Quantifying Adaptive Evolution in the Drosophila Immune System

It is estimated that a large proportion of amino acid substitutions in Drosophila have been fixed by natural selection, and as organisms are faced with an ever-changing array of pathogens and parasites to which they must adapt, we have investigated the role of parasite-mediated selection as a likely cause. To quantify the effect, and to identify which genes and pathways are most likely to be involved in the host–parasite arms race, we have re-sequenced population samples of 136 immunity and 287 position-matched non-immunity genes in two species of Drosophila. Using these data, and a new extension of the McDonald-Kreitman approach, we estimate that natural selection fixes advantageous amino acid changes in immunity genes at nearly double the rate of other genes. We find the rate of adaptive evolution in immunity genes is also more variable than other genes, with a small subset of immune genes evolving under intense selection. These genes, which are likely to represent hotspots of host–parasite coevolution, tend to share similar functions or belong to the same pathways, such as the antiviral RNAi pathway and the IMD signalling pathway. These patterns appear to be general features of immune system evolution in both species, as rates of adaptive evolution are correlated between the D. melanogaster and D. simulans lineages. In summary, our data provide quantitative estimates of the elevated rate of adaptive evolution in immune system genes relative to the rest of the genome, and they suggest that adaptation to parasites is an important force driving molecular evolution.     

Quantifying the Early Immune Response and Adaptive Immune Response Kinetics in Mice Infected with Influenza A Virus

Seasonal and pandemic influenza A virus (IAV) continues to be a public health threat. However, we lack a detailed and quantitative understanding of the immune response kinetics to IAV infection and which biological parameters most strongly influence infection outcomes. To address these issues, we use modeling approaches combined with experimental data to quantitatively investigate the innate and adaptive immune responses to primary IAV infection. Mathematical models were developed to describe the dynamic interactions between target (epithelial) cells, influenza virus, cytotoxic T lymphocytes (CTLs), and virus-specific IgG and IgM. IAV and immune kinetic parameters were estimated by fitting models to a large data set obtained from primary H3N2 IAV infection of 340 mice. Prior to a detectable virus-specific immune response (before day 5), the estimated half-life of infected epithelial cells is ∼1.2 days, and the half-life of free infectious IAV is ∼4 h. During the adaptive immune response (after day 5), the average half-life of infected epithelial cells is ∼0.5 days, and the average half-life of free infectious virus is ∼1.8 min. During the adaptive phase, model fitting confirms that CD8⁺ CTLs are crucial for limiting infected cells, while virus-specific IgM regulates free IAV levels. This may imply that CD4 T cells and class-switched IgG antibodies are more relevant for generating IAV-specific memory and preventing future infection via a more rapid secondary immune response. Also, simulation studies were performed to understand the relative contributions of biological parameters to IAV clearance. This study provides a basis to better understand and predict influenza virus immunity.Current strategies for preventing or decreasing the severity of influenza infection focus on increasing virus-neutralizing antibody titers through vaccination, as experience indicates that this is the best way to prevent morbidity and mortality. Influenza A virus (IAV) undergoes mutations of the genes encoding the hemagglutinin (HA) and neuraminidase (NA) proteins that the neutralizing antibodies are directed against. When the variation is low (antigenic drift), prior vaccination often confers substantial heterologous immunity against a new seasonal IAV strain. In contrast, major genetic changes (antigenic shift) can result in pandemic IAV strains, since for novel strains, the humoral immune response is a primary response, and heterologous immunity is lacking. The emergence of such pandemic strains and the fact that young children are more vulnerable to influenza diseases highlight the need to better understand which viral and immune parameters determine the outcome of infection with viruses novel to the individual.Conventional experimental methods to measure influenza virus immunity have been limited to animal models and studies of adult human peripheral blood leukocytes. The advantages of using animal models include the ability to intensively sample multiple tissues and to utilize genetic and other interventions, such as blocking or depleting antibodies, to dissect the contribution of individual arms of the immune system. However, it is easy to question the relevance of these experiments to humans because of the many important biological differences between human and murine immune systems (29). In both the animal and human systems, we are limited to measuring those parameters and variables for which assays are available, most of them being ex vivo. Parameters such as cell-to-cell spread of the virus in vivo, trafficking of immune cells to the lung, and the in vivo interactions in an intact immune system are much more difficult or impossible to measure with contemporary techniques, particularly in humans. Computational approaches have the potential to offset some of these limitations and provide additional insight into the kinetics of the IAV infection and the associated immune response.Animal models of influenza virus infection in which different arms of the immune system have been suppressed suggest that some components of the adaptive immune system are required for complete viral clearance, often termed a sterilizing immune response. For example, abrogation of the CD4 T-cell response by cytotoxic antibody therapy or through knockout of major histocompatibility complex (MHC) class II slightly delays viral clearance but has little overall effect on the ability to control the infection (21, 54, 55). Elimination of the CD8 T-cell response typically results in delayed viral clearance (12, 20, 47), although animals with intact CD4 T-cell and B-cell compartments are able to control the infection in the absence of CD8 T cells. Presumably, this occurs through antibody-mediated mechanisms (54). Most animals depleted of both CD8 T cells and B cells are not able to clear the virus, which results in death (14, 32, 53). CD4⁺ T cells certainly contribute to the control of IAV infection, although cytotoxic CD4 T cells are not frequently observed unless cultured in vitro (8, 22, 45). Thus, it is generally accepted that CD8 T cells and/or antibodies are sufficient for timely and complete IAV clearance. Studies that strictly separate the relative roles of CD8 T cells and virus-specific antibodies are less satisfying. Animals depleted of both CD4 and CD8 T cells generally do not control the infection, despite substantial production of anti-IAV IgM antibodies (4, 23, 33, 34). However, adoptive transfer of IAV-specific IgM or IgG antibodies is protective (40, 51), suggesting that the timing and magnitude of the antibody response, i.e., the affinity, avidity, and antibody isotype, are important protective factors.While murine gene knockout or lymphocyte depletion studies are highly informative, they also have a number of limitations. Most importantly, the near-complete ablation of one component of the adaptive immune system often causes profound and unpredictable effects on many other immune components. Although the reported experimental measurements are highly quantitative, they often focus only on a limited number of time points or measurements and do not capture the complexity of the altered, or intact, immune response. In contrast, high-frequency experimental sampling, coupled with mathematical modeling techniques and new statistical approaches, can give insights into the complex biology of IAV infection and test the assumptions inherent in the model. We have learned from other systems, particularly HIV (19, 35, 37, 38, 56), that quantitative analysis of the biology can reveal important factors that are not intuitively obvious. For example, our current estimates for the rates of HIV production and the life span of productively infected cells in vivo were obtained via mathematical modeling (35).Mathematical models have long been used to investigate viral dynamics and immune responses to viral infections, including influenza A virus (3, 5, 7, 15, 16, 31, 36, 48). We recently described a complex differential equation model to simulate and predict the adaptive immune response to IAV infection (24). This model involves 15 equations and 48 parameters, and because of its complexity, many of the parameter values that could not be directly measured were unidentifiable. Thus, it is difficult to estimate all model parameters by fitting experimental data directly to this complex model, although the model can be used to perform simulation predictions (25). This issue can, however, be addressed by reducing the model into smaller submodels with smaller but identifiable sets of parameters, which can be estimated from experimental data. In this paper, we describe such an approach which focuses on IAV infection and the immune response solely within the lung.In the present report, we have fitted a model of primary murine influenza virus infection to data. In naïve subjects, our data suggested that there is no adaptive immune response (e.g., IAV-specific CD8⁺ T cells or antibodies) detectable in the spleen, lymph nodes, or lung until approximately 5 days after infection; therefore, we have divided the analysis into the following two phases: the initial preadaptive (innate) phase and the later adaptive phase. We use direct experimental data from infection of mice with the H3N2 influenza virus A/X31 strain (2, 24) to obtain key kinetic parameters. The model fitting has revealed that the duration of the infection depends on a small set of immune components, and even large fluctuations in other arms of the immune system or IAV behavior have surprisingly little impact on the outcome of the infection.     

