Modeling study on photosynthetic-light response curves of a C4 plant,maize

Aims A light response curve can reflect a plant’s ability to utilize light, which is also a key tool in determining the relationship between photosynthetic capacity and environmental factors; however the model accuracies concerning the light response curve remain elusive. The objectives of this study were to compare and assess the model accuracies related to a light response curve and the effects of drought. Methods A field rain shelter was used to control the soil water conditions. To obtain photosynthesis parameters from the light response curve and the drought effects, the relevant models (including the rectangular model, non-rectangular hyperbolic model, modified rectangular hyperbolic model, exponential model, quadratic function model, and a newly modified model) were applied to fit the light response curves. The validity of each model was tested by analyzing the differences between the fitted values obtained by the models and the measured values. Important findings The newly modified model has been proved to performing relatively better in accurately describing the light response curve patterns, and credibly obtaining the crucial photosynthetic parameters such as the maximum net photosynthetic rate, light saturation point, light compensation point, and dark respiration rate, especially under high radiation conditions.     

亚热带10种蕨类植物光响应模型拟合及光合特性研究

通过合适的光响应模型来准确计算植物光合参数是研究植物光合特性的重要手段。为深入了解亚热带蕨类植物的光合特性,采用直角双曲线模型、非直角双曲线模型、指数模型和直角双曲线修正模型等4种常用光响应模型分别对10种亚热带蕨类植物进行光响应曲线拟合。通过分析决定系数(R~2)、均方根误差(RMSE)、平均绝对误差(MAE)、光饱和点(LSP)、光补偿点(LCP)、最大净光合速率(P_nmax)、暗呼吸速率(R_d)和表观量子效率(AQE)等9种参数,探讨亚热带蕨类植物的光响应模型拟合效果及其光合特性。结果表明：直角双曲线修正模型和非直角双曲线模型对本研究10种亚热带蕨类植物的拟合效果较好,其中直角双曲线修正模型的LSP拟合效果最好,非直角双曲线模型的拟合精度最高。光合参数的聚类分析和TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)综合评价法表明,10种亚热带蕨类植物的光合特性既具有相似性又存在物种特异性。黑鳞耳蕨(Polystichum makinoi(Tag...     

Enhancement models at high light intensities

The separate package and spillover models of photosynthetic enhancement are generalized and extended to light saturation assuming hyperbolic or exponential rate versus intensity curves. The available data are more consistent with the exponential model at high light intensities. Two significant conclusions follow: (a) the decreases in enhancement observed at high light intensities are accounted for by the curvatures of the light intensity curves for photosynthesis, and (b) nonlinearity of rate versus intensity curves may be sufficient to reduce enhancement greatly even when the intensity curves appear linear.     

木荷种源间光合作用参数分析

基于直角双曲线修正模型估算3个不同纬度的木荷种源(开平、太平和永丰种源)光补偿点、饱和点、最大净光合速率等参数,以便为评价不同木荷种源对环境的适应能力和优良种源选择等提供科学依据。结果表明:在3个不同纬度种源中,开平种源具有最高的净光合速率、最大净光合速率和较高的表观量子效率,且其生长速率最快;太平种源光饱和点最高,但其净光合速率、表观量子效率和最大净光合速率最低,其生长速率也最低;永丰种源具有较高的净光合速率、最大净光合速率和表观量子效率,其生长速率略高于太平种源。3个不同纬度木荷种源中,南部开平种源对当地环境具有较强的适应能力和生长潜力,具有较高的推广应用价值。     

Kinetics of the light-driven proton movement in model membranes containing bacteriorhodopsin.

The short-circuit photoresponse of model membranes containing bacteriorhodopsin to short (35 ms) and long (3.5 s) light pulses is described. It is shown that if the light pulse is short compared with the charging and discharging times of the model membrane, the temporal response of the light-driven proton pump can be measured. Photoactive planar model membranes were formed both from biomolecular lipid membranes and from solid 6-micrometers thick Teflon septa coated with lipid and bacteriorhodopsin. The kinetic response of the pump is independent of the planar model membrane system in which it is incorporated. Experimental evidence indicates that the shape of the leading and trailing edges of the photoresponse curve for the pump deviates from simple exponential behavior. The short-circuit photoresponse of spinach chloroplast in a planar model membrane was also studied for comparison purposes.     

