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.     

Phosphate-limited growth of Chromatium vinosum in continuous culture

Chromatium vinosum DSM 185 was grown in continuous culture at a constant dilution rate of 0.071 h^-1 with sulfide as the only electron donor. The organism was subjected to conditions ranging from phosphate limitation (S _R-phosphate=2.7 M and S _R-sulfide=1.8 mM) to sulfide limitation (S _R-phosphate=86 M and S _R-sulfide=1.8 mM). At values of S _R-phosphate below 7.5 M the culture was washed out, whereas S _R-phosphate above this value resulted in steady states. The saturation constant (K ) for growth on phosphate was estimated to be between 2.6 and 4.1 M. The specific phosphorus content of the cells increased from 0.30 to 0.85 mol P mg^-1 protein with increasing S _R-phosphate. The specific rate of phosphate uptake increased with increasing S _R-phosphate, and displayed a non-hyperbolic saturation relationship with respect to the concentration of phosphate in the inflowing medium. Approximation of a hyperbolic saturation function yielded a maximum uptake rate (V _max) of 85 nmol P mg^-1 protein h^-1, and a saturation constant for uptake (K _t) of 0.7 M. When phosphate was supplied in excess 8.5% of the phosphate taken up by the cells was excreted as organic phosphorus at a specific rate of 8 nmol P mg^-1 protein h^-1.Non-standard abbreviations BChla bacteriochlorophyll a - D dilution rate; _max, maximum specific growth rate - maximum specific growth rate if the substrate were not inhibitory - K saturation constant for growth on phosphate - V _max maximum rate of phosphate uptake - K _i saturation constant for phosphate uptake - K _i inhibition constant for growth in the presence of sulfide - S _R concentration of substrate in the inflowing medium     

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     

Anaerobic digestion of palm oil mill effluent and condensation water waste: an overall kinetic model for methane production and substrate utilization

The process of anaerobic digestion is viewed as a series of reactions which can be described kinetically both in terms of substrate utilization and methane production. It is considered that the rate limiting factor in the digestion of complex wastewaters is hydrolysis and this cannot be adequately described using a Monod equation. In contrast readily assimilable wastewaters conform well to this approach. A generalized equation has thus been derived, based on both the Monod and Contois equations, which serves extreme cases. The model was verified experimentally using continuous feed anaerobic digesters treating palm oil mill effluent (POME) and condensation water from a thermal concentration process. POME represents a complex substrate comprising of unhydrolyzed materials whereas the condensation water is predominantly short chain volatile fatty acids. Substrate removal and methane production in both cases could be predicted accurately using the generalized equation presented.List of Symbols A (=K_skY/K_h) Kinetic parameter - B Specific methane yield, 1 of CH₄/g of substrate added B₀ Maximum specific methane yield, 1 of CH₄/g of substrate added at infinity - C Empirical constant in Contois equation - F Volumetric substrate removal rate, g/l day - k Hydrolysed substrate transport rate coefficient, 1/days - K (=YC) Kinetic parameter in Chen-Hashimoto equation - K _h Substrate hydrolysis rate coefficient, 1/days - K _s Half-saturation constant for hydrolysed substrate, g/l - M _v Volumetric methane production rate, 1 of CH₄/l day - MS Mineral solids, g/l - MSS Mineral suspended soilds, g/l - POME Palm oil mill effluent - R (=S_r/S_T0) Refractory coefficient - S _h Concentration of hydrolysed substrate, g/l - S _u Intracellular concentration of hydrolysed substrate, g/l - S ₀ Input biodegradable substrate concentration, g/l - S Biodegradable substrate concentration in the effluent or in the digester, g/l - S _r Refractory feed substrate concentration, g/l - S _T0 (=S₀+S_r) Total feed substrate concentration, g/l - S _T (S+S_r) Total substrate concentration in the effluent, g/l - TS Total solids, g/l - TSS Total suspended solids, g/l - VFA Total volatile fatty acids, g/l - VS Volatile solids, g/l - VSS Volatile suspended solids, g/l - X Biomass concentration, g/l - Y Biomass yield coefficient, biomass/substrate mass - Hydraulic retention time, days. - Specific growth rate of microorganisms, l/days - _m Maximum specific growth rate of microorganisms, l/days The authors wish to express their gratitude to the Departamento de Postgrado y Especialización del CSIC and to the Consejería de Educación y Ciencia de la Junta de Andalucia for their financial support of this work.     

Enzyme production in a cell recycle fermentation system evaluated by computer simulations

Enzyme production in a cell recycle fermentation system was studied by computer simulations, using a mathematical model of -amylase production by Bacillus amyloliquefaciens. The model was modified so as to enable simulation of enzyme production by hypothetical organisms having different production kinetics at different fermentation conditions important for growth and production. The simulations were designed as a two-level factorial assay, the factor studied being fermentation with or without cell recycling, repression of product synthesis by glucose, kinetic production constants, product degradation by a protease, mode of fermentation, and starch versus glucose as the substrate carbon source.The main factor of importance for ensuring high enzyme production was cell recycling. Product formation kinetics related to the stationary growth phase combined with continuous fermentation with cell recycling also had a positive impact. The effect was greatest when two or more of these three factors were present in combinations, none of them alone guaranteeing a good result. Product degradation by a protease decreased the amount of product obtained; however, when combined with cell recycling, the protease effect was overshadowed by the increased production. Simulation of this type should prove a useful tool for analyzing troublesome fermentations and for identifying production organisms for further study in integrated fermentation systems.List of Symbols a proportionality constant relating the specific growth rate to the logarithm of G (h) - a ₁ reaction order with respect to starch concentration - a ₂ reaction order with respect to glucose concentration - c starch concentration (g/l) - c ₀ starch concentration in the feed (g/l) - D dilution rate (h^–1) - e intrinsic intracellular amylase concentration (g product/g cell mass) - E extracellular amylase concentration (g/l) - F volumetric flow rate (l/h) - G average number of genome equivalents of DNA/cell - K ₁ intracellular repression constant - K ₂ intracellular repression constant - K _s Monod saturation constant (g/l) - k ₃ product excretion rate constant (h^–1) - k _I translation constant (g product/g mRNA/h) - k _d first order decay constant (h^–1) - k _dw first order decay constant (h^–1) - k _gl rate constant for glucose production (g/l/h) - k _{m, dgr} saturation constant for product degradation (g/l) - k _st rate constant for starch hydrolysis (g/l/h) - k _t1 proportionality constant for amylase production (g mRNA/g substrate) - k _t2 proportionality constant for amylase production (g mRNA *h/g substrate) - k _w protease excretion rate constant (h^–1) - k _wt1 proportionality constant for protease production (g mRNA/g substrate) - k _wt2 proportionality constant for protease production (g mRNA *h/g substrate) - k _wI translation constant (g protease/g mRNA/h) - m maintenance coefficient (g substrate/g cell mass/h) - n number of binding sites for the co-repressor on the cytoplasmic repressor - Q repression function, K₁/K₂ less than or equal to 1.0 - Q _w repression function, K₁/K₂ less than or equal to 1.0 - r intrinsic amylase mRNA concentration (g mRNA/g cell mass) - r _m intrinsic protease mRNA concentration (g mRNA/g cell mass) - R _ex retention by the filter of the compounds x=: C starch, E amylase, or S glucose - R _t amylase transport rate (g product/g cell mass/h) - R _wt protease transport rate (g protease/g cell mass/h) - R _s rate of glucose production (g/l/h) - R _c rate of starch hydrolysis (g/l/h) - S ₀ feed concentration of free reducing sugar (g/l) - s extracellular concentration of reducing sugar (g/l) - t time (h) - V volume (1) - w intracellular protease concentration (g/l) - W extracellular protease concentration (g/l) - X cell mass concentration (dry weight) (g/l) - Y yield coefficient (g cell mass/g substrate) - substrate uptake (g substrate/g cell mass/h) - specific growth rate of cell mass (h^–1) - _d specific death rate of cells (h^–1) - _m maximum specific growth rate of cell mass (h^–1) - _m,dgr maximum specific rate of amylase degradation (h^–1) This study was supported by the Nordic Industrial Foundation Bioprocess Engineering Programme and the Center for Process Biotechnology, The Technical University of Denmark.     

A model for lipase production by Candida rugosa

A model adequately describing the lipase production by Candida rugosa has been developed, calibrated and validated using new experimental data. Process modelling has been done using CAMBIO software (Computer Aided Modelling of BIOprocesses), allowing to easy and interactively test various hypothesis and reaction schemes.Olive oil, oleic acid and glycerol has been used as substrates. The model satisfactorily describes the time evolution of biomass growth as well as lipase production in all cases. In particular diauxic behavior is successfully characterized.Model development process has helped in obtaining a 3-fold increase in lipase production when using oleic acid as substrate instead of the original olive oil used.List of Symbols Oil g/l Oil concentration - Fa g/l Fatty acids concentration - Gly g/l Glycerol concentration - Cr g/l Biomass (dry weight) - Lp U/ml Lipase - _p Oil hydrolysis rate - _gly Uptake rate on glycerol - _fa Uptake rate on fatty acids - _lp Increase rate of lipase - Y _ca Biomass/Fatty acids yield - Y _cg Biomass/Glycerol yield - Y _la Lipase/Fatty acids yield - k _l Specific growth rate on fatty acids - K _c Saturation constant - K _I Inhibition constant for lipase - k11 Specific growth rate on glycerol - k ₃ Oil hydrolysis parameter     

Phenol degradation by a psychrotrophic strain of Pseudomonas putida

Summary Cell growth and phenol degradation kinetics were studied at 10°C for a psychrotrophic bacterium, Pseudomonas putida Q5. The batch studies were conducted for initial phenol concentrations, S_o, ranging from 14 to 1000 mg/1. The experimental data for 14<=S_o<=200 mg/1 were fitted by non-linear regression to the integrated Haldane substrate inhibition growth rate model. The values of the kinetic parameters were found to be: _m=0.119 h^–1, K _S=5.27 mg/1 and K _I=377 mg/1. The yield factor of dry biomass from substrate consumed was Y=0.55. Compared to mesophilic pseudomonads previously studied, the psychrotrophic strain grows on and degrades phenol at rates that are ca. 65–80% lower. However, use of the psychrotrophic microorganism may still be economically advantageous for waste-water treatment processes installed in cold climatic regions, and in cases where influent waste-water temperatures exhibit seasonal variation in the range 10–30°C.Nomenclature K _S saturation constant (mg/l) - K _I substrate inhibition constant (mg/l) - specific growth rate (h^–1) - _m maximum specific growth rate without substrate inhibition (h^–1) - _max maximum achievable specific growth rate with substrate inhibition (h^–1) - S substrate (phenol) concentration (mg/l) - S_o initial substrate concentration (mg/l) - S_max substrate concentration corresponding to _max (mg/l) - t time (h) - X cell concentration, dry basis (mg DW/l) - X_f final cell concentration, dry basis (mg DW/l) - X_o initial cell concentration, dry basis (mg DW/l) - Y yield factor (mg DW cell produced/mg substrate consumed)     

Lactic acid production by batch fermentation of whey permeate: A mathematical model

Summary The batch fermentation of whey permeate to lactic acid was improved by supplementing the broth with enzyme-hydrolyzed whey protein. A mathematical model based on laboratory results predicts to a 99% confidence limit the kinetics of this fermentation. Cell growth, acid production and protein and sugar use rates are defined in quantifiable terms related to the state of cell metabolism. The model shows that the constants of the Leudeking-Piret model are not true constants, but must vary with the medium composition, and especially the peptide average molecular weight. The kinetic mechanism on which the model is based also is presented.Nomenclature K _i lactic acid inhibition constant (g/l) - K _pr protein saturation constant during cell growth (g/l) - K _pr protein saturation constant during maintenance (g/l) - K _s lactose saturation constant (g/l) - [LA] lactic acid concentration (g/l) - [PR] protein concentration (g/l) - [S] lactose concentration (g/l) - t time (h) - [X] cell mass concentration (g/l) - , fermentation constants of Leudeking and Piret - specific growth rate (l/h) - Y _{g, LA/S} acid yield during cell growth (g acid/g sugar) - Y _{m, LA/S} acid yield during maintenance (g acid/g sugar) - Y _x/pr yield (g cells/g protein) - specific sugar use rate during cell growth (g sugar/h·g cell) - specific sugar use rate during maintenance (g sugar/h·cell)     

A kinetic model and simulation of starch saccharification and simultaneous ethanol fermentation by amyloglucosidase and Zymomonas mobilis

A mathematical model is described for the simultaneous saccharification and ethanol fermentation (SSF) of sago starch using amyloglucosidase (AMG) and Zymomonas mobilis. By introducing the degree of polymerization (DP) of oligosaccharides produced from sago starch treated with -amylase, a series of Michaelis-Menten equations were obtained. After determining kinetic parameters from the results of simple experiments carried out at various substrate and enzyme concentrations and from the subsite mapping theory, this model was adapted to simulate the SSF process. The results of simulation for SSF are in good agreement with experimental results.List of Symbols g/g rate coefficient of production - _max 1/h maximum specific growth rate - E %, v/w AMG concentration - G ₁ mmol/l glucose concentration - G _c mmol/l glucose concentration consumed - G _f mmol/l glucose concentration formed - G _n mmol/l n-mer maltooligosaccharide concentration - K _i g/l ethanol inhibition constant for ethanol production - K _g mmol/l glucose inhibition constant for glucose production - K _p mmol/l glucose limitation constant for ethanol production - K _x mmol/l glucose limitation constant for cell growth - K _m,n mmol/l Michaelis-Menten constant for n-mer oligosaccharide - k _e %, v/w enzyme limitation constant - k _es proportional constant - k _{max, n} 1/s maximal velocity for n-mer digestion - k _s g/l substrate limitation constant - m _s g/g maintenance energy - MW _n g/mol molecular weight of n-mer oligosaccharide - P g/l ethanol concentration - P ₀ g/l initial ethanol concentration - P _m g/l maximal ethanol concentration - Q _pm g/(g · h) maximum specific ethanol production rate - S _n mmol/h branched n-mer oligosaccharide concentration - S ₀ g/l initial starch concentration - S _sta g/l starch concentration - S _tot g/l total sugar concentration - V _{max, n} 1/h maximum digestion rate of n-mer oligosaccharide - V ₀ g/(l · h) initial glucose formation rate - X g/l cell mass - X ₀ g/l initial cell mass - Y _p/s g/g ethanol yield - Y _x/s g/g cell mass yield     

Performance,kinetics, and substrate utilization in a continuous yeast fermentation with cell recycle by ultrafiltration membranes

Summary A continuous single stage yeast fermentation with cell recycle by ultrafiltration membranes was operated at various recycle ratios. Cell concentration was increased 10.6 times, and ethanol concentration and fermentor productivity both 5.3 times with 97% recycle as compared to no recycle. Both specific growth rate and specific ethanol productivity followed the exponential ethanol inhibition form (specific productivity was constant up to 37.5 g/l of ethanol before decreasing), similar to that obtained without recycle, but with greater inhibition constants most likely due to toxins retained in the system at hight recycle ratios.By analyzing steady state data, the fractions of substrate used for cell growth, ethanol formation, and what which were wasted were accounted for. Yeast metabolism varied from mostly aerobic at low recycle ratios to mostly anaerobic at high recycle ratios at a constant dissolved oxygen concentration of 0.8 mg/kg. By increasing the cell recycle ratio, wasted substrate was reduced. When applied to ethanol fermentation, the familiar terminology of substrate used for Maintenance must be used with caution: it is not the same as the wasted substrate reported here.A general method for determining the best recycle ratio is presented; a balance among fermentor productivity, specific productivity, and wasted substrate needs to be made in recycle systems to approach an optimal design.Nomenclature B Bleed flow rate, l/h - C _T Concentration of toxins, arbitrary units - D Dilution rate, h^-1 - F Filtrate or permeate flow rate, removed from system, l/h - F _o Total feed flow rate to system, l/h - K _s Monod form constant, g/l - P Product (ethanol) concentration, g/l - P _o Ethanol concentration in feed, g/l - PP} Adjusted product concentration, g/l - PD Fermentor productivity, g/l-h - R Recycle ratio, F/F _o - S Substrate concentration in fermentor, g/l - S _o Substrate concentration in feed, g/l - V Working volume of fermentor, l - V _MB Viability based on methylene blue test - X Cell concentration, g dry cell/l - X _o Cell concentration in feed, g/l - Y _ATP Cellular yield from ATP, g cells/mol ATP - Y _ATPS Yield of ATP from substrate, mole ATP/mole glucose - Y _G True growth yield or maximum yield of cells from substrate, g cell/g glucose - Y _P Maximum theoretical yield of ethanol from glucose, 0.511 g ethanol/g glucose - Y _P/S Experimental yield of product from substrate, g ethanol/g glucose - Y _x/s Experimental yield of cells from substrate, g cell/g glucose - S _NP/X Non-product associated substrate utilization, g glucose/g cell - k ₁, k₂, k₃, k₄ Constants - k ₁ ^APP , k ₂ ^APP Apparent k ₁, k₃ - k ₁ ^TRUE True k ₁ - m Maintenance coefficient, g glucose/g cell-h - m ^* Coefficient of substrate not used for growth nor for ethanol formation, g glucose/g cell-h - Specific growth rate, g cells/g cells-h, reported as h^-1 - _m Maximum specific growth rate, h^-1 - v Specific productivity, g ethanol/g cell-h, reported as h^-1 - v _m Maximum specific productivity, h^-1     

On-line parameter and state estimation of continuous cultivation by extended Kalman filter

Summary The on-line estimation of biomass concentration and of three variable parameters of the non-linear model of continuous cultivation by an extended Kalman filter is demonstrated. Yeast growth in aerobic conditions on an ethanol substrate is represented by an unstructured non-linear stochastic t-variant dynamic model. The filter algorithm uses easily accessible data concerning the input substrate concentration, its concentration in the fermentor and dilution rate, and estimates the biomass concentration, maximum specific growth rate, saturation constant and substrate yield coefficient. The microorganismCandida utilis, strain Vratimov, was cultivated on the ethanol substrate. The filter results obtained with the real data from one cultivation experiment are presented. The practical possibility of using this method for on-line estimation of biomass concentration, which is difficult to measure, is discussed.Nomenclature D dilution rate (h^-1) - DO₂ dissolved oxygen concentration (%) - E identity matrix - F Jacobi matrix of the deterministic part of the system equations g - g continuousn-vector non-linear real function - h m-vector non-linear real function - K Kalman filter gain matrix - K _S saturation constant (kgm^-3) - K_S expectation of the saturation constant estimate - M Jacobi matrix of the deterministic part of the measurement equations h - P(t₀) co-variance matrix of the initial values of the state - P(t_k/t_k) c-variance matrix of the error in (t _k|t _k) - P(t_k+1/t_k) co-variance matrix of the error in (t _k+1|t _k - Q co-variance matrix of the state noise - R co-variance matrix of the output noise - S substrate concentration (kgm^-3) - S _i input substrate concentration - t time - t _k discrete time instant with indexk=0, 1, 2,... - u(t) input vector - v(t_k) measurement (output) noise sequence - w(t) n-vector white Gaussian random process - x(t₀) initial state of the system - (t₀) expectation of the initial state values - x(t) n-dimensional state vector - x(t_k) state vector at the time instantt _k - (t_k|t_k) expectation of the state estimate at timet _k when measurements are known to the timet _k - (t_k+1|t_k) expectation of the state prediction - X biomass concentration (kgm^-3) - expectation of the biomass concentration estimate - y(t_k) m-dimensional output vector at the time instantt _k - Y _XIS substrate yield coefficient - _X|S expectation of the substrate yield coefficient estimate - specific growth rate (h^-1) - _M maximum specific growth rate (h^-1) - expectation of the maximum specific growth rate estimate - state transition matrix     

Updated model of the batch acetone-butanol fermentation

Summary The recent models of the Acetone-Butanol fermentation did not adequately describe the culture inhibition by the accumulating metabolites and were unable to simulate the acidogenic culture dynamics at elevated pH levels. The present updated modification of the model features a generalised inhibition term and a pH dependent terms for intracellular conversion of undissociated acids into solvent products. The culture dynamics predictions by the developed model compared well with experimental results from an unconventional acidogenic fermentation ofC. acetobutylicum.Nomenclature A acetone concentration in the fermentation broth, [g/L] - AA total concentration of dissociated and undissociated acetic acid, [g/L] - AA _undiss concentration of undissociated acetic acid, [g/L] - APS Absolute Parameter Sensitivity - AT acetoin concentration in the fermentation broth, [g/L] - B butanol concentration in the fermentation broth, [g/L] - BA total concentration of dissociated and undissociated butyric acid, [g/L] - BA _undiss concentration of undissociated butyric acid, [g/L] - E ethanol concentration in the fermentation broth, [g/L] - f(T) inhibition function as defined in Equation (2) - k ₁ constant in Equation (4), [g substrate/g biomass] - k ₂ constant in Equation (4), [g substrate/(g biomass.h)] - k ₁ constant in Equation (5), [g substrate/(g biomass] - k ₂ constant in Equation (5), [g substrate/(g biomass.h)] - k ₃ constant in Equation (6), [g butyric acid/g substrate] - k ₄ constant in Equation (6), [g butyric acid/(g biomass.h)] - k ₅ constant in Equation (7), [g butanol/g substrate] - k ₆ constant in Equation (8), [g acetic acid/g substrate] - k ₇ constant in Equation (8), [g acetic acid/(g biomass.h)] - k ₈ constant in Equation (9), [g acetone/g substrate] - k ₉ constant in Equation (10), [g ethanol/g substrate] - k ₁₀ constant in Equation (11), [g acetoin/g substrate] - k ₁₁ constant in Equation (12), [g lactic acid/g substrate] - K _I Inhibition constant, [g inhibitory products/L] - ke maintenance energy requirement for the cell, [g substrate/(g biomass.h)] - K _AA acetic acid saturation constant, [g acetic acid/L] - K _BA butyric acid saturation constant, [g butyric acid/L] - K _S Monod's saturation constant, [g substrate/L] - LA lactic acid concentration in the fermentation broth, [g/L] - m _i ,n _i constants in Equation (14) - n empirical constant, dependent on degree of inhibition. - P concentration of inhibitory products (B+BA+AA), [g/L] - P _max maximum value of product concentration to inhibit the fermentation, [g/L] - pK_a equilibrium constant - r _A rate of acetone production, [g acetone/L.h] - r _AA rate of acetic acid production, [g acetic acid/L.h] - r _AT rate of acetoin production, [g acetoin/L.h] - r _B rate of butanol production, [g butanol/L.h] - r _BA rate of butyric acid production, [g butyric acid/L.h] - r _E rate of ethanol production, [g ethanol/L.h] - RPS Relative Parameter Sensitivity - r _LA rate of lactic acid production, [g lactic acid/L.h] - r _S dS/dt=total substrate consumption rate, [g substrate/L.h] - r _S substrate utilization rate, [g substrate/L.h] - S substrate concentration in the fermentation broth, [g substrate/L] - S ₀ initial substrate concentration, [substrate/L] - t time, [h] - X biomass concentration, [g/L] - Y _X yield of biomass with respect to substrate, [g biomass/g substrate] - Y _{P i} yield of metabolic product with respect to substrate, [g product/g substrate] Derivatives dX/dt rate of biomass production, [g biomass/L.h] - dP _i /dt rate of product formation, [g product/L.h] Greek letters specific growth rate of the culture, [h^–1] - I specific growth rate of the culture in the presence of the inhibitory products, [h^–1] - µ_max maximum specific growth rate of the culture, [h^–1]     

Interrelation between penicillin productivity and growth rate

Summary Fermentations were carried out in an 801 tower-loop reactor with pellets of Penicillium chrysogenum. The development of the inner structure of the pellets with regard to various fermentation conditions was observed by means of histological preparations of the pellets. Under conditions of energy-source-limitation mycelial tip growth and lysis of other mycelial parts exist simultaneously. Thus the net growth rate (formation rate of cell mass) is higher than the gross growth rate (multiplication rate of cell mass). Under conditions of nitrogen limitation, gross growth rate and net growth rate are identical. A very strict correlation between gross growth rate and penicillin production rate was found as long as sufficient oxygen supply could be maintained and carbon catabolite repression was avoided. The energy source requirement of the biomass can be described with the sum of three terms that correspond to gross growth, lysis compensation growth and maintenance.Symbols a Constant 1/l h - b Constant - K Decay rate constant for product 1/h - K ₁ Substrate inhibition constant g/l - K _op Controls saturation constant for oxygen g/l - K _p Saturation constant for substrate g/l - m Maintenance coefficient 1/h - ms Apparent maintenance coefficient 1/h - O Dissolved oxygen concentration g/l - P Product concentration g/l - p Exponent of O - q Specific productivity 1/h - S Substrate concentration g/l - t Time h - t ₁ Beginning of production phase h - t ₂ Time of pellet dissolution h - V Liquid volume of fermentation broth l - X Dry cell mass concentration g/l - Y Yield of dry cell mass from energy substrate - g Specific gross growth rate of biomass 1/h - l Specific lysis rate of cell mass 1/h - n Specific net growth rate of cell mass 1/h - p Maximum specific rate of product formation 1/h     

On-line monitoring and modelling based process control of high rate nitrification — lab scale experimental results

This paper presents a new concept for the control of nitrification in highly polluted waste waters. The approach is based on mathematical modelling. To determine the substrate degradation rates of the microorganisms involved, a mathematical model using gas measurement is used. A fuzzy-controller maximises the capacity utilisation efficiencies. The experiments carried out in a lab-scale reactor demonstrate that even with highly varying ammonia concentrations in the influent, the nitrogen concentrations in the effluent can be kept within legal limits.List of Symbols c mg/l concentration - c mg/l gas concentration - H ₂ Henry-coefficient - k _L a 1/h mass transfer coefficient - mol/l dissociation constant - K _iS mg/l substrate inhibitor constant - k _iH mg/l inhibitor constant - k _S mg/l saturation constant - K _O2 mg/l oxygen saturation constant - r(B) mg/lh growth rate - r(S) mg/lh degradation reaction rate - t _v h retention time - T °C temperature - V 1 volume - V 1/h flow rate - Y g/g yield coefficient - k _b capacity utilisation efficiency - 1/h specific growth rate     

Influence of the ratio of the initial substrate concentration to biomass concentration on the performance of a sequencing batch reactor

Biomass behaviour and COD removal in a benchscale activated sludge reactor have been studied alternating anaerobic and aerobic conditions. Particular attention has been paid to the influence of the ratio of the initial substrate concentration (S ₀) to the initial biomass concentration (X ₀) on the reactor performance. Tests at very low ratios (S ₀/X ₀<2) demonstrate the existence of a threshold below which the reactor performance is seriously affected (S ₀/X ₀=0.5). Under conditions of total suppression of cell duplication, substrate maintenance requirements have also been calculated for the microbial consortium present in the activated sludges. The results obtained show that stressed biomass can survive conditions of substrate lack better than unstressed biomass.List of Symbols b h^–1 specific death rate - COD g/l chemical oxygen demand - DO g/l dissolved oxygen concentration - K _s g/l Monod saturation constant - MLSS g/l mixed liquor suspended solid concentration - P g/l phosphorus concentration - S g/l substrate concentration - S ₀ g/l initial substrate concentration - SS g/l suspended solid concentration - t h time - X g/l biomass concentration - X ₀ g/l initial biomass concentration - Y _SX g/g yield of growth on substrate - _max h^–1 maximum specific growth rate     

Circadian rhythmicity in a fermentation process?

Summary An idea is proposed for the role of the circadian rhythmicity in the control of the oscillatory behavior observed in the growth and product formation during the cell-retention continuous culture of Clostridium acetobutylicum. C. acetobutylicum is highly sensitive to the permeability of the cell membrane. A physical mechanism for the variability of the cytoplasmic membrane has been proposed suggesting that the performance of the cell membrane, due to its liquid crystalline structure, is influenced by the external forces (e.g. earth's magnetic field). A previously developed Physiological State Model was extended by incorporating the effect of external forces on the cell membrane permeability. The new mathematical model could simulate the observed oscillatory behavior of the microbial culture. Some experimental results in support of the theoretical predictions have been presented.Nomenclature a Anisotropy - B Butanol concentration in the fermentation broth (g/l) - B _i Intracellular butanol concentration (g/l) - B _ex Extracellular butanol concentration (g/l) - Mean value of the butyric acid solution concentration (g/l) - BA _i Intracellular butyric acid concentration (g/l) - BA _ex Extracellular butyric acid concentration (g/l) - D Dilution rate (l/h) - H Magnetizing force (oersted) - K Constant in Equation (1) - k B Constant in Equation (15) - K _BA Saturation constant - k _{BA 1} Constant in Equation (13) - k _{BA 2} Constant in Equation (13) - K _D Constant in Equation (13) - k _{G 1} Constant in Equation (8) - k _{G 2} Constant in Equation (8) - k _{G 3} Constant in Equation (9) - K _I Inhibition Constant - k _p Constant in Eq. (11) - K _S Monod constant - n Number of the active sugar transport sites - P Cellular membrane permeability (l/g wet cell·h) - q _S Specific rate of substrate utilization (g substrate/g biomass·h) - S Substrate concentration in the fermentation broth (g/l) - S _O Substrate concentration in the feed solution (g/l) - t Time (h) - X Total biomass concentration (g/l) - X ₁ Active biomass concentration (g/l) - X ₂ Non-active biomass concentration (g/l) Greek Letters Ratio of the dry to wet cell weight (g dry cell/g wet cell) - ₁ Constant in Equation (6) - ₂ Constant in Equation (6) - ₃ Constant in Equation (6) - Specific culture growth rate (1/h)     

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     

Diagnosing lactic acid fermentation based on specific rates of growth,substrate consumption and product formation

The on-line calculated specific rates of growth, substrate consumption and product formation were used to diagnose microbial activities during a lactic acid fermentation. The specific rates were calculated from on-line measured cell mass, and substrate and product concentrations. The specific rates were more sensitive indicators of slight changes in fermentation conditions than such monitored data as cell mass or product concentrations.List of Symbols 1/h specific rate of cell growth - 1/h specific rate of substrate consumption - 1/h specific rate of product formation - ^* dimensionless specific rate of cell growth - ^* dimensionless specific rate of substrate consumption - ^* dimensionless specific rate of product formation - _max 1/h maximum specific rate of cell growth - _max 1/h maximum specific rate of substrate consumption - _max 1/h maximum specific rate of product formation - X g/l cell mass concentration - S g/l substrate concentration - S ^* dimensionless substrate concentration - S ₀ g/l initial substrate concentration - P g/l product concentration     

Xylitol production from D-xylose byCandida guillermondii: Fermentation behaviour

Summary The ability ofCandida guillermondii to produce xylitol from xylose and to ferment individual non xylose hemicellulosic derived sugars was investigated in microaerobic conditions. Xylose was converted into xylitol with a yield of 0,63 g/g and ethanol was produced in negligible amounts. The strain did not convert glucose, mannose and galactose into their corresponding polyols but only into ethanol and cell mass. By contrast, fermentation of arabinose lead to the formation of arabitol. On D-xylose medium,Candida guillermondii exhibited high yield and rate of xylitol production when the initial sugar concentration exceeded 110 g/l. A final xylitol concentration of 221 g/l was obtained from 300 g/l D-xylose with a yield of 82,6% of theoretical and an average specific rate of 0,19 g/g.h.Nomenclature Q_p average volumetric productivity of xylitol (g xylitol/l per hour) - q_p average specific productivity of xylitol (g xylitol/g of cells per hour) - So initial xylose concentration (g/l) - tf incubation time (hours) - Y_P/S xylitol yield (g of xylitol produced/g of xylose utilized) - Y_E/S ethanol yield (g of ethanol produced/g of substrate utilized) - Y_X/S cells yield (g of cells/g of substrate utilized) - specific growth rate coefficient (h^–1) - _max maximum specific growth rate coefficient (h^–1)     

Polysulfide utilization by Thiocapsa roseopersicina

The purple sulfur bacterium Thiocapsa roseopersicina, being the dominant anoxygenic phototroph in microbial mats, was tested for growth on polysulfide as the electron donor for carbon dioxide fixation. Data collected in continuous cultures revealed _max to be 0.065 h^-1 and the saturation affinity constant K _s to be 6.7 M. The value of the inhibition constant K _i was estimated in batch cultures and was found to be approximately 1100 M. When grown on monosulfide, the organism was capable of trisulfide utilization without lag. Monosulfide-limited growth was established to have a _max of 0.091 h^-1 and K _s of 8.0 M. Field observations revealed polysulfide, present at supra-optimal concentrations, as a major pool of reduced sulfur in a laminated marine sediment ecosystem.Non-standard abbreviations DLP Direct Linear Plot - TS Total Sugar - SS Structural Sugar - P Protein - R _R concentration of growth limiting nutrient in reservoir vessel - S _nutrient residual concentration of growth-limiting nutrient in the culture vessel - S _{sulfur compound} concentration of sulfur in the corresponding compound - D dilution rate - _max maximum specific growth rate - K _s saturation constant - K _i inhibition constant Dedicated to Prof. Dr. Norbert Pfennig on the occasion of his 65th birthday