scholarly journals Aboave-Weaire’s law in epithelia results from an angle constraint in contiguous polygonal lattices

2019 ◽  
Author(s):  
Roman Vetter ◽  
Marco Kokic ◽  
Harold Gómez ◽  
Leonie Hodel ◽  
Bruno Gjeta ◽  
...  
Keyword(s):  
Surface Energy ◽  
Contact Surface ◽  
Driving Forces ◽  
Apical Cell ◽  
Topological Constraints ◽  
Lateral Contact ◽  
Energy Minimisation ◽  
Apical Side ◽  
A Cell ◽  
Apical Area

ABSTRACTIt has long been noted that the cell arrangements in epithelia, regardless of their origin, exhibit some striking regularities: first, the average number of cell neighbours at the apical side is (close to) six. Second, the average apical cell area is linearly related to the number of neighbours, such that cells with larger apical area have on average more neighbours, a relation termed Lewis’ law. Third, Aboav-Weaire’s (AW) law relates the number of neighbours that a cell has to that of its direct neighbours. While the first rule can be explained with topological constraints in contiguous polygonal lattices, and the second rule (Lewis’ law) with the minimisation of the lateral contact surface energy, the driving forces behind the AW law have remained elusive. We now show that also the AW law emerges to minimise the lateral contact surface energy in polygonal lattices by driving cells to the most regular polygonal shape, but while Lewis’ law regulates the side lengths, the AW law controls the angles. We conclude that global apical epithelial organization is the result of energy minimisation under topological constraints.

scholarly journals Minimisation of surface energy drives apical epithelial organisation and gives rise to Lewis’ law

2019 ◽  
Author(s):  
Marco Kokic ◽  
Antonella Iannini ◽  
Gema Villa-Fombuena ◽  
Fernando Casares ◽  
Dagmar Iber
Keyword(s):  
Cell Division ◽  
Cell Growth ◽  
Surface Energy ◽  
Driving Forces ◽  
Apical Cell ◽  
Cell Area ◽  
Cell Surfaces ◽  
Apical Area

ABSTRACTThe packing of cells in epithelia exhibits striking regularities, regardless of the organism and organ. One of these regularities is expressed in Lewis’ law, which states that the average apical cell area is linearly related to the number of neighbours, such that cells with larger apical area have on average more neighbours. The driving forces behind the almost 100-year old Lewis’ law have remained elusive. We now provide evidence that the observed apical epithelial packing minimizes surface energy at the intercellular apical adhesion belt. Lewis’ law emerges because the apical cell surfaces then assume the most regular polygonal shapes within a contiguous lattice, thus minimising the average perimeter per cell, and thereby surface energy. We predict that the linear Lewis’ law generalizes to a quadratic law if the variability in apical areas is increased beyond what is normally found in epithelia. We confirm this prediction experimentally by generating heterogeneity in cell growth in Drosophila epithelia. Our discovery provides a link between epithelial organisation, cell division and growth and has implications for the general understanding of epithelial dynamics.

scholarly journals Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Riccardo Sacco ◽  
Fabio Manganini ◽  
Joseph W. Jerome
Keyword(s):  
Driving Forces ◽  
The Novel ◽  
Thermodynamical Equilibrium ◽  
Finite Element Scheme ◽  
Equilibrium Conditions ◽  
Solution Map ◽  
Ion Flow ◽  
Stabilized Finite Element ◽  
A Cell ◽  
Biological Channels

AbstractIn this articlewe address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel,we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally,we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in [12]; and 2) the bipolar nanofluidic diode considered in [45].

Effect of changes in extracellular Cl on intracellular Cl activity in frog skin

1988 ◽  
Vol 254 (1) ◽  
pp. F95-F104 ◽  
Author(s):  
K. Drewnowska ◽  
T. U. Biber
Keyword(s):  
Frog Skin ◽  
Rana Pipiens ◽  
Initial Rate ◽  
Apical Cell ◽  
Disulfonic Acid ◽  
Free Solution ◽  
Granular Cells ◽  
Apical Side ◽  
Basolateral Side ◽  
Cl Permeability

