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concentration dependent transition for kinetic schemes A concentration dependent transition for Kinetic Scheme channels. The rate is expressed as the dissociation constant, Kd (mM) and the off-lifetime, reciprocal of the off-rate, tau-r (ms).
This is generally used as a subcomponent of the KSChannelEditor, and is fully documented there.
time dependent transition in a kinetic scheme A time dependent state transition in a kinetic scheme. The transition rates are specified as the forward and reverse lifetimes tau-f and tau-r (ms). These are the reciprocals of the transition rates.
A single state of a Kinetic Scheme channel. A single state of a Kinetic Scheme channel. Its only parameter is the conductance of the state in units of ions per ms per mV for relative concentrations of 1:10 mM of its permeant ion at 0 mV. The quantities posx and posy are its position in the drawing of the state diagram and have no significance for the behavior of the channel.
Channels based on kinetic schemes, _CMLINK(channel, KSChannel, KSChannel), are defined by the possible transitions between different states of the channel. The state diagram can be constructed by tearing off states or transitions and sticking them together. The transitions rates may be constant or depend on the voltage, or agent concentrations, and can be controlled with the corresponding voltage dependence or binding curves. The state diagram is constructed by dragging states and transitions from the top and sticking them together. Transitions stick to states, but not the converse. A transition can be lifted off with the right mouse button. See the _CMLINK(standard, CcmbNetEditor, CcmbNetEditor) for general properties of node-and-link components. Each state has its own relative conductance which appears near the middle on the right when the state is highlighted and can be set with the slider. State colors can be set from the menu on the state button when a state is highlighted. There are five types of transitions, from the left in the top of the main window: 1) time and voltage dependent, with the expression parameterized by the forward and reverse rates at zero membrane potential, effective charge, asymmetry and saturation. This provides a smooth transition between voltage dependent and independent rates. 2) Time dependent only, defined by forward and reverse lifetimes for this transition (nothing to do with lifetimes of the channel). 3) Voltage dependent, following Borg-Graham, parameterized as the effective gating charge (charge times the fraction of the field it moves through) _TT(z), moving between two wells which are of the same energy at a membrane potential _TT(V-half). The peak of the activation barrier is a fraction _TT(gamma) of the way between the two wells. The rate is set through its reciprocals, the characteristic transition time _TT(tau-x), and saturates at some peak rate, the reciprocal of _TT(tau-m). 4) Agent dependent, indicated by a + sign above the binding transition. The rates are defined by the dissociation constant _TT(K-d) and the off rate _TT(tau-r). 5) Multiplicative: the transition must contain a pointer to some other transition in the system and constant multipliers for the forward and reverse reaction. Transition parameters can be set by dragging the corresponding curves in the lower graphs, or with the sliders. When values are changed with the curves, the sliders do not continuously update but will do so if you move the mouse over them. The transitions of types 1 and 3 are formally equivalent, except for _TT(z = 0) when 3 breaks down, and the lower two displays are identical. Indeed, internally, reactions specified as type 3 are converted to type 1. A kinetic scheme may contain multiple gating complexes simply by defining disjoint blocks on the diagram. In this case, the relative conductance of the channel is the product of the relative conductances of all the complexes on it. Each state has a field _TT(Nserial) which sets the number of identical repeats of the complex to which it belongs. It is sufficient to set _TT(Nserial) for just one of the states on any complex to duplicate the whole complex.
kinetic scheme transition defined in terms of multiples of the rates in another transition A kinetic scheme transition that takes most its parameters from another transition but scales the forward and reverse rates by locally specified quantities.
Stochastic simulation of a set of kinetic scheme channels. You can vary the membrane potential as the simulation is running and the display shows how the state of each channel evolves. The total conductance and voltage history are also shown. The target channel is set with the menu at the bottom left. Other variables govern the number of channels, the membrane potential, and timestep. The _TT(replayRate) sets the rate of the simulation in ms of simulated time per second of real time. The _TT(frameRate) sets the preferred number of screen updates per second. More updates make for a smoother simulation, but may delay the calculation. Each channel is represented by a single bar with the evolution of the state of the channel indicated by the colors of the states, as in the _CMLINK(channel, KSChannelEditor, channel editor). Where the channel is composed of multiple serial gating complexes, the bar is divided into slices for each complex. Above the channel display is the normalized conductance in blue, and voltage history in black. The voltage may be changed as the simulation is progressing. Other parameter changes cause it to be restarted. In continuous mode, the display wraps continually across the window. If not in continuous mode, it stops when one screen is full and waits for a parameter to be changed before restarting.
