Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.

Health and Growth: Causality through Education

Purpose--The paper theoretically and empirically investigates the impact on human capital investment decisions and income growth of lowered life expectancy as a result of HIV/AIDS and other diseases. Design/methodology/approach--The theoretical model is a three-period overlapping generations model where individuals go through three stages in their life, namely, young, adult and old. The model extends existing theoretical models by allowing the probability of premature death to differ for individuals at different life stage, and by allowing for stochastic technological advances. The empirical investigation focuses on the effect of HIV/AIDS on life expectancy and on the role of health on educational investments and growth. We address potential endogeneity by using various strategies, such as controlling for country specific time-invariant unobservables and by using the male circumcision rate as an instrumental variable for HIV/AIDS prevalence. Findings--We show theoretically that an increased probability of premature death leads to less investment in human capital, and consequently slower growth. Empirically we show that HIV/AIDS has resulted in a substantial decline in life expectancy in African countries and these falling life expectancies are indeed associated with lower educational attainment and slower economic growth world wide. Originality/value--The theoretical and empirical findings reveal a causal link flowing from health to growth, which has been largely overlooked by the existing literature. The main implication is that health investments, that decrease the incidence of diseases like HIV/AIDS resulting on increases in life expectancy, through its complementarity with human capital investments lead to long run growth..

Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians. (C) 2012 Elsevier B.V. All rights reserved.

Nonlocal growth processes and conformal invariance

Up to now the raise-and-peel model was the single known example of a one-dimensional stochastic process where one can observe conformal invariance. The model has one parameter. Depending on its value one has a gapped phase, a critical point where one has conformal invariance, and a gapless phase with changing values of the dynamical critical exponent z. In this model, adsorption is local but desorption is not. The raise-and-strip model presented here, in which desorption is also nonlocal, has the same phase diagram. The critical exponents are different as are some physical properties of the model. Our study suggests the possible existence of a whole class of stochastic models in which one can observe conformal invariance.

STOCHASTIC MODEL FOR SIMULATING MAIZE YIELD

Maize is one of the most important crops in the world. The products generated from this crop are largely used in the starch industry, the animal and human nutrition sector, and biomass energy production and refineries. For these reasons, there is much interest in figuring the potential grain yield of maize genotypes in relation to the environment in which they will be grown, as the productivity directly affects agribusiness or farm profitability. Questions like these can be investigated with ecophysiological crop models, which can be organized according to different philosophies and structures. The main objective of this work is to conceptualize a stochastic model for predicting maize grain yield and productivity under different conditions of water supply while considering the uncertainties of daily climate data. Therefore, one focus is to explain the model construction in detail, and the other is to present some results in light of the philosophy adopted. A deterministic model was built as the basis for the stochastic model. The former performed well in terms of the curve shape of the above-ground dry matter over time as well as the grain yield under full and moderate water deficit conditions. Through the use of a triangular distribution for the harvest index and a bivariate normal distribution of the averaged daily solar radiation and air temperature, the stochastic model satisfactorily simulated grain productivity, i.e., it was found that 10,604 kg ha(-1) is the most likely grain productivity, very similar to the productivity simulated by the deterministic model and for the real conditions based on a field experiment.

Stochastic models and dynamic measures for the characterization of bistable circuits

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.

Two distinct filopodia populations at the growth cone allow to sense nanotopographical extracellular matrix cues to guide neurite outgrowth

BACKGROUND The process of neurite outgrowth is the initial step in producing the neuronal processes that wire the brain. Current models about neurite outgrowth have been derived from classic two-dimensional (2D) cell culture systems, which do not recapitulate the topographical cues that are present in the extracellular matrix (ECM) in vivo. Here, we explore how ECM nanotopography influences neurite outgrowth. METHODOLOGY/PRINCIPAL FINDINGS We show that, when the ECM protein laminin is presented on a line pattern with nanometric size features, it leads to orientation of neurite outgrowth along the line pattern. This is also coupled with a robust increase in neurite length. The sensing mechanism that allows neurite orientation occurs through a highly stereotypical growth cone behavior involving two filopodia populations. Non-aligned filopodia on the distal part of the growth cone scan the pattern in a lateral back and forth motion and are highly unstable. Filopodia at the growth cone tip align with the line substrate, are stabilized by an F-actin rich cytoskeleton and enable steady neurite extension. This stabilization event most likely occurs by integration of signals emanating from non-aligned and aligned filopodia which sense different extent of adhesion surface on the line pattern. In contrast, on the 2D substrate only unstable filopodia are observed at the growth cone, leading to frequent neurite collapse events and less efficient outgrowth. CONCLUSIONS/SIGNIFICANCE We propose that a constant crosstalk between both filopodia populations allows stochastic sensing of nanotopographical ECM cues, leading to oriented and steady neurite outgrowth. Our work provides insight in how neuronal growth cones can sense geometric ECM cues. This has not been accessible previously using routine 2D culture systems.

Technology Creation, Diffusion, and Growth Cycles

Standard macroeconomic models that assume an exogenous stochastic process for multifactor productivity offer the interpretation that recessions are the result of ''bad news'' (technological regress) and expansions are the result of ''good news'' (technological advancement). The view taken here is that both expansions and recessions are the result of ''good news'' in the sense that in both cases, aggregate production possibilities have increased. Recessions can be thought of as the transition from one technological frontier to the next.

