Biomaterial Database

Fractal model of ion-channel kinetics. 1987

L S Liebovitch, and J Fischbarg, and J P Koniarek, and I Todorova, and M Wang

Markov models with discrete states, such as closed in equilibrium with closed in equilibrium with open have been widely used to model the kinetics of ion channels in the cell membrane. In these models the transition probabilities per unit time (the kinetic rate constants) are independent of the time scale on which they are measured. However, in many physical systems, a property, L, depends on the scale, epsilon, at which it is measured such that L(epsilon) alpha epsilon 1-D where D is the fractal dimension. Such systems are said to be 'fractal'. Based on the assumption that the kinetic rates are given by k(t) alpha t1-D we derive a fractal model of ion-channel kinetics. This fractal model has fewer adjustable parameters, is more consistent with the dynamics of protein conformations, and fits the single-channel recordings from the corneal endothelium better than the discrete-state Markov model.

UI	MeSH Term	Description	Entries
D007473	Ion Channels	Gated, ion-selective glycoproteins that traverse membranes. The stimulus for ION CHANNEL GATING can be due to a variety of stimuli such as LIGANDS, a TRANSMEMBRANE POTENTIAL DIFFERENCE, mechanical deformation or through INTRACELLULAR SIGNALING PEPTIDES AND PROTEINS.	Membrane Channels,Ion Channel,Ionic Channel,Ionic Channels,Membrane Channel,Channel, Ion,Channel, Ionic,Channel, Membrane,Channels, Ion,Channels, Ionic,Channels, Membrane
D007700	Kinetics	The rate dynamics in chemical or physical systems.
D008390	Markov Chains	A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.	Markov Process,Markov Chain,Chain, Markov,Chains, Markov,Markov Processes,Process, Markov,Processes, Markov
D008565	Membrane Proteins	Proteins which are found in membranes including cellular and intracellular membranes. They consist of two types, peripheral and integral proteins. They include most membrane-associated enzymes, antigenic proteins, transport proteins, and drug, hormone, and lectin receptors.	Cell Membrane Protein,Cell Membrane Proteins,Cell Surface Protein,Cell Surface Proteins,Integral Membrane Proteins,Membrane-Associated Protein,Surface Protein,Surface Proteins,Integral Membrane Protein,Membrane Protein,Membrane-Associated Proteins,Membrane Associated Protein,Membrane Associated Proteins,Membrane Protein, Cell,Membrane Protein, Integral,Membrane Proteins, Integral,Protein, Cell Membrane,Protein, Cell Surface,Protein, Integral Membrane,Protein, Membrane,Protein, Membrane-Associated,Protein, Surface,Proteins, Cell Membrane,Proteins, Cell Surface,Proteins, Integral Membrane,Proteins, Membrane,Proteins, Membrane-Associated,Proteins, Surface,Surface Protein, Cell
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D011336	Probability	The study of chance processes or the relative frequency characterizing a chance process.	Probabilities
D011487	Protein Conformation	The characteristic 3-dimensional shape of a protein, including the secondary, supersecondary (motifs), tertiary (domains) and quaternary structure of the peptide chain. PROTEIN STRUCTURE, QUATERNARY describes the conformation assumed by multimeric proteins (aggregates of more than one polypeptide chain).	Conformation, Protein,Conformations, Protein,Protein Conformations
D011817	Rabbits	A burrowing plant-eating mammal with hind limbs that are longer than its fore limbs. It belongs to the family Leporidae of the order Lagomorpha, and in contrast to hares, possesses 22 instead of 24 pairs of chromosomes.	Belgian Hare,New Zealand Rabbit,New Zealand Rabbits,New Zealand White Rabbit,Rabbit,Rabbit, Domestic,Chinchilla Rabbits,NZW Rabbits,New Zealand White Rabbits,Oryctolagus cuniculus,Chinchilla Rabbit,Domestic Rabbit,Domestic Rabbits,Hare, Belgian,NZW Rabbit,Rabbit, Chinchilla,Rabbit, NZW,Rabbit, New Zealand,Rabbits, Chinchilla,Rabbits, Domestic,Rabbits, NZW,Rabbits, New Zealand,Zealand Rabbit, New,Zealand Rabbits, New,cuniculus, Oryctolagus
D003315	Cornea	The transparent anterior portion of the fibrous coat of the eye consisting of five layers: stratified squamous CORNEAL EPITHELIUM; BOWMAN MEMBRANE; CORNEAL STROMA; DESCEMET MEMBRANE; and mesenchymal CORNEAL ENDOTHELIUM. It serves as the first refracting medium of the eye. It is structurally continuous with the SCLERA, avascular, receiving its nourishment by permeation through spaces between the lamellae, and is innervated by the ophthalmic division of the TRIGEMINAL NERVE via the ciliary nerves and those of the surrounding conjunctiva which together form plexuses. (Cline et al., Dictionary of Visual Science, 4th ed)	Corneas
D004727	Endothelium	A layer of epithelium that lines the heart, blood vessels (ENDOTHELIUM, VASCULAR), lymph vessels (ENDOTHELIUM, LYMPHATIC), and the serous cavities of the body.	Endotheliums