A structured model for simulation of cultures of the cyanobacterium Spirulina platensis in photobioreactors: II. Identification of kinetic parameters under light and mineral limitations

A structured model for the culture of cyanobacteria in photobioreactors is developed on the basis of Schuster's approximations for radiative light transfer. This model is therefore limited to monodimensional geometries and kinetic aspects.Light-harvesting pigments play a crucial role in defining the profile of radiative transfer inside the culture medium and in controlling the metabolism, particularly the metabolic deviations induced by mineral limitations. Modeling therefore requires the biomass to be divided into several compartments, among which the light-harvesting compartment allows a working illuminated volume to be defined within the photobioreactor. This volume may change during batch cultures, largely decreasing as pigment concentration increases during growth but increasing as pigments are consumed during mineral limitation. This approach enables, in photobioreactors of simple parallelepipedic, geometries, kinetic parameters to be determined with high accuracy; this may then be extended to vessels of more complex geometries, such as cylindrical photobioreactors.The model is applied to controlled batch cultures of the cyanobacterium Spirulina platensis in parallelepipedic photobioreactors to assess its ability to predict the behavior of these microorganisms in conditions of light and mineral limitations. Results allowed the study of optimal operating condition for continuous cultures to be approached (c) 1992 John Wiley & Sons, Inc.     

On the quenching of the fluorescence yield in photosynthetic systems

A modified matrix model describing transfer of excitation energy in the photosynthetic pigment system is discussed. In addition to the antenna pigments and reaction centers of the simple matrix model, a coupling complex is postulated mediating energy transfer between antenna and reaction centers. The values of the parameters describing the transfer properties of the coupling complex can be chosen in such a way that a number of recent unexplained measurements of fluorescence properties of various purple bacteria can be described. If such coupling complexes are present in oxygen evolving organisms, some of their properties must be different from those of purple bacteria.     

A “parallel plate” electrostatic model for bimolecular rate constants applied to electron transfer proteins

A “parallel plate” model describing the electrostatic potential energy of protein-protein interactions is presented that provides an analytical representation of the effect of ionic strength on a bimolecular rate constant. The model takes into account the asymmetric distribution of charge on the surface of the protein and localized charges at the site of electron transfer that are modeled as elements of a parallel plate condenser. Both monopolar and dipolar interactions are included. Examples of simple (monophasic) and complex (biphasic) ionic strength dependencies obtained from experiments with several electron transfer protein systems are presented, all of which can be accommodated by the model. The simple cases do not require the use of both monopolar and dipolar terms (i.e., they can be fit well by either alone). The biphasic dependencies can be fit only by using dipolar and monopolar terms of opposite sign, which is physically unreasonable for the molecules considered. Alternatively, the high ionic strength portion of the complex dependencies can be fit using either the monopolar term alone or the complete equation; this assumes a model in which such behavior is a consequence of electron transfer mechanisms involving changes in orientation or site of reaction as the ionic strength is varied. Based on these analyses, we conclude that the principal applications of the model presented here are to provide information about the structural properties of intermediate electron transfer complexes and to quantify comparisons between related proteins or site-specific mutants. We also conclude that the relative contributions of monopolar and dipolar effects to protein electron transfer kinetics cannot be evaluated from experimental data by present approximations.     

A Flexible Calibration Method Using the Planar Target with a Square Pattern for Line Structured Light Vision System

A flexible calibration approach for line structured light vision system is proposed in this paper. Firstly a camera model is established by transforming the points from the 2D image plane to the world coordinate frame, and the intrinsic parameters of camera can be obtained accurately. Then a novel calibration method for structured light projector is presented by moving a planar target with a square pattern randomly, and the method mainly involves three steps: first, a simple linear model is proposed, by which the plane equation of the target at any orientations can be determined based on the square’s geometry information; second, the pixel coordinates of the light stripe center on the target images are extracted as the control points; finally, the points are projected into the camera coordinate frame with the help of the intrinsic parameters and the plane equations of the target, and the structured light plane can be determined by fitting these three-dimensional points. The experimental data show that the method has good repeatability and accuracy.     

