Voltage Clamp Experiments in Striated Muscle Fibres
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model has had a stimulus protocol added to it to allow simulation of action potentials. Unfortunately, the details of the stimulation defined in the original paper are not known and as such, the parameters of the stimulus (magnitude, duration, dimensions,) may not be appropriate. Currently, however, the model runs in PCEnv and is able to simulate a train of action potentials. COR will not currently run this model.
ValidateCellML detects unit inconsistencies within this model.
Model Structure
In this 1970 publication, Adrian, Chandler and Hodgkin developed a mathematical model of an action potential in frog striated muscle. Their model was based on data from voltage-clamp experiments, and they include descriptions of three currents:
INa
, a fast inward sodium current;
IK
, a slow outward potassium current; and
IL
, a leak current.
The style of the model equations is based on the The Hodgkin-Huxley Squid Axon Model, 1952. However, the authors acknowledge that the situation in striated muscle is complicated by tubular resistance and capacity. The transverse tubular system which exists in striated myocytes is represented in the model by a linear resistance and capacity in series.
Electrical circuit describing the current across the cell membrane
A schematic cell diagram describing the current flows across the cell membrane that are captured in the Hodgkin Huxley model.
The model has been described here in CellML (the raw CellML description of the Adrian et al. 1970 model can be downloaded in various formats as described in ).
As the paper was published in 1970, there is no online version. However, the complete reference is cited below:
Voltage Clamp Experiments in Striated Muscle Fibres. R. H. Adrian, W. K. Chandler, and A. L. Hodgkin. Journal of Physiology, (1970), 208, pp 607-644. PubMed ID: 5499787
In order to complete the model and run simulations, some parameters were also taken from the following paper:
Reconstruction of the Action Potential of Frog Sartorius Muscle. R. H. Adrian and L. D. Peachey. Journal of Physiology, (1973), 235, pp 103-131. PubMed ID: 4778131
$\mathrm{IStimC}=\mathrm{Istim}$
$\mathrm{AmC}=\mathrm{Am}$
$\mathrm{Istim}=\begin{cases}\mathrm{IstimAmplitude} & \text{if $(t\ge \mathrm{IstimStart})\land (t\le \mathrm{IstimEnd})\land (t-\mathrm{IstimStart}-\lfloor \frac{t-\mathrm{IstimStart}}{\mathrm{IstimPeriod}}\rfloor \mathrm{IstimPeriod}\le \mathrm{IstimPulseDuration})$}\\ 0 & \text{otherwise}\end{cases}$
$\frac{d \mathrm{Vm}}{d t}=\frac{\mathrm{Istim}-\mathrm{INa}+\mathrm{IK}+\mathrm{IL}+\mathrm{IT}}{\mathrm{Cm}}$
$\mathrm{INa}=\mathrm{gNa\_max}mmmh(\mathrm{Vm}-\mathrm{ENa})$
$\mathrm{alpha\_m}=\frac{\mathrm{alpha\_m\_max}(\mathrm{Vm}-\mathrm{Em})}{1.0-e^{\frac{\mathrm{Em}-\mathrm{Vm}}{\mathrm{v\_alpha\_m}}}}\mathrm{beta\_m}=\mathrm{beta\_m\_max}e^{\frac{\mathrm{Em}-\mathrm{Vm}}{\mathrm{v\_beta\_m}}}\frac{d m}{d t}=\mathrm{alpha\_m}(1.0-m)-\mathrm{beta\_m}m$
$\mathrm{alpha\_h}=\mathrm{alpha\_h\_max}e^{\frac{\mathrm{Eh}-\mathrm{Vm}}{\mathrm{v\_alpha\_h}}}\mathrm{beta\_h}=\frac{\mathrm{beta\_h\_max}}{1.0+e^{\frac{\mathrm{Eh}-\mathrm{Vm}}{\mathrm{v\_beta\_h}}}}\frac{d h}{d t}=\mathrm{alpha\_h}(1.0-h)-\mathrm{beta\_h}h$
$\mathrm{IK}=\mathrm{gK\_max}nnnn(\mathrm{Vm}-\mathrm{EK})$
