Current noise around steady states in discrete transport systems

Frehland, E.

doi:10.1016/0301-4622(78)87007-0

Cited by 38 publications

(21 citation statements)

References 14 publications

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“…In our previous paper we computed the spectral density of open-channel noise by applying the theory of Frehland (1978Frehland ( , 1982 to the entire kinetic scheme in Fig. 2A.…”

Section: Cumulants Of Shot Eventsmentioning

confidence: 99%

Open channel noise. VI. Analysis of amplitude histograms to determine rapid kinetic parameters

Heinemann

Sigworth

1991

Biophysical Journal

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Recently we reported that rapid fluctuations of ion currents flowing through open gramicidin A channels exceed the expected level of pure transport noise at low ion concentrations (Heinemann, S. H. and F. J. Sigworth. 1990. Biophys. J. 57:499-514). Based on comparisons with kinetic ion transport models we concluded that this excess noise is likely caused by current interruptions lasting approximately 1 microsecond. Here we introduce a method using the higher-order cumulants of the amplitude distribution to estimate the kinetics of channel closing events far below the actual time resolution of the recording system. Using this method on data recorded with 10 kHz bandwidth, estimates for gap time constants on the order of 1 microsecond were obtained, similar to the earlier predictions.

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“…In our previous paper we computed the spectral density of open-channel noise by applying the theory of Frehland (1978Frehland ( , 1982 to the entire kinetic scheme in Fig. 2A.…”

Section: Cumulants Of Shot Eventsmentioning

confidence: 99%

Open channel noise. VI. Analysis of amplitude histograms to determine rapid kinetic parameters

Heinemann

Sigworth

1991

Biophysical Journal

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“…As easily may be verified the fundamental solution matrix· is The result (2.22) can easily be understood as follows [6,13]: The first ^-shaped term on the right-hand side contains the correlations of the transitions with themselves (at the same time) and is known from the autocorrelation of Poissonian <5-pulse sequences (e. g. [16]); the second term contains the rates <Ö êñ (0> under the condition that at time 0 a transition í -» ì occurred, i.e., the system was in state ì. Both terms are proportional to the mean rate <Ö£ í > of transitions í -» ì.…”

Section: Fluctuation Analysis Of State Variablesmentioning

confidence: 99%

“…In a number of applications to current noise in biological membranes the general validity of the approach was demonstrated and the analysis of experiments could be made possible [6,13,14,15].…”

Section: Introductionmentioning

confidence: 98%

Stochastic Analysis of Discrete Markovian Systems. I. Steady State Fluctuations of Scalar and Vectorial Quantities

Frehland¹

1988

Journal of Non-Equilibrium Thermodynamics

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Subject of this paper is the stochastic analysis of the steady state fluctuations of scalar and vectorial quantities in discrete Markovian systems. The scalar variables are introduced as step functions assuming discrete values which describe the state of the system. The vectorial variables are assigned to the transitions between different states of the systems. Under the assumption that the transition times are short compared with the characteristic times of the system, these variables are defined by <5-pulse sequences. As fundamental stochastic equation a master equation is introduced. The fluctuation analysis of the scalar state variables is performed with the use of the classical master equation approach to fluctuations. For the stochastic analysis of the transitions we have developed a new approach. It makes possible the fluctuation analysis of vectorial processes (e. g. electric current) at nonequilibrium steady states. In this paper the theoretical foundations of this approach are given. Furthermore, it is explicitly shown that via rigorous balance equations the results for the steady state fluctuations of scalar variables as known from the classical master equation approach can be derived from the new formalism for vectorial quantities. IntroductionMany kinetic processes as chemical reactions or biological transport processes can be represented by Markovian processes which are continuous in time and discrete in state space (e.g. [1][2][3][4][5][6][7]). Ttie stochastic behaviour of these systems is usually described by master equations. The treatment of fluctuations around steady states, which may be equilibrium or nonequilibrium, can be performed by the well known master equation approach to fluctuations ([8, 3, 4]). More than twenty years ago in a classical paper a possible extension of the fluctuationdissipation (Nyquist) relation, relating the equilibrium fluctuations to the macroscopic response properties of the system, to nonequilibrium steady states was

