Does tumor growth follow a "universal law"?

A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analysed and compared with the prediction of a "universal" law, relating properly rescaled tumor masses and tumor growth times. The results support the notion that tumor growth follows such a universal law. Several important implications of this finding are discussed, including its relevance for tumor metastasis and recurrence, cell turnover rates, angiogenesis and invasion.     

The role of acetaldehyde and glycerol in the adaptation to ethanol stress of Saccharomyces cerevisiae and other yeasts

Ethanol inhibition is a commonly encountered stress condition during typical yeast fermentations and often results in reduced fermentation rates and production yields. While past studies have shown that acetaldehyde addition has a significant ameliorating effect on the growth of ethanol-stressed Saccharomyces cerevisiae , this study investigated the potential ameliorating effect of acetaldehyde on a wide range of ethanol-stressed yeasts. Acetaldehyde does not appear to be a universal ameliorating agent for yeasts exposed to ethanol stress. It is also shown that as a result of an ethanol stress, most yeasts rapidly produce glycerol as an alternative means of NAD⁺ regeneration rather than having a specific requirement for glycerol. The results strongly suggest that both ethanol and acetaldehyde exposure have a direct effect on the cellular NAD⁺/NADH ratio, which can manifest itself as modulations in glycerol production.     

Demonstration of a universal surface DNA computer

A fundamental concept in computer science is that of the universal Turing machine, which is an abstract definition of a general purpose computer. A general purpose (universal) computer is defined as one which can compute anything that is computable. It has been shown that any computer which is able to simulate Boolean logic circuits of any complexity is such a general purpose computer. The field of DNA computing was founded in 1994 by Adleman's solution of a 7-bit instance of the Hamiltonian path problem. This work, as well as most of the subsequent experimental and theoretical investigations in the area, focused primarily upon the solution of NP-complete problems, which are a subset of the larger universal class of problems. In the present work a surface DNA computer capable of simulating Boolean logic circuits is demonstrated. This was done by constructing NOR and OR gates and combining them into a simple logic circuit. The NOR gate is one of the universal gates in Boolean logic, meaning that any other logic gate can be built from it alone. The circuit was solved using DNA-based operations, demonstrating the universal nature of this surface DNA computing model.     

Interaction of CR6 (GADD45gamma ) with proliferating cell nuclear antigen impedes negative growth control

GADD45, MyD118, and CR6 (also termed GADD45alpha, beta, and gamma) comprise a family of genes that encode for related proteins playing important roles in negative growth control, including growth suppression. Data accumulated suggest that MyD118/GADD45/CR6 serve similar but not identical functions along different apoptotic and growth suppressive pathways. It is also apparent that individual members of the MyD118/GADD45/CR6 family are differentially induced by a variety of genetic and environmental stress agents. The MyD118, CR6, and GADD45 proteins were shown to predominantly localize within the cell nucleus. Recently, we have shown that both MyD118 and GADD45 interact with proliferating cell nuclear antigen (PCNA), a protein that plays a central role in DNA replication, DNA repair, and cell cycle progression, as well as with the universal cyclin-dependent kinase inhibitor p21. In this work we show that also CR6 interacts with PCNA and p21. Moreover, it is shown that CR6 interacts with PCNA via a domain that also mediates interaction of both GADD45 and MyD118 with PCNA. Importantly, evidence has been obtained that interaction of CR6 with PCNA impedes the function of this protein in negative growth control, similar to observations reported for MyD118 and GADD45.     

When growth models are not universal: evidence from marine invertebrates

The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates.     

Saturation of two-stream instability of an electron beam in plasma

The development and nonlinear saturation of two-stream instability of a warm nonrelativistic electron beam in a cold plasma are investigated numerically in the framework of a one-dimensional model. It is shown that, for a sufficiently large velocity spread of the electron beam, instability develops and saturates according to a universal law, the wave phase velocity remains the same in the saturation stage, and the maximum field is somewhat lower than that predicted by classical estimates and depends in a different way on the growth rate. The damping of plasma oscillations not only changes the instability growth rate, but also substantially decreases the maximum wave field.     

