Voltage-clamp errors cause anomalous interaction between independent ion channels
|
|
- Richard Lynch
- 5 years ago
- Views:
Transcription
1 AUDITORYAND VESTIBULAR SYSTEMS Voltage-clamp errors cause anomalous interaction between independent ion channels Hamilton E. Farris CA and Anthony J. Ricci Neuroscience Center and Kresge Hearing Labs, Louisiana State University Health Sciences Center, New Orleans, LA 70112, USA CA Corresponding Author: Received 23 March 2005; accepted 22 April 2005 In voltage-clamp, uncompensated series resistance results in steady-state voltage errors that scale with the amplitude of the elicited current and are often correctable o ine. However, while investigating mechanoelectric transduction currents at hair cells resting potential, voltage-gated calcium channels and calcium-activated potassium channels (BK) were activated in voltage-clamp by displacing the sensory hair bundle. This resulted from steady-state voltage errors (o1.5mv)induced by series resistance changing the holding potential.thus, uncompensated series resistance, interacting with an elicited current, resulted in a voltage error that could induce the erroneous activation of other currents. This error is not correctable o ine. Recognizing this type of error is critical when investigating multiple voltage-dependent conductances with steep voltage dependence. NeuroReport 16:943^947 c 2005 Lippincott Williams & Wilkins. Key words: Auditory hair cells; BK potassium channels; Calcium channels; Mechanoelectric transduction; Patch clamp; Series resistance INTRODUCTION Series resistance (SR) errors, associated with the whole-cell voltage-clamp technique have both steady-state and kinetic components [1]. Whereas the kinetic component sets the speed of the voltage-clamp circuit and is equivalent to the product of the SR and membrane capacitance, steady-state errors change the voltage at which a cell is being clamped, equivalent to the product of the SR and the elicited current. Typically, with small currents and low resistances, steadystate errors are not significant and the resulting small changes in voltage can be compensated offline. However, such compensation may not be possible under conditions in which multiple conductances are involved: activation of one conductance alters the voltage at which the cell is clamped and thus changes the activation properties of a second conductance. The significance of this problem is revealed when investigating the interaction between mechanically gated currents and voltage-sensitive conductances in auditory hair cells. Hair cells are mechanoreceptors whose receptor potential is regulated by the sum of several conductances. In addition to current through mechanoelectric transducer (MET) channels [2,3], conductances in the basolateral cell membrane, including L-type calcium channels and BK-type calcium-activated potassium channels, create the hair cell receptor potential [4]. Voltage-clamp investigation of MET channel properties near the hair cell s resting potential revealed that steady-state SR errors led to contamination of the MET currents through activation of the basolateral channels. The data presented here provide a clear example of the seriousness of this artifact, where a mechanically gated current activates a voltage-dependent current by changing the holding potential. METHODS Hair cells were recorded in the intact auditory papilla of turtles (Pseudemys scripta elegans), using established methods [5]. Procedures followed National Institutes of Health guidelines and were approved by the Institutional Animal Care and Use Committee. Turtles (carapace length mm) were rapidly decapitated and the head sectioned along the midline with a razor blade. Inner ear organs were removed and the papilla separated and mounted in a recording chamber using single strands of dental floss. Whole-cell patch recordings, with potassium as the major cation, were used to assess the characteristics of BK and MET conductances at resting potential. Electrodes were filled with (in mm): KCl (125), MgCl 2 (4), Na 2 ATP (5), creatine phosphate (5), D-glucose (8), ethyleneglycol-bis-(baminoethyl ether) N,N,N 0,N 0 -tetraacetic acid (EGTA) (5) and N-2-hydroxyethyl piperazine-n 0-2-ethanesulfonic acid (HEPES) (10), ph 7.2 for recordings. Either an Axopatch 200b or an EPC-8 amplifier was used for the recordings. Electrode resistances ranged from 1 to 3 MO. The extracellular solution contained (in mm): NaCl (125), KCl (4), MgCl 2 (2.2), CaCl 2 (2.8), Na HEPES (10), Na pyruvate (2), ascorbate (2), creatine (2) and D-glucose (6), ph 7.6 with NaOH and osmolality 275 mmol/kg. The bath contained Apamin (1 nm) to block SK potassium channels. Hair bundles were displaced using a rigid glass fiber, firepolished to a mm diameter and fixed to a piezoelectric bimorph [3,5]. The fiber tip was placed on the hair bundle just above the row of the shortest stereocilia. Whereas positive deflections toward the kinocilium opened MET channels, negative deflections away from the kinocilium closed them. The fiber s movement was driven with voltage c Lippincott Williams & Wilkins Vol 16 No 9 21 June
2 H. E. FARRIS AND A. J. RICCI steps from Signal Software using a CED D/A interface (Cambridge Electronic Design, Cambridge, UK) and filtered at 1 5 khz. All positive and negative displacements were greater than those needed to saturate the MET current [6]. BK activation curves were generated from tail currents following a series of 20-ms voltage steps (mean of 4 sweeps/ step) from a holding potential of ca 60 mv. Test solutions were either bath applied or pressure applied with a picospritzer (General Valve). All data are presented as mean7standard deviation. RESULTS A comparison of MET currents at a holding potential of 83 mv (where no other conductances are activated) with the MET currents near the hair cells resting potential ( 5475 mv) revealed smaller ( vs pa, n¼32) and slower (both activation and adaptation) currents in the more depolarized cells. Surprisingly, near the cell s resting potential, larger deflections of the hair bundle activated an outward conductance that superimposed upon the MET current (Fig. 1a and b), appearing as a decrease in the MET current over time. This was never observed at the more hyperpolarized potentials. The outward current following the deflection of the hair bundle (tail current) was used to characterize this conductance, as it was not contaminated by the MET current. The average amplitude of this current was pa (n¼32). This current had a steep voltage dependence ( mv, Fig. 1d) and a half activation of mv (n¼11), measured by fitting the 188/+579 nm (b) 188/+641 nm 0.9 V h = 83 mv 0.9 V h = 47 mv (c) +773 nm 54 mv 56 mv 60 mv 83mV (d) g/g max mv 51 mv Potential (mv) (e) (f) +624 nm step I/I max Stimulus duration (ms) Fig. 1. (a and b) Mechanical de ection of the hair bundle elicited saturating mechanoelectric transducer (MET) currents when holding at 83 mv but subsequently activated a second current (indicated by arrows) at 47 mv. Activation of this second current was steeply voltage-dependent. (c) Examples at di erent holding potentials. (d) shows the normalized voltage-conductance plot (E K used for reversal potential¼ 135 mv) t with a Boltzmann equation (see methods).whereas the black symbols and curve are for mechanical stimulation (V 1/2 ¼ mv; slope¼ mv), the gray curve represents conductance at di erent voltage steps (V 1/2 ¼ 537 mv; slope¼ mv n¼4; symbols not shown). Lower inset: ms duration 71mV steps were given during a 60 ms depolarizing step to a potential ( 50 mv) on the steep part of the activation curve, demonstrating BK sensitivity similar to the mechanically elicited outward tail currents. Scale bar: 100 pa, 10 ms. Upper inset: expanded x-axis with error bars. (e and f) Activation of this second current was fast. (e) varies the duration of the mechanical stimulus from 0.3 ms to12 ms demonstrating that the peak outward tail occurs with a stimulus of B3 ms.(f) is a summary plot of relative tail current amplitude against stimulus duration. An exponential t gave a time constant of ms (n¼8). Inset: expanded x-axis. Horizontal bars show time of mechanical displacements of the bundle with step size and direction indicated above (positive toward kinocilium). 944 Vol 16 No 9 21 June 2005
