A screening model to predict microalgae biomass growth in photobioreactors and raceway ponds

A microalgae biomass growth model was developed for screening novel strains for their potential to exhibit high biomass productivities under nutrient‐replete conditions in photobioreactors or outdoor ponds. Growth is modeled by first estimating the light attenuation by biomass according to Beer‐Lambert's Law, and then calculating the specific growth rate in discretized culture volume slices that receive declining light intensities due to attenuation. The model uses only two physical and two species‐specific biological input parameters, all of which are relatively easy to determine: incident light intensity, culture depth, as well as the biomass light absorption coefficient and the specific growth rate as a function of light intensity. Roux bottle culture experiments were performed with Nannochloropsis salina at constant temperature (23°C) at six different incident light intensities (10, 25, 50, 100, 250, and 850 µmol/m² s) to determine both the specific growth rate under non‐shading conditions and the biomass light absorption coefficient as a function of light intensity. The model was successful in predicting the biomass growth rate in these Roux bottle batch cultures during the light‐limited linear phase at different incident light intensities. Model predictions were moderately sensitive to minor variations in the values of input parameters. The model was also successful in predicting the growth performance of Chlorella sp. cultured in LED‐lighted 800 L raceway ponds operated in batch mode at constant temperature (30°C) and constant light intensity (1,650 µmol/m² s). Measurements of oxygen concentrations as a function of time demonstrated that following exposure to darkness, it takes at least 5 s for cells to initiate dark respiration. As a result, biomass loss due to dark respiration in the aphotic zone of a culture is unlikely to occur in highly mixed small‐scale photobioreactors where cells move rapidly in and out of the light. By contrast, as supported also by the growth model, biomass loss due to dark respiration occurs in the dark zones of the relatively less well‐mixed pond cultures. In addition to screening novel microalgae strains for high biomass productivities, the model can also be used for optimizing the pond design and operation. Additional research is needed to validate the biomass growth model for other microalgae species and for the more realistic case of fluctuating temperatures and light intensities observed in outdoor pond cultures. Biotechnol. Bioeng. 2013; 110: 1583–1594. © 2012 Wiley Periodicals, Inc.     

LiGAPS-Beef,a mechanistic model to explore potential and feed-limited beef production 1: model description and illustration

The expected increase in the global demand for livestock products calls for insight in the scope to increase actual production levels across the world. This insight can be obtained by using theoretical concepts of production ecology. These concepts distinguish three production levels for livestock: potential (i.e. theoretical maximum) production, which is defined by genotype and climate only; feed-limited production, which is limited by feed quantity and quality; and actual production. The difference between the potential or limited production and the actual production is the yield gap. The objective of this paper, the first in a series of three, is to present a mechanistic, dynamic model simulating potential and feed-limited production for beef cattle, which can be used to assess yield gaps. A novelty of this model, named LiGAPS-Beef (Livestock simulator for Generic analysis of Animal Production Systems – Beef cattle), is the identification of the defining factors (genotype and climate) and limiting factors (feed quality and available feed quantity) for cattle growth by integrating sub-models on thermoregulation, feed intake and digestion, and energy and protein utilisation. Growth of beef cattle is simulated at the animal and herd level. The model is designed to be applicable to different beef production systems across the world. Main model inputs are breed-specific parameters, daily weather data, information about housing, and data on feed quality and quantity. Main model outputs are live weight gain, feed intake and feed efficiency (FE) at the animal and herd level. Here, the model is presented, and its use is illustrated for Charolais and Brahman × Shorthorn cattle in France and Australia. Potential and feed-limited production were assessed successfully, and we show that FE of herds is highest for breeds most adapted to the local climate conditions. LiGAPS-Beef also identified the factors that define and limit growth and production of cattle. Hence, we argue the model has scope to be used as a tool for the assessment and analysis of yield gaps in beef production systems.     

A mechanistic model of algal photoinhibition induced by photodamage to photosystem-II

Photoinhibition is a central problem for the understanding of plasticity in photosynthesis vs. irradiance response. It effectively reduces the photosynthetic rate. In this contribution, we present a mechanistic model of algal photoinhibition induced by photodamage to photosystem-II. Photosystem-IIs (PSIIs) are assumed to exist in three states: open, closed and inhibited. Photosynthesis is closely associated with the transitions between the three states. The present model is defined by four parameters: effective cross section of PSII, number of PSIIs, turnover time of electron transfer chains and the ratio of rate constant of damage to that of repair of D1 proteins in PSIIs. It gives a photosynthetic response curve of phytoplankton to irradiance (PI-curve). Without photoinhibition, the PI-curve is in hyperbola with the first three parameters. The PI-curve with photoinhibition can be simplified to the same form as the hyperbola by replacing either the number of PSIIs with the number of functional PSIIs or the turnover time of electron transfer chains with the average turnover time.     