Intracellular Cl activity was measured in isolated frog skin (Rana pipiens) with double-barrel microelectrodes. The initial rate of Cl uptake was measured in Cl-depleted cells on reexposure to Cl on apical or basolateral side. In skins with high and low conductance, cell CL activity increased 1.33 and 0.14 mM/s with apical reexposure and 5.03 and 0.30 mM/s with basolateral reexposure, respectively. The initial Cl uptake was reduced on the apical side by 93% with 10(-3) M DIDS (4,4'-diisothiocyanostilbene-2,2ߗ-disulfonic acid) and on the basolateral side by 99% with 10(-3) M SITS (4-acetamido-4'-isothiocyanostilbene-2,2'-disulfonic acid) plus 10(-5) M bumetanide. The initial rate of Cl loss was measured when Cl was removed from the bath: addition of HCO3 to Cl- and HCO3-free solution caused an acceleration of Cl loss in absence but not in presence of DIDS on apical side. In contrast, Cl loss across the basolateral side was not enhanced by HCO3. In conclusion, Na-transporting cells have a substantial Cl permeability on both sides. HCO3-stimulated Cl loss provides evidence for Cl-HCO3 exchange and permits localization of this process in apical cell membranes of granular cells.

Identification of Na+/H+ exchange on the apical side of surface colonocytes using BCECF

1994 ◽  
Vol 267 (1) ◽  
pp. G119-G128 ◽  
Author(s):  
G. G. King ◽  
W. E. Lohrmann ◽  
J. W. Ickes ◽  
G. M. Feldman
Keyword(s):  
Apical Membrane ◽  
Basolateral Membrane ◽  
Apical Cell ◽  
Distal Colon ◽  
Transport Processes ◽  
Acetoxymethyl Ester ◽  
Apical Cell Membrane ◽  
Apical Side ◽  
Free Media ◽  
Phi Regulation

Colonocytes must regulate intracellular pH (pHi) while they transport H+ and HCO3-. To investigate the membrane transport processes involved in pHi regulation, colonocyte pHi was measured with 2,'7'-bis(2-carboxyethyl)-5(6)-carboxyfluorescein (BCECF) in intact segments of rat distal colon mounted on a holder that fits into a standard fluorometer cuvette and allows independent superfusion of mucosal and serosal surfaces. When NCECF-acetoxymethyl ester was in the mucosal solution only, BCECF loaded surface colonocytes with a high degree of selectivity. In HEPES-buffered solutions, basal pHi was 7.31 +/- 0.01 (n = 68), and pHi was dependent on extracellular Na+. Cells acidified in Na(+)-free solution, and pHi rapidly corrected when Na+ was returned. pHi recovered at 0.22 +/- 0.01 pH/min (n = 6) when Na+ was introduced into the mucosal solution and at 0.02 +/- 0.01 pH/min (n = 7) when Na+ was absent from the mucosal solution. The presence or absence of Na+ in the serosal solution did not affect pHi. This indicated that the Na(+)-dependent pHi recovery process is located in the apical cell membrane, but not in the basolateral membrane. Because amiloride (1 mM) inhibited Na(+)-dependent pHi recovery by 75%, Na+/H+ exchange appears to be present in the apical membrane. Because Na(+)-independent pHi recovery was not affected by K(+)-free media, 50 microM SCH-28080, 100 nM bafilomycin A1, or Cl(-)-free media, this transport mechanism does not involve a gastriclike H(+)-K(+)-ATPase, a vacuolar H(+)-ATPase, or a Cl-/base exchanger. In summary, pHi was selectively measured in surface colonocytes by this technique. In these cells, the Na+/H+ exchange activity involved in pHi regulation was detected in the apical membrane, but not in the basolateral membrane.

Improved unroofing protocols for cryo-electron microscopy, atomic force microscopy and freeze-etching electron microscopy and the associated mechanisms

Microscopy ◽  
2020 ◽  
Vol 69 (6) ◽  
pp. 350-359
Author(s):  
Nobuhiro Morone ◽  
Eiji Usukura ◽  
Akihiro Narita ◽  
Jiro Usukura
Keyword(s):  
Electron Microscopy ◽  
Atomic Force Microscopy ◽  
Cell Membrane ◽  
Apical Cell ◽  
Force Microscopy ◽  
Atomic Force ◽  
Cryo Electron Microscopy ◽  
Cytoplasmic Surface ◽  
A Cell ◽  
Freeze Etching

