Optimizing control of a continuous stirred tank fermenter using a neural network

Feedforward neural networks are a general class of nonlinear models that can be used advantageously to model dynamic processes. In this investigation, a neural network was used to model the dynamic behaviour of a continuous stirred tank fermenter in view of using this model for predictive control. In this system, the control setpoint is not known explicitly but it is calculated in such a way to optimize an objective criterion. The results presented show that neural networks can model very accurately the dynamics of a continuous stirred tank fermenter and, the neural model, when used recursively, can predict the state variables over a long prediction horizon with sufficient accuracy. In addition, neural networks can adapt rapidly to changes in fermentation dynamics.List of Symbols F Dimensionless flow rate (F/ V₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective cost function - K _i Dimensionless constant in Eq. (3) (k _i /s₀) - k _i kg/m³ Substrate inhibition constant in Haldane model - k _m Dimensionless constant in Eq. (3) (k _s /s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - n prediction horizon - S Dimensionless substrate concentration (s/s₀) - s kg/m³ Substrate concentration - t h Time - v Dimensionless volume (V/V₀) - V m³ Liquid volume in fermenter - W _ij , W _jk Weight matrices in neural network - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ) - 1/h Maximum specific growth rate - 1/h Specific growth rate - Dimensionless time ( t)     

Optimization and control of a continuous stirred tank fermenter using learning system

A variable structure learning automaton is used as an optimization and control of a continuous stirred tank fermenter. The algorithm requires no modelling of the process. The use of appropriate learning rules enables to locate the optimum dilution rate in order to maximize an objective cost function. It is shown that a hierarchical structure of automata can adapt to environmental changes and can also modify efficiently the domain of variation of the control variable in order to encompass the optimum value.List of Symbols f Random number - F Dimensionless flow rate (F/V ₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective function - K _i Dimensionless constant in Eq. (3) (k _i/s₀) - k _i · kg/m³ Substrate inhibition constant in Haldane model - K _m Dimensionless constant in equation (3) (k _s/s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - L Number of levels of the hierarchical system of automata - N Number of possible control actions - p Probability - S Dimensionless substrate concentration (s/s ₀) - s kg/m³ Substrate concentration - T Dimensionless sampling period - t h Time - v Dimensionless volume (V/V ₀) - V m³ Liquid volume in fermenter - W Input to the stochastic automaton - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ^*) - ^* h^–1 Maximum specific growth rate - h^–1 Specific growth rate - Dimensionless time ( t)     

Respiratory activity and growth kinetics of Candida yeasts related to carbon sources and available energy

Summary Three yeasts of the genus Candida (Candida intermedia, candida lipolytica and Candida tropicalis) were cultivated batchwise on three different carbon sources: glucose, acetate, and hexadecane. Growth curves, oxygen uptake rates, CO₂ evolution rates and the amount of oxygen required for biomass production were determined. The data were compared and discussed from the point of maximum specific growth rate, maximum oxygen uptake rate, carbon conversion into CO₂ and biomass, consumption of oxygen and available energy for cell synthesis. The results indicated a relationship between _m m, Y_s, Y_O, and for different carbon sources. Y_O and were in the same order of magnitude for acetate (0.58 and 0.38 respectively) and hexadecane (0.45 and 0.40 respectively). These values were remarkably lower than those for glucose (1.26 and 0.54 respectively).Symbols av e^– Available electrons per mol of substrate (dimensionless) - E_av Energy available per mol of substrate (dimensionless) - C_d Dissimilated carbon (%) - m Maximum specific rate of oxygen uptake (mMO₂ h^–1 g^–1) - RQ CO₂ evolved per O₂ consumed - mol. wt. Molecular weight - Y_ATP Biomass mass yield based on mol of ATP generated (g) - Biomass mass yield based on available energy (g) - Y_M Biomass mass yield based on mol of organic substrate (g) - Y_O Biomass mass yield based on oxygen consumed (gg^–1) - 1/Y_O Oxygen consumed for one gram of biomass produced (gg^–1) - Y_s Biomass mass yield based on organic substrate (dimensionless) - b Reductance degree of biomass (equiv. available electrons/g atom carbon) - s Reductance degree of organic substrate (equiv. available electrons/g atom carbon) - Fraction of energy in organic substrate which is converted to biomass - b Weight fraction carbon in biomass (dimensionless) - s Weight fraction carbon in organic substrate (dimensionless) - _m Maximum specific growth rate (h^–1)     

