Mathematical interpretation of dose-response curves

The dose-response of an individual organism can be described by a step functions if the organism survives when the dose is below a certain lethal level and dies when this level is exceeded. If, in a population of organism, the lethal dose for an individual has a unimodal distribution, the latter's properties will determine the shape of the population's response in the following manner. If the distribution is symmetric the dose-response curve has a symmetric sigmoid shape when plotted on linear coordinates. The location of the inflection point and the curve's slope around it are determined by the distribution's mode and variance. When the distribution is skewed, the dose-response curve has an asymmetric sigmoid shape which becomes reminiscent of an exponential decay when the distribution is strongly skewed to the right. The population's dose-response curve can be constructed by integration of the step changes over the distribution range. The step function representing the dose-response of an individual organism can be approximate by a Fermi function, and the distribution of an lethal doses can be represented by the Weibull distribution function. When the two functions are combined, the resulting dose-response of the populationS(X)), which is the fraction of survivors after exposure to a doseX, is given by:S(X)=∫ ₀ ¹ [1/{+exp{(X-X _c (φ))/a _i ]}]dω whereX _c (ω)={(1/b)[-ln(1-ω)]}^(1/n),n andb being the constants of the Weibull distribution anda _i an arbitrarily small number, i.e.a _i ≪[X−X _c (ϕ)], whose actual magnitude is of little significance. This model can be used to determine the underlying distributions of experimental dose-response relationship. It was applied to published survival data of microorganisms exposed to pulsed electric field, X-ray radiation and ozone to show that the different observed shapes of the dose-response curve, and shifts between them, can be expressed in terms of the correponding distribution parameters, namely the mode, variance and skewness.     

Enhancement of the gas-to-water ethene transfer coefficient by a dispersed water-immiscible solvent: effect of the cells

  For a mass-transfer-limited system, it was demonstrated that the volumetric ethene transfer coefficient (k _l a) from gas to water could be enhanced by dispersing adequate amounts of a water-immiscible organic liquid, namely the perfluorocarbon FC40, in the aqueous phase. When 26% (v/v) FC40 was dispersed in a culture of Mycobacterium parafortuitum an enhancement of k _l a, calculated on a total liquid volume basis, of 1.8 times was found. Steady-state experiments in the absence of microorganisms, however, showed a 1.2-fold enhancement of k _l a at 18.5% (v/v) FC40. At all FC40 volume fractions tested, enhancement factors with cells were higher than enhancements without cells; apparently the microorganisms or their excretion products affected the interfacial areas or characteristic phase dimensions. Received: 4 December 1995 / Received revision: 7 June 1996 / Accepted: 10 June 1996     

A kinetic model incorporating energy spilling for substrate removal in substrate-sufficient batch culture of activated sludge

Batch assays are currently used to study the kinetic behavior of microbial growth. However, it has been shown that the outcome of batch experiments is greatly influenced by the initial ratio of substrate concentration (S _o) to biomass concentration (X _o). Substrate-sufficient batch culture is known to have mechanisms of spilling energy that lead to significant nongrowth-associated substrate consumption, and the Monod equation is no longer appropriate. By incorporating substrate consumption associated with energy spilling into the balance of the substrate oxidation reaction, a kinetic model for the observed specific substrate consumption rate was developed for substrate-sufficient batch culture of activated sludge, and was further verified by experimental data. It was demonstrated that the specific substrate consumption rate increased with the increase of the S _o/X _o ratio, and the majority of substrate was consumed through energy spilling at high S _o/X _o ratios. It appears that the S _o/X _o ratio is a key parameter in regulating metabolic pathways of microorganisms. Received: 18 January 1999 / Received revision: 7 May 1999 / Accepted: 28 May 1999     

Degradation of 4-chlorophenol by enriched mixed cultures utilizing phenol and glucose as added growth substrate

Two mixed cultures, phenol-oxidizing (PO) and glucose-oxidizing (GO), were cultivated in two parallel chemostat reactors. The PO culture was enriched on phenol, and the GO culture was enriched on glucose. Batch biodegradation experiments were conducted to examine the degradation of 4-chlorophenol (4-CP) under various substrate conditions. The results indicate that in the absence of added growth substrate, 4-CP transformation by PO culture was complete at S _c ^o /X _o (initial 4-CP concentration/initial biomass concentration) 0.27 and that by GO culture was complete at S _c ^o /X _o = 0.09. In the presence of 5–500 mg phenol/l, the phenol dosage required to achieve the complete transformation of 4-CP was 60 mg/l at S _c ^o /X _o = 1, increasing to 120 mg/l at S _c ^o /X _o = 2, and to 180 mg/l at S _c ^o /X _o = 5. As glucose was added to the GO culture at a concentration of over 5–500 mg chemical oxygen demand (COD)/l, 4-CP was not completely transformed at S _c ^o /X _o = 5 [S _c ^o = 50 mg/l, X _o = 10 mg/l volatile suspended solids (VSS)]. These two cultures in utilizing added growth substrate were easily switched between glucose and phenol. Overall, the capacity of PO culture to degrade 4-CP, expressed as T _c (4-CP mass consumed /biomass inactivated, having unit of mg 4-CP/mg VSS), was 0.15–0.80, which compares with T _c values of 0.05–0.26 for GO culture. This work shows that adding phenol as a growth substrate is preferable over adding glucose, as it enhances 4-CP transformation, but a final choice should take into account both degradation efficiency and the risk of phenol toxicity.     

Relationship between oxygen saturation of mixed venous blood and pressure in the pulmonary artery trunk in healthy humans and patients with heart defects

The relationship between pulmonary artery pressure (P _LA) and oxygen saturation of mixed venous blood (S _V ) has been studied in subjects (1750 men and 1026 women) subdivided into 12 groups. Functional relationships have been found between P _LA and S _V , P _LA = f(S _V ), and S _V = f(P _LA), which were estimated using direct measurement of P _LA and S _V for each group. These factors have been found to obey the following dependences: P _LA = f(S _V ) and P _LA = a(S _V )^−b , where b = −0.2284a + 0.6564 in men and b = −0.285a + 1.2947 in women; S _V = f(P _LA) and S _V = c(P _LA)^−d , where d = −0.25131Ln(c) + 1.0212; R ² = 0.8993 in men and d = −1.9645Ln(c) + 2.852; and R ² = 0.9674 in women. Each group occupies a position on the curves specified by the equations. Subjects with the diagnosis of a functional heart murmur and patients with congenital aortic valve stenosis were grouped together to form the so-called normal group characterized by specific P _LA = f(S _V ) and S _V = f(P _LA) dependences. Male patients with coronary heart disease were also included in the normal group. An equation was derived to relate P _LA caused by different reasons with the corresponding saturation of mixed venous blood. In the case of the changing saturation of mixed venous blood, this equation gives the corresponding value of P _LA. Equilibrium between systemic and pulmonary circulations is established through interdependent changes in the physiological indices of blood circulation and gas exchange in humans.     

Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations

 In this paper we study the existence of one-dimensional travelling wave solutions u(x, t)=φ(x−ct) for the non-linear degenerate (at u=0) reaction-diffusion equation u _t =[D(u)u _x ] _x +g(u) where g is a generalisation of the Nagumo equation arising in nerve conduction theory, as well as describing the Allee effect. We use a dynamical systems approach to prove: 1. the global bifurcation of a heteroclinic cycle (two monotone stationary front solutions), for c=0, 2. The existence of a unique value c ^*>0 of c for which φ(x−c ^* t) is a travelling wave solution of sharp type and 3. A continuum of monotone and oscillatory fronts for c≠c ^*. We present some numerical simulations of the phase portrait in travelling wave coordinates and on the full partial differential equation. Received 15 December 1995; received in revised form 14 May 1996     

Crossover of a high-spin (S=7/2, 3/2) to a low-spin (S=1/2) iron-selenium cluster in FA and FB of photosystem I on rebinding of PsaC onto P700-FX cores

 PsaC is a tightly bound ferredoxin in the Photosystem I (PS I) reaction center which contains two [4Fe-4S] clusters named F_A and F_B. We recently proposed that the mixed-ligand F_B cluster in C14D_PsaC and the mixed-ligand F_A cluster in C51D_PsaC exist in a spin state of S=3/2, and that a spin state crossover to S=1/2 occurs when the PsaC mutants are rebound onto P700-F_X cores. Since EPR signals from a highly rhombic S=3/2 spin state can be difficult to study, wild-type PsaC was reconstituted with iron and selenium to introduce an easily detected S=7/2 spin state similar to that shown for Clostridial ferredoxin. When the unbound [4Fe-4Se] PsaC was chemically reduced, a sharp derivative resonance was found at g=5.171 attributed to the excited ±3/2 doublet from an S=7/2 spin multiplet. An additional peak was found at g=5.616 attributed to the superimposed ±1/2 and ±3/2 doublets from a highly rhombic S=3/2 spin multiplet, and an axial set of resonances found around g=2.0 attributed, in part, to a classical S=1/2 spin state. When the [4Fe-4Se] PsaC was rebound onto P700-F_X cores, the spin population derived from the S=7/2 and 3/2 spin states was negligible. Illumination of the rebuilt PS I complex at 15 K resulted in two rhombic sets of resonances, one with g values of 2.043, 1.941 and 1.854, diagnostic of F_A, and the other with g values of 2.067, 1.941 and 1.878, diagnostic of F_B. Chemical reduction with sodium dithionite at pH 10.5 or photoaccumulation by freezing during illumination resulted in a set of resonances with g values of 2.046, 1.938, 1.920 and 1.883, characteristic of a spin-coupled F_A ^–/F_B ^– pair. The spin state crossover in this iron chalcogenide cluster is the first known to be induced by protein-protein association and reinforces the hypothesis that an S=3/2 to 1/2 crossover occurs in the PS I-rebound mutants C14D_PsaC and C51D_PsaC. Received: 6 August 1996 / Accepted: 28 December 1996     

Resonance Raman fingerprinting of multiheme cytochromes from the cytochrome c 3 family

Resonance Raman (RR) spectroscopy was used to investigate conformational characteristics of the hemes of several ferricytochromes of the cytochrome c ₃ family, electron transfer proteins isolated from the periplasm and membranes of sulfate-reducing bacteria. Our analysis concentrated on the low-frequency region of the RR spectra, a fingerprint region that includes vibrations for heme-protein C–S bonds [ν(C_aS)]. It has been proposed that these bonds are directly involved in the electron transfer process. The three groups of tetraheme cytochrome c ₃ analyzed, namely Type I cytochrome c ₃ (TpIc ₃s), Type II cytochrome c ₃ (TpIIc ₃s) and Desulfomicrobium cytochromes c ₃, display different frequency separations for the two ν(C_aS) lines that are similar among members of each group. These spectral differences correlate with differences in protein structure observed among the three groups of cytochromes c ₃. Two larger cytochromes of the cytochrome c ₃ family display RR spectral characteristics for the ν(C_aS) lines that are closer to TpIIc ₃ than to TpIc ₃. Two other multiheme cytochromes from Desulfovibrio that do not belong to the cytochrome c ₃ family display ν(C_aS) lines with reverse relative areas in comparison with the latter family. This RR study shows that the small differences in protein structure observed among these cytochrome c ₃ correlate to differences on the heme–protein bonds, which are likely to have an impact upon the protein function, making RR spectroscopy a sensitive and useful tool for characterizing these cytochromes.     

Alkaline Serine Protease Is an Exotoxin of Vibrio alginolyticus in Kuruma Prawn,Penaeus japonicus

An extracellular lethal toxin produced by Vibrio alginolyticus strain Swy originally isolated from diseased kuruma prawn (Penaeus japonicus) was partially purified by Fast Protein Liquid Chromatography with hydrophobic interaction (Phenyl Sepharose High Performance) chromatography and gel filtration columns. The toxin is an alkaline serine protease, inhibited by phenyl-methylsulfonyl fluoride (PMSF), and showed maximal activity at pH 10, having a molecular weight of about 33 kDa estimated by SDS-PAGE and gel filtration chromatography. In addition, the toxin was also completely inhibited by FeCl₂ but partially inhibited by CaCl₂, CuCl₂, CoCl₂, MnCl₂, and ZnCl₂, and not inhibited by ethylenediamine tetraacetic acid (EDTA), ethylene glycol-bis(β-amino-ethyl ether) N,N,N′,N′-tetraacetic acid (EGTA), iodoacetamide, pepstatin A, sodium dodecyl sulfate (SDS), and N-tosyl-l-phenyl-alanine chloromethyl ketone (TPCK). Both the crude extracellular products (ECP) and the partially purified toxin are lethal for kuruma prawn at LD₅₀ values of 0.30 and 0.27 μg protein/g body weight, respectively. The addition of PMSF completely inhibited the lethal toxicity of both the ECP and the partially purified toxin, indicating that this serine protease is a lethal factor produced by the bacterium. The 33-kDa protease is, therefore, suggested to be a new toxic protease produced by V. alginolyticus strain Swy. Received: 12 April 1996 / Accepted: 31 July 1996     

Optical properties and optical constituents of the Faroe Islands shelf and off-shelf waters,North East Atlantic

The study comprises a data set of CTD, optical properties—K ₀(PAR), c _p, a(PAR), b(PAR)—and optical constituents—Chl a, SPM, CDOM—from 72 shelf and off-shelf stations in the Faroe Islands (62°N, 7°W) North East Atlantic, in early spring 2005. Results showed that shelf waters surrounding the islands were cold and low saline, whereas off-shelf waters were warmer (~1°C) and more saline (~0.05) PSU. A pronounced oceanographic front separated the two waters, and diffuse light attenuation K ₀(PAR), beam attenuation c _p, Chl a, absorption a(PAR), and scattering coefficient b(PAR) were all significantly higher on the shelf. Analyses showed that off-shelf light attenuation K ₀(PAR) was governed by Chl a, shown by a high (r ² = 0.64) Chl a–K ₀(PAR) correlation, whereas light attenuation on the shelf was governed by both Chl a, SPM, and CDOM in combination. A Chl a specific diffuse attenuation coefficient K₀^* ( \textPAR ) K_{0}^{*} \left( {\text{PAR}} \right) of 0.056 (m² mg⁻¹ Chl a) and a Chl a specific beam attenuation ( c_\textp^* c_{\text{p}}^{*} ) of 0.27 (m² mg⁻¹ Chl a) coefficients were derived for the off-shelf. It is pointed out that Chl a is the single variable that changes over time as no rivers with high SPM and CDOM enter the shelf area. Data were obtained in early spring, and Chl a concentrations were low ~0.5 mg Chl a m⁻³. Spring bloom Chl a are about 10 mg Chl a m⁻³ and estimations showed that shelf K ₀(PAR) will increase about 5 times and beam attenuation about 10 times. The Faroe Islands shelf–off-shelf waters is a clear example where physical conditions maintain some clear differences in optical properties and optical constituents. The complete data set is enclosed.     

Filling the vacuum chamber of a technological system with homogeneous plasma using a stationary glow discharge

Experimental study of a glow discharge with electrostatic confinement of electrons is carried out in the vacuum chamber volume V ≈ 0.12 m³ of a technological system “Bulat-6” in argon pressure range 0.005–5 Pa. The chamber is used as a hollow cathode of the discharge with the inner surface area S ≈ 1.5 m². It is equipped with two feedthroughs, which make it possible to immerse in the discharge plasma interchangeable anodes with surface area S _a ranging from ∼0.001 to ∼0.1 m², as well as floating electrodes isolated from both the chamber and the anode. Dependences of the cathode fall U _c = 0.4−3 kV on the pressure p at a constant discharge current in the range I = 0.2−2 A proved that aperture of the electron escape out of the electrostatic trap is equal to the sum S _o = S _a + S _f of the anode surface S _a and the floating electrode surface S _f . The sum S _o defines the lower limit p _o of the pressure range, in which U _c is independent of p. At p < p _o the cathode fall U _c grows up dramatically, when the pressure decreases, and the pressure p tends to the limit p ^ex, which is in fact the discharge extinction pressure. At p ≈ p ^ex electrons emitted by the cathode and the first generation of fast electrons produced in the cathode sheath spend almost all their energy up to 3 keV on heating the anode and the floating electrode up to 600–800°C and higher. In this case the gas in the chamber is being ionized by the next generations of electrons produced in the cathode sheath, their energy being one order of magnitude lower. When S _a < (2m/M)^1/2 S, where m is the electron mass and M is the ion mass, the anode may be additionally heated by plasma electrons accelerated by the anode fall of potential U _a up to 0.5 kV.     

Mapping quantitative trait loci associated with regeneration ability of seed callus in rice, Oryza sativa L.

 Quantitative trait loci (QTL) controlling the regeneration ability of rice seed callus were detected using 245 RFLP markers and 98 BC₁F₅ lines derived from two varieties, ‘Nipponbare’ and ‘Kasalath’. Regeneration ability was evaluated by two indices: average number of regenerated shoots per callus (NRS) and regeneration rate (RR). The BC₁F₅ lines showed continuous segregation for both indices. Five putative QTL for NRS (tentatively named qRg1, qRg2, qRg4a, qRg4b and qRg4c) located on chromosomes 1, 2 and 4 were detected. Digenic interaction among these detected QTL was not significant (P<0.01). Among the five QTL detected, four ‘Kasalath’ alleles and one ‘Nipponbare’ allele increased NRS. According to an estimate based on the nearest marker loci, the five QTL accounted for 38.5% of the total phenotypic variation of the BC₁F₅ lines. For RR, four putative QTL were detected on chromosomes 2 and 4, and all of these were in the same chromosomal regions as the NRS QTL. The four RR QTL accounted for 32.6% of the total phenotypic variation. Received: 7 November 1996 / Accepted: 25 April 1997     

Contributions to the theory of organismic sets: Leadership

The theory of organismic sets (Bull. Math. Biophysics,31, 159–189, 1969) is applied to the theory of leadership in human society. The ability of making decisions, required for leadership, is a product of the activities of the cells of the cerebral cortex, which are elements of the subsetS ₀₂ of the organismic set “man” (loc. cit.). Products of the activities of the elements of an organismic set do not need to be of a material nature. Such things as thoughts, feelings, attitudes, etc., are also products of the activitiesa ₁ of the elements. An individual can makeall necessary decisions for adaptation in a changing environment, when his subsetS ₀₂ contains as a proper subset a set {a ₁₂ ^′ ∼ ⊂S ₀₂ of activities. It is shown that such individuals are rare. If none exist, then the one who possesses a subset {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ of higher cardinalityc _m than any other individual, will be the leader. The possibility is discussed that fromN individualsN′ 〈N possess subsets {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ all of the same cardinalityc _m but differing in the type of their elements, thus resulting in several leaders. It is then discussed what determines which of theN −N′ individuals will choose a particular oneN′ individuals as leader. Cooperation and competition between leaders is discussed.     

Carbon isotope composition of boreal plants: functional grouping of life forms

 We tested the hypothesis that life forms (trees, shrubs, forbs, and mosses; deciduous or evergreen) can be used to group plants with similar physiological characteristics. Carbon isotope ratios (δ¹³C) and carbon isotope discrimination (Δ) were used as functional characteristics because δ¹³C and Δ integrate information about CO₂ and water fluxes, and so are useful in global change and scaling studies. We examined δ¹³C values of the dominant species in three boreal forest ecosystems: wet Picea mariana stands, mesic Populus tremuloides stands, and dry Pinus banksiana stands. Life form groups explained a significant fraction of the variation in leaf carbon isotope composition; seven life-form categories explained 50% of the variation in δ¹³C and 42% of the variation in Δ and 52% of the variance not due to intraspecific genetic differences (n=335). The life forms were ranked in the following order based on their values: evergreen trees<deciduous trees=evergreen and deciduous shrubs=evergreen forbs<deciduous forbs=mosses. This ranking of the life forms differed between deciduous (Populus) and evergreen (Pinus and Picea) ecosystems. Furthermore, life forms in the Populus ecosystem had higher discrimination values than life forms in the dry Pinus ecosystem; the Picea ecosystem had intermediate Δ values. These correlations between Δ and life form were related to differences in plant stature and leaf longevity. Shorter plants had lower Δ values than taller plants, resulting from reduced light intensity at lower levels in the forest. After height differences were accounted for, deciduous leaves had higher discrimination values than evergreen leaves, indicating that deciduous leaves maintained higher ratios of intracellular to ambient CO₂ (c _i/c _a) than did evergreen leaves in a similar environment within these boreal ecosystems. We found the same pattern of carbon isotope discrimination in a year with above-average precipitation as in a year with below-average precipitation, indicating that environmental fluctuations did not affect the ranking of life forms. Furthermore, plants from sites near the northern and southern boundaries of the boreal forest had similar patterns of discrimination. We concluded that life forms are robust indicators of functional groups that are related to carbon and water fluxes within boreal ecosystems. Received: 15 April 1996 / Accepted: 16 November 1996     

Characterization of cytochrome c 6 from the cyanobacterium Anabaena PCC 7119

 A soluble monoheme c–type cytochrome c ₆ has been isolated from the cyanobacterium Anabaena PCC 7119. It is a basic protein, with a molecular mass of 9.7 kDa, which accepts electrons from Anabaena ferredoxin in the ferredoxin-NADP⁺reductase-dependent NADPH cytochrome c reductase activity assay. The turnover of the reaction has an optimum pH at 7.5. Flavodoxin can also replace ferredoxin in this assay, but with only 20% efficiency. Plastocyanin from Anabaena PCC 7119, as well as the c ₆ cytochromes from the green algae Chlorella fusca and Monoraphidium braunii are also shown to accept electrons from Anabaena ferredoxin. The reduction potential of cytochrome c ₆ at pH 6.7 was determined to be 338 mV and is pH dependent, with pK _a ^ox=8.4±0.1 and pK _a ^red≈9.5. The ferric and ferrous cytochrome forms and their pH equilibria have been studied using visible, EPR and ¹H-NMR spectroscopies. The amino acid sequence and the visible and NMR spectroscopic data indicate that the heme iron has a methionine-histidine axial coordination in the pH range 5–11. However, the EPR data for the ferricytochrome are complex and show that in this pH range five distinct forms are present. Between pH 5 and 9 the spectrum is dominated by two rhombic species, with g–values at 2.94, 2.29, 1.43 and at 2.84, 2.34, 1.56, which interconvert with a pK _a of 8.4. The NMR data also show a main interconversion between two cytochrome forms at this pH, which coincides with that determined from the pH dependence of the reduction potential. Both these forms were associated with a methionine-histidine heme-iron coordination by correlation with the visible and NMR spectral data, although having crystal field parameters atypical for this type of coordination. Anabaena cytochrome c ₆ is one more example of a heme protein for which the widely used crystal field analysis of the EPR data (truth diagram) fails to unequivocally determine the type of heme-iron ligation. Received: 17 May 1996 / Accepted: 13 January 1997     

Effects of prolonged bed rest on cardiovascular oxygen transport during submaximal exercise in humans

The hypothesis was tested that prolonged bed rest impairs O₂ transport during exercise, which implies a lowering of cardiac output Q˙ _c and O₂ delivery (_aO₂). The following parameters were determined in five males at rest and at the steady-state of the 100-W exercise before (B) and after (A) 42-day bed rest with head-down tilt at −6°: O₂ consumption (V˙O₂), by a standard open-circuit method; Q˙ _c, by the pressure pulse contour method, heart rate ( f _c), stroke volume (Q _h), arterial O₂ saturation, blood haemoglobin concentration ([Hb]), arterial O₂ concentration (C _aO₂), and Q˙ _aO₂. The V˙O₂ was the same in A and in B, as was the resting f _c. The f _c at 100 W was higher in A than in B (+17.5%). The Q _h was markedly reduced (−27.7% and −22.2% at rest and 100 W, respectively). The Q˙ _c was lower in A than in B [−27.6% and −7.8% (NS) at rest and 100 W, respectively]. The C _aO₂ was lower in A than in B because of the reduction in [Hb]. Thus also Q˙ _aO₂ was lower in A than in B (−32.0% and −11.9% at rest and at 100 W, respectively). The present results would suggest a down-regulation of the O₂ transport system after bed rest. Accepted: 22 April 1998     

Uptake of lactose and continuous lactic acid fermentation by entrapped non-growing Lactobacillus helveticus in whey permeate

 Continuous production of lactic acid from lactose has been carried out in a stirred-tank reactor with non-growing Lactobacillus helveticus entrapped in calcium alginate beads. A considerably longer operation half-life was obtained in a continuously operated reactor than in a batch-operated reactor. It is possible to simulate the action of entrapped non-growing cells on the basis of information from diffusion and kinetic experiments with suspended free cells. The simulation fit the experimental data over a broad range of substrate concentrations if the specific lactic acid production rate, q _P, was used as a variable parameter in the model. The dynamic mathematical model used is divided into three parts: the reactor model, which describes the mass balance in a continuously operated stirred-tank reactor with immobilized biomass, the mass-transfer model including both external diffusion and internal mass transfer, and the kinetic model for uptake of substrate on the basis of a Michaelis-Menten-type mechanism. From kinetic data obtained for free biomass experiments it was found, with the use of non-linear parameter estimation techniques, that the conversion rate of lactose by L. helveticus followed a Michaelis-Menten-type mechanism with K _S at half-saturation=0.22±0.01 g/l. The maximum specific lactose uptake rate for growing cells, q _S,max, varied between 4.32±0.02 g lactose g cells^-1 h^-1 and 4.89 ±0.02 g lactose g cells^-1 h^-1. The initial specific lactose uptake rate for non-growing cells, q _S,0, was found to be approximately 40% of the maximum specific lactose uptake rate for growing cells. Received: 4 October 1995/Received last revision: 23 April 1996/Accepted: 29 April 1996     

Experimental data and calculated parameters in FeS polymetallic centers in proteins

 Covariance between J and B parameters and indetermination of the actual symmetry suggest caution in making general statements about their values in Fe_nS_n centers. The Fe₄S₄ ³⁺ case is further complicated by electronic isomerism and lack of information on the actual symmetry. Electronic ground states and relative J and B values are discussed in the light of hyperfine coupling values. Received: 12 January 1996 / Accepted: 26 January 1996     

Site-directed mutagenesis of a phenylalanine residue strictly conserved in cytochromes c 3

 Reduction of the haems in tetrahaem cytochromes c ₃ is a cooperative process, i.e., reduction of each of the haems depends on the redox states of the other haems. Furthermore, electron transfer is coupled to proton transfer (redox-Bohr effect). Two of its haems and a strictly conserved nearby phenylalanine residue, F20, in Desulfovibrio vulgaris (Hildenborough) cytochrome c ₃ form a structural motif that is present in all cytochromes c ₃ and also in cytochrome c oxidase. A putative role for this phenylalanine residue in the cooperativity of haem reduction was investigated. Therefore, this phenylalanine was replaced, with genetic techniques, by isoleucine and tyrosine in D. vulgaris (Hildenborough) cytochrome c ₃. Cyclic voltammetry studies revealed a small increase (30 mV) in one of the macroscopic redox potentials in the mutated cytochromes. EPR showed that the main alterations occurred in the vicinity of haem I, the haem closest to residue 20 and one of the haems responsible for positive cooperativities in electron transfer of D. vulgaris cytochrome c ₃. NMR studies of F20I cytochrome c ₃ demonstrated that the haem core architecture is maintained and that the more affected haem proton groups are those near the mutation site. NMR redox titrations of this mutated protein gave evidence for only small changes in the relative redox potentials of the haems. However, electron/electron and proton/electron cooperativity are maintained, indicating that this aromatic residue has no essential role in these processes. Furthermore, chemical modification of the N-terminal amino group of cytochrome c ₃ backbone, which is also very close to haem I, had no effect on the network of cooperativities. Received: 25 June 1996 / Accepted: 26 August 1996     

Long-term c i /c a response of trees in western North America to atmospheric CO2 concentration derived from carbon isotope chronologies

To evaluate how the land carbon reservoir has been responding to the rising CO₂ concentration of the atmosphere, it is important to study how plants in natural forests adjust physiologically to the changing atmospheric conditions. Many experimental studies have addressed this issue, but it has been difficult to scale short-term experimental observations to long-term ecosystem-level responses. This paper derives carbon-isotope-related variables for the past 100–200 years from measurements on trees from natural forests. Calculations show that the c _i/c _a ratios [c _i/c _a is the ratio of the CO₂ concentration (μmol mol⁻¹) in the intercellular space of leaves to that in the atmosphere] of the trees were constant or increased slightly before the 20th century, but changed more rapidly in the 20th century; some increased, some decreased, and some stayed constant. In contrast, the CO₂ concentration inside plant leaves increased monotonically for all trees. Received: 12 June 1997 / Accepted: 29 June 1998