# This program was used to make Figure 5A, right panel in "Calcium Effects # on ATP Production and Consumption Have Regulatory Roles on Oscillatory Islet # Activity", by J. P. McKenna, J. Ha, M. J. Merrins, L. S. Satin, A. Sherman, # and R. Bertram, Biophysical Journal, 110:733-742, 2016. # # Variables: # v = membrane potential # skv = activation variable for the delayed rectifier # cac = free cytosolic calcium concentration # caer = free ER calcium concentration # f6p = F6P concentration # fbp = F16BP concentration # atpc = cytosolic ATP concentration # # Important auxilliary variables: # PKAR = the PKAR fluorescence # Perceval = the Perceval-HR fluorescence ######################## # Glycolytic component # ######################## ## glucokinase (GK) p jgk=9.45e-5 ## glucose 6-phosphate isomerase (GPI) !kgpi=19/3 ## phosphofructokinase (PFK), adapted from Smolen 1995 p fpfkm=1 p kpfkbas=.06, kpfkamp=.03, kpfkf6p=5e4 p famp=.02, fmt=20, ffbp=.2, fbt=20, fatp=20 ### PFK-M p vpfkm=9e-4 p kpfkfbp=1, kpfkatp=2.5e-4 pow[0..63]=mod(flr(flr([j]/4)*2^(mod([j],4)-3)),2) w[0..15]=\ (amp/kpfkamp)^shift(pow0,4*[j])*\ (fbp/kpfkfbp)^shift(pow0,4*[j]+1)*\ (f6p^2/kpfkf6p)^shift(pow0,4*[j]+2)*\ (atpc^2/kpfkatp)^shift(pow0,4*[j]+3)/\ famp^(shift(pow0,4*[j])*shift(pow0,4*[j]+2))/\ fmt^(shift(pow0,4*[j])*shift(pow0,4*[j]+3))/\ ffbp^(shift(pow0,4*[j]+1)*shift(pow0,4*[j]+2))/\ fbt^(shift(pow0,4*[j]+1)*shift(pow0,4*[j]+3))/\ fatp^(shift(pow0,4*[j]+2)*shift(pow0,4*[j]+3)) jpfkm=vpfkm*((1-kpfkbas)*w14 + \ kpfkbas*(w2+w3+w6+w7+w10+w11+w14+w15)) \ / (sum(0,15)of(shift(w0,i'))) ### PFK-C p vpfkc=.00144 p kpfkcfbp=10, kpfkcatp=.0001136360 wc[0..15]=\ (amp/kpfkamp)^shift(pow0,4*[j])*\ (fbp/kpfkcfbp)^shift(pow0,4*[j]+1)*\ (f6p^2/kpfkf6p)^shift(pow0,4*[j]+2)*\ (atpc^2/kpfkcatp)^shift(pow0,4*[j]+3)/\ famp^(shift(pow0,4*[j])*shift(pow0,4*[j]+2))/\ fmt^(shift(pow0,4*[j])*shift(pow0,4*[j]+3))/\ ffbp^(shift(pow0,4*[j]+1)*shift(pow0,4*[j]+2))/\ fbt^(shift(pow0,4*[j]+1)*shift(pow0,4*[j]+3))/\ fatp^(shift(pow0,4*[j]+2)*shift(pow0,4*[j]+3)) jpfkc=vpfkc*((1-kpfkbas)*wc14 + \ kpfkbas*(wc2+wc3+wc6+wc7+wc10+wc11+wc14+wc15)) \ / (sum(0,15)of(shift(wc0,i'))) jpfk=fpfkm*jpfkm+(1-fpfkm)*jpfkc ## lower glycolysis (LG) p sumkp=.5 klg=.5*sumkp ## pyruvate dehydrogenase (PDH) p vpdh=3.7e-4, kpdhcam=.1, kca=5 cam=kca*cac jpdh=vpdh/(1+kpdhcam/cam)*sqrt(fbp) ####################################### # ATP production/hydrolysis