Mathematical modeling of the evolution of resistance and aggressiveness of high-grade serous ovarian cancer from patient CA-125 time series.

A time-series analysis of serum Cancer Antigen 125 (CA-125) levels was performed in 791 patients with high-grade serous ovarian cancer (HGSOC) from the Australian Ovarian Cancer Study to evaluate the development of chemoresistance and response to therapy. To investigate chemoresistance and better predict the treatment effectiveness, we examined two traits: resistance (defined as the rate of CA-125 change when patients were treated with therapy) and aggressiveness (defined as the rate of CA-125 change when patients were not treated). We found that as the number of treatment lines increases, the data-based resistance increases (a decreased rate of CA-125 decay). We use mathematical models of two distinct cancer cell types, treatment-sensitive cells and treatment-resistant cells, to estimate the values and evolution of the two traits in individual patients. By fitting to individual patient HGSOC data, our models successfully capture the dynamics of the CA-125 level. The parameters estimated from the mathematical models show that patients with inferred low growth rates of treatment-sensitive cells and treatment-resistant cells (low model-estimated aggressiveness) and a high death rate of treatment-resistant cells (low model-estimated resistance) have longer survival time after completing their second-line of therapy. These findings show that mathematical models can characterize the degree of resistance and aggressiveness in individual patients, which improves our understanding of chemoresistance development and could predict treatment effectiveness in HGSOC patients.

Strategy maps: Generalised giving-up densities for optimal foraging.

Finding a common currency for benefits and hazards is a major challenge in optimal foraging theory, often requiring complex computational methods. We present a new analytic approach that builds on the Marginal Value Theorem and giving-up densities while incorporating the nonlinear effect of predation risk. We map the space of all possible environments into strategy regions, each corresponding to a discrete optimal strategy. This provides a generalised quantitative measure of the trade-off between foraging rewards and hazards. This extends a classic optimal diet choice rule-of-thumb to incorporate the hazard of waiting for better resources to appear. We compare the dynamics of optimal decision-making for three foraging life-history strategies: One in which fitness accrues instantly, and two with delays before fitness benefit is accrued. Foragers with delayed-benefit strategies are more sensitive to predation risk than resource quality, as they stand to lose more fitness from a predation event than instant-accrual foragers.

Are Staphylococcus aureus Carrier Types Evidence of Population Heterogeneity?

Asymptomatic colonization by Staphylococcus aureus is a precursor for infection, so identifying the mode and source of transmission which leads to colonization could help in targeting interventions. Longitudinal studies have shown that some people are persistently colonized for years, while others seem to carry S. aureus for weeks or less, and conventional wisdom attributes this disparity to an underlying risk factor in the persistently colonized. We analyze published data with mathematical models of acquisition and carriage to compare this hypothesis with alternatives. The null model assumed a homogeneous population and still produced highly variable colonization durations (mean = 101.7 weeks; 5th percentile, 5.2 weeks; 95th percentile, 304.7 weeks). Simulations showed that this inherent variability, combined with censoring in longitudinal cohort studies, is sufficient to produce the appearance of "persistent carriers," "intermittent carriers," and "noncarriers" in data. Our estimates for colonization duration exhibited sensitivity to the assumption that false-positive test results can occur despite being rare, but our model-based approach simultaneously estimates specificity and sensitivity along with epidemiologic parameters. Our results show it is plausible that S. aureus colonizes people indiscriminately, and improved understanding of the types of exposures which result in colonization is essential.

A minimal model of learning: quantifying the cost and benefit of learning in changing environments.

Many organisms have the ability to learn, but the costs and benefits of learning are difficult to quantify. We construct a minimal mathematical model of learning in which a forager attempts to maximize the amount of resources (food) it collects in a changing environment. Our model has two learning parameters: α, corresponding to the duration of the forager's memory, and [Formula: see text], corresponding to how much the forager explores the environment to learn more about it. We analyse the effect of different regimes of environmental change on the optimal memory and exploration parameters [Formula: see text]. By comparing the fitness outcomes from learning foragers to the outcomes from foragers following fixed strategies, we explicitly quantify the fitness benefit (or cost) of learning as a function of environmental change. We find that in many environments, the marginal benefit of learning is surprisingly small. In every environment, it is possible to implement learning in such a way that performance is as bad or worse than following a fixed strategy. In some environments, even the best implementations of our minimal model of learning perform worse than the best fixed strategy. Finally, we find that variance in resource values negatively biases foragers' estimates for those values, potentially explaining experimental results showing that animals prefer less variable resources.