Structure-function investigations of bacterial photosynthetic reaction centers

During photosynthesis light energy is converted into energy of chemical bonds through a series of electron and proton transfer reactions. Over the first ultrafast steps of photosynthesis that take place in the reaction center (RC) the quantum efficiency of the light energy transduction is nearly 100%. Compared to the plant and cyanobacterial photosystems, bacterial RCs are well studied and have relatively simple structure. Therefore they represent a useful model system both for manipulating of the electron transfer parameters to study detailed mechanisms of its separate steps as well as to investigate the common principles of the photosynthetic RC structure, function, and evolution. This review is focused on the research papers devoted to chemical and genetic modifications of the RCs of purple bacteria in order to study principles and mechanisms of their functioning. Investigations of the last two decades show that the maximal rates of the electron transfer reactions in the RC depend on a number of parameters. Chemical structure of the cofactors, distances between them, their relative orientation, and interactions to each other are of great importance for this process. By means of genetic and spectral methods, it was demonstrated that RC protein is also an essential factor affecting the efficiency of the photochemical charge separation. Finally, some of conservative water molecules found in RC not only contribute to stability of the protein structure, but are directly involved in the functioning of the complex.     

Efficient modelling of foliage distribution and crown dynamics in monolayer tree species

In response to the computational limitations of individual leaf-based tree growth models, this article presents a new approach for the efficient characterisation of the spatial distribution of foliage in monolayered trees in terms of 2D foliage surfaces. Much like the recently introduced 3D leaf area density, this concept accommodates local crown plasticity, which is a common weak point in large-scale growth models. Recognizing phototropism as the predominant driver of spatial crown expansion, we define the local light gradient on foliage surfaces. We consider the partial differential equation describing the evolution of a curve expanding along the light gradient and present an explicit solution. The article concludes with an illustration of the incorporation of foliage surfaces in a simple tree growth model for European beech (Fagus sylvatica L.), and discusses perspectives for applications in functional-structural models.     

Comments on “Modified wind chill temperatures determined by a whole body thermoregulation model and human-based convective coefficients” by Ben Shabat,Shitzer and Fiala (2013) and “Facial convective heat exchange coefficients in cold and windy environments estimated from human experiments” by Ben Shabat and Shitzer (2012)

Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) present revised charts for wind chill equivalent temperatures (WCET) and facial skin temperatures (FST) that differ significantly from currently accepted charts. They credit these differences to their more sophisticated calculation model and to the human-based equation that it used for finding the convective heat transfer coefficient (Ben Shabat and Shitzer, Int J Biometeorol 56:639-651, 2012). Because a version of the simple model that was used to create the current charts accurately reproduces their results when it uses the human-based equation, the differences that they found must be entirely due to this equation. In deriving it, Ben Shabat and Shitzer assumed that all of the heat transfer from the surface of their cylindrical model was due to forced convection alone. Because several modes of heat transfer were occurring in the human experiments they were attempting to simulate, notably radiation, their coefficients are actually total external heat transfer coefficients, not purely convective ones, as the calculation models assume. Data from the one human experiment that used heat flux sensors supports this conclusion and exposes the hazard of using a numerical model with several adjustable parameters that cannot be measured. Because the human-based equation is faulty, the values in the proposed charts are not correct. The equation that Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) propose to calculate WCET should not be used.     

Enzymatic synthesis of perlauric acid using Novozym 435

For the biocatalytic synthesis of perlauric acid, Novozym 435 (Candida antarctica lipase immobilized on polyacrylic resin) was found to be the most active catalyst and toluene was the most suitable solvent. The effects of various parameters on conversion and rates of reaction were studied in the absence of mass transfer limitations. Reusability studies indicated that there was enzyme deactivation and from a preliminary study of the deactivation, it was observed that the deactivation obeys a pseudo-first-order model. Lineweaver–Burk plots indicated the formation of a ternary complex. A model based on ordered bi–bi mechanism was found to fit the initial rate data very well and using this model, some kinetic parameters were calculated by non-linear regression analysis.     

