Physics and CompSci Research
Computational model of virus diffusion in human airway surface liquid with applications to gene therapy Vivek A. Pisharody & Kanan A. Shah ABSTRACT It is well-established that many diseases, such as influenza and the common cold, are transmitted by the respiratory route. However, little is known about the mechanics of virion movement within the airways. Recently, computational fluid dynamics models have shed light on particle deposition in the airways, yet the post-deposition motion of particles through airway surface fluid (ASL) is largely unknown. In this paper, we present a stochastic model of antibody diffusion in human airway surface liquid. Ciliary clearance, antibody-induced trapping mechanisms, and virus neutralization are considered. Additionally, this model was applied to adeno-associated virus 6 (AAV6), a strong candidate vector for respiratory gene therapy. Simulations were conducted in the MATLAB computing environment. While this model is intended for future use in analyzing candidate vectors for respiratory gene therapy, it is also broadly applicable to understanding the motion of other viruses in the ASL.
Introduction Purpose and Motivation Many illnesses, from the common cold to influenza, are transmitted through the respiratory tract. As we breathe, viruses are inhaled and settle on the surface of the airways [23]. However, the airway epithelium is protected by a layer of airway surface liquid (ASL) that traps inhaled particles [7]. This ASL is continuously cleared toward the esophagus by the tiny, whip-like cilia of the epithelial cells [2]. Once at the esophagus, the ASL and its trapped particles are swallowed and subsequently destroyed by the acidic contents of the stomach [19]. Furthermore, antibodies (Ab) present in the ASL bind to the virions, slowing them through interactions with mucin fibers while also reducing their ability to bind to and infect cells [23]. Clearly, the ASL layer serves as a crucial defense against many respiratory viruses. Only those virions that diffuse across the ASL prior to swallowing and prior to Ab neutralization can infect cells [9]. Unfortunately, laboratory experiments on virus characteristics in the human lung are difficult to design and conduct. As of yet, there is little understanding of how virions are able to reach epithelium in spite of ASL defenses [6]. Improved knowledge of virus movement and neutralization mechanics may lead to improved treatments for viral diseases, as well as improved use of viruses for alternative applications. This serious lack of understanding is important from both immunological and medical perspectives. In this paper, we present a computational model of virion diffusion across the ASL that takes into account mucociliary clearance mechanisms, antibody-induced trapping in mucus, and virion neutralization intended for use in analyzing possible gene therapy vectors. This model is also broadly applicable to simulate the diffusion of viruses across the ASL. We also present an application of
this model to Adeno-Associated Virus 6 (AAV6), a strong candidate for gene therapy applications [11]. Airway Physiology The ASL, the first line of defense against inhaled pathogens, consists of a lubricating periciliary layer (PCL) directly on top of the epithelium and an outer mucus layer [3]. The mucus layer consists primarily of water (98%), salts (≈ 1%), and glycosylated mucin proteins (≈ 1%) [22]. The PCL fluid characteristics are poorly understood, but is thought to maintain its lower viscosity through osmosis across the epithelium [5]. The low viscosity of PCL enables the whip-like cilia of respiratory epithelia to “beat” at frequencies of up to approximately 200 Hz. Each mature epithelial cell may have up to two-hundred cilia [22]. The tips of these cilia penetrate the mucus layer, propelling the mucus and PCL layers, and anything within them, including proteins, virions, and bacteria, toward the esophagus at a rate of tens of microns per second [20]. The structure of the airways resembles a series of branching, tubular segments, the uppermost of which is the trachea. This large airway branches into two smaller primary bronchi, which later bifurcate into multiple bronchioles [24]. Each level of branches is assigned a generation number in order to group structures that are at a similar depth in the lungs; the trachea is G0, the primary bronchi is G1, and so on [1]. The total number of airway segments in the g-th generation is 2g. With increasing generation number, the diameter and length, and therefore surface area, of each tubular airway decreases, but the number of tubular segments per generation increases. Mucus thickness and velocity decrease as well [16]. Where two deeper generations are joined, the ridge between them is referred to as the carina, or carinal ridge[8]. As ASL is cleared from a deeper generation to a higher generation, approximately 85% of the lower generation’s Volume 3 | 2013-2014 | 63
Physics and CompSci Research ASL volume passes around the carina, while the remaining 15% move over the ridge. Due to reduced ciliary clearance efficiency at the carinal ridge, this 15% of ASL is delayed by as much as 10-15 minutes at the bifurcation [12].