Exponential function of chymotrypsin action

Enzyme kinetics are usually described by the hyperbolic Michaelis-Menten equation, but they can also be described by the following exponential function: -dS/dt = Vm [1 - exp (-S/Km)]. The time-dependent decrease of the substrate (-dS/dt) is an exponential function of maximal velocity (Vm), the Michaelis constant (Km) and the actual substrate value (S). This exponential function is based on the assumption that the association of the substrate-enzyme complex is a concentration-dependent process, whereas the transformation of the substrate-enzyme complex is time-dependent. It can be shown that this exponential function is a more general solution of which the hyperbolic Michaelis-Menten equation is a special derivative under the conditions of low substrate (S) and high constant (Km) values. If the association process is time-dependent, the decline in substrate values will show a more concave curve. However, exponential functions in general are more concave than hyperbolic functions. Probably, therefore, the enzyme action of chymotrypsin could be described more appropriately by the present exponential function than by the conventional hyperbolic function.     

Delays in inactivation development and activation kinetics in myxicola giant axons

Na inactivation was studied in Myxicola (two-pulse procedure, 6-ms gap between conditioning and test pulses). Inactivation developed with an initial delay (range 130-817 microseconds) followed by a simple exponential decline (time constant tau c). Delays (deviations from a simple exponential) are seen only for brief conditioning pulses were gNa is slightly activated. Hodgkin-Huxley kinetics with series resistance, Rs, predict deviations from a simple exponential only for conditioning pulses that substantially activate gNa. Reducing INa fivefold (Tris substitution) had no effect on either tau c or delay. Delay in not generated by Rs or by contamination from activation development. The slowest time constant in Na tails is approximately 1 ms (Goldman and Hahin, 1978) and the gap was 6 ms. Shortening the gap to 2 ms had no effect on either tau c or delay. Delay is a true property of the channel. Delay decreased with more positive conditioning potentials, and also decreased approximately proportionally with time to peak gNa during the conditioning pulse, as expected for sequentially coupled activation and inactivation. In a few cases the difference between Na current values for brief conditioning pulses and the tau c exponential could be measured. Difference values decayed exponentially with time constant tau m. The inactivation time course is described by a model that assumes a process with the kinetics of gNa activation as a precursor to inactivation.     

From Experiment to Theory: What Can We Learn from Growth Curves?

Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic–exponential, exponential–linear, exponential–linear–saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.     

The effect of p-phenylenediamine and dibromothymoquinone on the postosynthetic electron transport and proton pump activities of isolated barley chloroplats

The effect of p-phenylenediamine and dibromothymoquinone (DBMIB) on photosynthetic electron transport was studied using thylakoids from barley chloroplasts. p-Phenylenediamine (0.1 mm) converted the light saturation curve for electron transport between water and ferricyanide from a hyperbolic one saturating at low light intensity into a linear one which was not saturated at any light intensity studied. DBMIB at a concentration of 1 μm had little inhibitory effect on the basal electron transport activity of coupled thylakoids in either the presence or the absence of 0.1 mmp-phenylenediamine. However, activity was inhibited by DBMIB after uncoupling with 60 mm methylamine. These results may indicate that there is a rate-limiting step in electron transport at or after plastoquinone which is circumvented by phenylenediamine. Its appearance or elaboration could explain the conversion of a linear light saturation curve to a hyperbolic one during chloroplast development. The movement of protons into thylakoids upon illumination was reduced about 50% by 1 μm DBMIB, a concentration which maximally inhibits ferricyanide-Hill activity after uncoupling. Fifty percent inhibition occurred irrespective of whether or not phenylenediamine was included in the reaction mixture. Most of the residual DBMIB-insensitive pH change was inhibited by 3 μm 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea (DCMU), suggesting that photosystem II was required for the latter activity. In the presence of both DBMIB and DCMU, proton pump activity could be reestablished by including isoascorbate and p-phenylenediamine in the reaction mixture.     

A simple model of radiation action in cells based on a repair saturation mechanism.

This paper describes a new theoretical model for the response of cells to radiation. This model is based on the existence of a lesion interaction mechanism in the cell, along with processes of recovery and repair that are able to repair the damage produced by radiation in the cells. Such a mechanism makes the cells evolve from a sublethal state to a normal one. Repair and recovery are not instantaneous, but are produced over an average period that we suppose is represented by an exponential function. The probability of cellular recovery and repair is also affected by radiation. These mechanisms become less probable as the dose administered to the cell increases (repair saturation mechanism). This model is suitable for instantaneous doses as well as for arbitrary dose rates. Results obtained from the model for normal tissues and low doses are approximately equal to those obtained by the linear-quadratic model or by the incomplete repair model. The model yields a survival curve with an exponential tail for high doses and for long periods of irradiation.     

