{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 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 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 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "writeline(default, \+ \"Maple Housekeeping\"):\n restart;\n digits := 5;\n interface(d isplayprecision=3);\n\n" }}{PARA 6 "" 1 "" {TEXT -1 18 "Maple Housekee ping" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'digitsG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4518 " # ----------------------------- ---------------------------------\nwriteline(default,\"Constants\"):\n \nwriteline(default,\"Equilibrium voltages, mV\"):\nwriteline(defaul t,\" Sodium, Potassium, Leak\");\n vNa:=35;\n vK:=-67; # ow n data Fig 3.\n \n # Max Leak conductance and reversal potential mea sured\n # from trace of 18 mV and 1 nA\n # leak conductance smaller \+ than IK - see infinity worksheet \n vLeak:=-20;\nwriteline(defaul t,\"Fixed leak conductance\"):\n gLeak :=0.02; # muS\n\n # ------- -------------------------------------------------------\n # time inde pendent functions ................\n \n # Sodium current m and h ... \+ Connor calls them a and b\n # they were in ms so divide by 1000\nwrit eline(default,\"Sodium current\"):\nwriteline(default,\" maximum co nductance, m and h components \"):\nwriteline(default,\" with max v alue and time constant as functions of voltage\"):\n gbarNa:=7.0; # default value is 7 - also use 9.3 and 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(default,\" maximum conductance, N A and NB components \"):\nwriteline(default,\" with max value and t ime constant as functions of voltage\"):\n # maintained Potassium Cur rent IK NA, NB\n # all own data\n # slow and fast components\n gba rKA := 1.44 ;\n NAinf := v -> 1/(1 + exp((14.9-v)/16.6)) ; \n tauN A := 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 - 0.0000 7 * v ; \n \nwriteline(default,\"Transient Potassium current\"):\nwri teline(default,\" maximum conductance, a and b components \"):\nwri teline(default,\" with max value and time constant as functions of \+ voltage\"): \n #Transient K current 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 -> 0.0018 - 0.00003 * v ;\n # inactivati on - 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 Fi g 2B \n ## v = -74, h = 6.4 in Connor & 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, star t from holding voltage (-50 mV)\"):\n v0:=-50; \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\nv:= -10 ;\n \nwriteli ne(default,\"Current equations\"):\nwriteline(default,\" Sodium cur rent\"):\nwriteline(default,\" Sustained Potassium current\"):\nwri teline(default,\" Transient Potassium current\"):\nwriteline(defaul t,\" 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+ILeak ;\n \n #\n # odes for opening and closing chann els...............