3 SERIES RESISTANCE ERROR AND MULTIPLE CURRENTS data with a Boltzmann function: g=g max ¼ 1=ð1 þ e ðv 1=2 VÞ=K Þ,where V 1/2 is the half-activating voltage and K is the limiting slope (voltage dependence). These activation properties are remarkably similar to those of the basolateral BK conductance, which had a half activation of 537 mv and a slope factor of mv (n¼4; Fig. 1d). BK currents, comparable in amplitude to the outward tail, are elicited by 71 mv steps from a potential on the steep part of the BK activation curve (Fig. 1d, inset). The current activated faster than MET current activation (Fig. 1e). Stimulus durations as short as 3 ms could elicit a peak response (time constant to peak of ms; n¼8) (Fig. 1f). Because the cell was in voltage-clamp during these recordings two possibilities arose as to the mechanism of activation: direct mechanical activation or calcium-induced activation. The first question addressed was about what channel is responsible for this additional conductance and how this channel is activated given that the cell is in voltage-clamp mode. The similarity in activation properties implicated BK potassium conductance. Data exist suggesting that BK channels can be mechanosensitive [7,8]; to test whether activation of this current was due to either direct mechanical coupling or MET channel activation, the MET current was blocked with tubocurarine (Fig. 2a, 200 mm) [9,10]. Blocking the MET current abolished BK current activation, suggesting that activation was not due to a mechanical coupling, but was indirect and driven by MET current activation. Given that the cells were in voltage-clamp, it was surmised that perhaps Ca 2+, through the MET channels, was activating a BK current that, in order to account for the rapid kinetics, needed to be in the stereocilia or in close proximity to the MET channels. Bath application of potassium (125 mm) caused the current to reverse polarity and become inward (Fig. 2c, n¼10) [11,12], while bath application of tetraethyl ammonium (TEA, 3 mm) blocked the current (Fig. 2b, n¼11), supporting the conclusion that a potassium channel distinct from the MET channel was being activated. Intracellular Cs + also blocked the current (Fig. 2d, n¼3), further demonstrating that this was a potassium conductance. However, local application of the high K + solution (n¼10) or TEA (n¼3) to the sensory hair bundle and apical cell surface had no effect on this conductance, indicating that the channels were not located on the apical surface or stereocilia. To further test whether the channel being activated was Ca 2+ -dependent, the internal Ca 2+ buffer was changed from 5 mm EGTA to 1 mm BAPTA, resulting in a depolarizing shift of the activation curve, from mv to 4571mV, (n¼8 for BAPTA cells) consistent with a Ca 2+ - dependent conductance [13,14]. Because both Ca 2+ diffusion down the stereocilia [15] and Ca 2+ release from stores would be too slow for the measured BK activation kinetics, the source of Ca 2+ at this point was unclear. Might voltage-dependent calcium channels activate despite being in voltage-clamp? This question was answered by simultaneously stimulating the bundle mechanically and bath applying Nimodipine, which blocks L-type Ca 2+ channels in these hair cells [16], while leaving MET channels unaffected [10]. While no effect was found on the MET (c) nm (b) +482 nm nm (d) +375 nm 0 1 (e) Curare 1mM K Nimodipine +879 nm 0 1 current, the potassium conductance was blocked, suggesting that its activation followed the activation of an L-type Ca 2+ channel (Fig. 2e, n¼8). Nimodipine had no effect when locally applied to the hair bundle. How then does a voltage-dependent conductance become activated while the cell is in voltage-clamp? SR errors have both temporal and steady-state consequences. Voltageclamp speed is equal to the product of cell capacitance and uncompensated SR. Average hair cell capacitance of 1273 pf (n¼32) and uncompensated SR of 472 MO (n¼32) gives a clamp speed of 48 ms. Thus, clamp speed is unlikely to be responsible for the activation of the BK or Ca 2+ current, because the conductance is activated on a much Wash TEA mv 80 mv Fig. 2. BK channel activated secondarily to mechanical stimulation near the hair cell s resting potential. Blocking the mechanoelectric transducer (MET) current with curare demonstrates that the MET current is required for the activation of the secondary conductance. (b^d) demonstrate that the second current is a potassium current independent of the MET current as it is sensitive to tetraethyl ammonium (b), reverses with elevated K (c; note expected increase in MET current for K re. Na [11,12]) and is not carried by Cs (d). (e) Nimodipine block of L-type Ca 2+ current, presumably activated by clamp error, prevented subsequent activation of the BK current, demonstrating that the activation was voltage-driven. Vol 16 No 9 21 June
4 H. E. FARRIS AND A. J. RICCI +619 nm 2.8 mm Ca 2+ 5 mm Ca SR error (mv) Fig. 3. Steady-state series resistance (SR) errors are responsible for the activation of Ca 2+ and BK channels. Lowering external Ca 2+ increases the mechanoelectric transducer (MET) current amplitude with a corresponding increase in BK amplitude. (b) shows a direct correlation between the uncompensated SR voltage error and the amplitude of the BK current during MET current activation. The solid line represents the predicted current amplitudes from the BK current^voltage plot shown in Fig.1d, which was measured using voltage steps (n¼4). slower time course (see Fig. 1) and is insensitive to the duration of the stimulus (cells would be clamped within B150 ms and thus only the steady-state error would be predicted after this time). Steady-state SR errors alter the voltage to which a cell is clamped by a value equivalent to the product of the uncompensated SR and the elicited current. In the present set of experiments, steady-state errors are estimated as less than 1.5 mv and thus under most situations would not be expected to create significant errors. However, the sensitivity of the BK conductance is such that it activates over B2 mv, and at rest, a significant portion of the current is activated [13]. As larger MET currents would be expected to result in larger SR error, it is predicted that increasing the MET current amplitude would depolarize the cell further, activating more BK current. By applying low Ca 2+ to the apical hair bundle, the MET current amplitude increased as a result of removal of a Ca 2+ block of the channel [11]. Performing this experiment near the hair cell s resting potential increased the BK current amplitude (Fig. 3a) because of the increased MET current, supporting the conclusion that the MET current amplitude determined the level of BK channel activation, likely due to a steadystate SR error. Additionally, because Ca 2+ entry through the MET channels was reduced during low Ca 2+ application [11], the increased BK current argues against a direct activation from this source of Ca 2+. Further support of a SR artifact is the relationship between the voltage error associated with uncompensated SR and the magnitude of the BK current activated during mechanical stimulation (Fig. 3b). The solid line in Fig. 3b was plotted using currents predicted by the BK activation curve (Fig. 1d gray) for each SR voltage error. DISCUSSION Data presented demonstrate that mechanical stimulation of the sensory hair bundle near the cell s resting potential leads to rapid activation of an L-type Ca 2+ current and subsequent activation of the BK calcium-activated potassium current. These channels are likely the basolateral channels and are not localized near the MET channels. The fact that these channels are activated while in voltage-clamp mode implicates steady-state SR errors as the underlying (b) mechanism. The consequence of this error is that the MET currents cannot be analyzed independently at the cell s resting potential because of contamination by other conductances. Pharmacological antagonists would be required to block the BK or calcium current (Fig. 2) to investigate the MET properties. This solution, however, limits the ability to investigate the physiological response properties of the cell. The implications of this problem are far reaching in that many biophysical investigations of excitable cells rely on voltage-clamp protocols for isolating multiple types of voltage-gated conductances without considering how small SR errors might lead to interaction between conductances. For example, cells often have multiple potassium conductances with different activation kinetics. Voltage errors due to uncompensated SR interacting with the conductance that activates more hyperpolarized will contaminate the properties of the second conductance in a manner that cannot be corrected offline. The example presented here for the hair cell is straightforward in that current through a mechanically gated channel is instigating the error and any voltage changes must be artifacts, as no change occurs in the command voltage. In contrast, in most excitable cells where multiple voltage steps are employed, leading to different voltage errors, the effects on additional conductances will be much more complex. The hair cell example used here illustrates just how SR errors can prevent accurate measures of simultaneously activating conductances. When recording at resting potential to examine the functional interactions between the mechanical and basolateral conductances, the BK conductance exacerbates SR artifacts because of the steepness of its activation curve. CONCLUSION The effect of steady-state SR errors, determined by the SR and the current amplitude, on holding potential can typically be corrected offline, if only a single conductance is involved. Present work demonstrates that when multiple conductances are involved, such errors result in erroneous activation properties being recorded that are uncorrectable offline. REFERENCES 1. Sakmann B, Neher E (eds). Single Channel Recording. New York: Plenum Press; Hudspeth AJ. The cellular basis of hearing: the biophysics of hair cells. Science 1985; 2: Crawford AC, Fettiplace R. The mechanical properties of ciliary bundles of turtle cochlear hair cells. J Physiol (Lond) 1985; 364: Wu YC, Art JJ, Goodman MB, Fettiplace R. A kinetic description of the calcium-activated potassium channel and its application to electrical tuning of hair cells. Prog Biophys Mol Biol 1995; 63: Ricci AJ, Fettiplace R. The effects of calcium buffering and cyclic AMP on mechano-electrical transduction in turtle auditory hair cells. J Physiol (Lond) 1997; 501: Ricci AJ, Wu YC, Fettiplace R. The endogenous calcium buffer and the time course of transducer adaptation in auditory hair cells. J Neurosci 1998; 18: Mienville J, Barker JL, Lange GD. Mechanosensitive properties of BK channels from embryonic rat neuroepithelium. J Membr Biol 1996; 153: Allard B, Couble ML, Magloire H, Bleicher F. Characterization and gene expression of high conductance calcium-activated potassium channels displaying mechanosensitivity in human odontoblasts. J Biol Chem 2000; 275: Vol 16 No 9 21 June 2005
5 SERIES RESISTANCE ERROR AND MULTIPLE CURRENTS 9. Glowatzki E, Ruppersberg JP, Zenner HP, Rusch A. Mechanically and ATP-induced currents of mouse outer hair cells are independent and differentially blocked by d-tubocurarine. Neuropharmacology 1997; 36: Farris HE, LeBlanc CL, Goswami J, Ricci AJ. Probing the pore of the auditory hair cell mechanotransducer channel in turtle. J Physiol 2004; 558: Ricci AJ, Gray-Keller M, Fettiplace R. Tonotopic variations of calcium signalling in turtle auditory hair cells. J Physiol (Lond) 2000; 524 (Pt 2): Naraghi M, Neher E. Linearized buffered Ca2 + diffusion in microdomains and its implications for calculation of [Ca2 + ] at the mouth of a calcium channel. J Neurosci 1997; 17: Lumpkin EA, Hudspeth AJ. Regulation of free Ca2 + concentration in hair-cell stereocilia. J Neurosci 1998; 18: Schnee ME, Ricci AJ. Biophysical and pharmacological characterization of voltage-gated calcium currents in turtle auditory hair cells. J Physiol 2003; 549: Ricci AJ, Fettiplace R. Calcium permeation of the turtle hair cell mechanotransducer channel and its relation to the composition of endolymph [published erratum appears in J Physiol (Lond) 1998 Mar 15;507 (Pt 3):939]. J Physiol (Lond) 1998; 506: Ohmori H. Mechano-electrical transduction currents in isolated vestibular hair cells of the chick. J Physiol (Lond) 1985; 359: Acknowledgements: Funding: NIHRO1DC03896 to A. J.R. and NRSA to H.E.F.The authors thank J. Magee, R.Fettiplace, M. Schnee and B. Kachar for discussions of this work. Vol 16 No 9 21 June
Biophysical and pharmacological characterization of voltagegated calcium currents in turtle auditory hair cells
J Physiol (2003), 549.3, pp. 697 717 DOI: 10.1113/jphysiol.2002.037481 The Physiological Society 2003 www.jphysiol.org Biophysical and pharmacological characterization of voltagegated calcium currents
More informationNeuroscience Center of Excellence College: Case Western Reserve University Kresge Hearing Labs Degree: BA in Chemistry ( )
NAME: ANTHONY RICCI, PH.D. PRESENT POSITION AND ADDRESS: EDUCATION: Assistant Professor High School: Cathedral Prep (NYC) Neuroscience Center of Excellence College: Case Western Reserve University Kresge
More informationThe mammalian cochlea possesses two classes of afferent neurons and two classes of efferent neurons.