Factors governing algal growth in photobioreactors: the “open” versus “closed” debate

Until recently, most large commercial scale microalgal production systems employed open systems. However, several large-scale closed systems have now been built and, for the first time, actual comparisons can be made. There are major operational differences between open and closed photobioreactors and, consequently, the growth physiology of the microalgae is different between the two systems. Several of the factors governing growth can, within certain boundaries, be manipulated while others are specific to the cultivation system. Crucial factors are the optical depth, turbulence, light acclimated state of the organism, nutrient availability and metabolite accumulation. In the final analyses, systems are used for specific purposes and each will determine which system is the most suitable, since there is no universal all-purpose photobioreactor.     

A simple algal production system designed to utilize the flashing light effect

Arrays of foils similar in design to airplane wings have been placed in an algal culture flume to create systematic mixing. Vortices are produced in the culture due to the pressure differential created as water flows over and under the foils. In a flume having a flow rate of 30 cm/s, the foil arrays produced vortices with rotation rates of ca. 0.5-1.0 Hz. This rotation rate is satisfactory to take advantage of the flashing light effect if the culture is sufficiently dense. Solar energy conversion efficiencies in an experimental culture of P. tricornutum increased 2.2-2.4 fold with the foil arrays in place versus controls with no foil arrays and solar energy conversion efficiencies averaged 3.7% over a three-month period. Five-day running means of solar energy conversion efficiencies reached as high as 10% during the three-month period. The use of foil arrays appears to be an effective and inexpensive way to utilize the flashing light effect in a dense algal culture system.     

Image analysis - a simple method of algal culture growth assessment

A non-destructive method for the relative growth quantification of algae or cyanobacteria in the culture has been developed. It is based on image analysis and does not require any special equipment. Results provided by this method were compared with those provided by a chlorophyll a assessment, with a correlation factor of over 88%.     

Using a logical model to predict the growth of yeast

Background  

A logical model of the known metabolic processes in S. cerevisiae was constructed from iFF708, an existing Flux Balance Analysis (FBA) model, and augmented with information from the KEGG online pathway database. The use of predicate logic as the knowledge representation for modelling enables an explicit representation of the structure of the metabolic network, and enables logical inference techniques to be used for model identification/improvement.     

LiGAPS-Beef,a mechanistic model to explore potential and feed-limited beef production 3: model evaluation

LiGAPS-Beef (Livestock simulator for Generic analysis of Animal Production Systems – Beef cattle) is a generic, mechanistic model designed to quantify potential and feed-limited growth, which provides insight in the biophysical scope to increase beef production (i.e. yield gap). Furthermore, it enables identification of the bio-physical factors that define and limit growth, which provides insight in management strategies to mitigate yield gaps. The aim of this paper, third in a series of three, is to evaluate the performance of LiGAPS-Beef with independent experimental data. After model calibration, independent data were used from six experiments in Australia, one in Uruguay and one in the Netherlands. Experiments represented three cattle breeds, and a wide range of climates, feeding strategies and cattle growth rates. The mean difference between simulated and measured average daily gains (ADGs) was 137 g/day across all experiments, which equals 20.1% of the measured ADGs. The root mean square error was 170 g/day, which equals 25.0% of the measured ADGs. LiGAPS-Beef successfully simulated the factors that defined and limited growth during the experiments on a daily basis (genotype, heat stress, digestion capacity, energy deficiency and protein deficiency). The simulated factors complied well to the reported occurrence of heat stress, energy deficiency and protein deficiency at specific periods during the experiments. We conclude that the level of accuracy of LiGAPS-Beef is acceptable, and provides a good basis for acquiring insight in the potential and feed-limited production of cattle in different beef production systems across the world. Furthermore, its capacity to identify factors that define or limit growth and production provides scope to use the model for yield gap analysis.     