\nwriteline(default,\"Differential equations\"):\nw riteline(default,\" ODEs for Sodium current\"):\n odem:=diff(m(t) ,t)=(minf(v(t))-m(t))/taum(v(t));\n odeh:=diff(h(t),t)=(hinf(v(t))-h (t))/tauh(v(t));\nwriteline(default,\" ODEs for Sustained Potassium current\"):\n odeNA:=diff(NA(t),t)=(NAinf(v(t))-NA(t))/tauNA(v(t)); \n odeNB:=diff(NB(t),t)=(NBinf(v(t))-NB(t))/tauNB(v(t));\nwriteline( default,\" ODEs for Transient Potassium current\"):\n odea:=diff( a(t),t)=(ainf(v(t))-a(t))/taua(v(t));\n odeb:=diff(b(t),t)=(binf(v(t ))-b(t))/taub(v(t));\n \n # end of calculations of ODEs\n \n# ----- --------------------------------------------------------- \nwriteline (default,\"Solve system of ODEs\"): \n sol100:=dsolve( \{ odem, \+ odeh, odeNA, odeNB, odea, odeb, \n m(0)=m0, h(0)=h0, \n \+ NA(0)=NA0, NB(0)=NB0, \n a(0)=a0, b(0)=b0\}, \n \+ \{m(t), h(t), NA(t), NB(t), a(t), b(t)\}, \n type=numeric, met hod=lsode ) ;\nwriteline(default,\"Plotting...\"): \nwriteline(defaul t,\" Setup plot\"): \n maxT := 0.03; # max s for plot \n maxPT \+ := 200 ; # points to plot\n\nconvert(v0,string); \nconvert (v,string); \nsHead := cat (\"Holding: \", %%, \" pulse: \", % );\n" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 2 " \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 238 "writ eline(default,\" Plotting current vs time\"): \n with (plots, odep lot);\n \n odeplot(sol100,[t,ITotal, color=black], 0..maxT, view = [0 ..maxT,\n -120..120], numpoints=maxPT , title = sHead, labels=[ \"time, s\",\"current nA\"]) ; \n \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 6 "" 1 "" {TEXT -1 9 "Constants" }}{PARA 6 "" 1 "" {TEXT -1 24 "Equilibrium voltages, mV" }}{PARA 6 "" 1 "" {TEXT -1 27 " Sodium, Potassium, Leak" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#G" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$vNaG\"#N" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vKG!#n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vLeakG! #?" }}{PARA 6 "" 1 "" {TEXT -1 22 "Fixed leak conductance" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&gLeakG$\"\"#!\"#" }}{PARA 6 "" 1 "" {TEXT -1 14 "Sodium current" }}{PARA 6 "" 1 "" {TEXT -1 44 " maximum cond uctance, m and h components " }}{PARA 6 "" 1 "" {TEXT -1 60 " with \+ max value and time constant as functions of voltage" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%'gbarNaG$\"#q!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%minfGf*6#%\"vG6\"6$%)operatorG%&arrowGF(*&\"\"\"F-,&F-F--%$expG6 #,&\"\"$!\"\"*&#F-\"\")F-9$F-F4F-F4F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%taumGf*6#%\"vG6\"6$%)operatorG%&arrowGF(,&$\"+++++I! #8\"\"\"*&#F0\"$D\"F0*&F0F0,&F0F0-%$expG6#,&*&$\"+++++]!#5F09$F0F0$\"+ ++++?!\")F0F0!\"\"F0F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%hin fGf*6#%\"vG6\"6$%)operatorG%&arrowGF(*&\"\"\"F-,&F-F--%$expG6#,&$\"+Y* y:j(!\"*F-*&$\"+Z*y:j#!#5F-9$F-F-F-!\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%tauhGf*6#%\"vG6\"6$%)operatorG%&arrowGF(,&$\"+++++B! #7\"\"\"*&#\"\"$\"$+#F0*&F0F0,&F0F0-%$expG6#,&*&$\"+Z*y:j#!#5F09$F0F0$ \"+Tot%R'!\"*F0F0!\"\"F0F0F(F(F(" }}{PARA 6 "" 1 "" {TEXT -1 27 "Susta ined Potassium current" }}{PARA 6 "" 1 "" {TEXT -1 46 " maximum con ductance, NA and NB components " }}{PARA 6 "" 1 "" {TEXT -1 60 " wi th max value and time constant as functions of voltage" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'gbarKAG$\"$W\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&NAinfGf*6#%\"vG6\"6$%)operatorG%&arrowGF(*&\"\"\"F-, &F-F--%$expG6#,&$\"+:O!f(*)!