Empirical and mathematical models on the relationship between patient age and nosocomial infection

This paper proposes two models, one a purely empirical one and the others a mathematical one, which depict the relationship between patient age and nosocomial infection rate. The empirical model is based on the two age-specific phenomena, the acquisition of resistance to infection with age mainly in the early years of life and the deterioration of existing resistance mechanisms with ageing predominantly in the later years of life. The net effect of these two factors is shown to approximate into a quadratic relationship betwen age and nosocomial infection rate, like the type demonstrated in earlier experimental studies. The second mathematical model is derived from studies on cancer research and here the relationship between age and nosocomial infection rate for patients in the age group 30–70 years is represented by a log linear model. The model was tested against experimental data derived from large surveys on nosocomial infection and the resulting correlation coefficient was 0.98. The model was an extremely good fit when tested against posto-operative wound infection rates as well as nasal carriage rate of antibiotic resistant Staph. aureus. Furthermore, when patients in the survey were subdivided into groups of male patients and female patients and into two groups based on the type of operative wound, the model was still found to be a very good fit to the experimental data. This confirmed the validity of the model even in the presence of other patient-related parameters. Finally, the model was tested against the results of a totally different experimental study conducted elsewhere and the resulting correlation coefficient was 0.999, which confirmed the validity of the model in a universal context.     

Pest population stability under sterile releases

The stability of a pest population is one of the critical features to be examined when considering a control strategy for a given pest species. Four models involviing sterile male releases are examined for various stability characteristics; the models examined were: (i) a simple one stage model with no species interactions, (ii) a two life-stage model, (iii) a model involving two competing species, (iv) a model in which the pest is under predation. Of the four, the simple model was the most stable and the predation model was the least stable under continued sterile releases.     

A conceptual model of tree behaviour improves the visual assessment of tree condition

A conceptual model describing the response of two Australian floodplain eucalypts, river red gum (Eucalyptus camaldulensis) and black box (Eucalyptus largiflorens), to changes in water availability was developed based on field observations. This model was incorporated into a percentage based visual method estimating two tree crown parameters, crown extent and density. Extent is the amount of foliage at the periphery of the assessable crown; density is the density of assessable crown foliage. Polychoric correlation was used to determine the level of agreement between two experienced observers assessing river red gum and black box trees using a simple percentage scale and a percentage scale supported by the conceptual model. Trees were evaluated using the model by determining their position on a trajectory of water stress related decline and response. In both cases observer estimates of crown extent and density were significantly correlated. With the exception of red gum crown density the correlation coefficients were higher for the model supported scale. Using a conceptual model of tree response to water availability improved observer agreement. Supporting subjective assessment systems with a conceptual model is recommended to improve observer agreement in cases where a distinct model of the dominant stressor can be defined.     

Immune surveillance and neoplasia—II A two-stage mathematical model

In a previous paper (DeLisi and Rescigno, 1977) a model for the interaction of tumor cells and killer lymphocytes was presented. Although that model was highly simplified, the qualitative behavior was in accord with intuitive expectations and a wide range of data. It could not however account forde novo tumor development. In this paper a slightly more realistic model is presented by introducing a delay in the formation of killer lymphocytes. This is done by requiring two stages in the production of a killer. We show that introduction of this second stage allows tumor development from even a single cell, thus removing an important limitation of two variable systems.     

Channel opening motion of alpha7 nicotinic acetylcholine receptor as suggested by normal mode analysis

The gating motion of the human nicotinic acetylcholine receptor (nAChR) alpha7 was investigated with normal mode analysis (NMA) of two homology models. The first model, referred to as model I, was built from both the Lymnaea stagnalis acetylcholine binding protein (AChBP) and the transmembrane (TM) domain of the Torpedo marmorata nAChR. The second model, referred to as model C, was based solely on the recent electron microscopy structure of the T. marmorata nAChR. Despite structural differences, both models exhibit nearly identical patterns of flexibility and correlated motions. In addition, both models show a similar global twisting motion that may represent channel gating. The similar results obtained for the two models indicate that NMA is most sensitive to the contact topology of the structure rather than its finer detail. The major difference between the low-frequency motions sampled for the two models is that a symmetrical pore-breathing motion, favoring channel opening, is present as the second most dominant motion in model I, whilst largely absent from model C. The absence of this mode in model C can be attributed to its less symmetrical architecture. Finally, as a further goal of the present study, an approximate open channel model, consistent with many experimental findings, has been produced.     