Role of mitochondria in ethanol tolerance of Saccharomyces cerevisiae

The presence of active mitochondria and oxidative metabolism is shown to be essential to maintain low inhibition levels by ethanol of the growth rate (), fermentation rate (v) or respiration rate () of Saccharomyces cerevisiae wild type strain S288C. Cells which have respiratory metabolism show K _i (ethanol inhibition constant) values for , v and , higher (K _i>1 M) than those of petite mutants or grande strains grown in anaerobiosis (K _i=0.7 M). In addition, the relationship between or v and ethanol concentration is linear in cells with respiratory metabolism and exponential in cells lacking respiration. When functional mitochondria are transferred to petite mutants, the resulting strain shows K _i values similar to those of the grande strain and the inhibition of and v by increasing ethanol concentrations becomes linear.     

Growth of the thermotolerant yeast,Candida valida,on ethanol: Dependences of maximal growth rate and cell biomass yield on temperature

Summary Growth of Candida valida on ethanol in pH-auxostat and chemostat has been studied. Maximal growth rate, _m, and cell biomass yield, Y _s, display the Arrhenius dependence on temperature within the ranges 18°–30° C and 30°–36° C and an abrupt fall above 36° C. The temprature dependence of both parameters has breaks at 30° C and 36° C. Activation energies have been measured for both _m and Y _s. The reason for a weaker effect of temperature on Y _s than on _m is discussed.     

Growth yields and growth rates of Desulfovibrio vulgaris (Marburg) growing on hydrogen plus sulfate and hydrogen plus thiosulfate as the sole energy sources

Desulfovibrio vulgaris (Marburg) was grown on H₂ plus sulfate and H₂ plus thiosulfate as the sole energy sources and acetate plus CO₂ as the sole carbon sources. Conditions are described under which the bacteria grew exponentially. Specific growth rates () and molar growth yields (Y) at different pH were determined. and Y were found to be strongly dependent on the pH. Highest growth rates and molar growth yields were observed for growth on H₂ plus sulfate at pH 6.5 (=0.15h^-1; Y _{SO 4} ^2- =8.3g·mol^-1) and for growth on H₂ plus thiosulfate at pH 6.8 (=0.21h^-1; Y _{S 2}O ₃ ² =16.9g·mol^-1).The growth yields were found to increase with increasing growth rates: plots of 1/Y versus 1/ were linear. Via extrapolation to infinite growth rates a Y _SO4 ^2- /max of 12.2g·mol^-1 and a YS₂O ₃ ^2- /max of 33.5g·mol^-1 was obtained.The growth yield data are interpred to indicate that dissimilatory sulfate reduction to sulfide is associated with a net synthesis of 1 mol of ATP and that near to 3 mol of ATP are formed during dissimilatory sulfite reduction to sulfide.     

Effect of growth temperature on the morphology and performance ofZymomonas mobilis ATCC 29 191 in batch and continuous culture