Quantifying the Length and Variance of the Eukaryotic Cell Cycle Phases by a Stochastic Model and Dual Nucleoside Pulse Labelling

A fundamental property of cell populations is their growth rate as well as the time needed for cell division and its variance. The eukaryotic cell cycle progresses in an ordered sequence through the phases and and is regulated by environmental cues and by intracellular checkpoints. Reflecting this regulatory complexity, the length of each phase varies considerably in different kinds of cells but also among genetically and morphologically indistinguishable cells. This article addresses the question of how to describe and quantify the mean and variance of the cell cycle phase lengths. A phase-resolved cell cycle model is introduced assuming that phase completion times are distributed as delayed exponential functions, capturing the observations that each realization of a cycle phase is variable in length and requires a minimal time. In this model, the total cell cycle length is distributed as a delayed hypoexponential function that closely reproduces empirical distributions. Analytic solutions are derived for the proportions of cells in each cycle phase in a population growing under balanced growth and under specific non-stationary conditions. These solutions are then adapted to describe conventional cell cycle kinetic assays based on pulse labelling with nucleoside analogs. The model fits well to data obtained with two distinct proliferating cell lines labelled with a single bromodeoxiuridine pulse. However, whereas mean lengths are precisely estimated for all phases, the respective variances remain uncertain. To overcome this limitation, a redesigned experimental protocol is derived and validated in silico. The novelty is the timing of two consecutive pulses with distinct nucleosides that enables accurate and precise estimation of both the mean and the variance of the length of all phases. The proposed methodology to quantify the phase length distributions gives results potentially equivalent to those obtained with modern phase-specific biosensor-based fluorescent imaging.     