Circulating immune cell phenotype dynamics reflect the strength of tumor-immune cell interactions in patients during immunotherapy.

The extent to which immune cell phenotypes in the peripheral blood reflect within-tumor immune activity prior to and early in cancer therapy is unclear. To address this question, we studied the population dynamics of tumor and immune cells, and immune phenotypic changes, using clinical tumor and immune cell measurements and single-cell genomic analyses. These samples were serially obtained from a cohort of advanced gastrointestinal cancer patients enrolled in a trial with chemotherapy and immunotherapy. Using an ecological population model, fitted to clinical tumor burden and immune cell abundance data from each patient, we find evidence of a strong tumor-circulating immune cell interaction in responder patients but not in those patients that progress on treatment. Upon initiation of therapy, immune cell abundance increased rapidly in responsive patients, and once the peak level is reached tumor burden decreases, similar to models of predator-prey interactions; these dynamic patterns were absent in nonresponder patients. To interrogate phenotype dynamics of circulating immune cells, we performed single-cell RNA sequencing at serial time points during treatment. These data show that peripheral immune cell phenotypes were linked to the increased strength of patients' tumor-immune cell interaction, including increased cytotoxic differentiation and strong activation of interferon signaling in peripheral T cells in responder patients. Joint modeling of clinical and genomic data highlights the interactions between tumor and immune cell populations and reveals how variation in patient responsiveness can be explained by differences in peripheral immune cell signaling and differentiation soon after the initiation of immunotherapy.

Uncertainty quantification for ecological models with random parameters.

There is often considerable uncertainty in parameters in ecological models. This uncertainty can be incorporated into models by treating parameters as random variables with distributions, rather than fixed quantities. Recent advances in uncertainty quantification methods, such as polynomial chaos approaches, allow for the analysis of models with random parameters. We introduce these methods with a motivating case study of sea ice algal blooms in heterogeneous environments. We compare Monte Carlo methods with polynomial chaos techniques to help understand the dynamics of an algal bloom model with random parameters. Modelling key parameters in the algal bloom model as random variables changes the timing, intensity and overall productivity of the modelled bloom. The computational efficiency of polynomial chaos methods provides a promising avenue for the broader inclusion of parametric uncertainty in ecological models, leading to improved model predictions and synthesis between models and data.

Is mammography screening beneficial: An individual-based stochastic model for breast cancer incidence and mortality.

The benefits of mammography screening have been controversial, with conflicting findings from various studies. We hypothesize that unmeasured heterogeneity in tumor aggressiveness underlies these conflicting results. Based on published data from the Canadian National Breast Screening Study (CNBSS), we develop and parameterize an individual-based mechanistic model for breast cancer incidence and mortality that tracks five stages of breast cancer progression and incorporates the effects of age on breast cancer incidence and all-cause mortality. The model accurately reproduces the reported outcomes of the CNBSS. By varying parameters, we predict that the benefits of mammography depend on the effectiveness of cancer treatment and tumor aggressiveness. In particular, patients with the most rapidly growing or potentially largest tumors have the highest benefit and least harm from the screening, with only a relatively small effect of age. However, the model predicts that confining mammography to populations with a high risk of acquiring breast cancer increases the screening benefit only slightly compared with the full population.

ATM and ATR Activation Through Crosstalk Between DNA Damage Response Pathways.

