dP0/dt = -P0*k_off + P1*k_on + P2*k_coop
dP1/dt = P0*k_off - P1*k_on - P2*k_coop
dP2/dt = 2*P0*k_off + 2*P1*k_on - 2*P2*k_off - 2*P2*k_on - 2*P3*k_coop
dP3/dt = 2*P2*k_coop + 2*P2*k_on - 4*P3*k_coop - 2*P3*k_off - 3*P3*k_on - 2*P4*k_coop + P5*k_off
dP4/dt = 4*P0*k_off + 2*P1*k_on - 2*P2*k_off - 2*P2*k_on - 2*P3*k_off + P3*k_on - 2*P4*k_coop - P4*k_off - 4*P4*k_on - 2*P5*k_off - P6*k_on + 2*P7*k_coop + P8*k_off
dP5/dt = 2*P0*k_coop + 4*P0*k_on - 2*P2*k_on + 4*P3*k_coop + P3*k_on - P4*k_coop - P5*k_coop - 3*P5*k_off - 2*P5*k_on - P8*k_coop - P9*k_coop
dP6/dt = -3*P6*k_on + 3*P9*k_off
dP7/dt = 6*P0*k_off + 2*P1*k_on - P10*k_on + 2*P11*k_coop + P12*k_off - 6*P2*k_off - 2*P2*k_on + P3*k_on + 3*P4*k_off - P4*k_on - 3*P5*k_off - P6*k_on - 2*P7*k_coop - P7*k_off - 5*P7*k_on + P8*k_off + 3*P9*k_off
dP8/dt = -6*P0*k_coop - 6*P0*k_on + P12*k_coop + P13*k_coop + 2*P14*k_off + 6*P2*k_coop + 6*P2*k_on - 3*P4*k_coop + 3*P4*k_on + 3*P5*k_coop + 3*P5*k_on - 2*P7*k_coop - 5*P8*k_coop - 2*P8*k_off - 3*P8*k_on - 3*P9*k_coop - 3*P9*k_on
dP9/dt = 2*P15*k_off + P6*k_on - 2*P9*k_coop - P9*k_off - 2*P9*k_on
dP10/dt = -4*P10*k_on + 4*P16*k_off
dP11/dt = 2*P1*k_on - P10*k_on - P11*k_off - 6*P11*k_on + P13*k_off - P17*k_on - 2*P18*k_coop + P19*k_off - 2*P2*k_on + P3*k_on - P4*k_on - P6*k_on - P7*k_on
dP12/dt = -12*P0*k_coop - 12*P0*k_off - 12*P0*k_on - 2*P11*k_coop - 5*P12*k_coop - 4*P12*k_off - 4*P12*k_on + P13*k_coop + 6*P13*k_off + 4*P14*k_off + 12*P15*k_off - 4*P16*k_coop - 8*P16*k_off - 4*P16*k_on - 4*P18*k_off + 4*P19*k_coop/3 + 4*P19*k_off/3 + 12*P2*k_coop + 12*P2*k_off + 12*P2*k_on - 2*P20*k_coop/3 + 5*P20*k_off/6 + P21*k_off/2 - 12*P3*k_off - 2*P4*k_coop + 2*P4*k_off - 2*P4*k_on + 6*P5*k_coop + 6*P5*k_off + 6*P5*k_on - 4*P7*k_coop - 8*P7*k_off + 4*P7*k_on - 2*P8*k_coop + 2*P8*k_off - 2*P8*k_on - 6*P9*k_coop - 6*P9*k_off - 6*P9*k_on
dP13/dt = 12*P0*k_off + P11*k_coop + P11*k_off/2 + P12*k_off - 2*P13*k_coop - 5*P13*k_off - 4*P13*k_on + 4*P16*k_off + 2*P18*k_off + P19*k_coop/3 - P19*k_off/2 - 12*P2*k_off - 2*P20*k_coop/3 + P20*k_off - P22*k_coop + P22*k_off/2 + P23*k_off + 2*P4*k_off - 6*P5*k_off + P7*k_coop + 7*P7*k_off/2 + 2*P8*k_off + 6*P9*k_off
dP14/dt = 12*P0*k_coop + 12*P0*k_on + P11*k_coop/2 - P12*k_coop - 3*P13*k_coop - 4*P14*k_coop - 3*P14*k_off - 2*P14*k_on - 6*P15*k_coop - 3*P15*k_on + 2*P16*k_coop + 2*P18*k_coop - P19*k_coop/2 - 4*P2*k_coop - 6*P2*k_on + P20*k_coop + P22*k_coop/2 + P23*k_coop - 2*P24*k_coop + 3*P25*k_off - 2*P3*k_coop - 3*P3*k_on - 4*P4*k_coop - 6*P5*k_coop - 6*P5*k_on + 3*P7*k_coop/2 + 2*P8*k_coop + 2*P8*k_on - 2*P9*k_coop
dP15/dt = -2*P0*k_off - P14*k_off - 2*P15*k_coop - 4*P15*k_off - P15*k_on + 2*P2*k_off - P25*k_off + 2*P3*k_off - P4*k_off + 2*P5*k_off - P8*k_off + 2*P9*k_coop - P9*k_off + 2*P9*k_on
dP16/dt = P10*k_on - 2*P16*k_coop - P16*k_off - 3*P16*k_on + 2*P24*k_off + P26*k_off
dP17/dt = -5*P17*k_on + 5*P22*k_off
dP18/dt = 3*P11*k_off/2 + 2*P11*k_on + 2*P13*k_off - 2*P18*k_coop - 4*P18*k_off - 7*P18*k_on + 7*P19*k_off/6 - P20*k_off/3 + 3*P22*k_off/2 + P23*k_off + 2*P27*k_coop - 2*P27*k_off - P28*k_off - 3*P7*k_off/2
dP19/dt = -12*P0*k_on - 4*P11*k_coop + 6*P11*k_off + 5*P11*k_on - P12*k_on - 4*P13*k_coop - 17*P13*k_off - P13*k_on - 18*P14*k_off - 54*P15*k_off + 18*P16*k_off - 4*P16*k_on + 6*P18*k_coop + 17*P18*k_off - 14*P19*k_coop/3 - 17*P19*k_off/3 - 5*P19*k_on + 18*P2*k_off + 12*P2*k_on + 4*P20*k_coop/3 + 37*P20*k_off/12 - 3*P21*k_off/4 - 4*P22*k_coop + 6*P22*k_off - 5*P22*k_on - 2*P23*k_coop + P23*k_off - 18*P24*k_off + 4*P27*k_coop - P27*k_off + 2*P28*k_coop + 7*P28*k_off + 2*P29*k_coop + 9*P29*k_off + 36*P3*k_off - P30*k_off - 36*P4*k_off - 2*P4*k_on + 6*P5*k_on + 4*P7*k_coop + 12*P7*k_off + P7*k_on - 18*P8*k_off - 2*P8*k_on - 18*P9*k_off - 6*P9*k_on