1 2 The mammalian cochlea possesses two classes of afferent neurons and two classes of efferent neurons. Type I afferents contact single inner hair cells to provide acoustic analysis as we know it. Type
More informationNeuroscience 201A Problem Set #1, 27 September 2016
Neuroscience 201A Problem Set #1, 27 September 2016 1. The figure above was obtained from a paper on calcium channels expressed by dentate granule cells. The whole-cell Ca 2+ currents in (A) were measured
More informationWhat is the effect on the hair cell if the stereocilia are bent away from the kinocilium?
CASE 44 A 53-year-old man presents to his primary care physician with complaints of feeling like the room is spinning, dizziness, decreased hearing, ringing in the ears, and fullness in both ears. He states
More informationCochlear anatomy, function and pathology I. Professor Dave Furness Keele University
Cochlear anatomy, function and pathology I Professor Dave Furness Keele University d.n.furness@keele.ac.uk Aims and objectives of these lectures Introduction to gross anatomy of the cochlea Focus (1) on
More informationSupplementary Information
Hyperpolarization-activated cation channels inhibit EPSPs by interactions with M-type K + channels Meena S. George, L.F. Abbott, Steven A. Siegelbaum Supplementary Information Part 1: Supplementary Figures
More informationPrestin-Driven Cochlear Amplification Is Not Limited by the Outer Hair Cell Membrane Time Constant
Article Prestin-Driven Cochlear Amplification Is Not Limited by the Outer Hair Cell Membrane Time Constant Stuart L. Johnson, 1 Maryline Beurg, 2 Walter Marcotti, 1, * and Robert Fettiplace 3, * 1 Department
More informationChapter 3: Anatomy and physiology of the sensory auditory mechanism
Chapter 3: Anatomy and physiology of the sensory auditory mechanism Objectives (1) Anatomy of the inner ear Functions of the cochlear and vestibular systems Three compartments within the cochlea and membranes
More informationMechanoelectric Transduction of Adult Inner Hair Cells
1006 The Journal of Neuroscience, January 31, 2007 27(5):1006 1014 Cellular/Molecular Mechanoelectric Transduction of Adult Inner Hair Cells Shuping Jia, 1 Peter Dallos, 2 and David Z. Z. He 1 1 Hair Cell
More informationThe mammalian cochlea possesses two classes of afferent neurons and two classes of efferent neurons.
1 The mammalian cochlea possesses two classes of afferent neurons and two classes of efferent neurons. Type I afferents contact single inner hair cells to provide acoustic analysis as we know it. Type
More informationCalcium-Dependent Synaptic Vesicle Trafficking Underlies Indefatigable Release at the Hair Cell Afferent Fiber Synapse
Article Calcium-Dependent Synaptic Vesicle Trafficking Underlies Indefatigable Release at the Hair Cell Afferent Fiber Synapse Michael E. Schnee, 1 Joseph Santos-Sacchi, 3 Manuel Castellano-Muñoz, 1 Jee-Hyun
More informationWhat does it mean to analyze the frequency components of a sound? A spectrogram such as that shown here is the usual display of frequency components
1 2 3 4 What does it mean to analyze the frequency components of a sound? A spectrogram such as that shown here is the usual display of frequency components as a function of time here during the production
More informationHuman TRPC6 Ion Channel Cell Line
TECHNICAL DATA SHEET ValiScreen Ion Channel Cell Line Caution: For Laboratory Use. A research product for research purposes only Human TRPC6 Ion Channel Cell Line Product No.: AX-012-C Lot No.: 512-548-A
More informationRelation between Membrane Potential Changes and Tension in Barnacle Muscle Fibers
Relation between Membrane Potential Changes and Tension in Barnacle Muscle Fibers CHARLES EDWARDS, SHIKO CHICHIBU, and SUSUMU HAGIWARA From the Department of Physiology, University of Minnesota, Minneapolis,
More informationIs action potential threshold lowest in the axon?
Supplementary information to: Is action potential threshold lowest in the axon? Maarten H. P. Kole & Greg J. Stuart Supplementary Fig. 1 Analysis of action potential (AP) threshold criteria. (a) Example
More informationFast Calcium Currents in Cut Skeletal Muscle Fibres of the Frogs Rana temporaria and Xenopus laevis
Gen. Physiol. Biophys. (1988), 7, 651-656 65! Short communication Fast Calcium Currents in Cut Skeletal Muscle Fibres of the Frogs Rana temporaria and Xenopus laevis M. HENČĽK, D. ZACHAROVÁ and J. ZACHAR
More informationTHE INTERPLAY BETWEEN ACTIVE HAIR BUNDLE MECHANICS AND ELECTROMOTILITY IN THE COCHLEA
451 THE INTERPLAY BETWEEN ACTIVE HAIR BUNDLE MECHANICS AND ELECTROMOTILITY IN THE COCHLEA DÁIBHID Ó MAOILÉIDIGH, FRANK JÜLICHER Max Planck Institute für Physik komplexer Systeme, Nöthnitzerstr. 38, 01187
More informationSample Lab Report 1 from 1. Measuring and Manipulating Passive Membrane Properties
Sample Lab Report 1 from http://www.bio365l.net 1 Abstract Measuring and Manipulating Passive Membrane Properties Biological membranes exhibit the properties of capacitance and resistance, which allow
More informationMechanical Properties of the Cochlea. Reading: Yost Ch. 7
Mechanical Properties of the Cochlea CF Reading: Yost Ch. 7 The Cochlea Inner ear contains auditory and vestibular sensory organs. Cochlea is a coiled tri-partite tube about 35 mm long. Basilar membrane,
More informationDOI: /jphysiol The Physiological Society Rapid Report
Journal of Physiology (2002), 541.3, pp. 665 672 DOI: 10.1113/jphysiol.2002.020503 The Physiological Society 2002 www.jphysiol.org Rapid Report Phosphorylation-dependent differences in the activation properties
More informationSensory Transduction and Adaptation in Inner and Outer Hair Cells of the Mouse Auditory System
J Neurophysiol 98: 3360 3369, 2007. First published October 17, 2007; doi:10.1152/jn.00914.2007. Sensory Transduction and Adaptation in Inner and Outer Hair Cells of the Mouse Auditory System Eric A. Stauffer
More informationNature Methods: doi: /nmeth Supplementary Figure 1. Activity in turtle dorsal cortex is sparse.
