Flux balancing of light and nutrients in a biofilm photobioreactor for maximizing photosynthetic productivity

This article reports a combined experimental and numerical study on the efficient operation of Porous Substrate Bioreactors. A comprehensive model integrating light transport, mass transport, and algal growth kinetics was used to understand the productivity of photosynthetic biofilms in response to delivery rates of photons and nutrients. The reactor under consideration was an evaporation driven Porous Substrate Bioreactor (PSBR) cultivating the cyanobacteria Anabaena variabilis as a biofilm on a porous substrate which delivers water and nutrients to the cells. In an unoptimized experimental case, this reactor was operated with a photosynthetic efficiency of 2.3%, competitive with conventional photobioreactors. Moreover, through a scaling analysis, the location at which the phosphate delivery rate decreased the growth rate to half of its uninhibited value was predicted as a function of microorganism and bioreactor properties. The numerical model along with the flux balancing techniques presented herein can serve as tools for designing and selecting operating parameters of biofilm based cultivation systems for maximum productivity. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:348–359, 2014     

Transport characteristics of molecular motors

Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically studied with respect to its energetic efficiency and quality expressed by an effective diffusion coefficient. We demonstrate the role of friction and non-equilibrium driving on the transport quantifiers and identify regions of a parameter space where motors are optimally transported.     

Repeated applications of a transdermal patch: analytical solution and optimal control of the delivery rate

The integral transform technique was implemented to solve a mathematical model developed for percutaneous drug absorption. The model included repeated application and removal of a patch from the skin. Fick's second law of diffusion was used to study the transport of a medicinal agent through the vehicle and subsequent penetration into the stratum corneum. Eigenmodes and eigenvalues were computed and introduced into an inversion formula to estimate the delivery rate and the amount of drug in the vehicle and the skin. A dynamic programming algorithm calculated the optimal doses necessary to achieve a desired transdermal flux. The analytical method predicted profiles that were in close agreement with published numerical solutions and provided an automated strategy to perform therapeutic drug monitoring and control.     

Chemical reactions and membranes: A macroscopic basis for active transport II. Non-linear aspects

The physical principles that material and charge are conserved provide a basis for the design of a membrane capable of performing active ion transport in which the connection between “metabolic energy” input and the ion transport process itself is electrical rather than material. Molecular interactions between components in this system are irrelevant to its function. A second model built on the same principles performs active ion transport in a statically symmetrical membrane. The basis of its operation is a weakly stable unsymmetrical concentration profile arising from an enzyme-catalyzed reaction occurring within the membrane. The function of this membrane is irreversibly terminated (“killed”) by interference either with intramembrane concentration gradients or with the reactions which maintain them. Hence, any attempt to study this system by breaking it apart destroys the basis of its function. The existence of these models reveals the logical insufficiency of the molecular biologist's approach to understanding the basis of active transport: Neither the experimental techniques for structure determination (disruption, purification, characterization, and reconstitution) nor the fundamental question of that discipline (What is the molecular connection between &*|… ?) of the molecular biologist are applicable to the study or interpretation of these model systems. While the model systems are artificial, they incorporate only widely applicable concepts of physical chemistry and biochemical kinetics. The is no reason for excluding such mechanisms in natural membrane transport systems. If they are present, then more effective strategies of investigation will be required.     

Properties of the stochastic energization-relaxation channel model for vectorial ion transport

A model for the primary active transport by an ion pump protein is proposed. The model, the "energization-relaxation channel model," describes an ion pump as a multiion channel that undergoes stochastic transitions between two conformational states by external energy supply. When the potential profile along ion transport pathway is asymmetrical, a net ion flux is induced by the transitions. In this model, the coupling of the conformational change and ion transport is stochastic and loose. The model qualitatively reproduces known properties of active transport such as the effect of ion concentration gradient and membrane potential on the rate of transport and the inhibition of ion transport at high ion concentration. We further examined the effect of various parameters on the ion transport properties of this model. The efficiency of the coupling was almost 100% under some conditions.     

