HILLE,B .Ionic Channels of Excitable Membranes . Sunderland, MA: Siedited by G. S. Oxford and C. M. Armstrong. New York: Rockefeller nauer, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....The PNP theory thus incorporates the channel structure and its solution yields the potential, concentration and flux of ions in the system in a self consistent manner. There is one other approach that has been fruitfully employed to model biological ion channels, namely, the reaction rate theory [6]. In this approach, an ion channel is represented by a series of ion binding sites separated by barriers, and ions are assumed to hop from one biding site to another, the probability of each hop determined by the height of the energy barrier. Many useful insights have been gleaned in the past ....

....each of the methods, referring mathematical details to more comprehensive publications. We discuss the merits and shortcomings of each computational approach. Detailed accounts of recent experimental findings on ion channels are not given here; the reader is referred to the latest edition of Hille [6], which provides an excellent source of information in this regard. The paper is organized as follows. We first describe the principles underlying the continuum theories, stochastic dynamics, and molecular dynamics, stressing the strengths and weaknesses of each approach. We then discuss briefly ....

B. Hille, Ionic Channels of Excitable Membranes, 3rd ed., Sinauer Associates, Sunderland, MA, 2001.

.... and electric potential inside and outside the neuron membrane, and the activity of special proteins embedded in the neuronal membrane which enable ions to flow inside (or outside) of the neuron (see Chapter 2) The biophysical building blocks of neurons are inherently noisy and unreliable [64, 88]. A clear question is then, what are the e#ects of biophysical design and specifically of neuronal noise on the computation and coding of neurons (see [190] Since the pioneering work of Adrian [8] we know that the common alphabet of spike and no spike is common to all spiking neurons, ....

....in all the individuals. Thus the neural code has a quantifiable mixture of individuality and universality. We present a rather wide review of the biological and mathematical background of this work (based mostly on the books by Nicholls, Martin and Wallace [126] Koch [88] Tuckwell [182] Hille [64], Dayan and Abbott [37] Cover and Thomas [35] Rieke, Warland, de Ruyter van Steveninck and Bialek, 143] Chapter 2 introduces the basic biophysics of neuronal design and function morphology, ion channels, synapses and spiking (focusing on modelling) Chapter 3 presents the basic tools of ....

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B. Hille. Ionic Channels of Excitable Membrane. Sinauer Associates, 2nd ed., 1992.

....coordination of muscle contraction including the pumping action of the heart, and ionic transport in every cell and organ are carried out through ionic channels. Ionic current pulses have been observed experimentally in a wide variety of channels in the membranes of many types of cells (see Ref. [1] and references therein) These current pulses are of rectangular wave shape with constant heights and are distributed stochastically in time. In this investigation we simulate stochastic in time rectangular current pulses for an electrodi usion model of the biological channel. We will consider ....

.... p max E p max V 10l c (15) for the at tops of the ion density p. V 0 implies I 0. This expression produces a linear Ohm s law. Experimental data on channels however indicate that Ohm s law for the biological channel is often nonlinear, e.g. sublinear see Fig. 6 on p. 328 of Hille [1]. The sublinearity in the experimental IV curve must come from e ects neglected in our model (for example, a nonuniform spatial distribution of xed charge or a signi cant series resistance arising in the bath or at the interface between the bath and channel [10] In our nite channel model, ....

B. Hille, Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer, 1992.

....for this movement assumes that the ion and the channel do not interact during transport. In this limit, the permeability coefficient is the only relevant parameter determining the dynamics of transport. In the presence of a membrane potential, the diffusion flux of ions can be described by Eq. 2 (Hille, 1992; Weiss, 1996) 2) where i denotes the ionic species (Cl 2 , K 1 , or H 1 ) P i is the permeability of the membrane to ion i, S is the surface area of the compartment, C i is the concentration of the ion in the cytoplasm (C) or lumen (L) z i is the valance of the ion, and U is the ....

.... with experimentally predicted membrane potentials (Endresen et al. 2000) To account for the effects of surface charge, we include a phenomenological potential difference between the bulk cytoplasm and the organelle s outer leaflet, DC C,0 , and the bulk lumen and the inner leaflet, DC L,0 (Hille, 1992). These potentials modify all ionic concentrations at these surfaces by a Boltzmann factor: 4) where the surface concentrations are denoted by a zero subscript. Given the typical surface potentials measured for negative phospholipid bilayers bathed in frog Ringer s solution, this theory predicts ....

