{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "writeline(default, \+ \"Maple Housekeeping\"):\n restart;\n digits := 5;\n interface(d isplayprecision=3);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5265 " # --------------------------------------------------------------\nwr iteline(default,\"Constants\"):\n \nwriteline(default,\"Equilibrium v oltages, mV\"):\nwriteline(default,\" Sodium, Potassium, Leak\");\n vNa:=35;\n vK:=-67; # own data Fig 3.\n \n # Max Leak condu ctance and reversal potential measured\n # from trace of 18 mV and 1 \+ nA\n # leak conductance smaller than IK - see infinity worksheet \+ \n vLeak:=-20;\nwriteline(default,\"Fixed leak conductance\"):\n g Leak :=0.02; # muS\n\n # ------------------------------------------- -------------------\n # time independent functions ................\n \n # Sodium current m and h ... Connor calls them a and b\n # they \+ were in ms so divide by 1000\nwriteline(default,\"Sodium current\"):\n writeline(default,\" maximum conductance, m and h components \"):\n writeline(default,\" with max value and time constant as functions \+ of voltage\"):\n gbarNa:=7.0; #default value is 7 - also use 9.3 an d 4.9\n minf := v -> 1/(1 + exp((24+v)/(-8))) ;\n taum := v -> (0. 3+ 8/(1 + exp((v+40)/2.0)))/1000 ; \n hinf := v -> 1/(1 + exp((29.0 +v)/3.8)) ;\n tauh := v -> (2.3 + 15/(1 + exp((v+24.3)/3.8)))/1000 ; \n \nwriteline(default,\"Sustained Potassium current\"):\nwriteline(de fault,\" maximum conductance, NA and NB components \"):\nwriteline( default,\" with max value and time constant as functions of voltage \"):\n # maintained Potassium Current IK NA, NB\n # all own data\n \+ # slow and fast components\n gbarKA := 1.44 ;\n NAinf := v -> 1/(1 + exp((14.9-v)/16.6)) ; \n tauNA := v -> 0.0383 - 0.00041 * v ; \n \n gbarKB := 2.88 ;\n NBinf := v -> 1/(1 + exp((8.6-v)/14.6)) ; \+ \n tauNB := v -> 0.0057 - 0.00007 * v ; \n \nwriteline(default,\"Tr ansient Potassium current\"):\nwriteline(default,\" maximum conduct ance, a and b components \"):\nwriteline(default,\" with max value \+ and time constant as functions of voltage\"): \n #Transient K curren t IA a b\n gbarA := 12; \n \n # activation (measured values)\n ainf := v -> 1/(1 + exp((12.4+v)/(-14.1))) ; \n taua := v -> 0.00 18 - 0.00003 * v ;\n # inactivation - some uncertainty in literature \+ so use own\n ## v = -71, h = 6.6 (measured)\n ## v = -97, h = 6.2 in Alekseev & Zayzin BBA 1148:100 Fig 2B \n ## v = -74, h = 6.4 in Conn or & Stevens J Physiol 317:27 fig 5\n ## \n binf := v -> 1/(1 + exp ((v+71)/6.6)) ; \n taub := v -> 0.026 + 0.00022 * v ;\n \n # ---- ----------------------------------------------------------\nwriteline( default,\"Initial conditions, start from equilibrium voltage (-52.5 mV )\"):\n v0:=-52.5; # approx eqm level -52.5 mV, \nwriteline(default, \" Sodium current\"):\n m0:=minf(v0);\n h0:=hinf(v0);\nwritelin e(default,\" Sustained Potassium current\"):\n NA0:=NAinf(v0);\n \+ NB0:=NBinf(v0);\nwriteline(default,\" Transient Potassium current \"):\n a0:=ainf(v0);\n b0:=binf(v0);\n \n \nwriteline(default,\" Current equations\"):\nwriteline(default,\" Sodium current\"):\nwri teline(default,\" Sustained Potassium current\"):\nwriteline(defaul t,\" Transient Potassium current\"):\nwriteline(default,\" Leak \+ current\"):\nwriteline(default,\" Total ionic current\"):\n INa : = (v(t)-vNa) * gbarNa*m(t)^3*h(t);\n IK := (v(t)-vK) * ( (gbarKA * NA(t)^2) + (gbarKB * NB(t)) ); \n IA := (v(t)-vK) * gbarA *a(t)^4 *b(t);\n ILeak:=(v(t)-vLeak)*gLeak; \n \n ITotal := INa+IK+IA+ILe ak ;\n \n # --------------------------------------------------------- -----\n # calculate the equilibrium current as a function of voltage \nwriteline(default,\"Equilibrium current as function of voltage\"):\n writeline(default,\" Sodium current\"):\nwriteline(default,\" Su stained Potassium current\"):\nwriteline(default,\" Transient Potas sium current\"):\nwriteline(default,\" Leak current\"):\n # Na cu rrent\n subs (m(t)=minf(t),INa);\n subs (h(t)=hinf(t),%);\n INai nf := subs (v(t)=t,%);\n\n # delayed K current\n subs (NA(t)=NAinf (t), IK);\n subs (NB(t)=NBinf(t), %);\n IKinf := subs (v(t)=t,%); \n\n # transient K current\n subs (a(t)=ainf(t), IA);\n subs (b( t)=binf(t), %);\n IAinf := subs (v(t)=t,%);\n \n # leak current\n ILeakinf := subs (v(t)=t,ILeak);\n\nwriteline(default,\" Total E quilibrium current\"):\n ITotalinf := INainf + IKinf + IAinf + ILeak inf ;\n\n\n\nwriteline(default,\"Plotting Time constants and equilibri um values\"):\nwriteline(default,\" Sodium current\"):\nwriteline(d efault,\" Sustained Potassium current\"):\nwriteline(default,\" \+ Transient Potassium current\"):\nwriteline(default,\" Total Equilib rium current\"):\n\n plot ([taum(v), tauh(v)], v=-100..100,y=0.0..0. 010,legend=[\"taum\", \"tauh\"], \n title = \"Time constants for Sodium Current\");\n plot ([minf(v), hinf(v)], v=-100..100,legend=[ \"minf\", \"hinf\"], \n title = \"Equilibrium proportion for Sod ium Current\");\n\n plot ([tauNA(v), tauNB(v)], v=-100..100,legend=[ \"tau Na\", \"tau Nb\"], \n title = \"Time constants for Sustain ed Potassium Current\");\n plot ([NAinf(v), NBinf(v)], v=-100..100,le gend=[ \"NAinf\", \"NBinf\"], \n title = \"Equilibrium proportio n for Sustained Potassium Current\");\n\n plot ([ainf(v), binf(v)], v =-100..100, legend=[\"aInf\", \"bInf\"], \n title = \"Time const ants for Transient Potassium Current\");\n plot ([taua(v), taub(v)], \+ v=-100..100,legend=[\"taua\", \"taub\"], \n title = \"Equilibriu m proportion for Transient Potassium Current\");\n" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 335 " # plot as function of voltage\n plot ([INainf , IKinf, IAinf, ILeakinf, ITotalinf],\n t=-80..-40, y=-2.0..2.0,\n \+ labels = [`voltage, mV`, `current, nA`],\n legend =[\"INainf\", \+ \"IKinf\", \"IAinf\", \"ILeakinf\", \"ITotalinf\"],\n linestyle =[2 ,3,4,4,1],\n color = [black,red,green,blue,magenta],\n title = \+ \"Equilibrium current\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "6" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }