Permeability properties of cell-to-cell channels: Kinetics of fluorescent tracer diffusion through a cell junction

Summary We have analyzed the intracellular and cell-to-cell diffusion kinetics of fluorescent tracers in theChironomus salivary gland. We use this analysis to investigate whether membrane potential-induced changes in junctional permeability are accompanied by changes in cell-to-cell channel selectivity. Tracers of different size and fluorescence wavelength were coinjected into a cell, and the fluorescence was monitored in this cell and an adjacent one. Rate constants,k _j , for cell-to-cell diffusion were derived by compartment model analysis, taking into account (i) cell-to-cell diffusion of the tracers; (ii) their loss from the cells; (iii) their binding (sequestration) to cytoplasmic components; and (iv) their relative mobility to cytoplasm, as determined separately on isolated cells. In cell pairs, we compared a tracer'sk _j with the electrical cell-to-cell conductance,g _j .At cell membrane resting potential, thek _j 's ranged 3.8–9.2×10^–3 sec^–1 for the small carboxyfluorescein (mol wt 376) to about 0.4×10^–3 sec^–1 for a large fluorescein-labeled sugar (mol wt 2327). Cell membrane depolarization reversibly reducedg _j andk _j for a large and a small tracer, all in the same proportion. This suggests that membrane potential controls the number of open channels, rather than their effective pore diameter or selectivity. From the inverse relation between tracer mean diameter and relativek _j we calculate an effective, permeation-limiting diameter of approximately 29 Å for the insect cell-to-cell channel. Intracellular diffusion was faster than cell-to-cell diffusion, and it was not solely dependent on tracer size. Rate constants for intracellular sequestration and loss through nonjunctional membrane were large enough to become rate-limiting for cell-to-cell tracer diffusion at low junctional permeabilities.     

Steady-state diffusion through a finite pore into an infinite reservoir: An exact solution

An outline is given of an analysis that leads to an exact solution for the problem of steady-state diffusion through a finite thick pore into an infinite region surrounding the mouth of the pore. From this exact formula a simple expression for the flux is derived. This expression approximates the flux with a relative error of less than 3.42 per cent independently of the ratiol/a wherel is the length of the pore anda its radius. If desired, more accurate expressions for the flux can be obtained from the exact solution. This research was supported in part by Contract Nonr 595(17), Office of Naval Research, U.S. Navy.     

ALGORITHM FOR APPLICATION OF FOURIER ANALYSIS FOR BIORHYTHMIC BASELINES OF PHARMACODYNAMIC INDIRECT RESPONSE MODELS

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k_in (t) and a first-order loss constant k_out. If k_in(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response R_b(t) to recover the equation for k_in(t). Fourier analysis provides an approximate equation for R_b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k_in(t), yielding the equation involving R_b(t). A computer program was developed to perform the square L²-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate k_in(t) using ADAPT II. The pharmacodynamic parameters k_out and IC₅₀ were estimated from the model equation with k_in(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of k_in(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method. (Chronobiology International, 17(1), 77–93, 2000)     

Kinetics of ligand binding to a cluster of membrane-associated receptors

The process of ligand binding to a cluster of membrane-associated receptors is examined theoretically. The theoretical model proposed involves the diffusion of ligands from the solution to the disc-like cluster of receptors on the surface of the spherical cell. When the ligand hits the internal part of the disc-like cluster, it begins to move laterally until it leaves the disc through its outer surface or is bound by one of the receptors inside the disc. If the ligand leaves the cluster, it returns to the solution and hits the disc again after a certain period, etc. According to our model the transition from a diffusion-limited to a reaction-limited process of binding is determined by the dimensionless parameter Dt _c/a ², where D is the lateral diffusion coefficient,t _c is the characteristic time of reaction, anda is the radius of the disc-like cluster. The forward rate constantk _f turns out to be a function of . Comparing the results of our calculations ofk _f with some experimental data we found that agreement is achieved at high , i.e. the process of ligand binding by clustered receptors is predominantly reaction-limited.     