Molecular dynamics study of ion transport in transmembrane protein channels

Ion transport through biological membranes often takes place via pore-like protein channels. The elementary process of this transport can be described as a motion of the ion in a quasi-periodic multi-well potential. In this study molecular dynamics simulations of ion transport in a model channel were performed in order to test the validity of reaction-rate theory for this process. The channel is modelled as a hexagonal helix of infinite length, and the ligand groups interacting with the ion are represented by dipoles lining the central hole of the channel. The dipoles interact electrostatically with each other and are allowed to oscillate around an equilibrium orientation. The coupled equations of motion for the ion and the dipoles were solved simultaneously with the aid of a numerical integration procedure. From the calculated ion trajectories it is seen that, particularly at low temperatures, the ion oscillates back and forth in the trapping site many times before it leaves the site and jumps over the barrier. The observed oscillation frequency was found to be virtually temperature-independent (nu 0 approximately equal to 2 X 10(12) s-1) so that the strong increase of transport rate with temperature results almost exclusively from the Arrhenius-type exponential dependence of jump probability w on 1/T. At higher temperatures simultaneous jumps over several barriers occasionally occur. Although the exponential form of w(T) was in agreement with the predictions of rate theory, the activation energy Ea as determined from w(T) was different from the barrier height which was calculated from the static potential of the ion in the channel; the actual transport rate was 1 X 10(3) times higher than the rate predicted from the calculated barrier height. This observation was interpreted by the notion that ion transport in the channel is strongly influenced by thermal fluctuations in the conformation of the ligand system which in turn give rise to fluctuations of barrier height.     

An inverse algorithm for a mathematical model of an avian urine concentrating mechanism

A nonlinear optimization technique, in conjunction with a single-nephron, single-solute mathematical model of the quail urine concentrating mechanism, was used to estimate parameter sets that optimize a measure of concentrating mechanism efficiency, viz., the ratio of the free-water absorption rate to the total NaCl active transport rate. The optimization algorithm, which is independent of the numerical method used to solve the model equations, runs in a few minutes on a 1000 MHz desktop computer. The parameters varied were: tubular permeabilities to water and solute; maximum active solute transport rates of the ascending limb of Henle and the collecting duct (CD); length of the prebend enlargement (PBE) of the descending limb; fractional solute delivery to the CD; solute concentration of tubular fluid entering the CD at the cortico-medullary boundary; and rate of exponential CD population decrease along the medullary cone. Using a base-case parameter set and parameter bounds suggested by physiologic experiments, the optimization algorithm identified a maximum-efficiency set of parameter values that increased efficiency by 40% above base-case efficiency; a minimum-efficiency set reduced efficiency by about 41%. When maximum-efficiency parameter values were computed as medullary length varied over the physiologic range, the PBE was found to make up 88% of a short medullary cone but only 8% of a long medullary cone.     

A tridomain model for potassium clearance in optic nerve of Necturus

Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.     

Fluctuation-driven directional flow in biochemical cycle: further study of electric activation of Na,K pumps

Directional flow of information and energies is characteristic of many types of biochemical reactions, for instance, ion transport, energy coupling during ATP synthesis, and muscle contraction. Can a fluctuating force field, or a noise, induce such a directional flux? Previous work has shown that Na,K-ATPase of human erythrocyte can absorb free energy from an externally applied random-telegraph-noise (RTN) electric field to pump Rb+ up its concentration gradient. However, the RTN field used in these experiments was constant in amplitude and would not mimic fluctuating electric fields of a cell membrane. Here we show that electric fields which fluctuate both in life time and in amplitude, and thus, better mimicking the transmembrane electric fields of a cell, can also induce Rb+ pumping by Na,K-ATPase. A Gaussian-RTN-electric field, or a field with amplitude fluctuating according to the Gaussian distribution, with varied standard deviation (sigma), induced active pumping of Rb+ in human erythrocyte, which was completely inhibited by ouabain. Increased values for sigma led to a nonmonotonic reduction in pumping efficiency. A general formula for calculating the ion transport in a biochemical cycle induced by fluctuating electric field has been derived and applied to a simple four-state electroconformational coupling (ECC) model. It was found that the calculated efficiency in the energy coupling decreased with increasing sigma value, and this effect was relatively small and monotonic, whereas experimental data were more complex: monotonic under certain sets of conditions but nonmonotonic under different sets. The agreement in general features but disagreement in some fine features suggest that there are other properties of the electric activation process for Na,K-ATPase that cannot be adequately described by the simple ECC model, and further refinement of the ECC model is required.     