Figure 1. Electron microscope images of airway epithelia. (a) SEM image of ciliated and non-ciliated epithelial cells from the trachea.
Figure 2: In the respiratory system, whiplike cilia beat in a wave-like patter, moving the ASL up towards the esophagus, where it is swallowed and destroyed [20]. (b) Time-sequence SEM images of a cross section of rabbit tracheal culture. The motion of the cilia can be inferred from the sequential images. The PCL and mucus layers of the ASL are also visible. Gene therapy and suitability of viruses Viruses can enter the body through numerous openings, including the nose and mouth. Once inside, viruses attempt to attach to host cells with varying degrees of specificity and implant their own genetic information into the host cell’s DNA, thereby hijacking the cell’s reproductive machinery to create more viruses which subsequently attack other cells[4]. Recently, researchers have attempted to repurpose viruses’ ability to insert strands of DNA into existing cellular DNA in gene therapy to repair or replace defective genetic information [17]. Virus-delivered gene therapy is currently being investigated for a variety of re64 | 2013-2014 | Volume 3
spiratory diseases, including cystic fibrosis (CF), chronic obstructive pulmonary disease (COPD), a-antitrypsin deficiency in the lungs, and inherited chronic obstructive pulmonary disease (COPD). However, viruses must overcome a variety of immune response mechanisms prior to infecting cells. The ASL itself, as well as the many antibodies in it, serves as a strong defense against viruses. Viruses have only a limited time window in which to diffuse across the ASL before they are carried to the esophagus and swallowed[14]. Distributed throughout the ASL, antibodies have the ability to bind to antigens on the virus surface, preventing these antigen binding sites from attaching to a host cell [17]. The paratype, the binding tip of the Ab, attaches to the virus; the size of the antibody also blocks nearby antigen binding sites. In the respiratory tract, the most prevalent antibody is broadly-neutralizing Immunoglobulin-G (IgG) [18]. In general, the binding rates between antibodies and a given virus are not necessarily the same as the binding rates of antibodies to other viruses, even within the same airway generation. Thus, certain antibodies are more suitable for gene therapy applications than others [10]. In addition to antibodies, the respiratory tract defends against virions by phagocytosis by macrophages. This process, however, is much slower than antibody interactions, and, for the time scales and regions of the lung simulated, macrophagy is not significant. For example, cystic fibrosis is a serious genetic disease resulting from a mutation in the cystic fibrosis transmembrane conductance regulator (CFTR) gene [21]. The CFTR gene affects trans-membrane transport in many organs; in the respiratory system, it affects mucociliary transport mechanisms and leads to thick, viscous mucus. Ineffective elimination coupled with continued production leads to a buildup of ASL within the lungs and airways. Traditionally, much CF research has focused on loosening thick ASL and preventing bacterial infections within the airways. In the case of cystic fibrosis, gene therapy may be able to replace existing, incorrectly coded CFTR genes with correct genetic information. Thus, virus-delivered gene therapy has the potential to play a major role in treating CF. Understanding the motion of viruses within the ASL will likely elucidate this emerging therapeutic option [15]. Model Unfortunately, experiments on virion motion in living organisms are difficult to design and conduct. Thus, computational models serve as necessary tools for understanding ASL characteristics and role in immunology. In addition, computational models can aid in planning lab experiments. Running simulations allows researchers to analyze ideas quickly and relatively inexpensively before conducting experiments. Many existing models largely focus on airflow and
Physics and CompSci Research mucus transport but do not consider particle diffusion through the respiratory tract itself. For example, a recent computational model simulates particle clearance in cystic fibrosis lungs [14]. However, this model, unlike our model does not simulate individual particle clearance or penetration to the epithelium. Instead, the model focuses on mass particle clearance. Existing models do not simulate particle diffusion, a critical mechanism for gene therapy. Our work introduces a new model that incorporates particle diffusion, penetration, and clearance, and is broadly applicable to understanding virus motion. We anticipate that this model will be primarily used to better understand gene therapy vectors. To illustrate the capabilities of this model, we present a specific application to Adeno-Associated Virus 6 (AAV6), a strong candidate for respiratory gene therapy, in order to illustrate the modeling capabilities of this method. AAV6 is considered a strong candidate vector for gene therapy. Despite its ability to infect both dividing and nondividing cells, AAV6 does not trigger replication and cell lysis except in the presence of so-called “helper viruses.” Serotype 6 is considered especially well suited to respiratory applications [10]. The model described herein can be used to analyze virus neutralization patterns as well.
