Determination of effective diffusivity of substrate in biological films and particles

Summary Particle supported biofilms of uniform thickness were generated in an aerobic fluidized-bed reactor with phenol as the carbon source. A method was developed for determining the effective diffusivities of oxygen and phenol using trypan blue, a vital stain as the tracer. The effective diffusivities of oxygen and phenol were found to be 2.72×10^–6 cm²/s and 1.12×10^–6 cm²/s respectively.Nomenclature C_i initial solute concentration in bulk, g/cm³ - C_t solute concentration in bulk at time t, g/cm³ - C bulk solute concentration at equilibrium, g/cm³ - D molecular diffusivity, cm²/s - D effective diffusivity, cm²/s - D_o D_p D_tb molecular diffusivity of oxygen, phenol and trypan blue, cm²/s - D_o, D_p, D_tb effective diffusivity of oxygen, phenol and trypan blue, cm²/s - D_s molecular diffusivity of substrate, cm²/s - D_s effective diffusivity of substrate, cm²/s - K partition coefficient - M_t amount of solute in the particle at time t, g - M amount of solute in the particle at equilibrium, g - r particle radius, cm - r _bp radius of the particle with biofilm, cm - S substrate concentration, g/cm³ - S_b substrate concentration in bulk, g/cm³ - S_i initial substrate concentration, g/cm³ - V₁ solute molar volume, cm³/g mol Greek Symbols bf porosity of the biofilm - tortuosity factor     

New solution method for equations of reaction and mass transfer in biocatalyst particles

Summary For numerical solution of the reaction-mass transfer equations for immobilised biocatalysts it may be better to start integration at the particle surface and proceed inwards: calculations are targetted on the region to which practically interesting changes are often confined (because concentrations are effectively zero in the interior); and during iterative solution wrong initial estimates may be rejected after detecting anomalies early in the integration.Symbols C_b substrate concentration in bulk (mol m^–3) - c dimensionless substrate concentration (C/C_b) (-) - D_e effective diffusion coefficient (m²s^–1) - Da Damkohler number (V.r_o ²/D_e.K_s) (-) - K_s substrate concentration kinetic coefficient (mol m^–3) - k_e external mass transfer coefficient (ms^–1) - r_o bead radius (m) - Sh Sherwood number (k_e.r_o/D_e) (-) - V maximum rate per unit volume in beads (mol m^–3s^–1) - x dimensionless distance from bead centre (r/r_o) (-) - dimensionless kinetic coefficient (K_s/C_b) (-) - _o effectiveness factor (-)     

Action potentials inAcetabularia: Measurement and simulation of voltage-gated fluxes

Summary Amounts and temporal changes of the release of the tracer ions K⁺ (⁸⁶Rb⁺),²²Na⁺, and³⁶Cl^– as well as of H⁺ in the course of action potentials inAcetabularia have been recorded. New results and model calculations confirm in quantitative terms the involvement of three major ion transport systemsX in the plasmalemma: Cl^– pumps, K⁺ channels, and Cl^– channels (which are marked in the following by the prefixes,P, K andC) with their equilibrium voltages _X V _e and voltage/time-dependent conductances, which can be described by the following, first approximation. Let the maximum (ohmic) conductance of each of the three populations of transporter species be about the same (_P L, _KL,_C L=1) but voltage gating be different: the pump ( _{p V e} about –200 mV) being inactivated (open,oclosed,c) at positive going transmembrane voltages,V _m; the K⁺ channels (_K V _e about –100 mV) are inactivated at negative goingV _m; and the Cl^– channels (_C V _e: around 0 mV), which are normally closed (c) at a restingV _m (near_PV_e) go through an intermediate open (o) state at more positiveV _m before they enter a third shut state (s) in series. Model calculations, in which voltage sensitivities are expressed by the factorf=exp(V _mF/(2RT)), simulate, the action potential fairly well with the following parameters (_PK_co10/f ks^–1,_PK_oc1000·f ks^–1,_KK_co200·f ks^–1,_Kk_oc2/f ks^–1,_cK_co500·f ks^–1,_CK_oc5/f ks^–1,_CK_so0.1/f ks^–1,_Ck_os20·f ks^–1). It is also shown that the charge balance for the huge transient Cl^– efflux, which frequently occurs during an action potential, can be accounted for by the observation of a corresponding release of Na⁺.     

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)     

Penicillin recovery from aqueous solutions by continuous foam flotation

Summary Penicillin G recovery is investigated in a continuous flotation column in the presence of different collectors which form a complex with penicillin. The performance of the penicillin recovery was investigated as a function of the mole ratio () of collector-to-penicillin and the aliphatic chain length of the collector. At =1 and low penicillin concentrations (e.g., 20 mg·1^-1), high foam liquid concentrations (680 mg·l^-1), low residue concentrations (12 mg·l^-1) and high penicillin separation (56) can be attained. At =4 the separation increases to 150, and 95% of the penicillin can be recovered.Symbols C_p penicillin concentration in feed (mg·l^-1) - C_R penicillin concentration in outlet liquid (mg·l^-1) - C_S penicillin concentration in foam liquid (mg·l^-1) - C_S/C_P penicillin enrichment (-) - C_S/C_R penicillin separation (-) - % Pen in S penicillin yield in foam liquid (%) - VV}_S foam liquid volume flow (ml·min^-1) - VV}_P feed (ml·min^-1) - VV_{N 2} nitrogen flow rate (ml·s^-1) - temperature     