Summary Increasing the temperature in chemostat culture ofZymomonas mobilis ATCC 29 191 with low and high glucose concentrations was found to result in a decreasing frequency of septation leading to the formation of long filaments and in increasing outer membrane blebbing. Whether this effect is strain specific or universal inZymomonas is, unknown. Improvements in the fermentation kinetics could be achieved at elevated temperatures, with an optimum at 33°C. Temperatures >30°C induced uncoupled growth in chemostat cultures ofZ. mobilis ATCC 29 191. The results of this study emphasize the importance of temperature regulation in optimizing the performance of continuous fermentations withZymomonas.Nomenclature D Dilution rate, 1/h - _max Maximum specific growth rate, 1/h - S _R Initial substrate concentration, g glucose/1 - S Amount of glucose consumed, g glucose/1 - S ₀ Effluent substrate concentration, g glucose/1 - X Biomass concentration - g cells/1 - [P] Amount of product formed, g ethanol/1 - [P] Product concentrations, g ethanol/l - Y _x/s Growth yield, g cells/g glucose used - Y _p/s Product yield, g ethanol/g glucose used - O _s Specific rate of glucose uptake, g glucose/g cells/h - Q _p Specific rate of ethanol formation, g ethanol/g cells/h - VP Volumetric productivity, g ethanol/1/h - t Fermentation time, h Corresponding author     

Image processing technique for measuring specific growth rates of Gibberella fujikuroi

Summary Two methods were compared for estimating of Gibberella fujikuroi grown with different proportions of glucose and starch. They were, =Ln2 (V_r/Le) on Petri dish (V_r= rate of tip extension and L_e= mean hyphal length) and, ₂=d (LnX)/dt in stirred fermenter. Values of ₁ and ₂ were in close agreement with each other.     

On the effect of glucono-δ-lactone on the yeast Pichia polymorpha

Investigation has been made into the action of glucono--lactone on living cells of Pichia polymorpha in relation to the uptake of D-(U-¹⁴C) glucose, and the incorporation of (2-¹⁴C) uracil and L-(U-¹⁴C)-threonine into RNA and protein respectively. Other factors such as the action of glucono--lactone on cell morphology and on enzymic synthesis have also been studied. The action of this compound on -glucanase has been found to take place in the hydrolytic power and not in the synthesis.     

The comparative effects of IL-1 and TNF on AMN-anti-Ly 2.1 immunoconjugate therapy

The administration of mTNF and hIL-1 was investigated for their potential to increase the anti-tumor activity of AMN-anti-Ly-2.1 against the Ly-2.1⁺ murine thymoma ITT(1) 75 NS E3. Dose response studies using mTNF alone demonstrated a single 10g iv injection produced 30% inhibition in tumor size while 3 doses of 1g administered on alternative days produced 70% tumor inhibition. By contrast, hIL-1 was unable to significantly reduce E3 tumor size using single doses up to 10g or a total of 30g administered in 3 doses (iv or ip). However, intratumor injection of hIL-1 (20g injected in 2 doses) produced 20% inhibition in tumor size. Combination therapy using AMN immunoconjugates with mTNF showed enhanced antitumor activity compared to each agent alone. Biodistribution studies revealed that anti-tumor activity, was due to increased localization (2–3 fold) of AMN immunoconjugates in the presence of mTNF- whereas huIL-1 was without effect unless accompanying toxicity was seen. Clearly for this tumor, mTNF potentiated the effects of AMN immunoconjugates. Despite the shared biological properties of these cytokines, mTNF is superior to hIL- for augmenting drug immunoconjugate.Abbreviations AMN Aminopterin - CBF₁ (C57BL6xBALB/c)F₁ mice - DMSO Dimethyl sulfoxide - E3 ITT(1)75NS E3 - HAMA human-anti-mouse antibody - i.p. intraperitoneal(ly) - I.T. intratumor - i.v. intravenous(ly) - hIL-1 recombinant human Interleukin-1-alpha - MoAb monoclonal antibody - PBS phosphate buffered saline - SE standard error - s.c. subcutaneous(ly) - mTNF recombinant murine tumor necrosis factor-alpha     

The influence of temperature on glucose-6-phosphate dehydrogenase and 6-phosphogluconate dehydrogenase and the regulation of these enzymes in a mesophilic and a thermophilic cyanobacterium

