S1 Appendix. Notation, equations, and parameters Kathryn G. Link2Y , Michael T. Stobb3Y , Jorge A. Di Paola5† , Keith B. Neeves Aaron L. Fogelson1,2‡ , Suzanne S. Sindi3‡ , Karin Leiderman4‡* ,
5,6†
,
1 Department of Mathematics, University of Utah, Salt Lake City, UT, USA 2 Department of Bioengineering, University of Utah, Salt Lake City, UT, USA 3 Department of Applied Mathematics, University of California, Merced, Merced, CA, USA 4 Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, USA 5 Department of Pediatrics, University of Colorado School of Medicine, Aurora, CO, USA 6 Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, CO, USA Y These authors contributed equally to this work. †These authors contributed equally to this work. ‡These authors contributed equally to this work. *Corresponding author:
[email protected] S1-S4 Tables list input parameters that describe the physical processes and coagulation reactions we consider listed in S5-S12 Tables. Zi and Ei refer to zymogen i and enzyme i in solution. A superscript ’m’ indicates a membrane-bound versions of these proteins (e.g., E7m refers to the TF:VIIa complex and E5m refers to Factor Va bound to the platelet surface). Concentrations are denoted in a similar way but with lower-case z and e. A complex of Zi and Ej is denoted Zi : Ej and its concentration is denoted [Zi : Ej ]. Special symbols are used for the platelet-bound ‘tenase’ VIIIa:IXa and ‘prothrombinase’ Va:Xa complexes, T EN = VIIIa:IXa and P RO= Va:Xa, and [T EN ] and [P RO] denote their respective concentrations. The special symbol T F P Ia is used for the fluid-phase complex TFPI:Xa, and [T F P Ia] denotes its concentration. The inhibitors are denoted AP C and T F P I and their concentrations are denoted [AP C] and [T F P I]. The concentrations of unactivated, subendothelial bound, and activated but not subendothelial bound platelets are denoted P L, P Las , and P Lva , respectively. Platelet binding sites for coagulation proteins are denoted Pi or Pi∗ . The former refers to binding sites for the zymogen i or for zymogen and enzyme i. The latter refers to binding sites only for enzyme i. The number of Pi or Pi∗ binding sites is denoted Ni or Ni∗ . The concentration pi or p∗i of each of these binding sites is needed in the model equations. It is obtained by multiplying the corresponding Ni or Ni∗ , respectively, by the concentration of activated platelets P Las + P Lav . Further discussion of model assumptions and parameter estimation can be found in [1, 2].