New insights into fish ion regulation and mitochondrion-rich cells

Compared to terrestrial animals, fish have to cope with more-challenging osmotic and ionic gradients from aquatic environments with diverse salinities, ion compositions, and pH values. Gills, a unique and highly studied organ in research on fish osmoregulation and ionoregulation, provide an excellent model to study the regulatory mechanisms of ion transport. The present review introduces and discusses some recent advances in relevant issues of teleost gill ion transport and functions of gill ionocytes. Based on accumulating evidence, a conclusive model of NaCl secretion in gills of euryhaline teleosts has been established. Interpretations of results of studies on freshwater fish gill Na+/Cl- uptake mechanisms are still being debated compared with those for NaCl secretion. Current models for Na+/Cl- uptake are proposed based on studies in traditionally used model species. Many reported inconsistencies are claimed to be due to differences among species, various experimental designs, or acclimation conditions. Having the benefit of advanced techniques in molecular/cellular biology, functional genomics, and model animals, several new notions have recently been raised concerning relevant issues of Na+/Cl- uptake pathways. Several new windows have been opened particularly in terms of molecular mechanisms of ionocyte differentiation and energy metabolite transport between gill cells during environmental challenge.     

Molecular modeling of blood-brain barrier nutrient transporters: in silico basis for evaluation of potential drug delivery to the central nervous system

For drugs that act in the brain, the blood-brain barrier (BBB) is a considerable physical barrier which influences the distribution of drugs to the brain. The BBB is essentially impermeable for hydrophilic and/or charged compounds. Nutrient membrane transporters have an important physiological role in the transport of essential substances across the BBB required for normal brain function. We and others have shown that these transporters may have utility as drug delivery vectors, thereby increasing brain distribution of these compounds via these systems. In this review, we evaluate molecular (in silico) models of BBB transport proteins. Few BBB membrane transporters have been crystallized, but their crystal structures have a possibility for use in homology modeling. Other techniques commonly used are 2D quantitative structure-activity relationships (QSAR), as well as 3D-QSAR techniques including comparative molecular field analysis (CoMFA) and comparative similarity index analysis (CoMSIA). Each of these models provides valuable information for ascertaining their potential basis for BBB transport and brain drug delivery.     

Channelling auxin action: modulation of ion transport by indole-3-acetic acid

The growth hormone auxin is a key regulator of plant cell division and elongation. Since plants lack muscles, processes involved in growth and movements rely on turgor formation, and thus on the transport of solutes and water. Modern electrophysiological techniques and molecular genetics have shed new light on the regulation of plant ion transporters in response to auxin. Guard cells, hypocotyls and coleoptiles have advanced to major model systems in studying auxin action. This review will therefore focus on the molecular mechanism by which auxin modulates ion transport and cell expansion in these model cell types.     

A gastric acid secretion model.

A theory of gastric acid production and self-protection is formulated mathematically and examined for clinical and experimental correlations, implications, and predictions using analytic and numerical techniques. In our model, gastric acid secretion in the stomach, as represented by an archetypal gastron, consists of two chambers, circulatory and luminal, connected by two different regions of ion exchange. The capillary circulation of the gastric mucosa is arranged in arterial-venous arcades which pass from the gastric glands up to the surface epithelial lining of the lumen; therefore the upstream region of the capillary chamber communicates with oxyntic cells, while the downstream region communicates with epithelial cells. Both cell types abut the gastric lumen. Ion currents across the upstream region are calculated from a steady-state oxyntic cell model with active ion transport, while the downstream ion fluxes are (facilitated) diffusion driven or secondarily active. Water transport is considered iso-osmotic. The steady-state model is solved in closed form for low gastric lumen pH. A wide variety of previously performed static and dynamic experiments on ion and CO2 transport in the gastric lumen and gastric blood supply are for the first time correlated with each other for an (at least) semiquantitative test of current concepts of gastric acid secretion and for the purpose of model verification. Agreement with the data is reported with a few outstanding and instructive exceptions. Model predictions and implications are also discussed.     

