Structural dynamics of tight junctions modulate the properties of the epithelial barrier

RESEARCH ARTICLE Structural dynamics of tight junctions modulate the properties of the epithelial barrier Aapo TervonenID*, Teemu O. Ihalainen, Soile Nymark, Jari Hyttinen Faculty of Medicine and Health Technology and BioMediTech Institute, Tampere University, Tampere, Finland *[email protected] Abstract Tight junctions are dynamic structures that are crucial in establishing the diffusion and electrical barrier of epithelial monolayers. Dysfunctions in the tight junctions can impede this barrier function and lead to many pathological conditions. Unfortunately, detailed understanding of the non-specific permeation pathway through the tight junctions, the so-called leak pathway, is lacking. We created computational models of the leak pathway to describe the two main barrier measures, molecular permeability and transepithelial electric resistance while using common structural dynamics. Our results showed that the proposed alternatives for the leak pathway, the bicellular strand opening dynamics and the tricellular pores, contribute together with distinct degrees, depending on the epithelium. The models can also capture changes in the tight junction barrier caused by changes in tight junction protein composition. In addition, we observed that the molecular permeability was markedly more sensitive to changes in the tight junction structure and strand dynamics compared with transepithelial electric resistance. The results highlight that our model creates a good methodological framework to integrate knowledge on the tight junction structure as well as to provide insights and tools to advance tight junction research. Introduction Epithelial cell monolayers cover body surfaces and line different organs. These tissues separate the underlying organs from their surroundings by creating tight barriers, and cell-cell junctions play a crucial role in this process. The most significant components for the barrier function are the tight junctions (TJs). These dynamic structures bring the membranes of adjacent cells into close contact, and thus seal the paracellular space between them. Due to their important role in the epithelial function, it is not surprising that there are several diseases, such as inflammatory bowel disease and celiac disease, which are linked to dysfunctions in TJ proteins or in the TJ complexes themselves [1,2]. In these pathological conditions, the epithelium usually becomes leaky [3], and thus rendering it unfit for its task. In the present work, we PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 1 / 26 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Tervonen A, Ihalainen TO, Nymark S, Hyttinen J (2019) Structural dynamics of tight junctions modulate the properties of the epithelial barrier. PLoS ONE 14(4): e0214876. https://doi. org/10.1371/journal.pone.0214876 Editor: Michael Koval, Emory University School of Medicine, UNITED STATES Received: December 13, 2018 Accepted: March 21, 2019 Published: April 9, 2019 Copyright: ©2019 Tervonen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the manuscript and its Supporting Information files. Funding: The study was funded by: Rector’s Graduate School of Tampere University of Technology (AT); Academy of Finland (www.aka.fi/ en) projects (grant numbers 252225 (AT, JH), 298638 (AT, JH), 287287 (SN), and 294054 (SN)), Academy of Finland postdoctoral (grant number 267471) (TOI) and research fellow funding (grant number 308315) (TOI); and the Emil Aaltonen Foundation (emilaaltonen.fi/apurahat/in-english/) investigate the dynamic properties of the epithelial barrier by developing a computational model of TJ structure. In epithelia, TJs encircle the cells near the apical side, as shown in Fig 1A, and they are categorized into bicellular and tricellular junctions [4]. Bicellular TJs (bTJs) appear as a network of anastamosing strands on the cell membranes between two cells [5,6] and tricellular TJs (tTJs) form at the intersections of three cells [7] (Fig 1B). Generally, the bTJ strands are considered to be composed of different proteins; however, it has been proposed that lipids might have an important role in TJ formation [8–12]. According to the protein model, the strands comprise transmembrane proteins that bind to the respective proteins in the neighboring cells [13,14]. The main transmembrane proteins in the strands are claudins, of which there are several types, and occludin [13,15]. These proteins are connected to the actomyosin cytoskeleton via scaffolding proteins, such as ZO-1 [13]. Near the tTJs, the bTJ strand network extends vertically and converges near a 10-nm-diameter central tube [4,7,16]. It is not completely understood how these proteins form the strands or how the lipids might fit into this ensemble [11– 13]. However, progress has been made as structural bTJ strand models were recently proposed [14,17] based on the claudin crystal structure [18,19]. TJ tightness varies between epithelial tissues and tasks [20]. These differences arise, for example, from the number of strands [21] and the bTJs’ protein composition, which has a large impact on the ion permeability of the strands [22]. Additionally, TJ barrier is not a static structure, since it is regulated by changes in the TJ protein composition and through the actomyosin cytoskeleton [23,24]. The properties of the epithelial barrier are usually characterized by how ions and small molecules permeate through the epithelium [25]. Transepithelial electrical resistance (TER) is the most straightforward measurement of the ion permeability since it simply measures the instantaneous electrical resistance of the tissue [26]. In low-TER epithelia, the TJs define the total epithelial resistance due to the considerably higher resistance of the transcellular pathway formed by the cell bodies [27–30]. However, the transcellular component becomes more significant as Fig 1. Tight junction structure and model simplification. (A) A schematic figure showing how the tight junctions (TJs) encircle the apical end of the paracellular space between the epithelial cells, and thus form the barrier. (B) Close up of the bTJ strands (top) that form a network dividing the space between the cells into compartments and the tTJ central tube at the intersection of three cells (bottom). (C) A 2D depiction of the TJ strands and the compartment ultrastructure, based on the cutting plane shown in b. This structure is further simplified to form the 2D TJ strand network used in the model. https://doi.org/10.1371/journal.pone.0214876.g001 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 2 / 26 (SN). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. the TER increases. The permeability of noncharged molecules has been approached by studying how small tracer molecules, such as polyethylene glycols (PEGs) [31–36], dextrans [16,37, 38], and mannitol [33,39], traverse the epithelial barrier. Especially different sizes of PEGs have been an invaluable tool when studying how molecular size (<1 kDa) affects the TJ permeation [31–36], since they have been shown to permeate paracellularly [40,41]. Molecules and ions are hypothesized to permeate through the TJs via two routes: pore and leak pathways [31,33,42,43]. Although these pathways were defined based on the permeability of noncharged molecules [31,33], they can be extended to the context of the TER. The pore pathway is a high-throughput pathway for molecules with a radius smaller than 0.4 nm through pores formed by some claudins [31–33]. The ion permeability of these pores depends on the ion-specificity of the claudins forming them [44]. The leak pathway is a nonspecific, low-throughput pathway with an assumed size limit of over 6 nm [20,31,33,45]. The origin of this pathway is debated, the two main candidates being 1) the pores in the tTJ central tubes and 2) transient bTJ strand breaks [16,20,22,33,45–48]. The tTJ pores have been shown to enable macromolecule diffusion: Krug et al. [16] showed that 3-kDa dextran passes through the epithelium via the tTJ pores and suggested that they could form the leak pathway. They further showed that changes in the expression of tricellulin, a TJ protein found especially in the tTJs, affected the permeability of macromolecules, but only minor changes in the permeability of small (<1 kDa) molecules or in TER were seen [16]. The bTJ strands have been shown to remodel constantly at the protein-level [43,49] as well as at the strand-level in transfected fibroblasts by constant strand breaking and sealing events [46,50]. The bTJ strand breaks have also been observed in freeze fracture electron microscope images [16,51–53]. Furthermore, Van Itallie and coworkers recently showed that the connection