PLOS
1/23
[T F ]avail
=
m m m [T F ] − z7m − em 7 − [Z7 : E10 ] − [Z7 : E2 ] − [Z10 : E7 ]
−[Z9 : E7m ] − [T P F I : E10 : E7m ] − [Z7m : E9 ] pavail P LAS
=
pP LAS − [P Lsa ]
pavail 5
=
m m m m p5 − z5m − em 5 − [Z5 : E10 ] − [Z5 : E2 ]
−[AP C : E5m ] − [P RO] − [Z2m : P RO] pavail 8
=
m m m m p8 − z8m − em 8 − [T EN ] − [Z8 : E10 ] − [Z8 : E2 ] m m −[Z10 : T EN ] − [AP C : E8m ] − [T EN ∗ ] − [Z10 : T EN ∗ ]
pavail 9
=
m p9 − z9m − em 9 − [T EN ] − [Z10 : T EN ] h,m m∗ −[Z9m : E11 ] − [Z9m : E11 ]
p∗,avail 9
=
∗ m ∗ p∗9 − em∗ 9 − [T EN ] − [Z10 : T EN ]
pavail 10
=
m m m m m p10 − z10 − em 10 − [Z5 : E10 ] − [Z8 : E10 ] m m −[P RO] − [Z2m : P RO] − [Z10 : T EN ] − [Z10 : T EN ∗ ]
pavail 2
=
p2 − z2m − [Z2m : P RO]
p∗,avail 2
=
h,m∗ m m m m m m p∗2 − em : E2m ] 2 − [Z5 : E2 ] − [Z8 : E2 ] − [Z11 : E2 ] − [E11
pavail 11
=
h,m m m m m p11 − z11 − eh,m 11 − [Z9 : E11 ] − [Z11 : E2 ]
∗,avail p11
=
h,m∗ m m∗ p∗11 − eh,m∗ − em∗ : E2m ] 11 − [Z9 : E11 ] − [E11 11
avail
=
[T M ]
PLOS
([T M ] − [T M : E2ec ] − [T M : E2ec : AP C])
2/23
d z7 dt
= kflow (z7up − z7 ) − k7on z7 [T F ]avail + k7off z7m − kz+7 :e2 z7 e2 +kz−7 :e2 [Z7 : E2 ] − kz+7 :e10 z7 e10 + kz−7 :e10 [Z7 : E10 ]
d e7 dt
on avail = kflow (eup + k7off em 7 7 − e7 ) − k7 e7 [T F ]
+kzcat [Z7 : E2 ] + kzcat [Z7 : E10 ] 7 :e2 7 :e10 d m z dt 7
= k7on z7 [T F ]avail − k7off z7m − kz+7m :e10 z7m e10 + kz−7m :e10 [Z7m : E10 ] −kz+7m :e2 z7m e2 + kz−7m :e2 [Z7m : E2 ] − z7m
d m e dt 7
1 d [P Lsa ] avail dt pP LAS
= k7on e7 [T F ]avail − k7off em 7 − m −kT+P F I:e10 :E m em 7 [T F P I : E10 ] + kT P F I:e10 :E m [T P F I : E10 : E7 ] 7
+kzcat [Z7m m 7 :e10 +(kzcat m 10 :e7
+
: E10 ] +
7
kzcat [Z7m m 7 :e2
kz−10 :em )[Z10 7
:
E7m ]
: E2 ]
− kz+10 :em z10 em 7 7
− m +(kzcat )[Z9 : E7m ] − kz+9 :em z9 em m + k 7 − e7 z9 :em 9 :e7 7 7
d z10 dt
1 d [P Lsa ] avail dt pP LAS
up on off m = kflow (z10 − z10 ) − k10 z10 pavail + k10 z10 − kz+10 :em z10 em 10 7 7
+kz−10 :em [Z10 : E7m ] 7 d e10 dt
ec on avail off m = kflow (eup + k10 e10 10 − e10 ) − kdiff (e10 − e10 ) − k10 e10 p10 + m cat +kzcat + kz−7 :e10 )[Z7 : E10 ] − kz7:e10 z7 e10 m [Z10 : E7 ] + (kz :e 10 :e7 7 10
+(kzcat + kz−7m :e10 )[Z7m : E10 ] − kz+7 :e10 z7m e10 m 7 :e10 m
in −kT+F P I:e10 e10 [T F P I] + kT−F P I:e10 [T F P I : E10 ] − kAT :e10 e10
d m z dt 10