a channel defined as Kinetic Scheme - state diagram and transition rates A simple kinetic scheme channel, comprising a list of states (KSState), a list of transition rates between them (KSRate), and a conductance law (IVLaw). The channel can be treated either as single channel which evolves stochastically, or in the ensemble limit as deterministic conductance. There may be more than one gating complex: if the states fall into separate groups with no transitions linking them, then these groups are assumed to represent independent serial gating complexes and the channel conductance is the product of the maximal conductance in the IVLaw with the product of the open fractions of the individual gating complexes. See the dedicated user interface for information on how to construct KSChannel objects.
voltage dependent transition in a kinetic scheme A voltage dependent rate for a state transition in a kinetic scheme. It follows the same form as Borg-Graham's modified Hodgkin-Huxley equations. The equivalent gating charge is z, half potential, Vhalf (mV), and position of the activation particle within the transit of the gating particle is gamma: 0 < gamma < 1. The transition rates are expressed through their reciprocals, the characteristic timescales, tau-x near Vhalf, and tau-m (tau-m << tau-x), the saturation timescale for extreme potentials. The transition is computed from the forward and reverse rates, alpha and beta, given by: _SCODE private final double alpha (double v) { double a = Math.exp (ebykt * (gamma) * z * (v - Vhalf)) / tau_x; a = 1. / (1. / a + tau_m); return a; } private final double beta (double v) { double b = Math.exp (-ebykt * (1. - gamma) * z * (v - Vhalf)) / tau_x; b = 1. / (1. / b + tau_m); return b; } _ECODE where ebykt = e / kT, about 0.042
A set of ion channels for use in active membranes. The set defines, for each included channel, the average membrane density in channels per square micron. Each channel is an instance of the _GUIDE(KSChannel, KSChannel) component (Kinetic Scheme Channel) which is a generalization of Hodgkin-Huxley style channels to multiple states and multiple gating complexes, but restricted to Boltzmann equations for the transition probabilities between states. The channel set is constructed as a special case of a _GLOBALGUIDE(standard, QuantifiedList, QuantifiedList) and its interface is the _GLOBALGUIDE(standard, QuantifiedListEditor, standard interface) for such lists.
Stochastic simulation of a set of kinetic scheme channels.
superclass of all possible transitions in kinetic schemes The superclass of all possible transitions in kinetic schemes. At this level only the two end states are specified.
calculation methods for excised patches containing kinetic scheme channels Preliminary calculation methods for kinetic scheme (KSChannel) channels in excised patches. This is a temporary class which ignores the IVlaw in the KSChannel, and instead specifies a reversal potential, Erev (mV) for the channel. There are nchan channels in the patch, and the simulation is run for runtime (ms) in steps of timestep. Optionally noise is added as an AR1 process of amplitude noiseAmp (pA) and regression parameter noiseRP. this class will be superseded with something more realistic * * *
state occupancy of a set of kinetic scheme channels
current-voltage relation for kinetic scheme channels A current-voltage relation for kinetic scheme channels (KSChannel objects). Presently the type is specified by the conductanceModel parameter which is one of: Ohmic (1); GHK (2) the Goldman-Hodgkin-Katz constant field equations; PNP (3) The Poisson-Nernst-Planck equations for conduction in a pore; or Eyring (4) Eyring rate theory. Each of these IV laws requires a distinct set of parameters. Eventually IVlaw will be subclassed to contain the appropriate data.
voltage dependent transition in a kinetic scheme A voltage dependent or independent rate for a state transition in a kinetic scheme. The rate is defined by the forward and reverse _TT(r-f) and _TT(r-r) (per ms) for zero membrane potential instead of the midpoint potential as in KSRateVhalf. This gives a continuous transition to voltage-independent transitions, so this transition may be used instead of both KSRateVhalf and KSRateTime. The equivalent gating charge is z, and the position of the activation particle within the transit of the gating particle is gamma: 0 < gamma <. An additional quantity _TT(r-m) imposes a saturation rate for the transition (cf Borg-Graham...). Such saturation may be an appropriate approximation when, for example, a single state is used to represent multiple physical states where the transition in question can only occur from one of the states. The transition is computed from the forward and reverse rates, alpha and beta, given by: _SCODE static final double alpha (double v, double rf, double rr, double z, double gamma, double rm) { double a = rf * Math.exp (ebykt * (gamma) * z * v); a = 1. / (1. / a + 1./rm); return a; } static final double beta (double v, double rf, double rr, double z, double gamma, double rm) { double b = rr * Math.exp (-ebykt * (1. - gamma) * z * v); b = 1. / (1. / b + 1./rm); return b; } _ECODE where ebykt = e / kT, about 0.042 mV _POW(-1).