Explaining Economic Growth: Factor Accumulation, Total Factor Productivity Growth, and Production Efficiency Improvement

This paper examines cross-country patterns of economic growth by estimating a stochastic frontier production function for 80 developed and developing countries and decomposing output change into factor accumulation, total factor productivity growth, and production efficiency improvement. In addition, this paper incorporates the quality of inputs in analyzing output growth, where the productivity of capital depends on its average age, while the productivity of labor depends on its average level of education. Our growth decomposition involves five geographic regions - Africa, East Asian, Latin America, South Asia, and the West. Factor growth, especially capital accumulation, generally proves much more important than either the improved quality of factors or total factor productivity growth in explaining output growth. The quality of capital positively and significantly affects output growth in all groups. The quality of labor, however, only possesses a positive and significant effect on output growth in Africa, East Asia, and the West. Labor quality owns a negative and significant effect in Latin America and South Asia.

Agglomeration Economies in Japan: Technical Efficiency, Growth and Unemployment

This paper examines if the effects of agglomeration economies get manifested in technical efficiency and generate faster economic growth and higher (lower) levels of employment (unemployment). Using the prefecture level data for each of the two-digit groups of industries in Japan, the paper estimates region-specific technical efficiency index based on the stochastic frontier production function framework. The results of the factor analysis show that in most of the industry-groups (with a few exceptions) efficiency has a positive association with external scale variable(s). Though the relationship is not seen to be very strong, it would be equally erroneous to ignore the effect of agglomeration economies on efficiency. In the case of some of the light goods industries the agglomeration effect is relatively stronger. Further, economic growth varies positively with external scale variable(s) and unemployment rate tends to fall with respect to growth and concentration. All this tends to suggest that measures against industrial concentration may be counter-productive, particularly in the context of globalisation when countries are in dire need of raising productivity.

Sustainability of irrigated farming systems in a Tunisian region: A recursive stochastic programming analysis

The aim of this study was to evaluate the sustainability of farm irrigation systems in the Cébalat district in northern Tunisia. It addressed the challenging topic of sustainable agriculture through a bio-economic approach linking a biophysical model to an economic optimisation model. A crop growth simulation model (CropSyst) was used to build a database to determine the relationships between agricultural practices, crop yields and environmental effects (salt accumulation in soil and leaching of nitrates) in a context of high climatic variability. The database was then fed into a recursive stochastic model set for a 10-year plan that allowed analysing the effects of cropping patterns on farm income, salt accumulation and nitrate leaching. We assumed that the long-term sustainability of soil productivity might be in conflict with farm profitability in the short-term. Assuming a discount rate of 10% (for the base scenario), the model closely reproduced the current system and allowed to predict the degradation of soil quality due to long-term salt accumulation. The results showed that there was more accumulation of salt in the soil for the base scenario than for the alternative scenario (discount rate of 0%). This result was induced by applying a higher quantity of water per hectare for the alternative as compared to a base scenario. The results also showed that nitrogen leaching is very low for the two discount rates and all climate scenarios. In conclusion, the results show that the difference in farm income between the alternative and base scenarios increases over time to attain 45% after 10 years.

Mammary tumor suppression by transforming growth factor beta 1 transgene expression.

In cell culture, type alpha transforming growth factor (TGF-alpha) stimulates epithelial cell growth, whereas TGF-beta 1 overrides this stimulatory effect and is growth inhibitory. Transgenic mice that overexpress TGF-alpha under control of the mouse mammary tumor virus (MMTV) promoter/enhancer exhibit mammary ductal hyperplasia and stochastic development of mammary carcinomas, a process that can be accelerated by administration of the chemical carcinogen 7,12-dimethylbenz[a]anthracene. MMTV-TGF-beta 1 transgenic mice display mammary ductal hypoplasia and do not develop mammary tumors. We report that in crossbreeding experiments involving the production of mice carrying both the MMTV-TGF-beta 1 and MMTV-TGF-alpha transgenes, there is marked suppression of mammary tumor formation and that MMTV-TGF-beta 1 transgenic mice are resistant to 7,12-dimethylbenz[a]anthracene-induced mammary tumor formation. These data demonstrate that overexpression of TGF-beta 1 in vivo can markedly suppress mammary tumor development.

The stochastic Gross-Pitaevskii equation: II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.

Assessing the performance of a nucleus estate and smallholder scheme for oil palm production in West Sumatra: a stochastic frontier analysis

In this paper, we study the performance of smallholders in a nucleus estate and smallholder (NES) scheme in oil palm production schemein West Sumatra by measuring their technical efficiency using a stochastic frontier production function. Our results indicate a mean technical efficiency of 66%, which is below what we would have expected given the uniformity of the climate, soils and plantation construction among the sample farmers. The use of progressive farmers as a means of disseminating extension advice does not appear to have been successful, and more rigorous farmer selection procedures need to be put in place for similar schemes and for general agricultural extension in future. No clear relationship was established between technical efficiency and the use of female labour, suggesting there is no need to target extension services specifically at female labourers in the household. Finally, education was found to have an unexpectedly negative impact on technical efficiency, indicating that farmers with primary education may be more important than those with secondary and tertiary education as targets of development schemes and extension programs entailing non-formal education. (C) 2003 Elsevier Ltd. All rights reserved.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.