A stochastic model in tumor growth

A stochastic model of solid tumor growth based on deterministic Gompertz law is presented. Tumor cells evolution is described by a one-dimensional diffusion process limited by two absorbing boundaries representing healing threshold and patient death (carrying capacity), respectively. Via a numerical approach the first exit time problem is analysed for the process inside the region restricted by the boundaries. The proposed model is also implemented to simulate the effects of a time-dependent therapy. Finally, some numerical results are obtained for the specific case of a parathyroid tumor.     

Antarctic terrestrial ecosystem and role of pigments in enhanced UV-B radiations

The terrestrial ecosystem of Antarctica are among the most extreme on earth, challenging the communities and making their existence difficult by rapidly increasing annual summer influx of solar ultraviolet radiations (UV-R), extremely cold conditions and lesser availability of nutrients. Spring time ozone depletion is due to release of chlorofluorocarbons in the earth atmosphere and is a serious cause of concern among environmentalists. Antarctic continent is mostly dominated by cryptogamic plants with limited distribution in different parts of the icy continent however; their distribution is mostly confined to Sub-Antarctic region. By the virtue of light requirement, cryptogams are exposed to extreme seasonal fluctuation in photosynthetically active radiation (PAR), and ultraviolet (UV) radiation which are closely associated with photosynthetic pigments in photoautotrophic organisms. Antarctic cryptogams cope up the stress imposed by UV radiation by the development of efficient systems for repairing damage by synthesis of screening compounds such as UV-B absorbing pigments and anthocyanin compounds. A major part of the UV absorbing compounds are appeared to be constitutive in lichens which are usnic acid, perlatolic acid and fumarphotocetraric acid which is particularly induced by UV-B. Secondary metabolites such as phenolics, atranorin, parietin and melanin also enhance the plant defense, by different molecular targets in specific solar irradiance and potential for increased antioxidative protection to UV induced vulnerability.     

Specific features of X-ray generation by plasma focus chambers with deuterium and deuterium–tritium fillings

The process of hard X-ray (HXR) generation in plasma focus (PF) chambers was studied experimentally. The radiation was recorded using scintillation detectors with a high time resolution and thermoluminescent detectors in combination with the method of absorbing filters. Time-resolved analysis of the processes of neutron and X-ray generation in PFs is performed. The spectra of HXR emission from PF chambers with deuterium and deuterium–tritium fillings are determined. In experiments with PF chambers filled with a deuterium–tritium mixture, in addition to the HXR pulse with photon energies of up to 200–300 keV, a γ-ray pulse with photon energies of up to 2.5–3.0 MeV is recorded, and a mechanism of its generation is proposed.     

On the quasi-stationary distribution of the Ross malaria model.

Approximations are derived for the quasi-stationary distribution of the fully stochastic version of the classical Ross malaria model. The approximations are developed in two stages. In the first stage, the Ross process is approximated with a bivariate Markov chain without an absorbing state. The second stage of the approximation uses ideas from perturbation theory to derive explicit expressions that serve as approximations of the joint stationary distribution of the approximating process. Numerical comparisons are made between the approximations and the quasi-stationary distribution.     

Reversibility and the age of an allele II. Two-allele models,with selection and mutation

A Markov process with absorbing boundaries may be made recurrent by returning the process to the interior whenever a boundary is reached. The age of such a process may be defined as the length of time since the last return event. Examples drawn from two-allele genetic models are discussed, in which reversibility of the return process means that the age of an allele, whose present frequency in the population is known, has the same probability distribution as its future extinction time. Some discrete models are not reversible, yet if approximated by diffusion processes, the (approximate) age distribution is the same as the future extinction time distribution. Various results in the literature are unified by this viewpoint.     

Some results on light penetration of an absorbing medium

Two results on light penetration of an absorbing medium are presented in this paper: (1) It is shown, using the general light penetration law of Mannet al. (1977), that a random distribution of absorbing bodies (cells, leaves, etc.) is most efficient at intercepting direct beam (parallel) light. (2) A transmission coefficient is added to the general law in a manner similar to Monteith's (1965). This leads to the partitioning of the radiation regime beneath an absorbing medium into unintercepted, once intercepted, twice intercepted, etc., components. We are thus enabled to calculate the mean radiation intensity beneath the absorbing medium. This research was initiated under NSF research grant BMS 7504108 Project 3189, and USFS grant (19–200) #89–106.     