Supplementary Figure 1 Activity in turtle dorsal cortex is sparse. a. Probability distribution of firing rates across the population (notice log scale) in our data. The range of firing rates is wide but
More informationTHE COCHLEAR AMPLIFIER: IS IT HAIR BUNDLE MOTION OF OUTER HAIR CELLS?
JOURNAL OF OTOLOGY THE COCHLEAR AMPLIFIER: IS IT HAIR BUNDLE MOTION OF OUTER HAIR CELLS? LI Yi 1, He David Z 2 Abstract Cochlear outer hair cells (OHCs) are involved in a mechanical feedback loop in which
More informationSupplementary Information. Errors in the measurement of voltage activated ion channels. in cell attached patch clamp recordings
Supplementary Information Errors in the measurement of voltage activated ion channels in cell attached patch clamp recordings Stephen R. Williams 1,2 and Christian Wozny 2 1 Queensland Brain Institute,
More informationThe transformation of sound stimuli into electrical signals
The transformation of sound stimuli into electrical signals Robert Fettiplace 2 1 Introduction Our sense of hearing depends on the correct performance of about 15 000 hair cells in each cochlea that serve
More informationBRIEF COMMUNICATION CALCIUM- AND VOLTAGE-ACTIVATED POTASSIUM CHANNELS IN HUMAN MACROPHAGES. frequency of channel opening increased with depolarization
BRIEF COMMUNICATION CALCIUM- AND VOLTAGE-ACTIVATED POTASSIUM CHANNELS IN HUMAN MACROPHAGES ELAINE K. GALLIN Physiology Department, Armed Forces Radiobiology Research Institute, Bethesda, Maryland 20814
More informationNeurophysiology of Nerve Impulses
M52_MARI0000_00_SE_EX03.qxd 8/22/11 2:47 PM Page 358 3 E X E R C I S E Neurophysiology of Nerve Impulses Advance Preparation/Comments Consider doing a short introductory presentation with the following
More informationLidocaine alters the input resistance and evokes neural activity in crayfish sensory neurons
20 Gen. Physiol. Biophys. (2007), 26, 20 26 Lidocaine alters the input resistance and evokes neural activity in crayfish sensory neurons M. B. Keceli and N. Purali Hacettepe University, Medical Faculty,
More informationNEURONS Chapter Neurons: specialized cells of the nervous system 2. Nerves: bundles of neuron axons 3. Nervous systems
NEURONS Chapter 12 Figure 12.1 Neuronal and hormonal signaling both convey information over long distances 1. Nervous system A. nervous tissue B. conducts electrical impulses C. rapid communication 2.
More informationAmeen Alsaras. Ameen Alsaras. Mohd.Khatatbeh
9 Ameen Alsaras Ameen Alsaras Mohd.Khatatbeh Nerve Cells (Neurons) *Remember: The neural cell consists of: 1-Cell body 2-Dendrites 3-Axon which ends as axon terminals. The conduction of impulse through
More informationBIONB/BME/ECE 4910 Neuronal Simulation Assignments 1, Spring 2013
BIONB/BME/ECE 4910 Neuronal Simulation Assignments 1, Spring 2013 Tutorial Assignment Page Due Date Week 1/Assignment 1: Introduction to NIA 1 January 28 The Membrane Tutorial 9 Week 2/Assignment 2: Passive
More informationSupplementary Figure 1. Basic properties of compound EPSPs at
Supplementary Figure 1. Basic properties of compound EPSPs at hippocampal CA3 CA3 cell synapses. (a) EPSPs were evoked by extracellular stimulation of the recurrent collaterals and pharmacologically isolated
More informationNeuroscience 201A (2016) - Problems in Synaptic Physiology
Question 1: The record below in A shows an EPSC recorded from a cerebellar granule cell following stimulation (at the gap in the record) of a mossy fiber input. These responses are, then, evoked by stimulation.
More informationto vibrate the fluid. The ossicles amplify the pressure. The surface area of the oval window is
Page 1 of 6 Question 1: How is the conduction of sound to the cochlea facilitated by the ossicles of the middle ear? Answer: Sound waves traveling through air move the tympanic membrane, which, in turn,
More informationNerve. (2) Duration of the stimulus A certain period can give response. The Strength - Duration Curve
Nerve Neuron (nerve cell) is the structural unit of nervous system. Nerve is formed of large numbers of nerve fibers. Types of nerve fibers Myelinated nerve fibers Covered by myelin sheath interrupted
More informationSEPARATION OF HYDROGEN ION CURRENTS IN INTACT MOLLUSCAN NEURONES
J. exp. Biol. 145, 439-454 (1989) 439 Printed in Great Britain The Company of Biologists Limited 1989 SEPARATION OF HYDROGEN ION CURRENTS IN INTACT MOLLUSCAN NEURONES BY M. P. MAHAUT-SMTTH* Department
More informationAuditory System. Barb Rohrer (SEI )
Auditory System Barb Rohrer (SEI614 2-5086) Sounds arise from mechanical vibration (creating zones of compression and rarefaction; which ripple outwards) Transmitted through gaseous, aqueous or solid medium
More informationThe magnificent outer hair cell of Corti's organ
The magnificent outer hair cell of Corti's organ Yale University J. Santos-Sacchi School of Medicine, New Haver, CT, USA Abstract The outer hair cell is one of two receptor cell types in the organ of Corti.