Azide treatment enhances cell-to-cell diffusion in staminal hairs ofSetcreasea purpurea

Summary The effect of azide on the diffusion of fluorescent molecular probes was examined in staminal hairs ofSetcreasea purpurea. Staminal hairs were treated with azide before being microinjected with fluorescent molecular probes of different size, charge, and structure. The cell-to-cell movement of these fluorescent molecules was videotaped, analyzed, and coefficients of diffusion through plasmodesmata (D) and coefficients of diffusion across the tonoplast (k₁) were calculated and compared to those of untreated cells. The D was larger and the k₁ was smaller for many fluorescent probes in azide treated cells compared to normal, untreated cells. In addition, the cell-to-cell diffusion selectivity based on molecule structure, size and charge no longer existed in azide treated cells. An average D of 3.3×10^–8cm²/s and an average k₁ of 2.9×10^–7/m²/s was calculated for the molecular probes tested. New size limits for permeation were observed indicating that the plasmodesmata had become enlarged.Abbreviations CF carboxyfluorescein - D diffusion coefficient for molecular probes in intercellular pores - FITC-Ang fluorescein isothiocyanate-angiotensin II - k₁ coefficient of diffusive loss across the tonoplast     

Interconvertible Kinetic States of t-Butylbicycloorthobenzoate Binding Sites of the γ-Aminobutyric AcidA Ionophores

The kinetics of t-[³H]butylbicycloorthobenzoate (TBOB) binding to the convulsant sites of the γ-aminobutyric acid_A (GABA_A) receptor-ionophore complex were examined in synaptosomal membrane preparations of rat brain. On and off rates of TBOB binding were accelerated by 1 μM GABA and decelerated by 1 μM bicuculline methochloride, a GABA_A antagonist. The presence of GABA and bicuculline methochloride created rapid and slow phases of dissociation, respectively. The three groups of rate constants distinguished for the dissociation of 4 nM and 30 nM [³H]TBOB represent multiaffinity states of the convulsant sites depending on the presence of GABA or bicuculline methochloride. Apparent association rate constants do not obey the equation k_app=k_off±k_on [TBOB] without assuming interconvertibility of the kinetic states during binding. Avermectin B_1a (AVM B_1a), a chloride channel opening agent, accelerated the association and dissociation of TBOB and resulted in a biphasic effect on TBOB binding, i.e., enhancement at low concentrations (EC₅₀, 7.8 nM) followed by displacement at high concentrations (IC₅₀ 6.3 μM) of AVM B_1a. AVM B_1a resulted in similar biphasic effects on t- [³⁵S]butylbicyclophosphorothionate binding. DIDS, an isothiocyanatostilbene derivative with irreversible anion channel blocking effect, selectively inhibited basal [³H]TBOB binding (IC₅₀ 125 μM DIDS) leaving the enhancement by AVM B_1a unaffected.     

Thermochemical Characterization of the Growth Metabolism of the 2,4-Dichlorophenol-Degrading Strain Pseudomonas GT241-1 by Microcalorimetry

By using an LKB-2277 Bioactivity Monitor and the ampoule method, the heat output of the growth metabolism of a 2,4-dichlorophenol-degrading bacterial strain, Pseudomonas strain GT241-1, has been determined at 30°C. From the thermogenic curves, it can be established that the thermokinetic equation of their growth metabolism is P _t = P _{t = 0} exp(k _m t), dP/dt = k _m P ¹, with the order of growth metabolism n = 1. The experimental results indicate that the relationship between the metabolic power (P) and the cell concentration (C) and the relationship between the metabolic power of each cell (P ₀) and the cell concentration can be characterized by the following thermal equations, respectively: C = a + kP and lnC = a+kP ₀ or d dC/dP ₀ = KC ¹. The order of the P ₀ –C equation n is also 1. These results are very significant for environmental sciences, biology, and thermochemistry.     

Brownian Dynamics Simulations of Colloidal Liquids: Hydrodynamics and Stress Relaxation

Abstract

We describe the statistical mechanics background and additional algorithmic features of a recently proposed simple mean-field Brownian Dynamics algorithm formulated to include many-body hydrodynamics, using a local density approximation for the friction coefficient. We show that the equations of motion satisfy the incompressibility of phase space. We make further developments to the model, computing the hydrodynamic effects on the shear stress relaxation function. We show that stress relaxation takes place over two well-defined regimes, in both cases with and without mean field hydrodynamics, MFH. At short times ta ²/D ₀ < 10^?3, where a is the radius of the colloidal particle and D ₀ is the self-diffusion coefficient at infinite dilution, decay of the stress autocorrelation function, C_s(t) is essentially independent of volume fraction and does not fit to a simple analytic form. At longer times than ta ²/D ₀ < 10^?2 the decay has the fractional exponential form ～exp(-t ^β) with β ? 1. The transition between these two regimes coincides with a rapid fall in the time-dependent diffusion coefficient from the so-called short-time to long-time values. We do not find any evidence for power law decay in the C_s(t) as predicted by recent mode-coupling based analytical expansions.     

Syngas fermentation to biofuel: Evaluation of carbon monoxide mass transfer coefficient (kLa) in different reactor configurations

Lignocellulosic biomass such as agri‐residues, agri‐processing by‐products, and energy crops do not compete with food and feed, and is considered to be the ideal renewable feedstocks for biofuel production. Gasification of biomass produces synthesis gas (syngas), a mixture primarily consisting of CO and H₂. The produced syngas can be converted to ethanol by anaerobic microbial catalysts especially acetogenic bacteria such as various clostridia species.One of the major drawbacks associated with syngas fermentation is the mass transfer limitation of these sparingly soluble gases in the aqueous phase. One way of addressing this issue is the improvement in reactor design to achieve a higher volumetric mass transfer coefficient (k_La). In this study, different reactor configurations such as a column diffuser, a 20‐μm bulb diffuser, gas sparger, gas sparger with mechanical mixing, air‐lift reactor combined with a 20‐μm bulb diffuser, air‐lift reactor combined with a single gas entry point, and a submerged composite hollow fiber membrane (CHFM) module were employed to examine the k_La values. The k_La values reported in this study ranged from 0.4 to 91.08 h^?1. The highest k_La of 91.08 h^?1 was obtained in the air‐lift reactor combined with a 20‐μm bulb diffuser, whereas the reactor with the CHFM showed the lowest k_La of 0.4 h^?1. By considering both the k_La value and the statistical significance of each configuration, the air‐lift reactor combined with a 20‐μm bulb diffuser was found to be the ideal reactor configuration for carbon monoxide mass transfer in an aqueous phase. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2011     

Using CFD simulations and statistical analysis to correlate oxygen mass transfer coefficient to both geometrical parameters and operating conditions in a stirred-tank bioreactor

Optimization of a bioreactor design can be an especially challenging process. For instance, testing different bioreactor vessel geometries and different impeller and sparger types, locations, and dimensions can lead to an exceedingly large number of configurations and necessary experiments. Computational fluid dynamics (CFD), therefore, has been widely used to model multiphase flow in stirred-tank bioreactors to minimize the number of optimization experiments. In this study, a multiphase CFD model with population balance equations are used to model gas–liquid mixing, as well as gas bubble distribution, in a 50 L single-use bioreactor vessel. The vessel is the larger chamber in an early prototype of a multichamber bioreactor for mammalian cell culture. The model results are validated with oxygen mass transfer coefficient (k_La) measurements within the prototype. The validated model is projected to predict the effect of using ring or pipe spargers of different sizes and the effect of varying the impeller diameter on k_La. The simulations show that ring spargers result in a superior k_La compared to pipe spargers, with an optimum sparger-to-impeller diameter ratio of 0.8. In addition, larger impellers are shown to improve k_La. A correlation of k_La is presented as a function of both the reactor geometry (i.e., sparger-to-impeller diameter ratio and impeller-to-vessel diameter ratio) and operating conditions (i.e., Reynolds number and gas flow rate). The resulting correlation can be used to predict k_La in a bioreactor and to optimize its design, geometry, and operating conditions.     