Cells losing the ability to self-regulate in response to damage are a hallmark of cancer. When a cell encounters damage, regulatory pathways estimate the severity of damage and promote repair, cell cycle arrest, or apoptosis. This decision-making process would be remarkable if it were based on the total amount of damage in the cell, but because damage detection pathways vary in the rate and intensity with which they promote pro-apoptotic factors, the cell's real challenge is to reconcile dissimilar signals. Crosstalk between repair pathways, crosstalk between pro-apoptotic signaling kinases, and signals induced by damage by-products complicate the process further. The cell's response to [Formula: see text] and UV radiation neatly illustrates this concept. While these forms of radiation produce lesions associated with two different pro-apoptotic signaling kinases, ATM and ATR, recent experiments show that ATM and ATR react to both forms of radiation. To simulate the pro-apoptotic signal induced by [Formula: see text] and UV radiation, we construct a mathematical model that includes three modes of crosstalk between ATM and ATR signaling pathways: positive feedback between ATM/ATR and repair proteins, ATM and ATR mutual upregulation, and changes in lesion topology induced by replication stress or repair. We calibrate the model to agree with 21 experimental claims about ATM and ATR crosstalk. We alter the model by adding or removing specific processes and then examine the effects of each process on ATM/ATR crosstalk by recording which claims the altered model violates. Not only is this the first mathematical model of ATM/ATR crosstalk, it provides a strong argument for treating pro-apoptotic signaling as a holistic effort rather than attributing it to a single dominant kinase.

Arabidopsis mRNA decay landscape arises from specialized RNA decay substrates, decapping-mediated feedback, and redundancy.

The decay of mRNA plays a vital role in modulating mRNA abundance, which, in turn, influences cellular and organismal processes. In plants and metazoans, three distinct pathways carry out the decay of most cytoplasmic mRNAs: The mRNA decapping complex, which requires the scaffold protein VARICOSE (VCS), removes a protective 5' cap, allowing for 5' to 3' decay via EXORIBONUCLEASE4 (XRN4, XRN1 in metazoans and yeast), and both the exosome and SUPPRESSOR OF VCS (SOV)/DIS3L2 degrade RNAs in the 3' to 5' direction. However, the unique biological contributions of these three pathways, and whether they degrade specialized sets of transcripts, are unknown. In Arabidopsis, the participation of SOV in RNA homeostasis is also unclear, because Arabidopsis sov mutants have a normal phenotype. We carried out mRNA decay analyses in wild-type, sov, vcs, and vcs sov seedlings, and used a mathematical modeling approach to determine decay rates and quantify gene-specific contributions of VCS and SOV to decay. This analysis revealed that VCS (decapping) contributes to decay of 68% of the transcriptome, and, while it initiates degradation of mRNAs with a wide range of decay rates, it especially contributes to decay of short-lived RNAs. Only a few RNAs were clear SOV substrates in that they decayed more slowly in sov mutants. However, 4,506 RNAs showed VCS-dependent feedback in sov that modulated decay rates, and, by inference, transcription, to maintain RNA abundances, suggesting that these RNAs might also be SOV substrates. This feedback was shown to be independent of siRNA activity.

How Should Cancer Models Be Constructed?

Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

Prospective multicenter randomized patient recruitment and sample collection to enable future measurements of sputum biomarkers of inflammation in an observational study of cystic fibrosis.

BACKGROUND: Biomarkers of inflammation predictive of cystic fibrosis (CF) disease outcomes would increase the power of clinical trials and contribute to better personalization of clinical assessments. A representative patient cohort would improve searching for believable, generalizable, reproducible and accurate biomarkers. METHODS: We recruited patients from Mountain West CF Consortium (MWCFC) care centers for prospective observational study of sputum biomarkers of inflammation. After informed consent, centers enrolled randomly selected patients with CF who were clinically stable sputum producers, 12 years of age and older, without previous organ transplantation. RESULTS: From December 8, 2014 through January 16, 2016, we enrolled 114 patients (53 male) with CF with continuing data collection. Baseline characteristics included mean age 27 years (SD = 12), 80% predicted forced expiratory volume in 1 s (SD = 23%), 1.0 prior year pulmonary exacerbations (SD = 1.2), home elevation 328 m (SD = 112) above sea level. Compared with other patients in the US CF Foundation Patient Registry (CFFPR) in 2014, MWCFC patients had similar distribution of sex, age, lung function, weight and rates of exacerbations, diabetes, pancreatic insufficiency, CF-related arthropathy and airway infections including methicillin-sensitive or -resistant Staphylococcus aureus, Pseudomonas aeruginosa, Burkholderia cepacia complex, fungal and non-tuberculous Mycobacteria infections. They received CF-specific treatments at similar frequencies. CONCLUSIONS: Randomly-selected, sputum-producing patients within the MWCFC represent sputum-producing patients in the CFFPR. They have similar characteristics, lung function and frequencies of pulmonary exacerbations, microbial infections and use of CF-specific treatments. These findings will plausibly make future interpretations of quantitative measurements of inflammatory biomarkers generalizable to sputum-producing patients in the CFFPR.

