327 research outputs found
On a Boltzmann mean field model for knowledge growth
In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll [15]. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show local in time existence and uniqueness for the fully coupled system. Furthermore we focus on the construction and existence of special solutions, which relate to exponential growth in time - so called balanced growth path solutions. Finally we illustrate the behavior of solutions for the full system and the balanced growth path equations with numerical simulations
The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity
We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours to cytotoxic therapy
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton-Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose. © EDP Sciences, SMAI, 2013
Influence of Silver Nitrate on Somatic Embryogenesis Induction in Arabica Coffee (Coffea arabica L.).
Plant somatic embryogenesis (SE) has been defined as the formation of embryos from a single or group of haploid or somatic cells [1, 2]. Low frequency (LFSE) and high frequency somatic embryogenesis (HFSE) have been described. In the first type, somatic embryos are induced directly from pro-embryogenic cells of explants, while in the second, they originate from embryogenic callus [1]. It has been suggested that in LFSE the origin of somatic embryos is unicellular, whereas in HFSE has been described as unicellular or multicellular [3]. SE is a powerful biotechnological tool used to propagate elite plants or to conserve important genotypes [4]. Moreover, SE offers an efficient in vitro regeneration approach as a fundamental step in plant genetic improvement for studying basic aspects of ontogenesis of somatic embryos [5]. In Coffea spp., the first studies of SE have been reported at the beginning of 1970 [6]. Since then, a large quantity of LFSE and HFSE protocols have been optimized demonstrating that coffee is not a recalcitrant species for SE [4]. In the LFSE the somatic embryos are obtained faster (approximately 70 days) using only one medium meanwhile in HFSE several media are used and somatic embryo formation takes 9-10 months [4]. Although, in LFSE small number of somatic embryos are obtained (around 10 per explant) compared to hundreds of somatic embryos obtained per gram of embryogenic calli [4], the unicellular origin of somatic embryos in LFSE represents an advantage for the chemical and physical mutagenesis, genetic transformation and genetic editing, since prevents or reduces the appearance of chimeras [7]. In C. arabica and C. canephora many factors (such as genotype, explant type, the physiological state, age and growth conditions of the donor plants, the season of collection, nutrient composition of the medium, the volume of dissolved CO2 or O2 in the culture flask, and plant growth regulators) that affect LFSE induction have been studied [3, 8, 9, 10, 11, 12, 13]. However, few studies reported the effect of silver nitrate on LFSE using leaf explants of C. arabica L. and to the best of our knowledge it has not been analyzed using Caturra and CatuaĂ, which are two economic important producer cultivars in Costa Rica. Since SE is genotype dependent, the culture medium need to be modified for the different genotypes [7].Therefore, the objective of this study was to determine the influence of the benzyladenine (BAP), indole-3-acetic acid (IAA), and silver nitrate (AgNO3) on low frequency somatic embryogenesis using leaf explants of Coffea arabica L. cultivars Caturra and CatuaĂ
Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model
Practically, all chemotherapeutic agents lead to drug resistance. Clinically,
it is a challenge to determine whether resistance arises prior to, or as a
result of, cancer therapy. Further, a number of different intracellular and
microenvironmental factors have been correlated with the emergence of drug
resistance. With the goal of better understanding drug resistance and its
connection with the tumor microenvironment, we have developed a hybrid
discrete-continuous mathematical model. In this model, cancer cells described
through a particle-spring approach respond to dynamically changing oxygen and
DNA damaging drug concentrations described through partial differential
equations. We thoroughly explored the behavior of our self-calibrated model
under the following common conditions: a fixed layout of the vasculature, an
identical initial configuration of cancer cells, the same mechanism of drug
action, and one mechanism of cellular response to the drug. We considered one
set of simulations in which drug resistance existed prior to the start of
treatment, and another set in which drug resistance is acquired in response to
treatment. This allows us to compare how both kinds of resistance influence the