component # ####################################### p kic=0 p actot=2.5, amtot=15 p amp=.5 #p amp=500 adpc=actot-atpc atpm=amtot-adpm ## adenine nucleotide translocator (ANT) !volmtoc=39/532 p kadpm=12.5, kadpmpdh=.0047, vant=7.245e-5, fjant=.11, kantam=2, psim=164, FRT=.037 adpm=kadpm/exp(jpdh/kadpmpdh) jant=volmtoc*vant*(kic*fjant+(1-kic)/(1+kantam*adpm/atpm))*exp(FRT/2*psim) ## hydrolysis (hyd) p khyd=2.34e-5, khydbas=8.1e-6 jhyd=(khyd*cac+khydbas)*atpc ########################### # Ionic current component # ########################### p cm=5300 ## Ca channels/pumps !fc=1/115 p vca=25 ### voltage-activated Ca (Ca(V)) current p gcav=180, vcav=-20 !hcav=1/12 scavinf=1/(1+exp(vcav-v)^hcav) icav=gcav*scavinf*(v-vca) ### plasma membrane Ca ATPase (PMCA) flux !F=20000000/207 p kpmca=.0414 jmem=-(icav/2/F + kpmca*cac) ### endoplasmic reticulum (ER) flux !volctoer=620/23 p fer=.01 p kerout=4.14e-5, kerin=.0828 jerout=kerout*(caer-cac) jerin=kerin*cac jer=jerout-jerin ## K channels p vk=-75 ### voltage-activated K (K(V)) current p gkv=486, vkv=-16, hkv=.2 #!taukv=1000/9 taukv=111. skvinf=1/(1+exp(vkv-v)^hkv) ikv=gkv*skv*(v-vk) ### Ca-activated K (K(Ca)) current p gkca=18, kkcaca=.5, hkcaca=2 skcainf=1/(1+(kkcaca/cac)^hkcaca) ikca=gkca*skcainf*(v-vk) ### K(ATP), adapted from Magnus and Keizer, 1998 p dz=0 p gkatp=2960 p kdd=17, ktd=26, ktt=1 mgadp=165*adpc adp3m=135*adpc atp4m=50*atpc skatpinf=\ (.08*(1+2*mgadp/kdd) + .89*(mgadp/kdd)^2)/\ ((1+mgadp/kdd)^2 * (1+adp3m/ktd+atp4m/ktt)) ikatp=(1-dz)*gkatp*skatpinf*(v-vk)+dz*gkatp*(v-vk) ########################## # Differential Equations # ########################## v'=-(ikv+icav+ikca+ikatp)/cm skv'=(skvinf-skv)/taukv cac'=fc*(jmem+jer) caer'=-fer*volctoer*jer f6p'=1/(1+kgpi)*(jgk-jpfk) fbp'=1/(1+klg)*(jpfk-.5*jpdh) atpc'=jant-jhyd ################## # XPP parameters # ################## @ meth=cvode, toler=1.0e-10, atoler=1.0e-10, dt=20.0 @ maxstor=9999999,bounds=10000000, bell=0 # Fig 5A right: early PKAR nadir global 0 tmin {kadpmpdh=.0034} v(0)=-65.1055588097 skv(0)=0.0000542517 cac(0)=0.1144077598 caer(0)=296.5458216306 f6p(0)=265.7003852308 fbp(0)=0.3703376461 atpc(0)=1.1074945965 @ xp=tmin, yp=pkar @ total=300000, xlo=0, xhi=5, ylo=0, yhi=.4 aux cam=cam aux pkar=fbp/(2+fbp) aux perceval=(atpc/adpc)/(1+atpc/adpc) aux fbpflux1=jpfk aux fbpflux2=jpdh/2 aux atpcflux1=jant aux atpcflux2=jhyd tmin=t/60000 aux tmin=t/60000 done