Cell recycling studies for α-amylase production by Bacillus amyloliquefaciens

Production of -amylase by a strain of Bacillus amyloliquefaciens was investigated in a cell recycle bioreactor incorporating a membrane filtration module for cell separation. Experimental fermentation studies with the B. amyloliquefaciens strain WA-4 clearly showed that incorporating cell recycling increased -amylase yield and volumetric productivity as compared to conventional continuous fermentation. The effect of operating conditions on -amylase production was difficult to demonstrate experimentally due to the problems of keeping the permeate and bleed rates constant over an extended period of time. Computer simulations were therefore undertaken to support the experimental data, as well as to elucidate the dynamics of -amylase production in the cell recycle bioreactor as compared to conventional chemostat and batch fermentations. Taken together, the simulations and experiments clearly showed that low bleed rate (high recycling ratio) various a high level of -amylase activity. The simulated fermentations revealed that this was especially pronounced at high recycling ratios. Volumetric productivity was maximum at a dilution rate of around 0.4 h^–1 and a high recycling ratio. The latter had to exceed 0.75 before volumetric productivity was significantly greater than with conventional chemostat fermentation.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 - B bleed rate (h^–1) - C starch concentration (g/l) - C ₀ starch concentration in the feed (g/l) - D dilution rate (h^–1) - D _E volumetric productivity (KNU/(mlh)) - e intracellular -amylase concentration (g/g cell mass) - E extracellular -amylase concentration (KNU/ml) - F volumetric flow rate (l/h) - G average number of genome equivalents of DNA per cell - k _l intracellular equilibrium constant - k ₂ intracellular equilibrium constant - k _s Monod saturation constant (g/l) - k ₃ excretion rate constant (h^–1) - k _d first order decay constant (h^–1) - k _gl rate constant for glucose production - k _st rate constant for starch hydrolysis - k _t1 proportionality constant for -amylase production (gmRNA/g substrate) - k ₁ translation constant (g/(g mRNAh)) - KNU kilo Novo unit - m maintenance coefficient (g substrate/(g cell massh)) - n number of binding sites for the co-repressor on the cytoplasmic repressor - Q repression function K₁/K₂Q1.0 - R ratio of recycling - R _s rate of glucose production (g/lh) - r _c rate of starch hydrolysis (g/(lh)) - R _eX retention by the filter of the compounds X: starch or -amylase - r intracellular -amylase mRNA concentration (g/g cell mass) - r _C volumetric productivity of starch (g/lh) - r _E volumetric productivity of intracellular -amylase (KNU/(g cell massh)) - r _r volumetric productivity of intracellular mRNA (g/(g cell massh)) - r _e volumetric productivity of extracellular -amylase (KNU/(mlh)) - r _s volumetric productivity of glucose (g/(lh)) - r _X volumetric productivity of cell mass (g/(lh)) - S ₀ free reducing sugar concentration in the feed (g/l) - S extracellular concentration of reducing sugar (g/1) - t time (h) - V volume (l) - X cell mass concentration (g/l) - Y yield coefficient (g cell mass/g substrate) - Y _E/S yield coefficient (KNU -amylase/g substrate) - Y _E total amount of -amylase produced (KNU) - substrate uptake (g substrate/(g cell massh)) - 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) This study was supported by Bioprocess Engineering Programme of the Nordic Industrial Foundation and the Center for Process Biotechnology, the Technical University of Denmark.     

Verification studies of a simplified model for the removal of dichloromethane from waste gases using a biological trickling filter