between ZO-1 and claudins stabilizes the movement of the strands while, interestingly, not affecting the break frequency [50]. In addition, ZO-1 knockdown and double ZO-1/2 knockdown have been demonstrated to increase the leak pathway permeability while only slightly affecting the TER [34,54]. Based on these findings, it has been suggested that structural dynamics in the strands could enable a step-by-step passage for molecules too large to pass through claudin pores. However, the slow dynamics in the strand structure would not be visible in the almost-instantaneous TER measurement [22,33,34,46,48]. Moreover, Liang & Weber [20] suggested that these two pathways are not mutually exclusive. In recent years, experimental research on the TJ structure and function has been abundant and many important advances have been made [14,18,55–58]. However, the small size of the TJs and the molecules passing through them, together with the fast time scales of the events, make TJs and especially their structural dynamics challenging to study experimentally. Computational models complement experimental work and provide an excellent tool to investigate the characteristics of the TJ barrier in more detail. Most of the previous computational models of the TJ barrier [47,59–64] describe a simplified and static TJ structure and do not include any level of structural dynamics. Weber and coworkers have constructed models describing the transient opening behavior of the claudin pores without the strand-level dynamics [65,66]. To the best of our knowledge, the only computational model to include the strand dynamics is a percolation analysis model of the TJ strands as a random resistor network by Washiyama et al. [67]. However, a model that describes the structural TJ dynamics in relation to both the molecular permeability and the TER seems to be lacking. In this work, we developed computational models for both the molecular permeability and the TER with common structural dynamics to investigate the origin of the leak pathway. We fitted the models to experimental data from two strains of MDCK monolayers and Caco-2 monolayer to parametrize the TJ structure. This, in addition to studying the leak pathway, enabled us to investigate how the different properties of this dynamic system affect the Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 3 / 26 molecular permeability and the TER. With our models, we aim to fill the gap in knowledge between the structural and the functional properties of the TJs. Model description Modeling framework The computational models of the dynamic TJ structure for both the molecular permeability and TER use common geometry and dynamic parameters. Both models are divided into the bTJ and the tTJ components. The bTJ geometry is constructed as a two-dimensional structure with a uniformed depth based on the vertical model plane cutting through the TJs in the thin lateral space between the cells as shown in Fig 1B. The real TJ strand network structure is further simplified to an overlapping tile-like ordered network (Figs 1C and 2). Only a section of the strand network is modeled, but the models are averaged for the whole epithelium by long simulation times and by running them multiple times. The main assumptions of the models are as follows: • TJs form the governing barrier against ionic and permeation of noncharged molecules in the epithelium • Leak pathway is formed by both the static tricellular pores and by the bicellular strand dynamics, as suggested by Liang & Weber [20] • tTJ pores are assumed to be similar between epithelia • bTJ strands are impermeable to molecules too large to pass through claudin pores but not to ions • bTJ strands undergo stochastic breaking and resealing events in the scale of seconds to tens of seconds Fig 2. Schematic description of the molecular permeability and TER models. Schematic descriptions of the molecular permeability and the TER models as well as the geometrical parameters. An example of the geometrical idea of the models with three strands and the width of three compartments. (A) The molecular permeability model comprises bTJ compartments (numbered 1–7) lined by the TJ strands and the basal and apical compartments below and above the TJs, respectively. Rate constants k ij describe the rate of permeation from compartment ito j. We assume low concentration in the apical compartment, and thus omit the backflow into the small compartments. To describe the strand breaks, the rate constant values are varied based on given probabilities that depend on length of strand between the compartments. (B) The TER model consists of a similar geometry, but instead of compartments the basic model units are the current loops (numbered 1–10). The outer current loop (number 11) has a voltage source (V s ) to enable the computation of the total resistance. Resistance R ij is the resistance of the strand shared by current loops iand j, except for those with i=j, when the resistor is not shared by other loops. Again, the resistances vary based on given probabilities that depend on the length of strand between the compartments. (C) Illustration of the geometrical parameters that describe the bTJ strands. n strand , strand number; h comp , small compartment height; w comp , small compartment width; w TJ TJ half-width; h strand , height of single bTJ strand; l break , size of the break in the bTJ strand. https://doi.org/10.1371/journal.pone.0214876.g002 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 4 / 26 • bTJ strands have homogeneous properties throughout the network • In the time scale of the model, molecular diffusion rate and fluid resistance inside the compartments have no effect on permeability and TER, respectively. The bTJ molecular permeability model is based on a multi-compartmental approach. Thus, the strand dynamics and the geometry presented as an example structure in Fig 2A are incorporated into rate constants that describe the permeation between the compartments lined by the bTJ strands. The rate constants depend on a stochastic component that describes the strand state as either intact or broken, and whose value changes based on given probabilities. The amount of substance in the basal compartment below the strand network remains constant and the amount of substance in the apical compartment above the strand network is used to calculate the molecular permeability. The model is simulated using a PEG molecule with the mass of 547 Da (calculated radius of 0.51 nm), since it is unable to permeate through the claudin pores and has been used in many experimental permeability studies. The static tTJ pore pathway is combined with the bTJ results afterwards. The bTJ resistance model uses the same geometry and dynamics as the molecular permeability model. However, the system is solved using nodal analysis and Kirchhoff’s circuit laws. An example resistor network system is shown in Fig 2B. Current loops form in the resistor network as depicted, and Kirchhoff’s loop rule is used for each loop, combined into an equation group, and solved. The dynamics and the geometry shown in Fig 2B are incorporated into the resistances between the compartments. In a similar way to the permeability model, the tTJ resistance is calculated separately and summed with the bTJ simulation results. Molecular permeability model The permeabilities of the bTJ and the tTJ components are calculated separately and then combined in the end based on the parallel connection. The bTJ molecular permeability model is constructed using a multi-compartmental approach. The amount of substance in the small bTJ compartments as a function of time is described by an equation of the form dqiðtÞ dt¼X n j6¼iðkjiðtÞqjðtÞ kijðtÞqiðtÞÞ;ð1Þ where q i (t) is the amount of substance in compartment iat time tand k ji (t) is the time-dependent rate constant for permeation from compartment jto i(s –1 ). Because the model is in 2D, the unit of q i is m –1 instead of unity. This is taken into account when the results are calculated with Eq 8. Since we consider the apical compartment to be considerably larger than the small bTJ compartments, we assume that the concentration in it remains very low. Thus, we can ignore the backflow of molecules from the apical compartment into the bTJ compartments, as shown in Fig 2A. The amount of substance in the basal compartment is assumed to remain constant (dq basal (t)/dt= 0). Because we assume no molecular permeation through an intact strand, the rate constants for the permeation between the compartments depends only on the strand break permeability coefficient: kijðtÞ ¼ lbreakrijðtÞ Ai Pbreak;ð2Þ where l break is the size of the break in the strand, as indicated in Fig 2C (m), r ij (t) is a function describing the state of the strand