Figure 3. Diagram of model
Method Our model begins where these earlier models leave off; we start with the deposition of virions in the ASL. Previous models have used computational fluid dynamics (CFD) to simulate airflow properties and particle deposition concentrations in early airway generations [24]. According to these models, as particles are breathed in, those with diameters on the order of 0.1 μm or smaller are also trapped in the highest generations of the airways because their relatively small radii and masses make Brownian effects significant. For a spherical particle, the StokesEinstein equation gives the diffusivity coefficient D of a particle undergoing Brownian motion:
where kB is the Boltzmann constant, T is the temperature, R is the hydrodynamic radius of the particle, and η is the dynamic viscosity of the fluid through which the particle moves [15]. A larger diffusivity coefficient increases the distance that a particle can diffuse in a given time interval. Particles with small radii are thus more likely to drift into contact with the airway walls. Particles with larger radii have lower diffusivities, making Brownian effects negligible. However, the relatively large inertia of large-radii particles prevents them from moving smoothly with the airstream at the bifurcations at the ends of generations. These models predict that particles with diameters on the order of 1.0 μm or larger collide with and become trapped in nasal hairs or mucus in the uppermost parts of the airways, in part because [13]. Particles with diameters between 1.0 μm and 0.1 μm, such as the AAV6 virion (diameter 0.025 μm), travel deeper into the lung before colliding with airway walls [15]. The size of the AAV6 virion makes efficient delivery for gene therapy applications possible. Models of lung deposition patterns indicate that virion deposition is nearly uniform by area in upper airway generations, with elevated deposition rates near the insides of bifurcations between generations; because the area of these bifurcations is small, we assume that virions are initially deposited uniformly by area on the surface of the ASL [15]. As mucus is a hydrogel, its structure consists of a matrix of fibers inundated with an interstitial fluid composed primarily of water. Due to their small size relative to the average pore size of this mesh, antibodies and virions can diffuse across the matrix mesh through interstitial fluid. We approximate the viscosity of this interstitial fluid with the viscosity of water. Though the left generations of the lung, and in particular, the left bronchus, are usually shorter that the right generations, a symmetrical lung model is commonly used because a significant reduction of complexity can be achieved with little change in qualitative results [13]. Table 1 lists the lung characteristics used in this model. As phagocytosis and thermal degradation are only significant on much longer time scales, they are not incorporated into this model. As very little is known about PCL fluid, computational models often assume it function similarly to the mucus layer. The respiratory tract branches into a series of generations; with increasing generation number, the mucus layer is known to decrease in depth. As the relationship between PCL layer depth and generation number is poorly understood; it is assumed to remain constant in this and other models. In this model, each virus i is assigned a pair of (xi, zi) Volume 3 | 2013-2014 | 65
Physics and CompSci Research coordinates. The x-coordinate represents the particle’s distance from the esophagus, where x = 0; the z-coordinate represents the particle’s distance from the epithelium, where z = 0. The diffusion of viruses is simulated by Brownian motion. In each time step Δt, the position of each virus is updated according to the following equations, Table 1: Characteristics of the symmetric lung used in this model.