$\mathrm{alpha\_n}=\frac{\mathrm{alpha\_n\_max}(\mathrm{Vm}-\mathrm{En})}{1.0-e^{\frac{\mathrm{En}-\mathrm{Vm}}{\mathrm{v\_alpha\_n}}}}\mathrm{beta\_n}=\mathrm{beta\_n\_max}e^{\frac{\mathrm{En}-\mathrm{Vm}}{\mathrm{v\_beta\_n}}}\frac{d n}{d t}=\mathrm{alpha\_n}(1.0-n)-\mathrm{beta\_n}n$
$\mathrm{IL}=\mathrm{gL\_max}(\mathrm{Vm}-\mathrm{EL})$
$\mathrm{IT}=\frac{\mathrm{Vm}-\mathrm{Vt}}{\mathrm{Rs}}$
$\frac{d \mathrm{Vt}}{d t}=\frac{\mathrm{Vm}-\mathrm{Vt}}{\mathrm{Rs}\mathrm{Ct}}$
Journal of Physiology
The T-tubular current component contains the differential equations
governing the current that occurs as the result of a potential difference
between the cell membrane and the T-tubular system.
The T-tubular Vt component calculates the voltage in the membrane
of the T-tubular system.
Bioengineering Institute, The University of Auckland
James Lawson
The leak current component contains the differential equations
governing the time independent current leakage from the cell.
2009-05-05T11:14:24+12:00
The potassium current component contains the differential equations
governing this voltage and time dependent outward current.
10000
100000
0.001
bdf15
Skeletal Myocyte
The Adrian-Chandler-Hodgkin Model of the Skeletal Myocyte Action
Potential, 1970
Mammalia
keyword
cardiac
electrophysiology
myofilament mechanics
skeletal muscle
L
Peachey
D
The definition of the voltage-dependent activation gating
kinetics for the sodium ion channel (the m gate).
2007-11-12T12:20:00+13:00
This model has had a stimulus protocol added to it to allow simulation of action potentials. Unfortunately, the details of the stimulation defined in the original paper are not known and as such, the parameters of the stimulus (magnitude, duration, dimensions,) may not be appropriate. Currently, however, the model runs in PCEnv 0.2 and is able to simulate a train of action potentials. COR will not currently run this model.
James
Lawson
Richard
m.buist@auckland.ac.nz
A stimulus protocol (with the same parameters as the Beeler Reuter 97, as the required parameters are unknown) has been added to this model to allow simulation of action potentials.
A
Hodgkin
L
5499787
1973-01-01
Reconstruction of the action potential of frog sartorius muscle
235
103
131
R
Adrian
H
Altered documentation such that the semicolons are now with the correct comments in the list.
This component contains the differential equations
governing the time dependence of the n gate of the potassium channel.
Martin
Buist
L
Voltage clamp experiments in striated muscle fibres
208
607
644
1970-01-01
The sodium current component contains the differential equations
governing the influx of sodium ions through the cell surface
membrane into the cell.
Martin Buist
This component defines the calculation of dV/dt, the ordinary differential
equation for the transmembrane potential.
4778131
R
Adrian
H
2003-10-29T00:00:00+00:00
W
Chandler
D
2007-06-11T13:17:56+12:00
Catherine
Lloyd
May
Journal of Physiology
Updated curation status
This component defines the variables that are externally set and
passed into the model along with the variables within the model that
are to be available externally.
The University of Auckland
Bioengineering Institute
This is the CellML description of Adrian, Chandler and Hodgkin's mathematical model of membrane action potentials of mammalian striated skeletal muscle. It describes four ionic currents and uses Hodgkin-Huxley type equations.
The voltage-dependent inactivation gate for the sodium channel (the
h gate).
James
Lawson
Richard