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.

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.

Estimation of evolutionary distances under stationary and nonstationary models of nucleotide substitution

Estimation of evolutionary distances has always been a major issue in the study of molecular evolution because evolutionary distances are required for estimating the rate of evolution in a gene, the divergence dates between genes or organisms, and the relationships among genes or organisms. Other closely related issues are the estimation of the pattern of nucleotide substitution, the estimation of the degree of rate variation among sites in a DNA sequence, and statistical testing of the molecular clock hypothesis. Mathematical treatments of these problems are considerably simplified by the assumption of a stationary process in which the nucleotide compositions of the sequences under study have remained approximately constant over time, and there now exist fairly extensive studies of stationary models of nucleotide substitution, although some problems remain to be solved. Nonstationary models are much more complex, but significant progress has been recently made by the development of the paralinear and LogDet distances. This paper reviews recent studies on the above issues and reports results on correcting the estimation bias of evolutionary distances, the estimation of the pattern of nucleotide substitution, and the estimation of rate variation among the sites in a sequence.

Instability of signaling resolution models of parent–offspring conflict

Recent signaling resolution models of parent–offspring conflict have provided an important framework for theoretical and empirical studies of communication and parental care. According to these models, signaling of need is stabilized by its cost. However, our computer simulations of the evolutionary dynamics of chick begging and parental investment show that in Godfray’s model the signaling equilibrium is evolutionarily unstable: populations that start at the signaling equilibrium quickly depart from it. Furthermore, the signaling and nonsignaling equilibria are linked by a continuum of equilibria where chicks above a certain condition do not signal and we show that, contrary to intuition, fitness increases monotonically as the proportion of young that signal decreases. This result forces us to reconsider much of the current literature on signaling of need and highlights the need to investigate the evolutionary stability of signaling equilibria based on the handicap principle.

The mechanism of cancer-mediated conversion of plasminogen to the angiogenesis inhibitor angiostatin

Angiostatin, a potent naturally occurring inhibitor of angiogenesis and growth of tumor metastases, is generated by cancer-mediated proteolysis of plasminogen. Human prostate carcinoma cells (PC-3) release enzymatic activity that converts plasminogen to angiostatin. We have now identified two components released by PC-3 cells, urokinase (uPA) and free sulfhydryl donors (FSDs), that are sufficient for angiostatin generation. Furthermore, in a defined cell-free system, plasminogen activators [uPA, tissue-type plasminogen activator (tPA), or streptokinase], in combination with one of a series of FSDs (N-acetyl-l-cysteine, d-penicillamine, captopril, l-cysteine, or reduced glutathione] generate angiostatin from plasminogen. An essential role of plasmin catalytic activity for angiostatin generation was identified by using recombinant mutant plasminogens as substrates. The wild-type recombinant plasminogen was converted to angiostatin in the setting of uPA/FSD; however, a plasminogen activation site mutant and a catalytically inactive mutant failed to generate angiostatin. Cell-free derived angiostatin inhibited angiogenesis in vitro and in vivo and suppressed the growth of Lewis lung carcinoma metastases. These findings define a direct mechanism for cancer-cell-mediated angiostatin generation and permit large-scale production of bioactive angiostatin for investigation and potential therapeutic application.

Molecular origin of cancer: Catechol estrogen-3,4-quinones as endogenous tumor initiators

