{ diff(x1, t) = ((-1)*k2*x1/(k3 + x1) + 1*k4*x2/(k5 + x2))/k1,
  diff(x2, t) = (1*k2*x1/(k3 + x1) + (-1)*k4*x2/(k5 + x2))/k1,
  diff(x3, t) = ((-1)*k6*x1*x3/(k7 + x3) + 1*k8*x4/(k9 + x4))/k1,
  diff(x4, t) = (1*k6*x1*x3/(k7 + x3) + (-1)*k8*x4/(k9 + x4))/k1,
  diff(x5, t) = ((-1)*k10*x4*x5/(k11 + x5) + 1*k12*x6/(k13 + x6))/k1,
  diff(x6, t) = (1*k10*x4*x5/(k11 + x5) + (-1)*k12*x6/(k13 + x6))/k1,
  diff(x7, t) = ((-1)*k14*x6*x7/(k15 + x7) + 1*k16*x8/k17/(1 + x8/k17 + k18/k19))/k1,
  diff(x8, t) = (1*k14*x6*x7/(k15 + x7) + (-1)*k16*x8/k17/(1 + x8/k17 + k18/k19))/k1 }