dP20/dt = 12*P0*k_off - 6*P0*k_on - 2*P11*k_coop - 3*P11*k_off/4 + P11*k_on - P12*k_on/2 + 4*P13*k_coop - 25*P13*k_off + 5*P13*k_on/2 - 15*P14*k_off - 45*P15*k_off + 18*P16*k_off - 2*P16*k_on + 22*P18*k_off + 5*P19*k_coop/3 - 91*P19*k_off/12 + 3*P2*k_off + 6*P2*k_on - 13*P20*k_coop/3 + 11*P20*k_off/12 - 5*P20*k_on - 3*P21*k_off/4 - 2*P22*k_coop - 3*P22*k_off/4 - P22*k_on + 2*P23*k_coop + P23*k_off/2 - 15*P24*k_off - 3*P26*k_off - 4*P27*k_coop + 7*P27*k_off - 2*P28*k_coop + 13*P28*k_off/2 - 5*P29*k_coop + 12*P29*k_off + 30*P3*k_off - P30*k_off/2 - 3*P31*k_coop + 3*P31*k_off - 3*P32*k_off/2 - 27*P4*k_off - P4*k_on - 6*P5*k_off + 3*P5*k_on + 2*P7*k_coop + 75*P7*k_off/4 - P7*k_on - 12*P8*k_off - P8*k_on - 9*P9*k_off - 3*P9*k_on
dP21/dt = 8*P0*k_coop - 132*P0*k_off + 26*P0*k_on + 28*P11*k_coop - 107*P11*k_off/4 + P11*k_on + 10*P12*k_coop + 23*P12*k_on/2 + 2*P13*k_coop + 225*P13*k_off + 21*P13*k_on/2 - 16*P14*k_coop + 153*P14*k_off - 16*P14*k_on - 48*P15*k_coop + 459*P15*k_off - 48*P15*k_on + 8*P16*k_coop - 206*P16*k_off - 2*P16*k_on - 20*P18*k_coop - 192*P18*k_off - 32*P18*k_on + 7*P19*k_coop/3 + 661*P19*k_off/12 + 16*P19*k_on/3 + 8*P2*k_coop - 21*P2*k_off - 10*P2*k_on - 14*P20*k_coop/3 - 527*P20*k_off/12 + 10*P20*k_on/3 - 5*P21*k_coop + 19*P21*k_off/4 - 3*P21*k_on + 28*P22*k_coop - 107*P22*k_off/4 + 15*P22*k_on + 2*P23*k_coop + 5*P23*k_off/2 - 16*P24*k_coop + 153*P24*k_off - 16*P24*k_on - 8*P26*k_coop + 33*P26*k_off - 8*P26*k_on - 8*P27*k_coop - 39*P27*k_off - 10*P28*k_coop - 131*P28*k_off/2 - 17*P29*k_coop - 66*P29*k_off + 32*P3*k_coop - 306*P3*k_off + 32*P3*k_on + 7*P30*k_off/2 - 3*P31*k_coop - 9*P31*k_off + 4*P32*k_coop + P32*k_off/2 - 8*P33*k_coop - 20*P33*k_off + 4*P34*k_off - 20*P4*k_coop + 293*P4*k_off - P4*k_on - 4*P5*k_coop + 66*P5*k_off - 13*P5*k_on - 20*P7*k_coop - 717*P7*k_off/4 - 17*P7*k_on - 12*P8*k_coop + 120*P8*k_off - 9*P8*k_on - 12*P9*k_coop + 87*P9*k_off - 3*P9*k_on
dP22/dt = P17*k_on - 2*P22*k_coop - P22*k_off - 4*P22*k_on + 2*P33*k_off + 2*P35*k_off
dP23/dt = 27*P0*k_coop/2 - 9*P0*k_off + 12*P0*k_on - 25*P11*k_coop/8 - 11*P11*k_off/4 - P11*k_on + 5*P12*k_coop/4 + P12*k_off/2 + P12*k_on + 29*P13*k_coop/4 + 85*P13*k_off/3 - 4*P13*k_on + 6*P14*k_coop + 18*P14*k_off + 18*P15*k_coop + 62*P15*k_off - 11*P16*k_coop/2 - 79*P16*k_off/3 + 4*P16*k_on - 17*P18*k_coop/2 - 143*P18*k_off/6 + 8*P18*k_on + 31*P19*k_coop/24 + 241*P19*k_off/36 - P19*k_on - 39*P2*k_coop/2 - 9*P2*k_off - 12*P2*k_on - 4*P20*k_coop/3 - 205*P20*k_off/72 + 2*P20*k_on + P21*k_coop/4 + 31*P21*k_off/24 - 25*P22*k_coop/8 - 11*P22*k_off/4 - P22*k_on - 17*P23*k_coop/4 - 7*P23*k_off/3 - 3*P23*k_on + 6*P24*k_coop + 18*P24*k_off + 5*P26*k_off - 9*P27*k_coop/2 - 35*P27*k_off/6 - 7*P28*k_coop/4 - 17*P28*k_off/3 - 5*P29*k_coop/2 - 67*P29*k_off/6 - 12*P3*k_coop - 44*P3*k_off + P30*k_coop/4 - P31*k_coop/2 - 11*P31*k_off/3 + 5*P32*k_coop/4 + 7*P32*k_off/6 - 4*P33*k_coop - 13*P33*k_off/3 + 2*P34*k_off/3 - P35*k_coop/2 - P35*k_off + P36*k_coop/2 + 8*P37*k_off + 73*P4*k_coop/4 + 239*P4*k_off/6 + 2*P4*k_on - 27*P5*k_coop/4 + 9*P5*k_off/2 - 6*P5*k_on - 19*P7*k_coop/8 - 283*P7*k_off/12 + 5*P7*k_on + 33*P8*k_coop/4 + 35*P8*k_off/2 + 2*P8*k_on + 51*P9*k_coop/4 + 27*P9*k_off/2 + 6*P9*k_on
dP24/dt = 2*P16*k_coop + 2*P16*k_on - 2*P24*k_coop - 2*P24*k_off - 2*P24*k_on + 2*P37*k_off
dP25/dt = -2*P0*k_coop + 2*P0*k_on - P11*k_coop/2 + 2*P13*k_coop + 4*P14*k_coop + 2*P14*k_on + 4*P15*k_coop + 2*P15*k_on - 2*P16*k_coop - 2*P18*k_coop + P19*k_coop/2 - 2*P2*k_on - P20*k_coop - P22*k_coop/2 - P23*k_coop + 2*P24*k_coop - 4*P25*k_off - 2*P3*k_coop - 2*P3*k_on + 3*P4*k_coop + P4*k_on + P5*k_coop - P5*k_on - 3*P7*k_coop/2 + P8*k_coop + P8*k_on + P9*k_coop + P9*k_on