Detection of two QTL on chicken chromosome 14 for keyhole lymphet heamocyanin

A keyhole lymphet heamocyanin is an antigen which triggers Th1 type of immune response. A QTL for a primary immune response towards keyhole lymphet heamocyanin has been detected on chicken chromosome 14 in three populations. The results from the most recent population were inconsistent and varied depending on the applied QTL detection model. The major goal of the current study was the reanalysis of this data using a 2 QTL model. Additionally, in order to provide more accurate estimates of QTL effects and positions, epistasis between the QTL was considered as a potential important contributor to quantitative traits. Four statistical models were assumed: M1: A model assuming marginal additive effects of two QTL; M2: A model assuming marginal and epistatic additive effects of two QTL; M3: A model assuming marginal additive and dominance effects of two QTL; M4: A model assuming marginal additive and dominance effects of two QTL and all possible pairwise epistases. Two QTL with significant additive and dominance effects were detected on chicken chromosome 14 using model M3. One QTL was detected at 63 cM between MCW0123 and ROS0005, another at 76 cM between ROS0005 and MCW0225/NTN2Lsts1 (FDR = 0.0051). Modelling only additive effects resulted in a significantly worse fit. On the other hand, including epistatic effects did not improve fit significantly. The current study confirms previous reports of the QTL location on GGA14. A notable finding of this study is recognition of two closely related QTL for a keyhole lymphet heamocyanin response at the distal part of chicken chromosome 14.     

地表反照率不同计算方法对干旱区流域蒸散反演结果的影响——以新疆三工河流域为例

地表蒸散是维持地球表面水量平衡和热量平衡的重要环节,SEBAL模型作为一种快速且有效的反演地表蒸散的遥感物理模型方法,在地表蒸散研究中得到广泛应用。地表反照率作为影响地表能量平衡的重要因素,同时也是SEBAL模型的重要输入参数,因此不同的地表反照率计算方法对SEBAL模型的反演结果有重要影响。以新疆三工河流域为研究区,利用Landsat8 OLI/TIRS数据,以应用最为广泛的Smith地表反照率计算法和Liang地表反照率计算法两种方法计算地表反照率,并输入SEBAL模型中反演日蒸散量,比较分析两种地表反照率计算方法对蒸散反演结果的影响,得出以下结论:(1)两种地表反照率计算方法下经SEBAL模型得到的日蒸散量与实测值拟合程度均较高,不同年份下线性拟合决定系数大于0.75,但是使用Smith方法计算出的地表反照率结合SEBAL模型得到的日蒸散量与实测值拟合程度更高;(2)通过RMSE等精度指标比较两种地表反照率计算方法下基于SEBAL模型反演的日蒸散量,结果显示,Smith地表反照率计算方法下反演的日蒸散量精度略高;(3)Smith地表反照率计算方法下最终得到的区域日均蒸散量高于使用Liang地表反照率计算方法最终得到的区域日均蒸散量,夏季差异最大,差异为0.64 mm/d,其他季节差异较小,差异约为0.2 mm/d。(4)进一步比较研究日内两种地表反照率计算方法得到的地表反照率,结果显示,Smith地表反照率计算法得到的地表反照率均值均小于同时期Liang地表反照率计算法得到的地表反照率均值。     