− on off m m m = k10 z10 pavail − k10 z10 − kz+10 m :ten z10 [T EN ] + kz :ten [Z10 : T EN ] 10 10 − m ∗ m ∗ −kz+10 m :ten z10 [T EN ] + kz :ten [Z10 : T EN ] 10
d m e dt 10
on off m m = k10 e10 pavail − k10 e10 + kzcat [Z10 : T EN ] m 10 10 :ten − + m m m m +(kzcat m m + k m m )[Z5 : E10 ] − k m m z5 e10 z5 :e10 z5 :e10 5 :e10 − + m m m m +(kzcat m m + k m m )[Z8 : E10 ] − k m m z8 e10 z8 :e10 z8 :e10 8 :e10 + m m cat m ∗ +ke−m m [P RO] − kem :em e10 e5 + kz m :ten [Z10 : T EN ] 10 5 :e10 5 10
PLOS
3/23
d z5 dt
=
kflow (z5up − z5 ) − k5on z5 pavail + k5off z5m − kz+5 :e2 z5 e2 + kz−5 :e2 [Z5 : E2 ] 5 e2 + act v s act [P L] +n5 kadh pavail P LAS + kplt [P La ] + [P La ] + ke2 (e2 + 0.001)
d e5 dt
=
on avail kflow (eup + k5off em 5 5 − e5 ) − k5 e5 p5 − + +kzcat [Z5 : E2 ] + ke5:AP C [AP C : E5 ] − ke5:AP C [AP C]e5 5 :e2
d m z dt 5
=
− m k5on z5 pavail − k5off z5m − kz+5m :em z m em [Z5m : E10 ] 5 10 + kz5m :em 10 5 10 − −kz+5m :em z5m em [Z5m : E2m ] 2 + kz5m :em 2 2
d m e dt 5
=
cat m m m k5on e5 pavail − k5off em [Z5m : E10 ] + kzcat m m [Z5 : E2 ] 5 5 + kz5m :em 10 5 :e2
+ke−m :AP C [AP C : E5m ] − ke+m :AP C [AP C]em 5 5
5
m m −ke+m e10 + ke−m me m [P RO] 5 :e10 5 5 :e10
d z8 dt
=
kflow (z8up − z8 ) − k8on z8 pavail + k8off z8m − kz+8 :e2 z8 e2 + kz−8 :e2 [Z8 : E2 ] 8
d e8 dt
=
on avail cat kflow (eup + k8off em 8 + kz8 :e2 [Z8 : E2 ] − 0.005e8 8 − e8 ) − k8 e8 p8
+ke−8 :AP C [AP C : E8 ] − ke+8 :AP C [AP C]e8 d m z dt 8
=
− m k8on z8 pavail − k8off z8m − kz+8m :em z m em [Z8m : E10 ] 8 10 + kz8m :em 10 8 10 − −kz+8m :em z8m em [Z8m : E2m ] 2 + kz8m :em 2 2
d m e dt 8
=
cat m m m k8on e8 pavail − k8off em [Z8m : E10 ] + kzcat m m [Z8 : E2 ] 8 8 + kz8m :em 10 8 :e2 − m m −ke+m :AP C [AP C]em 8 + kem :AP C [AP C : E8 ] − 0.005e8 8
8
− + m m m m∗ ∗ −ke+m + ke−m m e9 e8 + kem :em [T EN ] − kem :em e8 e9 m [T EN ] 8 :e9 8 9 8 9 8 :e9
PLOS
4/23
d z9 dt
− = kflow (z9up − z9 ) − k9on pavail z9 + k9off z9m − kz+9 :em z9 em [Z9 : E7m ] 9 7 + kz9 :em 7 7 h −kz+ :eh z9 eh11 + kz− :eh [Z9 : E11 ] − kz+9 :e11 z9 e11 + kz−9 :e11 [Z9 : E11 ] 9
d e9 dt
9
11
11
ec on avail cat = kflow (eup e9 + k9off em [Z9 : E7m ] 9 + kz9 :em 9 − e9 ) − kdiff (e9 − e9 ) − k9 p9 7 in cat − + −kAT :e9 e9 + (kz7:e9 + kz7 :e9 )[Z7 : E9 ] − kz7 :e9 z7 e9
+(kzcat + kz−7m :e9 )[Z7m : E9 ] − kz+7m :e9 z7m e9 m 7 :e9 cat h cat −k9on p∗,avail e9 + k9off em∗ 9 + kz9 :eh [Z9 : E11 ] + kz9 :e11 [Z9 : E11 ] 9 11
d m z dt 9
z9m eh,m 11 z9 :eh,m 11