A quantitative approach to analyze binding diffusion kinetics by confocal FRAP

Most of the important types of interactions that occur in cells can be characterized as binding-diffusion type processes, and can be quantified by kinetic rate constants such as diffusion coefficients (D) and binding rate constants (k_on and k_off). Confocal FRAP is a potentially important tool for the quantitative analysis of intracellular binding-diffusion kinetics, but how to dependably extract accurate kinetic constants from such analyses is still an open question. To this end, in this study, we developed what we believe is a new analytical model for confocal FRAP-based measurements of intracellular binding-diffusion processes, based on a closed-form equation of the FRAP formula for a spot photobleach geometry. This approach incorporates a binding diffusion model that allows for diffusion of both the unbound and bound species, and also compensates for binding diffusion that occurs during photobleaching, a critical consideration in confocal FRAP analysis. In addition, to address the problem of parametric multiplicity, we propose a scheme to reduce the number of fitting parameters in the effective diffusion subregime when D's for the bound and unbound species are known. We validate this method by measuring kinetic rate constants for the CAAX-mediated binding of Ras to membranes of the endoplasmic reticulum, obtaining binding constants of k_on ∼ 255/s and k_off ∼ 31/s.     

On-line estimation of kLa by an analog computer

A new method was developed for estimating the volumetric oxygen transfer coefficient, k_La, in a fermentor. Various methods were investigated for the on-line estimation of k_La with an analog computer employing a steepest-descent calculation technique. The method by which k_La is estimated (by minimizing the error residue of the model) was found to be very applicable. A method for the simultaneous estimation of the volumetric oxygen transfer coefficient and respiration rate in biological systems is also presented.     

Phloroglucinol protects retinal pigment epithelium and photoreceptor against all‐trans‐retinal–induced toxicity and inhibits A2E formation

Among retinal macular diseases, the juvenile recessive Stargardt disease and the age‐related degenerative disease arise from carbonyl and oxidative stresses (COS). Both stresses originate from an accumulation of all‐trans‐retinal (atRAL) and are involved in bisretinoid formation by condensation of atRAL with phosphatidylethanolamine (carbonyl stress) in the photoreceptor and its transformation into lipofuscin bisretinoids (oxidative stress) in the retinal pigment epithelium (RPE). As atRAL and bisretinoid accumulation contribute to RPE and photoreceptor cell death, our goal is to select powerful chemical inhibitors of COS. Here, we describe that phloroglucinol, a natural phenolic compound having anti‐COS properties, protects both rat RPE and mouse photoreceptor primary cultures from atRAL‐induced cell death and reduces hydrogen peroxide (H₂O₂)‐induced damage in RPE in a dose‐dependent manner. Mechanistic analyses demonstrate that the protective effect encompasses decrease in atRAL‐induced intracellular reactive oxygen species and free atRAL levels. Moreover, we show that phloroglucinol reacts with atRAL to form a chromene adduct which prevents bisretinoid A2E synthesis in vitro. Taken together, these data show that the protective effect of phloroglucinol correlates with its ability to trap atRAL and to prevent its further transformation into deleterious bisretinoids. Phloroglucinol might be a good basis to develop efficient therapeutic derivatives in the treatment of retinal macular diseases.     

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     

Simulations of Flexible Manifolds

Monte Carlo simulations of flexible two-dimensional model membranes embedded in three space dimensions are reported. We explain in detail the techniques how to simulate fluid open membranes and fluid closed membranes (vesicles). It is shown that polymerized open membranes are rough and flat. Accordingly, the two larger components of the inertia tensor are proportional to the number of monomers of the surface, λ₃ ≈ λ₂ ～ N, whereas the smallest λ₁ ～ N ^0.65. Polymerized vesicles are isotropic and their mean square radius of gyration is R ² ～ λ _k ～ N. In contrast, fluid membranes and vesicles exhibit crumpled shapes with λ _k ～ N ^0.8 for k = 1,2,3. A monomer on a fluid surface exhibits a time-dependent mean squared displacement of r ² (t) ～ t ^0.8.     