Cancer is a disease that begins with mutation of critical genes: oncogenes and tumor suppressor genes. Our research on carcinogenic aromatic hydrocarbons indicates that depurinating hydrocarbon–DNA adducts generate oncogenic mutations found in mouse skin papillomas (Proc. Natl. Acad. Sci. USA 92:10422, 1995). These mutations arise by mis-replication of unrepaired apurinic sites derived from the loss of depurinating adducts. This relationship led us to postulate that oxidation of the carcinogenic 4-hydroxy catechol estrogens (CE) of estrone (E1) and estradiol (E2) to catechol estrogen-3,4-quinones (CE-3, 4-Q) results in electrophilic intermediates that covalently bind to DNA to form depurinating adducts. The resultant apurinic sites in critical genes can generate mutations that may initiate various human cancers. The noncarcinogenic 2-hydroxy CE are oxidized to CE-2,3-Q and form only stable DNA adducts. As reported here, the CE-3,4-Q were bound to DNA in vitro to form the depurinating adduct 4-OHE1(E2)-1(α,β)-N7Gua at 59–213 μmol/mol DNA–phosphate whereas the level of stable adducts was 0.1 μmol/mol DNA–phosphate. In female Sprague–Dawley rats treated by intramammillary injection of E2-3,4-Q (200 nmol) at four mammary glands, the mammary tissue contained 2.3 μmol 4-OHE2-1(α,β)-N7Gua/molDNA–phosphate. When 4-OHE1(E2) were activated by horseradish peroxidase, lactoperoxidase, or cytochrome P450, 87–440 μmol of 4-OHE1(E2)-1(α, β)-N7Gua was formed. After treatment with 4-OHE2, rat mammary tissue contained 1.4 μmol of adduct/mol DNA–phosphate. In each case, the level of stable adducts was negligible. These results, complemented by other data, strongly support the hypothesis that CE-3,4-Q are endogenous tumor initiators.

A test of alternative models of diversification in tropical rainforests: Ecological gradients vs. rainforest refugia

Comparison of mitochondrial and morphological divergence in eight populations of a widespread leaf-litter skink is used to determine the relative importance of geographic isolation and natural selection in generating phenotypic diversity in the Wet Tropics Rainforest region of Australia. The populations occur in two geographically isolated regions, and within each region, in two different habitats (closed rainforest and tall open forest) that span a well characterized ecological gradient. Morphological differences among ancient geographic isolates (separated for several million years, judging by their mitochondrial DNA sequence divergence) were slight, but morphological and life history differences among habitats were large and occurred despite moderate to high levels of mitochondrial gene flow. A field experiment identified avian predation as one potential agent of natural selection. These results indicate that natural selection operating across ecological gradients can be more important than geographic isolation in similar habitats in generating phenotypic diversity. In addition, our results indicate that selection is sufficiently strong to overcome the homogenizing effects of gene flow, a necessary first step toward speciation in continuously distributed populations. Because ecological gradients may be a source of evolutionary novelty, and perhaps new species, their conservation warrants greater attention. This is particularly true in tropical regions, where most reserves do not include ecological gradients and transitional habitats.

PEG-3, a nontransforming cancer progression gene, is a positive regulator of cancer aggressiveness and angiogenesis

Cancer is a progressive disease culminating in acquisition of metastatic potential by a subset of evolving tumor cells. Generation of an adequate blood supply in tumors by production of new blood vessels, angiogenesis, is a defining element in this process. Although extensively investigated, the precise molecular events underlying tumor development, cancer progression, and angiogenesis remain unclear. Subtraction hybridization identified a genetic element, progression elevated gene-3 (PEG-3), whose expression directly correlates with cancer progression and acquisition of oncogenic potential by transformed rodent cells. We presently demonstrate that forced expression of PEG-3 in tumorigenic rodent cells, and in human cancer cells, increases their oncogenic potential in nude mice as reflected by a shorter tumor latency time and the production of larger tumors with increased vascularization. Moreover, inhibiting endogenous PEG-3 expression in progressed rodent cancer cells by stable expression of an antisense expression vector extinguishes the progressed cancer phenotype. Cancer aggressiveness of PEG-3 expressing rodent cells correlates directly with increased RNA transcription, elevated mRNA levels, and augmented secretion of vascular endothelial growth factor (VEGF). Furthermore, transient ectopic expression of PEG-3 transcriptionally activates VEGF in transformed rodent and human cancer cells. Taken together these data demonstrate that PEG-3 is a positive regulator of cancer aggressiveness, a process regulated by augmented VEGF production. These studies also support an association between expression of a single nontransforming cancer progression-inducing gene, PEG-3, and the processes of cancer aggressiveness and angiogenesis. In these contexts, PEG-3 may represent an important target molecule for developing cancer therapeutics and inhibitors of angiogenesis.

