Modeling photoheterotrophic growth kinetics of Rhodospirillum rubrum inrectangular photobioreactors

Based on a previously established model for radiant light transfer in photobioreactors (PBR), taking into account absorption and scattering of light, a new knowledge model for coupling radiant light energy available and local growth kinetics in PBRs for the photoheterotrophic bacteria Rhodospirillum rubrum is discussed. A revised method is presented for the calculation of the absorption and scattering coefficients. The specific characteristics of the electron-transfer chains in such microorganisms leads to definition of three different metabolic zones in the PBR, explaining the behavior of mean kinetics observed in a wide range of incident light fluxes. The model is validated in rectangular PBRs for five different carbon sources and proved robust and fully predictive. This approach can be considered for simulation and model-based predictive control of PBRs cultivating photoheterotrophic microorganisms.     

Simulation of algae growth in a bench-scale bubble column reactor

The growth of the marine red microalga Porphyridium sp. in a bubble-column photobioreactor was simulated. The proposed model constitutes a dynamic integration of the kinetics of photosynthesis and photoinhibition with the fluid dynamics of the bubble column, including the effects of shear stress on the kinetics of growth. The kinetic data used in the model were obtained in independent experiments run in a thin-film photobioreactor with defined light/dark cycles. The maintenance term was modified to take into account the effects of liquid flow in the bioreactor on the growth rate. A hybrid method proposed for the approximate solution of the equations gave an appreciable reduction of the calculation time. Extrapolations of the model indicated the possibility of predicting the optimal diameter for an assembly of bubble column photobioreactors. Satisfactory fit was found with the experimental results of biomass growth in a 13-liter bubble column.     

The kinetics of photoinactivation and long-term photosensitivity of pigmented and nonpigmented strains of the smut fungusUstilago violacea

White, pink, pumpkin, and yellow strains ofUstilago violacea containing high and low levels of cytochrome c and various carotenes were subjected to high light intensities to characterize the kinetics of photoinactivation. Additionally, these strains were grown at two light intensities to characterize their long-term resistance to photoinactivation. The orange strain 2.D37291S and yellow strain 1.C2y had the highest carotene contents and were the most light resistant in the kinetics and growth experiments. The pink strains 2.C425, AB278a-1, and 1.C421 accumulated cytochrome c as well as carotenes. These strains were slightly more photosensitive than the yellow or orange strains in the kinetics experiment but were much more sensitive in the growth experiment. The phytoene-containing white strain 2.C419, which contains a small amount of cytochrome c, had a high level of resistance to light in the kinetics and growth experiments. The carotene-less strains were most sensitive in the kinetics experiment but not in the growth experiment. The overall photosensitivity ofU. violacea strains is related to the carotene and cytochrome c contents.     

Enhancing the growth of Physcomitrella patens by combination of monochromatic red and blue light - a kinetic study

In the current work we demonstrate the relevance of monochromatic light conditions in moss plant cell culture. Light intensity and illumination wavelength are important cultivation parameters due to their impact on growth and chlorophyll formation kinetics of the moss Physcomitrella patens. This moss was chosen as a model organism due to its capability to produce complex recombinant pharmaceutical proteins. Filamentous moss cells were cultivated in mineral medium in shaking flasks. The flasks were illuminated by light emitting diodes (LED) providing nearly monochromatic red and blue light as well as white light as a reference. A maximum growth rate of 0.78 day((1) was achieved under additional CO(2) aeration and no growth inhibition was observed under high light illumination. The application of dual red and blue light is the most effective way to reach high growth and chlorophyll formation rates while minimizing energy consumption of the LEDs. These observations are discussed as effects of photo sensory pigments in the moss. The combination of monochromatic red and blue light should be considered when a large scale process is set up.     

Shoot and Root Activities During Steady-state Plant Growth

A simple model for steady-state plant growth is described. Thegrowth constant, measured during steady-state exponential growth,is related to the specific activities of the shoot and the root,enabling the effects of certain environmental variables (light,carbon dioxide and nitrogen) on the growth constant to be examined.The model is used to interpret data on the growth kinetics ofwheat (Macdowall, 1972a, b, c).     