dP26/dt = 2*P16*k_on - 4*P26*k_coop - 2*P26*k_off - 2*P26*k_on + 2*P37*k_off
dP27/dt = 12*P0*k_off + 2*P11*k_coop + 2*P11*k_off + 2*P11*k_on + P12*k_off - P13*k_off + 4*P16*k_off - 2*P18*k_coop - 2*P18*k_on + 2*P19*k_off/3 - 12*P2*k_off + 2*P20*k_off/3 + 2*P22*k_off - 2*P23*k_off - 4*P27*k_coop - 4*P27*k_off - 8*P27*k_on + 2*P28*k_off + 2*P4*k_off - 6*P5*k_off + 2*P7*k_off + 2*P8*k_off + 6*P9*k_off
dP28/dt = 3*P0*k_coop/2 - 18*P0*k_off - 49*P11*k_coop/8 - 17*P11*k_off/2 - 7*P11*k_on/2 + P12*k_coop/4 + P12*k_off + 25*P13*k_coop/4 + 190*P13*k_off/3 - 4*P13*k_on + 6*P14*k_coop + 42*P14*k_off + 18*P15*k_coop + 134*P15*k_off - 19*P16*k_coop/2 - 178*P16*k_off/3 - 13*P18*k_coop/2 - 169*P18*k_off/3 + 9*P18*k_on - P19*k_coop/24 + 275*P19*k_off/18 - 11*P19*k_on/6 - 15*P2*k_coop/2 - 24*P2*k_off - 5*P20*k_coop/3 - 383*P20*k_off/36 + 5*P20*k_on/3 + P21*k_coop/4 + 29*P21*k_off/12 - 49*P22*k_coop/8 - 17*P22*k_off/2 - 7*P22*k_on/2 + 3*P23*k_coop/4 + 2*P23*k_off/3 + 3*P23*k_on + 6*P24*k_coop + 42*P24*k_off + 8*P26*k_off - P27*k_coop/2 - 43*P27*k_off/3 + 4*P27*k_on - 27*P28*k_coop/4 - 62*P28*k_off/3 - 6*P28*k_on - 5*P29*k_coop/2 - 77*P29*k_off/3 - 12*P3*k_coop - 92*P3*k_off + P30*k_coop/4 + P30*k_off + P31*k_coop/2 - 14*P31*k_off/3 + 5*P32*k_coop/4 + 14*P32*k_off/3 - 4*P33*k_coop - 34*P33*k_off/3 + 2*P34*k_off/3 - P35*k_coop/2 - 2*P35*k_off + P36*k_coop/2 - 6*P36*k_off + 8*P37*k_off - 6*P38*k_off + 65*P4*k_coop/4 + 277*P4*k_off/3 - 3*P5*k_coop/4 + 9*P5*k_off - 27*P7*k_coop/8 - 305*P7*k_off/6 + 7*P7*k_on/2 + 25*P8*k_coop/4 + 39*P8*k_off + 27*P9*k_coop/4 + 33*P9*k_off
dP29/dt = 6*P0*k_coop - P0*k_off/2 + 6*P0*k_on + P11*k_coop/2 + 33*P11*k_off/8 + P12*k_coop/2 - 3*P12*k_off/4 + P12*k_on/2 + P13*k_coop/2 - 87*P13*k_off/4 - P13*k_on/2 - 17*P14*k_off - 51*P15*k_off + 2*P16*k_coop + 41*P16*k_off/2 + 2*P16*k_on + 43*P18*k_off/2 + P18*k_on + 5*P19*k_coop/6 - 127*P19*k_off/24 + P19*k_on/3 - 6*P2*k_coop + 35*P2*k_off/2 - 6*P2*k_on + P20*k_coop/3 + 29*P20*k_off/6 + P20*k_on/3 - 3*P21*k_off/4 + P22*k_coop/2 + 33*P22*k_off/8 + 9*P23*k_off/4 - 17*P24*k_off - P26*k_off - 2*P27*k_coop + 9*P27*k_off/2 + 25*P28*k_off/4 - 5*P29*k_coop + 11*P29*k_off/2 - 6*P29*k_on + 34*P3*k_off - 3*P30*k_off/4 - P31*k_coop + P31*k_off/2 - 7*P32*k_off/4 + 4*P33*k_off + 3*P35*k_off/2 + 3*P36*k_off/2 + 2*P38*k_off - P39*k_off + P4*k_coop - 151*P4*k_off/4 + P4*k_on - 3*P5*k_coop + P5*k_off/4 - 3*P5*k_on + 3*P7*k_coop/2 + 131*P7*k_off/8 + 2*P7*k_on + P8*k_coop - 67*P8*k_off/4 + P8*k_on + 3*P9*k_coop - 69*P9*k_off/4 + 3*P9*k_on
dP30/dt = -93*P0*k_coop/2 + 261*P0*k_off/2 - 58*P0*k_on - 193*P11*k_coop/8 + 657*P11*k_off/8 - 21*P11*k_on - 15*P12*k_coop/4 - 33*P12*k_off/4 - 4*P12*k_on + 85*P13*k_coop/4 - 1765*P13*k_off/4 - 36*P13*k_on + 30*P14*k_coop - 324*P14*k_off - 16*P14*k_on + 90*P15*k_coop - 1032*P15*k_off - 48*P15*k_on - 83*P16*k_coop/2 + 887*P16*k_off/2 + 10*P16*k_on - 23*P18*k_coop/2 + 779*P18*k_off/2 + 53*P18*k_on - 41*P19*k_coop/24 - 2327*P19*k_off/24 - 55*P19*k_on/3 + 33*P2*k_coop/2 + 387*P2*k_off/2 + 74*P2*k_on - 31*P20*k_coop/12 + 899*P20*k_off/12 + 155*P20*k_on/12 + 3*P21*k_coop/2 - 37*P21*k_off/2 - P21*k_on/4 - 193*P22*k_coop/8 + 657*P22*k_off/8 - 21*P22*k_on - 25*P23*k_coop/4 + 73*P23*k_off/4 + 23*P23*k_on + 30*P24*k_coop - 324*P24*k_off - 16*P24*k_on + 6*P26*k_coop - 60*P26*k_off + 10*P26*k_on + 37*P27*k_coop/2 + 131*P27*k_off/2 + 32*P27*k_on - 7*P28*k_coop/4 + 431*P28*k_off/4 - 14*P28*k_on - 3*P29*k_coop/2 + 283*P29*k_off/2 - 18*P29*k_on - 60*P3*k_coop + 708*P3*k_off + 32*P3*k_on - 15*P30*k_coop/4 - 49*P30*k_off/4 - 4*P30*k_on - 9*P31*k_coop/2 + 7*P31*k_off/2 + 17*P32*k_coop/4 - 65*P32*k_off/4 + 2*P33*k_coop + 76*P33*k_off + 10*P33*k_on - 5*P34*k_off + 15*P35*k_coop/2 + 33*P35*k_off/2 + 10*P35*k_on + 17*P36*k_coop/2 - 69*P36*k_off/2 - 60*P37*k_off + 4*P38*k_coop - 66*P38*k_off + 4*P39*k_coop + 57*P39*k_off + 193*P4*k_coop/4 - 2809*P4*k_off/4 - 55*P4*k_on + 4*P40*k_coop - 12*P40*k_off - 6*P41*k_off + 93*P5*k_coop/4 - 261*P5*k_off/4 + 29*P5*k_on - 139*P7*k_coop/8 + 2891*P7*k_off/8 + 31*P7*k_on + 81*P8*k_coop/4 - 1209*P8*k_off/4 - 29*P8*k_on + 27*P9*k_coop/4 - 1035*P9*k_off/4 - 45*P9*k_on