#5F-*&$\"+'Q'4Cg!#6F-9$F-!\"\"F-F;F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tauNAGf*6#%\"vG6\"6$%)operatorG%& arrowGF(,&$\"$$Q!\"%\"\"\"*&$\"#T!\"&F09$F0!\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'gbarKBG$\"$)G!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&NBinfGf*6#%\"vG6\"6$%)operatorG%&arrowGF(*&\"\"\"F-,&F-F--%$e xpG6#,&$\"+e4T!*e!#5F-*&$\"+o]J\\o!#6F-9$F-!\"\"F-F;F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tauNBGf*6#%\"vG6\"6$%)operatorG%&arrowGF( ,&$\"#d!\"%\"\"\"*&$\"\"(!\"&F09$F0!\"\"F(F(F(" }}{PARA 6 "" 1 "" {TEXT -1 27 "Transient Potassium current" }}{PARA 6 "" 1 "" {TEXT -1 44 " maximum conductance, a and b components " }}{PARA 6 "" 1 "" {TEXT -1 60 " with max value and time constant as functions of volt age" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&gbarAG\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ainfGf*6#%\"vG6\"6$%)operatorG%&arrowGF(*&\"\"\"F -,&F-F--%$expG6#,&$\"+UiK%z)!#5!\"\"*&$\"+#e)>#4(!#6F-9$F-F6F-F6F(F(F( " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%tauaGf*6#%\"vG6\"6$%)operatorG% &arrowGF(,&$\"#=!\"%\"\"\"*&$\"\"$!\"&F09$F0!\"\"F(F(F(" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%binfGf*6#%\"vG6\"6$%)operatorG%&arrowGF(*&\" \"\"F-,&F-F--%$expG6#,&*&$\"+:::::!#5F-9$F-F-$\"+wvvv5!\")F-F-!\"\"F(F (F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%taubGf*6#%\"vG6\"6$%)operato rG%&arrowGF(,&$\"#E!\"$\"\"\"*&$\"#A!\"&F09$F0F0F(F(F(" }}{PARA 6 "" 1 "" {TEXT -1 55 "Initial conditions, start from holding voltage (-50 \+ mV)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v0G!#]" }}{PARA 6 "" 1 "" {TEXT -1 18 " Sodium current" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# m0G*&\"\"\"F&,&F&F&-%$expG6##\"#8\"\"%F&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h0G$\"+Y:Ng**!#5" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ Sustained Potassium current" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$NA0 G$\"+)Gt`'>!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$NB0G$\"+&f%eu%#a0G$\"+6p\"p\\'!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b0G$\"+#))pb)R!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG!#5" }}{PARA 6 "" 1 "" {TEXT -1 17 "Current equations" }} {PARA 6 "" 1 "" {TEXT -1 18 " Sodium current" }}{PARA 6 "" 1 "" {TEXT -1 31 " Sustained Potassium current" }}{PARA 6 "" 1 "" {TEXT -1 31 " Transient Potassium current" }}{PARA 6 "" 1 "" {TEXT -1 16 " Leak current" }}{PARA 6 "" 1 "" {TEXT -1 23 " Total ionic curr ent" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$INaG,$*($\"%]J!\"\"\"\"\")-% \"mG6#%\"tG\"\"$F*-%\"hGF.F*F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#I KG,&*&$\"%3#)!\"#\"\"\")-%#NAG6#%\"tG\"\"#F*F**&$\"&;k\"F)F*-%#NBGF.F* F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#IAG,$*(\"$%o\"\"\")-%\"aG6#% \"tG\"\"%F(-%\"bGF,F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ILeakG$ \"#?!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ITotalG,,*($\"%]J!\"\" \"\"\")-%\"mG6#%\"tG\"\"$F*-%\"hGF.F*F)*&$\"%3#)!