between compartments iand j,A i is the area of compartment Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 5 / 26 i(m 2 ), and P break is the permeability coefficient of the strand break of indefinite length (m s –1 ). In a 3D model, break area and compartment volume would be used instead of the break size and compartment area, respectively [68]. Function r ij (t) can have a value of either 0 or 1, describing intact and broken states, respectively. The value of r ij (t) can change with given probabilities: If the strand is intact, a break will form with the probability p break (m –1 s –1 ), and if the strand is broken, it will seal with the probability p seal (s –1 ). To obtain the break forming probability for a section of strand between two compartments, p break must be multiplied by the length of that section. This means that longer sections of strand have higher value of p break . Based on the time scale of the dynamics, the possible changes in the strand states were chosen to happen every second. The initial state of the strands can be either intact or broken. The probability of them being in either state is calculated with Markov chain after infinite time: pij;intact pij;broken � �¼1 2 1 2 � � 1pbreaklij pbreaklij pseal 1pseal " #1 ;ð3Þ where p ij,intact and p ij,broken are the probabilities of the strand section between compartments i and jbeing in intact or broken states initially, respectively, and l ij is the length of the strand section between those compartments (m). Since the break size is taken into account in Eq 2,P break is calculated relative to the amount of TJs in the entire epithelium, and thus making it dependent on the cell boundary length per area of epithelium: Pbreak ¼�TJD0Hsðrm=wTJ Þ hstrand ;ð4Þ where � TJ is the relative area of the TJs in the epithelium, D 0 is the aqueous diffusion coefficient of the permeating molecule (m 2 s –1 ), H s (r m /w TJ ) is the break slit hindrance factor that depends on the molecular radius r m (m) and on the TJ half-width w TJ (m), and h strand is the bTJ strand height (m) (See Fig 2C for an illustration of the geometrical parameters) [69]. Parameter � TJ is calculated as �TJ ¼2wTJlcb;ð5Þ where l cb is the cell boundary length per area of epithelium (m –1 ). Function H s describes how the break walls affect the diffusion of a molecule of a given size and was derived by Dechadilok & Deen [70] by fitting a polynomial to computational results as HsðlÞ ¼ 1þ9 16 llnðlÞ 1:19358lþ0:4285l30:3192l4þ0:08428l5;ð6Þ where λ=r m /w TJ . With zero initial conditions for the bTJ compartments, there is a so-called lag phase in the beginning of a simulation, especially with systems having more horizontal strands and lower value of p break . During this phase, the increase in the amount of substance in the apical compartment (q apical ) is nonlinear. Since the permeability is calculated from the linear phase in q apical , the simulation is made to enter straight into this phase by setting the initial values of the amount of substance in each of the small bTJ compartments to the equilibrium state during the linear phase. This is done by simulating the permeability model multiple times and for a long time with zero initial conditions to obtain the equilibrium values for each compartment row. Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 6 / 26 The constant amount of substance for the basal compartment is set to qbasal ¼cbasalNAAbasal;ð7Þ where c basal is the basal compartment concentration (M), N A is Avogadro’s constant (6.022 ×10 23 mol –1 ), and A basal is the area of the basal compartment, replacing the volume since the model is in 2D (m 2 ). The system of differential equations described by Eq 1 is solved using Matlab’s (Release 2015b, The MathWorks, Inc., Natick, Massachusetts, United States) ode23 ordinary differential equation solver. This solver uses second and third order Runge-Kutta formulas, and we found that it gives the same results as the more robust fourth and fifth order Runge-Kutta solver (ode45), while being considerably faster. The simulation is run multiple times and the linear phase of the average q apical curve is used to calculate the bTJ permeability coefficient: PbTJ ¼dqapicalðtÞ dt 1 wmodelcbasal ;ð8Þ where w model is the width of the model system (m), which replaces the area in this 2D model. Next, a first degree polynomial is fitted to the linear phase of the average q apical to obtain the slope. Since the relative area of the junctions in the epithelium is considered in Eq 4,P bTJ is already scaled for the bTJs in the whole epithelium. The tTJ central tubes are modeled as static pores, and an equation similar to Eq 4 is used: PtTJ ¼�tTJD0Hpðrm=rtTJÞ htTJ ;ð9Þ where � tTJ is the relative area of the tricellular pores in the epithelium, H p (r m /r tTJ ) is pore hindrance factor, r tTJ is the tricellular pore radius (m), and h tTJ is the tricellular pore height (m) [69]. The relative area of the pores is calculated as �tTJ ¼pr2 tTJrtTJ;ð10Þ where ρ tTJ is the density of the tricellular junctions in an epithelium (m –2 ). The equation for H p was also derived by Dechadilok & Deen [70] by fitting a polynomial to computational results as HpðlÞ ¼ 1þ9 8llnðlÞ 1:56034lþ0:528155l2þ1:91521l32:81903l4 þ0:270788l5þ1:10115l60:435933l7 ;ð11Þ where λ=r m /r tTJ . This equation is more accurate than the much-used Renkin equation when λis close to unity [70]. The total epithelial TJ permeability is finally calculated based on the parallel connection between the two pathways as PTJ ¼PbTJ þPtTJ:ð12Þ The required properties of the permeating molecule for this model are the molecular radius and the aqueous diffusion coefficient. Since we use a PEG oligomer with a mass of 547 Da, an equation relating the mass of a PEG oligomer to its size is used [71]: rm¼0:29M0:454 m;ð13Þ where r m is in Å(0.1 nm) and M m is the molecular mass (Da). The aqueous diffusion Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 7 / 26 coefficient is calculated with an empirical relationship derived by Avdeef [61]: D0¼9:9�109M0:453 m:ð14Þ The default simulation time for the bTJ model is two hours and the stochastic behavior is further averaged by running the simulations 512 times. We found that the results were not affected by further averaging. The simulations were run using the Finnish IT Center for Science’s (CSC) Taito supercluster using parallel computing (nodes with two 12-core Intel Haswell E5-2690v3 processors running at 2.6 GHz and 128 GB of DRR4 memory operating at 2133 MHz). A Matlab implementation of the permeability model is given in S1 File. TER model In the TER model, the bTJ and tTJ components are again calculated separately and connected in parallel in the end. The bTJ resistance model is constructed as a network of dynamic resistors (Fig 2B). Since we are interested in the resistance, the strand capacitance is ignored. For each current loop i(Fig 2B), the equation is of the form X n j RijðtÞIiX n i6¼j RijðtÞIj¼ Vs;for the outer current loop 0;otherwise (;ð15Þ where R ij (t) is the time-dependent resistance of the section of strand that is shared by current loops iand j(O), I i is the current in loop i(A), and V s is the voltage applied by the external source in the outer loop (V). The strand dynamics are incorporated into the resistances R ij (t), making them analogous to the rate constants in the bTJ permeability model. Because ions can also pass through the intact strands, R ij (t) depends on both the intact strand and break resistances: RijðtÞ ¼ ðlij lbreakÞrijðtÞ Rstrand þrijðtÞ Rbreak � �1 ;ð16Þ where l ij ,l break , and r ij (t) have been described in the bTJ permeability model, R strand is the intact strand resistance per strand length (Om), and R break is the resistance of a break (O). The break resistance is calculated with the equation Rbreak ¼remhstrand Abreak ;ð17Þ where ρ em is the resistivity of the extracellular medium (Om) and A break is the area of the break in the strand (m 2 ), calculated as 2w TJ l break . Although the TER measurement is basically instantaneous, the bTJ resistance model is simulated for a long time to average the results. The current flowing in the outer loop I outer (A) is used to calculate the bTJ resistance at each time point with Ohm’s law: RbTJðtÞ ¼ Vs IouterðtÞ wmodel lcb ;ð18Þ where the factor w model /l cb scales the results for the whole epithelium. To solve the bTJ model, the linear system defined by Eq 15 is transformed to matrix form and solved using Matlab. Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 8 / 26 The pores in the tTJ tubes are modeled as a static and their resistance is calculated as RtTJ ¼remhtTJ prtTJ2rtTJ :ð19Þ For each simulation time point of the bTJ resistance model, the total TER is calculated based on the parallel connection as TERðtÞ ¼ 1 RbTJðtÞþ1 RtTJ � �1 :ð20Þ Finally, to obtain the average TER for the simulation, the time average is taken from the results. The simulation time is 10 6 seconds and the simulations were run using the CSC’s Taito supercluster with serial computing. A Matlab implementation of the TER model is given in S2 File. Parameter values Here we describe the default values of the model parameters. The TJ structure in our model is described by bTJ compartment dimensions, strand number (n strand ), strand height (h strand ), TJ half-width (w TJ ), tricellular pore radius (r tTJ ), and tricellular pore height (h tTJ ). The TJ dynamics are described by break forming and sealing probabilities (p break and p seal , respectively), and break size (l break ). Although there is a lot a variety in the TJ strand morphology [5,72–75], we used one strand morphology since the main focus is the break dynamics. The chosen bTJ compartment width (w comp ) and height (h comp ) were both 100 nm. These values are in the range of the bTJ compartment sizes found in the freeze-fracture replicas [5,72–75] as well as by Kaufmann et al. using super-resolution microscopy [76]. The horizontal number of the compartments in the simulated systems was set to 50 and the heights of the apical and basal compartments in the molecular permeability model were both set to 200 nm. Based on the strand numbers in MDCK monolayers (3–5 strands) [52,53,74,77], Caco-2 monolayers (4–5 strands) [78], and retinal pigment epithelium (4 strands) [39], the default strand number was set to n strand = 4. The value of h strand = 6 nm was based on the electron microscopy of TJ freeze-fracture replicas and the TJ strand architecture model by Suzuki et al. [14]. TJ half-width was chosen as w TJ = 4 nm, estimated based on the architecture model by Suzuki et al. [14] and transmission electron microscope images [54,79,80]. The dimensions of the tricellular pores, r tTJ = 5 nm and h tTJ = 1 μm, were taken from the measured values from freeze-fracture replicas [7,16]. The dynamic parameters of the strand dynamics were more uncertain due to the lack of experimental data. The strand breaks were assumed to remain open on average around 30 seconds based on the time scale of the dynamics in the transfected fibroblasts [46,50]. This led to the break sealing probability of p seal = 0.033 s –1 . The break size was approximated based on the figures and videos by Sasaki et al. [46] and by Van Itallie et al. [50], leading to a value of l break = 20 nm. This value was also used to quantify breaks by Rosenthal and coworkers [52,53]. The break forming probability (p break ) is fitted in the Results section based on the literature data. Due to the time scale of the dynamics and computational limitations, we restricted the possible state changes in the strands to occur every second. The basal compartment concentration and the voltage of the external source used to measure the resistance are scaling parameters and do not affect the results. The chosen values were c basal = 1 mM and V s = 1 V, respectively. Also, the resistive properties of the breaks and the strands are needed. The resistivity of the extracellular medium required for the breaks was ρ em = 0.537 Om [16]. The value of the strand resistance (R strand ) depends on the epithelium, and is fitted in the Results section. Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 9 / 26 time for 5-strand MDCK II and 2-strand MDCK C7 were close to each other, although having a large difference in the actual permeability coefficients. The same biphasic behavior can be seen in the lag times when the barrier became tighter. The lag times grew slowly for MDCK II as n strand was increased. However, with the higher strand numbers for MDCK II and for all the results for MDCK C7, the increase in n strand led to considerably larger changes in the lag times. Comparison with steady-state models To test if the results produced by the dynamic bTJ models presented here could be reached with simpler methods, we created steady-state (SS) bTJ models that assumed a static system with an average number of breaks per strand for both barrier properties. In the SS bTJ permeability model, the compartment rows were reduced into a single large compartment between the strands, since the compartments in the same row could be assumed to be in equilibrium. The SS bTJ resistance model similarly assumed to only contain horizontal strands, and thus simplifying the model to a series connection of identical strands. The number of static open breaks for both SS models was defined from Eq 3. For comparison, we ran the simulations for the varying strand number for both MDCK II and C7 presented in the previous section, and the results of the comparison are shown in Fig 6. It can be clearly seen that the SS models were not able to produce comparable results for bTJ permeability nor for bTJ resistance. The permeabilities predicted by the SS model were well above those produced by our dynamic model (Fig 6A). Moreover, the SS permeabilities showed very little change overall when the strand number was increased from 2 to 6. As for the bTJ resistance, the values produced by the SS model were approximately one and two orders of magnitude lower, respectively, than those from our dynamic model for MDCK II and C7 (Fig 6B). Parameter sensitivity analysis Finally, we performed a sensitivity analysis on certain model parameters by individually altering their values ±25%. The chosen parameters for both models were break forming and sealing probabilities (p break and p seal , respectively), break size (l break ), cell boundary length per area (l cb ), and tTJ pore density (ρ tTJ ). Strand resistance (R strand ) was additionally included for the Fig 6. Comparison between the dynamic and steady-state models. Comparison between the bTJ results of our dynamic (dyn) model (squares) and a simple steady-state (SS) model (circles) for (A) permeability and (B) resistance. The simulations were run both for MDCK II (red and blue) and C7 (orange and cyan). https://doi.org/10.1371/journal.pone.0214876.g006 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 16 / 26 TER model. Parameters l cb and ρ tTJ both depend on the cell size, and thus are not independent from each other. However, by changing them individually we could observe the relative roles of these parameters. We ran the analysis for both the average MDCK II and the MDCK C7 using the same default values of l cb (0.282 μm –1 ) and ρ tTJ (0.049 μm –2 ) as with the strand number simulations. The results comparing the sensitivity simulations with the standard simulations are shown in Fig 7. The permeability of MDCK II was very sensitive to the changes in the strand dynamics, since alterations in the break probabilities led to large changes in the permeability. The variance of these parameters had a significantly smaller effect on the MDCK II TER. While the alterations in l break affected the MDCK II permeability, they had no effect on TER. Alterations in the values of l cb and ρ tTJ had similar levels of influence on the MDCK II permeability. The MDCK II TER was unchanged by the variance of ρ tTJ . However, it was affected more by the variance of l cb than the permeability. Finally, the changes in TER were equal to the alterations in R strand for MDCK II, indicating direct proportionality. The results were extremely different for MDCK C7. Due to the lower level of strand dynamics, the alterations in the parameters describing the breaks (p break ,p seal , and l break ) had no effect on either permeability or TER. This was also the case with l cb for permeability. On the other hand, the results indicate direct dependence of permeability on ρ tTJ for MDCK C7. The impacts of both l cb and ρ tTJ were similar for TER, but smaller than the parameter value variations. Finally, the influence of R strand for MDCK C7 was smaller than for MDCK II. Fig 7. Parameter sensitivity analysis. Results of the parameter sensitivity analysis. We varied the values of the chosen parameters by ±25% and both the permeability and TER simulation results were compared with the normal system. The analysis was conducted for average MDCK II permeability (A) and TER (C) as well as MDCK C7 permeability (B) and TER (D). p break , break forming probability; p seal , break sealing probability; l break , break size; l cb , strand length per area; ρ tTJ , tricellular TJ pore density; R strand , strand resistance. https://doi.org/10.1371/journal.pone.0214876.g007 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 17 / 26 Discussion Tight junctions (TJs) are an indispensable part of the epithelia that form the barriers between many of the body’s compartments, and yet not enough is known about their structure or structural