Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.     

Growth and Antithraquinone Biosynthesis by Galium mollugo L. Cells in Batch and Chemostat Culture

The kinetics of growth, nutrient uptake, and anthraquinone biosynthesisby suspension cultures of Galium mollugo L. cells were examinedin batch and continuous (chemostat) culture. In batch culture,although the initial growth rate was constant (minimum doublingtime = 35 h) characteristic changes in cell composition wereobserved during the growth cycle particularly cell dry weight(between 3.9 and 9.2 g/10⁹ cells), cell anthraquinone (22–80mg/10⁹ cells), and cell protein (0.7–1.6 g/10⁹ cells).Using a chemostat steady state growth was established at twodifferent specific growth rates with mean doubling times of40 h and 25 h. Phosphate was established as the growth-limitingnutrient in chemostat culture at a concentration of 11 µgP ml^–1. In steady state growth at a doubling time of 40h the cell composition remained constant although this was differentfrom any cells grown in batch culture. The cell anthraquinonelevel in steady state growth was between 7 and 30 times lowerthan in batch culture. This result raises the question of therelative importance of growth rate and the growth-limiting nutrientin determining accumulation of secondary products by culturedplant cells.     

Carbon budgets in batch and continuous cultures: How can we understand natural physiology of marine phytoplankton?

Monitoring of respiratory and organic losses from carbon assimilationfor the diatom Thalassiosira pseudonana shows very slight (about5%) total carbon losses in continuous culture. Although correlationbetween batch and continuous culture cellular chemistry wasless than ideal, batch culture exponential phase cells showedcarbon metabolism similar to that for the continuous culture.In both cases, growth rates were in excess of 1.5 divisionsd^–1 and total carbon losses in the batch exponential phasewere similar (<10%) to those in the continuous culture. Estimatesof growth rates from C-14 uptake and particulate carbon matchedthose from changes in cell numbers in the batch culture andthat from the dilution rate in the continuous culture. In batchculture, immediately after starting the culture and in stationaryphase, carbon losses from respiration, organic excretion, andcellular degradation were large (>50%). To understand phytoplanktonphysiology in nature, it is necessary to find what effects growthrate and population density have on carbon losses and to ascertainwhether or not steady state conditions really pertain to theocean.     

Influence du d?bit d'eau de mer dans un dispositif de culture ? fibres creuses dialysantes sur la croissance phytoplanctonique et 1'extraction des nitrates du milieu

It is demonstrated that the productive capacity of mass dialysisculture of phytoplankton is intimately related to the rate offlow of nutrient medium along the membrane. Comparison of culturesof Phaeodactylum tricornutum, subject to different medium flowrates (92 versus 250 ml.min^–1) during a 17-day growthperiod, reveals increased productivity (in terms of cell numbers,chlorophyll a, dry weight, cell nitrogen, cell carbon, ATP)at the higher flow rate. Differences are most pronounced inthe latter stages of growth (i.e., linear and stationary) attainingratios between 2 and 3 for cell nitrogen, cell carbon and ATP.Lower C/N ratios for the greater yielding culture translatesas enhanced osmotic diffusion as well as cellular assimilationof nitrates. The positive effects of increasing medium flowrate on phytoplankton growth result from improved dialyzer performancewith respect to low molecular weight solutes. This is evidencedin the proportionately greater values obtained for mass transferof nitrate-nitrogen. Accordingly, measures of nitrate clearanceindicate a progression from 29 to 85 ml.min^–1 in responseto augmenting sea water flow from 32 to 292 ml.min ^–1.The culture apparatus recently developed consists of a separatedialysis unit (a hollow-fiber cartridge used in hemodialysis)coupled to a temperature-controlled growth chamber. Culturesreceive a continuous flow of natural sea water and are grownin the batch dialysis mode. The main advantages of this methodrelate to its potential for large-scale, axenic algal culturebased on the abundant source of cheap nutrients that constitutesnatural sea water.     

