Browsing by Subject "Stochastic Processes"

Now showing 1 - 10 of 10
  • Thumbnail Image
    ItemOpen Access
    HPV clearance and the neglected role of stochasticity.
    (PLoS Comput Biol, 2015-03) Ryser, MD; Myers, ER; Durrett, R
    Clearance of anogenital and oropharyngeal HPV infections is attributed primarily to a successful adaptive immune response. To date, little attention has been paid to the potential role of stochastic cell dynamics in the time it takes to clear an HPV infection. In this study, we combine mechanistic mathematical models at the cellular level with epidemiological data at the population level to disentangle the respective roles of immune capacity and cell dynamics in the clearing mechanism. Our results suggest that chance-in form of the stochastic dynamics of basal stem cells-plays a critical role in the elimination of HPV-infected cell clones. In particular, we find that in immunocompetent adolescents with cervical HPV infections, the immune response may contribute less than 20% to virus clearance-the rest is taken care of by the stochastic proliferation dynamics in the basal layer. In HIV-negative individuals, the contribution of the immune response may be negligible.
  • Thumbnail Image
    ItemOpen Access
    Inference for nonlinear epidemiological models using genealogies and time series.
    (PLoS Comput Biol, 2011-08) Rasmussen, David A; Ratmann, Oliver; Koelle, Katia
    Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.
  • Thumbnail Image
    ItemOpen Access
    Low demographic variability in wild primate populations: fitness impacts of variation, covariation, and serial correlation in vital rates.
    (Am Nat, 2011-01) Morris, William F; Altmann, Jeanne; Brockman, Diane K; Cords, Marina; Fedigan, Linda M; Pusey, Anne E; Stoinski, Tara S; Bronikowski, Anne M; Alberts, Susan C; Strier, Karen B
    In a stochastic environment, long-term fitness can be influenced by variation, covariation, and serial correlation in vital rates (survival and fertility). Yet no study of an animal population has parsed the contributions of these three aspects of variability to long-term fitness. We do so using a unique database that includes complete life-history information for wild-living individuals of seven primate species that have been the subjects of long-term (22-45 years) behavioral studies. Overall, the estimated levels of vital rate variation had only minor effects on long-term fitness, and the effects of vital rate covariation and serial correlation were even weaker. To explore why, we compared estimated variances of adult survival in primates with values for other vertebrates in the literature and found that adult survival is significantly less variable in primates than it is in the other vertebrates. Finally, we tested the prediction that adult survival, because it more strongly influences fitness in a constant environment, will be less variable than newborn survival, and we found only mixed support for the prediction. Our results suggest that wild primates may be buffered against detrimental fitness effects of environmental stochasticity by their highly developed cognitive abilities, social networks, and broad, flexible diets.
  • Thumbnail Image
    ItemOpen Access
    Modeling deterministic effects in hematopoietic system caused by chronic exposure to ionizing radiation in large human cohorts.
    (Health Phys, 2010-09) Akushevich, Igor V; Veremeyeva, Galina A; Dimov, Georgy P; Ukraintseva, Svetlana V; Arbeev, Konstantin G; Akleyev, Alexander V; Yashin, Anatoly I
    A new model of the hematopoietic system for humans chronically exposed to ionizing radiation allows for quantitative description of the initial hematopoiesis inhibition and subsequent increase in the risks of late stochastic effects such as leukemia. This model describes the dynamics of the hematopoietic stem cell compartment as well as the dynamics of each of the three blood cell types (leukocytes, erythrocytes, and platelets). The model parameters are estimated from the results of other experiments. They include the steady-state numbers of hematopoietic stem cells and peripheral blood cell lines for an unexposed organism, amplification parameters for each blood cell line, parameters describing the proliferation and apoptosis, parameters of feedback functions regulating the steady-state numbers, and characteristics of radiosensitivity in respect to cell death and non-lethal cell damages. The dynamic model of hematopoiesis is applied to the data on a subcohort of the Techa River residents with hematological measurements (e.g., blood counts) performed in 1950-1956 (which totals to about 3,500 exposed individuals). Among well-described effects observed in these data are the slope values of the dose-effect curves describing the hematopoietic inhibition and the dose rate patterns of the fractions of cytopenic states (e.g., leukopenia, thrombocytopenia). The model has been further generalized by inclusion of the component describing the risk of late stochastic effects. The risks of the development of late effects (such as leukemia) in population groups with specific patterns of early reactions in hematopoiesis (such as leukopenia induced by ionizing radiation) are investigated using simulation studies and compared to data.
  • Thumbnail Image
    ItemOpen Access
    Modeling hematopoietic system response caused by chronic exposure to ionizing radiation.