Mechanistic Models of Conflict between Ant Colonies and Their Consequences for Territory Scaling.

Territory size in social insects depends on the rules by which border conflicts are resolved. We present three mechanistic mathematical models of conflict, inspired by the behavior of the pavement ant Tetramorium immigrans, to predict the advantage of larger colonies in pairwise contests and the resulting scaling of territory size with worker force. The models track the number of ants in the nest traveling to and from the boundary or engaged at the boundary. Ants at the boundary base their recruitment response on the relative numbers of ants from the two colonies. With two colonies, our central result is that the larger colony gains a territory disproportionately larger than the ratio of worker forces would indicate. This disproportionate territory control determines the scaling relation of territory size with worker force in a population. In two dimensions, if territory size were proportional to worker force, the slope of the scaling relation between log territory size and log worker force would be 1.0. With disproportionate territories, this slope is larger and can be explicitly approximated in terms of model parameters, and it is steepest when colonies are packed close to each other, when ants run quickly, or when colonies are small. A steeper slope exaggerates the advantage of larger colonies, creating a positive feedback that could amplify the inequality of the worker force distribution.

Microbial Interactions in the Cystic Fibrosis Airway.

Interactions in the airway ecology of cystic fibrosis may alter organism persistence and clinical outcomes. Better understanding of such interactions could guide clinical decisions. We used generalized estimating equations to fit logistic regression models to longitudinal 2-year patient cohorts in the Cystic Fibrosis Foundation Patient Registry, 2003 to 2011, in order to study associations between the airway organisms present in each calendar year and their presence in the subsequent year. Models were adjusted for clinical characteristics and multiple observations per patient. Adjusted models were tested for sensitivity to cystic fibrosis-specific treatments. The study included 28,042 patients aged 6 years and older from 257 accredited U.S. care centers and affiliates. These patients had produced sputum specimens for at least two consecutive years that were cultured for methicillin-sensitive Staphylococcus aureus, methicillin-resistant S. aureus, Pseudomonas aeruginosa, Burkholderia cepacia complex, Stenotrophomonas maltophilia, Achromobacter xylosoxidans, and Candida and Aspergillus species. We analyzed 99.8% of 538,458 sputum cultures from the patients during the study period. Methicillin-sensitive S. aureus was negatively associated with subsequent Paeruginosa. Paeruginosa was negatively associated with subsequent B. cepacia complex, Axylosoxidans, and Smaltophilia. Bcepacia complex was negatively associated with the future presence of all bacteria studied, as well as with that of Aspergillus species. Paeruginosa, B. cepacia complex, and S. maltophilia were each reciprocally and positively associated with Aspergillus species. Independently of patient characteristics, the organisms studied interact and alter the outcomes of treatment decisions, sometimes in unexpected ways. By inhibiting P. aeruginosa, methicillin-sensitive S. aureus may delay lung disease progression. Paeruginosa and B. cepacia complex may inhibit other organisms by decreasing airway biodiversity, potentially worsening lung disease.

Human Rhinovirus Diversity and Evolution: How Strange the Change from Major to Minor.