dynamics. In this work, we have developed a computational model of the dynamic TJ structure to study the origin and the properties of the leak pathway—the nonspecific permeation pathway through the TJs. This was done by simulating the epithelial molecular permeability of a PEG oligomer and transepithelial electrical resistance (TER) with the same structural strand dynamics for different epithelial monolayers and scenarios. The model combines the current knowledge and theory of the dynamic TJ structure into a computational framework. There are experimental findings that attest to both candidates for the leak pathway: the tricellular junction pores and the bicellular strand dynamics. Krug et al. [16] observed that 3-kDa dextran mainly diffuses through the tTJ pores, and through the bTJs to a lesser extent. While our model did not extend to macromolecule permeation, the limited size of the strand breaks would result in the tTJ pores being the main pathway for the molecules of this size. Krug et al. also calculated the role of the tTJ pores to be minuscule for ion permeation due to their rarity [16]. At the moment, there is no direct evidence of the dynamic bTJ strand breaking and sealing events forming the leak pathway, but it has been theorized [20,22,33,47,48]. Although dynamic strand breaks have been observed in transfected fibroblasts [46,50] and static breaks in freeze-fracture images [16,51–53], no strand breaks were detected by Weber et al. in their bTJ patch clamp measurements [56]. They discussed multiple reasons for this, including that the breaks may not be distinguishable from the patch seal break [56]. It is, however, also possible that the strong electrode seal between the pipette and the junctional membrane might stabilize the strands mechanically and therefore prevent the strand level dynamics. While one of the assumptions in our models was that the leak pathway is formed by both the bTJ strand dynamics and tTJ pores, interestingly, the permeability leak pathway of the MDCK C7 was formed solely by the tTJ pores. Whereas the relative roles of two pathways in permeability varied greatly between our four MDCK II fitting results, they all showed that the tTJ pores by themselves were incapable of producing the measured permeability values. A possible cause for the variation between the MDCK II results is the cell culture times in the experiments. The reported respective culturing periods for the MDCK IIa, IIb, and IId were from 4 to 8 days, from 7 to 10 days, and 10 days [33,34,54]. There was no culture time directly reported for MDCK IIc [83]. This indicates that longer culturing periods might have led to a higher significance of the bTJ pathway and to a higher level of strand dynamics. However, since the amount of the data is limited, this might be a coincidence. Similar to MDCK II, approximately half of the permeability leak pathway was formed by the bTJ dynamics for Caco-2. As for the TER, the MDCK II was dominated by the bTJ pathway, as was also calculated by Krug et al. [16]. On the contrary, the impact of tTJ pores on the Caco-2 and the MDCK C7 was significant, due to the higher strand resistance. Thus, as theorized by Liang & Weber [20], our model suggests that the tTJ pores and the bTJ strand dynamics may both contribute to the leak pathway with varying degrees. Moreover, the significance of these two alternatives was different for permeability and TER. The tTJ pores were the prominent permeation pathway only for epithelia with more stable strands, since the extremely rare breaks did not enable fast step-by-step permeation. The strand dynamics had a lesser role in determining the bTJ resistance, as the strand resistance, and thus their molecular composition was the dominating factor. The tTJ pores became more important only with the higher strand resistances. This two-component leak pathway is further supported by how changes in the expression of occludin and tricellulin, effect the macromolecular permeation. Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 18 / 26 Although it is not completely understood how, the expression of levels of occludin, mainly located in the bTJ strands, have been shown to regulate the leak pathway permeability [45,83, 85,86]. On the other hand, Krug et al. [16,87] have shown that increased expression of tricellulin leads to a decreased permeability of >4-kDa dextrans and vice versa. Although there was diversity in the cell sizes, the main differences between the epithelial barriers rose from the distinct levels of the bTJ strand dynamics and strand resistances. Of the epithelia considered here, Caco-2 was found to have the most dynamic strands. The obtained break forming probabilities for the MDCK II results were quite similar to each other, while MDCK C7 had extremely limited strand dynamics. Surprisingly, while the strands of Caco-2 were the most dynamic, its strand resistance was comparable to that of the MDCK C7. In addition, the large difference in measured TER between MDCK II and C7 was also observed in the obtained strand resistances, which is in line with the current understanding that the TER is mainly defined by the conductive properties of the claudins, especially claudin-2, found in the strands [33,74,88]. The strand resistances of every epithelia were significantly higher than the strand break resistance. However, due to the rarity of the breaks, especially full openings, the strand resistances largely defined the overall TER, as shown by the sensitivity analysis. The MDCK C7 TER measured by Van Itallie et al. [33] was considerably smaller than the originally measured values (460 vs. 5650 Ocm 2 ) [84]. Our simulations show that this difference is explained by the cell size, since the C7 cells of Van Itallie et al. [33] are distinctly smaller than those of Gekle et al. [84], which leads to smaller length of bTJs and number of tTJ per area and thus higher TER. Further, although the claudin-2 dynamics model by Weber et al. [66] used a 3-strand model instead of the 4-strand used here and their description of the leak pathway differed from ours, there are surprising similarities. The calculated steady-state strand resistance defined for their claudin-2-transfected high-resistance MDCK I model equals to approximately 0.32 GOμm, which is close to our claudin-2-containing MDCK II values. Our models showed what kind of changes in the dynamic structure could lead to the observed experimental changes in the TJ barrier properties. Van Itallie et al. [34] found that ZO-1 stabilizes the TJ barrier, and therefore we described the decrease in stability caused by the ZO-1 knockdown by an increase in the strand break forming probability. The permeability results of the double ZO-1/2 knockdown study by Fanning et al. [54] were similarly replicated by changing this parameter. The higher change in the break forming probability in the double knockdown is in line with the observations that the two ZOs have redundant roles [54,89], and thus knocking out both of them should decrease the strand stability even more. The decreased stability caused by the lack of binding between claudin-2 and ZO-1 was recently visualized in fibroblasts by Van Itallie et al. [50]. Interestingly, they found no difference in the number of breaks with or without this binding. However, this result might have been caused by the nonepithelial model system. On the other hand, we did not consider possible changes in the bTJ strand number or morphology due to the knockdowns. Umeda et al. [89] showed that ZO-1 knockout/ZO-2 knockdown completely eliminated the bTJ strands, accompanied by extremely low TER compared with the control. However, we expected that the strand number was not greatly affected by the ZO-1 and double ZO-1/2 knockdowns, since only a minor change in TER was reported [34,54]. In addition, since we also had to increase the strand resistances to fit the TER model to these data, our results indicate that these knockdowns might also affect the strand resistance in a presently unknown manner. The understanding regarding the role of the bTJ strand number in the properties of the epithelial barrier has changed over time. TER was originally found to depend exponentially on bTJ strand number [21]. This was hypothesized to arise from transient pores in the compartmentalized bTJ strand network [21,90]. However, this idea has been refuted since TER is now known to mainly depend on the TJ claudin composition [5,74,88]. Our results agree that the Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 19 / 26 dependence of TER on the strand number is not straightforward and show a complex dependence on strand resistance that is defined by the protein composition, the strand number, as well as the level of structural dynamics. The saturation towards