Intra-airway gas mixing during high-frequency ventilation

We examined the intra-airway gas transport mediated by high-frequency oscillations (HFO) in 10 nonintubated healthy volunteers using a method based on comparisons of single-breath N2-washout curves obtained after various durations of breath hold or high-frequency oscillations. With a mathematical analysis based on Fick's law of diffusion we computed the local transport parameter, effective diffusivity, during oscillations of frequency 2-24 Hz and tidal volume 10-120 ml and during breath hold alone. Local effective diffusivity increased with both oscillatory frequency and tidal volume at all levels in the tracheobronchial tree; the enhancing effect of tidal volume on local effective diffusivity was more pronounced than that of frequency so that effective diffusivity was greater with larger tidal volume at fixed frequency-tidal volume product (f . VT). The greatest enhancement of gas mixing within the lung during HFO (over breath hold) was seen in the central airways. In previous studies examining CO2 removal rate during HFO (J. Clin. Invest. 68: 1475, 1981), we found that CO2 output was also greater with larger tidal volume at fixed f . VT, and we attributed this to an end constraint imposed by a fresh gas bias flow. Results of the current study, performed without a bias flow, indicate that bias flow end constraint does not solely account for the observed dependence of CO2 output on frequency and tidal volume.     

A stirred bath technique for diffusivity measurements in cell matrices

A stirred bath technique was developed for determining effective diffusivities in cell matrices. The technique involves cell immobilization in a dilute gel which has negligible effect on solute diffusion. Agar and collagen were tested as immobilizing gels. Agar gel was shown to have minor interactions with the diffusion of various biological molecules, and was used for immobilization of Ehrlich Ascites Tumor (EAT) cells. Diffusivities of glucose and lactic acid were measured in EAT matrices for cell loadings between 20 and 45 vol %. Treatment with glutaraldehyde was effective in quenching the metabolic activity of the cells while preserving their physical properties and diffusive resistance. The measured data agree favorably with predictions based on Maxwell's equation for effective diffusion in a periodic composite material. The stirred bath technique is useful for diffusivity determinations in immobilized matrices or free slurries, and is applicable to both microbial and mammalian cell systems.     

Mathematical and experimental analyses of antibody transport in hollow-fiber-based specific antibody filters

We are developing hollow fiber-based specific antibody filters (SAFs) that selectively remove antibodies of a given specificity directly from whole blood, without separation of the plasma and cellular blood components and with minimal removal of plasma proteins other than the targeted pathogenic antibodies. A principal goal of our research is to identify the primary mechanisms that control antibody transport within the SAF and to use this information to guide the choice of design and operational parameters that maximize the SAF-based antibody removal rate. In this study, we formulated a simple mathematical model of SAF-based antibody removal and performed in vitro antibody removal experiments to test key predictions of the model. Our model revealed three antibody transport regimes, defined by the magnitude of the Damk?hler number Da (characteristic antibody-binding rate/characteristic antibody diffusion rate): reaction-limited (Da /= 10). For a given SAF geometry, blood flow rate, and antibody diffusivity, the highest antibody removal rate was predicted for diffusion-limited antibody transport. Additionally, for diffusion-limited antibody transport the predicted antibody removal rate was independent of the antibody-binding rate and hence was the same for any antibody-antigen system and for any patient within one antibody-antigen system. Using SAF prototypes containing immobilized bovine serum albumin (BSA), we measured anti-BSA removal rates consistent with transport in the intermediate regime (Da approximately 3). We concluded that initial SAF development work should focus on achieving diffusion-limited antibody transport by maximizing the SAF antibody-binding capacity (hence maximizing the characteristic antibody-binding rate). If diffusion-limited antibody transport is achieved, the antibody removal rate may be raised further by increasing the number and length of the SAF fibers and by increasing the blood flow rate through the SAF.     

