//genesis /* FILE INFORMATION ** The 1991 Traub set of voltage and concentration dependent channels ** Implemented as tabchannels by : Dave Beeman ** R.D.Traub, R. K. S. Wong, R. Miles, and H. Michelson ** Journal of Neurophysiology, Vol. 66, p. 635 (1991) ** ** This file depends on functions and constants defined in defaults.g ** As it is also intended as an example of the use of the tabchannel ** object to implement concentration dependent channels, it has extensive ** comments. Note that the original units used in the paper have been ** converted to SI (MKS) units. Also, we define the ionic equilibrium ** potentials relative to the resting potential, EREST_ACT. In the ** paper, this was defined to be zero. Here, we use -0.060 volts, the ** measured value relative to the outside of the cell. */ /* November 1999 update for GENESIS 2.2: Previous versions of this file used a combination of a table, tabgate, and vdep_channel to implement the Ca-dependent K Channel - K(C). This new version uses the new tabchannel "instant" field, introduced in GENESIS 2.2, to implement an "instantaneous" gate for the multiplicative Ca-dependent factor in the conductance. This allows these channels to be used with the fast hsolve chanmodes > 1. */ // CONSTANTS float EREST_ACT = -0.060 /* hippocampal cell resting potl */ float ENA = 0.115 + EREST_ACT // 0.055 float EK = -0.015 + EREST_ACT // -0.075 float ECA = 0.140 + EREST_ACT // 0.080 float SOMA_A = 3.320e-9 // soma area in square meters /* For these channels, the maximum channel conductance (Gbar) has been calculated using the CA3 soma channel conductance densities and soma area. Typically, the functions which create these channels will be used to create a library of prototype channels. When the cell reader creates copies of these channels in various compartments, it will set the actual value of Gbar by calculating it from the cell parameter file. */ //======================================================================== // Tabulated Ca Channel //======================================================================== function make_Ca_hip_traub91 if ({exists Ca_hip_traub91}) return end create tabchannel Ca_hip_traub91 setfield ^ \ Ek {ECA} \ // V Gbar { 40 * SOMA_A } \ // S Ik 0 \ // A Gk 0 \ // S Xpower 2 \ Ypower 1 \ Zpower 0 /* Often, the alpha and beta rate parameters can be expressed in the functional form y = (A + B * x) / (C + {exp({(x + D) / F})}). When this is the case, case, the command "setupalpha chan gate AA AB AC AD AF BA BB BC BD BF" can be used to simplify the process of initializing the A and B tables for the X, Y and Z gates. Although setupalpha has been implemented as a compiled GENESIS command, it is also defined as a script function in the neurokit/prototypes defaults.g file. Although this command can be used as a "black box", its definition shows some nice features of the tabchannel object, and some tricks we will need when the rate parameters do not fit this form. */ // Converting Traub's expressions for the gCa/s alpha and beta functions // to SI units and entering the A, B, C, D and F parameters, we get: setupalpha Ca_hip_traub91 X 1.6e3 \ 0 1.0 {-1.0 * (0.065 + EREST_ACT) } -0.01389 \ {-20e3 * (0.0511 + EREST_ACT) } \ 20e3 -1.0 {-1.0 * (0.0511 + EREST_ACT) } 5.0e-3 /* The Y gate (gCa/r) is not quite of this form. For V > EREST_ACT, alpha = 5*{exp({-50*(V - EREST_ACT)})}. Otherwise, alpha = 5. Over the entire range, alpha + beta = 5. To create the Y_A and Y_B tables, we use some of the pieces of the setupalpha function. */ // Allocate space in the A and B tables with room for xdivs+1 = 50 