network (Lck, ZAP-70 constant, no CD8), ZAP-docking levels = 3 , Lck-MM intermediates: False
== reduced network: species=18 complexes=21 linkage=2 rank=16 deficiency=3 reactions=35 weakly_rev=False
   linkage-class deficiencies [0, 0]  sum 0  terminal SLCs per LC [1, 1]
   Deficiency One Theorem hypotheses satisfied: False
rate constants (irreversible reactions):
   J0+     TCR + pMHC1 -> Complex                   k = 100
   J0-     Complex -> TCR + pMHC1                   k = 1/100
   J185+   TCR_ZAP -> TCR                           k = 1/10
   J10+    Complex_ZAP -> TCR_ZAP + pMHC1           k = 1
   J10-    TCR_ZAP + pMHC1 -> Complex_ZAP           k = 1
   J5+     Complex_ITAM1_PP -> Complex_ZAP          k = 1/10
   J5-     Complex_ZAP -> Complex_ITAM1_PP          k = 1/100
   J4+     Complex_ITAM1_P -> Complex_ITAM1_PP      k = 1
   J2+     Complex -> Complex_ITAM1_P               k = 1/100
   J7+     Complex_ZAP -> Complex_ZAP_ITAM2_P       k = 100
   J9+     Complex_ZAP_ITAM2_P -> Complex_ZAP_ITAM2_PP k = 1
   J15+    Complex_ZAP_ITAM2_PP -> TCR_ZAP + pMHC1  k = 1/100
   J14+    Complex_ZAP_ITAM2_P -> TCR_ZAP + pMHC1   k = 1
   J248+   TCR_2ZAP -> TCR_ZAP                      k = 1/1000
   J12+    Complex_ITAM1_P -> TCR + pMHC1           k = 1
   J13+    Complex_ITAM1_PP -> TCR + pMHC1          k = 10
   J240+   Complex_ZAP_ITAM2_PP -> Complex_2ZAP     k = 1
   J240-   Complex_2ZAP -> Complex_ZAP_ITAM2_PP     k = 1/10
   J245+   Complex_2ZAP -> TCR_2ZAP + pMHC1         k = 100
   J245-   TCR_2ZAP + pMHC1 -> Complex_2ZAP         k = 1/100
   J243+   Complex_2ZAP -> Complex_2ZAP_ITAM3_P     k = 1
   J244+   Complex_2ZAP_ITAM3_P -> Complex_2ZAP_ITAM3_PP k = 1
   J247+   Complex_2ZAP_ITAM3_PP -> TCR_2ZAP + pMHC1 k = 1
   J251+   TCR_3ZAP -> TCR_2ZAP                     k = 1
   J246+   Complex_2ZAP_ITAM3_P -> TCR_2ZAP + pMHC1 k = 1
   J249+   Complex_2ZAP_ITAM3_PP -> Complex_3ZAP    k = 1/1000
   J249-   Complex_3ZAP -> Complex_2ZAP_ITAM3_PP    k = 1
   J250+   Complex_3ZAP -> TCR_3ZAP + pMHC1         k = 1
   J250-   TCR_3ZAP + pMHC1 -> Complex_3ZAP         k = 1
   J255+   Complex_3ZAP -> Complex_3ZAP_P           k = 1
   J256+   Complex_3ZAP_P -> Complex_3ZAP_2P        k = 1
   J257+   Complex_3ZAP_2P -> Complex_3ZAP_3P       k = 1
   J258+   Complex_3ZAP_P -> TCR_3ZAP + pMHC1       k = 1
   J259+   Complex_3ZAP_2P -> TCR_3ZAP + pMHC1      k = 1
   J260+   Complex_3ZAP_3P -> TCR_3ZAP + pMHC1      k = 1
numerical: local max phi=0.962951 at L=2.884e-02 ; subsequent min phi=0.061297 at L=1.380e+02
L1 = 6/625  L3 = 410   phi(L1) = 0.954512798009  phi(L3) = 0.0926544433847
R_tot = 308985806878679027119754571114189984611091/649532279582020475676233757039525805625  (~475.705)
L_tot = 11797485703149968343038054650385971589943/25981291183280819027049350281581032225  (~454.076)
exact steady state at L = 6/625 : f(x)=0 verified exactly; totals R_tot, L_tot match; all 18 coordinates positive
exact steady state at L = 410 : f(x)=0 verified exactly; totals R_tot, L_tot match; all 18 coordinates positive
g(L)=L+R_tot*phi(L)-L_tot : g(99/10000)>0 and g(11/125)<0 exactly -> a third steady state with L in between
third root L2 in [0.0867243253404, 0.0867243253405]
steady state at L1: reduced char. poly degree 16; Routh-Hurwitz first column all positive: True
steady state at L3: reduced char. poly degree 16; Routh-Hurwitz first column all positive: True
middle state (approximate): eigenvalues with largest real parts: 0.00494+0i, 3.269e-15+0i, 1.922e-16+0i, -0.1439+0i