dP31/dt = -6*P0*k_on - 3*P11*k_off/4 + P11*k_on/2 - P12*k_on/2 + 9*P13*k_off/2 + 3*P13*k_on/2 + 3*P14*k_off + 9*P15*k_off - 4*P16*k_off - 2*P16*k_on - 9*P18*k_off/2 + P18*k_on + 5*P19*k_off/4 + P19*k_on/2 - 3*P2*k_off + 6*P2*k_on - 9*P20*k_off/8 + P21*k_off/8 - 3*P22*k_off/4 + P22*k_on/2 - P23*k_coop + 3*P24*k_off - 3*P27*k_off/2 + P28*k_coop - P28*k_off + P29*k_coop - 5*P29*k_off/2 - 6*P3*k_off - 4*P31*k_coop - 5*P31*k_off - 6*P31*k_on + P32*k_off/2 - P33*k_off + P36*k_off + 2*P39*k_off + 7*P4*k_off - P4*k_on + 3*P5*k_on - 13*P7*k_off/4 - 5*P7*k_on/2 + 3*P8*k_off - P8*k_on + 3*P9*k_off - 3*P9*k_on
dP32/dt = 9*P0*k_coop - 63*P0*k_off/2 + 14*P0*k_on + 11*P11*k_coop/4 - 87*P11*k_off/8 + 15*P11*k_on/2 + 3*P12*k_coop/2 + 3*P12*k_off/4 + P12*k_on + 51*P13*k_coop/2 + 255*P13*k_off/4 + 5*P13*k_on + 12*P14*k_coop + 48*P14*k_off - 4*P14*k_on + 36*P15*k_coop + 156*P15*k_off - 12*P15*k_on - 15*P16*k_coop - 133*P16*k_off/2 + 6*P16*k_on - 27*P18*k_coop - 105*P18*k_off/2 - 8*P18*k_on + 107*P19*k_coop/12 + 107*P19*k_off/8 + 9*P19*k_on/2 - 21*P2*k_coop - 33*P2*k_off/2 - 10*P2*k_on - 16*P20*k_coop/3 - 37*P20*k_off/4 - 3*P20*k_on/4 + P21*k_coop/2 + 3*P21*k_off - P21*k_on/4 + 11*P22*k_coop/4 - 87*P22*k_off/8 + 15*P22*k_on/2 + 11*P23*k_coop/2 - 15*P23*k_off/4 + 4*P23*k_on + 12*P24*k_coop + 48*P24*k_off - 4*P24*k_on + 12*P26*k_off - 2*P26*k_on - 15*P27*k_coop - 9*P27*k_off/2 - 12*P27*k_on - 25*P28*k_coop/2 - 49*P28*k_off/4 - 4*P28*k_on - 21*P29*k_coop - 25*P29*k_off/2 - 10*P29*k_on - 24*P3*k_coop - 108*P3*k_off + 8*P3*k_on + P30*k_coop/2 + 3*P30*k_off/4 - 8*P31*k_coop + 7*P31*k_off/2 - 4*P31*k_on - 7*P32*k_coop/2 - 13*P32*k_off/4 - 4*P32*k_on - 6*P33*k_coop - 8*P33*k_off - 2*P33*k_on + P34*k_off - 3*P35*k_coop - 3*P35*k_off/2 - 2*P35*k_on - P36*k_coop + 3*P36*k_off/2 + 12*P37*k_off - 2*P38*k_coop + 8*P38*k_off - 11*P39*k_off + 63*P4*k_coop/2 + 395*P4*k_off/4 - 3*P4*k_on + 4*P40*k_off + 14*P41*k_off/13 - 8*P42*k_off/13 - 9*P5*k_coop/2 + 63*P5*k_off/4 - 7*P5*k_on - 71*P7*k_coop/4 - 445*P7*k_off/8 - 3*P7*k_on/2 + 27*P8*k_coop/2 + 171*P8*k_off/4 - P8*k_on + 33*P9*k_coop/2 + 129*P9*k_off/4 + 3*P9*k_on
dP33/dt = 21*P0*k_off/2 + 13*P11*k_off/8 - P12*k_off/4 - 275*P13*k_off/12 - 13*P14*k_off - 43*P15*k_off + 121*P16*k_off/6 + 115*P18*k_off/6 - 433*P19*k_off/72 + 7*P2*k_off/2 + 133*P20*k_off/36 - 5*P21*k_off/6 + 2*P22*k_coop + 13*P22*k_off/8 + 2*P22*k_on - 13*P23*k_off/12 - 14*P24*k_off - 4*P26*k_off + 37*P27*k_off/6 + 73*P28*k_off/12 + 53*P29*k_off/6 + 29*P3*k_off - P30*k_off/4 + 11*P31*k_off/6 - 19*P32*k_off/12 - 2*P33*k_coop + 5*P33*k_off/3 - 3*P33*k_on - P34*k_off/3 - P35*k_off/2 + P36*k_off/2 - 4*P37*k_off - P38*k_off + 3*P39*k_off - 347*P4*k_off/12 - 3*P41*k_off/13 - 2*P42*k_off/13 + P43*k_off - 21*P5*k_off/4 + 445*P7*k_off/24 - 45*P8*k_off/4 - 35*P9*k_off/4