Evolution of life history strategies for an asexual annual plant model

At any given moment in time a plant is partitioning total growth mass into its various component parts such as leaves, roots, reproductive material, etc. The view is taken that the plant has evolved a life history strategy to control this partitioning process. This paper illustrates the utility of optimal control theory for use in determining life history strategies which maximize fitness for a given asexual plant model. The optimal control methods are first used on a model previously analyzed by Professor Dan Cohen, who used a different method. His results of a change from 100% vegetable growth to 100% reproductive growth at a fixed switching time is again obtained. This 100% switching result is shown to be more generally applicable by using a qualitatively described model. However the switching time in general is shown to be a function of both leaf mass and time remaining to the end of the growing season. The allocation to toxin production is also considered. It is shown that under this model an inequality between system parameters must be satisfied before the plant should allocate growth to toxin production. Although the particular model explored here may rarely be realistic in nature, these same methods of optimal control theory can be applied in a similar fashion to many other proposed models of plant resource allocation.     

A two-component regulator of universal stress protein expression and adaptation to oxygen starvation in Mycobacterium smegmatis

We identified a response regulator in Mycobacterium smegmatis which plays an important role in adaptation to oxygen-starved stationary phase. The regulator exhibits strong sequence similarity to DevR/Rv3133c of M. tuberculosis. The structural gene is present on a multigene locus, which also encodes a sensor kinase. A devR mutant of M. smegmatis was adept at surviving growth arrest initiated by either carbon or nitrogen starvation. However, its culturability decreased several orders of magnitude below that of the wild type under oxygen-starved stationary-phase conditions. Two-dimensional gel analysis revealed that a number of oxygen starvation-inducible proteins were not expressed in the devR mutant. Three of these proteins are universal stress proteins, one of which is encoded directly upstream of devR. Another protein closely resembles a proposed nitroreductase, while a fifth protein corresponds to the alpha-crystallin (HspX) orthologue of M. smegmatis. None of the three universal stress proteins or nitroreductase, and a considerably lower amount of HspX was detected in carbon-starved wild-type cultures. A fusion of the hspX promoter to gfp demonstrated that DevR directs gene expression when M. smegmatis enters stationary phase brought about, in particular, by oxygen starvation. To our knowledge, this is the first time a role for a two-component response regulator in the control of universal stress protein expression has been shown. Notably, the devR mutant was 10(4)-fold more sensitive than wild type to heat stress. We conclude that DevR is a stationary-phase regulator required for adaptation to oxygen starvation and resistance to heat stress in M. smegmatis.     

Differences in tetranectin immunoreactivity between benign and malignant breast tissue

Summary Tetranectin (TN) is a human, plasminogen kringle 4 binding plasma protein with ubiquitous cellular distribution and lectin-like characteristics. By means of the peroxidase-antiperoxidase staining technique a polyclonal and a monoclonal antibody were used to demonstrate TN within the intracellular as well as the extracellular compartment of invasive breast carcinoma. Whereas cell associated TN was universal showing only quantitative differences depending of the growth pattern of the tumor, 78 of 133 tumors displayed TN extracellularly as well. The occurrence of this stromal TN immunoreactivity was closely associated with desmoplasia, recognized morphologically by an increase in fibroblastic cells and immunohistochemically by an intense staining for the connective tissue glycoprotein fibronectin (FN). Benign breast tissue displayed a universal, intense cytoplasmic but no extracellular reaction for TN, with the exception of rare foci of granulation tissue and around dilated cysts. Functional studies have shown that human embryonal lung fibroblasts increase their release of TN to the growth medium upon stimulation. The presence of TN extracellularly within fibroblast-rich foci of desmoplasia (and granulation tissue) suggests that a similar increased release of the protein takes place in vivo during active states. Desmoplasia has been found to have a protective effect on tumor cell propagation and metastasis in a murine model. The molecular interactions, which are responsible for this effect, are undoubtedly complex. However, TN may, by its specific binding to kringle 4 of plasminogen and its high affinity for sulphated polysaccharides, add to the understanding of how plasminogen activation is modulated at the local extracellular level.     