A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

This paper develops a simple mathematical model of the sitting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive attempt to address the question of how unchecked sprouting of the parent vessel is avoided at the initiation of angiogenesis, based on the idea that feedback regulation processes play the dominant role. No chemical interaction between the proangiogenic and antiangiogenic factors is assumed. The model is based on corneal pocket experiments, and provides a mathematical analysis of the initial spacing of angiogenic sprouts.     

Coupled effects of irradiance and iron on the growth of a harmful algal bloom-causing microalga Scrippsiella trochoidea

Effects of irradiance and iron on the growth of a typical harmful algal blooms (HABs) causative dinoflagellate, Scrippsiella trochoidea, were investigated under various irradiances (high light: 70 μmol m^?2 s^?1 and low light: 4 μmol m^?2 s^?1) and iron concentrations (low iron: 0.063 mg L^?1, medium iron: 0.63 mg L^?1 and high iron: 6.3 mg L^?1), and evaluated by the parameters of algal cell density, specific growth rate, optical density and chlorophyll a content. The results indicated that there was significant difference in the cell density of dinoflagellate S. trochoidea between high light and low light intensity treatments across the entire experiments, 7-fold higher at high irradiance as compared with low irradiance, which was further enhanced by the iron concentration. It was found that the maximum cell density of 25 × 10⁴ cell mL^?1 occurred under the combination of high light intensity and high iron concentration, followed by 23 × 10⁴ cell mL^?1 in the combination of high light and medium iron, and 20 × 10⁴ cell mL^?1 in the combination of high light and low iron. There was no significant effect of iron concentration on the cell density under low light intensity. The cell density maintained about 3 × 10⁴ cell mL^?1 across all combinations of iron concentrations and low light in the end of experiments. Such interactive effects of light intensity and iron level dependent were also observed for the specific growth rate, OD₆₈₀ and chlorophyll a content of S. trochoidea. The maximum values of specific growth rate, OD₆₈₀ and chlorophyll a content peaked at the condition of high irradiance and high iron, which were 0.22 d^?1, 0.282 and 0.673 mg L^?1, respectively. In general, their values increased significantly with the increasing of iron concentration at high irradiance, whereas no significant difference was observed among three iron concentrations at low irradiance, all remaining approximately 0.06 d^?1, 0.03 and 0.050 mg L^?1, respectively. Those results suggest that there may be a strong interactive effect between irradiance and iron on microalgal growth and their physiological characteristics. The combination of high light and high iron concentration may accelerate algal cell growth and pigment biosynthesis, thus leading to massive occurrence of HABs.     

Integrating demographic data and a mechanistic dispersal model to predict invasion spread of Rhododendron ponticum in different habitats

Understanding the invasion potential of a species in different habitat types within the non-native range is crucial in prioritising management and control efforts, and in the protection of vulnerable habitats through monitoring. Here, using the invasive shrub Rhododendron ponticum as a case study, we integrate information on both the demographics and spatial dynamics within an individual-based, spatially-explicit model to investigate invasion potential in different habitats. Firstly, empirical demographic data were used to establish relationships between demographic traits, such as height and fecundity, and habitat variables. The outputs from models fitted using a Generalised Linear Model approach were then incorporated into an individual-based simulation model of plant spread to investigate the invasion potential in different habitats using a factorial design of treatments. Plant height, and thus seed release height, was the main driver of invasion speed through an increase in dispersal potential, which resulted in the highest invasion speeds predicted for evergreen woodlands, and relatively low speeds for open habitats. Conversely, invasion density was driven by plant fecundity and seedling survival and not dispersal potential; the highest invasion densities were predicted for open habitats, with relatively low densities for evergreen habitats. Deciduous woodland had features resulting in intermediate invasion potential, both in terms of speed and density and may, therefore be the habitat that is most vulnerable to relatively rapid and dense invasion.     

Optimizing algal biomass production in an outdoor pond: a simulation model

A deterministic simulation model was developed to predict production rates of the marine prymnesiophyteIsochrysis galbana in an outdoor algal mass culture system. The model consists of photoadapation, gross photosynthesis and respiration sections. Actual physiological and biophysical laboratory data, obtained from steady state cultures grown under a wide range of irradiance levels, were used in calculating productivity. The resulting values were used to assess optimal operational parameters to maximize algal biomass production. The model predicted a yearly averaged production rate of 9.7 g C m^?2d^?1, which compared well with field data reported in the literature. The model evaluated the effect of pond depth and chlorophyll concentration on potential production rate in various seasons. The model predicted that a yearly averaged chlorophyll areal density of 0.65 g m^?2 will yield the maximal production rate. Chlorophyll areal density should be seasonally adjusted to give maximal production. This adjustment could be done either by changing pond depth or chlorophyll concentration. The model predicted that under optimal operational conditions, the diurnal respiration losses averaged 35% of gross photosynthesis. The calculated growth rate for maximal productivity ranged between 0.15 and 0.24 d^?1, suggesting an optimal hydraulic retention time of 6.7 and 4.2 d for various seasons.     