dP34/dt = -227*P0*k_coop/4 + 87*P0*k_off/2 - 97*P0*k_on - 395*P11*k_coop/16 + 127*P11*k_off/8 - 49*P11*k_on/4 - 81*P12*k_coop/8 + 5*P12*k_off/4 - 23*P12*k_on/2 + 379*P13*k_coop/8 - 895*P13*k_off/12 + 93*P13*k_on/2 + 67*P14*k_coop - 45*P14*k_off + 32*P14*k_on + 177*P15*k_coop - 179*P15*k_off + 84*P15*k_on - 321*P16*k_coop/4 + 515*P16*k_off/6 - 65*P16*k_on - 177*P18*k_coop/4 + 160*P18*k_off/3 - 31*P18*k_on + 157*P19*k_coop/48 - 839*P19*k_off/72 + 71*P19*k_on/12 + 79*P2*k_coop/4 - 7*P2*k_off/2 + 89*P2*k_on - 115*P20*k_coop/24 + 109*P20*k_off/72 - 29*P20*k_on/6 + 7*P21*k_coop/2 - 109*P21*k_off/24 + 2*P21*k_on - 395*P22*k_coop/16 + 127*P22*k_off/8 - 49*P22*k_on/4 + 13*P23*k_coop/8 - 209*P23*k_off/12 + 51*P23*k_on/2 + 37*P24*k_coop - 40*P24*k_off + 8*P24*k_on + 12*P25*k_off - 7*P26*k_coop - 20*P26*k_off + 4*P26*k_on + 91*P27*k_coop/4 + 25*P27*k_off/3 + P27*k_on - 145*P28*k_coop/8 + 227*P28*k_off/12 - 30*P28*k_on - 61*P29*k_coop/4 + 59*P29*k_off/3 - 27*P29*k_on - 140*P3*k_coop + 139*P3*k_off - 76*P3*k_on + 11*P30*k_coop/8 + 5*P30*k_off/4 - 17*P31*k_coop/4 + 73*P31*k_off/6 - 6*P31*k_on - 21*P32*k_coop/8 + 97*P32*k_off/12 - P32*k_on + 55*P33*k_off/3 - 6*P33*k_on - 4*P34*k_coop - 26*P34*k_off/3 - 2*P34*k_on - 39*P35*k_coop/4 + 5*P35*k_off/2 - P35*k_on + 7*P36*k_coop/4 - 59*P36*k_off/2 - 24*P37*k_coop - 44*P37*k_off - 12*P37*k_on - P38*k_coop - 32*P38*k_off + 6*P39*k_off + 711*P4*k_coop/8 - 1249*P4*k_off/12 + 49*P4*k_on/2 + 2*P40*k_off - 8*P41*k_off/13 - 14*P42*k_off/13 - 6*P43*k_coop + 5*P43*k_off - 12*P44*k_off + 227*P5*k_coop/8 - 87*P5*k_off/4 + 97*P5*k_on/2 - 889*P7*k_coop/16 + 1679*P7*k_off/24 - 211*P7*k_on/4 + 415*P8*k_coop/8 - 183*P8*k_off/4 + 21*P8*k_on/2 + 69*P9*k_coop/8 - 73*P9*k_off/4 - 81*P9*k_on/2
dP35/dt = 21*P0*k_off + 13*P11*k_off/4 - P12*k_off/2 - 275*P13*k_off/6 - 26*P14*k_off - 86*P15*k_off + 121*P16*k_off/3 + 115*P18*k_off/3 - 433*P19*k_off/36 + 7*P2*k_off + 133*P20*k_off/18 - 5*P21*k_off/3 + 13*P22*k_off/4 + 2*P22*k_on - 13*P23*k_off/6 - 28*P24*k_off - 8*P26*k_off + 37*P27*k_off/3 + 73*P28*k_off/6 + 53*P29*k_off/3 + 58*P3*k_off - P30*k_off/2 + 11*P31*k_off/3 - 19*P32*k_off/6 + 22*P33*k_off/3 - 2*P34*k_off/3 - 4*P35*k_coop - 3*P35*k_off - 3*P35*k_on + P36*k_off - 8*P37*k_off - 2*P38*k_off + 6*P39*k_off - 347*P4*k_off/6 - 6*P41*k_off/13 - 4*P42*k_off/13 - P43*k_off - 21*P5*k_off/2 + 445*P7*k_off/12 - 45*P8*k_off/2 - 35*P9*k_off/2
dP36/dt = -37*P0*k_coop/4 + 3*P0*k_off - 19*P0*k_on + 75*P11*k_coop/16 - 15*P11*k_off/4 + P11*k_on/4 - 7*P12*k_coop/8 + P12*k_off/2 - P12*k_on/2 - 83*P13*k_coop/8 + 10*P13*k_off + 13*P13*k_on/2 - 13*P14*k_coop + 9*P14*k_off + 2*P14*k_on - 39*P15*k_coop + 27*P15*k_off + 6*P15*k_on + 49*P16*k_coop/4 - 11*P16*k_off - 7*P16*k_on + 49*P18*k_coop/4 - 21*P18*k_off/2 - 2*P18*k_on - 31*P19*k_coop/16 + 19*P19*k_off/12 + 13*P19*k_on/12 + 89*P2*k_coop/4 - 11*P2*k_off + 17*P2*k_on + 25*P20*k_coop/8 - 49*P20*k_off/24 - 5*P20*k_on/12 - P21*k_coop/2 + 3*P21*k_off/8 + P21*k_on/4 + 75*P22*k_coop/16 - 15*P22*k_off/4 + P22*k_on/4 + 35*P23*k_coop/8 - P23*k_off + 3*P23*k_on/2 - 13*P24*k_coop + 8*P24*k_off + 2*P24*k_on + P26*k_coop + 4*P26*k_on - 3*P27*k_coop/4 - 3*P27*k_off/2 + 9*P28*k_coop/8 - 7*P28*k_off/2 - 2*P28*k_on + 5*P29*k_coop/4 - 11*P29*k_off/2 + 26*P3*k_coop - 19*P3*k_off - 4*P3*k_on - 3*P30*k_coop/8 + P30*k_off/2 + P31*k_coop/4 - 4*P31*k_on - 3*P32*k_coop/8 + P32*k_off + 2*P33*k_coop - 3*P33*k_off + 7*P35*k_coop/4 - 2*P35*k_off + P35*k_on - 15*P36*k_coop/4 - 7*P36*k_off - 4*P36*k_on + 3*P38*k_coop - 8*P38*k_off - 2*P39*k_coop + 10*P39*k_off - 239*P4*k_coop/8 + 41*P4*k_off/2 - P4*k_on/2 - 2*P40*k_coop - 6*P41*k_off/13 - 4*P42*k_off/13 - P43*k_off + 37*P5*k_coop/8 - 3*P5*k_off/2 + 19*P5*k_on/2 + 121*P7*k_coop/16 - 29*P7*k_off/4 - 29*P7*k_on/4 - 119*P8*k_coop/8 + 19*P8*k_off/2 - 5*P8*k_on/2 - 141*P9*k_coop/8 + 19*P9*k_off/2 - 15*P9*k_on/2
dP37/dt = 2*P24*k_coop + 2*P24*k_on + 2*P26*k_coop + P26*k_on - 2*P37*k_coop - 3*P37*k_off - P37*k_on + P44*k_off