Rhinoviruses are the most common causes of the common cold. Their many distinct lineages fall into "major" and "minor" groups that use different cell surface receptors to enter host cells. Minor-group rhinoviruses are more immunogenic in laboratory studies, although their patterns of transmission and their cold symptoms are broadly similar to those of the major group. Here we present evolutionary evidence that minor-group viruses are also more immunogenic in humans. A key finding is that rates of amino acid substitutions at exposed sites in the capsid proteins VP2, VP3, and VP1 tend to be elevated in minor-group relative to major-group viruses, while rates at buried sites show no consistent differences. A reanalysis of historical virus watch data also indicates a higher immunogenicity of minor-group viruses, consistent with our findings about evolutionary rates at amino acid positions most directly exposed to immune surveillance. The increased immunogenicity and speed of evolution in minor-group lineages may contribute to the very large numbers of rhinovirus serotypes that coexist while differing in virulence.IMPORTANCE Most colds are caused by rhinoviruses (RVs). Those caused by a subset known as the minor-group members of rhinovirus species A (RV-A) are correlated with the inception and aggravation of asthma in at-risk populations. Genetically, minor-group viruses are similar to major-group RV-A, from which they were derived, although they tend to elicit stronger immune responses. Differences in their rates and patterns of molecular evolution should be highly relevant to their epidemiology. All RV-A strains show high rates of amino acid substitutions in the capsid proteins at exposed sites not previously identified as being immunogenic, and this increase is significantly greater in minor-group viruses. These findings will inform future studies of the recently discovered RV-C, which also appears to exacerbate asthma in adults and children. In addition, these findings draw attention to the difficult problem of explaining the long-term coexistence of many serotypes of major- and minor-group RVs.

Modeling factors that regulate cell cooperativity in the zebrafish posterior lateral line primordium.

Collective cell migration is an integral part of organismal development. We consider migration of the zebrafish primordium during development of the posterior lateral line, a sensory system that detects water movement patterns. Experiments have shown that the chemokine ligand CXCL12a and its receptors CXCR4b and CXCR7b are key players for driving migration of the primordium, while FGF signaling helps maintain cohesion. In this work, we formulate a mathematical model of a laser ablated primordium separated into two smaller cell collectives: a leading collective that responds to local CXCL12a levels and a trailing collective that migrates up a local FGF gradient. Our model replicates recent experimental results, while also predicting a "runaway" behavior when FGF gradient response is inhibited. We also use our model to estimate diffusion coefficients of CXCL12a and FGF in the lateral line.

Loose coupling in the bacterial flagellar motor.

Physiological properties of the flagellar rotary motor have been taken to indicate a tightly coupled mechanism in which each revolution is driven by a fixed number of energizing ions. Measurements that would directly test the tight-coupling hypothesis have not been made. Energizing ions flow through membrane-bound complexes formed from the proteins MotA and MotB, which are anchored to the cell wall and constitute the stator. Genetic and biochemical evidence points to a "power stroke" mechanism in which the ions interact with an aspartate residue of MotB to drive conformational changes in MotA that are transmitted to the rotor protein FliG. Each stator complex contains two separate ion-binding sites, raising the question of whether the power stroke is driven by one, two, or either number of ions. Here, we describe simulations of a model in which the conformational change can be driven by either one or two ions. This loosely coupled model can account for the observed physiological properties of the motor, including those that have been taken to indicate tight coupling; it also accords with recent measurements of motor torque at high load that are harder to explain in tight-coupling models. Under loads relevant to a swimming cell, the loosely coupled motor would perform about as well as a two-proton motor and significantly better than a one-proton motor. The loosely coupled motor is predicted to be especially advantageous under conditions of diminished energy supply, or of reduced temperature, turning faster than an obligatorily two-proton motor while using fewer ions.

Cross-immunity between strains explains the dynamical pattern of paramyxoviruses.

Viral respiratory tract diseases pose serious public health problems. Our ability to predict and thus, be able to prepare for outbreaks is strained by the complex factors driving the prevalence and severity of these diseases. The abundance of diseases and transmission dynamics of strains are not only affected by external factors, such as weather, but also driven by interactions among viruses mediated by human behavior and immunity. To untangle the complex out-of-phase annual and biennial pattern of three common paramyxoviruses, Respiratory Syncytial Virus (RSV), Human Parainfluenza Virus (HPIV), and Human Metapneumovirus (hMPV), we adopt a theoretical approach that integrates ecological and immunological mechanisms of disease interactions. By estimating parameters from multiyear time series of laboratory-confirmed cases from the intermountain west region of the United States and using statistical inference, we show that models of immune-mediated interactions better explain the data than those based on ecological competition by convalescence. The strength of cross-protective immunity among viruses is correlated with their genetic distance in the phylogenetic tree of the paramyxovirus family.