entries, // covering the range xmin = -0.1 to xmax = 0.05. float xmin = -0.1 float xmax = 0.05 int xdivs = 49 call Ca_hip_traub91 TABCREATE Y {xdivs} {xmin} {xmax} // Fill the Y_A table with alpha values and the Y_B table with (alpha+beta) int i float x,dx,y dx = (xmax - xmin)/xdivs x = xmin for (i = 0 ; i <= {xdivs} ; i = i + 1) if (x > EREST_ACT) y = 5.0*{exp {-50*(x - EREST_ACT)}} else y = 5.0 end setfield Ca_hip_traub91 Y_A->table[{i}] {y} setfield Ca_hip_traub91 Y_B->table[{i}] 5.0 x = x + dx end // For speed during execution, set the calculation mode to "no interpolation" // and use TABFILL to expand the table to 3000 entries. setfield Ca_hip_traub91 Y_A->calc_mode 0 Y_B->calc_mode 0 call Ca_hip_traub91 TABFILL Y 3000 0 end /**************************************************************************** Next, we need an element to take the Calcium current calculated by the Ca channel and convert it to the Ca concentration. The "Ca_concen" object solves the equation dC/dt = B*I_Ca - C/tau, and sets Ca = Ca_base + C. As it is easy to make mistakes in units when using this Calcium diffusion equation, the units used here merit some discussion. With Ca_base = 0, this corresponds to Traub's diffusion equation for concentration, except that the sign of the current term here is positive, as GENESIS uses the convention that I_Ca is the current flowing INTO the compartment through the channel. In SI units, the concentration is usually expressed in moles/m^3 (which equals millimoles/liter), and the units of B are chosen so that B = 1/(ion_charge * Faraday * volume). Current is expressed in amperes and one Faraday = 96487 coulombs. However, in this case, Traub expresses the concentration in arbitrary units, current in microamps and uses tau = 13.33 msec. If we use the same concentration units, but express current in amperes and tau in seconds, our B constant is then 10^12 times the constant (called "phi") used in the paper. The actual value used will be typically be determined by the cell reader from the cell parameter file. However, for the prototype channel we wlll use Traub's corrected value for the soma. (An error in the paper gives it as 17,402 rather than 17.402.) In our units, this will be 17.402e12. ****************************************************************************/ //======================================================================== // Ca conc //======================================================================== function make_Ca_hip_conc if ({exists Ca_hip_conc}) return end create Ca_concen Ca_hip_conc setfield Ca_hip_conc \ tau 0.01333 \ // sec B 17.402e12 \ // Curr to conc for soma Ca_base 0.0 addfield Ca_hip_conc addmsg1 setfield Ca_hip_conc \ addmsg1 "../Ca_hip_traub91 . I_Ca Ik" end /* This Ca_concen element should receive an "I_Ca" message from the calcium channel, accompanied by the value of the calcium channel current. As we will ordinarily use the cell reader to create copies of these prototype elements in one or more compartments, we need some way to be sure that the needed messages are established. Although the cell reader has enough information to create the messages which link compartments to their channels and to other adjacent compartments, it most be provided with the information needed to establish additional messages. This is done by placing the message string in a user-defined field of one of the elements which is involved in the message. The cell reader recognizes the added field names "addmsg1", "addmsg2", etc. as indicating that they are to be evaluated and used to set up messages. The paths are relative to the element which