where the Wx and Wz are standard normal random variables, vg is the speed of the mucus relative to the epithelium in the g-th generation in which the particle is currently located and tends to decrease as the generation number increases. D’ is the diffusivity of the virus adjusted for a two-dimensional simulation. As ASL is cleared from a deeper generation to a higher generation, approximately 85% of the lower generation’s ASL volume passes around the carina, while the remaining 15% move over the ridge. Due to reduced ciliary clearance efficiency at the carinal ridge, this 15% of ASL is delayed by as much as 10-15 minutes at the bifurcation [12]. As virions diffuse through the ASL, they may encounter antibodies (Ab). The binding and unbinding of Ab can be written in the form of the following reaction:
Here, the notation Vn,N denotes a virion with N total binding sites, of which n are currently unavailable for binding. The reaction kinetics are:
When large numbers of virion-antibody interactions are simulated, this reaction can be analyzed probabilistically. Assuming that Ab binding is a Markovian process – that is, Ab binding rates for a given virion at time t +Δt are independent of the state of the particle at times before t – the probability that a given virion will undergo a binding or unbinding event are:
The probability of multiple events occurring during Δt are o(Δt); for small (< 1) Δt , multiple binding can be neglected. These binding rates will depend upon the particular virus and Ab simulated. Viruses in actual airways will diffuse until they are either cleared through the esophagus or penetrate the ASL and reach the epithelium. To produce realistic values for clearance and penetration rates, the method described above is iterated until all simulated viruses initially deposited in the airways have been cleared through the esophagus or penetrated the epithelium. In this paper, we refer to this time as the biologically significant time interval, TBS.
An Application to Gene Therapy
where ko f f is the kinetic rate constant of this forward reaction (gaining an Ab) and kon is the rate constant of the reverse reaction (losing an Ab). When an antibody binds to a virion, the n is updated. In doing so, steric hindrance must be taken into account. In the case of AAV6, each virus has approximately 60 trimeric binding antigens, each of which contains of 3 binding sites. However, each bound antibody physically obstructs an additional 5 binding sites. Although the average AAV6 virion has 180 binding sites, only a maximum of 30 antibodies can actually bind to a AAV6. Of the virions that crossed to the epithelium in our simulation, an average of 6 antibodies were bound to each virion. Thus, each bound antibody reduces n by 6. 66 | 2013-2014 | Volume 3
Parameters To demonstrate the capabilities and utility of this model, we implemented this simulation for the AAV6 virus, a strong candidate for respiratory gene therapy. The use of AAV6 in respiratory gene therapy has been previously explored in clinical trials. Parameters of the model, including characteristics of AAV6, are listed in Table 2. The diffusivity of AAV6 in respiratory mucus was calculated using the radius of AAV6 and the Stokes-Einstein relationship. This model was implemented in MATLAB. Due to computing constraints, this model, as implemented, could not be run to TBS on sets of greater than 15,000 viruses for times greater than 1.5 hours. By 1.5 hours, all viruses were cleared through the esophagus or penetrated through the epithelium, and all of the mucus present at the beginning of the simulation had traveled to the esophagus.
Physics and CompSci Research
Figure 5. Plot of x positions of selected virions originally deposited in different generations over time.
Table 2. Model parameters used in AAV6 simulation. Virus Motion Figures 4 and 5 provide a sample of the motion all particles in the simulation undergo. As a virus particle undergoes Brownian motion, its z position, or distance from the epithelium, fluctuates between the epithelium and the air-mucus interface. As an example, Figure 4 shows the z positions of selected particles that start in different generations. As expected, each particle moves in a seemingly patternless manner regardless of generation. When averaged, however, particle z positions decrease over time as particles diffuse toward the epithelium. Virus particles are also moved toward the esophagus by mucocilliary clearance mechanisms, which lead to a steadily decreasing x position. Figure 5 shows the x positions of the same particles plotted in Figure 4. However, because the particle also undergoes Brownian motion in the x direction, particle positions in Figure 5 do not form a smooth curve. In Figures 4 and 5, the particles that began in the first and fourth generation penetrated the epithelium, at which point their z positions became zero and their x positions became constant. The figures show that when a particle penetrates to the epithelium (z = 0), the corresponding x position of the particle remains constant from that time step forward, as the particle is no longer being pushed upward by mucociliary clearance mechanisms. In addition, when the particle is cleared to the esophagus (x = 0), the particleâ&#x20AC;&#x2122;s z position stops changing and the path ends, as the particle is no longer a part of the simulation.
At the end of TBS, 1.12% of all virus particles penetrated the ASL to reach the epithelium, while 98.88% of the particles had been cleared to the esophagus, as shown in Figure 6b. Effect of Antibody Concentration Though Ab binding reduces virion diffusivity because of mucus affinity, it does not completely stop virion motion; most AAV6 virions reaching the epithelium have bound antibodies. However, Ab do reduce the average infectivity of viruses reaching the epithelium. The average effective infectivity, defined as the percent of Ab sites occupied, was 50%. Figure 6c shows the distribution of antibodies bound per virion at the end of the simulation. Almost all virions have between 15 and 19 antibodies bound to them by the time they have reached the epithelium.