The removal of dichloromethane from waste gases in a biological trickling filter was studied experimentally as well as theoretically within the concentration range of 0–10,000 ppm. A stable dichloromethane elimination performance was achieved during two years of operation, while the start-up of the system only amounted to several weeks at constant inlet concentrations. The trickling filter system was operated co-currently as well as counter-currently.However, experimental and theoretical results revealed that the relative flow direction of the mobile phases did not significantly affect the elimination performance. Moreover, it was found that the gas-liquid mass-transfer resistance in the trickling filter bed applied was negligible, which leaves the biological process inside the biofilm to be the rate limiting step.A simplified model was developed, the Uniform-Concentration-Model, which showed to predict the filter performance close to the numerical solutions of the model equations. This model gives an analytical expression for the degree of conversion and can thus be easily applied in practice.The dichloromethane eliminating performance of the trickling filter described in this paper, is reflected by a maximum dichloromethane elimination capacity EC _max=157 g/(m³ · h) and a critical liquid concentration C _lcr=45 g/m³ at a superficial liquid velocity of 3.6 m/h, inpendent of the gas velocity and temperature.List of Symbols a _s m²/m³ specific area - a _w m²/m³ specific wetted area - A m² cross-sectional area - C _g g/m³ gas phase concentration - C _go g/m³ inlet gas phase concentration - C _gocr g/m³ critical gas phase concentration - C _g ^* C_g/C_go dimensionless gas concentration - C _l g/m³ liquid concentration - C _lcr g/m³ critical liquid concentration - C _lcr ^* mC_lcr/C_go dimensionless critical concentration - c _li g/m³ substrate concentration at liquid-biofilm interface - C _l ^* mC_l/C_go dimensionless liquid concentration - C _o g/m³ oxygen concentration inside the biofilm - C _oi g/m³ oxygen concentration at liquid-biofilm interface - C_s g/m³ substrate concentration inside the biofilm - C _si g/m³ substrate concentration at liquid-biofilm interface - D _eff m²/h effective diffusion coefficient in the biofilm - D _o m²/h effective diffusion coefficient for oxygen in the biolayer - E mu_g/u_l extraction factor - E _act kJ/mol activation energy for the biological reaction - EC g/(m³· h) K _o a _w : elimination capacity, or the amount of substrate degraded per unit of reactor volume and time - EC _max g/(m³ · h) K _o a_w: maximum elimination capacity - f degree of conversion - h m coordinate in height - H m height of the packed bed - K ₀ g/(m³ · h) _maxX_b/Y zeroth order reaction defined per unit of biofilm volume - k _og m/h overall gas phase mass transfer coefficient - K ^* dimensionless constant given by Eq. (A.5) - K _l ^* dimensionless constant given by Eq. (A.6) - K ₂ ^* dimensionless constant given by Eq. (A.6) - m C _g /C_l gas liquid distribution coefficient - N g/(m² · h) liquid-biofilm interfacial flux of substrate - N _og k_oga_wH/u_g number of gas phase transfer units - N _r k_o a_w H/u_g C_go number of reaction units - OL g/(m³· h) u _g C _go /H organic load - r _s g/(m³ ·h) zeroth order substrate degradation rate given by Eq. (1) - R _s g/(g TSS ·h) specific activity - T K absolute temperature - u _g m/h superficial gas velocity - u _t m/h superficial liquid velocity - X _b g TSS/m₃ biomass concentration inside biofilm - X _s g TSS/m₃ liquid suspended biomass concentration - x m coordinate inside the biofilm - Y g TSS/(g_DCM) yield coefficient Greek Symbols dimensionless parameter given by Eq. (2) - m averaged biofilm thickness - biofilm effectiveness factor given by Eqs. (7a)–(7c) - m penetration depth of substrate into the biofilm - _max d^–1 microbiological maximum growth rate - v _o stoichiometric utilization coefficient for oxygen - v _s stoichiometric utilization coefficient for substrate - dimensionless height in the filter bed - h H/u _g superficial gas phase contact time - _o (K ₀ /DC _ii )^1/2 - _o C _o /C _oi dimensionless oxygen concentration inside the biofilm - _s C _s /C _si dimensionless substrate concentration inside the biofilm Experimental results, verifying the model presented will be discussed Part II (to be published in Vol. 6, No. 4)     

Membrane potential and surface potential in mitochondria: Uptake and binding of lipophilic cations

Summary The uptake and binding of the lipophilic cations ethidium⁺, tetraphenylphosphonium⁺ (TPP⁺), triphenylmethylphosphonium⁺ (TPMP⁺), and tetraphenylarsonium⁺ (TPA⁺) in rat liver mitochondria and submitochondrial particles were investigated. The effects of membrane potential, surface potentials and cation concentration on the uptake and binding were elucidated. The accumulation of these cations by mitochondria is described by an uptake and binding to the matrix face of the inner membrane in addition to the binding to the cytosolic face of the inner membrane. The apparent partition coefficients between the external medium and the cytosolic surface of the inner membrane (K' _o) and the internal matrix volume and matrix face of the inner membrane (K' _i) were determined and were utilized to estimate the membrane potential from the cation accumulation factorR _c according to the relation =RT/ZF ln [(R _cV_o–K'_o)/(V_i+K'_i)] whereV _o andV _i are the volume of the external medium and the mitochondrial matrix, respectively, andR _c is the ratio of the cation content of the mitochondria and the medium. The values of estimated from this equation are in remarkably good agreement with those estimated from the distribution of⁸⁶Rb in the presence of valinomycin. The results are discussed in relation to studies in which the membrane potential in mitochondria and bacterial cells was estimated from the distribution of lipophilic cations.     

Cell recovery by continuous flotation

Summary Cell recovery by means of continuous flotation of the Hansenula polymorpha cultivation medium without additives was investigated as a function of the cultivation conditions as well as of the flotation equipment construction and flotation operational parameters. The cell enrichment and separation is improved at high liquid residence times, high aeration rates, small bubble sizes, increasing height of the aerated column, and diameter of the foam column. Increasing cell age and cultivation with nitrogen limitation reduce the cell separation.Symbols C_P cell mass concentration in medium g·l^–1 - C_R cell mass concentration in residue g·l^–1 - C_S cell mass concentration in foam liquid g·l^–1 - V equilibrium foam volume cm³ - V gas flow rate through the aerated liquid column cm³·s^–1 - V_F feed rate to the flotation column ml/min - ¹ V _S/V foaminess s - mean liquid residence time in the column s     

