network (Lck, ZAP-70 constant, no CD8), ZAP-docking levels = 3 , Lck-MM intermediates: True
== reduced network: species=27 complexes=30 linkage=2 rank=25 deficiency=3 reactions=53 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):
   J1+     Complex -> Node3                         k = 1/100
   J1-     Node3 -> Complex                         k = 1
   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+     Node6 -> Complex_ITAM1_PP                k = 1000
   J2+     Node3 -> Complex_ITAM1_P                 k = 1000
   J3+     Complex_ITAM1_P -> Node6                 k = 1
   J3-     Node6 -> Complex_ITAM1_P                 k = 1
   J6+     Complex_ZAP -> Node10                    k = 100
   J6-     Node10 -> Complex_ZAP                    k = 1
   J7+     Node10 -> Complex_ZAP_ITAM2_P            k = 1000
   J8+     Complex_ZAP_ITAM2_P -> Node12            k = 1
   J8-     Node12 -> Complex_ZAP_ITAM2_P            k = 1
   J9+     Node12 -> Complex_ZAP_ITAM2_PP           k = 1000
   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
   J241+   Complex_2ZAP -> Node136                  k = 1
   J241-   Node136 -> Complex_2ZAP                  k = 1
   J243+   Node136 -> Complex_2ZAP_ITAM3_P          k = 1000
   J242+   Complex_2ZAP_ITAM3_P -> Node138          k = 1
   J242-   Node138 -> Complex_2ZAP_ITAM3_P          k = 1
   J244+   Node138 -> Complex_2ZAP_ITAM3_PP         k = 1000
   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
   J252+   Complex_3ZAP -> Node143                  k = 1
   J252-   Node143 -> Complex_3ZAP                  k = 1
   J255+   Node143 -> Complex_3ZAP_P                k = 1
   J253+   Complex_3ZAP_P -> Node145                k = 1
   J253-   Node145 -> Complex_3ZAP_P                k = 1
   J256+   Node145 -> Complex_3ZAP_2P               k = 1
   J254+   Complex_3ZAP_2P -> Node147               k = 1
   J254-   Node147 -> Complex_3ZAP_2P               k = 1
   J257+   Node147 -> 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=0.963013 at L=2.884e-02 ; subsequent min phi=0.061373 at L=1.380e+02
L1 = 6/625  L3 = 410   phi(L1) = 0.954571769614  phi(L3) = 0.0927070160470
R_tot = 6408607950825016594617581048838168747665471574005931367518959615367564319553121649/13471908884316115223283515891785262405028675549526973399967711286412713425247500  (~475.702)
L_tot = 12235211125411855246143439539353979297161549262149500008958382071551863452761968/26943817768632230446567031783570524810057351099053946799935422572825426850495  (~454.101)
exact steady state at L = 6/625 : f(x)=0 verified exactly; totals R_tot, L_tot match; all 27 coordinates positive
exact steady state at L = 410 : f(x)=0 verified exactly; totals R_tot, L_tot match; all 27 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 [0.0868569802114, 0.0868569802115]
steady state at L1: reduced char. poly degree 25; Routh-Hurwitz first column all positive: True
steady state at L3: reduced char. poly degree 25; Routh-Hurwitz first column all positive: True
middle state (approximate): eigenvalues with largest real parts: 0.004946+0i, 4.845e-14+0i, -6.605e-15+0i, -0.144+0i