A
B
Figure 4. Plot of z positions of selected virions originally deposited in different generations over time
C
Figure 6. Summary of the output of model as applied to AAV6. (A) Penetration versus the concentration of antibodies. (B) Percentage of viruses cleared and penetrated after 1.5 hours. (C) Percent of viruses that reach the epithelium by number of bound antibodies. Volume 3 | 2013-2014 | 67
Physics and CompSci Research Though it is conceptually clear that increased IgG concentration reduces virus penetration and virus infectivity, and vice versa, the impact of individual variation in IgG concentrations is not known qualitatively. To evaluate the model’s sensitivity to IgG concentration, simulations with antibody concentrations ranging from 0.1 μg/ml to 100 μg/ml, as shown in 6a. The percent of virions reaching the epithelium decreases rapidly as the concentration of antibodies increases. In addition, to show the role of antibodies in the respiratory tract, the model was simulated without Ab interactions influencing virion diffusion. Without antibodies, 92% of the virions reached the epithelium. With a concentration of 1 ug/ml, this number had significantly decreased to 45%, indicating that antibodies play a significant role in respiratory defense.
Discussion and Conclusion Conclusion Antibodies were found to play a significant role in defending the respiratory tract against virions. When the diffusion of AAV-6 was simulated with no antibodies present in the system, 92% of all virions had crossed the ASL and reached the epithelium. In addition, the diffusion of AAV6 was simulated for IgG concentrations ranging from 0.1 μg/ml to 100 μg/ml to show the effect of antibody concentrations on virion diffusion. As antibody concentration increases, the penetration proportion of AAV-6 decreases exponentially. This confirms that neutralizing antibodies can be a major barrier to aerosol gene therapy. So far, we have applied our model to study the AAV6 virus, a strong candidate for gene therapy for cystic fibrosis. An average person has an AAV6- specific IgA concentration of 15 μg/ml. With this concentration, about 1.12% of all deposited AAV6 particles reach the cell epithelium and have an 50% effective infectivity. 97% of all particles that had penetrated the epithelium had between 15 and 19 antibodies attached to them. This small window for the number of antibodies attached suggests that the antibodies on viruses distribution has reached its equilibrium point. Simulating these interactions for a longer time, thus, will not change the number of antibodies bound to the penetrated viruses. In addition, particles deposited in the fourth generation have a higher penetration rate, but those in the second generation have a higher effective infectivity. However, the difference in penetration rate between the second and fourth generations is greater than the difference in bound antibodies between the second and fourth generations, indicating virions initially deposited in the fourth generation are more effective in providing gene therapy. Experiments can be run to validate the point that AAV-6 virions initially deposited in the fourth generation of the respiratory tract will result in the most effective gene therapy, as this results in the highest penetration.
68 | 2013-2014 | Volume 3
Discussion The new model introduced here is a valuable tool in analyzing the mechanics of virus motion and antibody interactions. The broad applicability of our model to different viruses and antibodies, as well as its extensibility to new scenarios, enables its use in a variety of scenarios to answers diverse questions. This model will be useful in analyzing virus diffusion and interactions between antibodies and virions in the airway surface liquid of the respiratory tract. Our model will need to be verified by in vivo or clinical data, but our predictions are well-aligned with observations made by others in terms of poor viral efficacy. Most models focus on mucus transport but do not consider diffusion through the respiratory tract. Our model goes beyond the latest computational model for virion diffusion through the ASL by simulating not only particle clearance due to mucocilliary mechanisms but also virion penetration to the epithelium. In addition, unlike many current models, we account for antibody interactions with virions in the mucus. These critical aspects of virion interactions with the airway surface liquid gives our model greater predictive power in gene therapy and drug delivery applications than existing models. By understanding these interactions better, we can gain insight into the role mucus plays in the transmissions of viruses. Mucus is often overlooked by scientists despite its importance to health because there is usually little curiosity or interest in mucus. An accurate computational model of virion diffusion through mucus is critical for evaluating and developing mucosal-administered viral gene therapy. This model can also be used to analyze drug delivery by removing antibody interactions from the file. These models are a more convenient and cost-effective way to evaluate the barriers that obstruct the transport of existing drugs, predict the effectiveness of new drugs, and design drugs with desirable properties in mucus.