Characterization of second site mutations show that fast proton transfer to QB − is restored in bacterial reaction centers of Rhodobacter sphaeroides containing the Asp-L213 → Asn lesion

The structural basis for proton coupled electron transfer to Q_B in bacterial reaction centers (RCs) was studied by investigating RCs containing second site suppressor mutations (Asn M44 Asp, Arg M233 Cys, Arg H177 His) that complement the effects of the deleterious Asp L213 Asn mutation [DN(L213)]. The suppressor RCs all showed an increased proton coupled electron transfer rate k _AB ⁽²⁾(Q_A ^–Q_B ^– + H⁺ Q_AQ_BH^–) by at least 10³ (pH 7.5) and a recombination rate k _BD (D⁺Q_AQ_B ^– DQ_AQ_B) 15–40 times larger than the value found in DN(L213) RCs. Proton transfer was studied by measuring the dependence of k _AB ⁽²⁾ on the free energy for electron transfer (G_et). k _AB ⁽²⁾ was independent of G_et in DN(L213) RCs, but dependent on G_et in native and all suppressor RCs. This shows that proton transfer limits the k _AB ⁽²⁾ reaction with a rate of 0.1s^–1 in DN(L213) RCs but is not rate limiting and at least 10⁸-fold faster in native and 10⁵-fold faster in the suppressor RCs. The increased rate of proton transfer by the suppressor mutations are proposed to be due to: (i) a reduction in the barrier to proton transfer by providing a more negative electrostatic potential near Q_B ^–; and/or (ii) structural changes that permit fast proton transfer through the network of protonatable residues and water molecules near Q_B.     

Do neurons have a voltage or a current threshold for action potential initiation?

The majority of neural network models consider the output of single neurons to be a continuous, positive, and saturating firing ratef(t), while a minority treat neuronal output as a series of delta pulses (t — t _i ). We here argue that the issue of the proper output representation relates to the biophysics of the cells in question and, in particular, to whether initiation of somatic action potentials occurs when a certain thresholdvoltage or a thresholdcurrent is exceeded. We approach this issue using numerical simulations of the electrical behavior of a layer 5 pyramidal cell from cat visual cortex. The dendritic tree is passive while the cell body includes eight voltage- and calcium-dependent membrane conductances.We compute both the steady-state (I ^static (V _m )) and the instantaneous (I _o (V_m)) I–V relationships and argue that the amplitude of the local maximum inI ^static (V _m ) corresponds to the current thresholdI _th for sustained inputs, while the location of the middle zero-crossing ofI _o corresponds to a fixed voltage thresholdV _th for rapid inputs. We confirm this using numerical simulations: for rapid synaptic inputs, spikes are initiated if the somatic potential exceedsV _th, while for slowly varying inputI _th must be exceeded. Due to the presence of the large dendritic tree, no charge thresholdQ _th exists for physiological input.Introducing the temporal average of the somatic membrane potential (V _m) while the cell is spiking repetitively, allows us to define a dynamic I-V relationship ^dynamic ((V _m)). We find an exponential relationship between (V _m) and the net current sunk by the somatic membrane during spiking (diode-like behavior). The slope ofI/dynamic((V _m)) allows us to define a dynamic input conductance and a time constant that characterizes how rapidly the cell changes its output firing frequency in response to a change in its input.     

Relationship Between Photosystem 2 Electron Transport and Photosynthetic CO2 Assimilation Responses to Irradiance in Young Apple Tree Leaves

The responses to irradiance of photosynthetic CO₂ assimilation and photosystem 2 (PS2) electron transport were simultaneously studied by gas exchange and chlorophyll (Chl) fluorescence measurement in two-year-old apple tree leaves (Malus pumila Mill. cv. Tengmu No.1/Malus hupehensis Rehd). Net photosynthetic rate (P _N) was saturated at photosynthetic photon flux density (PPFD) 600-1 100 (mol m^-2 s^-1, while the PS2 non-cyclic electron transport (P-rate) showed a maximum at PPFD 800 mol m^-2 s^-1. With PPFD increasing, either leaf potential photosynthetic CO₂ assimilation activity (F_d/F_s) and PS2 maximal photochemical activity (F_v/F_m) decreased or the ratio of the inactive PS2 reaction centres (RC) [(F_i – F_o)/(F_m – F_o)] and the slow relaxing non-photochemical Chl fluorescence quenching (q_s) increased from PPFD 1 200 mol m^-2 s^-1, but cyclic electron transport around photosystem 1 (RFp), irradiance induced PS2 RC closure [(F_s – F_o)/F_m – F_o)], and the fast and medium relaxing non-photochemical Chl fluorescence quenching (q_f and q_m) increased remarkably from PPFD 900 (mol m^-2 s^-1. Hence leaf photosynthesis of young apple leaves saturated at PPFD 800 mol m^-2 s^-1 and photoinhibition occurred above PPFD 900 mol m^-2 s^-1. During the photoinhibition at different irradiances, young apple tree leaves could dissipate excess photons mainly by energy quenching and state transition mechanisms at PPFD 900-1 100 mol m^-2 s^-1, but photosynthetic apparatus damage was unavoidable from PPFD 1 200 mol m^-2 s^-1. We propose that Chl fluorescence parameter P-rate is superior to the gas exchange parameter P _N and the Chl fluorescence parameter F_v/F_m as a definition of saturation irradiance and photoinhibition of plant leaves.     

