volume data over a time course and offers a quantitative definition for additivity of drug effects, relative to which synergism and antagonism are interpreted. We begin by fitting data from individual mice receiving at most one drug to a differential equation tumor growth/drug effect model and combine individual parameter estimates to obtain population statistics. Using two null hypotheses: (i) combination therapy is consistent with additivity or (ii) combination therapy is equivalent to treating with the more effective single agent alone, we compute predicted tumor growth trajectories and their distribution for combination treated animals. We illustrate this approach by comparing entire observed and expected tumor volume trajectories for a data set in which HER-2/neu-overexpressing MCF-7 human breast cancer xenografts are treated with a humanized, anti-HER-2 monoclonal antibody (rhuMAb HER-2), doxorubicin, or one of five proposed combination therapy schedules.

The paradox of alloreactivity and self MHC restriction: Quantitative analysis and statistics

Although 1–24% of T cells are alloreactive, i.e., respond to MHC molecules encoded by a foreign haplotype, it is generally believed that T cells cannot recognize foreign peptides binding foreign MHC molecules. We show using a quantitative model that, if T cell selection and activation are affinity-driven, then an alloreactivity of 1–24% is incompatible with the textbook notion that self MHC restriction is absolute. If an average of 1% of clones are alloreactive, then according to our model, at most 20-fold more clones should, on average, be activated by antigens presented on self MHC than by antigens presented on foreign MHC. This ratio is at best 5 if alloreactivity is 5%. These results describe average properties of the murine immune system, but not the outcome of individual experiments. Using supercomputer technology, we simulated 100,000 MHC restriction experiments. Although the average restriction ratio was 7.1, restriction was absolute in 10% of the simulated experiments, greater than 100, although not absolute, in 29%, and below 6 in 24%. This extreme variability agrees with experimental estimates. Our analysis suggests that alloreactivity and average self MHC restriction both cannot be high, but that a low average restriction level is compatible with high levels in a significant number of experiments.

Human Immunodeficiency Virus Reverse Transcriptase and Protease Sequence Database: an expanded data model integrating natural language text and sequence analysis programs

The HIV Reverse Transcriptase and Protease Sequence Database is an on-line relational database that catalogs evolutionary and drug-related sequence variation in the human immunodeficiency virus (HIV) reverse transcriptase (RT) and protease enzymes, the molecular targets of anti-HIV therapy (http://hivdb.stanford.edu). The database contains a compilation of nearly all published HIV RT and protease sequences, including submissions from International Collaboration databases and sequences published in journal articles. Sequences are linked to data about the source of the sequence sample and the antiretroviral drug treatment history of the individual from whom the isolate was obtained. During the past year 3500 sequences have been added and the data model has been expanded to include drug susceptibility data on sequenced isolates. Database content has also been integrated with didactic text and the output of two sequence analysis programs.

A feedback-controlled ensemble model of the stress-responsive hypothalamo-pituitary-adrenal axis

The present work develops and implements a biomathematical statement of how reciprocal connectivity drives stress-adaptive homeostasis in the corticotropic (hypothalamo-pituitary-adrenal) axis. In initial analyses with this interactive construct, we test six specific a priori hypotheses of mechanisms linking circadian (24-h) rhythmicity to pulsatile secretory output. This formulation offers a dynamic framework for later statistical estimation of unobserved in vivo neurohormone secretion and within-axis, dose-responsive interfaces in health and disease. Explication of the core dynamics of the stress-responsive corticotropic axis based on secure physiological precepts should help to unveil new biomedical hypotheses of stressor-specific system failure.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).