More informationSystems Neuroscience Oct. 16, Auditory system. http:
Systems Neuroscience Oct. 16, 2018 Auditory system http: www.ini.unizh.ch/~kiper/system_neurosci.html The physics of sound Measuring sound intensity We are sensitive to an enormous range of intensities,
More informationHST 721 Efferent Control Lecture October 2004
HST 721 Efferent Control Lecture October 2004 1 Stapedius Muscle Central Circuitry 2 Hypotheses for MEM Function A. Stapedius 1. Extend Dynamic Range - a gain control system 2. Protect the Inner Ear from
More informationChapter 5 subtitles GABAergic synaptic transmission
CELLULAR NEUROPHYSIOLOGY CONSTANCE HAMMOND Chapter 5 subtitles GABAergic synaptic transmission INTRODUCTION (2:57) In this fifth chapter, you will learn how the binding of the GABA neurotransmitter to
More informationCorrelation between Membrane Potential Responses and Tentacle Movement in the Dinoflagellate Noctiluca miliaris
ZOOLOGICAL SCIENCE 21: 131 138 (2004) 2004 Zoological Society of Japan Correlation between Membrane Potential Responses and Tentacle Movement in the Dinoflagellate Noctiluca miliaris Kazunori Oami* Institute
More informationSimNeuron. Current-and Voltage-Clamp Experiments in Virtual Laboratories. Tutorial
SimNeuron Tutorial 1 Contents: SimNeuron Current-and Voltage-Clamp Experiments in Virtual Laboratories 1. Lab Design 2. Basic CURRENT-CLAMP Experiments Tutorial 2.1 Action Potential, Conductances and Currents.
More informationSalamanca Study Abroad Program: Neurobiology of Hearing
Salamanca Study Abroad Program: Neurobiology of Hearing Synaptics and the auditory nerve R. Keith Duncan University of Michigan rkduncan@umich.edu Review Resources Reviews: Safieddine et al., 2012, The
More informationSUPPLEMENTARY INFORMATION. Supplementary Figure 1
SUPPLEMENTARY INFORMATION Supplementary Figure 1 The supralinear events evoked in CA3 pyramidal cells fulfill the criteria for NMDA spikes, exhibiting a threshold, sensitivity to NMDAR blockade, and all-or-none
More informationNS200: In vitro electrophysiology section September 11th, 2013
NS200: In vitro electrophysiology section September 11th, 2013 Quynh Anh Nguyen, 4 th Year Nicoll Lab quynhanh.nguyen@ucsf.edu N276 Genentech Hall, Mission Bay Outline Part I: Theory Review of circuit
More informationNeurons of the Bed Nucleus of the Stria Terminalis (BNST)
Neurons of the Bed Nucleus of the Stria Terminalis (BNST) Electrophysiological Properties and Their Response to Serotonin DONALD G. RAINNIE a Harvard Medical School and Department of Psychiatry, Brockton
More informationInteraction of Scorpion -Toxins with Cardiac Sodium Channels: Binding Properties and Enhancement of Slow Inactivation
Interaction of Scorpion -Toxins with Cardiac Sodium Channels: Binding Properties and Enhancement of Slow Inactivation Haijun Chen and Stefan H. Heinemann From the Research Unit Molecular and Cellular Biophysics,
More informationQuestions. Question 1!
Questions Question 1 In a laboratory, scientists often study neurons in isolation, outside of a living creature, in a dish. In this setting, one can have a good deal of control over the local ionic environment
More informationTetrapentylammonium block of chloramine-t and veratridine modi ed rat brain type IIA sodium channels
British Journal of Pharmacology (2001) 132, 1755 ± 1760 ã 2001 Nature Publishing Group All rights reserved 0007 ± 1188/01 $15.00 Tetrapentylammonium block of chloramine-t and veratridine modi ed rat brain
More informationHST 721 Lecture 4: Mechanics, electromotility and the cochlear amplifier
HST 721 Lecture 4: Mechanics, electromotility and the cochlear amplifier 1 Cochlear Mechanics: Measures of Basilar Membrane Motion 2 Cochlear Mechanics: Measures of Basilar Membrane Motion Bekesy s experiments
More informationTmc1 is necessary for normal functional maturation and survival of inner and outer hair cells in the mouse cochlea
J Physiol 574.3 (2006) pp 677 698 677 Tmc1 is necessary for normal functional maturation and survival of inner and outer hair cells in the mouse cochlea Walter Marcotti 1, Alexandra Erven 2, Stuart L.
More informationSodium and Gating Current Time Shifts Resulting from Changes in Initial Conditions
Sodium and Gating Current Time Shifts Resulting from Changes in Initial Conditions ROBERT E. TAYLOR and FRANCISCO BEZANILLA From the Laboratory of Biophysics, National Institute of Neurological and Communicative
More informationThe lagena a presumptive vestibular epithelium found at the low frequency end of the auditory end organ, is absent from mammals.
1 Structure and Function of the Auditory and Vestibular System 1 Increasing elaboration of the auditory end organ during evolution. Increasing length of the cochlea associated with higher frequency hearing.