Intensity of microcarrier collisions in turbulent flow

A model is developed, allowing estimation of the share of inelastic interparticle collisions in total energy dissipation for stirred suspensions. The model is restricted to equal-sized, rigid, spherical particles of the same density as the surrounding Newtonian fluid. A number of simplifying assumptions had to be made in developing the model. According to the developed model, the share of collisions in energy dissipation is small.List of Symbols b parameter in velocity distribution function (Eq. (28)) - c _K factor in Kolmogoroff spectrum law (Eq. (20)) - D _t(r _p ) m²/s characteristic dispersivity at particle radius scale (Eq. (13)) - E(k, t) m³/s² energy spectrum as function of k and t (Eq. (16)) - E _K (k) m³/s² energy spectrum as function of k in Kolmogoroff-region (Eq. (20)) - E _p dimensionless mean kinetic energy of a colliding particle (Eq. (36)) - E _cp dimensionless kinetic energy exchange in a collision (Eq. (37)) - G(x, s) dimensionless energy spectrum as function of x and s (Eq. (16)) - G _B(x) dimensionless energy spectrum as function of x for boundary region (Eq. (29)) - G _K(x) dimensionless energy spectrum as function of x for Kolmogoroff-region (Eq. (21)) - g m/s² gravitational acceleration - I _cp dimensionless collision intensity per particle (Eq. (38)) - I _cv dimensionless volumetric collision intensity (Eq. (39)) - k l/m reciprocal of length scale of velocity fluctuations (Eq. (17)) - K dimensionless viscosity (Eq. (13)) - n(2) dimensionless particle collision rate (Eq. (12)) - n(r) l/s particle exchange rate as function of distance from observatory particle center (Eq. (7)) - r m vector describing position relative to observatory particle center (Eq. (2)) - r m scalar distance to observatory particle center (Eq. (3)) - r _pm particle radius (Eq. (1)) - s dimensionless time (Eq. (10)) - SC kg/ms³ Severity of collision (Eq. (1)) - t s time (Eq. (2)) - u(r, t) m/s velocity vector as function of position vector and time (Eq. (2)) - u(r, t) m/s magnitude of velocity vector as function of position vector and time (Eq. (3)) - u _r(r, t) m/s radial component of velocity vector as function of position vector and time (Eq. (3)) - u _r (r, t) m/s magnitude of radial component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u _gsm/s superficial gas velocity - u(r) m/s root mean square velocity as function of distance from observatory particle center (Eq. (3)) - u_r(r) m/s root mean square radial velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s root mean square latitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s Root mean square longitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - w(x) dimensionless root mean square velocity as function of dimensionless distance from observatory particle center (Eq. (11)) - V _pm³ particle volume (Eq. (36)) - w(2) dimensionless root mean square collision velocity (Eq. (34)) - w ^* parameter in boundary layer velocity equation (Eq. (24)) - x dimensionless distance to particle center (Eq. (9)) - x ^* value of x where G _Band G _K-curves touch (Eq. (32)) - x _K dimensionless micro-scale (Kolmogoroff-scale) of turbulence (Eq. (15)) - volumetric particle hold-up - m²/s³ energy dissipation per unit of mass - m²/s kinematic viscosity - kg/m³ density - (r) m³/s fluid-exchange rate as function of distance to observatory particle center - Latitudinal co-ordinate (Eq. (5)) - Longitudinal co-ordinate (Eq. (5))     

Electrical characteristics of mollusk giant neurons

The following electrical parameters of giant neurons of the molluskPlanorbis corneus were determined: the time constant , the ratio between the input conductance of the axon membrane and the conductance of the soma membrane , the input resistance of the neuron R_N and axon r_a, the total r_s and specific R_s resistance of the soma membrane. To determine and the course of the transition process during membrane polarization by a square pulse of input current was analyzed. R_N was estimated from the electrotonic potential V after the end of the transition process; r_s and r_a were calculated by the equations r_s=R_N·(1+) and r_a=r_s/. The surface area of the soma membrane (for calculating R_s) was estimated from its capacitance. It was assumed that the specific capacitance of the membrane is 1 µ F/cm². According to these calculations the surface area of the soma may be more than ten times greater than the surface area of a sphere of the same diameter. The results showed that R_s can vary appreciably in different neurons from 20·10³ to 200·10³ ·cm². The time constant of the different neurons varies from 20 to 200 msec; usually the value of did not exceed 1.0 and it varied from nearly zero to 1.5. Changes in temperature and ionic composition of the external solution led to changes in the parameters r_a and r_s and also of and . Various responses of the soma and axon membranes to changes in the composition of the external solution were noted and they can be regarded as an index of some properties of the membrane in these regions of the cells.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 4, No. 6, pp. 651–658, November–December, 1972.     