    (Radiat Environ Biophys, 2011-05) Akushevich, Igor V; Veremeyeva, Galina A; Dimov, Georgy P; Ukraintseva, Svetlana V; Arbeev, Konstantin G; Akleyev, Alexander V; Yashin, Anatoly I
    A new model of the hematopoietic system response in humans chronically exposed to ionizing radiation describes the dynamics of the hematopoietic stem cell compartment as well as the dynamics of each of the four blood cell types (lymphocytes, neutrophiles, erythrocytes, and platelets). The required model parameters were estimated based on available results of human and experimental animal studies. They include the steady-state number of hematopoietic stem cells and peripheral blood cell lines in an unexposed organism, amplification parameters for each blood line, parameters describing proliferation and apoptosis, parameters of feedback functions regulating the steady-state numbers, and characteristics of radiosensitivity related to cell death and non-lethal cell damage. The model predictions were tested using data on hematological measurements (e.g., blood counts) performed in 1950-1956 in the Techa River residents chronically exposed to ionizing radiation since 1949. The suggested model of hematopoiesis is capable of describing experimental findings in the Techa River Cohort, including: (1) slopes of the dose-effect curves reflecting the inhibition of hematopoiesis due to chronic ionizing radiation, (2) delay in effect of chronic exposure and accumulated character of the effect, and (3) dose-rate patterns for different cytopenic states (e.g., leukopenia, thrombocytopenia).
  • Thumbnail Image
    ItemOpen Access
    New stochastic carcinogenesis model with covariates: an approach involving intracellular barrier mechanisms.
    (Math Biosci, 2012-03) Akushevich, Igor; Veremeyeva, Galina; Kravchenko, Julia; Ukraintseva, Svetlana; Arbeev, Konstantin; Akleyev, Alexander V; Yashin, Anatoly I
    In this paper we present a new multiple-pathway stochastic model of carcinogenesis with potential of predicting individual incidence risks on the basis of biomedical measurements. The model incorporates the concept of intracellular barrier mechanisms in which cell malignization occurs due to an inefficient operation of barrier cell mechanisms, such as antioxidant defense, repair systems, and apoptosis. Mathematical formalism combines methodological innovations of mechanistic carcinogenesis models and stochastic process models widely used in studying biodemography of aging and longevity. An advantage of the modeling approach is in the natural combining of two types of measures expressed in terms of model parameters: age-specific hazard rate and means of barrier states. Results of simulation studies allow us to conclude that the model parameters can be estimated in joint analyses of epidemiological data and newly collected data on individual biomolecular measurements of barrier states. Respective experimental designs for such measurements are suggested and discussed. An analytical solution is obtained for the simplest design when only age-specific incidence rates are observed. Detailed comparison with TSCE model reveals advantages of the approach such as the possibility to describe decline in risk at advanced ages, possibilities to describe heterogeneous system of intermediate cells, and perspectives for individual prognoses of cancer risks. Application of the results to fit the SEER data on cancer risks demonstrates a strong predictive power of the model. Further generalizations of the model, opportunities to measure barrier systems, biomedical and mathematical aspects of the new model are discussed.
  • Thumbnail Image
    ItemOpen Access
    Non-neutral vegetation dynamics.
    (PLoS One, 2006-12-20) Marani, M; Zillio, T; Belluco, E; Silvestri, S; Maritan, A
    The neutral theory of biodiversity constitutes a reference null hypothesis for the interpretation of ecosystem dynamics and produces relatively simple analytical descriptions of basic system properties, which can be easily compared to observations. On the contrary, investigations in non-neutral dynamics have in the past been limited by the complexity arising from heterogeneous demographic behaviours and by the relative paucity of detailed observations of the spatial distribution of species diversity (beta-diversity): These circumstances prevented the development and testing of explicit non-neutral mathematical descriptions linking competitive strategies and observable ecosystem properties. Here we introduce an exact non-neutral model of vegetation dynamics, based on cloning and seed dispersal, which yields closed-form characterizations of beta-diversity. The predictions of the non-neutral model are validated using new high-resolution remote-sensing observations of salt-marsh vegetation in the Venice Lagoon (Italy). Model expressions of beta-diversity show a remarkable agreement with observed distributions within the wide observational range of scales explored (5 x 10(-1) m divided by 10(3) m). We also consider a neutral version of the model and find its predictions to be in agreement with the more limited characterization of beta-diversity typical of the neutral theory (based on the likelihood that two sites be conspecific or heterospecific, irrespective of the species). However, such an agreement proves to be misleading as the recruitment rates by propagules and by seed dispersal assumed by the neutral model do not reflect known species characteristics and correspond to averages of those obtained under the more general non-neutral hypothesis. We conclude that non-neutral beta-diversity characterizations are required to describe ecosystem dynamics in the presence of species-dependent properties and to successfully relate the observed patterns to the underlying processes.
  • No Thumbnail Available
    ItemOpen Access
    Phylodynamic inference for structured epidemiological models.
    (PLoS Comput Biol, 2014-04) Rasmussen, David A; Volz, Erik M; Koelle, Katia
    Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.
  • Thumbnail Image
    ItemOpen Access
    Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators.
    (Phys Rev E Stat Nonlin Soft Matter Phys, 2015-12) Karapetyan, Sargis; Buchler, Nicolas E
    Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.
  • Thumbnail Image
    ItemOpen Access
    Stochastic E2F activation and reconciliation of phenomenological cell-cycle models.
    (PLoS Biol, 2010-09-21) Lee, Tae J; Yao, Guang; Bennett, Dorothy C; Nevins, Joseph R; You, Lingchong
    The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.