Effects of Nutrient Limitation and {gamma}-Irradiation on Tracheary Element Differentiation and Cell Division in Single Mesophyll Cells of Zinnia elegans

The effects of nutrient limitation and -irradiation on trachearyelement differentiation and cell division were investigatedusing single cells isolated from the mesophyll of Zinnia elegans.When the phosphate concentration of the medium was reduced to10 µM (1/50 of Fukuda and Komamine's medium, 1980a), thefrequency of cell division during 4 days of culture decreased,while the frequency of tracheary element differentiation wasunaffected. -Irradiation with a dose of 92 Gy at 36 h of culturepreferentially and thoroughly suppressed cell division withoutreducing the number of tracheary elements formed. The appearanceof secondary cell wall thickenings was delayed by irradiation,but synchrony was maintained. Thus the Zinnia system previouslyreported [Fukuda and Komamine (1980a) Plant Physiol. 65: 57]was improved to give a more useful system for the study of cytodifferentiation,in which tracheary element formation occurred from single cellswithout cell division. ¹Present address: Biological Institute, Faculty of Science,Tohoku University, Sendai, Miyagi 980, Japan. (Received November 28, 1985; Accepted February 22, 1986)     

Preservation of the Differentiated State of Mesophyll Cells In Vitro

Under a variety of light conditions, and in a modified NT mediumcontaining sucrose as a carbon source, isolated mesophyll cellsof Calystegia sepium started cell divisions after 72 h. Alternately,under light-dark alterations (12: 12 h; 1.35–1.50 W m^–2of cool white light), and culture in the NT medium lacking anorganic carbon source, and made iso-osmotic by the additionof mannitol, the cells preserved their differentiated stateas regards cell size, cell form, colour and size and distributionof chloroplasts for one week. Later on, they changed their characterand cell division was started. Calystegia sepium, mesophyll cells, differentiated state, in vitro culture     

A Simple and Inexpensive Design of Chemostat Enabling Steady-state Growth of Acer pseudoplatanus L. Cells under Phosphate-limiting Conditions

Operational and constructional details are given of a relativelysimple and inexpensive chemostat designed for the continuousculture of plant cells in suspension. This apparatus permitscontrol of the growth rate of sycamore, Acer pseudoplatanusL. cells in steady-state conditions. By alteration of the rateof input of medium different steady-state growth rates wereobtained over a wide range (mean doubling times from 182 h to36 h). In order to establish a growth-limiting nutrient thetime course of nutrient uptake in batch culture was measured.In batch culture the maximum growth obtained was proportionalto the initial concentration of phosphate when this was belowa concentration of 17 µg P per ml (as phosphate). It isalso shown in chemostat culture that the steady-state cell densityis proportional to the phosphate concentration in the mediumwhen this is below 17 µg P per ml (as phosphate). Phosphatewas therefore established to be the growth rate-limiting nutrientin chemostat culture at a concentration of 8•5 µgP per ml (as phosphate).     

Assimilation numbers in cultures of marine phytoplankton

During exponential growth in batch culture, assimilation numbersof eleven algal species ranged from 1.6–20.8, with a meanvalue of 5.3 g C/g Chlorophyll a/hr. The highest assimilationnumber of 20.8 g C/g Chlorophyll a/hr was observed in Coccolithuspelagicus, due to the relatively low concentration of chlorophylla/cell. The assimilation number declined from exponential tostationary phase in batch cultures for ten algal species, butincreased with age in batch culture in Amphiprora paludasa (abenthic diatom). The assimilation number declined with decreasinggrowth rate in nitrate-limited chemostat cultures of Phaeodactylumtricornutum and in iron-limited chemostat cultures of Phaeodactylumtricornutum and Isochrysis galbana.     

DIEL PERIODICITY OF PHOTOSYNTHESIS AND CELL DIVISION COMPARED IN THALASSIOSIRA WEISSFLOGII (BACILLARIOPHYCEAE)1

Diel patterns of photosynthesis and cell division were examined in Thalassiosira weissflogii Grun. (clone Actin) grown in nitrogen-limited cyclostat culture. Ammonia (NH₄+) was either supplied continuously or as a daily pulse to cultures grown in constant light or in a light: dark cycle. When either nitrogen or light was supplied periodically, both cell division and photosynthetic capacity were periodic. When both nitrogen and light were supplied periodically, cell division was coupled to the N-pulse whereas periodicities of photosynthetic capacity were modified but remained coupled to the light-dark cycle. Diel oscillations in photosynthesis were i) largely independent of cellular pigmentation and ii) similar for light-limiting and saturating irradiances. Periodicity in photosynthetic capacity also persisted following transfer of non-dividing batch cultures to constant light. Results suggest that photosynthesis but not cell division was coupled to a circadian clock in T. weissflogii. A circadian rhythm of photosynthesis may optimize carbon assimilation in phytoplankton exposed to intermittent nutrient supply by ensuring that maximum photosynthetic capacity occurs during the day.     