More informationVestibular physiology
Vestibular physiology 2017 Utricle A flat epithelium: horizontal in the upright head Utricle Hair cells: no axons hair cells Utricle Hair cells synapse onto 8th nerve afferents. 8th nerve afferents Hair
More informationElectrophysiology. General Neurophysiology. Action Potentials
5 Electrophysiology Cochlear implants should aim to reproduce the coding of sound in the auditory system as closely as possible, for best sound perception. The cochlear implant is in part the result of
More informationSUPPLEMENTARY INFORMATION
doi: 1.138/nature588 SUPPLEMENTARY INFORMATION Supplemental Information Sensory neuron sodium channel Na v 1.8 is essential for pain at cold temperatures Katharina Zimmermann*, Andreas Leffler*, Alexandru
More informationFiring Pattern Formation by Transient Calcium Current in Model Motoneuron
Nonlinear Analysis: Modelling and Control, Vilnius, IMI, 2000, No 5 Lithuanian Association of Nonlinear Analysts, 2000 Firing Pattern Formation by Transient Calcium Current in Model Motoneuron N. Svirskienė,
More informationTemporal Contrast Adaptation in Salamander Bipolar Cells
The Journal of Neuroscience, December 1, 2001, 21(23):9445 9454 Temporal Contrast Adaptation in Salamander Bipolar Cells Fred Rieke Department of Physiology and Biophysics, University of Washington, Seattle,
More informationIntramembrane Charge Movement and L-Type Calcium Current in Skeletal Muscle Fibers Isolated from Control and mdx Mice
Biophysical Journal Volume 84 January 2003 251 265 251 Intramembrane Charge Movement and L-Type Calcium Current in Skeletal Muscle Fibers Isolated from Control and mdx Mice C. Collet,* L. Csernoch, y and
More informationTHE EFFECT OF ZINC ON CALCIUM AND HYDROGEN ION CURRENTS IN INTACT SNAIL NEURONES BY M. P. MAHAUT-SMITH*
/. exp. Biol. 145, 455-464 (1989) 455 Printed in Great Britain The Company of Biologists Limited 1989 THE EFFECT OF ZINC ON CALCIUM AND HYDROGEN ION CURRENTS IN INTACT SNAIL NEURONES BY M. P. MAHAUT-SMITH*
More information9.01 Introduction to Neuroscience Fall 2007
MIT OpenCourseWare http://ocw.mit.edu 9.01 Introduction to Neuroscience Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 9.01 Recitation (R02)
More informationSupporting Online Material for
www.sciencemag.org/cgi/content/full/317/5841/183/dc1 Supporting Online Material for Astrocytes Potentiate Transmitter Release at Single Hippocampal Synapses Gertrudis Perea and Alfonso Araque* *To whom
More informationabolished, the transient outward chloride current normally activated by membrane
J. Physiol. (1984), 357, pp. 173-183 173 With 7 text-ftgure8 Printed in Great Britain CHLORIDE CURRENT INDUCED BY INJECTION OF CLCIUM INTO XENOPUS OOCYTES BY R. MILEDI ND I. PRKER From the Department of
More informationSo now to The Ear. Drawings from Max Brodel, an Austrian artist who came to Johns Hopkins in the 1920s. My point in showing this figure is to
So now to The Ear. Drawings from Max Brodel, an Austrian artist who came to Johns Hopkins in the 1920s. My point in showing this figure is to emphasize the intricate and well-protected structure of the
More informationDifferences in ionic currents between canine myocardial and Purkinje cells
ORIGINAL RESEARCH Physiological Reports ISSN 2051-817X Differences in ionic currents between canine myocardial and Purkinje cells Mario Vassalle & Leonardo Bocchi Department of Physiology and Pharmacology,
More informationDynamics of calcium regulation of chloride currents in Xenopus oocytes
Dynamics of calcium regulation of chloride currents in Xenopus oocytes AKINORI KURUMA AND H. CRISS HARTZELL Department of Cell Biology, Emory University School of Medicine, Atlanta, Georgia 30322-3030
More information1- Cochlear Impedance Telemetry
INTRA-OPERATIVE COCHLEAR IMPLANT MEASURMENTS SAMIR ASAL M.D 1- Cochlear Impedance Telemetry 1 Cochlear implants used presently permit bi--directional communication between the inner and outer parts of
More informationAuditory System Feedback
Feedback Auditory System Feedback Using all or a portion of the information from the output of a system to regulate or control the processes or inputs in order to modify the output. Central control of
More informationOpen- and closed-state fast inactivation in sodium channels Differential effects of a site-3 anemone toxin
Research paper Channels 5:1, 1-16; January/February 2011; 2011 Landes Bioscience research paper Open- and closed-state fast inactivation in sodium channels Differential effects of a site-3 anemone toxin
More informationSUPPLEMENTARY INFORMATION
Supplementary Figure 1. Normal AMPAR-mediated fepsp input-output curve in CA3-Psen cdko mice. Input-output curves, which are plotted initial slopes of the evoked fepsp as function of the amplitude of the
More informationQuantal Analysis Problems
Quantal Analysis Problems 1. Imagine you had performed an experiment on a muscle preparation from a Drosophila larva. In this experiment, intracellular recordings were made from an identified muscle fibre,
More informationProperties of single voltage-dependent K + channels in dendrites of CA1 pyramidal neurones of rat hippocampus
J Physiol 559.1 (24) pp 187 23 187 Properties of single voltage-dependent K + channels in dendrites of CA1 pyramidal neurones of rat hippocampus Xixi Chen and Daniel Johnston Department of Neuroscience,
More informationAction Potentials Are Required for the Lateral Transmission of Glycinergic Transient Inhibition in the Amphibian Retina
The Journal of Neuroscience, March 15, 1998, 18(6):2301 2308 Action Potentials Are Required for the Lateral Transmission of Glycinergic Transient Inhibition in the Amphibian Retina Paul B. Cook, 1 Peter
More informationMembrane Structure, Resting membrane potential, Action potential. Biophysics seminar
Membrane Structure, Resting membrane potential, Action potential Biophysics seminar 09.09.2013. Membrane structure Biological membranes consists of lipids and proteins to bind with non-covalent bond. Phospholipids
More informationNeurobiology Biomed 509 Sensory transduction References: Luo , ( ), , M4.1, M6.2
Neurobiology Biomed 509 Sensory transduction References: Luo 4.1 4.8, (4.9 4.23), 6.22 6.24, M4.1, M6.2 I. Transduction The role of sensory systems is to convert external energy into electrical signals
More informationStructure, Energy Transmission and Function. Gross Anatomy. Structure, Function & Process. External Auditory Meatus or Canal (EAM, EAC) Outer Ear
Gross Anatomy Structure, Energy Transmission and Function IE N O ME 1 Structure, Function & Process 4 External Auditory Meatus or Canal (EAM, EAC) Outer third is cartilaginous Inner 2/3 is osseous Junction
More informationCellular Neurobiology BIPN 140 Fall 2016 Problem Set #1
Cellular Neurobiology BIPN 140 Fall 2016 Problem Set #1 1. (Antonia) You are studying a neuron with an arterial cuff under a microscope. However, you knock over a bunch of chemicals onto the plate because
More informationLecture 6 Hearing 1. Raghav Rajan Bio 354 Neurobiology 2 January 28th All lecture material from the following links unless otherwise mentioned:
Lecture 6 Hearing 1 All lecture material from the following links unless otherwise mentioned: 1. http://wws.weizmann.ac.il/neurobiology/labs/ulanovsky/sites/neurobiology.labs.ulanovsky/files/uploads/purves_ch12_ch13_hearing
More informationDrugs, Drug Targets and You: Patch Clamping
Drugs, Drug Targets and You: Patch Clamping Introduction To elucidate how an ion channel operates, one needs to examine the factors that influence its opening and closing as well as measure the resulting
More informationThe acquisition of mechano-electrical transducer current adaptation in auditory hair cells requires myosin VI
The acquisition of mechano-electrical transducer current adaptation in auditory hair cells requires myosin VI Article (Published Version) Marcotti, Walter, Corns, Laura F, Goodyear, Richard J, Rzadzinska,
More informationThe Structure and Function of the Auditory Nerve
The Structure and Function of the Auditory Nerve Brad May Structure and Function of the Auditory and Vestibular Systems (BME 580.626) September 21, 2010 1 Objectives Anatomy Basic response patterns Frequency
More informationDifferential effects of Zn 2+ on activation, deactivation, and inactivation kinetics in neuronal voltage-gated Na + channels
DOI 10.1007/s00424-011-0972-z ION CHANNELS, RECEPTORS AND TRANSPORTERS Differential effects of Zn 2+ on activation, deactivation, and inactivation kinetics in neuronal voltage-gated Na + channels Maximiliano
More informationPLATEAU-GENERATING NERVE CELLS IN HELIX: PROPERTIES OF THE REPOLARIZING VOLTAGE-GATED AND Ca 2+ -ACTIVATED POTASSIUM CURRENTS
J. exp. Biol. 152, 211-241 (1990) 211 Printed in Great Britain The Company of Biologists Limited 1990 PLATEAU-GENERATING NERVE CELLS IN HELIX: PROPERTIES OF THE REPOLARIZING VOLTAGE-GATED AND Ca 2+ -ACTIVATED
More informationWhat is Anatomy and Physiology?