Tracking a fluctuating environment: a study of sampling

The problem of how animals keep track of unpredictable changes in the profitability of foraging sites was studied. An optimality model was used to predict the frequency with which a forager should sample a foraging site in which the probability of reward fluctuates randomly between high and low. The alternative foraging site is stable and offers an intermediate probability of reward. The model was tested with pigeons in a shuttle-box the two ends of which represented the two foraging sites. The pigeons succeeded in tracking the changes in the fluctuating site and the payoff attained was close to the optimum. Variations in the frequency of sampling between experimental treatments were in qualitative agreement with the model for some treatments but not others. The quantitative details of sampling behaviour were not as predicted by the optimality model, but many features could be accounted for by a mechanistic model of choice. The pigeons' choice rule, although different from that of the optimality model, is one that produces near-optimal payoffs under the conditions of this experiment.     

Third form of the precursor to the major merozoite surface antigens of Plasmodium falciparum.

The precursor to the major merozoite surface antigens of Plasmodium falciparum appears to be encoded by two distinctly different (dimorphic) alleles able to undergo limited recombination. We analyzed 18 previously uncharacterized P. falciparum isolates to test the dimorphic model. All but one, a Thailand isolate, conformed to the dimorphic model, and this isolate conformed to the dimorphic model in all but variable block 2. Sequence analysis revealed that block 2 of isolate CSL2 was a third form. Hence, the dimorphic model is not strictly correct. Recombination between alleles was found only within two conserved blocks near the 5' end of the gene.     

A photophysical model for diphenylhexatriene fluorescence decay in solvents and in phospholipid vesicles.

The fluorescence decay of 1,6-diphenyl-1,3,5-hexatriene (DPH) in pure solvents and in phospholipid vesicles has been measured using frequency domain fluorometry. Data analysis uses a model with two energetically close excited states. The model explains the high quantum yield and the double exponential decay of DPH observed in some pure solvents and in phospholipid vesicles. This model assumes that after excitation to a first excited state, there is a rapid interconversion to a lower excited state and that most of the emission occurs from this state. The interconversion rates between the two excited states determine the average lifetime. For DPH in solvents, we find that the interconversion rates are solvent and temperature dependent. For DPH in phospholipid vesicles, we find that the back reaction rate from excited state 2 to excited state 1 (R12) is what determines the fluorescence properties. The phospholipid phase transition affects only this back reaction rate. The model was analyzed globally for a range of solvents, temperatures and vesicle composition. Of the six parameters of the model, only two, the interconversion rates between the two excited states, varied in all different samples examined. For DPH in phospholipid vesicles, there is an additional feature of the model, which is related to the apparent distribution of the rate R12. Significantly better fits were obtained using a continuous lorentzian distribution of interconversion rates. The resulting lifetime distribution was asymmetric and showed a definite narrowing above the phase transition.     

Analysis and modelling of effects of leaf rust and Septoria tritici blotch on wheat growth

A model to predict Septoria tritici blotch (STB) and leaf rust effects on wheat growth was constructed and evaluated in two steps. At the leaf scale, Bastiaans' approach that predicts the relative photosynthesis of a wheat leaf infected with a single disease, was extended to the case of two diseases, one biotrophic and one necrotrophic by considering the leaf rust-STB complex. A glasshouse experiment with flag leaves inoculated either singly with one disease or with two diseases combined was performed to check the leaf damage model. No interaction of the two diseases on photosynthesis loss was observed when they occurred simultaneously on the same leaf. In a second step, the single-leaf model was extended to the canopy scale to model the effects of the leaf rust-STB complex on the growth of a wheat crop. The model predicts the effects of disease on the growth of an affected crop relative to the growth of a healthy crop. The canopy model accounted for different contributions to photosynthetic activity of leaf layers, derived from their position in the canopy and their natural leaf senescence. Treatments differing in nitrogen fertilization, microclimatic conditions, and wheat cultivars were implemented in a field experiment to evaluate the model. The model accurately estimated the effect of disease on crop growth for each cultivar, with differences from experimental values lower than 10%, which suggests that this model is well suited to aid an understanding of disease effects on plant growth. A reduction in green leaf area was the main effect of disease in these field experiments and STB accounted for more than 70% of the reduction in plant growth. Simulations suggested that the production of rust spores may result in a loss of biomass from diseased crops and that stem photosynthesis may need to be considered in modelling diseased crop growth.     

