Jan P. Koniarek

Ion channel kinetics: a model based on fractal scaling rather than multistate Markov processes

Abstract Ion channels have been modeled as consisting of a small number of discrete conformational states such as closed ⇌ closed ⇌ open, and the transitions between the states treated as a Markov process. We derive an alternative model based on a fractal scaling of the kinetic rate constants k, namely that k = At1-D, where t is time, A the kinetic setpoint, and D the fractal dimension. By measuring the effective kinetic rate constants at different time scales, we show how to determine if single channel records are best represented by models with discrete Markov states or continuum fractal kinetics. The fractal model suggests that the multiple closed states postulated by Markov models to fit the histograms of closed times may not exist but are an artifact of trying to fit the sum of exponentials to histograms that are not the sum of exponentials. The fractal model is also more consistent with the conformational dynamics of proteins. Analysis of patch clamp recordings from an epithelium, the corneal endothelium, shows that its channels have fractal rather than Markov kinetics.

Scanning Slit Confocal Microscopic Observation of Cell Morphology and Movement within the Normal Human Anterior Cornea

PURPOSE Noninvasive in vivo observations of the anterior human cornea were performed to study cell structure and dynamics. Cellular elements were identified by their location, morphology, and pattern of movement. The hypothesis that cells in the epithelial layer of the normal cornea migrate centripetally was tested. METHODS Using a scanning slit confocal microscope with a new 0.75-numeric aperture contact objective, individual cells of normal human corneas were observed over time, quantifying the velocity and direction of cellular movement within the basal epithelial layer. RESULTS Basal epithelial cells, wing cells, the basal epithelial nerve plexus, and the subepithelial nerve plexus were identified readily. Centripetal motion was observed for three corneal cell types: basal epithelial cells, basal epithelial nerves, and unidentified cellular elements (possibly Langerhans cells). The unidentified cellular elements moved along the length of the basal epithelial nerves. The basal epithelial nerve plexus maintained a roughly stable topology as it slid centripetally. New nerve material appeared at the site of entry of the nerve into the epithelium. No growth cones were present at the distal termini of the growing epithelial nerves. CONCLUSION In the midperiphery of the normal human cornea, basal epithelial cells and nerves slide centripetally, probably in concert. Unidentified cellular elements used the basal epithelial nerve plexus as a pathway for intraepithelial movement. Observations in this study suggest that neurite growth occurred by the addition of new membrane material along the length of the axon rather than at a distal growth cone.

Effects of ambient bicarbonate, phosphate and carbonic anhydrase inhibitors on fluid transport across rabbit corneal endothelium

Bicarbonate has been long held to be indispensable for fluid pumping by the endothelium; however, such need has been disputed recently. We investigated this issue and found that: (1) the corneal endothelium pumps fluid equally well (at 6-8 microliters hr-1 cm-2) whether the bathing solution contains 43 mM bicarbonate or 10 mM phosphate, (2) if bicarbonate and most of the phosphate are absent, fluid pumping is noticeably lowered (2-4 microliters hr-1 cm-2), (3) carbonic anhydrase inhibitors (5 mM acetazolamide; 0.1, 0.2 and 0.3 mM ethoxzolamide) block this lowered fluid pumping, and (4) in the absence of external bicarbonate, 20 mM HEPES is insufficient to preserve adequate fluid pumping. These results are consistent with existing models for endothelial transport in which exogenous and endogenous CO2 are converted to HCO3- by carbonic anhydrase, with HCO3- fueling the transport mechanism and therefore the fluid pump.

The mechanism of fluid and electrolyte transport across corneal endothelium: critical revision and update of a model.

A model for endothelial transport is updated to include recent evidence. We discuss electrolyte movements based on a Na+-K+ ATPase, a Na+-H+ exchanger, a Na+-HCO3 coupler, a Cl- -HCO-3 exchanger, a K+-Cl-coupler, and K+ and anion channels. We discuss near-isotonic transport of fluid on the basis of recent findings of high endothelial osmotic permeability.

Transport of fluid by lens epithelium

We report for the first time that cultured lens epithelial cell layers and rabbit lenses in vitro transport fluid. Layers of the alphaTN4 mouse cell line and bovine cell cultures were grown to confluence on permeable membrane inserts. Fluid movement across cultured layers and excised rabbit lenses was determined by volume clamp (37 degrees C). Cultured layers transported fluid from their basal to their apical sides against a pressure head of 3 cmH2O. Rates were (in microliter. h-1. cm-2) 3.3 +/- 0.3 for alphaTN4 cells (n = 27) and 4.7 +/- 1.0 for bovine layers (n = 6). Quinidine, a blocker of K+ channels, and p-chloromercuribenzenesulfonate and HgCl2, inhibitors of aquaporins, inhibited fluid transport. Rabbit lenses transported fluid from their anterior to their posterior sides against a 2.5-cmH2O pressure head at 10.3 +/- 0.62 microliter. h-1. lens-1 (n = 5) and along the same pressure head at 12.5 +/- 1.1 microliter. h-1. lens-1 (n = 6). We calculate that this flow could wash the lens extracellular space by convection about once every 2 h and therefore might contribute to lens homeostasis and transparency.We report for the first time that cultured lens epithelial cell layers and rabbit lenses in vitro transport fluid. Layers of the αTN4 mouse cell line and bovine cell cultures were grown to confluence on permeable membrane inserts. Fluid movement across cultured layers and excised rabbit lenses was determined by volume clamp (37°C). Cultured layers transported fluid from their basal to their apical sides against a pressure head of 3 cmH2O. Rates were (in μl ⋅ h-1 ⋅ cm-2) 3.3 ± 0.3 for αTN4 cells ( n = 27) and 4.7 ± 1.0 for bovine layers ( n = 6). Quinidine, a blocker of K+ channels, and p-chloromercuribenzenesulfonate and HgCl2, inhibitors of aquaporins, inhibited fluid transport. Rabbit lenses transported fluid from their anterior to their posterior sides against a 2.5-cmH2O pressure head at 10.3 ± 0.62 μl ⋅ h-1 ⋅ lens-1( n = 5) and along the same pressure head at 12.5 ± 1.1 μl ⋅ h-1 ⋅ lens-1( n = 6). We calculate that this flow could wash the lens extracellular space by convection about once every 2 h and therefore might contribute to lens homeostasis and transparency.