higher strand numbers comes from the increasing relative role of the static tTJ pathway. Moreover, the results of TER as a function of time show the immensely varying behavior of the resistance in the epithelia with different levels of strand dynamics and numbers. To the best of our knowledge, there have been no experimental studies that directly investigate the effect of strand number on molecular permeability. Colegio et al. [75] showed that an increase in strand number caused by the increased claudin-2 and -4 expression had no effect on the permeability of mannitol that diffuses via the leak pathway. However, based on their freeze-fracture images [75], the strand numbers were in the range of the permeability saturation shown in our simulations, and thus mannitol permeability should remain unchanged, indicating agreement with our results. The saturation in our results was caused by the tTJ pores, as the permeability of the bTJ pathway become lower than that of the tTJ pathway. The unaveraged permeability simulation raw data revealed vastly different permeability behavior depending on the strand numbers and levels of breaking dynamics. The observed biphasic behavior in the permeability simulations is most likely a property of the dynamic network system. In the high-permeability side of this behavior, the change in the number of the full opening events in the strand network caused by alterations in the strand number or level of dynamics led to large changes in permeability. However, since the low-permeability end of this behavior depends on the step-by-step diffusion between the compartments, the alterations in the strand number or dynamics have a lesser effect on the permeability. Overall, our results concerning the effect of strand number, the ZO knockdowns, as well as the sensitivity analysis showed that changes in the bTJ structure or dynamics lead to considerably larger changes in the molecular permeability compared with the TER. Thus, measuring only the TER might hide important unseen changes in molecular permeability and in the barrier properties. The TER is a good indicator of epithelial condition and is straightforward to measure, but it contains a lot of uncertainty due to the differences in measurement setup and conditions. Our results strengthen the idea that both the molecular permeability and the TER are needed to properly define the TJ as a barrier [91,92]. Our comparison with the steady-state models showed that they are not able to reproduce the same behavior as our dynamic models. Since there were constant breaks in the steady-state model, the changes in the strand number or the number of breaks had only a minor effect on the permeability and the TER. Nevertheless, our models had their limitations concerning both the chosen parameter values and the geometry. Because of the lack of rigorous experimental data, we were forced to estimate and fit the probabilities of the strand dynamics and build the model partially with assumptions and hypotheses available in the literature. Moreover, the TJ strand morphology is very diverse and heterogeneous, the number of strands varies within an epithelium [39,55,77,78,93], and the strands typically become tighter towards the apical direction [13]. Also, the expression of tricellulin differs between the epithelia, but the effects of its expression level on the TER and the permeability of molecules with similar size to 547-Da PEG were minor [16]. Further, many molecules permeate the epithelia through the cells using active transport processes, which are difficult to model due to their specificity. However, the PEG oligomers are hydrophilic [40], indicating that they mainly diffuse via the TJs. Thus, our model reflects the PEG-based permeability measurements. In addition, our model lacks the claudin-2 pore dynamics that have previously been observed [56,66]. However, we opted to exclude these dynamics, since their effect has not been characterized for noncharged molecules. Finally, although there is evidence that the TJs form the main conduction pathway [27, 28], Gu¨nzel et al. [26] calculated that for many epithelia the transcellular resistance affects the Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 20 / 26 overall TER or is even lower than the paracellular resistance. This indicates that our assumption that TJs define the TER will not work for every epithelium and condition. We demonstrated that our dynamic structure models can reproduce the basic TJ barrier behavior. With the simplified structure and dynamics, the models enable the comparison between the molecular permeability and the TER under the same dynamic context at the level of the TJs. We showed that the TJ strand breaking dynamics can drastically alter both of these barrier properties independently of each other, highlighting the importance of both measures for characterizing the epithelial barrier. Furthermore, our results indicated that the leak pathway may be formed both by the tTJ pores and the bTJ strand dynamics with varying degrees, but differently for the permeability and the TER. Our models create a good methodological framework that can be used to integrate knowledge on TJ structure, parametrize experimental measurements, and produce hypotheses that can be studied experimentally. Refined versions of the models could include a more realistic strand network as well as inhomogeneities in the strands. This would provide tools to study how diseases that affect the TJ structure alter the properties of the epithelial barrier. Supporting information S1 File. Tight junctions permeability model. A Matlab model file of the tight junctions molecular permeability model. (ZIP) S2 File. Tight junctions TER model. A Matlab model file of the tight junctions transepithelial electric resistance model. (ZIP) Acknowledgments We thank Daniel Garcı ´a Leo ´n, Dr. Michelangelo Paci, Julia Johansson, Jussi Koivuma¨ki, and Peter Heath for helpful comments and the Finnish IT Center for Science (CSC) for computational resources. Author Contributions Conceptualization: Aapo Tervonen, Teemu O. Ihalainen, Soile Nymark, Jari Hyttinen. Data curation: Aapo Tervonen. Formal analysis: Aapo Tervonen. Funding acquisition: Aapo Tervonen, Jari Hyttinen. Investigation: Aapo Tervonen. Methodology: Aapo Tervonen. Project administration: Aapo Tervonen, Jari Hyttinen. Resources: Aapo Tervonen. Software: Aapo Tervonen. Supervision: Aapo Tervonen, Teemu O. Ihalainen, Jari Hyttinen. Validation: Aapo Tervonen, Soile Nymark. Visualization: Aapo Tervonen. Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 21 / 26 Writing – original draft: Aapo Tervonen. Writing – review & editing: Aapo Tervonen, Teemu O. Ihalainen, Soile Nymark, Jari Hyttinen. References 1. Shen L, Su L, Turner JR. Mechanisms and functional implications of intestinal barrier defects. Digest Dis. 2009; 27:443–9. https://doi.org/10.1159/000233282 2. Barmeyer C, Schulzke JD, Fromm M. Claudin-related intestinal diseases. Semin Cell Dev Biol. 2015; 42:30–8. https://doi.org/10.1016/j.semcdb.2015.05.006 PMID: 25999319 3. Mullin JM, Agostino N, Rendon-Huerta E, Thornton JJ. Keynote review: Epithelial and endothelial barriers in human disease. Drug Discov Today. 2005; 10:359–408. https://doi.org/10.1016/S1359-6446(05) 03379-9 4. Ikenouchi J, Furuse M, Furuse K, Sasaki H, Tsukita S, Tsukita S. Tricellulin constitutes a novel barrier at tricellular contacts of epithelial cells. J Cell Biol. 2005; 171:939–45. https://doi.org/10.1083/jcb. 200510043 PMID: 16365161 5. Stevenson BR, Anderson JM, Goodenough DA, Mooseker MS. Tight junction structure and ZO-1 content are identical in two strains of Madin-Darby canine kidney cells which differ in transepithelial resistance. J Cell Biol. 1988; 107:2401–8. https://doi.org/10.1083/jcb.107.6.2401 PMID: 3058723 6. Rahner C, Fukuhara M, Peng S, Kojima S, Rizzolo LJ. The apical and basal environments of the retinal pigment epithelium regulate the maturation of tight junctions during development. J Cell Sci. 2004; 117:3307–18. https://doi.org/10.1242/jcs.01181 PMID: 15226402 7. Staehelin LA. Further Observations on the Fine Structure of Freeze-Cleaved Tight Junctions. J Cell Sci. 1973; 13:763–86. PMID: 4203962 8. Hein M, Post A, Galla HJ. Implications of a non-lamellar lipid phase for the tight junction stability. Part I: Influence of basic amino acids, pH and protamine on the bilayer-hexagonal II phase behaviour of PScontaining PE membranes. Chemistry and physics of lipids. 1992; 63(3):213–221. https://doi.org/10. 1016/0009-3084(92)90037-P PMID: 1493615 9. Hein M, Madefessel C, Haag B, Teichmann K, Post A, Galla HJ. Implications of a non-lamellar lipid phase for the tight junction stability: Part II: Reversible modulation of transepithelial resistance in high and low resistance MDCK-cells by basic amino acids, Ca2+, protamine and protons. Chem Phys Lipids. 