# Model assumptions: # All multimerization is linear and cooperative # in the formation of the dATP-CytC-Apaf1 complex, dATP binds Apaf-1 first # cytochrome C plays a single (not dual) role # Known issues: # cooperative protease binding constants conflict in fig 5 and table 2 # cooperative apaf-1 multimerization binding constants conflict in fig 4 and table 2 # caspace-3 activation constants conflict in table 1 and fig 6 # Experiments: # Fig 2-1 # Output: Afc rate (fc/min) # Input: # range of values for Cytochrome C (0...120) # 3 values of unbinding constant a1m (2, 20, 2000) # 10 values of binding constant a1p (0.1, 0.2...1.0) # time = 180 (s) # Fig 2-2 # Output: Afc rate (fc/min) # Input: # range of values for Apaf-1 (0...70) # two values of unbinding constant a1m (2, 20) # 10 values of binding constant a1p (0.1, 0.2...1.0) # time = 180 (s) begin model begin parameters NA 6.02214129e23 # Avogadro's number, per mole V 1e-12 # simulation volume, liters # Initial Concentrations D_init 5000e-9*NA*V C_init 1200e-9*NA*V A_init 4e-9*NA*V P9_init 20e-9*NA*V P3_init 15e-9*NA*V V_init 40000e-9*NA*V # Rate Constants # dATP binding to apaf-1 # slow binding # all parameters taken from fig 2 a1p 10e9/NA/V a1m 2000e-9*NA*V a2 2e-9*NA*V # cytochrome C binding to dATP-apaf-1 complex # fast binding # all parameters taken from fig 2 b1p 1000e9/NA/V b1m 2000e-9*NA*V b2 0.5e-9*NA*V # cooperative APAF-1 multimerization # binding constants (rnp) from table 2 # unbinding constants (rnm) from table 1 and fig 4 # formation (rnf) constants from table 1 and fig 4 r1p 2e9/NA/V r1m 2000e-9*NA*V r1f 10e-9*NA*V r2p 4e9/NA/V r2m 2000e-9*NA*V r2f 10e-9*NA*V r3p 8e9/NA/V r3m 2000e-9*NA*V r3f 10e-9*NA*V r4p 16e9/NA/V r4m 2000e-9*NA*V r4f 10e-9*NA*V r5p 32e9/NA/V r5m 2000e-9*NA*V r5f 10e-9*NA*V r6p 64e9/NA/V r6m 2000e-9*NA*V r6f 10e-9*NA*V # cooperative procaspase binding # binding constants (rnp) from table 2 # unbinding constants (rnm) from fig 5 # formation (rnf) constants from fig 5 d1p 20e9/NA/V d1m 20000e-9*NA*V d1f 100e-9*NA*V d2p 50e9/NA/V d2m 20000e-9*NA*V d2f 100e-9*NA*V d3p 80e9/NA/V d3m 20000e-9*NA*V d3f 100e-9*NA*V d4p 110e9/NA/V d4m 20000e-9*NA*V d4f 100e-9*NA*V d5p 140e9/NA/V d5m 20000e-9*NA*V d5f 100e-9*NA*V d6p 170e9/NA/V d6m 20000e-9*NA*V d6f 100e-9*NA*V d7p 200e9/NA/V d7m 20000e-9*NA*V d7f 100e-9*NA*V # Procaspace 9 activation # value from table 1 m1 3e-9*NA*V # also 0.5 # caspace 9 release # value from table 1 w1 0.5e-9*NA*V v1p 6e9/NA/V v1m 1000e-9*NA*V v2 20e-9*NA*V z1p 5000e9/NA/V z1m 500000e-9*NA*V z2 90e-9*NA*V end parameters begin molecule types A(a) D(d) AD(ad) C(c) S1(s) S2(s) S3(s) S4(s) S5(s) S6(s) S7(s) P9(p) H1(h) H2(h) H3(h) H4(h) H5(h) H6(h) Hi(h) Ha(h) P3(p) C3(c) C9() V(v) F() end molecule types begin seed species D(d) D_init C(c) C_init A(a) A_init P9(p) P9_init P3(p) P3_init V(v) V_init end seed species begin observables Molecules Afc_flourescent F() #Molecules Caspace3_tot C3() #Molecules Caspace3_free C3(c) #Molecules Active_holoenzyme_tot Ha() #Molecules Caspace9 C9() end observables begin reaction rules # APAF-1, dATP and Cytochrome C A(a) + D(d) <-> A(a!1).D(d!1) a1p, a1m A(a!1).D(d!1) -> AD(ad) a2 AD(ad) + C(c) <-> AD(ad!1).C(c!1) b1p, b1m AD(ad!1).C(c!1) -> S1(s) b2 # APAF-1 multimerization S1(s) + S1(s) <-> S1(s!1).S1(s!1) r1p, r1m S1(s!1).S1(s!1) -> S2(s) r1f S2(s) + S2(s) <-> S2(s!1).S2(s!1) r2p, r2m S2(s!1).S2(s!1) -> S3(s) r2f S3(s) + S3(s) <-> S3(s!1).S3(s!1) r3p, r3m S3(s!1).S3(s!1) -> S4(s) r3f S4(s) + S4(s) <-> S4(s!1).S4(s!1) r4p, r4m S4(s!1).S4(s!1) -> S5(s) r4f S5(s) + S5(s) <-> S5(s!1).S5(s!1) r5p, r5m S5(s!1).S5(s!1) -> S6(s) r5f S6(s) + S6(s) <-> S6(s!1).S6(s!1) r6p, r6m S6(s!1).S6(s!1) -> S7(s) r6f # Formation and Activation of holoenzyme S7(s) + P9(p) <-> S7(s!1).P9(p!1) d1p, d1m S7(s!1).P9(p!1) -> H1(h) d1f H1(h) + P9(p) <-> H1(h!1).P9(p!1) d2p, d2m H1(h!1).P9(p!1) -> H2(h) d2f H2(h) + P9(p) <-> H2(h!1).P9(p!1) d3p, d3m H2(h!1).P9(p!1) -> H3(h) d3f H3(h) + P9(p) <-> H3(h!1).P9(p!1) d4p, d4m H3(h!1).P9(p!1) -> H4(h) d4f H4(h) + P9(p) <-> H4(h!1).P9(p!1) d5p, d5m H4(h!1).P9(p!1) -> H5(h) d5f H5(h) + P9(p) <-> H5(h!1).P9(p!1) d6p, d6m H5(h!1).P9(p!1) -> H6(h) d6f H6(h) + P9(p) <-> H6(h!1).P9(p!1) d7p, d7m H6(h!1).P9(p!1) -> Hi(h) d7f Hi(h) -> Ha(h) m1 Ha(h) -> C9() + S7(s) w1 # Caspase-3 activation P3(p) + Ha(h) <-> P3(p!1).Ha(h!1) v1p, v1m P3(p!1).Ha(h!1) -> C3(c) v2 # DEVD-Afc is hydrolized by free caspace-3 V(v) + C3(c) <-> V(v!1).C3(c!1) z1p, z1m V(v!1).C3(c!1) -> F() z2 end reaction rules end model #ACTIONS generate_network({overwrite=>1}); simulate_ssa({t_end=>1800,n_steps=>50});