The activities and kinetics of the enzymes G6PDH (glucose-6-phosphate dehydrogenase) and 6PGDH (6-phosphogluconate dehydrogenase) from the mesophilic cyanobacterium Synechococcus 6307 and the thermophilic cyanobacterium Synechococcus 6716 are studied in relation to temperature. In Synechococcus 6307 the apparent K _m's are for G6PDH: 80M (substrate) and 20M (NADP⁺); for 6PGDH: 90M (substrate) and 25M (NADP⁺). In Synechococcus 6716 the apparent K _m's are for G6PDH: 550M (substrate) and 30M (NADP⁺); for 6PGDH: 40M (substrate) and 10M (NADP⁺). None of the K _m's is influenced by the growth temperature and only the K _m's of G6PDH for G6P are influenced by the assay temperature in both organisms. The idea that, in general, thermophilic enzymes possess a lower affinity for their substrates and co-enzymes than mesophilic enzymes is challenged.Although ATP, ribulose-1,5-bisphosphate, NADPH and pH can all influence the activities of G6PDH and 6PGDH to a certain extent (without any difference between the mesophilic and the thermophilic strain), they cannot be responsible for the total deactivation of the enzyme activities observed in the light, thus blocking the pentose phosphate pathway.Abbreviations G6PDH glucose-6-phosphate, dehydrogenase - 6PGDH 6-phosphogluconate dehydrogenase - G6P glucose-6-phosphate - 6PG 6-phosphogluconate - RUDP ribulose-1,5-bisphosphate - Tricine N-Tris (hydroxymethyl)-methylglycine     

Responses of nitrogen-fixing and nitrate-supplied alfalfa (Medicago sativa L.) to iron chelates in an alkaline hydroponic medium

Ferric ethylenediamine di-(o-hydroxyphenylacetate) (FeEDDHA) and ferric hydroxyethylethylenediaminetriacetic acid (FeHEDTA) were evaluated as Fe sources for hydroponic growth of alfalfa (Medicago sativa L., cv. Mesilla), either dependent on N₂ fixation or supplied with NO₃. The hydroponic medium was maintained at pH 7.5 by addition of CaCO₃. Nitrogen-fixing cultures were inoculated with Rhizobium meliloti 102 F51 and grown in medium without added nitrogen. After five to seven weeks of growth under greenhouse conditions, plants were harvested. Nitrogen fixation was measured by the acetylene reduction method.When FeEDDHA was supplied, growth of alfalfa, whether dependent on N₂ fixation or supplied with NO₃, was severely limited at concentrations typically used in hydroponic medium (10 or 20 M). Maximum yield of NO₃-supplied alfalfa was obtained at 100 M while maximum yield of N₂-fixing alfalfa was obtained in the range of 33 to 200 M FeEDDHA. Nodule fresh weights and N₂ fixation rates increased with FeEDDHA concentration up to 33 M and remained essentially constant up to 200 M. With FeHEDTA, maximum yields of both NO₃-grown and N₂-fixing alfalfa were obtained at 10 M. Growth of NO₃-supplied plants was inhibited at 200 M FeHEDTA while growth of N₂-fixing plants was inhibited at 100 M FeHEDTA. The numbers of nodules per plant increased between 3.3 and 10 M FeHEDTA; however, inhibition of nodule formation occurred at a concentration of 33 M or higher. Nodule weights per plant and N₂ fixation rates were depressed at 3.3 M as well as at 100 M FeHEDTA. The results suggest that alfalfa dependent on N₂ fixation is more sensitive to limited Fe availability than alfalfa supplied with NO₃.     

Influence of iron(III) and pyoverdine on extracellular proteinase and lipase production by Pseudomonas fluorescens B52