The effect of myoglobin-facilitated oxygen transport on the basal metabolism of papillary muscle.

A mathematical model of oxygen diffusion into cylindrical papillary muscles is presented. The model partitions total oxygen flux into its simple and myoglobin-facilitated components. The model includes variable sigmoidal, exponential, or hyperbolic functions relating oxygen partial pressure to both fractional myoglobin saturation and rate of oxygen consumption. The behavior of the model was explored for a variety of saturation- and consumption-concentration relations. Facilitation of oxygen transport by myoglobin was considerable as indexed both by the elevation of oxygen partial pressure on the longitudinal axis of the muscle and by the fraction of total oxygen flux at the muscle center contributed by oxymyoglobin. Despite its facilitation of oxygen flux at the muscle center, myoglobin made only a negligible contribution to the total oxygen consumption averaged over the muscle cross-section. Hence the presence of myoglobin fails to explain either the experimentally determined basal metabolism-muscle radius relation or the stretch effect observed in isolated papillary muscle.     

光响应曲线的指数改进模型与常用模型比较

光响应曲线的参数是研究植物生理状态的重要指标, 常用的光响应曲线模型无法准确地计算出光饱和点和最大净光合速率。该文利用光响应曲线新模型——指数改进模型、直角双曲线模型、直角双曲线修正模型、非直角双曲线模型和指数模型, 拟合高粱(Sorghum bicolor)、苋(Amaranthus tricolor)、大麦(Hordeum vulgare)和半夏(Pinellia ternata)的光响应曲线, 并随机选取部分数据进行检验, 得到了各模型计算出的主要生理参数, 并对这些数据进行了比较分析, 讨论了各模型之间的优缺点和准确性, 描述了C₃、C₄植物光响应的适宜性。结果表明, 基于C₃植物得到的指数改进模型和直角双曲线修正模型能较准确地计算出C₃、C₄植物饱和光强和最大净光合速率, 并在描述光响应曲线时比另外3个模型具有更高的精确性和适宜性。实验结果可为光响应曲线模型在C₃和C₄光合途径植物中的应用提供参考。     

Optical Saturation as a Versatile Tool to Enhance Resolution in Confocal Microscopy

One of the most actively developing areas in fluorescence microscopy is the achievement of spatial resolution below Abbe's diffraction limit, which restricts the resolution to several hundreds of nanometers. Most of the approaches in use at this time require a complex optical setup, a difficult mathematical treatment, or usage of dyes with special photophysical properties. In this work, we present a new, to our knowledge, approach in confocal microscopy that enhances the resolution moderately but is both technically and computationally simple. As it is based on the saturation of the transition from the ground state to the first excited state, it is universally applicable with respect to the dye used. The idea of the method presented is based on a principle similar to that underlying saturation excitation microscopy, but instead of applying harmonically modulated excitation light, the fluorophores are excited by picosecond laser pulses at different intensities, resulting in different levels of saturation. We show that the method can be easily combined with the concept of triplet relaxation, which by tuning the dark periods between pulses helps to suppress the formation of a photolabile triplet state and effectively reduces photobleaching. We demonstrate our approach imaging GFP-labeled protein patches within the plasma membrane of yeast cells.     

Simple growth laws and selection consequences

It is commonly thought that various types of population growth can be satisfactorily modelled as deviations from an inherently exponential (malthusian) growth law. Consideration of kinetic results from research on the origin of life, laser physics and more-conventional population dynamics makes it clear, however, that in certain cases the simplest and mechanistically most satisfactory assumption is either a basic subexponential or a hyperbolic growth law. Although these simple growth laws cannot be used instead of more-complicated models of density-dependent population growth when exact quantities are important, the insight gained by thinking them over can be substantial. Ideas about species packing, for example, await reconsideration.     