Genetic instability of cancer cells is proportional to their degree of aneuploidy

Genetic and phenotypic instability are hallmarks of cancer cells, but their cause is not clear. The leading hypothesis suggests that a poorly defined gene mutation generates genetic instability and that some of many subsequent mutations then cause cancer. Here we investigate the hypothesis that genetic instability of cancer cells is caused by aneuploidy, an abnormal balance of chromosomes. Because symmetrical segregation of chromosomes depends on exactly two copies of mitosis genes, aneuploidy involving chromosomes with mitosis genes will destabilize the karyotype. The hypothesis predicts that the degree of genetic instability should be proportional to the degree of aneuploidy. Thus it should be difficult, if not impossible, to maintain the particular karyotype of a highly aneuploid cancer cell on clonal propagation. This prediction was confirmed with clonal cultures of chemically transformed, aneuploid Chinese hamster embryo cells. It was found that the higher the ploidy factor of a clone, the more unstable was its karyotype. The ploidy factor is the quotient of the modal chromosome number divided by the normal number of the species. Transformed Chinese hamster embryo cells with a ploidy factor of 1.7 were estimated to change their karyotype at a rate of about 3% per generation, compared with 1.8% for cells with a ploidy factor of 0.95. Because the background noise of karyotyping is relatively high, the cells with low ploidy factor may be more stable than our method suggests. The karyotype instability of human colon cancer cell lines, recently analyzed by Lengnauer et al. [Lengnauer, C., Kinzler, K. W. & Vogelstein, B. (1997) Nature (London) 386, 623–627], also corresponds exactly to their degree of aneuploidy. We conclude that aneuploidy is sufficient to explain genetic instability and the resulting karyotypic and phenotypic heterogeneity of cancer cells, independent of gene mutation. Because aneuploidy has also been proposed to cause cancer, our hypothesis offers a common, unique mechanism of altering and simultaneously destabilizing normal cellular phenotypes.

Polymer Models of Meiotic and Mitotic Chromosomes

Polymers tied together by constraints exhibit an internal pressure; this idea is used to analyze physical properties of the bottle-brush–like chromosomes of meiotic prophase that consist of polymer-like flexible chromatin loops, attached to a central axis. Using a minimal number of experimental parameters, semiquantitative predictions are made for the bending rigidity, radius, and axial tension of such brushes, and the repulsion acting between brushes whose bristles are forced to overlap. The retraction of lampbrush loops when the nascent transcripts are stripped away, the oval shape of diplotene bivalents between chiasmata, and the rigidity of pachytene chromosomes are all manifestations of chromatin pressure. This two-phase (chromatin plus buffer) picture that suffices for meiotic chromosomes has to be supplemented by a third constituent, a chromatin glue to understand mitotic chromosomes, and explain how condensation can drive the resolution of entanglements. This process resembles a thermal annealing in that a parameter (the affinity of the glue for chromatin and/or the affinity of the chromatin for buffer) has to be tuned to achieve optimal results. Mechanical measurements to characterize this protein–chromatin matrix are proposed. Finally, the propensity for even slightly chemically dissimilar polymers to phase separate (cluster like with like) can explain the apparent segregation of the chromatin into A+T- and G+C-rich regions revealed by chromosome banding.

d-β-Hydroxybutyrate protects neurons in models of Alzheimer's and Parkinson's disease

The heroin analogue 1-methyl-4-phenylpyridinium, MPP+, both in vitro and in vivo, produces death of dopaminergic substantia nigral cells by inhibiting the mitochondrial NADH dehydrogenase multienzyme complex, producing a syndrome indistinguishable from Parkinson's disease. Similarly, a fragment of amyloid protein, Aβ1–42, is lethal to hippocampal cells, producing recent memory deficits characteristic of Alzheimer's disease. Here we show that addition of 4 mM d-β-hydroxybutyrate protected cultured mesencephalic neurons from MPP+ toxicity and hippocampal neurons from Aβ1–42 toxicity. Our previous work in heart showed that ketone bodies, normal metabolites, can correct defects in mitochondrial energy generation. The ability of ketone bodies to protect neurons in culture suggests that defects in mitochondrial energy generation contribute to the pathophysiology of both brain diseases. These findings further suggest that ketone bodies may play a therapeutic role in these most common forms of human neurodegeneration.

Stretching lattice models of protein folding

A new class of experiments that probe folding of individual protein domains uses mechanical stretching to cause the transition. We show how stretching forces can be incorporated in lattice models of folding. For fast folding proteins, the analysis suggests a complex relation between the force dependence and the reaction coordinate for folding.