= k9on pavail z9 − k9off z9m − k +m 9
+ k −m
z9 :eh,m 11
h,m ] [Z9m : E11
− m m∗ −kz+m :em∗ z9m em∗ 11 + kz m :em∗ [Z9 : E11 ] 9
d m e dt 9
11
9
11
− + m m = k9on pavail e9 − k9off em m [T EN ] − kem :em e8 e9 9 9 + k em 8 :e9 8 9 h,m m cat m m∗ +kzcat m :eh,m [Z9 : E11 ] + kz m :em∗ [Z9 : E11 ] 9 11 9
11
d z2 dt
= kflow (z2up − z2 ) − k2on pavail z2 + k2off z2m 2
d e2 dt
ec cat m = kflow (eup 2 − e2 ) − kdiff (e2 − e2 ) + kz2m:P RO [Z2 : P RO] on ∗,avail off m in −k2∗ p2 e2 + k2∗ e2 − kAT :e2 e2
+(kzcat + kz−5 :e2 )[Z5 : E2 ] − kz+5 :e2 z5 e2 5 :e2 +(kzcat + kz−8 :e2 )[Z8 : E2 ] − kz+8 :e2 z8 e2 8 :e2 +(kzcat + kz−7 :e2 )[Z7 : E2 ] − kz+7 :e2 z7 e2 7 :e2 +(kzcat + kz−7m :e2 )[Z7m : E2 ] − kz+7m :e2 z7m e2 m 7 :e2 −kz+11 :e2 z11 e2 + (kz−11 :e2 + kzcat )[Z11 : E2 ] 11 :e2 −ke+h
11 :e2
eh11 e2 + (ke−h
11 :e2
h + kecat h :e )[E11 : E2 ] 2 11
d m z dt 2
= k2on pavail z2 − k2off z2m − kz+m :P RO z2m P RO + kz−m :P RO [Zzm : P RO] 2
d m e dt 2
− + on avail off m m m m m = k2∗ p2 e2 − k2∗ e2 + (kzcat m m + k m m )[Z5 : E2 ] − k m m z5 e2 z5 :e2 z5 :e2 5 :e2
2
2
− + m m m m +(kzcat m m + k m m )[Z8 : E2 ] − k m m z8 e2 z8 :e2 z8 :e2 8 :e2 − m m cat m m −kz+11 m :em z11 e2 + (kz m :em + kz m :em )[Z11 : E2 ] 11 2 2 11 2
−k +h,m∗ e11
PLOS
eh,m∗ em 2 11 :em 2
+ (k −h,m∗ e11
:em 2
h,m∗ : E2m ] + kecat h,m∗ m )[E11 :e 11
2
5/23
d [T EN ] dt
=
+ m m −ke−m m [T EN ] + kem :em e8 e9 8 :e9 8 9 m m +(kzcat + kz−10 :T EN )[Z10 : T EN ] − kz+m :T EN z10 [T EN ] m 10 :T EN 10
d [P RO] dt
=
+ m m −ke−m m [P RO] + kem :em e10 e5 5 :e10 5 10
+(kzcat + kz−m :P RO )[Z2m : P RO] − kz+m :P RO z2m [P RO] m 2 :P RO 2
d [P Lsa ] dt
=
d [P L] dt
=
d [P Lva ] dt
=
2
+ − + s v avail kadh pavail P LAS [P L] − kadh [P La ] + kadh [P La ] pP LAS
p + v s act kflow [P L]up − [P L] − kadh pavail P LAS + kplt [P La ] + [P La ] e2 act [P L] +ke2 e2 + 0.001 − + kadh [P Lsa ] − kadh [P Lva ] pavail P LAS act act + kplt [P Lva ] + [P Lsa ] + ke2
d [T F P I] dt
e2 [P L] e2 + 0.001
= kflow ([T P F I]up − [T F P I]) − kT+F P I:e10 e10 [T F P I] +kT−F P I:e10 [T F P I : Xa]
d [T F P I : E10 ] dt
= −kflow [T F P I : E10 ] + kT+F P I:e10 e10 [T F P I] −kT−F P I:e10 [T F P I : E10 ] + kT−F P I:e10 :em [T F P I : E10 : E7m ] 7
−kT+F P I:e10 :em em 7 [T F P I 7 d [T F P I : E10 : E7m ] dt
= −kT−F P I:e10 :em [T F P I : E10 : E7m ] 7
+kT+F P I:e10 :em em 7 [T F P I 7 −[T F P I : E10
PLOS
: E10 ]
: E10 ]
d 1 : E7m ] [P Lsa ] avail dt pP LAS
6/23
d [AP C] dt