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.     

A model for early death caused by radiation pneumonitis and pulmonary fibrosis after inhaling insoluble radioactive particles

Large radiation doses to the lung can cause early death from cardiopulmonary insufficiency resulting from radiation pneumonitis and pulmonary fibrosis. A model for early death following inhalation of insoluble radioactive particles is propose. The model is based on three assumptions: (1) early death results from damage to a cluster of cells from a large number of cell clusters at risk, (2) the dose that causes early death depends on how the radiation is delivered in time and (3) the cell clusters at risk to damage are equally sensitive ro radiation. Results from asymptotic theory of extreme values, along with biophysical considerations, suggest that the cumultive distribution function for the absorbed radiation dose to the production of pulmonary injury sufficient to cause early death is best estimated by the third asymptotic distribution without a threshold. This distribution function is identical to the Weibull cumulative distribution function. Data for Beagle dogs after inhaling relatively insoluble forms of alpha- or beta-gamma-emitting particles are shown to support the Weibull model.     

Photochemical survival principle in molecular evolution

The role of solar radiation in molecular evolution is considered. The evolutionary trend is toward utilization of longer wavelength photons. In this process the short wavelength (ultraviolet) photons become detrimental and a protective atmosphere is becoming a necessity. It is proposed that for evolution to proceed, a conservation relation must be satisfied between the constructive and destructive actions of solar radiation on the one hand and the relative rates of biological synthesis and destruction on the other hand. This conservation relation requires that the rate of photosynthesis by visible light exceeds the photodestruction by the short ultraviolet. The thickness and absorbing properties of a selective atmosphere and the ratio of the quantum yield of synthesis to that of destruction are the parameters entering the conservation relation. Calculations have been performed of the minimum atmosphere necessary for later periods of molecular evolution.     

Description of radiation- and ultrasound-induced cell death by a stochastic process

Cell survival is a stochastic process with the stochastic component being strongly dependent on the irradiation conditions. This process is described by a stochastic model which allows differentiation between the deterministic and stochastic components of survival. The proposed model is tested for four irradiation experiments (2 with ionizing radiation and 2 with ultrasound) and very good agreement with experimental results is demonstrated. It identifies the higher stochasticity of the cell survival for the temporally varying radiation fields and provides the possibility to compare the stochasticity of survival in different radiation fields.     

低剂量微波辐射对增强UV-B辐射损伤菘蓝幼苗抗氧化酶活性的影响

为了探讨低剂量微波对增强UV-B辐射损伤菘蓝(Isatis indigotica Fort.)的修复作用,将经过10.08 kJ·m-2·d-1辐射损伤(PAR=220 μmol·m-2·s-1)的菘蓝幼苗分别经0、3、6、9和12 s等不同时间的微波辐照(126 mW·cm-2,2 450 MHz),然后测定其幼苗MDA含量、紫外吸收物质含量、抗坏血酸含量以及3种抗氧化酶SOD、CAT和POD活性.结果表明,增强UV-B辐射损伤菘蓝在微波的作用下其菘蓝幼苗中SOD、CAT和POD活性及紫外吸收物质含量、抗坏血酸含量提高,MDA含量得到显著的降低,说明微波对增强UV-B辐射伤害菘蓝幼苗具有修复作用.但是,随着微波剂量的增加,这种修复效应减弱,甚至消失.上述参数的变化说明适量时间的微波处理可以提高菘蓝对增强UV-B辐射的抵抗能力,并在此基础上初步探讨了微波的修复机理.     

Nitric oxide is involved in integration of UV‐B absorbing compounds among parts of clonal plants under a heterogeneous UV‐B environment