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Hille, B. 1992. Ionic Channels of Excitable Membranes. 2nd ed.

....of the heart) and ionic transport in every cell and organ. A substantial fraction of all drugs employed by physicians act directly or indirectly on channels. Ionic current pulses have been observed experimentally in a wide variety of channels in the membranes of many types of cells (see Ref. [1] and references therein) These current pulses are of rectangular wave shape with constant heights and are distributed stochastically in time. In this investigation we demonstrate the existence of stochastic in time rectangular current pulse traveling waves for a simpli ed electrodi usion model of ....

....expect a phase transition in the behavior of solutions as the frequency of noise falls below once per baseline orbit. It is possible that the two phases may correspond to the two qualitatively distinct forms of gating ( activation and inactivation ) experimentally observed in most ionic channels [1]. 4 Connection to Physical Parameter Values We consider here the ow of K ions through a channel of diameter 7 A and length 10 A. K channels play a central role in electrical signaling in the nervous system. A typical nerve cell has hundreds of thousands of K channels. For the ....

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B. Hille, Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer, 1992. 15

....ion channel structures that have been solved remain small compared to the wealth of structures available for soluble proteins. Whilst the structural information on ion channels may be comparatively small, the electrophysiological properties of single ion channels have been extensively investigated [2]. These studies show that most of the properties of ion channels can be explained in terms of the physical chemistry of ion ow in a narrow tube of water (the channel) that crosses the membrane. A number of approaches have been used to study features of ion channel structure based on single ....

B. Hille, Ionic Channels of Excitable Membranes (2nd ed.), Sinauer, 1991.

.... of the Na K pump as well as an enhanced imbalance of passive Na and K conductances have been discussed [Pierau et al. 1974; Braun et al. 1980, Schafer Braun, 1990] But the highest temperature coe#cients have been described for the ionic kinetics, i.e. the time constant of current activation [Hille, 1992]. According to these findings and recent computer simulations [Longtin Hinzer, 1995] see also [Rinzel Ermentrout, 1989] we mainly varied the activation kinetics with a Q10 of 3.0 and slighty changed the maximum conductances with a Q10 of 1.3. We do not consider the rather complex ....

Hille, B. [1992] Ionic Channels of Excitable Membranes (Sinauer Associates Inc., Sunderland, Mass.).

....given above, we did not study the growth time of MEPCs or their frequency and amplitude. The main part of the decay phase of a MEPC is apparently due to a change in the conformation of acetylcholine receptor channel molecules: this closes the channel and decreases the inward synaptic current (Hille, 1992). Our results indicate that the rate constant of conformational changes of receptor channel molecules is not affected by thermal acclimation. Our general conclusion is that the time relationships of peripheral synaptic transmission are well regulated in frogs and not susceptible to the effects of ....

HILLE, B. (1992). Ionic Channels of Excitable Membranes. 2nd edition, 607pp. Sunderland, MA: Sinauer Associates.

....model for this movement assumes that the ion and the channel do not interact during transport. In this limit, the permeability coefficient is the only relevant parameter determining the dynamics of transport. In the presence of a membrane potential the diffusion flux of ions can be described by (Hille, 1992; Weiss, 1996) JPS [C ] C ] e 1e ii iL iC = zU i zU zU (2) where i denotes the ionic species (Cl , K , or H ) P i is the permeability of the membrane to ion i, S is the surface area of the compartment, C i is the concentration of the ion in the cytoplasm (C) ....

.... experimentally predicted membrane potentials (Endresen et al. 2000) In order to account for the effects of surface charge, we include a phenomenological potential difference between the bulk cytoplasm and the organelle s outer leaflet, C,0 , and the bulk lumen and the inner leaflet, L,0 (Hille, 1992). These potentials, called zeta potentials, modify all ionic concentrations at these surfaces by a Boltzmann factor: C ] C ] C ] C ] iL,0 iL iC,0 iC = exp exp , zF RT zF RT iL iC 0 0 (4) where the surface concentrations are denoted by ....

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Hille, B. 1992. Ionic Channels of Excitable Membranes. 2nd ed. Sinauer Associates, Inc., Sunderland, MA. 607 pp.