dP38/dt = 3*P0*k_coop + 21*P0*k_off/2 + 12*P0*k_on - 19*P11*k_coop/4 + 17*P11*k_off/8 + P11*k_on/2 + P12*k_coop/2 - P12*k_off/4 + 43*P13*k_coop/2 - 293*P13*k_off/12 + P13*k_on/2 + 18*P14*k_coop - 15*P14*k_off + 54*P15*k_coop - 49*P15*k_off - 21*P16*k_coop + 133*P16*k_off/6 + 2*P16*k_on - 22*P18*k_coop + 62*P18*k_off/3 - 7*P18*k_on/2 + 65*P19*k_coop/12 - 457*P19*k_off/72 + 4*P19*k_on/3 - 21*P2*k_coop + 11*P2*k_off/2 - 12*P2*k_on - 67*P20*k_coop/12 + 287*P20*k_off/72 - 25*P20*k_on/24 + 3*P21*k_coop/4 - 23*P21*k_off/24 - P21*k_on/8 - 19*P22*k_coop/4 + 17*P22*k_off/8 + P22*k_on/2 - 5*P23*k_coop/2 - 7*P23*k_off/12 + P23*k_on/2 + 18*P24*k_coop - 16*P24*k_off - 4*P26*k_off - 3*P26*k_on - 4*P27*k_coop + 17*P27*k_off/3 - 7*P27*k_on/2 - 11*P28*k_coop/2 + 73*P28*k_off/12 - P28*k_on - 8*P29*k_coop + 25*P29*k_off/3 - 9*P29*k_on/2 - 36*P3*k_coop + 33*P3*k_off + P30*k_coop/2 - P30*k_off/4 - 3*P31*k_coop + 11*P31*k_off/6 + 2*P31*k_on + 3*P32*k_coop/2 - 13*P32*k_off/12 + P32*k_on/2 - 4*P33*k_coop + 11*P33*k_off/3 - P33*k_on - P34*k_off/3 - P35*k_coop - P35*k_off/2 - 3*P36*k_coop - P36*k_off/2 - P36*k_on - 4*P37*k_off - 10*P38*k_coop - 5*P38*k_on + 2*P39*k_coop - 9*P39*k_off + 81*P4*k_coop/2 - 395*P4*k_off/12 + 4*P4*k_on + 2*P40*k_coop + 4*P41*k_off/13 - 6*P42*k_off/13 - P43*k_off + P45*k_off - 3*P5*k_coop/2 - 21*P5*k_off/4 - 6*P5*k_on - 65*P7*k_coop/4 + 481*P7*k_off/24 + 3*P7*k_on/2 + 37*P8*k_coop/2 - 53*P8*k_off/4 + 3*P8*k_on + 39*P9*k_coop/2 - 43*P9*k_off/4 + 6*P9*k_on
dP39/dt = 3*P0*k_coop/2 - 21*P0*k_off/2 + 13*P0*k_on/2 - 13*P11*k_coop/8 - 17*P11*k_off/8 + 21*P11*k_on/8 + P12*k_coop/4 + P12*k_off/4 - P12*k_on/4 + 33*P13*k_coop/4 + 293*P13*k_off/12 - 53*P13*k_on/4 + 6*P14*k_coop + 15*P14*k_off - 10*P14*k_on + 18*P15*k_coop + 49*P15*k_off - 30*P15*k_on - 15*P16*k_coop/2 - 133*P16*k_off/6 + 27*P16*k_on/2 - 17*P18*k_coop/2 - 62*P18*k_off/3 + 23*P18*k_on/2 + 17*P19*k_coop/8 + 457*P19*k_off/72 - 67*P19*k_on/24 - 15*P2*k_coop/2 - 11*P2*k_off/2 + 7*P2*k_on/2 - 2*P20*k_coop - 287*P20*k_off/72 + 31*P20*k_on/12 + P21*k_coop/4 + 23*P21*k_off/24 - P21*k_on/2 - 13*P22*k_coop/8 - 17*P22*k_off/8 + 21*P22*k_on/8 - P23*k_coop/4 + 7*P23*k_off/12 + 5*P23*k_on/4 + 6*P24*k_coop + 16*P24*k_off - 10*P24*k_on + 4*P26*k_off - 2*P26*k_on - 5*P27*k_coop/2 - 17*P27*k_off/3 + 3*P27*k_on/2 - 11*P28*k_coop/4 - 73*P28*k_off/12 + 11*P28*k_on/4 - 9*P29*k_coop/2 - 25*P29*k_off/3 + 7*P29*k_on/2 - 12*P3*k_coop - 33*P3*k_off + 20*P3*k_on + P30*k_coop/4 + P30*k_off/4 - P30*k_on/4 - 3*P31*k_coop/2 - 11*P31*k_off/6 + 7*P31*k_on/2 + 5*P32*k_coop/4 + 13*P32*k_off/12 - P32*k_on/4 - 2*P33*k_coop - 11*P33*k_off/3 + 2*P33*k_on + P34*k_off/3 - P35*k_coop/2 + P35*k_off/2 + P35*k_on/2 - 3*P36*k_coop/2 + P36*k_off/2 - P36*k_on/2 + 4*P37*k_off - 2*P38*k_coop + 4*P38*k_off - 6*P39*k_coop - 11*P39*k_off - 5*P39*k_on + 57*P4*k_coop/4 + 395*P4*k_off/12 - 81*P4*k_on/4 + 4*P41*k_off/13 - 6*P42*k_off/13 + P43*k_off - 3*P5*k_coop/4 + 21*P5*k_off/4 - 13*P5*k_on/4 - 47*P7*k_coop/8 - 481*P7*k_off/24 + 87*P7*k_on/8 + 25*P8*k_coop/4 + 53*P8*k_off/4 - 33*P8*k_on/4 + 27*P9*k_coop/4 + 43*P9*k_off/4 - 27*P9*k_on/4
dP40/dt = -27*P0*k_coop/4 + 3*P0*k_off/2 - 6*P0*k_on + P11*k_coop/16 - 21*P11*k_off/8 - 5*P11*k_on/4 - 5*P12*k_coop/8 + P12*k_off/4 - P12*k_on/2 - 5*P13*k_coop/8 + 11*P13*k_off/4 + 5*P13*k_on/2 - 3*P14*k_coop + 3*P14*k_off - 9*P15*k_coop + 9*P15*k_off + 3*P16*k_coop/4 - 9*P16*k_off/2 - 3*P16*k_on + 9*P18*k_coop/4 - 3*P18*k_off - P18*k_on + P19*k_coop/48 - 3*P19*k_off/8 + 7*P19*k_on/12 + 39*P2*k_coop/4 - 7*P2*k_off/2 + 6*P2*k_on - P20*k_coop/6 - 3*P20*k_off/8 - 7*P20*k_on/6 - P21*k_coop/8 + P21*k_off/8 + P22*k_coop/16 - 21*P22*k_off/8 - 5*P22*k_on/4 + 5*P23*k_coop/8 + P23*k_off/4 - P23*k_on/2 - 3*P24*k_coop + 2*P24*k_off - 3*P27*k_coop/4 + 3*P28*k_coop/8 - 7*P28*k_off/4 + P29*k_coop/4 - 2*P29*k_off + 6*P3*k_coop - 7*P3*k_off - P30*k_coop/8 + P30*k_off/4 - P31*k_coop/4 + P31*k_off/2 - 5*P32*k_coop/8 + 3*P32*k_off/4 - 2*P33*k_off - P33*k_on + P35*k_coop/4 - 3*P35*k_off/2 - P36*k_coop/4 - P36*k_off/2 + P38*k_off - 3*P39*k_off - 57*P4*k_coop/8 + 29*P4*k_off/4 - 4*P40*k_coop - 4*P40*k_off - 4*P40*k_on + 3*P41*k_off/13 + 2*P42*k_off/13 - P43*k_off + 27*P5*k_coop/8 - 3*P5*k_off/4 + 3*P5*k_on + 11*P7*k_coop/16 - 15*P7*k_off/8 - 7*P7*k_on/4 - 33*P8*k_coop/8 + 13*P8*k_off/4 - P8*k_on - 51*P9*k_coop/8 + 11*P9*k_off/4 - 3*P9*k_on
dP41/dt = -3*P0*k_coop - 198*P0*k_off - 29*P0*k_on + 61*P11*k_coop/4 - 103*P11*k_off/2 + 51*P11*k_on/4 - P12*k_coop/2 + 9*P12*k_off - 3*P12*k_on/2 - 113*P13*k_coop/2 + 1912*P13*k_off/3 - 100*P13*k_on - 60*P14*k_coop + 370*P14*k_off - 74*P14*k_on - 180*P15*k_coop + 1194*P15*k_off - 222*P15*k_on + 63*P16*k_coop - 1654*P16*k_off/3 + 83*P16*k_on + 57*P18*k_coop - 1687*P18*k_off/3 + 213*P18*k_on/2 - 163*P19*k_coop/12 + 3113*P19*k_off/18 - 121*P19*k_on/4 + 63*P2*k_coop - 198*P2*k_off + 103*P2*k_on + 50*P20*k_coop/3 - 4031*P20*k_off/36 + 199*P20*k_on/8 - 5*P21*k_coop/2 + 269*P21*k_off/12 - 23*P21*k_on/8 + 61*P22*k_coop/4 - 103*P22*k_off/2 + 51*P22*k_on/4 + 33*P23*k_coop/2 + 98*P23*k_off/3 + 10*P23*k_on - 60*P24*k_coop + 396*P24*k_off - 74*P24*k_on + 84*P26*k_off + 5*P26*k_on - 3*P27*k_coop - 577*P27*k_off/3 + 65*P27*k_on/2 + 11*P28*k_coop/2 - 557*P28*k_off/3 + 43*P28*k_on/2 + P29*k_coop - 845*P29*k_off/3 + 99*P29*k_on/2 + 120*P3*k_coop - 798*P3*k_off + 148*P3*k_on - P30*k_coop/2 + 9*P30*k_off - 3*P30*k_on/2 + 3*P31*k_coop - 248*P31*k_off/3 + 37*P31*k_on + 31*P32*k_coop/2 + 122*P32*k_off/3 + 8*P32*k_on + 4*P33*k_coop - 346*P33*k_off/3 + 17*P33*k_on + 26*P34*k_off/3 + P35*k_coop + 8*P35*k_off + 3*P35*k_on + 7*P36*k_coop - 22*P36*k_off + 84*P37*k_off + 24*P38*k_coop - 14*P38*k_off + 19*P38*k_on - 42*P39*k_coop - 26*P39*k_off - 37*P39*k_on - 249*P4*k_coop/2 + 2545*P4*k_off/3 - 343*P4*k_on/2 - 16*P40*k_coop - 20*P40*k_off + 2*P40*k_on - 48*P41*k_coop/13 - 4*P41*k_off - 24*P41*k_on/13 + 20*P42*k_coop/13 + 4*P42*k_off + 10*P42*k_on/13 + 26*P43*k_off - 7*P45*k_off - 20*P46*k_off + 3*P5*k_coop/2 + 99*P5*k_off + 29*P5*k_on/2 + 191*P7*k_coop/4 - 2999*P7*k_off/6 + 281*P7*k_on/4 - 121*P8*k_coop/2 + 337*P8*k_off - 161*P8*k_on/2 - 123*P9*k_coop/2 + 297*P9*k_off - 177*P9*k_on/2
dP42/dt = 9*P0*k_coop/2 - 15*P0*k_off + 31*P0*k_on/4 - 27*P11*k_coop/8 - 3*P11*k_off/4 - 33*P11*k_on/16 + 3*P12*k_coop/4 - P12*k_off/2 + 5*P12*k_on/8 + 79*P13*k_coop/4 - P13*k_off/2 + 121*P13*k_on/8 + 12*P14*k_coop + 4*P14*k_off + 7*P14*k_on + 36*P15*k_coop + 16*P15*k_off + 21*P15*k_on - 33*P16*k_coop/2 - 5*P16*k_off - 43*P16*k_on/4 - 41*P18*k_coop/2 + 5*P18*k_off - 67*P18*k_on/4 + 125*P19*k_coop/24 - 19*P19*k_off/12 + 215*P19*k_on/48 - 33*P2*k_coop/2 + 11*P2*k_off - 59*P2*k_on/4 - 53*P20*k_coop/12 + 5*P20*k_off/3 - 83*P20*k_on/24 + P21*k_coop/2 + P21*k_off/2 + P21*k_on/4 - 27*P22*k_coop/8 - 3*P22*k_off/4 - 33*P22*k_on/16 + 5*P23*k_coop/4 - 7*P23*k_off/2 + 23*P23*k_on/8 + 12*P24*k_coop + 4*P24*k_off + 7*P24*k_on + 4*P26*k_off - P26*k_on - 17*P27*k_coop/2 + 9*P27*k_off - 39*P27*k_on/4 - 33*P28*k_coop/4 + 11*P28*k_off/2 - 63*P28*k_on/8 - 29*P29*k_coop/2 + 13*P29*k_off - 63*P29*k_on/4 - 24*P3*k_coop - 12*P3*k_off - 14*P3*k_on + 3*P30*k_coop/4 - P30*k_off/2 + 5*P30*k_on/8 - 9*P31*k_coop/2 + 7*P31*k_off - 27*P31*k_on/4 + 11*P32*k_coop/4 - 5*P32*k_off/2 + 21*P32*k_on/8 - 6*P33*k_coop + 4*P33*k_off - 6*P33*k_on - 3*P35*k_coop/2 + P35*k_off - 5*P35*k_on/4 - 21*P36*k_coop/2 + 7*P36*k_off - 39*P36*k_on/4 + 4*P37*k_off - 10*P38*k_coop + 8*P38*k_off - 9*P38*k_on - 2*P39*k_coop - 3*P39*k_on + 123*P4*k_coop/4 + 3*P4*k_off/2 + 173*P4*k_on/8 - 2*P40*k_coop + 4*P40*k_off - 3*P40*k_on - 6*P41*k_coop/13 - 3*P41*k_on/13 - 82*P42*k_coop/13 - 10*P42*k_off - 41*P42*k_on/13 + 4*P45*k_off + 4*P46*k_off - 9*P5*k_coop/4 + 15*P5*k_off/2 - 31*P5*k_on/8 - 105*P7*k_coop/8 - 17*P7*k_off/4 - 139*P7*k_on/16 + 51*P8*k_coop/4 + 3*P8*k_off/2 + 69*P8*k_on/8 + 57*P9*k_coop/4 - 7*P9*k_off/2 + 87*P9*k_on/8