Abstract Unroofing, which is the mechanical shearing of a cell to expose the cytoplasmic surface of the cell membrane, is a unique preparation method that allows membrane cytoskeletons to be observed by cryo-electron microscopy, atomic force microscopy, freeze-etching electron microscopy and other methods. Ultrasound and adhesion have been known to mechanically unroof cells. In this study, unroofing using these two means was denoted sonication unroofing and adhesion unroofing, respectively. We clarified the mechanisms by which cell membranes are removed in these unroofing procedures and established efficient protocols for each based on the mechanisms. In sonication unroofing, fine bubbles generated by sonication adhered electrostatically to apical cell surfaces and then removed the apical (dorsal) cell membrane with the assistance of buoyancy and water flow. The cytoplasmic surface of the ventral cell membrane remaining on the grids became observable by this method. In adhesion unroofing, grids charged positively by coating with Alcian blue were pressed onto the cells, thereby tightly adsorbing the dorsal cell membrane. Subsequently, a part of the cell membrane strongly adhered to the grids was peeled from the cells and transferred onto the grids when the grids were lifted. This method thus allowed the visualization of the cytoplasmic surface of the dorsal cell membrane. This paper describes robust, improved protocols for the two unroofing methods in detail. In addition, micro-unroofing (perforation) likely due to nanobubbles is introduced as a new method to make cells transparent to electron beams.

pH in principal cells of frog skin (Rana pipiens): dependence on extracellular Na+

1988 ◽  
Vol 255 (5) ◽  
pp. F930-F935 ◽  
Author(s):  
K. Drewnowska ◽  
E. J. Cragoe ◽  
T. U. Biber
Keyword(s):  
Frog Skin ◽  
Rana Pipiens ◽  
Apical Cell ◽  
Ringer Solution ◽  
Feedback Mechanism ◽  
Open Circuit ◽  
Apical Cell Membrane ◽  
Principal Cells ◽  
Apical Side ◽  
Basolateral Side

Measurements of intracellular pH (pHi) and of apical cell membrane potential (Va) were made in principal cells of frog skin (Rana pipiens) with double-barrel microelectrodes under open-circuit conditions. The tissues were pretreated with stilbenes (10(-3) M) and bathed in HCO3- -free NaCl Ringer solution that was buffered with 6 mM N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (pH 7.8). Substitution of extracellular Na+ on both sides of the epithelium with N-methyl-D-glucamine caused intracellular acidification by 0.27 pH units. Restoration of Na+ on the apical side alone or on both sides caused a pHi recovery of 0.24 and 0.28 pH units, respectively, whereas return of Na+ on the basolateral side caused no recovery. Recovery of pHi on restoration of Na+ to the apical side was prevented by 10(-5) M 5-(N-ethyl-N-isopropyl)-amiloride. In individual preparations there was no correlation between pHi recovery due to return of apical Na+ and changes in Va. The average change in pHi was several times greater than the one expected from voltage clamp-induced changes in Va at constant extracellular Na+. The results suggest the presence of a Na+-H+ exchange on the apical side of principal cells. Such a process could be part of a negative feedback mechanism for regulation of Na+ entry via apical Na+ channels into principal cells.

pH in principal cells of frog skin (Rana pipiens): effects of amiloride and potential

1988 ◽  
Vol 255 (5) ◽  
pp. F922-F929 ◽  
Author(s):  
K. Drewnowska ◽  
T. U. Biber
Keyword(s):  
Cell Membrane ◽  
Voltage Clamp ◽  
Frog Skin ◽  
Rana Pipiens ◽  
Apical Cell ◽  
Disulfonic Acid ◽  
Intracellular Acidification ◽  
Apical Cell Membrane ◽  
Principal Cells ◽  
Apical Side

Intracellular pH (pHi) and apical cell membrane potential (Va) were determined in principal cells of frog skin (Rana pipiens) with double-barrel micro-electrodes. In the Northern and Southern varieties, respectively, pHi is 0.38 and 0.26 pH units below bath pH. Amiloride, applied apically, causes reversible intracellular acidification at concentrations of 10(-5) M or higher. Voltage clamp-induced hyperpolarization and depolarization of Va result in intracellular acidification and alkalinization, respectively. This response of pHi is inhibited or abolished when the apical side is treated with 10(-3) M 4,4'-diisothiocyanostilbene-2,2'-disulfonic acid (DIDS). Amiloride-induced intracellular acidification is not exclusively due to the hyperpolarization of Va that accompanies amiloride treatment since 1) amiloride causes greater acidification than equivalent voltage clamp-induced hyperpolarization of Va, 2) amiloride-induced acidification persists in DIDS-treated tissues, and 3) there is no correlation between hyperpolarization of Va and intracellular acidification occurring after amiloride. We conclude that pHi is below the extracellular pH. Amiloride causes intracellular acidification that may be in part connected with hyperpolarization of Va. However, a major component of amiloride-induced acidification is due to other factors, possibly inhibition of apical Na+-H+ exchange. The inhibitory effect of apically applied DIDS suggests that the voltage dependent changes in pHi are related to movement of HCO3 (or OH) ions across the apical cell membrane.

scholarly journals Antibodies to the major insoluble milk fat globule membrane-associated protein: specific location in apical regions of lactating epithelial cells.