Factors associated with the production of extracellular lipase and proteinase by Pseudomonas fluorescens B52 during the late-log, early-stationary phase of grown were examined. Active lipase production by resting cell suspensions was observed when cells were harvested during the log phase (A₆₀₀ of 0.3–0.9) Resting suspensions of younger cells (A₆₀₀<0.1) synthesized lipase after a significant lag. Addition of cells of the proteinase-and lipasedeficient mutant P. fluorescens RM14 to B52 cells at low density resulted in stimulation of lipase and proteinase production. Similar results were found using cell-free culture fluid of RM14. Gel filtration on Biogel P2 revealed that the stimulatory factor co-chromatographed with the iron(III) siderophore, pyoverdine. Partially purified pyoverdine stimulated enzyme synthesis at a concentration of 6 M while having no effect on activity of preformed enzyme. Production of pyoverdine and extracellular enzymes was also stimulated by transferrin, a strong iron(III) binding protein. Growth of B52 in deferrated media was limited to 27% of that found with untreated media. Maximum pyoverdine, proteinase and lipase synthesis was obtained at a final iron(III) concentration of 5.75 M. Growth was maximal in 8.75 M iron(III) while synthesis of pyoverdine, proteinase and lipase was reduced to 3.6, 6.6 and 30% respectively in 23.75 M iron(III). Lipase activity in cell-free culture fluid was slightly inhibited by the addition of up to 400 M iron(III) while proteinase activity was unaffected. In dilute cell suspensions, lipase synthesis was more sensitive to iron(III) than was proteinase (50% inhibition at 1.6 M and a maximum of 40% inhibition at 5.0 M, respectively). In the case of lipase, added pyoverdine was able to partially protect enzyme production from the effects of iron(III). The results are consistent with a role for iron(III) in the regulation of extracellular lipase and proteinase synthesis by P. fluorescens.Contribution No. 677 from the Food Research Centre     

The quantitative analysis of chromosome pairing and chiasma formation based on the relative frequencies of M I configurations

Whilst reliable estimates of chiasma frequencies can usually not be obtained, the probability (b) of a chromosome arm to be bound by at least one chiasma can often be determined. In the absence of interference this probability equals (1–e ^–2), where 2 is the average chiasma frequency of the chromosome arm and the average crossover frequency or map length. In the presence of interference is shown to retain its genetic meaning as an additive metric that may describe the chromosome arm or other distinctive chromosome segment in terms of genetic recombination. It is a form of potential map length, comparable to, but numerically different from the regular map length. It is termed provisionally crossing-over potential.A chromosome with armsm andn with crossing-over potentials and will form ring bivalents with a frequency (1–e ^–2).(1–e ^–2); open bivalents with a frequency (1–e ^–2).e ^–2+(1–e ^–2).e ^–2; univalent pairs with a frequencye ^–2.e ^–2. Estimates of these frequencies yield equations from which and may be solved. In rye (Secale cereale) their ratio (q) is approximately two and differs from the mitotic arm length ratio of 1.4, indicating localization of chiasmata in the long arms.Graphs are given to show how, with constantq, the relation between the probabilitiesb _m andb _n of the two arms being bound changes with changing averageb.Data are presented on chiasma frequencies in M I, and compared with the frequencies expected in the absence of interference to give an impression of the degree of interference. Apparent fusion of chiasmata simulates interference.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part I: The full model and some of its limits

In this paper we give an analytical reformulation of Holling's (1966) simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density.Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - b maximum pursuit duration in the mantid (_p(0)) - c satiation threshold for search - c satiation threshold for pursuit in the mantid: c=c(b-D_s/v)/b - D _m maximum sighting distance - D _p pursuit distance - D _s strike distance - expectation operator - f, f ₀ rate of change of satiation during search - f ₁ rate of change of satiation during prey handling - F functional response: number of prey eaten per unit of time by one predator - g rate constant of effective prey encounter in the gobbler and sucker - g₀ rate constant of prey encounter - g₁ probability of no prey loss from pursuit - g₂ probability of no prey escaping during pursuit - H Holling secretary correction factor in the sucker: fraction of the time spent searching - k _R density of R - k_T probability density of maximum prey handling time - K probability that maximum prey handling time is _e, i.e. pursuit duration is zero - K _R distribution function of R - N number of prey caught - p (marginal) density of S - p₀ density of S in search - p₁ simultaneous density of S and T - P probability - p ₁ marginal density of S in handling prey - q probability of strike success - R ratio of realized to maximum sighting distance - s, S satiation - satiation axis - t time - handling time axis - u eating speed - U homogeneous(0,1) random variable - v pursuit speed - V exponential(1) random variable - w prey weight - W exponential(_m) random variable - x prey density - ratio of maximum successful pursuit duration to meal duration (_pm/_e) - _pm - relative duration of successful pursuit (_p/_pm) - ratio of shortest to largest sighting distance - x_e - time already spent handling a prey item - rate of prey loss during prey handling - prey escape rate during pursuit - prey biomass density (xw) - , T maximum time still to be spent handling a prey item - _e meal duration - _m maximum handling time ( _e+ _p) - _p duration of successful pursuit - _pm maximum duration of successful pursuit (_p(0)) - hazard rate - _m maximum of hazard rate - scaled functional response (wF) - minimal i-state space     