= kflow [AP C]up − [AP C] − kdiff [AP C] − [AP C ec ] − + m m +(kecat m :AP C + k m e :AP C )[AP C : E5 ] − kem :AP C e5 [AP C] 5 5
5
− + m m +(kecat m :AP C + k m e :AP C )[AP C : E8 ] − kem :AP C e8 [AP C] 8 8
8
+(kecat + ke−5 :AP C )[AP C : E5 ] − ke+5 :AP C e5 [AP C] 5 :AP C +(kecat + ke−8 :AP C )[AP C : E8 ] − ke+8 :AP C e8 [AP C] 8 :AP C d [AP C : E8m ] dt
cat = ke+m :AP C em + ke−m :AP C )[AP C : E8m ] 8 [AP C] − (kem 8 :AP C
d [AP C : E5m ] dt
cat = ke+m :AP C em + ke−m :AP C )[AP C : E5m ] 5 [AP C] − (kem 5 :AP C
8
8
5
5
d [AP C : E5 ] dt
= ke+5 :AP C e5 [AP C] − (kecat + ke−5 :AP C )[AP C : E5 ] 5 :AP C
d [AP C : E8 ] dt
= ke+8 :AP C e8 [AP C] − (kecat + ke−8 :AP C )[AP C : E8 ] 8 :AP C
d [Z7 : E2 ] dt
= kflow [Z7 : E2 ]up − [Z7 : E2 ] + kz+7 :e2 z7 e2 −(kzcat + kz−7 :e2 )[Z7 : E2 ] 7 :e2
d [Z7 : E10 ] dt
= kflow [Z7 : E10 ]up − [Z7 : E10 ] + kz+7 :e10 z7 e10 −(kzcat + kz−7 :e10 )[Z7 : E10 ] 7 :e10
d [Z m : E10 ] dt 7
= kz+7m :e10 z7m e10 − (kzcat + kz−7m :e10 )[Z7m : E10 ] m 7 :e10 −[Z7m : E10 ]
d [Z m : E2 ] dt 7
= kz+7m :e2 z7m e2 − (kzcat + kz−7m :e2 )[Z7m : E2 ] m 7 :e2 −[Z7m : E2 ]
d [Z10 : E7m ] dt
d 1 [P Lsa ] avail dt pP LAS
cat = kz+10 :em z10 em + kz−10 :em )[Z10 : E7m ] 7 − (kz10 :em 7 7 7
−[Z10 : E7m ]
PLOS
d 1 [P Lsa ] avail dt pP LAS
1 d [P Lsa ] avail dt pP LAS
7/23
d [Z m : T EN ] dt 10 d [Z5 : E2 ] dt
m m = kz+m :T EN z10 [T EN ] − (kzcat + kz−10 :T EN )[Z10 : T EN ] m 10 :T EN 10
= kflow [Z5 : E2 ]up − [Z5 : E2 ] + kz+5 :e2 z5 e2 −(kzcat + kz−5 :e2 )[Z5 : E2 ] 5 :e2
d m [Z m : E10 ] dt 5
cat m = kz+5m :em z m em + kz−5m :em )[Z5m : E10 ] 10 − (kz5m :em 10 10 10 5
d [Z m : E2m ] dt 5
cat = kz+5m :em z5m em + kz−5m :em )[Z5m : E2m ] 2 − (kz5m :em 2 2 2
d m [Z m : E10 ] dt 8
cat m = kz+8m :em z m em + kz−8m :em )[Z8m : E10 ] 10 − (kz8m :em 10 10 8 10
d [Z m : E2m ] dt 8
cat z8m em = kz+8m :em + kz−8m :em )[Z8m : E2m ] 2 − (kz8m :em 2 2 2
d [Z8 : E2 ] dt
= kflow [Z8 : E2 ]up − [Z8 : E2 ] + kz+8 :e2 z8 e2 −(kzcat + kz−8 :e2 )[Z8 : E2 ] 8 :e2
d [Z9 : E7m ] dt
cat = kz+9 :em z9 em + kz−9 :em )[Z9 : E7m ] 7 − (kz9 :em 7 7 7
−[Z9 : E7m ] d [Z m : P RO] dt 2 d [T F ] dt d m∗ e dt 9 d [T EN ∗ ] dt
d 1 [P Lsa ] avail dt pP LAS
= kz+m :P RO z2m [P RO] − (kzcat + kz−m :P RO )[Z2m : P RO] m 2 :P RO 2
= −[T F ]
2
d 1 [P Lsa ] avail dt pP LAS
− + ∗ m m∗ = k9on p∗,avail e9 − k9off em∗ m [T EN ] − kem :em e8 e9 9 + k em 9 8 :e9 8 9 + m m∗ ∗ = −ke−m m [T EN ] + kem :em e8 e9 8 :e9 8 9 m m +(kzcat + kz−10 :T EN )[Z10 : T EN ∗ ] − kz+m :T EN z10 [T EN ∗ ] m 10 :T EN 10