Mass cultivation of Tetrahymena thermophila yielding high cell densities and short generation times

Summary A cheap medium, composed of skimmed milk powder, yeast extract, and glucose, for mass cultivation of the protozoon Tetrahymena thermophila has been developed. Cell concentrations of 5 x 10⁶ cells/ml and unprecedented short generation times of only 1.4 h were determined in batch cultures. During the exponential phase of growth, daughter cells initiated a new cell division even before the previous division had been completed, resulting in the formation of cell chains. Addition of glucose extended the stationary phase. Using a bench-top fermentor supplied with a digital control unit the utilization of nutrient components in batch culture was monitored. Milk protein and glucose were consumed completely, but lactose only partly. Correspondence to: A. Tiedtke     

Pyrimidine Nucleotide Biosynthesis in Vinca rosea Cells: Changes in the Activity of the de novo and Salvage Pathways during Growth in a Suspension Culture

Marked changes in the activity of the ‘de novo’and ‘salvage’ pathways of pyrimidine biosynthesisduring growth of Vinca rosea cells in a batch suspension culturewere observed. The activity of these pathways was investigated by determiningthe contribution of ¹⁴C of [2-¹⁴Cluracil, 12-¹⁴Cluridine. and[6-¹⁴Clorotate to the cell constituents and by measuring theactivity of the several enzymes of these pathways. During the lag phase of the culture, ‘uracil-’ and‘uridine-salvage’ pathways made the predominantcontribution to nucleotide biosynthesis, but, following theinitiation of cell division, the ‘de novo’ pathwayfor nucleotide biosynthesis operated appreciably. These results suggest that nucleotide synthesis during cellgrowth in a suspension culture can be divided into two stages:a ‘turnover stage’, during the lag phase of cellgrowth, and a ‘true biosynthetic stage’, which isinitiated in the cell division phase.     

螺旋藻批式与连续培养及其生长动力学

在内循环气升式光生物反应器中,分别研究了螺旋藻细胞在批式和连续培养条件下的生长特性,结果表明：Richards模型和指数衰减模型可较好地描述批式培养时细胞和碳源底物浓度与培养时间的关系;批式培养时最大细胞生长速率为0371g/d/L,细胞对碳的得率系数为3.439g/gC;连续培养时随着稀释率的增大,细胞和底物浓度分别呈下降和上升趋势;连续培养时最大细胞产率为0.362g/L/d,最佳稀释率为0.45/d,细胞对碳的得率系数为2.050g/gC;所提出的连续培养动力学模型可较好地拟合实验数据。     

Predator-prey interactions between Isochrysis galbana and Oxyrrhis marina. III. Mathematical modelling of predation and nutrient regeneration

A mathematical model was derived to simulate ingestion, growthand nitrogen (N) regeneration for the phagotrophic dinoflagellateOxyrrhis marina. Two types of experimental study were undertaken:prey-deplete O.marina were supplied with lsochrysis galbanain continuous darkness (thus preventing growth of the prey),and predator-prey interactions were also followed in culturesmaintained in a light-dark cycle (allowing growth of the prey).During light-dark cycles, Oxyrrhis volume increased more inthe light phase than in the dark. Digestion of isochrysis lasted{small tilde}0.3 days. with an average maximum ingestion rateof 55 prey predator–1 day–1 During active predation,30% of Oxyrrhis-carbon (C) was lost from the particulate phase:per day, with this loss falling to 10%: per day at the cessationof herbivory when cannibalism became noticeable. Ingestion wasmodelled as a function of prey density, C-loss and divisionas functions of cellular predator C. with cannibalism by Oxyrrhisalso included. Two N-regeneration expressions were investigated:one proposed by D.A.Caron and J.C.Goldman (Journal of Protozoology.35, 247–249, 1988) and an alternative function which relatedN regeneration to intracellular carbon and N based on the conceptof an optimal Oxyrrhis C:N ratio. The latter was more successfulin simulating batch culture data and did not require a priorcalculation of Oxyrrhis gross growth efficiency. The model ofOxyrrhis numbers, C and N contained only nine parameters whosevalues were fully obtainable from batch culture experiments.By using this model, we were able to use a single parameterset to simulate the transient dynamics of Oxyrrhis ingestingN-replete and N-stressed prey. Further experiments in whichOxyrrhis grew on Isochrysis in light-dark cycles were simulatedby combining the Oxyrrhis model with the nutrient-processingmodel for Isochrysis of K.Davidson et al. (Journal of PlanktonResearch, 15, 351–359, 1993). The dynamics of the fullpredator-prey model were found to be sensitive to the levelof sophistication of the prey model; the Quota model was foundto be less successful than the nutrient-processing prey model.Theoretical model runs indicated the importance of being ableto simulate changes in both prey numbers and biomass, and alsoin including realistic equations for nutrient regeneration frompredators in microbial predator-prey models.     

