From cell death to embryo arrest: Mathematical models of human preimplantation embryo development

Human preimplantation embryos exhibit high levels of apoptotic cells and high rates of developmental arrest during the first week in vitro. The relation between the two is unclear and difficult to determine by conventional experimental approaches, partly because of limited numbers of embryos. We apply a mixture of experiment and mathematical modeling to show that observed levels of cell death can be reconciled with the high levels of embryo arrest seen in the human only if the developmental competence of embryos is already established at the zygote stage, and environmental factors merely modulate this. This suggests that research on improving in vitro fertilization success rates should move from its current concentration on optimizing culture media to focus more on the generation of a healthy zygote and on understanding the mechanisms that cause chromosomal and other abnormalities during early cleavage stages.

Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models.

Most models of tumorigenesis assume that the tumor grows by increased cell division. In these models, it is generally supposed that daughter cells behave as do their parents, and cell numbers have clear potential for exponential growth. We have constructed simple mathematical models of tumorigenesis through failure of programmed cell death (PCD) or differentiation. These models do not assume that descendant cells behave as their parents do. The models predict that exponential growth in cell numbers does sometimes occur, usually when stem cells fail to die or differentiate. At other times, exponential growth does not occur: instead, the number of cells in the population reaches a new, higher equilibrium. This behavior is predicted when fully differentiated cells fail to undergo PCD. When cells of intermediate differentiation fail to die or to differentiate further, the values of growth parameters determine whether growth is exponential or leads to a new equilibrium. The predictions of the model are sensitive to small differences in growth parameters. Failure of PCD and differentiation, leading to a new equilibrium number of cells, may explain many aspects of tumor behavior--for example, early premalignant lesions such as cervical intraepithelial neoplasia, the fact that some tumors very rarely become malignant, the observation of plateaux in the growth of some solid tumors, and, finally, long lag phases of growth until mutations arise that eventually result in exponential growth.

Antibody-mediated inhibition of the growth of larvae from an insect causing cutaneous myiasis in a mammalian host

Many insects feed on blood or tissue from mammalian hosts. One potential strategy for the control of these insects is to vaccinate the host with antigens derived from the insect. The larvae of the fly Lucilia cuprina feed on ovine tissue and tissue fluids causing a cutaneous myiasis associated with considerable host morbidity and mortality. A candidate vaccine antigen, peritrophin 95, was purified from the peritrophic membrane, which lines the gut of these larvae. Serum from sheep vaccinated with peritrophin 95 inhibited growth of first-instar L. cuprina larvae that fed on this serum. Growth inhibition was probably caused by antibody-mediated blockage of the normally semipermeable peritrophic membrane and the subsequent development of an impervious layer of undefined composition on the gut lumen side of the peritrophic membrane that restricted access of nutrients to the larvae. The amino acid sequence of peritrophin 95 was determined by cloning the DNA complementary to its mRNA. The deduced amino acid sequence codes for a secreted protein containing a distinct Cys-rich domain of 317 amino acids followed by a mucin-like domain of 139 amino acids. The Cys-rich domain may be involved in binding chitin. This report describes a novel immunological strategy for the potential control of L. cuprina larvae that may have general application to the control of other insect pests.

Dynamics of maize endosperm development and DNA endoreduplication.

Endosperm development in Zea mays is characterized by a period of intense mitotic activity followed by a period in which mitosis is essentially eliminated and the cell cycle becomes one of alternating S and G phases, leading to endoreduplication of the nuclear DNA. The endosperm represents a significant contribution to the grain yield of maize; thus, methods that facilitate the study of cellular kinetics may be useful in discerning cellular and molecular components of grain yield. Two mathematical models have been developed to describe the kinetics of endosperm growth. The first describes the kinetics of mitosis during endosperm development; the second describes the kinetics of DNA endoreduplication during endosperm development. The mitotic model is a modification of standard growth curves. The endoreduplication model is composed of six differential equations that represent the progression of nuclei from one DNA content to another during the endoreduplication process. Total nuclei number per endosperm and the number of 3C, 6C, 12C, 24C, 48C, and 96C nuclei per endosperm (C is the haploid DNA content per nucleus) for inbred W64A from 8 to 18 days after pollination were determined by flow cytometry. The results indicate that the change in number of nuclei expressed as a function of the number of days after pollination is the same from one yearly crop to another. These data were used in the model to determine the endosperm growth rate, the maximum nuclei number per endosperm, and transition rates from one C value to the next higher C value. The kinetics of endosperm development are reasonably well represented by the models. Thus, the models provide a means to quantify the complex pattern of endosperm development.