Description of by-product inhibiton effects on biodesulfurization of dibenzothiophene in biphasic media

As several authors have reported previously, the Biodesulfurization of hydrodesulfurization recalcitrants, such as dibenzothiophene, is not yet commercially viable because mass transfer limitations and feedback inhibition effects are produced during the conversion. This work has been focused to investigate the inhibition process in aqueous and oil-water systems with two different aerobic biocatalysts types, Rhodococcus erythropolis IGTS8 and Pseudomonas putida CECT 5279. The results obtained have proven that global DBT desulfurization process using CECT 5279 was not clearly deactivated due to final product accumulation, under the experimental conditions assayed. Consistently, the desulfurization pattern has been described with the Michaelis-Menten equation, determining the kinetic parameters. On other hand, the assays have shown that important mass transfer limitations produced the decrease of the yields obtained with this Gram(-) strain in biphasic media. With strain IGTS8 it was observed lower mass transfer problems, but contrary the reaction was severely affected by the final product accumulation, in both aqueous and biphasic systems. Therefore it has been proposed an enzymatic kinetic model with competitive inhibition to describe the BDS evolution pattern when this Gram(+) strain was used.     

Thermal effects of a short light flash on biological tissues. I. An optical and thermal model

By summarizing the reference data and own calculations, a simple model for the optical and thermal properties of two-component biological tissues was proposed, as applied to the investigations of thermal fields in human tissues under external irradiation. The model comprises a small number of input variable parameters (total hemoglobin, blood oxygenation degree, and volume fraction of blood vessels) and enables one to find all optical characteristics necessary to compute the light fields in the tissue and set the thermal source function. Thermal parameters that determine heat transfer in the two-component medium were calculated with regard for the conditions of heat exchange between the components and heat transfer at the interface with various environments.     

Evaluation of feeding strategies in carbon-regulated secondary metabolite production through mathematical modeling

There is now growing evidence that the production of many secondary metabolic by microorganisms is subjected to carbon-catabolite regulation. Even though the exact mode of this regulation is not yet clear, an engineering analysis of the production process is still possible based upon a suitable hypothesis. By way of simulation of penicillin fermentation data obtained from the literature, a mechanistic model involving a substrate inhibition kinetics of product formation has been verified in this paper. Such a model has been found successful not only in predicting simple sugar-feeding strategy, but also a complicated computer guided strategy based upon controlling biomass growth rates in the tropo and idiophases. Using this model, for strategies for sugar feeding into penicillin fermentation have been investigated. These results show that similar penicillin productivities can be obtained using any of these strategies provided fermentations are carried out under optimal conditions corresponding to the strategy chosen. Effect of maximum oxygen transfer capacity of the fermentor under the conditions of fungal growth has been incorporated using an upper limit of biomass concentration on achievement of which the fermentations must be stopped due to serious oxygen limitations. Results of model simulations with such limits throw light upon the way in which different fermentors may behave with respect to product formation.     

Kinetic modeling of light limitation and sulfur deprivation effects in the induction of hydrogen production with Chlamydomonas reinhardtii: Part I. Model development and parameter identification

Chlamydomonas reinhardtii is a green microalga capable of turning its metabolism towards H2 production under specific conditions. However this H2 production, narrowly linked to the photosynthetic process, results from complex metabolic reactions highly dependent on the environmental conditions of the cells. A kinetic model has been developed to relate culture evolution from standard photosynthetic growth to H2 producing cells. It represents transition in sulfur-deprived conditions, known to lead to H2 production in Chlamydomonas reinhardtii, and the two main processes then induced which are an over-accumulation of intracellular starch and a progressive reduction of PSII activity for anoxia achievement. Because these phenomena are directly linked to the photosynthetic growth, two kinetic models were associated, the first (one) introducing light dependency (Haldane type model associated to a radiative light transfer model), the second (one) making growth a function of available sulfur amount under extracellular and intracellular forms (Droop formulation). The model parameters identification was realized from experimental data obtained with especially designed experiments and a sensitivity analysis of the model to its parameters was also conducted. Model behavior was finally studied showing interdependency between light transfer conditions, photosynthetic growth, sulfate uptake, photosynthetic activity and O2 release, during transition from oxygenic growth to anoxic H2 production conditions.     

Enzyme localization as a mechanism of apparent active transport

A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.     