1981 ◽  
Vol 89 (3) ◽  
pp. 485-494 ◽  
Author(s):  
W W Franke ◽  
H W Heid ◽  
C Grund ◽  
S Winter ◽  
C Freudenstein ◽  
...  
Keyword(s):  
Epithelial Cells ◽  
Milk Fat ◽  
Lipid Production ◽  
Apical Cell ◽  
Cell Types ◽  
Specific Marker ◽  
Milk Lipid ◽  
Apical Surface ◽  
Milk Fat Globule ◽  
A Cell

Milk lipid globules of various species are surrounded by a membrane structure that is separated from the triglyceride core of the globule by a densely staining fuzzy coat layer of 10- to 50-nm thickness. This internal coat structure remains attached to the membrane during isolation and extraction with low- and high-salt buffers, is insoluble in nondenaturing detergents, and is enriched in an acidic glycoprotein (butyrophilin) with an apparent Mr of 67,000. Guinea pig antibodies against this protein, which show cross-reaction with the corresponding protein in some (goat) but not other (human, rat) species, have been used for localization of butyrophilin on frozen sections of various tissues from cow by immunofluorescence and electron microscopy. Significant reaction is found only in milk-secreting epithelial cells and not in other cell types of mammary gland and various epithelial tissues. In milk-secreting cells, the staining is restricted to the apical cell surface, including budding milk lipid globules, and to the periphery of the milk lipid globules contained in the alveolar lumina. These findings indicate that butyrophilin, which is constitutively secreted by surface budding in coordination with milk lipid production, is located at the apical surface and is not detected at basolateral surfaces, in endoplasmic reticulum, and in Golgi apparatus. This protein structure represents an example of a cell type-specific cytoskeletal component in a cell apex. It is suggested that this antigen provides a specific marker for the apical surface of milk-secreting cells and that butyrophilin is involved in the vectorial discharge of milk lipid globules.

Immunocytochemical localization of Na+-HCO3− cotransporters and carbonic anhydrase dependence of fluid transport in corneal endothelial cells

2004 ◽  
Vol 286 (6) ◽  
pp. C1434-C1442 ◽  
Author(s):  
Friedrich P. J. Diecke ◽  
Quan Wen ◽  
Jose M. Sanchez ◽  
Kunyan Kuang ◽  
Jorge Fischbarg
Keyword(s):  
Endothelial Cells ◽  
Carbonic Anhydrase ◽  
Fluid Transport ◽  
Apical Membrane ◽  
Apical Cell ◽  
Corneal Endothelial Cells ◽  
Fresh Tissue ◽  
Factors Affecting ◽  
Apical Side ◽  
Carbonic Anhydrase Iv

In corneal endothelium, there is evidence for basolateral entry of HCO3− into corneal endothelial cells via Na+-HCO3− cotransporter (NBC) proteins and for net HCO3− flux from the basolateral to the apical side. However, how HCO3− exits the cells through the apical membrane is unclear. We determined that cultured corneal endothelial cells transport HCO3− similarly to fresh tissue. In addition, Cl− channel inhibitors decreased fluid transport by at most 16%, and inhibition of membrane-bound carbonic anhydrase IV by benzolamide or dextran-bound sulfonamide decreased fluid transport by at most 29%. Therefore, more than half of the fluid transport cannot be accounted for by anion transport through apical Cl− channels, CO2 diffusion across the apical membrane, or a combination of these two mechanisms. However, immunocytochemistry using optical sectioning by confocal microscopy and cryosections revealed the presence of NBC transporters in both the basolateral and apical cell membranes of cultured bovine corneal endothelial cells and freshly isolated rabbit endothelia. This newly detected presence of an apical NBC transporter is consistent with its being the missing mechanism sought. We discuss discrepancies with other reports and provide a model that accounts for the experimental observations by assuming different stoichiometries of the NBC transport proteins at the basolateral and apical sides of the cells. Such functional differences might arise either from the expression of different isoforms or from regulatory factors affecting the stoichiometry of a single isoform.

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