Influence of the Antibiotic Ciprofloxacin on Culture of Allium longicuspis Callus-derived Protoplasts

A major problem of in vitro plant culture techniques is chroniccontamination by microorganisms. Calli derived from basal partsof leaves of Allium longicuspis Regel (Alliaceae) and culturedin a medium without antibiotic contain most probably latentcontaminating microorganisms. These calli were used as the sourcematerial for isolation and culture of protoplasts. Isolatedprotoplasts were cultured in the presence of the antibioticciprofloxacin, and the protoplast viability, cell wall regenerationand cell division were studied as a function of the antibioticconcentration. Whatever the antibiotic concentration, protoplast-derivedcells kept significantly higher viability for at least 3 weekscompared with those cultured without antibiotic. As to cellwall regeneration after 2 d, it was not affected by the antibioticexcept at the highest concentration tested (100 mg l^-1). Sporadicfirst cell division was observed after 2-6 d of culture in thepresence of ciprofloxacin while, in its absence, cell divisionwas never apparent before 10 d of culture.Copyright 1995, 1999Academic Press Allium, bacteria, cell division, cell wall regeneration, ciprofloxacin, contamination, garlic, mycoplasma, protoplast culture, viability     

Simultaneous production of buds on mother and daughter cells of Saccharomyces cerevisiae in the presence of hydroxyurea

Individual budding yeast cells, Saccharomyces cerevisiae, enclosedin small culture chambers were observed through two buddingcycles to examine their behavior during growth and division.In the nutrient medium (YHG medium), the duration of the buddingcycles was 77 min for mother cells and 90 min for daughter cells;a 13-min time lag between the two durations. Continuous exposureof cells to 16 or 32 mM hydroxyurea extended the duration ofthe cycles and increased the volume of the cells, resultingin the formation of abnormally large and equal-sized mother-daughterpairs. Each cell of these pairs subsequently produced buds simultaneously.Stained cell nuclei showed simultaneous nuclear division. Thissynchronous budding on mother-daughter pairs was repeated inthe next budding cycle. The coordination of growth with divisionis discussed in relation to these results. (Received August 11, 1979; )     

Continuous Cultivation of Glucose-Limited Bean Cells (Phaseolus vulgaris L.) in a Modified Bacterial Fermentor

A commercially available bacterial fermentor was modified toallow the continuous cultivation of glucose-limited bean cells(Phaseolus vulgaris L.) at a defined pH. A steady state wasreached using a dilution rate of 0?004 h^–1 and was maintainedfor 4 months; during this period the dry weight and packed cellvolume of the culture remained constant; the yield for glucosewas 0?34 (dry wt./dry wt) and for carbon 0?27 (g atom/g atom).Glucose-limited cells had lower C/N ratios both for cytoplasmand cell walls than cells in the exponential phase of growthin batch cultures.     

Elemental composition (C:N:P) and growth rates of bacteria and Rhodomonas grazed by Daphnia