....however, that the deterministic macroscopic currents arise as a result of the summation of stochastic microscopic currents flowing through ion channels in the membrane. Ion channels are protein macromolecules which switch randomly between discrete conformational states 6 due to thermal agitation (Hille, 1992). HH like voltage gated ion channels can be modeled as finite Markov chains where the conditional transition probabilities between the different conformational states are functions of the membrane voltage (Clay DeFelice, 1983; Strassberg DeFelice, 1993) The stochastic Markov version of the HH ....

Hille B., 1992. Ionic Channels of Excitable Membranes. Sinauer Associates: Sunderland, Massachusetts.

....spontaneous and missing spikes, all observed experimentally. Direct measurement of membranal noise has also been replicated successfully by such stochastic models [13] Neurons use many tens of thousands of ion channels to encode the synaptic current that reaches the soma into trains of spikes [14]. The number of ion channels that underlies the spike generation mechanism, and their types, depend on the activity of the neuron [15, 16] It is yet unclear how such changes may a ect the amount and nature of the information that neurons encode. Here we ask what is the information encoding ....

....state, see [12] for details) The potassium and sodium membrane conductances are given by, gK (V; t) K [n 4 ] gNa (V; t) Na [m 3 h 1 ] 3) where K and Na are the conductances of an ion channel for the K and Na respectively. We take the conductance of a single channel to be 20 pS [14] for both the K and Na channel types 1 . Each of the ion channels will thus respond stochastically by closing or opening its gates according to the kinetic model, uctuating around the average expected behavior. Figure 1 demonstrates the e ect of the ion 0 5 10 15 20 0 20 40 60 ....

Hille B. Ionic Channels of Excitable Membrane. Sinauer Associates, 2nd ed., 1992.

....PB theory, these applications usually involve bulk conditions with system sizes much larger than the Debye length, and the validity of the underlying mean field approximation is well established. Recent applications of the NP and PNP theories in ion channels (see Levitt, 1986; Cooper et al. 1988; Hille, 1992; Eisenberg, 1996, 1999 for reviews and further references) in contrast, involve systems with rather few ions and with dimensions smaller than the Debye length. Under these conditions, one would intuitively expect that keeping the integrity of ions would be essential to gain a realistic physical ....

....continuous quantities corresponding to macroscopic, space time averages of microscopic motion of individual ions. Due to their nonlinear nature, the PNP equations are notoriously difficult to solve analytically except in some very special cases, e.g. the classic Goldman Hodgkin Katz equation (Hille, 1992). More recent discussions of the analytical treatment of the PNP equations can be found in Syganow and von Kitzing (1995, 1999a, b) Here we consider the basic formalism of the PNP together with some special cases to indicate where and why the PNP theory may break down. These solutions will also ....

Hille, B. 1992. Ionic Channels of Excitable Membranes, 2nd Ed. Sinauer Associates Inc., Sunderland, MA.

....an energy barrier is erected near the constricted segment of the channel. Conductance concentration curve Experimentally, current across a biological ion channel increases monotonically with an increasing ionic concentration initially and then saturates with a further increase in concentration (Hille, 1992). Saturation of channel currents occurs when there is a rate limiting permeation process that is independent of ionic concentrations. For example, an ion arriving near the constricted membrane segment will be detained there for a period of time if, before traversing the narrow pore, it needs to ....

....can be gated electrostatically by rotating an appropriate number of charge moieties into and out of the protein lining. Current concentration curve Experimentally it has been shown that the current first increases with an increasing ionic concentration and then saturates (Rae et al. 1988; Hille, 1992). Such a relationship is expected to be found when the transport of ions across the channel is determined by two independent processes, one of which depends upon ion concentration and one that does not. In our simulations, for example, the time # 1 it takes for an ion to arrive near the ....

Hille, B. 1992. Ionic Channels of Excitable Membranes, 2nd Ed., Sinauer Associates, MA.

....currents flowing through ion specific membrane proteins (channels) depend non linearly on the voltage difference across the membrane (Johnston Wu, 1995) i = f(Vm ) 1) where i represents the ionic current through the channel and Vm is the membrane voltage. Often the current satisfies Ohm s law (Hille, 1992); i can be expressed as the product of the driving potential across the channel Vm Gamma E ch and the voltage (or ligand concentration) dependent channel conductance g ch as, i = g ch (V m ) V m Gamma E ch ) 2) where E ch (the membrane voltage for which i = 0) is the reversal potential of ....