A membrane model describing the effect of temperature on the water conductivity of erythrocyte membranes at subzero temperatures

Thermodynamic models show that the loss of intracellular water from human erythrocytes during freezing depends heavily upon the water conductivity of the erythrocyte membrane. These calculations, which are based on the simple extrapolation of ambient conductivity data to subzero temperatures, show that more than 95% of cell water is transferable during freezing, whereas experiments show that at least 20% of cell water is retained. A study of the effects of different published values for the membrane water conductivity on cell water retained during freezing shows that this discrepancy may be a consequence of the simple extrapolation procedure.For a homogeneous membrane system, absolute reaction rate theory was used to develop a surface-limited permeation model that includes the resistance to the flow of water not only through the interior region of the membrane but also across possible rate-limiting barriers at the solution-membrane interfaces. The model shows that it is unlikely that a single ratelimiting process dominates water transport in the red cell as it is being cooled from ambient to subzero temperatures. The effective membrane conductivity at subzero temperatures could possibly be much lower than a simple extrapolation of existing data would predict. With the aid of this model analytical predictions of intracellular water during freezing are more consistent with experimental observations.     

Evidence for Carrier-Mediated Transport of Monosaccharides in the Ehrlich Ascites Tumor Cell

Evidence for carrier-mediated transport of monosaccharides in the Ehrlich ascites tumor cells was provided through kinetic analysis of data obtained by: (a) studying sugar uptake by dilute cell suspensions with an optical densimetric apparatus, (b) studying sugar uptake by thicker cell suspensions by means of direct chemical analytical methods using packed cell plugs, (c) observing the effects of a competitive inhibitor upon sugar uptake with the chemical analytical method, and (d) measurement of tracer uptake of a high affinity sugar in thick cell suspensions in the absence of net movement. Quantitative application of the data obtained with the above experimental procedures to theoretical model systems derived for both carrier-mediated transport and simple passive diffusion indicated that the results were consonant with predictions for the carrier-mediated transport model, but could not be explained on the basis of uncomplicated diffusion.     

Determination of cell membrane permeability in concentrated cell ensembles

The method of volume averaging is used to analyze the process of diffusion in concentrated cell ensembles in which significant resistance to mass transfer is caused by the cellular membrane. A general closure scheme is given that allows for direct theoretical prediction of effective diffusivities for any cellular geometry. Numerical results are presented for the classical parallelepiped arrangement used to model cellular systems, and these results are used in conjunction with experimental studies of concentrated cell ensembles to determine membrane permeabilities for solute diffusion in several cellular systems. Membrane permeabilities are compared with predictions from other models of diffusion in cellular systems.     

A simple correlation for predicting effective diffusivities in immobilized cell systems

A simple correlation method has been developed to predict effective diffusivities of small molecules in heterogeneous materials such as immobilized cell systems. This correlation uses a single diffusivity measurement at one cell volume fraction to predict diffusivities for any other volume fraction of cell. The method has been applied to 20 sets of published diffusivity measurements in immobilized cell systems and accurately predicts affective diffusivities of molecules for the full range of cell fractions. It may also be used to predict effective diffusivities in heterogeneous materials in which the diffusivity of a molecule in each phase and the volume fraction of each phase are known. (c) 1996 John Wiley & Sons, Inc.     

Autocrine ligand binding to cell receptors. Mathematical analysis of competition by solution "decoys".

Autocrine ligands have been demonstrated to regulate cell proliferation, cell adhesion, and cell migration in a number of different systems and are believed to be one of the underlying causes of malignant cell transformation. Binding of these ligands to their cellular receptors can be compromised by diffusive transport of ligand away from the secreting cell. Exogenous addition of antibodies or solution receptors capable of competing with cellular receptors for these autocrine ligands has been proposed as a means of inhibiting autocrine-stimulated cell behavioral responses. Such "decoys" complicate cellular binding by offering alternative binding targets, which may also be capable of aiding or abating transport of the ligand away from the cell surface. We present a mathematical model incorporating autocrine ligand production and the presence of competing cellular and solution receptors. We elucidate effects of key system parameters including ligand diffusion rate, binding rate constants, cell density, and secretion rate on the ability of solution receptors to inhibit cellular receptor binding. Both plated and suspension cell systems are considered. An approximate analytical expression relating the key parameters to the critical concentration of solution "decoys" required for inhibition is derived and compared to the numerical calculations. We find that in order to achieve essentially complete inhibition of surface receptor binding, the concentration of decoys may need to be as much as four to eight orders of magnitude greater than the equilibrium disociation constant for ligand binding to surface receptors.     

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.     