Effects of dissolved oxygen concentration on lipase production by Rhizopus delemar

Summary The influence of the concentration of oxygen on lipase production by the fungus Rhizopus delemar was studied in different fermenters. The effect of oxygen limitation ( 47 mol/l) on lipase production by R. delemar is large as could be demonstrated in pellet and filamentous cultures. A model is proposed to describe the extent of oxygen limitation in pellet cultures. Model estimates indicate that oxygen is the limiting substrate in shake flask cultures and that an optimal inoculum size for oxygen-dependent processes can occur.Low oxygen concentrations greatly negatively affect the metabolism of R. delemar, which could be shown by cultivation in continuous cultures in filamentous growth form (D_optimal=0.086 h^-1). Continuous cultivations of R. delemar at constant, low-oxygen concentrations are a useful tool to scale down fermentation processes in cases where a transient or local oxygen limitation occurs.Symbols and Abbreviations CO Oxygen concentration in the gas phase at time = 0 (kg·m^-3) - C_{O 2i} Oxygen concentration at the pellet liquid interface (kg·m^-3) - C_{O 2i} Oxygen concentration in the bulk (kg·m^-3) - D Dilution rate (h^-1) - ID_{O 2} Diffusion coefficient for oxygen (m²·s^-1) - dw Dry weight of biomass (kg) - f Conversion factor (rs _{O 2} to oxygen consumption rate per m³) (-) - k Radial growth rate (m·s^-1) - K Constant - kla Volumetric mass transfer coefficient (s^-1) - klA Oxygen transfer rate (m^-3·s^-1) - kl Mass transfer coefficient (m·s^-1) - K _{O 2} Affinity constant for oxygen (mol·m^-3) - K _w Cotton plug resistance (m^-3·s^-1) - M Henry coefficient (-) - NV Number of pellets per volume (m^-3) - R Radius (m) - RO Radius of oxygen-deficient core (m) - RQ Respiration quotient (mol CO₂/mol O₂) - rs _{O 2} Specific oxygen consumption rate per dry weight biomass (kg O₂·s^-1[kg dw]^-1) - rX Biomass production rate (kg·m^-3·s^-1) - SG Soytone glucose medium (for shake flask experiments) - SG ₄ Soytone glucose medium (for tower fermenter and continuous culture experiments) - V Volume of medium (m^-3) - X Biomass (dry weight) concentration (kg·m^-3) - XR _o Biomass concentration within RO for a given X (kg·m^-3) - Y _{O 2} Biomass yield calculated on oxygen (kg dw/kg O₂) - Thiele modulus - Efficiency factor =1-(RO/R)³ (-) - Growth rate (m^-1·s^-1·kg^1/3) - Dry weight per volume of pellet (kg·m^-3)     

Intraparticle mass-transfer resistance and apparent time stability of immobilized yeast alcohol dehydrogenase

The stability and, consequently, the lifetime of immobilized enzymes (IME) are important factors in practical applications of IME, especially so far as design and operation of the enzyme reactors are concerned. In this paper a model is presented which describes the effect of intraparticle diffusion on time stability behaviour of IME, and which has been verified experimentally by the two-substrate enzymic reaction. As a model reaction the ethanol oxidation catalysed by immobilized yeast alcohol dehydrogenase was chosen. The reaction was performed in the batch-recycle reactor at 303 K and pH-value 8.9, under the conditions of high ethanol concentration and low coenzyme (NAD⁺) concentration, so that NAD⁺ was the limiting substrate. The values of the apparent and intrinsic deactivation constant as well as the apparent relative lifetime of the enzyme were calculated.The results show that the diffusional resistance influences the time stability of the IME catalyst and that IME appears to be more stabilized under the larger diffusion resistance.List of Symbols C _A, C_B, C_E mol · m^–3 concentration of coenzyme NAD⁺, ethanol and enzyme, respectively - C _p mol · m³ concentration of reaction product NADH - d _p mm particle diameter - D _eff m² · s^–1 effective volume diffusivity of NAD⁺ within porous matrix - k _d s^–1 intrinsic deactivation constant - K _A, K_A, K_B mol · m^–3 kinetic constant defined by Eq. (1) - K _A ^x mol · m^–3 kinetic constant defined by Eq. (5) - r _A mol · m^–3 · s^–1 intrinsic reaction rate - R m particle radius - R _v mol · m^–3 · s^–1 observed reaction rate per unit volume of immobilized enzyme - t _E s enzyme deactivation time - t _r s reaction time - V mol · m^–3 · s^–1 maximum reaction rate in Eq. (1) - V ^x mol · m^–3 · s^–1 parameter defined by Eq. (4) - V _f m³ total volume of fluid in reactor - w _s kg mass of immobilized enzyme bed - factor defined by Eqs. (19) and (20) - kg · m^–3 density of immobilized enzyme bed - unstableness factor - effectiveness factor - Thiele modulus - relative half-lifetime of immobilized enzyme Index o values obtained with fresh immobilized enzyme     

Flight of the honey bee VI: energetics of wind tunnel exhaustion flights at defined fuel content,speed adaptation and aerodynamics