Phytoplankton thermal responses adapt in the absence of hard thermodynamic constraints

To better predict how populations and communities respond to climatic temperature variation, it is necessary to understand how the shape of the response of fitness-related rates to temperature evolves (the thermal performance curve). Currently, there is disagreement about the extent to which the evolution of thermal performance curves is constrained. One school of thought has argued for the prevalence of thermodynamic constraints through enzyme kinetics, whereas another argues that adaptation can—at least partly—overcome such constraints. To shed further light on this debate, we perform a phylogenetic meta-analysis of the thermal performance curves of growth rate of phytoplankton—a globally important functional group—controlling for environmental effects (habitat type and thermal regime). We find that thermodynamic constraints have a minor influence on the shape of the curve. In particular, we detect a very weak increase of maximum performance with the temperature at which the curve peaks, suggesting a weak “hotter-is-better” constraint. Also, instead of a constant thermal sensitivity of growth across species, as might be expected from strong constraints, we find that all aspects of the thermal performance curve evolve along the phylogeny. Our results suggest that phytoplankton thermal performance curves adapt to thermal environments largely in the absence of hard thermodynamic constraints.     

Light and dark adaptation in Phycomyces phototropism

Light and dark adaptation of the phototropism of Phycomyces sporangiophores were analyzed in the intensity range of 10(-7)-6 W X m- 2. The experiments were designed to test the validity of the Delbruck- Reichardt model of adaptation (Delbruck, M., and W. Reichardt, 1956, Cellular Mechanisms in Differentiation and Growth, 3-44), and the kinetics were measured by the phototropic delay method. We found that their model describes adequately only changes of the adaptation level after small, relatively short intensity changes. For dark adaptation, we found a biphasic decay with two time constants of b1 = 1-2 min and b2 = 6.5-10 min. The model fails for light adaptation, in which the level of adaptation can overshoot the actual intensity level before it relaxes to the new intensity. The light adaptation kinetics depend critically on the height of the applied pulse as well as the intensity range. Both these features are incompatible with the Delbruck-Reichardt model and indicate that light and dark adaptation are regulated by different mechanisms. The comparison of the dark adaptation kinetics with the time course of the dark growth response shows that Phycomyces has two adaptation mechanisms: an input adaptation, which operates for the range adjustment, and an output adaptation, which directly modulates the growth response. The analysis of four different types of behavioral mutants permitted a partial genetic dissection of the adaptation mechanism. The hypertropic strain L82 and mutants with defects in the madA gene have qualitatively the same adaptation behavior as the wild type; however, the adaptation constants are altered in these strains. Mutation of the madB gene leads to loss of the fast component of the dark adaptation kinetics and to overshooting of the light adaptation under conditions where the wild type does not overshoot. Another mutant with a defect in the madC gene shows abnormal behavior after steps up in light intensity. Since the madB and madC mutants have been associated with the receptor pigment, we infer that at least part of the adaptation process is mediated by the receptor pigment.     

Linear-Arrhenius models for bacterial growth and death and vitamin denaturations

Summary The development of the quantitative, linear-Arrhenius model of Davey for predicting bacterial growth and death (inactivation) is reviewed. The applicability of the model to published data from independent researchers for both the growth phase and lag phase, involving combined environmental factors (T, a _w) is illustrated. Also illustrated is its applicability to thermal inactivation kinetics and vitamin denaturation (with combinedT, pH). Integration of the model to produce complex models describing the thermal sterilization of liquid is demonstrated. Advantages of the model, including its simplicity and the fact that the coefficients to build the model can be obtained easily by relatively unsophisticated users, are highlighted in a comparison with other models.Mention of brand or firm names does not constitute an endorsement by the US Department of Agriculture over others of a similar nature not mentioned.     