d [Z m : T EN ∗ ] dt 10
PLOS
m m = kz+m :T EN z10 [T EN ∗ ] − (kzcat + kz−10 :T EN )[Z10 : T EN ∗ ] m 10 :T EN 10
8/23
d ec e dt 2
ec ec in ec = kflow (eup 2 − e2 ) + kdiff (e2 − e2 ) − −kAT :e2 e2 avail −kTonM eec + kToffM [T M : E2ec ] 2 [T M ]
d [AP C ec ] dt
=
kflow [AP C]up − [AP C ec ] + kdiff ([AP C] − [AP C ec ]) +kPcatC:T M :eec [T M : E2ec : AP C] 2
d [T M : E2ec ] dt
=
avail kTonM eec − kToffM [T M : E2ec ] − kP+C:T M :eec [T M : E2ec ] 2 [T M ] 2
+(kP−C:T M :eec + kPcatC:T M :eec )[T M : E2ec : AP C] 2 2
d [T M : E2ec : AP C] dt
=
kP+C:T M :eec [T M : E2ec ] 2
−(kP−C:T M :eec 2
+ kPcatC:T M :eec )[T M : E2ec : AP C] 2
d ec e dt 9
ec ec in ec = kflow (eup 9 − e9 ) + kdiff (e9 − e9 ) − kAT :e9 e9
d ec e dt 10
ec ec in ec = kflow (eup 10 − e10 ) + kdiff (e10 − e10 ) − kAT :e10 e10
d z11 dt
up = kflow (z11 − z11 ) − kzon11 z11 pavail + kzoff z m − kz+11 :e2 z11 e2 11 11 11
+kz−11 :e2 [Z11 : E2 ] d h e dt 11
∗,avail h,m∗ h = kflow (eh,up − eh11 ) − keon∗ + keoff∗ h e11 p11 h e11 11 11
−keonh eh11 11 +(kz− :eh 9 11 −ke+h
11 :e2
d e11 dt
pavail 11 +
+
11
h,m keoff h e11 11
kzcat h )[Z9 9 :e11
eh11 e2 + ke−h
11 :e2
:
−
h E11 ]
kz+ :eh z9 eh11 9 11 + kzcat [Z11 : E2 ] 11 :e2
h in h [E11 : E2 ] − kAT :e11 e11
∗,avail on∗ = kflow (eup + keoff∗ em∗ 11 11 − e11 ) − ke11 e11 p11 11
−kz+9 :e11 z9 e11 + (kz−9 :e11 + kzcat )[Z9 : E11 ] 9 :e11 h in +kecat e h :e [E11 : E2 ] − kAT :e 11 11 2 11
PLOS
9/23
d m z dt 11
=
− m m m m kzon11 z11 pavail − kzoff z m − kz+11 m :em z11 e2 + kz m :em [Z11 : E2 ] 11 11 11 2 11 2
d h,m e dt 11
=
h,m m m + kzcat keonh eh11 pavail − keoff m m [Z11 : E2 ] h e11 11 11 :e2 11
11
−k +m h,m z9m eh,m 11 z9 :e11 d h,m∗ e dt 11
=
11
=
z9 :eh,m 11
m + kzcat ] m :eh,m )[Z9 : E11 9
11
∗,avail h,m∗ h − keoff∗ keon∗ h e11 p11 h e11 11
−k +h,m∗ m eh,m∗ em 2 e11 :e2 11 d m∗ e dt 11
h,m]
+ (k −m
+ k −h,m∗ e11
:em 2
h,m∗ [E11 : E2m ]
h,m∗ cat keon∗ e p∗,avail − keoff∗ em∗ : E2m ] 11 + keh,m∗ :em [E11 11 11 11 11 11
2
− cat m∗ −kz+m :em∗ z9m em∗ )[Z9m : E11 ] 11 + (kz m :em∗ + kz9m :em∗ 11 9
d h [Z9 : E11 ] dt
=
11
=
11
h up h kflow [Z9 : E11 ] − [Z9 : E11 ] + kz+ :eh z9 eh11 9
−(kz− :eh 9 11 d [Z9 : E11 ] dt
9
k
+
kzcat h )[Z9 9 :e11
flow [Z9 :E11 ]up −[Z9 :E11 ]
:
11
h E11 ]
+ k+
z9 :e11 z9 e11
−(kz−9 :e11 + kzcat )[Z9 : E11 ] 9 :e11 d h,m [Z m : E11 ] dt 9
=
d m∗ [Z m : E11 ] dt 9
=
d [Z11 : E2 ] dt