Energy requirements for growth and maintenance of Scenedesmus protuberans Fritsch in light-limited continuous cultures

Scenedesmus protuberans Fritsch was grown in light-limited continuous cultures with a light-dark cycle, at temperatures of 20° and 28° C. At 20° irradiances of 12 and 38 W m^–2 were used, at 28° 38 W m^–2.The relationships between growth rate and light uptake rate were of diphasic linear character. With the lower growth rates the relationships were defined with the parameters _e , i.e. the specific maintenance rate constant, and c, the true efficiency of light energy conversion into biomass. The _e -value was dependent on temperature, the c on irradiance.In cultures, incubated in prolonged darkness, decrease rates of biomass were comparable to the derived _e -values.Both diphasic linear relationships between growth rate and light uptake rate and the same order of magnitude of _e -values could be derived from literature data on other green algae.     

Transient state characteristics of adaptation to changes in light conditions for the cyanobacterium Oscillatoria agardhii

Transitions in growth irradiance level from 92 to 7 Em^-2 s^-1 and vice versa caused changes in the pigment contents and photosynthesis of Oscillatoria agardhii. The changes in chlorophyll a and C-phycocyanin contents during the transition from high to low irradiance (HL) were reflected in photosynthetic parameters. In the LH transition light utilization efficiencies of the cells changed faster than pigment contents. This appeared to be related to the lowering of light utilization efficiencies of photosynthesis. As a possible explanation it was hypothesized that excess photosynthate production led to feed back inhibition of photosynthesis. Time-scales of changes in the maximal rate of O₂ evolution were discussed as changes in the number of reaction centers of photosystem II in relation to photosynthetic electron transport. Parameters that were subject to change during irradiance transitions obeyed first order kinetics, but hysteresis occurred when comparing HL with LH transients. Interpretation of first order kinetic analysis was discussed in terms of adaptive response vs changes in growth rate.Non-standard abbreviations Chla chlorophyll a - CPC C-phycocyanin - PS II photosystem II - PS I photosystem I - RC II reaction center of photosystem II - P photosynthetic O₂-evolution - I irradiance, Em^-2 s^-1 - light utilization efficiency of cells, mmol O₂·mg dry wt^-1·h^-1/Em^-2 s^-1 - light utilization efficiency of photosynthetic apparatus, mol O₂·mol Chla ^-1·h^-1/Em^-2 s^-1 - P_max maximal rate of O₂ evolution by cells, mol O₂·mg dry wt^-1·h^-1 - P_max maximal rate of O₂ evolution by photosynthetic apparatus, mol O₂·mol·Chla ^-1·h^-1 - LL low light, E m^-2 s^-1 - HL high light, E m^-2 s^-1 - LH low to high light transition - HL high to low light transition - k specific rate of adaptation, h^-1 - specific growth rate, h^-1 - Q pool size of cell constituent, mol·mg dry wt^-1 - q net synthesis rate of cell constituent, mol·mg dry wt^-1·h^-1     

Analysis of gas exchange in seedlings of Acer saccharum: integration of field and laboratory studies