Thermal inactivation, denaturation and aggregation of mitochondrial aspartate aminotransferase

A comparative study of thermal denaturation and inactivation of aspartate aminotransferase from pig heart mitochondria (mAAT) has been carried out (10 mM Na phosphate buffer, pH 7.5). Analysis of the data on differential scanning calorimetry shows that thermal denaturation of mAAT follows the kinetics of irreversible reaction of the first order. The kinetics of thermal inactivation of mAAT follows the exponential law. It has been shown that the inactivation rate constant (k_in) is higher than the denaturation rate constant (k_den). The k_in/k_den ratio decreases from 28.8 ± 0.1 to 1.30 ± 0.09 as the temperature increases from 57.5 to 77 °C. The kinetic model explaining the discrepancy between the inactivation and denaturation rates has been proposed. The size of the protein aggregates formed at heating of mAAT at a constant rate (1 °C min^{− 1}) has been characterized by dynamic light scattering.     

Microalgal kinetics — a guideline for photobioreactor design and process development

Kinetics generally describes bio‐(chemical) reaction rates in dependence on substrate concentrations. Kinetics for microalgae is often adapted from heterotrophs and lacks mechanistic foundation, e.g. for light harvesting. Using and understanding kinetic equations as the representation of intracellular mechanisms is essential for reasonable comparisons and simulations of growth behavior. Summarizing growth kinetics in one equation does not yield reliable models. Piecewise linear or rational functions may mimic photosynthesis irradiance response curves, but fail to represent the mechanisms. Our modeling approach for photoautotrophic growth comprises physical and kinetic modules with mechanistic foundation extracted from the literature. Splitting the light submodel into the modules for light distribution, light absorption, and photosynthetic sugar production with independent parameters allows the transfer of kinetics between different reactor designs. The consecutive anabolism depends among others on nutrient concentrations. The nutrient uptake kinetics largely impacts carbon partitioning in the reviewed stoichiometry range of cellular constituents. Consecutive metabolic steps mask each other and demand a maximum value understandable as the minimum principle of growth. These fundamental modules need to be clearly distinguished, but may be modified or extended based on process conditions and progress in research. First, discussion of kinetics helps to understand the physiological situation, for which ranges of parameter values are given. Second, kinetics should be used for photobioreactor design, but also for gassing and nutrient optimization. Numerous examples are given for both aspects. Finally, measuring kinetics more comprehensively and precisely will help in improved process development.     

Growth kinetics of the photosynthetic bacterium Chlorobium thiosulfatophilum in a fed-batch reactor

Hydrogen sulfide dissolved in water can be converted to elementary sulfur or sulfate by the photosynthetic bacterium Chlorobium thiosulfatophilum. Substrate inhibition occurred at sulfide concentrations above 5.7 mM. Light inhibition was found at average light intensities of 40,000 lux in a sulfide concentration of 5 mM, where no substrate inhibition occurred. Light intensity, the most important growth parameter, was attenuated through both scattering by sulfur particles and absorption by the cells. Average cell and sulfur particle sizes were 1.1 and 9.4 mum, respectively. Cells contributed 10 times as much to the turbidity as sulfur particles of the same weight concentration. The light attenuation factor was mathematically modeled, considering both the absorption and scattering effects based on the Beer-Lambert law and the Rayleigh theory, which were introduced to the cell growth model. Optimal operational conditions relating feed rate vs. light intensity were obtained to suppress the accumulation of sulfate and sulfide and save light energy for 2- and 4-L fed-batch reactors. Light intensity should be greater for the same performance (H(2)S removal rate/unit cell concentration) in larger reactors due to the scaleup effect on light transmission. Knowledge of appropriate growth kinetics in photosynthetic fed-batch reactors was essential to increase feed rate and light intensity and therefore cell growth. A mathematical model was developed that describes the cell growth by considering the light attenuation factor due to scattering and absorption and the crowding effect of the cells. This model was in good agreement with the experimental results. (c) 1992 John Wiley & Sons, Inc.     