Introduction BI 212 BI 213 BI 211 Ecosystems Organs / organ systems Cells Organelles Communities Tissues Molecules Populations Organisms Campbell et al. Figure 1.4 Introduction What is Anatomy and Physiology?
More informationIntro. Comp. NeuroSci. Ch. 9 October 4, The threshold and channel memory
9.7.4 The threshold and channel memory The action potential has a threshold. In figure the area around threshold is expanded (rectangle). A current injection that does not reach the threshold does not
More informationNeurons. Pyramidal neurons in mouse cerebral cortex expressing green fluorescent protein. The red staining indicates GABAergic interneurons.
Neurons Pyramidal neurons in mouse cerebral cortex expressing green fluorescent protein. The red staining indicates GABAergic interneurons. MBL, Woods Hole R Cheung MSc Bioelectronics: PGEE11106 1 Neuron
More informationMechanism of Spontaneous Firing in Dorsomedial Suprachiasmatic Nucleus Neurons
The Journal of Neuroscience, September 15, 2004 24(37):7985 7998 7985 Cellular/Molecular Mechanism of Spontaneous Firing in Dorsomedial Suprachiasmatic Nucleus Neurons Alexander C. Jackson, Gui Lan Yao,
More informationFall Name Student ID
Name Student ID PART 1: Matching. Match the organelle to its function (11 points) 1.Proton motive force 2. Fluid Mosiac 3. Oxidative Phosphorylation 4. Pyruvate dehydrogenase 5. Electrochemical Force 6.
More informationNature Biotechnology: doi: /nbt Supplementary Figure 1. Analysis of hair bundle morphology in Ush1c c.216g>a mice at P18 by SEM.
Supplementary Figure 1 Analysis of hair bundle morphology in Ush1c c.216g>a mice at P18 by SEM. (a-c) Heterozygous c.216ga mice displayed normal hair bundle morphology at P18. (d-i) Disorganized hair bundles
More informationIvy/Neurogliaform Interneurons Coordinate Activity in the Neurogenic Niche
Ivy/Neurogliaform Interneurons Coordinate Activity in the Neurogenic Niche Sean J. Markwardt, Cristina V. Dieni, Jacques I. Wadiche & Linda Overstreet-Wadiche Supplementary Methods. Animals We used hemizygous
More informationThursday, January 22, Nerve impulse
Nerve impulse Transmembrane Potential caused by ions moving through cell membrane at different rates Two main ions of concern Na + - Sodium K + - potassium Cell membrane not freely permeable therefore
More informationK+ current (1K(Ca)), elicited by intracellular Ca2+ injection, reverses near -65 mv,
J. Physiol. (1985), 362, pp. 131-160 131 With 14 text-figures Printed in Great Britain CALCIUM-INDUCED INACTIVATION OF CALCIUM CURRENT CAUSES THE INTER-BURST HYPERPOLARIZATION OF APL YSIA BURSTING NEURONES
More informationSTRUCTURAL ELEMENTS OF THE NERVOUS SYSTEM
STRUCTURAL ELEMENTS OF THE NERVOUS SYSTEM STRUCTURE AND MAINTENANCE OF NEURONS (a) (b) Dendrites Cell body Initial segment collateral terminals (a) Diagrammatic representation of a neuron. The break in
More informationCOGS 107B Week 2. Hyun Ji Friday 4:00-4:50pm
COGS 107B Week 2 Hyun Ji Friday 4:00-4:50pm Lecture 3: Proprioception Principles: The Neuron Doctrine and The Law of Dynamic Polarization Proprioception Joint-protecting reflexes (ex. Knee jerk reflex)
More informationCellular Messengers. Intracellular Communication
Cellular Messengers Intracellular Communication Most common cellular communication is done through extracellular chemical messengers: Ligands Specific in function 1. Paracrines Local messengers (neighboring
More informationSupralinear increase of recurrent inhibition during sparse activity in the somatosensory cortex
Supralinear increase of recurrent inhibition during sparse activity in the somatosensory cortex Christoph Kapfer 1,2, Lindsey L Glickfeld 1,3, Bassam V Atallah 1,3 & Massimo Scanziani 1 The balance between
More informationSupporting Online Material for
www.sciencemag.org/cgi/content/full/312/5779/1533/dc1 Supporting Online Material for Long-Term Potentiation of Neuron-Glia Synapses Mediated by Ca 2+ - Permeable AMPA Receptors Woo-Ping Ge, Xiu-Juan Yang,
More informationGeneration of Twitch Tension in Frog Atrial Fibers by Na/Ca Exchange
Gen. Physiol. Biophys. (1988), 7, 29 38 29 Generation of Twitch Tension in Frog Atrial Fibers by Na/Ca Exchange A. K. FILIPPOV 1, S. M. TERTISHNIKOVA 1, T. I. BOUQUET', V. I. POROTIKOV 1 and V. I. ILYIN
More information