Future Work Future additions to model While this model attempts to include all factors that have a significant impact on virus diffusion through ASL, certain assumptions were made to reduce computational complexity. Although the majority of the antibodies in the ASL are IgG antibodies, other antibodies are present in smaller amounts but were not modeled due to computing constraints. Each additional type of Ab has different rate constants and different binding and unbinding kinetics. Though simulating these additional types of Ab would generally increase the complexity of the computations, the effects of IgA, one of these additional types of Ab, can be approximated relatively simply. Each IgA protein is superficially similar in structure to two IgG bound back-to-back and its effects are similar to two IgG molecules. Thus, the effect of IgA can be estimated by increasing the concentration of IgG input to the program. IgA does differ from
Physics and CompSci Research IgG in that IgA can enable to formation of multi-virus complexes by binding to different viruses on each side. We expect that this will reduce virion diffusion through mucus. In the context of the Stokes-Einstein equation, the effective hydrodynamic radius of these multi-virus complexes will be larger than the radii of individual virions, making the diffusivities of the multi-virion complexes smaller than the diffusivities of individual virions. Though qualitatively simple, multi-virus complexes are quantitatively very difficult to model. For non-spherical particles, the Stokes-Einstein equation is only an approximation; for large multi-virus complexes, the spatial conformation of the complex will affect the diffusivity. However, multivirus complexes likely require viruses to be closely spaced, and for virions with bound IgA to collide with other virions at sufficiently high energies. Furthermore recent work by our mentor suggests that IgA may have much lower affinity to mucin fibers than IgG, which we expected will increase rates of virus penetration of the epithelium. Based on these factors, we do not believe that IgA will have a significant impact on this particular simulation. However, in the future, we plan to implement IgA separately in our model, and provide a method of tracking other Ab types, as they may be significant in other scenarios with different parameters. Kon and Koff values for binding and unbinding kinetics are dependent upon the antibody and viruses being simulated. For AAV-6 with IgG antibodies, the system of antibodies attached to viruses reached its equilibrium point, and thus all viruses that penetrated the epithelium had between 15 and 19 antibodies attached to them. However, with a decreasing the Kon value, the system will not yet have reached the equilibrium point, thus resulting in a smaller number of antibodies bound per virus. In addition, viruses with a lower number of antibody binding sites would result in a fewer number of antibodies present when virions reach the epithelium. Thus, this model can be used to test the penetration rates of viruses with lower Kon values or fewer binding sites. Future Applications Though we applied our model to a particular virion, our model has broad applicability to other scenarios. For example, our model could be used to compare the suitability of candidate viruses for gene therapy. Variations in number of binding sites, radius, binding kinetics, etc. may influence the effective infectivity of a given viral vector. More generally, our model can be used to investigate the motion of pathogenic respiratory viruses in normal human lungs and also asthma lungs, as patients with asthma have lower mucus velocities since all ASL parameters can easily be changed in our model. Additionally, our model can be used to supplement analyses of hypotheses on the unresolved question of PCL composition.
Acknowledgements We would like to acknowledge Mr. Gotwals for his help and support through the Research in Computational Science Program at NCSSM, and Dr. Sam Lai and Dr. Alex Chen at UNC-Chapel Hill for their mentoring and great advice.