Influence of mass transfer limitations on determination of the half saturation constant for hydrogen uptake in a mixed-culture CH(4)-producing enrichment

There is strong evidence in the literature supporting the existence of significant mass transfer limitations on the kinetics of exogenous H(2) consumption by methanogens. The half saturation constant for H (2) uptake by a mixed-culture, CH(4) producing enrichment was measured using an experimental protocol that avoided internal mass transfer limitations. The value obtained was two orders of magnitude smaller than any other previously reported. A mathematical model for acetogenic syntrophic associations was developed to check the capacity of H(2) as electron transporter between syntrophic partners. It was found that H(2) diffusion could account for the rate of transport of electrons between the syntrophic microorganisms and that formate is not a necessary intermediate. The possibility that formate may be an intermediate in this system was not ruled out. A Monod-type kinetic equation was modified to include the observed H(2) threshold effect. This modified equation was used to predict the CH(4)-production rate in a batch-fed digester. The results show that the external and internal H(2) pools are kinetically coupled. (c) 1992 John Wiley & Sons, Inc.     

Modeling of a foamed emulsion bioreactor: II. model parametric sensitivity

The sensitivity of a conceptual model of a foam emulsion bioreactor (FEBR) used for the control of toluene vapors in air was examined. Model parametric sensitivity studies showed which parameters affect the removal of toluene (as model pollutant) in the FEBR the most significantly, and enabled definition of the limits of the process. Detailed examination of the results indicated that the process is highly complex and that both mass transfer and kinetic limitations can coexist in the bioreactor system. These results will help with the optimization of the design and operation of FEBRs.     

Scale-down of microalgae cultivations in tubular photo-bioreactors--a conceptual approach

Rational design of large-scale bioreactors is still suffering from inadequate scale-up of technical parameters from lab to large scale and from missing kinetic information concerning the physiological reactions of the specific strain under cultivation. Therefore, simulations of processes expected in large-scale have to be carried out as far as possible and experiments have to be performed in small-scale reactors mimicking the situation in large scale. This procedure is referred to as scale-down. In this paper a concept to accomplish this task is proposed. Firstly, interactions between light transfer, fluid dynamics, and microbial metabolism are described. Secondly, a procedure is given to decompose the interactions by simulation on the one hand and by finding physiological parameters in model reactors on the other. Light transfer can be calculated by Monte Carlo methods, while fluid dynamics is handled by CFD. Ideally illuminated model photo-bioreactors and pilot reactors with enforced flow field are proposed to measure physiological parameters especially induced by light/dark cycles generated by interaction of turbulences and light attenuation.     

A Monte Carlo study of the dynamics of G-protein activation.

To link quantitatively the cell surface binding of ligand to receptor with the production of cellular responses, it may be necessary to explore early events in signal transduction such as G-protein activation. Two different model frameworks relating receptor/ligand binding to G-protein activation are examined. In the first framework, a simple ordinary differential equation model is used to describe receptor/ligand binding and G-protein activation. In the second framework, the events leading to G-protein activation are simulated using a dynamic Monte Carlo model. In both models, reactions between ligand-bound receptors and G-proteins are assumed to be diffusion-limited. The Monte Carlo model predicts two regimes of G-protein activation, depending upon whether the lifetime of a receptor/ligand complex is long or short compared with the time needed for diffusional encounters of complexes and G-proteins. When the lifetime of a complex is relatively short compared with the diffusion time, the movement of ligand among free receptors by binding and unbinding ("switching") significantly enhances G-protein activation. Receptor antagonists dramatically reduce G-protein activation and, thus, signal transduction in this case, and significant clustering of active G-proteins near receptor/ligand complexes results. The simple ordinary differential equation model poorly predicts G-protein activation for this situation. In the alternative case, when diffusion is relatively fast, ligand movement among receptors is less important and the simple ordinary differential equation model and Monte Carlo model results are similar. In this case, there is little clustering of active G-proteins near receptor/ligand complexes. Results also indicate that as the GTPase activity of the alpha-subunit decreases, the steady-state level of alpha-GTP increases, although temporal sensitivity is compromised.