\"#F*)-%#NAGF.\"\"#F* F**&$\"&;k\"F6F*-%#NBGF.F*F**(\"$%oF*)-%\"aGF.\"\"%F*-%\"bGF.F*F*$\"#? F6F*" }}{PARA 6 "" 1 "" {TEXT -1 23 "Differential equations" }}{PARA 6 "" 1 "" {TEXT -1 27 " ODEs for Sodium current" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%%odemG/-%%diffG6$-%\"mG6#%\"tGF,,&*&$\"+UhILL!\"'\" \"\",&F2F2-%$expG6##!\"(\"\"%F2!\"\"F2*&$\"+UhILLF1F2F)F2F:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%odehG/-%%diffG6$-%\"hG6#%\"tGF,,&$\"+4O# \\`#!\"*\"\"\"*&$\"+V%4vy$!\"(F1F)F1!\"\"" }}{PARA 6 "" 1 "" {TEXT -1 40 " ODEs for Sustained Potassium current" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&odeNAG/-%%diffG6$-%#NAG6#%\"tGF,,&$\"+p()[-V!\"*\"\" \"*&$\"+m0\\eB!\")F1F)F1!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&od eNBG/-%%diffG6$-%#NBG6#%\"tGF,,&$\"+F2G:M!\")\"\"\"*&$\"+++]i:!\"(F1F) F1!\"\"" }}{PARA 6 "" 1 "" {TEXT -1 40 " ODEs for Transient Potassi um current" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%odeaG/-%%diffG6$-%\"a G6#%\"tGF,,&$\"+2))4$e#!\"(\"\"\"*&$\"+iZ!>w%F0F1F)F1!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%odebG/-%%diffG6$-%\"bG6#%\"tGF,,&$\"+x+io S!#7\"\"\"*&$\"+s1o,U!\")F1F)F1!\"\"" }}{PARA 6 "" 1 "" {TEXT -1 20 "S olve system of ODEs" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sol100Gf*6#% (x_lsodeG6'%$resG%)solnprocG%)outpointG%&ndsolG%\"iG6#%inCopyright~(c) ~2000~by~Waterloo~Maple~Inc.~All~rights~reserved.G6\"C(>%8_EnvDSNumeri cSaveDigitsG%'DigitsG>F4\"#9@%/%-_EnvInFsolveG%%trueG>8&-&%&evalfG6#F3 6#9$>F<-F?FA>8%f*6#F+6*F-%#_sG%#stG%#enG%,origcontrolG%#r1G%#r2G%&gini tG6#%aoCopyright~(c)~1993~by~the~University~of~Waterloo.~All~rights~re served.GE\\s#Q(complexF0%&falseGQ0soln_proceduresF0=F06#;\"\"!FZE\\[l \"FZ\"(cDS#C'@&-%'memberG6$FB7%Q&startF0Q%leftF0Q&rightF0O$FZFZ/FBQ'me thodF0O.Q&lsodeF0@)/FfoQ*classicalF0C$>F<\"\"*>8'F6/FfoQ%gearF0C$>F<\" #6>F^p\"#;/FfoFfoC$>F<\"\")>F^p\"#8YQSillegal~method~in~`dsolve/numeri c_solnproc_others`F0>8(=F06#;\"\"\"\"#TE\\[lJFcq\"\"'\"\"#Fao\"\"$Fao \"\"%Fcq\"\"&FcqFfq\"#5\"\"(FZFip$\"+)Gt`'>!#6F\\p$\"+&f%euFZ\"#?FZ\"#@FZ\"#AFZ\"#BFZ\"#CFZ\"#DFZ \"#EFZ\"#FFZ\"#GFZ\"#HFZ\"#IFZ\"#JFZ\"#KFZ\"#LFZ\"#MFZ\"#NFZ\"#OFZ\"#P FZ\"#QFZ\"#RFZ\"#SFZFdq!\"\">8+-%#ifG6%2FZFZ-%Ffv-%%copyG6#F_q-F^w6%FhqF`w%FC ontinuation~check:~continue~solutionG>&Ffv6#FhqFB@%1F4-%'evalhfG6#F4C$ >FF-%*traperrorG6#-F]z6#-%=dsolve/numeric_solnall_lsodeG6$%\"FG-%$varG 6#Ffv@$/FF%*lasterrorGC%>8)-%+searchtextG6$.F]z-%(convertG6$-%#opG6$Fc q7#FF%%nameG>8*-Fd[l6$.%)hardwareGFg[l@%50Fb[lFZ0F`\\lFZ-Fgz6$FizFfvYF FFi\\l@$/%:_Env_smart_dsolve_numericGF:@&32FaoFB2-9!6#F_oFB>Fc]lFB32FB Fao2FB-Fd]l6#F^o>Fj]lFBFhvF0F\\[lF0@$4-%%typeG6$F<.%(numericG@)-Fjn6$F <7(F]oF^oF_oQ)leftdataF0Q*rightdataF0Q+enginedataF0O-FFFA/FF^p-%(pointtoG6#&-FF6#F V6#FZO-.F^pFAZ%C$>F^v-FF6#F<7$/%\"tG&F^v6#Fcq-Fhu6$/&X*%)anythingG6\"F 0[gl!!%!!!\"(\"(%\"tG-%#NAG6#Feal-%#NBGFhal-%\"aGFhal-%\"bGFhal-%\"hGF hal-%\"mGFhal6#,&F_qFcqFcqFcq&F^vFcbl/F_q;FcqFfqF0YF0F0F0F0" }}{PARA 6 "" 1 "" {TEXT -1 11 "Plotting..." }}{PARA 6 "" 1 "" {TEXT -1 14 " \+ Setup plot" }}{PARA 11 "" 1 "" {XPPMATH 20 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