To gain information on extended flight energetics, quasi-natural flight conditions imitating steady horizontal flight were set by combining the tetheredflight wind-tunnel method with the exhaustion-flight method. The bees were suspended from a two-component aerodynamic balance at different, near optimum body angle of attack and were allowed to choose their own speed: their body mass and body weight was determined before and after a flight; their speed, lift, wingbeat frequency and total flight time were measured throughout a flight. These values were used to determine thrust, resultant aerodynamic force (magnitude and tilting angle), Reynolds number, total flight distance and total flight impulse. Flights in which lift was body weight were mostly obtained. Bees, flown to complete exhausion, were refed with 5, 10, 15 or 20 l of a 1.28-mol·l^-1 glucose solution (energy content w=18.5, 37.0, 55.5 or 74.0 J) and again flown to complete exhaustion at an ambient temperature of 25±1.5°C by a flight of known duration such that the calculation of absolute and relative metabolic power was possible. Mean body mass after exhaustion was 76.49±3.52 mg. During long term flights of 7.47–31.30 min similar changes in flight velocity, lift, thrust, aerodynamic force, wingbeat frequency and tilting angle took place, independent of the volume of feeding solution. After increasing rapidly within 15 s a more or less steady phase of 60–80% of total flight time, showing only a slight decrease, was followed by a steeper, more irregular decrease, finally reaching 0 within 20–30 s. In steady phases lift was nearly equal to resultant aerodynamic force; tilting angle was 79.8±4.0°, thrust to lift radio did not vary, thrust was 18.0±7.4% of lift, lift was somewhat higher/equal/lower than body mass in 61.3%, 16.1%, 22.6% of all totally analysable flights (n=31). The following parameters were varied as functions of volume of feeding solution (5–20 l in steps of 5 l) and energy content. (18.5–74.0 J in steps of 18.5 J): total flight time, velocity, total flight distance, mean lift, thrust, mean resultant aerodynamic force, tilting angle, total flight impulse, wingbeat frequency, metabolic power and metabolic power related to body mass, the latter related to empty, full and mean (=100 mg) body mass. The following positive correlations were found: L=1.069·10^-9 f ^2.538; R=1.629·10^-9 f ^2.464; P _m=7.079·10^-8 f ^2.456; P _m=0.008v+0.008; P _m=18.996L+0.022; P _m=19.782R+0.021; P _m=82.143T+0.028; P _m=1.245·bm _f ^1.424 ; P _{mrel e}=6.471·bm _f ^1.040 ; =83.248+0.385. The following negative correlations were found: V=3.939–0.032; T=1.324·10^-4–0.038·10^-4. Statistically significant correlations were not found in T(f), L(), R(), f(), P _m(bm _e), P _{m rel e}(bm _e), P _{m rel f}(bm _e), P _{m rel f}(bm _f).Abbreviations A(m²) frontal area - bl(m) body length - bm(mg) body mass - c(mol·1^-1) glucose concentration of feeding solution - c _D (dimensionless) drag coefficient, related to A - D(N) drag - F _w(N) body weight - F _wp weight of paper fragment lost at flight start - f wingbeat frequency (s^-1) - g(=9.81 m·s^-2) gravitational acceleration - I(Ns)=R(t) dt total impulse of a flight - L(N) lift vertical sustaining force component - P _m(J·s^-1=W) metabolic power - P_{m ret} (W·g^-1) metabolic power, related to body mass - R(N) resultant aerodynamic force - Re v·bl·v ^-1 (dimensionless) Reynolds number, related to body length - s(m) v(t) dt virtual flight distance of a flight - s(km) total virtual flight distance - T (N) thrust horizontal force component of horizontal flight - T _a (°C) ambient temperature - t(s) time - t _tot (s or min) total flight time - v(m·s^-1) flight velocity - v(l) volume of feeding solution - W (J) energy and energy content of V - ( °) body angle of attack between body longitudinal axis and flow direction - ( °) tilting angle ( 90°) between R and the horizont in horizontal flight v(=1.53·10^-5m²·s^-1 for air at 25°) kinematic viscosity - (=1.2 kg·m^-3 at 25°C) air density     