z9m eh,m 11 z9 :eh,m 11
k +m
− (k −m
z9 :eh,m 11
h,m m + kzcat m :eh,m )[Z9 : E11 ] 9
11
− cat m∗ kz+m :em∗ z9m em∗ )[Z9m : E11 ] 11 − (kz m :em∗ + kz9m :em∗ 11 9
11
9
11
= kflow [Z11 : E2 ]up − [Z11 : E2 ] +kz+11 :e2 z11 e2 − (kz−11 :e2 + kzcat )[Z11 : E2 ] 11 :e2
d [E h : E2 ] dt 11
h h : E2 ]up − [E11 : E2 ] = kflow [E11 +ke+h
11 :e2
d [Z m : E2m ] dt 11 d [E h,m∗ : E2m ] dt 11
PLOS
eh11 e2 − (ke−h
11 :e2
h + kecat h :e )[E11 : E2 ] 2 11
− m m cat m m = kz+11 m :em z11 e2 − (kz m :em + kz m :em )[Z11 : E2 ] 11 2 2 11 2
= k +h,m∗ e11
eh,m∗ em 2 11 :em 2
− (k −h,m∗ e11
:em 2
h,m∗ + kecat : E2m ] h,m∗ m )[E11 :e 11
2
10/23
S1 Table. INITIAL PLASMA LEVELS. Descriptions, notation and labels for each parameter associated with initial plasma levels are listed. The value of each parameter is found in the corresponding table listed above. Description Prothrombin Factor V Factor VII Factor VIII Factor IX Factor X Factor XI TFPI AT
Notation z2 z5 z7 z8 z9 z10 z11 [TFPI] in in in in kAT :e2 , kAT :e9 , kAT :e10 , kAT :e11
Label Z2 Z5 Z7 Z8 Z9 Z10 Z11 TFPI AT
Table S5 S5 S5 S5 S5 S5 S5 S5 S11
S2 Table. PLATELET CHARACTERISTICS. Descriptions, notation and labels for each parameter associated with platelet characteristics are listed. The value of each parameter is found in the corresponding table listed above. Description Platelet count Binding site number for II Binding site number for IIa Binding site number for V/Va Binding site number for VIII/VIIIa Binding site number for IX Binding site number for IXa Binding site number for X/Xa Binding site number for XI Binding site number for XIa Rate of unactivated platelets adhering to SE Rate of activated platelets adhering to SE Rate of platelet activation by platelet in solution Rate of platelet activation on SE Rate of platelet activation by thrombin
PLOS
Notation PLup N2 N2∗ N5 N8 N9 N9∗ N10 N11 ∗ N11 + kadh +,∗ kadh act kplt act,∗ kplt keact 2
Label PLup N2 N2* N5 N8 N9 N9* N10 N11 N11* kadh kadh1 kactplt kact*plt kacte2
Table S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S12 S12 S12 S12 S7
11/23
S3 Table. KINETIC RATE CONSTANTS. Descriptions, notation and labels for each parameter associated with kinetic rate constants are listed. The value of each parameter is found in the corresponding table listed above. Description Rates of activation of TF:VII by fX
Notation KM kzcat m :e 10
Label KZ7mE10M KZ7mE10CAT
Table S7 S7
7