岩溶植物光合-光响应曲线的两种拟合模型比较

用直角双曲线和非直角双曲线两种模型,对桂林岩溶区石山植物红背山麻杆（Alchornea trewioides）、九龙藤（Bauhinia championii）、青檀（Pteroceltis tatarinowii）和圆叶乌桕（Sapium rotundifolium）光合作用的光响应曲线进行拟合。结果表明,直角双曲线拟合的表观量子效率（α）、最大净光合速率（Pmax）、暗呼吸速率（Rd）、光补偿点（Lcp）和光饱和点（Lφ）数值均高于相应的非直角双曲线拟合结果;直角双曲线模型拟合的参数值大小和曲线变化趋势不符合实际情况;非直角双曲线模型拟合结果更符合生理意义。红背山麻杆和九龙藤具有较高的表观量子效率和较低的光补偿点,对光能的利用效率和耐荫性均强于圆叶乌桕和青檀。     

Denitrification and a numerical modelling approach for shallow waters

A numerical model (`DiffDeni') has been developed to describe the disappearance of nitrate from the water column of 10–200 cm deep waters. The disappearance is caused by bacterial denitrification in the sediments. The model employs the molecular diffusion constant, an acceleration factor describing eddy diffusion, and three bacterial growth constants, viz. the inoculum size, the maximum growth rate and the half saturation constant for the hyperbolic process. The values of these system-constants were varied over a wide range. The curves obtained were compared with the curves for well-defined situations, viz. in which diffusion takes place without any or with a complete, immediate reaction. These cases have analytical solutions, and were simulated closely by the model `DiffDeni', though this model is based on different assumptions. It is shown that, when the bacterial growth rate is above a critical value, a negative exponential curve describes the nitrate disappearance well. On the other hand, a more complicated negative exponential equation can be used to describe the first phase of this denitrification in which bacterial activity is low and nitrate behaves as a conservative compound. The change-over period from phase 1 (no reaction) to phase 2 (complete, immediate reaction) which may vary between <1 and 50 days cannot be described analytically (mathematically correctly). The influence of temperature on denitrification is assessed and it is shown that both bacterial activity and diffusion may influence the denitrification rate.     

Comparison of steady-state kinetics of thiophosphorylated versus unphosphorylated smooth muscle myosin

(i) The steady-state kinetic data obtained with purified gizzard and uterus smooth muscle myosins indicated the presence of a plateau region on the substrate-saturation curves. Hill plots of these data provided evidence for mixed positive and negative cooperative interactions. In contrast, when gizzard myosin was prepared according to the method of A. Sobieszek and R.D. Bremel (1975, Eur. J. Biochem.55, 49–60), the saturation curve in the presence of CaATP was hyperbolic and no cooperativity of the binding site(s) was discerned. However, in the presence of MgATP although the curve appeared hyperbolic the Hill plot of the data was biphasic with negative cooperativity at low MgATP concentration, (ii) When thiophosphorylated gizzard myosin was used for kinetic analysis, the plateau region in the presence of MnATP was eliminated from the saturation curve and this curve became hyperbolic. However, in the presence of MgATP, although the plateau was almost eliminated, the saturation curve was still biphasic with either no or greatly reduced negative cooperativity of binding sites at low MgATP concentrations but positive cooperativity of binding at high MgATP concentrations. In addition, the thiophosphorylation of myosin also increased the K_m and V of MgATP and MnATP, thus indicating weaker affinity for these substrates with thiophosphorylated myosin. (iii) Gizzard myosin also hydrolyzed other nucleotides (the order of rates being CTP = ITP > ATP = UTP > GTP), therefore saturation kinetics using different nucleotides as substrates was also carried out. The saturation curves with each nucleotide were different i.e., hyperbolic with CTP, sigmoid with GTP, hyperbolic with biphasic Hill plot with ITP, and possessing plateau with UTP. In addition, it was observed that the kinetic pattern with each nucleotide was very sensitive to temperature and pH.     

The impulse response of Chlamydomonas reinhardii in nitrite-limited chemostat culture

This article presents a clear experimental determination of the behavior of nutrient uptake rate, mean cell nutrient content, and specific growth rate following the injection of pulses of additional limiting nutrient into a chemostat culture of Chlamydomonas reinhardii. The uptake rate per cell is a hyperbolic function of external nutrient concentration. The specific growth rate is related to the mean cell nutrient content by a hysteresis loop. The data obtained is used to test the performance of the Caperon-Droop mean cell quota model. It is demonstrated that this model cannot be used under severe transient conditions, even when modified by the introduction of a discrete time delay, a simple memory function, or time-dependent intracellular nutrient processing.