Excitability with multiple thresholds. A new mode of dynamic behavior analyzed in a regulated biochemical system

We analyze in a biochemical model the phenomenon of excitability in which suprathreshold perturbations of a stable steady state are amplified in a pulsatory manner. The two-variable model is that of an autocatalytic enzyme reaction with recycling of product into the substrate. This model was previously studied for the coexistence between two stable periodic regimes (birhythmicity). We show that the multiplicity of dynamic behavioral modes extends to the phenomenon of excitability. Whereas excitable behavior is generally characterized by a single threshold for excitation, two distinct thresholds may coexist in this model. Moreover, in these conditions, two different plateaux are obtained for the response amplitude when the stimulus is gradually increased. By means of phase plane analysis we explain the origin of multiple thresholds for excitability and predict the conditions for their occurrence. Implications of the phenomenon for excitable cells, in particular for neurons, are discussed.     

Cross-bridge model of muscle contraction. Quantitative analysis

We recently presented, in a qualitative manner, a cross-bridge model of muscle contraction which was based on a biochemical kinetic cycle for the actomyosin ATPase activity. This cross-bridge model consisted of two cross-bridge states detached from actin and two cross-bridge states attached to actin. In the present paper, we attempt to fit this model quantitatively to both biochemical and physiological data. We find that the resulting complete cross-bridge model is able to account reasonably well for both the isometric transient data observed when a muscle is subjected to a sudden change in length and for the relationship between the velocity of muscle contraction in vivo and the actomyosin ATPase activity in vitro. This model also illustrates the interrelationship between biochemical and physiological data necessary for the development of a complete cross-bridge model of muscle contraction.     

Global dynamics of microbial competition for two resources with internal storage

We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model. B. Li’s research was partially supported by NSF grants DMS 0211614 and DMS 0616445. H. L. Smith’s research was supported in part by NSF grant DMS 0414270.     

Small-angle neutron-scattering and electron microscope studies of the chicken liver fatty acid synthase

A structural model for the chicken liver fatty acid synthase is proposed based on electron microscope and small-angle neutron-scattering studies of the enzyme. The model has the overall appearance of two side by side cylinders with dimensions of 160 X 146 X 73 A, with each subunit 160 A in length and 73 A in diameter. The model was constructed by dividing each cylinder into three domains having lengths of 32, 82, and 46 A, with the domain structures in the two subunits being related to each other by a dyad axis. The model is consistent with chemical cross-linking studies which indicated that the subunits are arranged in a head to tail fashion. The cross-linking studies further showed that the beta-ketoacyl synthase active site contains a cysteine and a pantetheine residue from adjacent subunits. It is proposed that the domains which catalyze the addition of C2 units from malonate to the growing fatty acid chain lie in the crevice between the two subunits and that the two independent sets of fatty acid-synthesizing centers lie on the major axis of the model on opposite ends of the molecular dyad.     

Mathematical modelling of the intravenous glucose tolerance test

 Several attempts at building a satisfactory model of the glucose-insulin system are recorded in the literature. The minimal model, which is the model currently mostly used in physiological research on the metabolism of glucose, was proposed in the early eighties for the interpretation of the glucose and insulin plasma concentrations following the intravenous glucose tolerance test. It is composed of two parts: the first consists of two differential equations and describes the glucose plasma concentration time-course treating insulin plasma concentration as a known forcing function; the second consists of a single equation and describes the time course of plasma insulin concentration treating glucose plasma concentration as a known forcing function. The two parts are to be separately estimated on the available data. In order to study glucose-insulin homeostasis as a single dynamical system, a unified model would be desirable. To this end, the simple coupling of the original two parts of the minimal model is not appropriate, since it can be shown that, for commonly observed combinations of parameter values, the coupled model would not admit an equilibrium and the concentration of active insulin in the “distant” compartment would be predicted to increase without bounds. For comparison, a simple delay-differential model is introduced, is demonstrated to be globally asymptotically stable around a unique equilibrium point corresponding to the pre-bolus conditions, and is shown to have positive and bounded solutions for all times. The results of fitting the delay-differential model to experimental data from ten healthy volunteers are also shown. It is concluded that a global unified model is both theoretically desirable and practically usable, and that any such model ought to undergo formal analysis to establish its appropriateness and to exclude conflicts with accepted physiological notions. Received: 22 June 1998 / Revised version: 24 February 1999     