Inhibition of transepithelial osmotic water flow by blockers of the glucose transporter

On the basis of evidence derived mostly from human erythrocytes, it has been suggested that water traverses cell membranes through membrane-spanning proteins such as the anion channel or the glucose transporter acting as water pores. However, specific inhibitors of such permeation processes have not been found to block water transport, and hence a precise identification of the water route has not been possible so far. We have investigated this issue by characterizing the osmotic flows across a fluid-transporting epithelium, the rabbit corneal endothelium. The rate of such flows was monitored continuously as a function of time. We confirmed prior findings of an inhibition by PCMBS on osmotic water flow, and lack of inhibition by DTNB and DIDS. On the other hand, we have found for the first time that several blockers of glucose facilitated diffusion, namely, phloretin (2 mM), phloridzin (2 mM), diallyldiethylstilbestrol (0.1 mM), cytochalasin B (20 micrograms/ml), and ethylidene-D-glucose (200 mM), all clearly inhibit osmotic flow. Our evidence is consistent with the hypothesis that both water and glucose may traverse these cell membranes through the same channel-like pathway contained in the glucose transporter membrane-spanning protein.

Ion channel kinetics

Proteins called ion channels, which are found in the lipid bilayer that forms the cell membrane, can have different shapes, called conformational states. Experimental evidence that the timing of switches between these states has fractal properties is examined. The physical interpretation of this phenomenon is discussed.<<ETX>>

Optical correlation functions applied to the random telegraph signal: how to analyze patch clamp data without measuring the open and closed times

Abstract The correlation functions used mostly to analyze data from photon correlation experiments can be used to analyze the random telegraph signal. Hence such functions can be used to determine the kinetic rate constants of ion channels in cell membranes directly from digitized patch clamp data by simple numerical integrations. Thus, it is not necessary to find, reconstruct, and measure the open and closed time intervals and to construct their frequency histograms in order to determine the rate constants of the observed channel.

Photographic patterns in macular images: representation by a mathematical model

Normal macular photographic patterns are geometrically described and mathematically modeled. Forty normal color fundus photographs were digitized. The green channel gray-level data were filtered and contrast enhanced, then analyzed for concentricity, convexity, and radial resolution. The foveal data for five images were fit with elliptic quadratic polynomials in two zones: a central ellipse and a surrounding annulus. The ability of the model to reconstruct the entire foveal data from selected pixel values was tested. The gray-level patterns were nested sets of concentric ellipses. Gray levels increased radially, with retinal vessels changing the patterns to star shaped in the peripheral fovea. The elliptic polynomial model could fit a high-resolution green channel foveal image with mean absolute errors of 6.1% of the gray-level range. Foveal images were reconstructed from small numbers of selected pixel values with mean errors of 7.2%. Digital analysis of normal fundus photographs shows finely resolved concentric elliptical foveal and star-shaped parafoveal patterns, which are consistent with anatomical structures. A two-zone elliptic quadratic polynomial model can approximate foveal data, and can also reconstruct it from small subsets, allowing improved macular image analysis.

Solutions containing miotic agents: Effects on corneal transendothelial electrical potential difference

Abstract• Background: Anterior chamber miotic solutions are widely used during anterior chamber surgery. We examined the effects of solutions containing miotic agents such as carbachol and/or acetylcholine on corneal endothelial pumping activity. • Methods: We monitored, in vitro, the transendothelial electrical potential difference of isolated rabbit corneal endothelial preparations. As controls, we used solutions without miotics. • Results: We found that a solution containing 55 mM acetylcholine and minimal amounts of salts (Miochol E) maintains transendothelial electrical potential difference some 30% above control levels for up to 4 h. Two other solutions, one including balanced salts and 0.55 mM carbachol (Miostat), the other a mixture of 0.19 mM carbachol and 55 mM acetylcholine plus minimal salts, are adequate to maintain the potential difference at control levels. Lastly, a solution with acetylcholine but without any salts (Miochol) greatly decreases the potential difference, to 30% of the control level, in 100 min. • Conclusion: Our results indicate that: (1) 55 mM (1%) acetylcholine stimulates the endothelial electrical potential difference; (2) addition of 0.19 mM (0.003%) carbachol negates the stimulatory effect of acetylcholine; and (3) absence of electrolytes severely depresses the endothelial electrical activity.