A macroscopic model of traffic jams in axons

The purpose of this paper is to develop a minimal macroscopic model capable of explaining the formation of traffic jams in fast axonal transport. The model accounts for the decrease of the number density of positively (and negatively) oriented microtubules near the location of the traffic jam due to formation of microtubule swirls; the model also accounts for the reduction of the effective velocity of organelle transport in the traffic jam region due to organelles falling off microtubule tracks more often in the swirl region. The model is based on molecular-motor-assisted transport equations and the hydrodynamic model of traffic jams in highway traffic. Parametric analyses of the model’s predictions for various values of viscosity of the traffic flow, variance of the velocity distribution, diffusivity of microtubule-bound and free organelles, rate constants for binding to and detachment from microtubules, relaxation time, and average motor velocities of the retrograde and anterograde transport, are carried out.     

Gene surfing in expanding populations

Large scale genomic surveys are partly motivated by the idea that the neutral genetic variation of a population may be used to reconstruct its migration history. However, our ability to trace back the colonization pathways of a species from their genetic footprints is limited by our understanding of the genetic consequences of a range expansion. Here, we study, by means of simulations and analytical methods, the neutral dynamics of gene frequencies in an asexual population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a "surfing" mechanism [Edmonds, C.A., Lillie, A.S., Cavalli-Sforza, L.L., 2004. Mutations arising in the wave front of an expanding population. Proc. Natl. Acad. Sci. 101, 975-979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixation and, closely related, (ii) the continual loss of genetic diversity (heterozygosity) at the wave front, characterizing the approach to fixation. Our stochastic simulations show that an effective population size can be assigned to the wave that controls the (observable) gradient in heterozygosity left behind the colonization process. This effective population size is markedly higher in the presence of cooperation between individuals ("pushed waves") than when individuals proliferate independently ("pulled waves"), and increases only sub-linearly with deme size. To explain these and other findings, we develop a versatile analytical approach, based on the physics of reaction-diffusion systems, that yields simple predictions for any deterministic population dynamics. Our analytical theory compares well with the simulation results for pushed waves, but is less accurate in the case of pulled waves when stochastic fluctuations in the tip of the wave are important.     

Distribution and diffusivity of a hydrophobic probe molecule in the interior of a membrane: theory and simulation.

We propose a simple model for the distribution of position and orientation and the diffusion of a hydrophobic probe molecule embedded in a membrane. The molecule experiences both a Maier-Saupe orienting potential as well as an enclosing potential of repulsion from the membrane walls. A statistical thermodynamics treatment of the model provides predictions of the location and orientation of the molecule within the membrane. In particular, we evaluate the order parameter of the molecule in terms of the model constants. The diffusivity of the probe is studied by Brownian dynamics simulation. For rotational diffusion, we check an available analytical approximate treatment that allows for the prediction of the dynamics in terms of equilibrium quantities. We also pay attention to quantities related to the initial and mean reorientational rate of the probe. For translational diffusion, we use the simulation results to analyze some general aspects of lateral and transversal diffusion.     

How a soluble enzyme can be forced to work as a transport system: description of an experimental design

The cellular transport systems which have been studied up to now have been found to be based on the functioning of specialized proteins anchored asymmetrically in cell membranes. In the present paper we show that a single soluble enzyme inserted at random in a gel slab can drive an uphill transport, provided that asymmetrical boundary conditions force the reversible reaction catalyzed by this enzyme to work forward on one face of the gel slab and backward on the other face. Experimentally, we have used a yeast alcohol dehydrogenase to induce an uphill transport of NADH. It cannot be excluded that comparable structurally symmetrical transport systems also exist in living cells. Such systems would be particularly well suited to preserving cell homeostasis with regard to small solutes.     

Static compression of articular cartilage can reduce solute diffusivity and partitioning: implications for the chondrocyte biological response.

Chondrocytes depend upon solute transport within the avascular extracellular matrix of adult articular cartilage for many of their biological activities. Alterations to bioactive solute transport may, therefore, represent a mechanism by which cartilage compression is transduced into cellular metabolic responses. We investigated the effects of cartilage static compression on diffusivity and partitioning of a range of model solutes including dextrans of molecular weights 3 and 40 kDa, and tetramethylrhodamine (a 430 Da fluorophore). New fluorescence methods were developed for real-time visualization and measurement of transport within compressed cartilage explants. Experimental design allowed for multiple measurements on individual explants at different compression levels in order to minimize confounding influences of compositional variations. Results demonstrate that physiological levels of static compression may significantly decrease solute diffusivity and partitioning in cartilage. Effects of compression were most dramatic for the relatively high molecular weight solutes. For 40 kDa dextran, diffusivity decreased significantly (p<0.01) between 8% and 23% compression, while partitioning of 3 and 40 kDa dextran decreased significantly (p<0.01) between free-swelling conditions and 8% compression. Since diffusivity and partitioning can influence pericellular concentrations of bioactive solutes, these observations support a role for perturbations to solute transport in mediating the cartilage biological response to compression.     

