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.

A theory for controlling cell cycle dynamics using a reversibly binding inhibitor

We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.

Coalescent estimates of HIV-1 generation time in vivo

The generation time of HIV Type 1 (HIV-1) in vivo has previously been estimated using a mathematical model of viral dynamics and was found to be on the order of one to two days per generation. Here, we describe a new method based on coalescence theory that allows the estimate of generation times to be derived by using nucleotide sequence data and a reconstructed genealogy of sequences obtained over time. The method is applied to sequences obtained from a long-term nonprogressing individual at five sampling occasions. The estimate of viral generation time using the coalescent method is 1.2 days per generation and is close to that obtained by mathematical modeling (1.8 days per generation), thus strengthening confidence in estimates of a short viral generation time. Apart from the estimation of relevant parameters relating to viral dynamics, coalescent modeling also allows us to simulate the evolutionary behavior of samples of sequences obtained over time.

From patterns to processes: Phase and density dependencies in the Canadian lynx cycle

Across the boreal forest of North America, lynx populations undergo 10-year cycles. Analysis of 21 time series from 1821 to the present demonstrates that these fluctuations are generated by nonlinear processes with regulatory delays. Trophic interactions between lynx and hares cause delayed density-dependent regulation of lynx population growth. The nonlinearity, in contrast, appears to arise from phase dependencies in hunting success by lynx through the cycle. Using a combined approach of empirical, statistical, and mathematical modeling, we highlight how shifts in trophic interactions between the lynx and the hare generate the nonlinear process primarily by shifting functional response curves during the increase and the decrease phases.

Host-parasite dynamics and outgrowth of virus containing a single K70R amino acid change in reverse transcriptase are responsible for the loss of human immunodeficiency virus type 1 RNA load suppression by zidovudine.

The association between human immunodeficiency virus type I (HIV-1) RNA load changes and the emergence of resistant virus variants was investigated in 24 HIV-1-infected asymptomatic persons during 2 years of treatment with zidovudine by sequentially measuring serum HIV-1 RNA load and the relative amounts of HIV-1 RNA containing mutations at reverse transcriptase (RT) codons 70 (K-->R), 41 (M-->L), and 215 (T-->Y/F). A mean maximum decline in RNA load occurred during the first month, followed by a resurgence between 1 and 3 months, which appeared independent of drug-resistance. Mathematical modeling suggests that this resurgence is caused by host-parasite dynamics, and thus reflects infection of the transiently increased numbers of CD4+ lymphocytes. Between 3 and 6 months of treatment, the RNA load returned to baseline values, which was associated with the emergence of virus containing a single lysine to arginine amino acid change at RT codon 70, only conferring an 8-fold reduction in susceptibility. Despite the relative loss of RNA load suppression, selection toward mutations at RT codons 215 and 41 continued. Identical patterns were observed in the mathematical model. While host-parasite dynamics and outgrowth of low-level resistant virus thus appear responsible for the loss of HIV-1 RNA load suppression, zidovudine continues to select for alternative mutations, conferring increasing levels of resistance.

State of the art in continuous speech recognition.

In the past decade, tremendous advances in the state of the art of automatic speech recognition by machine have taken place. A reduction in the word error rate by more than a factor of 5 and an increase in recognition speeds by several orders of magnitude (brought about by a combination of faster recognition search algorithms and more powerful computers), have combined to make high-accuracy, speaker-independent, continuous speech recognition for large vocabularies possible in real time, on off-the-shelf workstations, without the aid of special hardware. These advances promise to make speech recognition technology readily available to the general public. This paper focuses on the speech recognition advances made through better speech modeling techniques, chiefly through more accurate mathematical modeling of speech sounds.

Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

A numerical strategy for efficient modeling of the equatorial wave guide

Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloud-resolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss–Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloud-resolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.

Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Blood flow and oxygen delivery to human brain during functional activity: Theoretical modeling and experimental data

Coupling of cerebral blood flow (CBF) and cerebral metabolic rate for oxygen (CMRO2) in physiologically activated brain states remains the subject of debates. Recently it was suggested that CBF is tightly coupled to oxidative metabolism in a nonlinear fashion. As part of this hypothesis, mathematical models of oxygen delivery to the brain have been described in which disproportionately large increases in CBF are necessary to sustain even small increases in CMRO2 during activation. We have explored the coupling of CBF and oxygen delivery by using two complementary methods. First, a more complex mathematical model was tested that differs from those recently described in that no assumptions were made regarding tissue oxygen level. Second, [15O] water CBF positron emission tomography (PET) studies in nine healthy subjects were conducted during states of visual activation and hypoxia to examine the relationship of CBF and oxygen delivery. In contrast to previous reports, our model showed adequate tissue levels of oxygen could be maintained without the need for increased CBF or oxygen delivery. Similarly, the PET studies demonstrated that the regional increase in CBF during visual activation was not affected by hypoxia. These findings strongly indicate that the increase in CBF associated with physiological activation is regulated by factors other than local requirements in oxygen.