....as is shown in Figure 3. Thus, neglecting the noise due to the cytoplasmic resistance is a very reasonable approximation for our frequency range of interest (1 1000 Hz) 2. 2 Channel Noise The membrane conductances we consider here are a consequence of microscopic, stochastic ionic channels (Hille, 1992). Since these channels open and close randomly, fluctuations in the number of channels constitutes a significant source of noise. In this section, we restrict the discussion to voltage gated channels. However, ligand gated channels can also be analyzed using the techniques discussed here. In a ....

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Hille, B. 1992. Ionic Channels of Excitable Membranes. Sinauer Associates: Sunderland, Massachusetts.

....more natural interface (natural language, or graphical) could be built. The interface could then generate source for another simulator, C or FORTRAN code directly. 2 The Membrane The electrical properties of the neuronal cell all derive from cell membrane and its ability to conduct electricity [Hille]. In this section I will try to show how the relevant components and properties of the membrane can be represented as conceptual graphs. Lipid bi layer aqueous solution aqueous solution Hydrophylic end Hydrophobic end Figure 1: A pictorial representation of a cell membrane. The cell ....

Bertil Hille, Ionic Channels of Excitable Membranes, Sinauer, Sunderland, Massachusetts, 1984

....in this letter have wide applicability, a special emphasis will be placed on the problem of the gating of voltage sensitive ion channels. Ion channels are macromolecular pores in the membranes of electrically excitable cells through which different species of ions are selectively allowed to pass. [1] In voltage sensitive channels the coupling between membrane voltage and channel gating involves charges or electrical dipoles which act as sensors of the potential across the membrane. When the channel changes its conformational state these charges move, and produce capacitive currents called ....

....response of the driver must be at least as fast as the halfwidth of the pulse shown in Fig. 3(b) These pulses should have the same shape as the gating current pulses which are observed experimentally. Experimentally these pulses are observed to have a duration on the order of a few tens of s[1], so the voltage response of the driver must be of this order. If the driver is slower than this, the channels can be controlled, but the true potential cannot be determined with great accuracy. Lastly there is the problem of the excitation of other modes, and the added complexity this would add ....

B. Hille, Ionic Channels of Excitable Membranes (2nd Ed.) Sinauer Associates, Sunderland Mass. (1992).

....was a landmark of biophysics, and their equations are a prototype for most quantitative models for the electrophysiological properties of membranes that have been studied subsequently. Despite the importance of HH, understanding of the qualitative properties of their solutions is fragmentary [14]. We study systematically how an axon changes its type of response from repetitive firing to single action potentials, in the context of the HodgkinHuxley equations. Our approach relies upon the use of multiparameter bifurcation theory, a part of the modern theory of nonlinear dynamical systems. ....

B. Hille (1992), Ionic Channels of Excitable Membranes, Sinauer.

....27:291 331 (1994) 1. Introduction Biological neural networks are large systems of complex elements interacting through a complex array of connections. Individual neurons express a large number of active conductances (Connors et al. 1982; Adams Gavin, 1986; Llin as, 1988; McCormick, 1990; Hille, 1992) and exhibit a wide variety of dynamic behaviors on time scales ranging from milliseconds to many minutes (Llin as, 1988; Harris Warrick Marder, 1991; Churchland Sejnowski, 1992; Turrigiano et al. 1994) Neurons in cortical circuits are typically coupled to thousands of other neurons ....

Hille, B. (1992) Ionic Channels of Excitable Membranes. Sinauer Assoc., Sunderland, MA.

No context found.

HILLE,B .Ionic Channels of Excitable Membranes . Sunderland, MA: Siedited by G. S. Oxford and C. M. Armstrong. New York: Rockefeller nauer, 1992.

No context found.

Hille B (1992) Ionic Channels of Excitable Membranes. Sinauer Ass., Sunderland MA.

No context found.

Hille B. Ionic Channels of Excitable Membrane. Sinauer Associates, Sunderland, MA, 2nd edition, 1992.

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, 1995. HILLE B. Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer,

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Opin. Neurobiol. 9(6):663-669. Hille (1992) Ionic channels of excitable membranes. Sinauer Associates Inc., Sunderland, MA.

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Hille, B. (1992). Ionic Channels of Excitable Membranes. 2nd Ed. Sinauer.

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Hille, B.: Ionic Channels of Excitable Membranes, Sinauer Associates Inc., Sunderland, Mass., 1984. 8

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