The drift approximation solves the Poisson, Nernst-Planck, and continuum equations in the limit of large external voltages

Nearly linear current-voltage curves are frequently found in biological ion channels. Using the drift limit of the substantially non-linear Poisson-Nernst-Planck equations, we explain such behavior of diffusion-controlled charge transport systems. Starting from Gauss' law, drift, and continuity equations we derive a simple analytical current-voltage relation, which accounts for this deviation from linearity. As shown previously, the drift limit of the Nernst-Planck equation applies if the total electric current is dominated by the electric field, and integral contributions from concentration gradients are small. The simple analytical form of the drift current-voltage relations makes it an ideal tool to analyze experiment current-voltage curves. We also solved the complete Poisson-Nernst-Planck equations numerically, and determined current-voltage curves over a wide range of voltages, concentrations, and Debye lengths. The simulation fully supports the analytical estimate that the current-voltage curves of simple charge transport systems are dominated by the drift mechanism. Even those relations containing the most extensive approximations remained qualitatively within the correct order of magnitude. Received: 24 September 1998 / Revised version: 22 January 1999 / Accepted: 22 January 1999     

Atomistic modeling of water diffusion in hydrolytic biomaterials

One of the most promising applications of hydrolytically degrading biomaterials is their use as drug release carriers. These uses, however, require that the degradation and diffusion of drug are reliably predicted, which is complex to achieve through present experimental methods. Atomistic modeling can help in the knowledge-based design of degrading biomaterials with tuned drug delivery properties, giving insights on the small molecules diffusivity at intermediate states of the degradation process. We present here an atomistic-based approach to investigate the diffusion of water (through which hydrolytic degradation occurs) in degrading bulk models of poly(lactic acid) or PLA. We determine the water diffusion coefficient for different swelling states of the polymeric matrix (from almost dry to pure water) and for different degrees of degradation. We show that water diffusivity is highly influenced by the swelling degree, while little or not influenced by the degradation state. This approach, giving water diffusivity for different states of the matrix, can be combined with diffusion-reaction analytical methods in order to predict the degradation path on longer time scales. Furthermore, atomistic approach can be used to investigate diffusion of other relevant small molecules, eventually leading to the a priori knowledge of degradable biomaterials transport properties, helping the design of the drug delivery systems.     

Spatial configuration of charge and hydrophobicity tune particle transport through mucus

Mucus is a selectively permeable hydrogel that protects wet epithelia from pathogen invasion and poses a barrier to drug delivery. Determining the parameters of a particle that promote or prevent passage through mucus is critical, as it will enable predictions about the mucosal passage of pathogens and inform the design of therapeutics. The effect of particle net charge and size on mucosal transport has been characterized using simple model particles; however, predictions of mucosal passage remain challenging. Here, we utilize rationally designed peptides to examine the integrated contributions of charge, hydrophobicity, and spatial configuration on mucosal transport. We find that net charge does not entirely predict transport. Specifically, for cationic peptides, the inclusion of hydrophobic residues and the position of charged and hydrophobic residues within the peptide impact mucosal transport. We have developed a simple model of mucosal transport that predicts how previously unexplored amino acid sequences achieve slow versus fast passage through mucus. This model may be used as a basis to predict transport behavior of natural peptide-based particles, such as antimicrobial peptides or viruses, and assist in the engineering of synthetic sequences with desired transport properties.     

Vesicle adhesion reveals novel universal relationships for biophysical characterization

Adhesion plays an integral role in diverse biological functions ranging from cellular transport to tissue development. Estimation of adhesion strength, therefore, becomes important to gain biophysical insight into these phenomena. In this study, we use curvature elasticity to present non-intuitive, yet remarkably simple, universal relationships that capture vesicle–substrate interactions. These relationships not only provide efficient strategies to tease out adhesion energy of biological molecules but can also be used to characterize the physical properties of elastic biomimetic nanoparticles. We validate the modeling predictions with experimental data from two previous studies.