References
[1] J. E. Agnew. “Bronchiolar aerosol deposition and clearance”. In: European Respiratory Journal 9.6 ( June 1996), pp. 1118–1122. ISSN: 00000000. DOI: 10.1183/09031936.96.09061118. URL: http://erj.ersjournals. com/content/9/6/1118. [2] Alex Braiman and Zvi Priel. “Efficient mucociliary transport relies on efficient regulation of ciliary beating.” In: Respiratory physiology & neurobiology 163.1-3 (Nov. 2008), pp. 202–7. ISSN: 1569-9048. DOI: 10.1016/j. resp.2008.05.010. URL: http://www.ncbi.nlm.nih.gov/ pubmed/18586580. [3] Brian Button et al. “A periciliary brush promotes the lung health by separating the mucus layer from airway epithelia.” In: Science (New York, N.Y.) 337.6097 (Aug. 2012), pp. 937–41. ISSN: 1095-9203. DOI: 10.1126/ science.1223012. URL: http://www.ncbi.nlm.nih.gov/ pubmed/22923574. [4] Tom Chou and Maria R D’Orsogna. “Multistage adsorption of diffusing macromolecules and viruses.” In: The Journal of chemical physics 127.10 (Sept. 2007), p. 105101. ISSN: 0021-9606. DOI: 10.1063/1.2764053. URL: http://www.ncbi.nlm.nih.gov/pubmed/17867780. [5] RV Craster and OK Matar. “Surfactant transport on mucus films”. In: Journal of Fluid Mechanics 425 (2000), pp. 235–258. URL: http://journals.cambridge.org/abstract\_S0022112000002317. [6] Yen Cu and W M Saltzman. “Mathematical modeling of molecular diffusion through mucus”. In: 61.2 (2010), pp. 101–114. DOI: 10.1016/j.addr.2008.09.006.Mathematical. [7] Nico Derichs et al. “Hyperviscous airway periciliary and mucous liquid layers in cystic fibrosis measured by confocal fluorescence photobleaching.” In: FASEB journal : official publication of the Federation of American Societies for Experimental Biology 25.7 ( July 2011), pp. 2325–32. ISSN: 1530-6860. DOI: 10.1096/fj.10-179549. URL: http:// www.pubmedcentral.nih.gov/articlerender.fcgi?artid=311 4535\&tool=pmcentrez\&rendertype=abstract. [8] WMFoster, E Langenback, and E H Bergofsky. “Measurement of tracheal and bronchial mucus velocities in man: relation to lung clearance.” In: Journal of applied physiology: respiratory, environmental and exercise physiology 48.6 ( June 1980), pp. 965–71. ISSN: 0161-7567. URL: http://www.ncbi.nlm.nih.gov/pubmed/7380708. [9] Anthony R Geonnotti and David F Katz. “Dynamics of HIV neutralization by a microbicide formulation layer: biophysical fundamentals and transport theory.” In: Biophysical journal 91.6 (Sept. 2006), pp. 2121–30. ISSN: Volume 3 | 2013-2014 | 69
Physics and CompSci Research 0006-3495. DOI: 10.1529/biophysj.106.086322. URL: http://www.pubmedcentral.nih.gov/articlerender.fcgi?arti d=1557566\&tool=pmcentrez\&rendertype=abstract. [10] Brittney L Gurda et al. “Capsid Antibodies to Different Adeno-Associated Virus Serotypes Bind Common Regions.” In: Journal of virology June ( June 2013). ISSN: 1098-5514. DOI: 10.1128/JVI.00622-13. URL: http:// www.ncbi.nlm.nih.gov/pubmed/23760240. [11] Christine L Halbert, James M Allen, and A Dusty Miller. “Adeno-Associated Virus Type 6 ( AAV6 ) Vectors Mediate Efficient Transduction of Airway Epithelial Cells in Mouse Lungs Compared to That of AAV2 Vectors”. In: 75.14 (2001), pp. 6615–6624. DOI: 10.1128/ JVI.75.14.6615. [12] Werner Hofmann and Robert Sturm. “Stochastic model of particle clearance in human bronchial airways”. In: Journal of aerosol medicine 17.1 (2004), pp. 73–89. URL: http://online.liebertpub.com/doi/pdf/10. 