金黄色葡萄球菌AgrA/C双组分信号转导模型的构建与功能评价

【背景】抗生素的无序使用加剧了耐药性金黄色葡萄球菌超级菌株的出现,由其引发的感染已成为最难解决的感染性疾患。在生物体系外构建AgrA/C双组分系统的跨膜信号转导过程,对解决金黄色葡萄球菌的耐药性问题和发现新型抗菌药物具有重要的研究意义。【目的】人工模拟构建金黄色葡萄球菌AgrA/C双组分信号转导模型,为生物体外研究金黄色葡萄球菌双组分信号转导的机制及以其为靶点的药物筛选提供新途径。【方法】在大肠杆菌宿主细胞中大量表达AgrA和Agr C蛋白,利用亲和层析和分子筛凝胶层析对其进行分离纯化,利用非放射性凝胶阻滞实验(EMSA)检测AgrA蛋白活性,并检测Agr C激酶活性;进而利用脂质体介导法在体外组装AgrA/C双组分信号转导模型,应用EMSA方法进行评价。【结果】分离纯化得到AgrA和Agr C蛋白,二者纯度均达到90%以上,均具有活性。在生物体系外构建了金黄色葡萄球菌AgrA/C双组分信号转导模型,该系统可增强AgrA对DNA的延滞作用,具有信号传递功能。【结论】初步构建AgrA/C双组分信号转导模型,该模型具有信号传递能力,有望作为针对金黄色葡萄球菌开发新型抗菌药物的筛选平台。     

Modeling the water use efficiency of soybean and maize plants under environmental stresses: application of a synthetic model of photosynthesis-transpiration based on stomatal behavior

Understanding the variability of plant WUE and its control mechanism can promote the comprehension to the coupling relationship of water and carbon cycle in terrestrial ecosystem, which is the foundation for developing water-carbon coupling cycle model. In this paper, we made clear the differences of net assimilation rate, transpiration rate, and WUE between the two species by comparing the experiment data of soybean (Glycine max Merr.) and maize (Zea mays L.) plants under water and soil nutrient stresses. WUE of maize was about two and a half times more than that of soybean in the same weather conditions. Enhancement of water stresses led to the marked decrease of Am and Em of two species, but water stresses of some degree could improve WUE, and this effect was more obvious for soybean. WUE of the two species changed with psiL in a second-order curve relation, and the WUE at high fertilization was higher than that at low fertilization, this effect was especially obvious for maize. Moreover, according to the synthetic model of photosynthesis-transpiration based on stomatal behavior (SMPTSB) presented by Yu et al. (2001), the WUE model and its applicability were discussed with the data measured in this experiment. The WUE estimated by means of the model accorded well with the measured values. However, this model underestimated the WUE for maize slightly, thus further improvement on the original model was made in this study. Finally, by discussing some physiological factors controlling Am and WUE, we made clear the physiological explanation for differences of the relative contributions of stomata- and mesophyll processes to control of Am and WUE, and the applicability of WUE model between the two species. Because the requirement to stomatal conductance by unit change of net assimilation rate is different, the responses of opening-closing activity of stomata to environmental stresses are different between the two species. To obtain the same level of net assimilation rate, soybean has to open its stomata more widely to keep small stomatal resistance, as compared with maize.     

Central Upwind Scheme for a Compressible Two-Phase Flow Model

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.