On the diffusion of metabolic intermediates

A simple model of diffusible metabolic intermediates, produced in a spherical cell, is postulated. The rate of production of the intermediate is taken to be a linear function of its internal concentration. The intermediate is produced by the degradation of some precursor substance at a rate which is assumed to decrease with increasing internal concentration. Assuming the medium in which the cell is enclosed to be infinite in extent, and the external concentration of the intermediate constant, the time dependent and steady-state solutions of the diffusion problem involved are obtained. It is shown that production of the intermediate will not cease, for any value ofr≤r ₀, wherer ₀ is the radius of the cell. Possible application of this approach to the study of the occurrence of the lag phase in bacterial growth processes is indicated.     

Optical sensor enabled rocking T-flasks as novel upstream bioprocessing tools

During the past decade, novel disposable cell culture vessels (generally referred to as Process Scouting Devices or PSDs) have become increasingly popular for laboratory scale studies and seed culture generation. However, the lack of engineering characterization and online monitoring tools for PSDs makes it difficult to elucidate their oxygen transfer capabilities. In this study, a mass transfer characterization (k_La) of sensor enabled static and rocking T‐flasks is presented and compared with other non‐instrumented PSDs such as CultiFlask 50®, spinner flasks, and SuperSpinner D 1000®. We have also developed a mass transfer empirical correlation that accounts for the contribution of convection and diffusion to the volumetric mass transfer coefficient (k_La) in rocking T‐flasks. We also carried out a scale‐down study at matched k_La between a rocking T75‐flask and a 10 L (2 L filling volume) wave bioreactor (Cultibag®) and we observed similar DO and pH profiles as well as maximum cell density and protein titer. However, in this scale‐down study, we also observed a negative correlation between cell growth and protein productivity between the rocking T‐flask and the wave bioreactor. We hypothesize that this negative correlation can be due to hydrodynamic stress difference between the rocking T‐flask and the Cultibag. As both cell culture devices share key similarities such as type of agitation (i.e., rocking), oxygen transfer capabilities (i.e., k_La) and disposability, we argue that rocking T‐flasks can be readily integrated with wave bioreactors, making the transition from research‐scale to manufacturing‐scale a seamless process. Biotechnol. Bioeng. 2012;109: 2295–2305. © 2012 Wiley Periodicals, Inc.     

Modelling microalgal productivity in a High Rate Algal Pond based on wavelength dependent optical properties

A model is presented to predict algal biomass concentration and productivity in a High Rate Algal Pond (HRAP) at all possible combinations of incident photon flux density (PFD), pond depth and hydraulic retention time (HRT). The total extinction coefficientk _t and the absorption coefficient k_a of algal biomass were measured at 1 nm intervals. Thek _t values were used to calculate the underwater light climate, which included the spectral narrowing of the photon flux density with increasing depth. The number of quanta absorbed (QA) from the photosynthetic available radiation (PAR) was calculated using thek _a /k _t ratio and incident PFD at 1 nm intervals. Algal oxygen production is related to QA by the quantum requirement (QR), which was determined fromk _a ,and the slope of the photosynthesis versus irradiance curve (α). Based on this calculation we propose a new concept: the compensating absorption rate (CAR), which represents the rate of photon absorption necessary to balance oxygen consuming processes. The model calculated productivities using literature data on HRT, pond depth and incident PFD, that compared well with the actual measured productivities. To achieve optimal HRAP productivities under fluctuating climatological conditions, we propose a pond management strategy based on model simulations.     

Solutions to a degenerate system of parabolic equations from marine biology

Summary A system of parabolic and ordinary differential equations u _t = a ² u _xx + F(u, v, w), v _t = a ² v _xx + G(u, v, w),w _x = – k(u)w is studied which has been proposed by Radach and Maier-Reimer for the dynamics of phytoplankton and nutrient in dependence of light intensity. It is shown that there is a unique solution to this system satisfying given initial and boundary conditions. The solution depends continuously on the data. For specific nonlinearities F, G, and k bounds for the solutions are given.