The electrical response ofAvena coleoptile cortex to auxins

Solute mobilities of 28 compounds in isolated cuticular membranes (CM) from Capsicum annuum L. fruit, Citrus aurantium L. and Pyrus communis L. leaves were studied using unilateral desorption from the outer surface. First-order rate constants of desorption (k^*), which are directly proportional to the diffusion coefficient in the waxy outer limiting skins of cuticles were measured. When log k^* was plotted vs. molar volumes of test compounds linear graphs were obtained. The y-intercepts of these graphs (k^*) represent the mobility of a hypothetical molecule having zero molar volume and the slopes of the graphs () represent the size selectivity of the barrier and are related to the free volume available for diffusion. Thus, solute mobilities in cuticles are composed of two independent terms which are subtractive. If k^* and are known, k^* can be estimated for any solute from its molar volume (V_x) using the equation log k^*=log k^* –V_x. These parameters were used to analyse the effects of plant species, extraction of cuticular waxes and molecular structure of solutes on solute mobilities in plant cuticles. For aliphatic solutes, k^* was a factor of 10 smaller than for cyclic compounds, while was 0.011 and 0.012, respectively. The k^*-values for CM of the three species were very similar, but was higher for bitter-orange CM (0.012) than for those of pepper fruits and pear leaves (0.009). This has the consequence that differences in solute mobilities (k^*) among cuticles from different plan species increase with increasing molar volumes of solutes. Our data and our analysis provide evidence that constituents of cuticular waxes are mobile, at least in the solid amorphous wax fraction, but mobility decreases rapidly with increasing molar volume. For instance, if amounts to 0.01, mobilities of wax monomers decrease by a factor of 10 for every increase in molar volume of 100 cm³ · mol^–1. Thus, hexadecanoic acid is quite mobile in the amorphous wax fraction of Citrus (k^*=1.5×10^–6·s^–1), but for dotriacontane having twice the molar volume, k^* was only 2.5×10^–9·s^–1, which is almost three orders of magnitude smaller. Wax esters have even higher molar volumes and their mobilities will be even smaller (about 4×10^–12·s^–1 for a C₄₈-ester). Since low chain mobilities are a prerequisite for low mobilities and permeabilities, the selective advantage of high-molecular-weight wax monomers in plant cuticular waxes becomes obvious. Extracting cuticular waxes from pear leaf CM increased solute mobilities by a factor of 182, but it had no effect on size selectivity. We interpret this result as evidence to the effect that cuticular waxes reduce mobility by increasing tortuosity of the diffusion path, rather than by decreasing the mean free path of diffusional jumps and jump frequencies of diffusants.Abbreviations CM cuticular membrane(s) - 2,4-D 2,4-dichloro-phenoxyacetic acid - LAB lactic acid buffer - MX polymer matrix membranes - UDOS unilateral desorption from the outer surface     

Separation of supercoiled and open-circular plasmid DNA by liquid-liquid counter-current chromatography

We report for the first time the use of liquid-liquid counter-current chromatography (CCC) for the preparative scale fractionation of plasmid DNA. Almost complete fractionation of supercoiled and open circular plasmid DNA (6.9 kb) could be achieved using a phase system comprising 12.5% (w/w) PEG 600 and 18% (w/w) K₂HPO₄. Experiments were carried out on a Brunel J-type CCC machine (100 ml PTFE coil) at a mobile phase flow rate of 0.5 ml min^{– 1} and a rotational speed of 600 rpm. Compared to conventional HPLC techniques the capacity of CCC is not limited by the surface area of resin available for adsorption. Symbols: C _b, Concentration of plasmid in lower phase (g ml^–1); C _t, Concentration of plasmid in upper phase (g ml^–1); CV, Total volume of mobile phase present in the coil and connecting leads (ml); K, Equilibrium solute partition coefficient (K=C _t/C _b); OC, Open circular plasmid; SC, Supercoiled plasmid; S _f, Percentage stationary phase retention (S _f=V _s/V _c); t _s, Time for phase separation (s); V _b, Volume of bottom phase (ml); V _c, Coil volume (ml); V _m, Volume of mobile phase present in coil at equilibrium (ml); V _r, Volume ratio of two phases (V _r=V _t/V _b); V _s, Volume stationary phase present in coil at equilibrium (ml); V _t, Volume of top phase (ml); V _tot, Total volume of phase system (ml).     

A modified unstructured mathemathical model for the penicillin G fed-batch fermentation

Summary In this paper, an updated unstructured mathematical model for the penicillin G fed-batch fermentation is proposed, in order to correct some physical and biochemical shortcomings in the model of Heijnen et al. (1979,Biotechnol. Bioeng.,21, 2175–2201) and the model of Bajpai and Reuß (1980,J. Chem. Tech. Biotechnol.,30, 332–344). Its main features are the consistency for all values of the variables, and the ability to adequately describe different metabolic conditions of the mould. The model presented here can be considered as the translation of the latest advances in the biochemical knowledge of the penicillin biosynthesis.Nomenclature t time (h) - S amount of substrate in broth (g) - X amount of cell mass in broth (g) - P amount of product in broth (g) - V fermentor volume (L) - F input substrate feed rate (L/hr) - C _s S/V substrate concentration in broth (g/L) - C _x X/V cell mass concentration in broth (g/L) - C _P P/V product concentration in broth (g/L) - s _F substrate concentration in feed stream (g/L) - E _m parameter related to the endogenous fraction of maintenance (g/L) - E _p parameter related to the endogenous fraction of production (g/L) - K _x Contois saturation constant for substrate limitation of biomass production (g/g DM) - K _s Monod saturation constant for substrate limitation of biomss production (g/L) - K _p saturation constant for substrate limitation of product formation (g/L) - K _i substrate inhibition constant for product formation (g/L) - m _s maintenance constant (g/g DM hr) - k _h penicillin hydrolysis or degradation constant (hr^–1) - Y _x/s cell mass on substrate yield (g DM/g) - Y _p/s product on substrate yield (g/g) - specific substrate consumption rate (g/g DM hr) - specific growth rate (hr^–1) - _substr specific substrate to biomass conversion rate (hr^–1) - _x maximum specific substrate to biomass conversion rate (hr^–1) - specific production rate (g/g DM hr) - _p specific production constant (g/g DM hr)