1992; 63(3):223–233. https://doi.org/10.1016/0009-3084(92)90038-Q PMID: 1337316 10. Grebenka ¨mper K, Galla HJ. Translational diffusion measurements of a fluorescent phospholipid between MDCK-I cells support the lipid model of the tight junctions. Chem Phys Lipids. 1994; 71 (2):133–143. https://doi.org/10.1016/0009-3084(94)90066-3 PMID: 8076400 11. Lingaraju A, Long TM, Wang Y, Austin JR, Turner JR. Conceptual barriers to understanding physical barriers. Semin Cell Dev Biol. 2015; 42:13–21. https://doi.org/10.1016/j.semcdb.2015.04.008 PMID: 26003050 12. Zihni C, Mills C, Matter K, Balda MS. Tight junctions: from simple barriers to multifunctional molecular gates. Nat Rev Mol Cell Bio. 2016; 17:564–80. https://doi.org/10.1038/nrm.2016.80 13. Van Itallie CM, Anderson JM. Architecture of tight junctions and principles of molecular composition. Semin Cell Dev Biol. 2014; 36:157–65. https://doi.org/10.1016/j.semcdb.2014.08.011 PMID: 25171873 14. Suzuki H, Tani K, Tamura A, Tsukita S, Fujiyoshi Y. Model for the Architecture of Claudin-Based Paracellular Ion Channels through Tight Junctions. J Mol Biol. 2015; 427:291–7. https://doi.org/10.1016/j. jmb.2014.10.020 PMID: 25451028 15. Hewitt KJ, Agarwal R, Morin PJ. The claudin gene family: expression in normal and neoplastic tissues. BMC Cancer. 2006; 6:186. https://doi.org/10.1186/1471-2407-6-186 PMID: 16836752 16. Krug SM, Amasheh S, Richter JF, Milatz S, Gu¨nzel D, Westphal JK, et al. Tricellulin forms a barrier to macromolecules in tricellular tight junctions without affecting ion permeability. Mol Biol Cell. 2009; 20:3713–24. https://doi.org/10.1091/mbc.E09-01-0080 PMID: 19535456 17. Irudayanathan FJ, Trasatti JP, Karande P, Nangia S. Molecular Architecture of the Blood Brain Barrier Tight Junction Proteins–A Synergistic Computational and In Vitro Approach. J Phys Chem B. 2015; 120:77–88. https://doi.org/10.1021/acs.jpcb.5b09977 PMID: 26654362 18. Suzuki H, Nishizawa T, Tani K, Yamazaki Y, Tamura A, Ishitani R, et al. Crystal structure of a claudin provides insight into the architecture of tight junctions. Science. 2014; 344:304–7. https://doi.org/10. 1126/science.1248571 PMID: 24744376 19. Saitoh Y, Suzuki H, Tani K, Nishikawa K, Irie K, Ogura Y, et al. Tight junctions. Structural insight into tight junction disassembly by Clostridium perfringens enterotoxin. Science. 2015; 347:775–8. PMID: 25678664 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 22 / 26 20. Liang GH, Weber CR. Molecular aspects of tight junction barrier function. Curr Opin Pharmacol. 2014; 19:84–9. https://doi.org/10.1016/j.coph.2014.07.017 PMID: 25128899 21. Claude P. Morphological Factors Influencing Transepithelial Permeability: a Model for the Resistance of the Zonula Occludens. J Membrane Biol. 1978; 39:219–32. https://doi.org/10.1007/BF01870332 22. Gu¨nzel D, Yu ASL. Claudins and the modulation of tight junction permeability. Physiol Rev. 2013; 93:525–69. https://doi.org/10.1152/physrev.00019.2012 PMID: 23589827 23. Turner J. ‘Putting the squeeze’ on the tight junction: understanding cytoskeletal regulation. Semin Cell Dev Biol. 2000; 11:301–8. https://doi.org/10.1006/scdb.2000.0180 PMID: 10966864 24. Rodgers LS, Fanning AS. Regulation of epithelial permeability by the actin cytoskeleton. Cytoskeleton. 2011; 68:653–60. https://doi.org/10.1002/cm.20547 PMID: 22083950 25. Van Itallie CM, Anderson JM. The molecular physiology of tight junction pores. Physiology. 2004; 19:331–8. https://doi.org/10.1152/physiol.00027.2004 PMID: 15546850 26. Gu¨nzel D, Zakrzewski SS, Schmid T, Pangalos M, Wiedenhoeft J, Blasse C, et al. From TER to transand paracellular resistance: lessons from impedance spectroscopy. Ann NY Acad Sci. 2012; 1257:142–51. https://doi.org/10.1111/j.1749-6632.2012.06540.x PMID: 22671600 27. Gitter AH, Bertog M, Schulzke JD, Fromm M. Measurement of paracellular epithelial conductivity by conductance scanning. Pflug Arch Eur J Phy. 1997; 434:830–40. https://doi.org/10.1007/ s004240050472 28. Zhou Y, Chen CC, Weber AE, Zhou L, Baker LA, Hou J. Potentiometric-scanning ion conductance microscopy for measurement at tight junctions. Tissue Barriers. 2013; 1:e25585. https://doi.org/10. 4161/tisb.25585 PMID: 24533255 29. Benson K, Cramer S, Galla HJ. Impedance-based cell monitoring: barrier properties and beyond. Fluids and Barriers of the CNS. 2013; 10:5. https://doi.org/10.1186/2045-8118-10-5 PMID: 23305242 30. Srinivasan B, Kolli AR, Esch MB, Abaci HE, Shuler ML, Hickman JJ. TEER Measurement Techniques for In Vitro Barrier Model Systems. J Lab Autom. 2015; 20(2):107–126. https://doi.org/10.1177/ 2211068214561025 PMID: 25586998 31. Watson CJ, Rowland M, Warhurst G. Functional modeling of tight junctions in intestinal cell monolayers using polyethylene glycol oligomers. Am J Physiol-Cell Ph. 2001; 281:C388–97. https://doi.org/10. 1152/ajpcell.2001.281.2.C388 32. Watson CJ, Hoare CJ, Garrod DR, Carlson GL, Warhurst G. Interferon-gamma selectively increases epithelial permeability to large molecules by activating different populations of paracellular pores. J Cell Sci. 2005; 118:5221–30. https://doi.org/10.1242/jcs.02630 PMID: 16249235 33. Van Itallie CM, Holmes J, Bridges A, Gookin JL, Coccaro MR, Proctor W, et al. The density of small tight junction pores varies among cell types and is increased by expression of claudin-2. J Cell Sci. 2008; 121:298–305. https://doi.org/10.1242/jcs.021485 PMID: 18198187 34. Van Itallie CM, Fanning AS, Bridges A, Anderson JM. ZO-1 Stabilizes the Tight Junction Solute Barrier through Coupling to the Perijunctional Cytoskeleton. Mol Biol Cell. 2009; 20:3930–40. https://doi.org/ 10.1091/mbc.E09-04-0320 PMID: 19605556 35. Van Itallie CM, Holmes J, Bridges A, Anderson JM. Claudin-2-dependent changes in noncharged solute flux are mediated by the extracellular domains and require attachment to the PDZ-scaffold. Ann NY Acad Sci. 2009; 1165:82–7. https://doi.org/10.1111/j.1749-6632.2009.04052.x PMID: 19538292 36. Linnankoski J, Ma ¨kela ¨J, Palmgren J, Mauriala T, Vedin C, Ungell A, et al. Paracellular Porosity and Pore Size of the Human Intestinal Epithelium in Tissue and Cell Culture Models. J Pharm Sci. 2010; 99:2166–75. https://doi.org/10.1002/jps.21961 PMID: 19827099 37. Amasheh S, Meiri N, Gitter AH, Scho ¨neberg T, Mankertz J, Schulzke JD, et al. Claudin-2 expression induces cation-selective channels in tight junctions of epithelial cells. J Cell Sci. 2002; 115:4969–76. https://doi.org/10.1242/jcs.00165 PMID: 12432083 38. Pitka ¨nen L, Ranta VP, Moilanen H, Urtti A. Permeability of retinal pigment epithelium: effects of permeant molecular weight and lipophilicity. Invest Ophth Vis Sci. 2005; 46:641–6. https://doi.org/10.1167/ iovs.04-1051 39. Rajasekaran SA, Hu J, Gopal J, Gallemore R, Ryazantsev S, Bok D, et al. Na,K-ATPase inhibition alters tight junction structure and permeability in human retinal pigment epithelial cells. Am J Physiol-Cell Ph. 2003; 284:C1497–507. https://doi.org/10.1152/ajpcell.00355.2002 40. Ma TY, Hollander D, Krugliak P, Katz K. PEG 400, a hydrophilic molecular probe for measuring intestinal permeability. Gastroenterology. 1990; 98:39–46. https://doi.org/10.1016/0016-5085(90)91288-H PMID: 2293598 41. He YL, Murby S, Warhurst G, Gifford L, Walker D, Ayrton J, et al. Species differences in size discrimination in the paracellular pathway reflected by oral bioavailability of poly(ethylene glycol) and D-peptides. J Pharm Sci. 1998; 87:626–33. https://doi.org/10.1021/js970120d PMID: 9572915 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 23 / 26 42. Shen L, Weber CR, Raleigh DR, Yu D, Turner JR. Tight junction pore and leak pathways: a dynamic duo. Annu Rev Physiol. 2011; 73:283–309. https://doi.org/10.1146/annurev-physiol-012110-142150 PMID: 20936941 43. Capaldo CT, Nusrat A. Claudin switching: Physiological plasticity of the Tight Junction. Semin Cell Dev Biol. 2015; 42:22–9. https://doi.org/10.1016/j.semcdb.2015.04.003 PMID: 25957515 44. Krug SM, Gu¨nzel D, Conrad MP, Lee IFM, Amasheh S, Fromm M, et al. Charge-selective claudin channels. Ann N Y Acad Sci. 2012; 1257(1):20–28. https://doi.org/10.1111/j.1749-6632.2012.06555.x PMID: 22671585 45. Buschmann MM, Shen L, Rajapakse H, Raleigh DR, Wang Y, Wang Y, et al. Occludin OCEL-domain interactions are required for maintenance and regulation of the tight junction barrier to macromolecular flux. Mol Biol Cell. 2013; 24:3056–68. https://doi.org/10.1091/mbc.E12-09-0688 PMID: 23924897 46. Sasaki H, Matsui C, Furuse K, Mimori-Kiyosue Y, Furuse M, Tsukita S. Dynamic behavior of paired claudin strands within apposing plasma membranes. P Natl Acad Sci USA. 2003; 100:3971–6. https:// doi.org/10.1073/pnas.0630649100 47. Guo P, Weinstein AM, Weinbaum S. A dual-pathway ultrastructural model for the tight junction of rat proximal tubule epithelium. Am J Physiol-Renal. 