Development of a size-dependent aerosol deposition model utilising human airway epithelial cells for evaluating aerosol drug delivery

Aerosol delivery to the airways of the human respiratory tract, followed by absorption, constitutes an alternative route of administration for compounds unsuitable for delivery by conventional oral and parenteral routes. The target for aerosol drug delivery is the airways epithelium, i.e. tracheal, bronchial, bronchiolar and alveolar cells, which become the site of drug deposition. These epithelial layers also serve as a barrier to the penetration of inhaled material. An in vitro model for aerosol deposition and transport across epithelia in the human airways may be a good predictor of in vivo disposition. The present preliminary studies begin an investigation that blends the dynamics of aerosol delivery and the basis of an in vitro simulated lung model to evaluate the transport properties of a series of molecular weight marker compounds across human-derived bronchiolar epithelial cell monolayers. An Andersen viable cascade impactor was used as a delivery apparatus for the deposition of size-segregated particles onto monolayers of small airway epithelial cells and Calu-3 cells. It was shown that these cell layers can withstand placement in the impactor, and that permeability can be tested subsequent to removal from the impactor.     

Mechanistic analysis of electroporation-induced cellular uptake of macromolecules

Pulsed electric field has been widely used as a nonviral gene delivery platform. The delivery efficiency can be improved through quantitative analysis of pore dynamics and intracellular transport of plasmid DNA. To this end, we investigated mechanisms of cellular uptake of macromolecules during electroporation. In the study, fluorescein isothiocyanate-labeled dextran (FD) with molecular weight of 4,000 (FD-4) or 2,000,000 (FD-2000) was added into suspensions of a murine mammary carcinoma cell (4T1) either before or at different time points (ie, 1, 2, or 10 sec) after the application of different pulsed electric fields (in high-voltage mode: 1.2-2.0 kV in amplitude, 99 microsec in duration, and 1-5 pulses; in low-voltage mode: 100-300 V in amplitude, 5-20 msec in duration, and 1-5 pulses). The intracellular concentrations of FD were quantified using a confocal microscopy technique. To understand transport mechanisms, a mathematical model was developed for numerical simulation of cellular uptake. We observed that the maximum intracellular concentration of FD-2000 was less than 3% of that in the pulsing medium. The intracellular concentrations increased linearly with pulse number and amplitude. In addition, the intracellular concentration of FD-2000 was approximately 40% lower than that of FD-4 under identical pulsing conditions. The numerical simulations predicted that the pores larger than FD-4 lasted <10 msec after the application of pulsed fields if the simulated concentrations were on the same order of magnitude as the experimental data. In addition, the simulation results indicated that diffusion was negligible for cellular uptake of FD molecules. Taken together, the data suggested that large pores induced in the membrane by pulsed electric fields disappeared rapidly after pulse application and convection was likely to be the dominant mode of transport for cellular uptake of uncharged macromolecules.     

A quantitative study of electroporation showing a plateau in net molecular transport.

Electroporation is believed to involve a temporary structural rearrangement of lipid bilayer membranes, which results in ion and molecular transport across the membrane. The results of a quantitative study of molecular transport due to electroporation caused by a single exponential pulse are presented; transport of four molecules of different physical characteristics across erythrocyte ghost membranes is examined as a function of applied field strength. Flow cytometry is used to quantitatively measure the number of molecules transported for 10(4) to 10(5) individual ghosts for each condition. This study has four major findings: 1) Net transport first increases with field strength, but reaches a plateau at higher field strengths. Significant transport is found at or below 1 kV/cm, and transport plateaus begin at field strengths between 2 and 5 kV/cm depending on the molecule transported. 2) A single population of ghosts generally exists, but exhibits a wide distribution in the amount of molecular transport. 3) Under the conditions used, the direction of transport across the ghost membrane does not appear to affect molecular transport significantly. 4) Large numbers of ghosts may be destroyed by the electroporation procedure.     

Molecular simulation of realistic membrane models of alkylated PEEK membranes

Atomistic molecular modelling has proven to be a useful tool for the investigation of transport properties of small gas molecules in polymer membrane matrices. The quality of the predictions of these properties based on molecular simulation depends principally on the quality of the membrane model. The predicted gas transport properties of small gas molecules in the same glassy polymer membrane show often a large scatter in gas diffusion and solubility simulated values. In order to reduce the scatter in predicted gas transport properties in glassy polymer membranes, numerical analysis of structural features of the membrane model is used for pre-selecting only the realistic ones for further simulations using transition-state theory (TST) approach. Simulation results of gas solubility and diffusion in alkylated poly-ether–ether–ketone (PEEK) membranes will illustrate the approach.     

Atomistic Detailed Mechanism and Weak Cation-Conducting Activity of HIV-1 Vpu Revealed by Free Energy Calculations

The viral protein U (Vpu) encoded by HIV-1 has been shown to assist in the detachment of virion particles from infected cells. Vpu forms cation-specific ion channels in host cells, and has been proposed as a potential drug target. An understanding of the mechanism of ion transport through Vpu is desirable, but remains limited because of the unavailability of an experimental structure of the channel. Using a structure of the pentameric form of Vpu – modeled and validated based on available experimental data – umbrella sampling molecular dynamics simulations (cumulative simulation time of more than 0.4 µs) were employed to elucidate the energetics and the molecular mechanism of ion transport in Vpu. Free energy profiles corresponding to the permeation of Na⁺ and K⁺ were found to be similar to each other indicating lack of ion selection, consistent with previous experimental studies. The Ser23 residue is shown to enhance ion transport via two mechanisms: creating a weak binding site, and increasing the effective hydrophilic length of the channel, both of which have previously been hypothesized in experiments. A two-dimensional free energy landscape has been computed to model multiple ion permeation, based on which a mechanism for ion conduction is proposed. It is shown that only one ion can pass through the channel at a time. This, along with a stretch of hydrophobic residues in the transmembrane domain of Vpu, explains the slow kinetics of ion conduction. The results are consistent with previous conductance studies that showed Vpu to be a weakly conducting ion channel.     

Effect of blood flow on near-the-wall mass transport of drugs and other bioactive agents: a simple formula to estimate boundary layer concentrations

Transport of bioactive agents through the blood is essential for cardiovascular regulatory processes and drug delivery. Bioactive agents and other solutes infused into the blood through the wall of a blood vessel or released into the blood from an area in the vessel wall spread downstream of the infusion/release region and form a thin boundary layer in which solute concentration is higher than in the rest of the blood. Bioactive agents distributed along the vessel wall affect endothelial cells and regulate biological processes, such as thrombus formation, atherogenesis, and vascular remodeling. To calculate the concentration of solutes in the boundary layer, researchers have generally used numerical simulations. However, to investigate the effect of blood flow, infusion rate, and vessel geometry on the concentration of different solutes, many simulations are needed, leading to a time-consuming effort. In this paper, a relatively simple formula to quantify concentrations in a tube downstream of an infusion/release region is presented. Given known blood-flow rates, tube radius, solute diffusivity, and the length of the infusion region, this formula can be used to quickly estimate solute concentrations when infusion rates are known or to estimate infusion rates when solute concentrations at a point downstream of the infusion region are known. The developed formula is based on boundary layer theory and physical principles. The formula is an approximate solution of the advection-diffusion equations in the boundary layer region when solute concentration is small (dilute solution), infusion rate is modeled as a mass flux, and there is no transport of solute through the wall or chemical reactions downstream of the infusion region. Wall concentrations calculated using the formula developed in this paper were compared to the results from finite element models. Agreement between the results was within 10%. The developed formula could be used in experimental procedures to evaluate drug efficacy, in the design of drug-eluting stents, and to calculate rates of release of bioactive substances at active surfaces using downstream concentration measurements. In addition to being simple and fast to use, the formula gives accurate quantifications of concentrations and infusion rates under steady-state and oscillatory flow conditions, and therefore can be used to estimate boundary layer concentrations under physiological conditions.     

An Efficient Multi-Scale Modelling Approach for ssDNA Motion in Fluid Flow

The paper presents a multi-scale modelling approach for simulating macromolecules in fluid flows. Macromolecule transport at low number densities is frequently encountered in biomedical devices, such as separators, detection and analysis systems. Accurate modelling of this process is challenging due to the wide range of physical scales involved. The continuum approach is not valid for low solute concentrations, but the large timescales of the fluid flow make purely molecular simulations prohibitively expensive. A promising multi-scale modelling strategy is provided by the meta-modelling approach considered in this paper. Meta-models are based on the coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of macromolecules. The approach enables simulation of individual macromolecules at macroscopic time scales. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical model. Lack of robustness of the particle-corrector algorithm employed can lead to slow convergence and numerical instability. A new FAst Linear COrrector （FALCO） algorithm is introduced in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. Validation of the new particle corrector against a simple analytic solution is performed and improved convergence is demonstrated for ssDNA motion in a lid-driven micro-cavity.