1089/089426804322994488. [13] SM H¨ogberg. “Nanoparticle transport and deposition in the large conducting airways using CFD”. In: (2006). URL: http://epubl.ltu.se/1402-1617/2006/193/LTUEX-06193-SE.pdfhttps://pure.ltu.se/ws/files/30999496/ LTU-EX-06193-SE.pdf. [14] Julian Kirch et al. “Mucociliary clearance of micro- and nanoparticles is independent of size, shape and charge–an ex vivo and in silico approach.” In: Journal of controlled release : official journal of the Controlled Release Society 159.1 (Apr. 2012), pp. 128–34. ISSN: 1873-4995. DOI: 10.1016/j.jconrel.2011.12.015. URL: http://www. ncbi.nlm.nih.gov/pubmed/22226774. [15] Clement Kleinstreuer, Zhe Zhang, and Zheng Li. “Modeling airflow and particle transport/deposition in pulmonary airways.” In: Respiratory physiology & neurobiology 163.1-3 (Nov. 2008), pp. 128–38. ISSN: 1569-9048. DOI: 10.1016/j.resp.2008.07.002. URL: http://www. ncbi.nlm.nih.gov/pubmed/18674643. [16] Bonnie E Lai et al. “Transport theory for HIV diffusion through in vivo distributions of topical microbicide gels.” In: Biophysical journal 97.9 (Nov. 2009), pp. 2379– 87. ISSN: 1542-0086. DOI: 10.1016/j.bpj.2009.08.010. URL: http://www.pubmedcentral.nih.gov/articlerender. fcgi?artid=2770622\&tool=pmcentrez\&rendertype=abst ract. [17] Gary K Lee et al. “PEG conjugation moderately protects adeno-associated viral vectors against antibody neutralization.” In: Biotechnology and bioengineering 92.1 (Oct. 2005), pp. 24–34. ISSN: 0006-3592. DOI: 10.1002/bit.20562. URL: http://www.ncbi.nlm.nih.gov/ pubmed/15937953. [18] Youdong Mao et al. “Subunit organization of the membrane-bound HIV-1 envelope glycoprotein trimer.” In: Nature structural & molecular biology 19.9 (Sept. 2012), pp. 893–9. ISSN: 1545-9985. DOI: 10.1038/nsmb. 2351. URL: http://www.pubmedcentral.nih.gov/articlerender.fc gi?artid=3443289\&tool=pmcentrez\&rendertype=abstra ct. 70 | 2013-2014 | Volume 3
[19] H Matsui et al. “Coordinated clearance of periciliary liquid and mucus from airway surfaces.” In: The Journal of clinical investigation 102.6 (Sept. 1998), pp. 1125–31. ISSN: 0021-9738. DOI: 10.1172/JCI2687. URL: http : / / www . pubmedcentral . nih . gov / articlerender . fcgi ? artid = 509095 \ &tool = pmcentrez \&rendertype=abstract. [20] Sorin M Mitran. “Metachronal wave formation in a model of pulmonary cilia.” In: Computers & structures 85.11-14 ( Jan. 2007), pp. 763–774. ISSN: 0045-7949. DOI: 10.1016/j.compstruc.2007.01.015. URL: http:// www.pubmedcentral.nih.gov/articlerender.fcgi?artid=263 0197\&tool=pmcentrez\&rendertype=abstract. [21] A Multicenter. “Repeated Adeno-Associated Virus Serotype 2 Aerosol-Mediated Cystic Fibrosis Transmembrane Regulator Gene Transfer to the Lungs of Patients With Cystic Fibrosis *”. In: (2004), pp. 509–521. [22] D J Smith, E a Gaffney, and J R Blake. “Modelling mucociliary clearance.” In: Respiratory physiology & neurobiology 163.1-3 (Nov. 2008), pp. 178–88. ISSN: 15699048. DOI: 10.1016/j.resp.2008.03.006. URL: http:// www.ncbi.nlm.nih.gov/pubmed/18439882. [23] B O Stuart. “Deposition and clearance of inhaled particles.” In: Environmental health perspectives 55 (Apr. 1984), pp. 369–90. ISSN: 0091-6765. URL: http://www. pubmedcentral.nih.gov/articlerender.fcgi?artid=1568355\ &tool=pmcentrez\&rendertype=abstract. [24] R Sturm, W Hofmann, and G Scheuch. “Particle clearance in human bronchial airways: comparison of stochastic model predictions with experimental data”. In: Annals of Occupational . . . 46.Suppl. 1 ( Jan. 2002), pp. 329–333. ISSN: 0003-4878. DOI: 10.1093/annhyg/46. suppl\_1.329. URL: http://annhyg.oxfordjournals.org/ content/46/suppl\_1/329.full.pdf+htmlhttp://annhyg. oxfordjournals.org/content/46/suppl\_1/329.shorthttp:// annhyg.oxfordjournals.org/cgi/doi/10.1093/annhyg/46. suppl\_1.329.