2003; 285:F241–57. https://doi.org/10.1152/ajprenal. 00331.2002 48. Anderson JM, Van Itallie CM, Fanning AS. Setting up a selective barrier at the apical junction complex. Curr Opin Cell Biol. 2004; 16:140–5. https://doi.org/10.1016/j.ceb.2004.01.005 PMID: 15196556 49. Shen L, Weber CR, Turner JR. The tight junction protein complex undergoes rapid and continuous molecular remodeling at steady state. J Cell Biol. 2008; 181:683–95. https://doi.org/10.1083/jcb. 200711165 PMID: 18474622 50. Van Itallie CM, Tietgens AJ, Anderson JM. Visualizing the dynamic coupling of claudin strands to the actin cytoskeleton through ZO-1. Mol Biol Cell. 2017; 28:524–34. https://doi.org/10.1091/mbc.E16-100698 PMID: 27974639 51. Zeissig S, Burgel N, Gunzel D, Richter J, Mankertz J, Wahnschaffe U, et al. Changes in expression and distribution of claudin 2, 5 and 8 lead to discontinuous tight junctions and barrier dysfunction in active Crohn’s disease. Gut. 2007; 56:61–72. https://doi.org/10.1136/gut.2006.094375 PMID: 16822808 52. Rosenthal R, Milatz S, Krug SM, Oelrich B, Schulzke JD, Amasheh S, et al. Claudin-2, a component of the tight junction, forms a paracellular water channel. J Cell Sci. 2010; 123:1913–21. https://doi.org/10. 1242/jcs.060665 PMID: 20460438 53. Rosenthal R, Gu¨nzel D, Krug SM, Schulzke JD, Fromm M, Yu ASL. Claudin-2-mediated cation and water transport share a common pore. Acta Physiol. 2017; 219:521–36. https://doi.org/10.1111/apha. 12742 54. Fanning AS, Van Itallie CM, Anderson JM. Zonula occludens-1 and -2 regulate apical cell structure and the zonula adherens cytoskeleton in polarized epithelia. Mol Biol Cell. 2012; 23:577–90. https://doi.org/ 10.1091/mbc.E11-09-0791 PMID: 22190737 55. Gong Y, Renigunta V, Zhou Y, Sunq A, Wang J, Yang J, et al. Biochemical and biophysical analyses of tight junction permeability made of claudin-16 and claudin-19 dimerization. Mol Biol Cell. 2015; 26:4333–46. https://doi.org/10.1091/mbc.E15-06-0422 PMID: 26446843 56. Weber CR, Liang GH, Wang Y, Das S, Shen L, Yu ASL, et al. Claudin-2-dependent paracellular channels are dynamically gated. Elife. 2015; 4:e09906. https://doi.org/10.7554/eLife.09906 PMID: 26568313 57. Conrad MP, Piontek J, Gu¨nzel D, Fromm M, Krug SM. Molecular basis of claudin-17 anion selectivity. Cell Mol Life Sci. 2015; 73:185–200. https://doi.org/10.1007/s00018-015-1987-y PMID: 26194246 58. Fredriksson K, Itallie CMV, Aponte A, Gucek M, Tietgens AJ, Anderson JM. Proteomic analysis of proteins surrounding occludin and claudin-4 reveals their proximity to signaling and trafficking networks. PLoS ONE. 2015; 10:e0117074. https://doi.org/10.1371/journal.pone.0117074 PMID: 25789658 59. Ho NFH, Raub TJ, Burton PS, Barsuhn CL, Adson A, Audus KL, et al. Quantitative Approaches to Delineate Passive Transport Mechanisms in Cell Culture Monolayers. In: Amidon GL, Lee PI, Topp EM, editors. Transport Processes in Pharmaceutical Systems. Marcel Decker, Inc; 2000. p. 219– 316. 60. Saitoh R, Sugano K, Takata N, Tachibana T, Higashida A, Nabuchi Y, et al. Correction of permeability with pore radius of tight junctions in Caco-2 monolayers improves the prediction of the dose fraction of hydrophilic drugs absorbed by humans. Pharm Res. 2004; 21:749–55. https://doi.org/10.1023/B: PHAM.0000026423.48583.e2 PMID: 15180329 61. Avdeef A. Leakiness and size exclusion of paracellular channels in cultured epithelial cell monolayersinterlaboratory comparison. Pharm Res. 2010; 27:480–9. PMID: 20069445 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 24 / 26 62. Diecke FP, Cacace VI, Montalbetti N, Ma L, Kuang K, Iserovich P, et al. Comparative permeabilities of the paracellular and transcellular pathways of corneal endothelial layers. J Membrane Biol. 2011; 242:41–51. https://doi.org/10.1007/s00232-011-9375-5 63. Yu ASL, Cheng MH, Angelow S, Gu¨nzel D, Kanzawa SA, Schneeberger EE, et al. Molecular basis for cation selectivity in claudin-2-based paracellular pores: identification of an electrostatic interaction site. J Gen Physiol. 2009; 133:111–27. PMID: 19114638 64. Tervonen A, Vainio I, Nymark S, Hyttinen J. Prediction of Passive Drug Permeability Across the BloodRetinal Barrier. Pharm Res. 2014; 31:2297–311. https://doi.org/10.1007/s11095-014-1325-3 PMID: 24623477 65. Weber CR. Dynamic properties of the tight junction barrier. Ann NY Acad Sci. 2012; 1257:77–84. https://doi.org/10.1111/j.1749-6632.2012.06528.x PMID: 22671592 66. Weber CR, Turner JR. Dynamic modeling of the tight junction pore pathway. Ann NY Acad Sci. 2017; 1397:209–18. https://doi.org/10.1111/nyas.13374 PMID: 28605031 67. Washiyama M, Koizumi N, Fujii M, Kondoh M, Yagi K, Watanabe Y. Percolation analysis in electrical conductivity of madin-darby canine kidney and caco-2 cells by permeation-enhancing agents. Biol Pharm Bull. 2013; 36:384–9. https://doi.org/10.1248/bpb.b12-00786 PMID: 23449326 68. Usansky HH, Sinko PJ. Estimating Human Drug Oral Absorption Kinetics from Caco-2 Permeability Using an Absorption-Disposition Model: Model Development and Evaluation and Derivation of Analytical Solutions for k a and F a. J Pharmacol Exp Ther. 2005; 314(1):391–399. https://doi.org/10.1124/ jpet.104.076182 PMID: 15833900 69. Adson A, Raub TJ, Burton PS, Barsuhn CL, Hilgers AR, Ho NFH, et al. Quantitative approaches to delineate paracellular diffusion in cultured epithelial cell monolayers. J Pharm Sci. 1994; 83(11):1529– 1536. https://doi.org/10.1002/jps.2600831103 PMID: 7891269 70. Dechadilok P, Deen WM. Hindrance Factors for Diffusion and Convection in Pores. Ind Eng Chem Res. 2006; 45:6953–9. https://doi.org/10.1021/ie051387n 71. Ruddy SB, Hadzija BW. Iontophoretic permeability of polyethylene glycols through hairless rat skin: application of hydrodynamic theory for hindered transport through liquid-filled pores. Drug design and discovery. 1992; 8:207–24. PMID: 1525303 72. Balda MS, Whitney JA, Flores C, Gonza ´lez S, Cereijido M, Matter K. Functional dissociation of paracellular permeability and transepithelial electrical resistance and disruption of the apical-basolateral intramembrane diffusion barrier by expression of a mutant tight junction membrane protein. J Cell Biol. 1996; 134:1031–49. https://doi.org/10.1083/jcb.134.4.1031 PMID: 8769425 73. Jou TS, Schneeberger EE, Nelson WJ. Structural and functional regulation of tight junctions by RhoA and Rac1 small GTPases. J Cell Biol. 1998; 142:101–15. https://doi.org/10.1083/jcb.142.1.101 PMID: 9660866 74. Furuse M, Furuse K, Sasaki H, Tsukita S. Conversion of zonulae occludentes from tight to leaky strand type by introducing claudin-2 into Madin-Darby canine kidney I cells. J Cell Biol. 2001; 153:263–72. https://doi.org/10.1083/jcb.153.2.263 PMID: 11309408 75. Colegio OR, Van Itallie CM, Rahner C, Anderson JM. Claudin extracellular domains determine paracellular charge selectivity and resistance but not tight junction fibril architecture. Am J Physiol-Cell Ph. 2003; 284:C1346–54. https://doi.org/10.1152/ajpcell.00547.2002 76. Kaufmann R, Piontek J, Gru¨ll F, Kirchgessner M, Rossa J, Wolburg H, et al. Visualization and quantitative analysis of reconstituted tight junctions using localization microscopy. PLoS ONE. 2012; 7:e31128. https://doi.org/10.1371/journal.pone.0031128 PMID: 22319608 77. Sonoda N, Furuse M, Sasaki H, Yonemura S, Katahira J, Horiguchi Y, et al. Clostridium perfringens Enterotoxin Fragment Removes Specific Claudins from Tight Junction Strands: Evidence for Direct Involvement of Claudins in Tight Junction Barrier. J Cell Biol. 1999; 147:195–204. PMID: 10508866 78. Capaldo CT, Farkas AE, Hilgarth RS, Krug SM, Wolf MF, Benedik JK, et al. Proinflammatory cytokineinduced tight junction remodeling through dynamic self-assembly of claudins. Mol Biol Cell. 2014; 25:2710–9. https://doi.org/10.1091/mbc.E14-02-0773 PMID: 25031428 79. Tamura A, Tsukita S. Paracellular barrier and channel functions of TJ claudins in organizing biological systems: Advances in the field of barriology revealed in knockout mice. Semin Cell Dev Biol. 2014; 36:177–85. https://doi.org/10.1016/j.semcdb.2014.09.019 PMID: 25305579 80. Van Itallie CM, Tietgens AJ, Krystofiak E, Kachar B, Anderson JM. A complex of ZO-1 and the BAR Domain Protein TOCA-1 Regulates Actin Assembly at the Tight Junction. Mol Biol Cell. 2015; 26:2769– 87. https://doi.org/10.1091/mbc.E15-04-0232 PMID: 26063734 81. Schindelin J, Arganda-Carreras I, Frise E, Kaynig V, Longair M, Pietzsch T, et al. Fiji: an open-source platform for biological-image analysis. Nat Methods. 2012; 9:676–82. https://doi.org/10.1038/nmeth. 2019 PMID: 22743772 Structural dynamics in tight junctions PLOS ONE | https://doi.org/10.1371/journal.pone.0214876 April 9, 2019 25 / 26