First published online August 4, 2005
Journal of Experimental Biology 208, 3055-3063 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01755
Computer simulations of high-pass filtering in zebrafish larval muscle fibres
Steven D. Buckingham1 and
Declan W. Ali2,*
1 MRC Functional Genetics Unit, Department of Human Anatomy and Genetics,
University of Oxford, South Parks Road, Oxford, OX1 3QX, UK
2 University of Alberta, Department of Biological Sciences, Biological
Sciences Building, Edmonton, Alberta, Canada, T6G 2E9
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Fig. 1. Potassium currents (IK) and sodium currents
(INa) generated in a voltage-clamp simulation. (A) The
simulated potassium currents are those obtained during 100 ms depolarizations
from a holding potential of –90 mV to a range of potentials from
–70 to +60 mV in 10 mV steps. (B) The simulated sodium currents were
those obtained in response to a 1 ms depolarization to a range of potentials
from –70 to + 70 mV in 10 mV steps.
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Fig. 2. Simulated current-clamp experiments in which the model muscle fibre was
depolarized from resting potentials of around –70 mV. (A) The
depolarizing current was increased from 1 nA to 10 nA in 1 nA steps. In no
trace is repetitive discharging observed. (B) Simulated spikes elicited by a 3
nA depolarization immediately following a 10 ms prehyperpolarizing pulse
ranging from 0 (red trace) to 0.6 nA (in 0.1 nA steps; black traces) are
progressively reduced in amplitude.
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Fig. 3. Simulated muscle fibres are able to support spikes in response to rapid
depolarizations (A; black trace), which is enhanced when successive stimuli
are separated by a hyperpolarizing interval (A; red trace). (B) The rate of
recovery of the graded action potentials in response to the second
depolarization is faster when the cell is hyperpolarized by injecting 0.7 nA
of current during the interstimulus interval (red traces) than when no current
is injected (black traces). (C) A recording of the value of the sodium
inactivation variable, h, between two depolarizing stimuli separated
by an interval of 1 ms shows that h recovers more effectively when 2
nA of hyperpolarizing current is injected during the interstimulus interval
(red trace) compared with `control' (black trace). (D) If, however, the value
of h between the paired stimuli against an interpulse potential of
–70 mV is adjusted to the value that is recorded at the same time but
against an interpulse potential of –90 mV (red trace), the recovery of
the second action potential matches that obtained against a resting potential
of –90 mV.
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Fig. 4. Mapping of firing properties of the simulated zebrafish muscle onto the
V50s of activation and inactivation of the sodium current.
In each graph, the V50,act is plotted against the
V50,inact. This was repeated for stimuli of 0.5, 1, 2 and
4 nA (left to right in each row). The values obtained from in situ
recordings (Buckingham and Ali,
2004 ) are indicated with an x. (A) When the time constant of
inactivation is set to those values recorded experimentally (along with those
estimated for missing values of membrane potential; see Results), increasing
the amplitude of the depolarizing stimulus increases the parameter space over
which single spiking is observed but does not greatly increase the area over
which repetitive firing is observed between the 1 nA and 4 nA stimuli. (B) If
the values of the time constant of inactivation at every membrane potential
are doubled (representing a slowing of inactivation), the area of parameter
space over which repetitive firing is obtained increases and approaches the
parameter set observed in situ, but it is not affected by increasing
stimulus amplitude (left to right). Repetitive firing was defined as the
occurrence of more than one spike. Black areas, no spikes obtained; red areas,
once-only firing; green areas, repetitive firing.
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Fig. 5. Mapping of firing properties of the simulated zebrafish muscle cell onto
the maximum conductance densities of the potassium and sodium currents at
different rates of inactivation. The values obtained from in situ
recordings (Buckingham and Ali,
2004) are indicated with an x. (A) At the control rate of
inactivation, repetitive firing was not observed, even when the level of
sodium current is multiplied more than 10-fold, and is little affected by the
level of the potassium current. (B) When the values of the time constant of
inactivation at all membrane potentials are multiplied by 2, the range of
values over which repetitive firing is obtained is greatly increased. (C)
Multiplying the values of the time constant by 4 increases the area still
further. Black areas, no spikes obtained; red areas, once-only firing; green
areas, repetitive firing.
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Fig. 6. The steady-state activation and inactivation properties of the sodium
currents required to produce repetitive firing in the model (dotted lines) are
compared with those reported in situ (solid lines). The
V50s of activation and inactivation required were taken as
the coordinates in Fig. 4 of
the point that represents the minimum distance from the values obtained in
situ. Note that for repetitive firing to occur, there must be a
simultaneous right shift in inactivation and a left shift in activation.
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© The Company of Biologists Ltd 2005