A structured model for simulation of cultures of the cyanobacterium Spirulina platensis in photobioreactors: I. Coupling between light transfer and growth kinetics

The study of the interactions between physical limitation by light and biological limitations in photobioreactors leads to very complex partial differential equations. Modeling of light transfer and kinetics and the assessment of radiant energy absorded in photoreactors require an equation including two parameters for light absorption and scattering in the culture medium. In this article, a simple model based on the simplified, monodimensional equation of Schuster for radiative transfer is discussed. This approach provides a simple way to determine a working illuminated volume in which growth occurs, therefore allowing indentification of kinetic parameters. These parameters might then be extended to the analysis of more complex geometries such as cylindrical reactors. Moreover, this model allows the behavior of batch or continuous cultures of cyanobacteria under light and mineral limitations to be predicted. (c) 1992 John Wiley & Sons, Inc.     

Nucleation and growth of insulin fibrils in bulk solution and at hydrophobic polystyrene surfaces

A technique was developed for studying the nucleation and growth of fibrillar protein aggregates. Fourier transform infrared and attenuated total reflection spectroscopy were used to measure changes in the intermolecular beta-sheet content of bovine pancreatic insulin in bulk solution and on model polystyrene (PS) surfaces at pH 1. The kinetics of beta-sheet formation were shown to evolve in two stages. Combined Fourier transform infrared, dynamic light scattering, atomic force microscopy, and thioflavin-T fluorescence measurements confirmed that the first stage in the kinetics was related to the formation of nonfibrillar aggregates that have a radius of 13 +/- 1 nm. The second stage was found to be associated with the growth of insulin fibrils. The beta-sheet kinetics in this second stage were used to determine the nucleation and growth rates of fibrils over a range of temperatures between 60 degrees C and 80 degrees C. The nucleation and growth rates were shown to display Arrhenius kinetics, and the associated energy barriers were extracted for fibrils formed in bulk solution and at PS surfaces. These experiments showed that fibrils are nucleated more quickly in the presence of hydrophobic PS surfaces but that the corresponding fibril growth rates decrease. These observations are interpreted in terms of the differences in the attempt frequencies and energy barriers associated with the nucleation and growth of fibrils. They are also discussed in the context of differences in protein concentration, mobility, and conformational and colloidal stability that exist between insulin molecules in bulk solution and those that are localized at hydrophobic PS interfaces.     

Modelling of growth and product formation of Porphyridium purpureum

In this contribution experimental data and simulations of growth and product formation of the unicellular microalgae Porphyridium purpureum are presented. A mathematical model has been developed for a better understanding of growth and product formation in production plants. The model has been refined with the results of several cultivations in a new photobioreactor designed especially for the study of microalgal kinetics under highly defined illumination conditions. In this photobioreactor light is generated by an external light source and then distributed by means of optical fibres into an internal draft tube which also serves as irradiation element. All cultivations were performed in turbidostate mode. The influence of different light intensity changes, including stepwise change and light-dark cycles in the range from millisecond to second, has been investigated and the results were integrated into the mathematical model. The structured mathematical model consists of three levels: metabolic flux, control of macromolecules and the reactor level. A new linear optimization approach has been realized, enabling the model to describe even very different cultivation conditions. Output variables are among others the commercially interesting macromolecules of the microalgae, e.g. polysaccharides, pigments and polyunsaturated fatty acids. Thus, reliable predictions of the specific production rates of these products are possible for the production in a larger scale.     

Dynamics of the Elongation of Internodes in Maize (Zea mays L.). Effects of Shade Treatment on Elongation Patterns

The dynamics of elongation of individual maize internodes havepreviously been characterized under standard agronomic conditions.In this paper these dynamics are compared with those under ashading treatment. Shading was applied after the tip appearanceof leaf 6, using a black net that transmitted 20% of light,without altering spectral composition. Internode length wasdetermined as a function of thermal time by measuring the verticaldisplacement of individual leaf collars. Shading slowed plantdevelopment and caused significant reductions in internode length.The onset of the linear phase of elongation was delayed by shading,but its duration was not affected. The reduction in the linearelongation rate was almost totally responsible for the reductionin the final length of phytomers in the shade treatment. Theco-ordination between collar emergence and the onset of linearelongation remained. These results support the contention thatthe kinetics of internode elongation are controlled by the emergenceof leaf collars. Copyright 2000 Annals of Botany Company Zea mays L., internode, elongation, dynamics, model, shade, light, phytomer, stem, thermal time, photomorphogenesis     