Specific therapy regimes could lead to long-term immunological control of HIV

We use mathematical models to study the relationship between HIV and the immune system during the natural course of infection and in the context of different antiviral treatment regimes. The models suggest that an efficient cytotoxic T lymphocyte (CTL) memory response is required to control the virus. We define CTL memory as long-term persistence of CTL precursors in the absence of antigen. Infection and depletion of CD4+ T helper cells interfere with CTL memory generation, resulting in persistent viral replication and disease progression. We find that antiviral drug therapy during primary infection can enable the development of CTL memory. In chronically infected patients, specific treatment schedules, either including deliberate drug holidays or antigenic boosts of the immune system, can lead to a re-establishment of CTL memory. Whether such treatment regimes would lead to long-term immunologic control deserves investigation under carefully controlled conditions.

Models of immune memory: On the role of cross-reactive stimulation, competition, and homeostasis in maintaining immune memory

There has been much debate on the contribution of processes such as the persistence of antigens, cross-reactive stimulation, homeostasis, competition between different lineages of lymphocytes, and the rate of cell turnover on the duration of immune memory and the maintenance of the immune repertoire. We use simple mathematical models to investigate the contributions of these various processes to the longevity of immune memory (defined as the rate of decline of the population of antigen-specific memory cells). The models we develop incorporate a large repertoire of immune cells, each lineage having distinct antigenic specificities, and describe the dynamics of the individual lineages and total population of cells. Our results suggest that, if homeostatic control regulates the total population of memory cells, then, for a wide range of parameters, immune memory will be long-lived in the absence of persistent antigen (T1/2 > 1 year). We also show that the longevity of memory in this situation will be insensitive to the relative rates of cross-reactive stimulation, the rate of turnover of immune cells, and the functional form of the term for the maintenance of homeostasis.

Overexpression of the Bacillus thuringiensis (Bt) Cry2Aa2 protein in chloroplasts confers resistance to plants against susceptible and Bt-resistant insects

Evolving levels of resistance in insects to the bioinsecticide Bacillus thuringiensis (Bt) can be dramatically reduced through the genetic engineering of chloroplasts in plants. When transgenic tobacco leaves expressing Cry2Aa2 protoxin in chloroplasts were fed to susceptible, Cry1A-resistant (20,000- to 40,000-fold) and Cry2Aa2-resistant (330- to 393-fold) tobacco budworm Heliothis virescens, cotton bollworm Helicoverpa zea, and the beet armyworm Spodoptera exigua, 100% mortality was observed against all insect species and strains. Cry2Aa2 was chosen for this study because of its toxicity to many economically important insect pests, relatively low levels of cross-resistance against Cry1A-resistant insects, and its expression as a protoxin instead of a toxin because of its relatively small size (65 kDa). Southern blot analysis confirmed stable integration of cry2Aa2 into all of the chloroplast genomes (5,000–10,000 copies per cell) of transgenic plants. Transformed tobacco leaves expressed Cry2Aa2 protoxin at levels between 2% and 3% of total soluble protein, 20- to 30-fold higher levels than current commercial nuclear transgenic plants. These results suggest that plants expressing high levels of a nonhomologous Bt protein should be able to overcome or at the very least, significantly delay, broad spectrum Bt-resistance development in the field.

Construction of an improved mycoinsecticide overexpressing a toxic protease.

Mycoinsecticides are being used for the control of many insect pests as an environmentally acceptable alternative to chemical insecticides. A key aim of much recent work has been to increase the speed of kill and so improve commercial efficacy of these biocontrol agents. This might he achieved by adding insecticidal genes to the fungus, an approach considered to have enormous potential for the improvement of biological pesticides. We report here the development of a genetically improved entomopathogenic fungus. Additional copies of the gene encoding a regulated cuticle-degrading protease (Pr1) from Metarhizium anisopliae were inserted into the genome of M. anisopliae such that Pr1 was constitutively overproduced in the hemolymph of Manduca sexta, activating the prophenoloxidase system. The combined toxic effects of Pr1 and the reaction products of phenoloxidase caused larvae challenged with the engineered fungus to exhibit a 25% reduction in time of death and reduced food consumption by 40% compared to infections by the wild-type fungus. In addition, infected insects were rapidly melanized, and the resulting cadavers were poor substrates for fungal sporulation. Thus, environmental persistence of the genetically engineered fungus is reduced, thereby providing biological containment.