The corneal endothelium maintains the transparency of the cornea by transporting ions and fluid out of the corneal stroma to maintain the low level of hydration required for transparency. We propose to study the mechanisms of this transport to better understand the normal physiology of transport and thus how it is altered in disease. Transendothelial electrical potential difference, short circuit current, radioactive fluxes, and intracellular microelectrodes all measure ion flows through multiple pathways in the cell membrane simultaneously. Thus, the interpretation of those experimental results is often very complex and sometimes ambiguous. However, the recently invented patch clamp technique can measure the flows of ions through a single molecule, one pore in the cell membrane, and thus avoid these uncertainties. Unfortunately the patch clamp technique is now limited because 1) it takes a very long time to analyze the experimental data, 2) only patches with one pore can be used to measure pore kinetics, and 3) it cannot detect carriers (symports and antiports) or ion pumps (such as the soidum-potassium ATPase). We will overcome these limitations by designing and testing new mathematical techniques that will be able to 1) measure the kinetics of pores in patch clamp data much faster and more simply, 2) determine complex pore kinetics, 3) detect and measure net rates of cyclic pores, 4) extract kinetic data from patches with more than one pore, 5) identify pore-pore interactions, 6) study non-stationary kinetics, and 7) provide ways that ion pumps carriers and pumps could be measured using the patch clamp technique.

Agency
National Institute of Health (NIH)
Institute
National Eye Institute (NEI)
Type
Research Project (R01)
Project #
1R01EY006234-01A1
Application #
3262318
Study Section
Visual Sciences A Study Section (VISA)
Project Start
1986-07-01
Project End
1989-06-30
Budget Start
1986-07-01
Budget End
1987-06-30
Support Year
1
Fiscal Year
1986
Total Cost
Indirect Cost
Name
Columbia University (N.Y.)
Department
Type
Schools of Medicine
DUNS #
064931884
City
New York
State
NY
Country
United States
Zip Code
10027
Boxt, L M; Katz, J; Liebovitch, L S et al. (1994) Fractal analysis of pulmonary arteries: the fractal dimension is lower in pulmonary hypertension. J Thorac Imaging 9:8-13
Liebovitch, L S; Czegledy, F P (1992) A model of ion channel kinetics based on deterministic, chaotic motion in a potential with two local minima. Ann Biomed Eng 20:517-31
Liebovitch, L S; Selector, L Y; Kline, R P (1992) Statistical properties predicted by the ball and chain model of channel inactivation. Biophys J 63:1579-85
Liebovitch, L S; Toth, T I (1991) A model of ion channel kinetics using deterministic chaotic rather than stochastic processes. J Theor Biol 148:243-67
Liebovitch, L S; Toth, T I (1990) The akaike information criterion (AIC) is not a sufficient condition to determine the number of ion channel states from single channel recordings. Synapse 5:134-8
Liebovitch, L S; Toth, T I (1990) Using fractals to understand the opening and closing of ion channels. Ann Biomed Eng 18:177-94
Liebovitch, L S; Toth, T I (1990) Fractal activity in cell membrane ion channels. Ann N Y Acad Sci 591:375-91
Liebovitch, L S (1989) Testing fractal and Markov models of ion channel kinetics. Biophys J 55:373-7
Hernandez, J; Fischbarg, J; Liebovitch, L S (1989) Kinetic model of the effects of electrogenic enzymes on the membrane potential. J Theor Biol 137:113-25
Liebovitch, L S (1989) Analysis of fractal ion channel gating kinetics: kinetic rates, energy levels, and activation energies. Math Biosci 93:97-115

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