contains the message string in its added field. Thus, "../Ca_hip_traub91" refers to the sibling element Ca_hip_traub91 and "." refers to the Ca_hip_conc element itself. */ //======================================================================== // Tabulated Ca-dependent K AHP Channel //======================================================================== /* This is a tabchannel which gets the calcium concentration from Ca_hip_conc in order to calculate the activation of its Z gate. It is set up much like the Ca channel, except that the A and B tables have values which are functions of concentration, instead of voltage. */ function make_Kahp_hip_traub91 if ({exists Kahp_hip_traub91}) return end create tabchannel Kahp_hip_traub91 setfield ^ \ Ek {EK} \ // V Gbar { 8 * SOMA_A } \ // S Ik 0 \ // A Gk 0 \ // S Xpower 0 \ Ypower 0 \ Zpower 1 // Allocate space in the Z gate A and B tables, covering a concentration // range from xmin = 0 to xmax = 1000, with 50 divisions float xmin = 0.0 float xmax = 1000.0 int xdivs = 50 call Kahp_hip_traub91 TABCREATE Z {xdivs} {xmin} {xmax} int i float x,dx,y dx = (xmax - xmin)/xdivs x = xmin for (i = 0 ; i <= {xdivs} ; i = i + 1) if (x < 500.0) y = 0.02*x else y = 10.0 end setfield Kahp_hip_traub91 Z_A->table[{i}] {y} setfield Kahp_hip_traub91 Z_B->table[{i}] {y + 1.0} x = x + dx end // For speed during execution, set the calculation mode to "no interpolation" // and use TABFILL to expand the table to 3000 entries. setfield Kahp_hip_traub91 Z_A->calc_mode 0 Z_B->calc_mode 0 call Kahp_hip_traub91 TABFILL Z 3000 0 // Use an added field to tell the cell reader to set up the // CONCEN message from the Ca_hip_concen element addfield Kahp_hip_traub91 addmsg1 setfield Kahp_hip_traub91 \ addmsg1 "../Ca_hip_conc . CONCEN Ca" end //======================================================================== // Ca-dependent K Channel - K(C) - (vdep_channel with table and tabgate) //======================================================================== /* The expression for the conductance of the potassium C-current channel has a typical voltage and time dependent activation gate, where the time dependence arises from the solution of a differential equation containing the rate parameters alpha and beta. It is multiplied by a function of calcium concentration that is given explicitly rather than being obtained from a differential equation. Therefore, we need a way to multiply the activation by a concentration dependent value which is determined from a lookup table. This is accomplished by using the Z gate with the new tabchannel "instant" field, introduced in GENESIS 2.2, to implement an "instantaneous" gate for the multiplicative Ca-dependent factor in the conductance. */ function make_Kc_hip_traub91 if ({exists Kc_hip_traub91}) return end create tabchannel Kc_hip_traub91 setfield ^ \ Ek {EK} \ // V Gbar { 100.0 * SOMA_A } \ // S Ik 0 \ // A Gk 0 // S // Now make a X-table for the voltage-dependent activation parameter. float xmin = -0.1 float xmax = 0.05 int xdivs = 49 call Kc_hip_traub91 TABCREATE X {xdivs} {xmin} {xmax} int i float x,dx,alpha,beta dx = (xmax - xmin)/xdivs x = xmin for (i = 0 ; i <= {xdivs} ; i = i + 1) if (x < EREST_ACT + 0.05) alpha = {exp {53.872*(x - EREST_ACT) - 0.66835}}/0.018975 beta = 2000*{exp {(EREST_ACT + 0.0065 - x)/0.027}} - alpha else alpha = 2000*{exp {(EREST_ACT + 0.0065 - x)/0.027}} beta = 0.0 end setfield Kc_hip_traub91 X_A->table[{i}] {alpha} setfield Kc_hip_traub91 X_B->table[{i}] {alpha+beta} x = x + dx end // Expand the tables to 3000 entries to use without interpolation setfield Kc_hip_traub91 