Light adaptation of bacteriorhodopsin correlates with dielectric spectral kinetics in purple membrane

The retinal protein, bacteriorhodopsin (bR), has several potential bioelectronic applications and it is considered as a model for G-protein coupled receptors. Its electrical parameters, therefore, deserve particular attention. Such parameters could be determined by virtue of studying its dielectric spectrum in the low frequency range (20 Hz-1 MHz). The kinetics of dark-light adaptation of bR is reported in terms of electrical parameters of the purple membrane (PM) containing bR. The data have exhibited sudden pronounced increase in the ac-conductivity, upon illuminating the dark-adapted bR (DA-bR), which may be considered in further implications of bR for biotechnological applications. These changes turned out to be composed of, at least, two growing exponential components: one relatively fast followed by slower one. Their lifetime ratio exhibited decreases with increasing the frequency; meanwhile, their amplitude ratio displayed very exciting behavior at significant frequencies. This may correlate the kinetics of light adaptation to relaxations in PM. Moreover, the light adaptation has been observed to cause initial fast and large decreases in dc-conductivity with subsequent slower and smaller decreases. Changing the conductivity during the time of light adaptation reflects changes in the surface charge of the PM. The lifetimes of these events, therefore, help follow the kinetics of the pathway of conformational changes that might be occurring during light adaptation. The dipole moment (permanent and induced) of PM, in addition to, its size showed one exponential growth of comparable lifetime (approximately 7 min) during the light adaptation. The variation in PM size from dark to light state should be in keeping with that diffusion may influence the three-dimensional data storage in data processing based on bR.     

Short term phytochrome control of oat coleoptile and pea epicotyl growth

Continuous recordings of the effect of light on oat (Avena sativa L. cv. Victory) coleoptile and pea (Pisum sativum L. cv. Alaska) epicotyl growth were made. Using a single excised coleoptile 10 minutes of red light was found to promote growth after a latent period of 46 minutes. The stimulation was transient and was not far red-reversible. Blue and far red light also promoted growth with similar kinetics. The action of continuous red or far red light was similar to that of 10-minute light. The growth of the intact pea third internode (as well as excised segments) was strongly inhibited by red light, with a latent period of 80 minutes. This effect was far red-reversible, and far red and blue light caused only a slight inhibition of growth.     

The study of amorphous aggregation of tobacco mosaic virus coat protein by dynamic light scattering

The kinetics of heat-induced and cetyltrimethylammonium bromide induced amorphous aggregation of tobacco mosaic virus coat protein in Na(+)/Na(+) phosphate buffer, pH 8.0, have been studied using dynamic light scattering. In the case of thermal aggregation (52 degrees C) the character of the dependence of the hydrodynamic radius (R(h)) on time indicates that at certain instant the population of aggregates is split into two components. The size of the aggregates of one kind remains practically constant in time, whereas the size of aggregates of other kind increases monotonously in time reaching the values characteristic of aggregates prone to precipitation (R(h)=900-1500 nm). The construction of the light scattering intensity versus R(h) plots shows that the large aggregates (the start aggregates) exist in the system at the instant the initial increase in the light scattering intensity is observed. For thermal aggregation the R(h) value for the start aggregates is independent of the protein concentration and equal to 21.6 nm. In the case of the surfactant-induced aggregation (at 25 degrees C) no splitting of the aggregates into two components is observed and the size of the start aggregates turns out to be much larger (107 nm) than on the thermal aggregation. The dependence of R(h) on time for both heat-induced aggregation and surfactant-induced aggregation after a lapse of time follows the power law indicating that the aggregation process proceeds in the kinetic regime of diffusion-limited cluster-cluster aggregation. Fractal dimension is close to 1.8. The molecular chaperone alpha-crystallin does not affect the kinetics of tobacco mosaic virus coat protein thermal aggregation.