In the field, photosynthesis of Acer saccharum seedlings was rarely light saturated, even though light saturation occurs at about 100 mol quanta m^-2 s^-1 photosynthetic photon flux density (PPFD). PPFD during more than 75% of the daylight period was 50 mol m^-2 s^-1 or less. At these low PPFD's there is a marked interaction of PPFD with the initial slope (CE) of the CO₂ response. At PPFD-saturation CE was 0.018 mol m^-2 s^-1/(l/l). The apparent quantum efficiency (incident PPFD) at saturating CO₂ was 0.05–0.08 mol/mol. and PPFD-saturated CO₂ exchange was 6–8 mol m^-2 s^-1. The ratio of internal CO₂ concentration to external (C _i /C _a ) was 0.7 to 0.8 except during sunflecks when it decreased to 0.5. The decrease in C _i /C _a during sunflecks was the result of the slow response of stomates to increased PPFD compared to the response of net photosynthesis. An empirical model, which included the above parameters was used to simulate the measured CO₂ exchange rate for portions of two days. Parameter values for the model were determined in experiments separate from the daily time courses being sumulated. Analysis of the field data, partly through the use of simulations, indicate that the elimination of sunflecks would reduce net carbon gain by 5–10%.List of symbols A measured photosynthetic rate under any set of conditions (mol m^-2 s^-1) - A _m (atm) measured photosynthetic rate at saturating PPFD, 350 l/l CO₂ and 21% (v/v) O₂ (mol m^-2 s^-1) - C constant in equation of Smith (1937, 1938) - C _a CO₂ concentration in the air (l/l) - C _i CO₂ concentration in the intercellular air space (l/l) - C _i ^/* C _i corrected for CO₂ compensation point, i.e., C _i -I ^*, (l/l) - CE initial slope of the CO₂ response of photosynthesis (mol m^-2 s^-1/(l/l)) - CEM CE at PPFD saturation - E transpiration rate (mmol m^-2 s^-1) - F predicted photosynthetic rate (mol m^-2 s^-1) - G leaf conductance to H₂O (mol m^-2 s^-1) - I photosynthetic photon flux density (mol m^-2 s^-1) - N number of data points - P _m predicted photosynthetic rate at saturating CO₂ and given PPFD (mol m^-2 s^-1) - P _ml predicted photosynthetic rate at saturating CO₂ and PPFD (mol m^-2 s^-1) - R _d residual respiratory rate (mol m^-2 s^-1) - T _a air temperature (°C) - T _l leaf temperature (°C) - V reaction velocity in equation of Smith (1937, 1938) - V _max saturated reaction velocity in equation of Smith (1937, 1938) - VPA vapor pressure of water in the air (mbar/bar) - VPD vapor pressure difference between leaf and air (mbar/bar) - X substrate concentration in equation of Smith (1937, 1938) - initial slope of the PPFD response of photosynthesis at saturating CO₂ (mol CO₂/mol quanta) - (atm) initial slope of the PPFD response of photosynthesis at 340 l/l CO₂ and 21% (v/v) O₂ (mol CO₂/mol quanta) - I ^* CO₂ compensation point after correction for residual respiration (l/l) - PPFD compensation point (mol m^-2 s^-1)     

Distance-constraint approach to protein folding. I. Statistical analysis of protein conformations in terms of distances between residues