Quantifying the extinction vortex

We developed a database of 10 wild vertebrate populations whose declines to extinction were monitored over at least 12 years. We quantitatively characterized the final declines of these well-monitored populations and tested key theoretical predictions about the process of extinction, obtaining two primary results. First, we found evidence of logarithmic scaling of time-to-extinction as a function of population size for each of the 10 populations. Second, two lines of evidence suggested that these extinction-bound populations collectively exhibited dynamics akin to those theoretically proposed to occur in extinction vortices. Specifically, retrospective analyses suggested that a population size of n individuals within a decade of extinction was somehow less valuable to persistence than the same population size was earlier. Likewise, both year-to-year rates of decline and year-to-year variability increased as the time-to-extinction decreased. Together, these results provide key empirical insights into extinction dynamics, an important topic that has received extensive theoretical attention.     

Energy Landscape Reveals That the Budding Yeast Cell Cycle Is a Robust and Adaptive Multi-stage Process

Quantitatively understanding the robustness, adaptivity and efficiency of cell cycle dynamics under the influence of noise is a fundamental but difficult question to answer for most eukaryotic organisms. Using a simplified budding yeast cell cycle model perturbed by intrinsic noise, we systematically explore these issues from an energy landscape point of view by constructing an energy landscape for the considered system based on large deviation theory. Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier, and the landscape along this trajectory exhibits a generally flat shape. We explain the evolution of the system on this flat path by incorporating its non-gradient nature. Furthermore, we illustrate how this global landscape changes in response to external signals, observing a nice transformation of the landscapes as the excitable system approaches a limit cycle system when nutrients are sufficient, as well as the formation of additional energy wells when the DNA replication checkpoint is activated. By taking into account the finite volume effect, we find additional pits along the flat cycle path in the landscape associated with the checkpoint mechanism of the cell cycle. The difference between the landscapes induced by intrinsic and extrinsic noise is also discussed. In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.     

Quantifying the randomness of extinctions

Extinctions occur either randomly or in a more deterministic and predictable manner, with certain characteristics making some species more vulnerable to (local) extinction than others. Although the quantification of extinction randomness would better our understanding of the extinction causes and increase the predictability of future species losses, few quantification methods are currently available. To this purpose, we propose two indices based on a comparison of an a priori (expected) extinction series with an observed one. Whereas the first index requires data on the order of extinctions, the second index is only concerned with which species went extinct and which did not. Using a model for generating extinction data, we tested both indices successfully for accordance with the robustness prerequisites. Index outputs were furthermore unaffected by species richness, apart from decreased variation with rising species numbers. Because of its independence of non-extinct species and its focus on extinction sequences, the first randomness index seems especially useful for use in paleontological and paleo-ecological research. The second index is likely a good tool to study shorter term extinctions, for which the extinction order is often not known and for which the comparison with species that did persist is of greater interest. We use a real dataset to illustrate this. Finally, we discuss how it is possible to expand the use of this index toward identifying previously unknown extinction-promoting species characteristics, and toward a credible assessment of the extinction risk posed by global change.     

Quantifying the geometry of micropipets

Accurate knowledge of the internal diameter (id) of micropipet tips is important, because the ability to study many different aspects of biological membranes is a very sensitive function of tip size. The authors examined two methods used to characterize pipet tips: the digital manometric method (DMM) and bubble number method (BNM). For DMM, the authors compared the ability of Laplace's equation (model I) and a modified form of his equation (model II), which accounts for adhesion between the test fluid and glass Pressure measurements were made with a digital manometer, and ids at the tip were measured using scanning electron microscopy (SEM). The micropipet tips showed a slight asymmetry in id, with a approx 5% difference between maximum and minimum id. On average, model I overestimates the largest id by 2%. Model II overestimates the smaller id by 2%. For micropipet tips ranging from 1.00 to 5.00 μm, the corresponding uncertainties range from 20 to 100 nm. Making the normally hydrophilic glass surface hydrophobic strongly reduced threshold pressures when tested in water, but not 100% methanol. Compared to BNM, DMM was insensitive to changes in atmospheric pressure: BNM can be corrected for changes in atmospheric pressure. Convergence angle(s) can be determined from measurements of the pressure and the axial distance of the meniscus from the tip. The accuracy and precision of digital manometry approaches that of SEM. DMM should be particularly useful in selecting, micropipets for patch clamp studies of small vesicles (<10 μm), and may enable systematic selection of micropipets for many other experiments.     

Quantifying the Shape of Aging

In Biodemography, aging is typically measured and compared based on aging rates. We argue that this approach may be misleading, because it confounds the time aspect with the mere change aspect of aging. To disentangle these aspects, here we utilize a time-standardized framework and, instead of aging rates, suggest the shape of aging as a novel and valuable alternative concept for comparative aging research. The concept of shape captures the direction and degree of change in the force of mortality over age, which—on a demographic level—reflects aging. We 1) provide a list of shape properties that are desirable from a theoretical perspective, 2) suggest several demographically meaningful and non-parametric candidate measures to quantify shape, and 3) evaluate performance of these measures based on the list of properties as well as based on an illustrative analysis of a simple dataset. The shape measures suggested here aim to provide a general means to classify aging patterns independent of any particular mortality model and independent of any species-specific time-scale. Thereby they support systematic comparative aging research across different species or between populations of the same species under different conditions and constitute an extension of the toolbox available to comparative research in Biodemography.