Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age. The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. We then formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size: cells consume oxygen which in turns fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. This allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy

Senescence-Inflammatory Regulation of Reparative Cellular Reprogramming in Aging and Cancer

The inability of adult tissues to transitorily generate cells with functional stem cell-like properties is a major obstacle to tissue self-repair. Nuclear reprogramming-like phenomena that induce a transient acquisition of epigenetic plasticity and phenotype malleability may constitute a reparative route through which human tissues respond to injury, stress, and disease. However, tissue rejuvenation should involve not only the transient epigenetic reprogramming of differentiated cells, but also the committed re-acquisition of the original or alternative committed cell fate. Chronic or unrestrained epigenetic plasticity would drive aging phenotypes by impairing the repair or the replacement of damaged cells; such uncontrolled phenomena of in vivo reprogramming might also generate cancer-like cellular states. We herein propose that the ability of senescence-associated inflammatory signaling to regulate in vivo reprogramming cycles of tissue repair outlines a threshold model of aging and cancer. The degree of senescence/inflammation-associated deviation from the homeostatic state may delineate a type of thresholding algorithm distinguishing beneficial from deleterious effects of in vivo reprogramming. First, transient activation of NF-κB-related innate immunity and senescence-associated inflammatory components (e.g., IL-6) might facilitate reparative cellular reprogramming in response to acute inflammatory events. Second, para-inflammation switches might promote long-lasting but reversible refractoriness to reparative cellular reprogramming. Third, chronic senescence-associated inflammatory signaling might lock cells in highly plastic epigenetic states disabled for reparative differentiation. The consideration of a cellular reprogramming-centered view of epigenetic plasticity as a fundamental element of a tissue's capacity to undergo successful repair, aging degeneration or malignant transformation should provide challenging stochastic insights into the current deterministic genetic paradigm for most chronic diseases, thereby increasing the spectrum of therapeutic approaches for physiological aging and cancer

Quiescence: a mechanism for escaping the effects of drug on cell populations

We point out that a simple and generic strategy to lower the risk for extinction consists in the developing a dormant stage in which the organism is unable to multiply but may die. The dormant organism is protected against the poisonous environment. The result is to increase the survival probability of the entire population by introducing a type of zero reproductive fitness. This is possible, because the reservoir of dormant individuals act as a buffer that can cushion fatal fluctuations in the number of births and deaths which without the dormant population would have driven the entire population to extinction.Comment: 18 pages and 9 figure

Automated design of optimum longitudinal reinforcement for flexural and axial loading

The problem of a concrete cross section under flexural and axial loading is indeterminate due to the existence of more unknowns than equations. Among the infinite solutions, it is possible to find the optimum, which is that of minimum reinforcement that satisfies certain design constraints (section ductility, minimum reinforcement area, etc.). This article proposes the automation of the optimum reinforcement calculation under any combination of flexural and axial loading. The procedure has been implemented in a program code that is attached in the Appendix. Conventional-strength or high-strength concrete may be chosen, minimum reinforcement area may be considered (it being possible to choose between the standards ACI 318 or Eurocode 2), and the neutral axis depth may be constrained in order to guarantee a certain sectional ductility. Some numerical examples are presented, drawing comparisons between the results obtained by ACI 318, EC 2 and the conventional method

Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis

Positiv e-sense, single-stranded RN A viruses are im portant pathogens infecting almost all types of organ- isms. Experimental evidence from distributions of mutations and from viral RN A ampli¿cation suggest that these pathogens may follow different RN A replication modes, r anging from the stamping machine replication (SMR) to the geo metric replication (GR) mode. Although previous theoretical work has focuse d on the evolutionary dynamics of RNA viruses amplifying their genomes with dif fer ent strategies, little is known in ter ms of the bifurcations and transitions invol ving the so-called error threshold (mutation- induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation ac- cumulation and demographic stochasti city). Here we analyze a dynamical system describing the intracel- lular ampli¿cation of viral RN A genomes e volving on a single-peak ¿tness landscape focusing on thr ee cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and err or thr eshold, governe d by transcritical bifurcations that depend on parameters a (paramet er introducing the mode of replication), repl icat ive ¿tness of mutants ( k 1 ), and on the spontaneous degradation rate s of the sequences ( ¿ ). Our re sults re late the error catastrophe with lethal mutag enesis in a model with continuous populations of viral genome s. The form er case invol ves dominance of the mutant sequences, while the latter , a deterministic extinction of the viral RNAs during replication due to increased mutation. Fo r the lethal case the critical mutation ra te involving lethal mu- tagenesis is µ c = 1 - e / v a . Here, the SMR involv es lower critical mutation ra tes, being the system more robu st to lethal mutagenesis replicating closer to the GR mode. This resul t is also f ound for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the er r or threshold once the replication mode surpasses a threshold given by v a = ¿ /k 1Peer ReviewedPostprint (author's final draft

Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy

HIV-1 infected patients are effectively treated with highly active anti-retroviral therapy (HAART). Whilst HAART is successful in keeping the disease at bay with average levels of viral load well below the detection threshold of standard clinical assays, it fails to completely eradicate the infection, which persists due to the emergence of a latent reservoir with a half-life time of years and is immune to HAART. This implies that life-long administration of HAART is, at the moment, necessary for HIV-1-infected patients, which is prone to drug resistance and cumulative side effects as well as imposing a considerable financial burden on developing countries, those more afflicted by HIV, and public health systems. The development of therapies which specifically aim at the removal of this latent reservoir has become a focus of much research. A proposal for such therapy consists of elevating the rate of activation of the latently infected cells: by transferring cells from the latently infected reservoir to the active infected compartment, more cells are exposed to the anti-retroviral drugs thus increasing their effectiveness. In this paper, we present a stochastic model of the dynamics of the HIV-1 infection and study the effect of the rate of latently infected cell activation on the average extinction time of the infection. By analysing the model by means of an asymptotic approximation using the semi-classical quasi steady state approximation (QSS), we ascertain that this therapy reduces the average life-time of the infection by many orders of magnitudes. We test the accuracy of our asymptotic results by means of direct simulation of the stochastic process using a hybrid multi-scale Monte Carlo scheme