The elemental composition and growth rate of Rhodomonas andheterotrophic bacteria were studied in batch cultures in thepresence and absence of Daphnia and at two different levelsof phosphorus limitation. The elemental content of single cellswas measured with X-ray microanalysis. Simultaneously, dilutionexperiments were performed in order to estimate grazing losses,growth rates and dominant nutrient sources for bacteria andRhodomonas. The phosphorus:carbon (P:C) ratios of the bacteriawere generally higher in the experiment with the stronger Plimitation of the system. High P:C ratios were taken as an indicationthat bacteria were carbon limited. The presence of Daphnia resultedin a further increase in bacterial P:C ratios and increasedspecific growth rates. Thus, grazing increased the availabilityboth of inorganic nutrients and organic substrates, stimulatingthe growth of the bacteria. P:C ratios of Rhodomonas decreasedwith increasing P limitation of the system. Only at strong Plimitation did the presence of Daphnia result in increased P:Cratios of Rhodomonas compared with the control without daphnids.This study shows that the elemental content and growth rateof heterotrophic bacteria and Rhodomonas are influenced by grazingand nutrient regeneration by daphnids. The response is dynamicand depends on the level of nutrient limitation of the system. Present address: Department of Microbiology, University of BergenJahnebakken 5, NO-5020 Bergen, Norway     

CHANGES IN DOMOIC ACID PRODUCTION AND CELLULAR CHEMICAL COMPOSITION OF THE TOXIGENIC DIATOM PSEUDO-NITZSCHIA MULTISERIES UNDER PHOSPHATE LIMITATION1

Production of domoic acid (DA), a neurotoxin, by the diatom Pseudo-nitzschia multiseries (previously Nitzschia pungens f. multiseries) Hasle and its cellular chemical composition were studied in phosphate-limited chemostat continuous cultures and in subsequent batch cultures. Under steady-state chemostat conditions, DA production increased from 0.01 to 0.26 pg DA · cell^?1· d^?1 as the growth rate decreased. When the nutrient supply was discontinued (to produce a batch culture), DA production was enhanced by a factor of ca. 3. DA production was temporarily suspended upon addition of phosphate to the batch cultures but resumed 1 d later at a higher rate coincident with the decline of phosphate uptake. In both steady-state continuous culture and batch culture, more DA was produced when alkaline phosphatase activity (APA) was high. The association of high DA production with high levels of APA and high cellular N:P ratios strongly suggests that phosphate limitation enhances DA production. Also, DA production was high when other primary metabolism (e.g. uptake of carbon, nitrogen, phosphorus and silicon, and cell division) was low, but chlorophyll a and adenosine triphosphate were generally high. This suggests that the synthesis of DA requires a substantial amount of biogenic energy.     

Studies on the Growth in Culture of Plant Cells: XI. THE INFLUENCE OF SHAKING RATE ON THE GROWTH OF SUSPENSION CULTUEES

The influence of shaking rates (expressed as revolutions permin) on orbital shaking platforms (1 in (2.54 cm) diam. rotarymotion) on the growth of cell suspension cultures of Acer pseudoplatanusL. and Atropa belladonna cultivar lutea Döll are described.By following cell growth and respiration and the levels of oxygenand carbon dioxide in the media during the progress of incubationit is concluded that the reduction of growth at sub-optimalshaking rates is not due to oxygen deficiency or toxic accumulationof carbon dioxide. The growth of the Atropa cell suspensionin ‘closed systems’ has been studied by the developmentof modified culture vessels and evidence obtained that the reducedgrowth in the systems is due to the formation by the culturesof an unidentified volatile growth inhibitor and not to eitheroxygen depletion or toxic accumulation of either carbon dioxideor ethylene. It is suggested that the reduced growth in ‘opensystems’ cultures at sub-optimal shaking speeds is eitherdue to retention of this volatile inhibitor or to restrictionof nutrient uptake by the existence of a stationary liquid-phaseboundary to the cells.     

Studies on the Growth in Culture of Plant Cells: XII. A VERSATILE SYSTEM FOR THE LARGE SCALE BATCH OR CONTINUOUS CULTURE OF PLANT CELL SUSPENSIONS

A versatile large-scale batch culture unit has been developedfor the growth of plant cell suspension cultures. This unithas been modified to permit of intermittent or continuous renewalof culture medium and, in a modified form, incorporated intoopen continuous culture systems of the chemostat and turbidostattype. A fully automatic culture sampler has been incorporatedinto the basic culture unit. The culture systems described havebeen successfully operated using a cell suspension derived fromAcer pseudoplatanus and results are presented demonstratingsynchronous growth in batch culture, prolonged logarithmic increassein cell number under conditions of high aeration and culturemedium renewal, and steady states of growth resulting from automaticregulation of the optical density of the cell suspension andfrom fixed rates of displacement of cell suspension by new medium.The potentialities of the culture systems are discussed in thelight of the experimental results presented.