spatial and temporal dynamics of the developing tumor, and its clonal
diversity. We show that both pre-existing and acquired resistance can give rise
to three biologically distinct parameter regimes: successful tumor eradication,
reduced effectiveness of drug during the course of treatment (resistance), and
complete treatment failure
Mouse p53-deficient cancer models as platforms for obtaining genomic predictors of human cancer clinical outcomes
Mutations in the TP53 gene are very common in human cancers, and are associated with poor clinical outcome. Transgenic mouse models lacking the Trp53 gene or that express mutant Trp53 transgenes produce tumours with malignant features in many organs. We previously showed the transcriptome of a p53-deficient mouse skin carcinoma model to be similar to those of human cancers with TP53 mutations and associated with poor clinical outcomes. This report shows that much of the 682-gene signature of this murine skin carcinoma transcriptome is also present in breast and lung cancer mouse models in which p53 is inhibited. Further, we report validated gene-expression-based tests for predicting the clinical outcome of human breast and lung adenocarcinoma. It was found that human patients with cancer could be stratified based on the similarity of their transcriptome with the mouse skin carcinoma 682-gene signature. The results also provide new targets for the treatment of p53-defective tumours
Micro-Capsules in Shear Flow
This paper deals with flow-induced shape transitions of elastic capsules. The
state of the art concerning both theory and experiments is briefly reviewed
starting with dynamically induced small deformation of initially spherical
capsules and the formation of wrinkles on polymerized membranes. Initially
non-spherical capsules show tumbling and tank-treading motion in shear flow.
Theoretical descriptions of the transition between these two types of motion
assuming a fixed shape are at variance with the full capsule dynamics obtained
numerically. To resolve the discrepancy, we expand the exact equations of
motion for small deformations and find that shape changes play a dominant role.
We classify the dynamical phase transitions and obtain numerical and analytical
results for the phase boundaries as a function of viscosity contrast, shear and
elongational flow rate. We conclude with perspectives on timedependent flow, on
shear-induced unbinding from surfaces, on the role of thermal fluctuations, and
on applying the concepts of stochastic thermodynamics to these systems.Comment: 34 pages, 15 figure
Interactions between proteins bound to biomembranes
We study a physical model for the interaction between general inclusions
bound to fluid membranes that possess finite tension, as well as the usual
bending rigidity. We are motivated by an interest in proteins bound to cell
membranes that apply forces to these membranes, due to either entropic or
direct chemical interactions. We find an exact analytic solution for the
repulsive interaction between two similar circularly symmetric inclusions. This
repulsion extends over length scales of order tens of nanometers, and contrasts
with the membrane-mediated contact attraction for similar inclusions on
tensionless membranes. For non circularly symmetric inclusions we study the
small, algebraically long-ranged, attractive contribution to the force that
arises. We discuss the relevance of our results to biological phenomena, such
as the budding of caveolae from cell membranes and the striations that are
observed on their coats.Comment: 22 pages, 2 figure
Influence of shear flow on vesicles near a wall: a numerical study
We describe the dynamics of three-dimensional fluid vesicles in steady shear
flow in the vicinity of a wall. This is analyzed numerically at low Reynolds
numbers using a boundary element method. The area-incompressible vesicle
exhibits bending elasticity. Forces due to adhesion or gravity oppose the
hydrodynamic lift force driving the vesicle away from a wall. We investigate
three cases. First, a neutrally buoyant vesicle is placed in the vicinity of a
wall which acts only as a geometrical constraint. We find that the lift
velocity is linearly proportional to shear rate and decreases with increasing
distance between the vesicle and the wall. Second, with a vesicle filled with a
denser fluid, we find a stationary hovering state. We present an estimate of
the viscous lift force which seems to agree with recent experiments of Lorz et
al. [Europhys. Lett., vol. 51, 468 (2000)]. Third, if the wall exerts an
additional adhesive force, we investigate the dynamical unbinding transition
which occurs at an adhesion strength linearly proportional to the shear rate.Comment: 17 pages (incl. 10 figures), RevTeX (figures in PostScript
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