X_A->calc_mode 0 X_B->calc_mode 0 setfield Kc_hip_traub91 Xpower 1 call Kc_hip_traub91 TABFILL X 3000 0 // Create a table for the function of concentration, allowing a // concentration range of 0 to 1000, with 50 divisions. This is done // using the Z gate, which can receive a CONCEN message. By using // the "instant" flag, the A and B tables are evaluated as lookup tables, // rather than being used in a differential equation. float xmin = 0.0 float xmax = 1000.0 int xdivs = 50 call Kc_hip_traub91 TABCREATE Z {xdivs} {xmin} {xmax} int i float x,dx,y dx = (xmax - xmin)/xdivs x = xmin for (i = 0 ; i <= {xdivs} ; i = i + 1) if (x < 250.0) y = x/250.0 else y = 1.0 end /* activation will be computed as Z_A/Z_B */ setfield Kc_hip_traub91 Z_A->table[{i}] {y} setfield Kc_hip_traub91 Z_B->table[{i}] 1.0 x = x + dx end setfield Kc_hip_traub91 Z_A->calc_mode 0 Z_B->calc_mode 0 setfield Kc_hip_traub91 Zpower 1 // Make it an instantaneous gate (no time constant) setfield Kc_hip_traub91 instant {INSTANTZ} // Expand the table to 3000 entries to use without interpolation. call Kc_hip_traub91 TABFILL Z 3000 0 // Now we need to provide for messages that link to external elements. // The message that sends the Ca concentration to the Z gate tables is stored // in an added field of the channel, so that it may be found by the cell // reader. addfield Kc_hip_traub91 addmsg1 setfield Kc_hip_traub91 addmsg1 "../Ca_hip_conc . CONCEN Ca" end // The remaining channels are straightforward tabchannel implementations //======================================================================== // Tabchannel Na Hippocampal cell channel //======================================================================== function make_Na_hip_traub91 if ({exists Na_hip_traub91}) return end create tabchannel Na_hip_traub91 setfield ^ \ Ek {ENA} \ // V Gbar { 300 * SOMA_A } \ // S Ik 0 \ // A Gk 0 \ // S Xpower 2 \ Ypower 1 \ Zpower 0 setupalpha Na_hip_traub91 X {320e3 * (0.0131 + EREST_ACT)} \ -320e3 -1.0 {-1.0 * (0.0131 + EREST_ACT) } -0.004 \ {-280e3 * (0.0401 + EREST_ACT) } \ 280e3 -1.0 {-1.0 * (0.0401 + EREST_ACT) } 5.0e-3 setupalpha Na_hip_traub91 Y 128.0 0.0 0.0 \ {-1.0 * (0.017 + EREST_ACT)} 0.018 \ 4.0e3 0.0 1.0 {-1.0 * (0.040 + EREST_ACT) } -5.0e-3 end //======================================================================== // Tabchannel K(DR) Hippocampal cell channel //======================================================================== function make_Kdr_hip_traub91 if ({exists Kdr_hip_traub91}) return end create tabchannel Kdr_hip_traub91 setfield ^ \ Ek {EK} \ // V Gbar { 150 * SOMA_A } \ // S Ik 0 \ // A Gk 0 \ // S Xpower 1 \ Ypower 0 \ Zpower 0 setupalpha Kdr_hip_traub91 X \ {16e3 * (0.0351 + EREST_ACT)} \ // AA -16e3 \ // AB -1.0 \ // AC {-1.0 * (0.0351 + EREST_ACT) } \ // AD -0.005 \ // AF 250 \ // BA 0.0 \ // BB 0.0 \ // BC {-1.0 * (0.02 + EREST_ACT)} \ // BD 0.04 // BF end //======================================================================== // Tabchannel K(A) Hippocampal cell channel //======================================================================== function make_Ka_hip_traub91 if ({exists Ka_hip_traub91}) return end create tabchannel Ka_hip_traub91 setfield ^ \ Ek {EK} \ // V Gbar { 50 * SOMA_A } \ // S Ik 0 \ // A Gk 0 \ // S Xpower 1 \ Ypower 1 \ Zpower 0 setupalpha Ka_hip_traub91 X {20e3 * (0.0131 + EREST_ACT)} \ -20e3 -1.0 {-1.0 * (0.0131 + EREST_ACT) } -0.01 \ {-17.5e3 * (0.0401 + EREST_ACT) } \ 17.5e3 -1.0 {-1.0 * (0.0401 + EREST_ACT) } 0.01 setupalpha Ka_hip_traub91 Y 1.6 0.0 0.0 \ {0.013 - EREST_ACT} 0.018 \ 50.0 0.0 1.0 {-1.0 * (0.0101 + EREST_ACT) } -0.005 end