A statistical analysis of protein conformations in terms of the distance between residues, represented by their C atoms, is presented. We consider four factors that contribute to the determination of the distanced _i,i+k between a given pair ofith and(i+k)th residues in the native conformation of a globular protein: (1) the distancek along the chain, (2) the size of the protein, (3) the conformational states of theith to(i+k)th residues, and (4) the amino acid types of the and(i+k)th residues. In order to account for the dependence on the distancek along the chain, the statistics are taken for three ranges, viz., short, medium, and long ranges (k8; 9k20; andk21; respectively). In the statistics of short-range distances, a mean distanceD _k and its standard deviationS _k are calculated for each value ofk, with and without taking into account the conformational states of all residues fromi toi+k (factors 1 and 3). As an Appendix, the relations for converting from the distances between residues into other conformational parameters are discussed. In the statistics of long-range distances, a reduced distanced* _ij (the actual distance divided by the radius of gyration) is used to scale the data so that they become independent of protein size, and then a mean reduced distanceD _l (a, a) and its standard deviation _l (a, a) are calculated for each amino acid pair (a, a) (factors 2 and 4). The effect of the neighboring residues along the chain on the value of the distanced* _ij is explored by a linear regression analysis between the actual reduced distanced* _ij and the mean value over theD _l for all possible pairs of residues in the two segments of the (i–2)th to the (i+2)th and the (j–2)th to the (j+2)th residues. The effect is assessed in terms of the tangentA _l (a, a) of the calculated regression line for each amino acid pair (a, a). In the statistics of medium-range distances, only factors 1 and 4 are considered, to simplify the analysis. The scaled distanced _i,i+k =(d _i,i+k -D _k )/S _k is used to eliminate the dependence onk, the distance along the chain. The propertiesD _m (a, a), _m (a, a) andA _m (a, a) corresponding toD _l (a, a), _l (a, a), andA _l (a, a), and also calculated for each amino acid pair (a, a). The results are interpreted as follows: the smaller values ofD _l (a, a) andD _m (a, a) indicate a preference of the pair (a, a) for a contact (e.g., pairs between hydrophobic amino acids, and pairs of Cys with aromatic amino acids), and the larger values of these quantities indicate a preference for distant mutual location (e.g., pairs between strong hydrophilic amino acids); the smaller values of _l (a, a) and _m (a, a) indicate a strong preference for either contact or noncontact (e.g., pairs between hydrophobic amino acids, and pairs between strong hydrophobic and hydrophilic amino acids, respectively), and the larger values of these quantities indicate the ambivalent/neutral nature of the preference for contact and noncontact (e.g., pairs containing Ser or Thr); the smaller values ofA _l (a, a) andA _m (a, a) indicate that the distance of an (a, a) pair is determined independently of the amino acid character of the neighboring residues along the chain (e.g., some pairs of Cys or Met with other amino acids) and the larger values of these quantities indicare that such amino acid character contributes strongly to the determination of the distance (e.g., pairs containing Ser or Thr, and pairs between amino acids with small side chains). The difference between the statistics for the long- and medium-range distances is also discussed; the former reflect the difference between the hydrophobic and hydrophilic character of the residues, but the latter cannot be easily interpretable only in terms of hydrophobicity and hydrophilicity. The data analyzed here are used in the optimization of an object function to compute protein conformation in a subsequent paper.     

Effect of time delay in specific growth rate on the periodic operation of bioreactors with input multiplicities

The effect of time delay in specific growth rate () on the periodic operation of bioreactors with input multiplicities is theoretically analyzed for productivity improvement. A periodic rectangular pulse is applied either in feed substrate concentration (S_f) or in dilution rate (D). Periodic operation under feed substrate concentration cycling gives improvement in productivity at lower value of ¯S_f of the two steady-state multiplicities of S_f only when the time delay in is larger. Whereas the larger value of ¯S_f gives improvement in average productivity for all values of time delay. Dilution rate (D) cycling gives an improvement in average productivity particularly for larger time delay in . This improvement in average productivity is obtained only at smaller value of dilution rate out of the two steady-state input multiplicities of D.List of Symbols D 1/h dilution rate - F memory function - g dummy variable - K_i g/l substrate inhibition constant - K_m g/l substrate saturation constant - P g/l product concentration - P_m g/l product saturation constant - Q g/(hl) product cell produced per unit time - S g/l substrate concentration - S_f g/l feed substrate concentration - S_f,p g/l feed substrate concentration during fraction of a period - X g/l biomass concentration - Y_X/S g/g cell mass yield - w variable either S or Z - Z g/l weighted average of substrate concentration Greek Letters 1/h time delay parameter - ₁ , ₂ product yield parameters, g/g and 1/h - pulse width expressed as a fraction of a period - 1/h specific growth rate - _m 1/h maximum specific growth rate - h period of oscillation - – average value