Application of a noninhibitory growth model to predict the transient response in a chemostat

A method of adapting a kinetic model based on steady-state chemostat data to predict the transient performance of a chemostat culture is presented. The proposal provides for a time delay which can be considered equivalent to a period of reduced activity of the organism subsequent to the introduction of a step change in operating conditions. The adapted kinetic model gives substantially better performance in predicting the transient response of an experimental system than the unmodified kinetic model.     

Kinetics of enzymatic hydrolysis of cellulose: analytical description of a mechanistic model.

A generalized mechanistic model for the enzymatic hydrolysis of cellulose is developed and expressed mathematically. The model is based on Michaelis--Menten-type kinetics for concurrent random and endwise attack of the substrate involving end-product inhibitions and three types of enzymes: an endo-beta-1,4-glucanase, an exo-beta-1,4-glucanase, and beta-glucosidase. Basic parameters of the model which can explain synergistic and other effects observed experimentally are quantified and discussed. It is shown that cellulose degradation kinetics are expected to be strongly affected by the ratio of endo- to exocellulases in the reaction mixture as indicated by previous experimental data, and the substrate degree of polymerization, a factor not fully appreciated in previous studies, which appear to be overridingly important in many practical cases.     

Coupled effects of irradiance and iron on the growth of a harmful algal bloom-causing microalga Scrippsiella trochoidea

Effects of irradiance and iron on the growth of a typical harmful algal blooms (HABs) causative dinoflagellate, Scrippsiella trochoidea, were investigated under various irradiances (high light: 70 μmol m^?2 s^?1 and low light: 4 μmol m^?2 s^?1) and iron concentrations (low iron: 0.063 mg L^?1, medium iron: 0.63 mg L^?1 and high iron: 6.3 mg L^?1), and evaluated by the parameters of algal cell density, specific growth rate, optical density and chlorophyll a content. The results indicated that there was significant difference in the cell density of dinoflagellate S. trochoidea between high light and low light intensity treatments across the entire experiments, 7-fold higher at high irradiance as compared with low irradiance, which was further enhanced by the iron concentration. It was found that the maximum cell density of 25 × 10⁴ cell mL^?1 occurred under the combination of high light intensity and high iron concentration, followed by 23 × 10⁴ cell mL^?1 in the combination of high light and medium iron, and 20 × 10⁴ cell mL^?1 in the combination of high light and low iron. There was no significant effect of iron concentration on the cell density under low light intensity. The cell density maintained about 3 × 10⁴ cell mL^?1 across all combinations of iron concentrations and low light in the end of experiments. Such interactive effects of light intensity and iron level dependent were also observed for the specific growth rate, OD₆₈₀ and chlorophyll a content of S. trochoidea. The maximum values of specific growth rate, OD₆₈₀ and chlorophyll a content peaked at the condition of high irradiance and high iron, which were 0.22 d^?1, 0.282 and 0.673 mg L^?1, respectively. In general, their values increased significantly with the increasing of iron concentration at high irradiance, whereas no significant difference was observed among three iron concentrations at low irradiance, all remaining approximately 0.06 d^?1, 0.03 and 0.050 mg L^?1, respectively. Those results suggest that there may be a strong interactive effect between irradiance and iron on microalgal growth and their physiological characteristics. The combination of high light and high iron concentration may accelerate algal cell growth and pigment biosynthesis, thus leading to massive occurrence of HABs.     

Using a phytoplankton growth model to predict the fractionation of stable carbon isotopes

In the preceding paper in this issue, a phytoplankton growthmodel based on an analogy with chemical kinetics (the CR model)was re-derived, and a comparison made with the growth rate ofcultured phytoplankton assemblages extracted from temperatelakes. In this paper, further derivation of the CR model leadsto the same model of carbon isotope fractionation used by Rauet al. (Mar. Ecol. Prog. Ser., 133, 275–285, 1996). Boththe CR and Rau et al. models are compatible with the observationthat isotope fractionation during phytoplankton growth,     

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.