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“…20) are predicted for some semiconductors (Van der Ziel, 1970) but we know of none in practice. The only general method for predicting Sd for a given transport mechanism (Frehland, 1978) assumes that ions make instantaneous hops between a finite number of fixed binding sites, that the hops occur in a random, Markovian manner and that each hop contributes a pulse of displacement current in the bath, proportional to the electrical distance hopped. This method embodies the fact that the unitary pulses are not independent of each other, so single file transport and one-ion occupancy can be included.…”

Section: Appendixmentioning

confidence: 99%

Origins of open-channel noise in the large potassium channel of sarcoplasmic reticulum.

Hainsworth

Levis

Eisenberg

1994

The Journal of General Physiology

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A B S T R A C TOpen-channel noise was studied in the large potassium channel of the sarcoplasmic reticulum (SR). Inside-out patches were excised directly from the SR of split skeletal muscle fibers of lobster, with lobster relaxing ringer (LRR) in bath and pipette. The power spectrum of open-channel noise is very low and approximately flat in the 100 Hz-10 kHz frequency range. At 20~ with an applied voltage of 50 mV, the mean single-channel current (i) is 9 pA (mean single-channel conductance --180 pS) and the mean power spectral density 1.1 x 10 -29 AZ/Hz. The latter increases nonlinearly with (i), showing a progressively steeper dependence as (i) increases. At 20 mV, the mean power spectral density is almost independent of (i) and ~ 1.4 times that of the Johnson noise calculated for the equivalent ideal resistor with zero net current; at 70 mV it increases approximately in proportion to (i) 2. The mean power spectral density has a weak temperature dependence, very similar to that of (i), and both are well described by a Ql0 of 1.3 throughout the range 3-40~ Discrete ion transport events are thought to account for a significant fraction of the measured open-channel noise, probably ~ 30-50% at 50 inV. Brief interruptions of the single-channel current, due either to blockage of the open channel by an extrinsic aqueous species, or to intrinsic conformational changes in the channel molecule itself, were a possible additional source of open-channel noise. Experiments in modified bathing solutions indicate, however, that open-channel noise is not affected by any of the identified aqueous species present in LRR. In particular, magnesium ions, the species thought most likely to cause brief blockages, and calcium and hydrogen ions, have no detectable effect. This channel's openings exhibit many brief closings and substates, due to intrinsic gating of the channel. Unresolved brief full closings are calculated to make a negligible contribution (< 1%) to the measured power spectral density. The only significant source of noise due to band width-limited missed events is brief, frequent 80% substates (mean duration 20 ~s, mean frequency 1,000 s -1) which account for a small part of the measured power spectral density (~ 14%, at 50 mV, 20~ We conclude that a large fraction of the measured open-channel noise results from intrinsic conductance fluctuations, with a corner frequency higher than the resolution of our recordings, in the range 104-107 Hz. We infer the presence of motions within the channel molecule in this frequency range. INTRODUCTIONOpen-channel noise means any fluctuation in a single-channel current recording that is present only when the channel is open. Gaussian, apparently continuous current fluctuations are seen in the nicotinic end-plate channel (Sigworth, 1985) and in a stretch-activated cation channel (Eisenberg, Hainsworth, and Levis, 1987). These are thought to reflect fluctuations in the channel conductance, as a result of vibration within the channel molecule. In addition, discontinuous step changes in...

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Current noise around steady states in discrete transport systems

Cited by 38 publications

References 14 publications

Open channel noise. VI. Analysis of amplitude histograms to determine rapid kinetic parameters

Open channel noise. VI. Analysis of amplitude histograms to determine rapid kinetic parameters

Stochastic Analysis of Discrete Markovian Systems. I. Steady State Fluctuations of Scalar and Vectorial Quantities

Origins of open-channel noise in the large potassium channel of sarcoplasmic reticulum.

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