The Drivers of Acute and Long-term Care Clostridium difficile Infection Rates: A Retrospective Multilevel Cohort Study of 251 Facilities.

Background: Drivers of differences in Clostridium difficile incidence across acute and long-term care facilities are poorly understood. We sought to obtain a comprehensive picture of C. difficile incidence and risk factors in acute and long-term care. Methods: We conducted a case-cohort study of persons spending at least 3 days in one of 131 acute care or 120 long-term care facilities managed by the United States Veterans Health Administration between 2006 and 2012. Patient (n = 8) and facility factors (n = 5) were included in analyses. The outcome was the incidence of facility-onset laboratory-identified C. difficile infection (CDI), defined as a person with a positive C. difficile test without a positive test in the prior 8 weeks. Results: CDI incidence in acute care was 5 times that observed in long-term care (median, 15.6 vs 3.2 per 10000 person-days). History of antibiotic use was greater in acute care compared to long-term care (median, 739 vs 513 per 1000 person-days) and explained 72% of the variation in C. difficile rates. Importation of C. difficile cases (acute care: patients with recent long-term care attributable infection; long-term care: residents with recent acute care attributable infection) was 3 times higher in long-term care as compared to acute care (median, 52.3 vs 16.2 per 10000 person-days). Conclusions: Facility-level antibiotic use was the main factor driving differences in CDI incidence between acute and long-term care. Importation of acute care C. difficile cases was a greater concern for long-term care as compared to importation of long-term care cases for acute care.

The relationship between species richness and ecosystem variability is shaped by the mechanism of coexistence.

Theory relating species richness to ecosystem variability typically ignores the potential for environmental variability to promote species coexistence. Failure to account for fluctuation-dependent coexistence may explain deviations from the expected negative diversity-ecosystem variability relationship, and limits our ability to predict the consequences of increases in environmental variability. We use a consumer-resource model to explore how coexistence via the temporal storage effect and relative nonlinearity affects ecosystem variability. We show that a positive, rather than negative, diversity-ecosystem variability relationship is possible when ecosystem function is sampled across a natural gradient in environmental variability and diversity. We also show how fluctuation-dependent coexistence can buffer ecosystem functioning against increasing environmental variability by promoting species richness and portfolio effects. Our work provides a general explanation for variation in observed diversity-ecosystem variability relationships and highlights the importance of conserving regional species pools to help buffer ecosystems against predicted increases in environmental variability.

Convergence in leaf size versus twig leaf area scaling: do plants optimize leaf area partitioning?

BACKGROUND AND AIMS: Corner's rule states that thicker twigs bear larger leaves. The exact nature of this relationship and why it should occur has been the subject of numerous studies. It is obvious that thicker twigs should support greater total leaf area ([Formula: see text]) for hydraulical and mechanical reasons. But it is not obvious why mean leaf size ([Formula: see text]) should scale positively with [Formula: see text] We asked what this scaling relationship is within species and how variable it is across species. We then developed a model to explain why these relationships exist. METHODS: To minimize potential sources of variability, we compared twig properties from six co-occurring and functionally similar species: Acer grandidentatum, Amelanchier alnifolia, Betula occidentalis, Cornus sericea, Populus fremontii and Symphoricarpos oreophilus We modelled the economics of leaf display, weighing the benefit from light absorption against the cost of leaf tissue, to predict the optimal [Formula: see text] combinations under different canopy openings. KEY RESULTS: We observed a common [Formula: see text] by [Formula: see text] exponent of 0.6, meaning that [Formula: see text]and leaf number on twigs increased in a specific coordination. Common scaling exponents were not supported for relationships between any other measured twig properties. The model consistently predicted positive [Formula: see text] by [Formula: see text] scaling when twigs optimally filled canopy openings. The observed 0·6 exponent was predicted when self-shading decreased with larger canopy opening. CONCLUSIONS: Our results suggest Corner's rule may be better understood when recast as positive [Formula: see text] by [Formula: see text] scaling. Our model provides a tentative explanation of observed [Formula: see text] by [Formula: see text] scaling and suggests different scaling may exist in different environments.