作物生产力模型及其应用研究

从农业生态环境的角度论述了作物生产力模型的产生背景,讨论了作物生产力模型发展的幼年期、少年期、青年期和成熟期4个阶段,从科学研究,农业作物管理和农业决策分析等方面论述了作物生产力模型在保护农业生态环境中的作用,讨论了作物生产力模型的不足之处主要为简单的模型的地区适应性不强,而复杂的模型则由于参数的难以获取,且不同研究区域基础数据格式的一致性问题,也导致模型的地区适应性比较弱,因而提出要建立通用,统一的数据格式,以使作物生产力模型在不同地区易于推广应用;最后针对作物生产力模型普遍适应性能比较弱的问题,对作物生产力模型与地理信息系统的结合进行了研究,并综述了目前在作物生产力模型的界面友好化方面的一些工作,提出建立通用的作物生产力模型界面是今后发展的重点所在。     

A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories

The logistic or S-shaped curve of growth is one of the few universal laws in biology. It is certain that there exist specific genes affecting growth curves, but, due to a lack of statistical models, it is unclear how these genes cause phenotypic differentiation in growth and developmental trajectories. In this paper we present a statistical model for detecting major genes responsible for growth trajectories. This model is incorporated with pervasive logistic growth curves under the maximum likelihood framework and, thus, is expected to improve over previous models in both parameter estimation and inference. The power of this model is demonstrated by an example using forest tree data, in which evidence of major genes affecting stem growth processes is successfully detected. The implications for this model and its extensions are discussed.     

Generic model control of the specific growth rate in recombinant Escherichia coli cultivations

Generic model control is shown to be a powerful tool for keeping a microbial cultivation process close to its predetermined (optimized) control profile. This is demonstrated at the example of the green fluorescent protein expressed in genetically modified Escherichia coli host cells. It is shown that the process can be run very closely to a predefined complex profile of the specific cell growth rate mu(t). Controlling the experiments at many different growth conditions is a straightforward way of effectively collecting the data necessary for optimization of recombinant protein production systems. Although the process dynamics is rather complex, the model for the controller can be kept quite simple. The control technique, used here for specific growth rate control, is quite universal and can be applied for different biotechnological processes as well.     

Differences in tetranectin immunoreactivity between benign and malignant breast tissue.

Tetranectin (TN) is a human, plasminogen kringle 4 binding plasma protein with ubiquitous cellular distribution and lectin-like characteristics. By means of the peroxidase-antiperoxidase staining technique a polyclonal and a monoclonal antibody were used to demonstrate TN within the intracellular as well as the extracellular compartment of invasive breast carcinoma. Whereas cell associated TN was universal showing only quantitative differences depending of the growth pattern of the tumor, 78 of 133 tumors displayed TN extracellularly as well. The occurrence of this stromal TN immunoreactivity was closely associated with desmoplasia, recognized morphologically by an increase in fibroblastic cells and immunohistochemically by an intense staining for the connective tissue glycoprotein fibronectin (FN). Benign breast tissue displayed a universal, intense cytoplasmic but no extracellular reaction for TN, with the exception of rare foci of granulation tissue and around dilated cysts. Functional studies have shown that human embryonal lung fibroblasts increase their release of TN to the growth medium upon stimulation. The presence of TN extracellularly within fibroblast-rich foci of desmoplasia (and granulation tissue) suggests that a similar increased release of the protein takes place in vivo during active states. Desmoplasia has been found to have a protective effect on tumor cell propagation and metastasis in a murine model. The molecular interactions, which are responsible for this effect, are undoubtedly complex. However, TN may, by its specific binding to kringle 4 of plasminogen and its high affinity for sulphated polysaccharides, add to the understanding of how plasminogen activation is modulated at the local extracellular level.     

Correlating cell behavior with tissue topology in embryonic epithelia

Measurements on embryonic epithelial tissues in a diverse range of organisms have shown that the statistics of cell neighbor numbers are universal in tissues where cell proliferation is the primary cell activity. Highly simplified non-spatial models of proliferation are claimed to accurately reproduce these statistics. Using a systematic critical analysis, we show that non-spatial models are not capable of robustly describing the universal statistics observed in proliferating epithelia, indicating strong spatial correlations between cells. Furthermore we show that spatial simulations using the Subcellular Element Model are able to robustly reproduce the universal histogram. In addition these simulations are able to unify ostensibly divergent experimental data in the literature. We also analyze cell neighbor statistics in early stages of chick embryo development in which cell behaviors other than proliferation are important. We find from experimental observation that cell neighbor statistics in the primitive streak region, where cell motility and ingression are also important, show a much broader distribution. A non-spatial Markov process model provides excellent agreement with this broader histogram indicating that cells in the primitive streak may have significantly weaker spatial correlations. These findings show that cell neighbor statistics provide a potentially useful signature of collective cell behavior.     

Density-dependence as a size-independent regulatory mechanism

The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.     

Growth-dependent bacterial susceptibility to ribosome-targeting antibiotics

Bacterial growth environment strongly influences the efficacy of antibiotic treatment, with slow growth often being associated with decreased susceptibility. Yet in many cases, the connection between antibiotic susceptibility and pathogen physiology remains unclear. We show that for ribosome-targeting antibiotics acting on Escherichia coli, a complex interplay exists between physiology and antibiotic action; for some antibiotics within this class, faster growth indeed increases susceptibility, but for other antibiotics, the opposite is true. Remarkably, these observations can be explained by a simple mathematical model that combines drug transport and binding with physiological constraints. Our model reveals that growth-dependent susceptibility is controlled by a single parameter characterizing the ‘reversibility’ of ribosome-targeting antibiotic transport and binding. This parameter provides a spectrum classification of antibiotic growth-dependent efficacy that appears to correspond at its extremes to existing binary classification schemes. In these limits, the model predicts universal, parameter-free limiting forms for growth inhibition curves. The model also leads to non-trivial predictions for the drug susceptibility of a translation mutant strain of E. coli, which we verify experimentally. Drug action and bacterial metabolism are mechanistically complex; nevertheless, this study illustrates how coarse-grained models can be used to integrate pathogen physiology into drug design and treatment strategies.     

Solution structure and interaction with basic and acidic fibroblast growth factor of a 3-kDa human platelet factor-4 fragment with antiangiogenic activity.

Platelet factor-4 is a protein belonging to the family of ELR-negative CXC chemokines which binds to fibroblast growth factor and inhibits its mitogenic activity. Platelet factor-4 also inhibits tumor growth by mechanisms involving antiangiogenesis. Antiangiogenic activity in vitro has also been shown for the 24-residue C-terminal fragment of the protein, which decreases the affinity between basic fibroblast growth factor and its cell-surface receptor. In this study, the preferential conformation of this fragment in solution has been determined and has been found to be composed of two helical subdomains. In addition, we show that the fragment forms a specific 1:1 complex with acidic and basic fibroblast growth factors and that both subdomains are probably required for inhibition of fibroblast growth factor-driven mitogenesis. Finally, we show that the binding of the fragment alters the structure of the fibroblast growth factors, although some of such alterations do not seem related with the inhibition of mitogenic activity. Since this fragment has recently been shown to inhibit fibroblast growth factor-induced angiogenesis in vivo when injected intraperitoneally, these results are relevant for developing new antiangiogenic treatments.     

Sustained simultaneous glycolytic and insulin oscillations in beta-cells

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.     

Modelling the interaction of keratinocytes and fibroblasts during normal and abnormal wound healing processes

The crosstalk between fibroblasts and keratinocytes is a vital component of the wound healing process, and involves the activity of a number of growth factors and cytokines. In this work, we develop a mathematical model of this crosstalk in order to elucidate the effects of these interactions on the regeneration of collagen in a wound that heals by second intention. We consider the role of four components that strongly affect this process: transforming growth factor-β, platelet-derived growth factor, interleukin-1 and keratinocyte growth factor. The impact of this network of interactions on the degradation of an initial fibrin clot, as well as its subsequent replacement by a matrix that is mainly composed of collagen, is described through an eight-component system of nonlinear partial differential equations. Numerical results, obtained in a two-dimensional domain, highlight key aspects of this multifarious process, such as re-epithelialization. The model is shown to reproduce many of the important features of normal wound healing. In addition, we use the model to simulate the treatment of two pathological cases: chronic hypoxia, which can lead to chronic wounds; and prolonged inflammation, which has been shown to lead to hypertrophic scarring. We find that our model predictions are qualitatively in agreement with previously reported observations and provide an alternative pathway for gaining insight into this complex biological process.     

Regulation of ovulation number in mammals. A follicle interaction law that controls maturation

The assumption that developing follicles communicate through circulating hormones has been used to obtain a class of interaction laws that describe follicle growth. A specific member of this class has been shown to control ovulation number. Although all interacting follicles obey the same growth law and are given initial maturities that are chosen at random from a uniform distribution, ovulatory and atretic follicles emerge. Changing the parameters in the growth law can alter the most probable ovulation number values, anovulatory states are also admitted as possible solutions of the growth law. The behavior of the model is examined for interacting follicle populations of different size. Methods are suggested for identifying growth laws in particular mammals. These can be used to test the model from experimental data.