The dynamics of shapes of vesicle membranes with time dependent spontaneous curvature

We study the time evolution of the shape of a vesicle membrane under time-dependent spontaneous curvature by means of phase-field model. We introduce the variation in time of the spontaneous curvature via a second field which represents the concentration of a sub- stance that anchors with the lipid bilayer thus changing the local curvature and producing constriction. This constriction is mediated by the action on the membrane of an structure resembling the role of a Z ring. Our phase-field model is able to reproduce a number of dif- ferent shapes that have been experimentally observed. Different shapes are associated with different constraints imposed upon the model regarding conservation of membrane area. In particular, we show that if area is conserved our model reproduces the so-called L-form shape. By contrast, if the area of the membrane is allowed to grow, our model reproduces the formation of a septum in the vicinity of the constriction. Furthermore, we pro- pose a new term in the free energy which allows the membrane to evolve towards eventual pinching

Validación de la pantalla plana para el estudio de las ducciones y el campo de visión binocular única en sujetos sanos y pacientes con orbitopatía de grave

La presente tesis doctoral está centrada en la evaluación de las alteraciones oculomotoras que acontecen en la Orbitopatía de Graves (OG). Se organiza en un estudio principal de validación de la pantalla plana (PP) como instrumento de medición y dos estudios secundarios relacionados con el principal que nos aportan información sobre el uso y aplicaciones de esta ya que la diplopia afecta de forma importante a las actividades cotidianas de la vida de los pacientes que la padecen. Los cambios en la motilidad ocular de los pacientes con OG juegan un papel importante en los índices de actividad de la enfermedad. Estos cambios han sido tradicionalmente medidos con el perímetro de Goldmann, que evalúa el campo de visión binocular única, y con reflejo de luz en la córnea, que mide las ducciones. Dado que el perímetro de Goldmann ya no se fabrica y es difícil de encontrar, hemos buscado un método que nos permita evaluar estos parámetros y monitorizar los cambios en los mismos..

Computational modelling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modelling has contributed to unravelling its complexity. Many existing theoretical models of angiogenic sprouting are based on the 'snail-trail' hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate towards low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modelling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modelling components such models should include in order to investigate its functional role.Comment: 26 pages, 9 figures, 1 table. Submitted for publication to WIREs Mechanisms of Diseas

Relaciones entre gratitud y felicidad en estudiantes universitarios de Lima Metropolitana

Se analiza la probable relación entre gratitud, medida por la Escala de gratitud desarrollada por Alarcón y la felicidad, medida por la Escala de felicidad de Lima, ambas desarrolladas por el mismo autor. El estudio es de tipo sustantivo, con un diseño transeccional causal predictivo en el que participaron 300 personas, 147 varones y 153 mujeres, con edades entre 20 y 30 años, que se encuentran estudiando en universidades públicas y privadas de Lima Metropolitana. Entre los principales resultados observamos que los factores de la gratitud, reciprocidad y obligación moral correlacionan positiva y significativamente con la felicidad (r = .294, p < .01; r = .293, p < .01), así como con los factores sentido positivo de la vida, satisfacción con la vida y realización personal de la Escala de felicidad. El agradecer el beneficio recibido y la satisfacción que esto conlleva tiende a estar relacionado con actitudes y experiencias positivas hacia la vida, satisfacción por lo que se ha alcanzado y la autosuficiencia y tranquilidad emocional. Cualidad sentimental se relaciona positiva y significativamente con la felicidad (r = .218, p < .05) y con satisfacción con la vida. Entre la gratitud y la felicidad no se observan diferencias estadísticamente significativas entre varones y mujeres. Para determinar cuál o cuáles de los factores de la gratitud predicen mejor la felicidad, se ha realizado un análisis de regresión múltiple, identificando que la variable reciprocidad explica el 8.7 % de la varianza total de la variable felicidad. En conclusión, se observa que gratitud y felicidad correlacionan positiva y significativamente (r=.318, p < .01).Probable relationship between gratitude, as measured by the Scale developed by Alarcón gratitude and happiness, as measured by the Scale of Happiness Lima, is analyzed both developed by the same autor. The study is substantive in nature, with a predictive causal trans design in which 300 people, 147 males and 153 females, aged between 20 and 30 who are studying in public and private universities in Lima. Among the main results we note that the factors of gratitude, reciprocity and moral obligation positively and significantly correlated with happiness (r = .294, p < .01; r = .293, p < .01), as well as factors positive sense of life, life satisfaction and fulfillment of happiness scale. The benefit received thanks and satisfaction that entails tends to be related to positive experiences and attitudes towards life, satisfaction with what has been achieved and self-reliance and emotional tranquility. Emotional quality is positively and significantly associated with happiness (r = .218, p < .05) and satisfaction with life. Between gratitude and happiness no statistically significant differences between men and women are observed. To determine which of the factors best predict Gratitude happiness, there has been a multiple regression analysis, identifying varying reciprocity explains 8.7% of the total variance of the happiness variable. In conclusion, it appears that gratitude and happiness positively and significantly correlated (r = .318, p < .01)