dP43/dt = 2*P33*k_coop + 2*P33*k_on + 2*P35*k_coop + P35*k_on - 2*P43*k_coop - 3*P43*k_off - 2*P43*k_on + 2*P46*k_off
dP44/dt = 8*P37*k_coop + 4*P37*k_on - 4*P44*k_off
dP45/dt = -45*P0*k_coop - 27*P0*k_off/2 - 43*P0*k_on/2 - 21*P11*k_coop/4 - 31*P11*k_off/8 + 5*P11*k_on/8 + P12*k_coop/2 + 3*P12*k_off/4 - P12*k_on/4 + 487*P13*k_coop/6 + 589*P13*k_off/12 + 271*P13*k_on/12 + 48*P14*k_coop + 28*P14*k_off + 10*P14*k_on + 160*P15*k_coop + 90*P15*k_off + 38*P15*k_on - 221*P16*k_coop/3 - 251*P16*k_off/6 - 119*P16*k_on/6 - 197*P18*k_coop/3 - 263*P18*k_off/6 - 46*P18*k_on/3 + 761*P19*k_coop/36 + 971*P19*k_off/72 + 443*P19*k_on/72 - 7*P2*k_coop - 33*P2*k_off/2 + 19*P2*k_on/2 - 215*P20*k_coop/18 - 317*P20*k_off/36 - 145*P20*k_on/72 + 10*P21*k_coop/3 + 5*P21*k_off/3 + 25*P21*k_on/24 - 21*P22*k_coop/4 - 31*P22*k_off/8 + 5*P22*k_on/8 + 17*P23*k_coop/6 + 35*P23*k_off/12 + 41*P23*k_on/12 + 52*P24*k_coop + 30*P24*k_off + 12*P24*k_on + 16*P26*k_coop + 6*P26*k_off + 7*P26*k_on - 53*P27*k_coop/3 - 95*P27*k_off/6 - 16*P27*k_on/3 - 113*P28*k_coop/6 - 179*P28*k_off/12 - 59*P28*k_on/12 - 73*P29*k_coop/3 - 139*P29*k_off/6 - 17*P29*k_on/3 - 108*P3*k_coop - 60*P3*k_off - 26*P3*k_on + P30*k_coop/2 + 3*P30*k_off/4 - P30*k_on/4 - 13*P31*k_coop/3 - 43*P31*k_off/6 - 7*P31*k_on/6 + 23*P32*k_coop/6 + 41*P32*k_off/12 + 11*P32*k_on/12 - 32*P33*k_coop/3 - 28*P33*k_off/3 - 7*P33*k_on/3 + 4*P34*k_coop/3 + 2*P34*k_off/3 + 2*P34*k_on/3 + 3*P35*k_coop + P35*k_off/2 + 5*P35*k_on/2 + P36*k_coop - 5*P36*k_off/2 + P36*k_on/2 + 16*P37*k_coop + 6*P37*k_off + 8*P37*k_on + 8*P38*k_coop - 2*P38*k_off + 5*P38*k_on - 14*P39*k_coop - 2*P39*k_off - 9*P39*k_on + 619*P4*k_coop/6 + 781*P4*k_off/12 + 253*P4*k_on/12 - 2*P40*k_off + 12*P41*k_coop/13 + 2*P41*k_off/13 + 6*P41*k_on/13 + 8*P42*k_coop/13 + 10*P42*k_off/13 + 4*P42*k_on/13 + 4*P43*k_coop + 2*P43*k_off + 2*P43*k_on - 8*P45*k_coop - 7*P45*k_off - 4*P45*k_on - 2*P46*k_off + 45*P5*k_coop/2 + 27*P5*k_off/4 + 43*P5*k_on/4 - 821*P7*k_coop/12 - 911*P7*k_off/24 - 491*P7*k_on/24 + 81*P8*k_coop/2 + 103*P8*k_off/4 + 27*P8*k_on/4 + 59*P9*k_coop/2 + 93*P9*k_off/4 + 5*P9*k_on/4
dP46/dt = 42*P0*k_coop + 21*P0*k_on + 13*P11*k_coop/2 + 13*P11*k_on/4 - P12*k_coop - P12*k_on/2 - 275*P13*k_coop/3 - 275*P13*k_on/6 - 52*P14*k_coop - 26*P14*k_on - 172*P15*k_coop - 86*P15*k_on + 242*P16*k_coop/3 + 121*P16*k_on/3 + 230*P18*k_coop/3 + 115*P18*k_on/3 - 433*P19*k_coop/18 - 433*P19*k_on/36 + 14*P2*k_coop + 7*P2*k_on + 133*P20*k_coop/9 + 133*P20*k_on/18 - 10*P21*k_coop/3 - 5*P21*k_on/3 + 13*P22*k_coop/2 + 13*P22*k_on/4 - 13*P23*k_coop/3 - 13*P23*k_on/6 - 56*P24*k_coop - 28*P24*k_on - 16*P26*k_coop - 8*P26*k_on + 74*P27*k_coop/3 + 37*P27*k_on/3 + 73*P28*k_coop/3 + 73*P28*k_on/6 + 106*P29*k_coop/3 + 53*P29*k_on/3 + 116*P3*k_coop + 58*P3*k_on - P30*k_coop - P30*k_on/2 + 22*P31*k_coop/3 + 11*P31*k_on/3 - 19*P32*k_coop/3 - 19*P32*k_on/6 + 44*P33*k_coop/3 + 22*P33*k_on/3 - 4*P34*k_coop/3 - 2*P34*k_on/3 - 2*P35*k_coop - P35*k_on + 2*P36*k_coop + P36*k_on - 16*P37*k_coop - 8*P37*k_on - 4*P38*k_coop - 2*P38*k_on + 12*P39*k_coop + 6*P39*k_on - 347*P4*k_coop/3 - 347*P4*k_on/6 - 12*P41*k_coop/13 - 6*P41*k_on/13 - 8*P42*k_coop/13 - 4*P42*k_on/13 - 2*P43*k_coop - 2*P46*k_coop - 4*P46*k_off - P46*k_on + P47*k_off - 21*P5*k_coop - 21*P5*k_on/2 + 445*P7*k_coop/6 + 445*P7*k_on/12 - 45*P8*k_coop - 45*P8*k_on/2 - 35*P9*k_coop - 35*P9*k_on/2
dP47/dt = 10*P46*k_coop + 5*P46*k_on - 5*P47*k_off