In nature, ultraviolet‐B (UV‐B) radiation is highly heterogeneous, both spatially and temporally. Plants exposed to UV‐B radiation produce UV‐B absorbing compounds that function as a protective filter. For clonal plants under heterogeneous UV‐B radiation conditions, integration among ramets can allow irradiated ramets to benefit un‐irradiated ramets by causing them to increase their UV‐B absorbing compounds content. In this study, we evaluated integration between pairs of clonal ramets of Glechoma longituba under heterogeneous or homogeneous UV‐B conditions. We determined the levels of UV‐B absorbing compounds, nitric oxide (NO) and hydrogen peroxide (H₂O₂) and measured the activity of phenylalanine ammonia‐lyase (PAL) in connected ramet pairs under homogeneous or heterogeneous UV‐B conditions. Under heterogeneous UV‐B conditions, the UV‐B absorbing compounds content increased in leaves of irradiated and un‐irradiated ramets, but not in the connecting stolons. The NO content increased in irradiated and un‐irradiated leaves and stolons, but the H₂O₂ content did not. Application of NO synthesis inhibitors and an NO blocker to irradiated ramets blocked the increase in UV‐B absorbing compounds and PAL activity in un‐irradiated ramets. These results suggested that NO is involved in the integration process for UV‐B absorbing compounds among ramets. Our findings suggested that a UV‐B‐induced increase in NO transmits a signal to un‐irradiated ramets via the stolon, leading to an increase in PAL activity and UV‐B absorbing compounds content. The internal translocation of signal enables members of clonal networks to function as a whole unit and to mount an efficient defensive response to localized UV‐B radiation.     

A combined metabolic/polymerization kinetic model on the microbial production of poly(3-hydroxybutyrate)

In the present work, an integrated dynamic metabolic/polymerization kinetic model is developed for the prediction of the intracellular accumulation profile and the molecular weight distribution of poly(3-hydroxybutyrate) (P(3HB) or PHB) produced in microbial cultures. The model integrates two different length/time scales by combining a polymerization kinetic model with a metabolic one. The bridging point between the two models is the concentration of the monomer unit (i.e. 3-hydroxybutyryl-CoA) produced during the central aerobic carbon metabolism. The predictive capabilities of the proposed model are assessed by the comparison of the calculated biopolymer concentration and number average molecular weight with available experimental data obtained from batch and fed-batch cultures of Alcaligenes eutrophus and Alcaligenes latus. The accuracy of the proposed model was found to be satisfactory, setting this model a valuable tool for the design of the process operating profile for the production of different polymer grades with desired molecular properties.     

Ultraviolet-B radiation effects on the Mediterranean ruderal Dittrichia viscosa

Young seedlings of Dittrichia viscosa L. (syn. Inula viscosa (L.) Aiton) (Asteraceae) were extensively treated with artificial rain in order to remove the water soluble component of their epicuticular UV-B absorbing compounds. As a result, 75% of the epicuticular absorbing capacity at 300 nm was lost. The seedlings were subsequently grown in a naturaly lit glasshouse for 80 days under 0.06, 6.41 and 10.14 kJ m^-2 day ^-1 biologicaly effective UV-B radiation doses. The initial, pre-rain values of the water soluble, epicuticular UV-B absorbing potential was restored in about three weeks. During this transient period the plants were exposed to the enhanced UV-B radiation doses with part of their UV-B radiation screen removed. Although a trend for increased accumulation of epicuticular UV-B absorbing capacity was observed with increasing UV-B radiation doses, the allelopathic potential of the epicuticular material remained unchanged. Internal (cellular) UV-B absorbing compounds and chlorophylls were unaffected, but total carotenoids were increased, indicating a possible protective role against UV-B radiation damage. Leaf, stem and root dry mass were the same under all treatments but UV-B radiation caused a reduction in the dry mass invested per unit leaf area with a concomitant increase in leaf area. The importance of this UV-B radiation induced selective allocation of photosynthate to the production of assimilative surfaces is discussed.     

Selective light transmittance of translucent bracts in the Himalayan giant glasshouse plant Rheum nobile Hook. f. & Thomson (Polygonaceae)

Translucent bract transmittance of ultraviolet (UV) to infrared (IR) radiation (between 320 and 800 nm) and leaf anatomy were examined in a glasshouse plant, Rheum nobile Hook. f. & Thomson (Polygonaceae) to assess the function of avoiding injury by UV radiation while keeping the inflorescence warm by photosynthetically active (PA) and IR radiation. Although the translucent bracts and rosulate leaves transmitted little UV radiation, the former always transmit more PA and IR radiation. Additionally, the bracts transmit much more scattered solar radiation than direct radiation. The bracts are also anatomically different from the rosulate leaves. They have two or three layers of mesophyll cells with neither palisade nor spongy parenchymatous cells; in addition, the uppermost layer of mesophyll and the epidermis stain easily, and both are thought to play a role in attenuating UV radiation. The leaf epidermis of many land plants has UV absorbing pigments such as flavonoids, which absorb almost all UV radiation. Thus the role of the bracts of R. nobile is to protect the reproductive organs by absorbing UV radiation and to keep them warm by transmitting PA and IR radiation. The bracts are believed to have adapted function and form to the environment, in particular, to the weather conditions of the eastern Himalaya.     

A stochastic model of the dynamics of host-pathogen systems with mutation

In this paper a stochastic model of the dynamics of host-pathogen systems with mutation is constructed. In previous works deterministic models of host-pathogen systems with no mutation were considered. The evolution of the pathogen population in any generation of the host is formulated as a multidimensional birth and death process, while the evolution of genotypic frequencies in successive generations of the host is described by a solution of a nonlinear vector difference equation. A general solution of the differential equations of the multidimensional birth and death process is presented and expressions for the stationary distribution, whenever it exists, and the mean time to extinction, when absorbing states are present, are derived. Some answers to questions raised in the discussion of a previous paper (Mode, 1962) are also contained in this paper. The research reported in this paper was supported by the United States Atomic Energy Comission, Division of Biology and Medicine Project AT(45-1)-1729.     

The ability of abaxial and adaxial epidermis of sun and shade leaves to attenuate UV-A and UV-B radiation in relation to the UV absorbing capacity of the whole leaf methanolic extracts

The UV‐absorbing capacity (measured as A₃₁₀ cm^?2 and A₃₆₅ cm^?2 or A_UVR cm^?2) of the shade leaves of four representative evergreen sclerophylls of the Mediterranean region (Quercus coccifera, Q. ilex, Arbutus andrachne and A. unedo) was considerably lower than the corresponding one of sun leaves of the same species. However, fibre optic microprobe measurements showed that adaxial as well as abaxial epidermis of shade leaves of all examined plants, except abaxial epidermis of A. andrachne, were almost as effective as the corresponding ones of the sun leaves in screening out most of the incident UV‐B radiation. There is probably a threshold, under which the concentration of the UV‐B absorbing compounds in the protective tissues is not furthermore reduced, in spite of the low levels of the stress factor (UV‐B radiation) in the environment. On the other hand, the ability of both abaxial and adaxial epidermis to attenuate UV‐A radiation, except of adaxial leaf epidermis of Quercus species, depended on the UV absorbing capacity of the whole‐leaf extracts, with different correlation patterns between the two Quercus species and the two Arbutus species. This could be explained by the fact that shade leaves showed not only quantitative, but also qualitative differences (higher A₃₁₀/A₃₆₅ ratio) in the absorbance of their methanolic extracts compared to these of sun leaves. The results of the present study showed that we should not always correlate the depth of penetration of UV radiation into sun and shade leaves according to the corresponding UV absorbing capacity of the whole leaf methanolic extracts, without taking into account all the anatomical, developmental and biochemical (such as different composition and distribution of the UV‐absorbing compounds among the different protective tissues) peculiarities of the leaves of each species.     

Model of control of diurnal melatonin secretion by the solar radiation

The mathematical model of the control process of diurnal melatonin secretion under the influence of solar radiation on retina photoreceptors is proposed. Invariant relations for calculating melatonin secretion rate and its concentration in blood plasma are obtained. Spectral, time and energy characteristics of solar radiation synchronizing diurnal melatonin secretion and circadian rhythms in human are defined. A possibility of using the relations obtained is shown for arbitrary combination of calendar dates, local time of any time zone and geographical coordinates of a calculated point on earth surface. The adequacy of model is confirmed by coincidence of the calculation data with the results of independent experimental studies on diurnal secretion of melatonin and circadian rhythm in human. The model proposed can be used during investigation of diurnal secretion of melatonin and circadian rhythm in human.     

RADIATION AND CONVECTION IN CONIFERS

The transfer of energy to and from a conifer branch involves solar radiation, thermal radiation from the ground, atmosphere, and surroundings, thermal emission by the branch, and free convection in still air and forced convection in wind. It is necessary to know the actual surface area of the branch, the effective area for absorbing sunlight, the effective area for absorbing long wave thermal radiation and for emission, and the free and forced convection coefficients. These parameters are determined using silver castings of blue spruce and white fir branches suspended in an evacuated radiation chamber and in a wind tunnel. The actual surface area of a branch is determined by means of an electrolytic technique. Numerical examples are given for energy transfer in a natural environment for conifers and comparison is made to a broad deciduous type of leaf. The role of transpiration in the energy transfer process is discussed.