Rates of activation of fX by TF:VIIa
kz−m :e 10 7 KM kzcat m 10 :e
KZ7mE10MI KZ10E7mM KZ10E7mCAT
S7 S7 S7
KZ10E7mMI KZ9E7mM KZ9E7mCAT
S7 S7 S7
KZ9E7mMI K7ON K7OFF KZ7E10M KZ7E10CAT
S7 S7 S8 S8 S8
kz− :em 7 10 KM cat kz7 :e2 kz−7 :e2 KM kzcat 7 :e9 kz−7 :e9 KM kzcat 5 :e2 kz−5 :e2 KM kzcat 8 :e2 kz−8 :e2 + kz9 :e11 kzcat 9 :e11 kz−9 :e11 k+ h
KZ7E10MI KZ7E2M KZ7E2CAT KZ7E2MI KZ7E9M KZ7E9CAT KZ7E9MI KZ5E2M KZ5E2CAT KZ5E2MI KZ8E2M KZ8E2CAT KZ8E2MI KZ9E11P KZ9E11CAT KZ9E11MI KZ9E11P
S8 S8 S8 S8 S8 S8 S8 S8 S8 S8 S8 S8 S8 S8 S8 S8 S8
kcat
KZ9E11CAT
S8
KZ9E11MI
S8
KZ11E2P KZ11E2CAT KZ11E2MI K10ON K10OFF K5ON K5OFF K8ON K8OFF K9ON K9OFF K2ON, K2SON K2OFF, K2SOFF K11ON, K11SON K11OFF, K11SOFF
S8 S8 S9 S9 S9 S9 S9 S9 S9 S9 S9 S9 S9 S9 S10
7
Rates of activation of fIX by TF:VIIa
kz− :em 10 7 KM cat kz9 :em 7
Rates of binding of fVII/fVIIa to TF Rates of activation of TF:VII by fXa
kz− :em 9 7 k7on k7of f KM kzcat m 7 :e
10
Rates of activation of TF:VII by fIIa
Rates of activation of TF:VII by fIXa
Rates of activation of fV by fIIa
Rates of activation of fVIII by fIIa
Rates of activation of fIX by fXIa-fXIa
Rates of activation of fIX by fXIa-fXI
Rates of activation of fXI by fIIa
Rates of binding of fX/fXa to plt. surface Rates of binding of fV/fVa to plt. surface Rates of binding of fVIII/fVIIIa to plt. surface Rates of binding of fIX/fIXa to plt. surface Rates of binding of fII/fIIa to plt. surface Rates of binding of fXI/fXIa to plt. surface
PLOS
z9 :e11
z9 :eh 11 k− h z9 :e11 kz+11 :e2 kzcat 11 :e2 kz−11 :e2 on k10 of f k10 k5on k5of f k8on k8of f k9on k9of f k2on , k2on,∗ k2of f , k2of f,∗ on , k on,∗ k11 11 of f of f,∗ k11 , k11
12/23
S4 Table. KINETIC RATE CONSTANTS. Descriptions, notation and labels for each parameter associated with kinetic rate constants are listed. The value of each parameter is found in the corresponding table listed above. Description Rates of activation of fV by fXa on plt. surface
Notation KM kzcat m :em 5
Label KZ5mE10mM KZ5mE10mCAT
Table S10 S10
10
kz−m :em 5 10 KM cat kz5 :em
KZ5mE10mMI KZ5mE2mM KZ5mE2mCAT
S10 S10 S10
KZ5mE2mMI KZ8ME10MM KZ8ME10MCAT
S10 S10 S10
KZ8ME10MMI KZ8ME2MM KZ8mE2mCAT
S10 S10 S10
kz− :em 8 2 KM kzcat m 10 :T EN KM kzcat m :P RO
KZ8mE2mMI KZ10mTENM KZ10mTENCAT KZ2mPROM KZ2mPROCAT
S10 S10 S10 S10 S10
kz+m :em 11 2 kzcat m :em
KZ11mE2mP KZ11mE2mCAT
S10 S10
kz−m :em 11 2 KM kzcat m :em
KZ11mE2mMI KZ9mE11mP KZ9mE11mCAT
S10 S10 S10
kz−m :em
KZ9mE11mMI
S10
ke+m :em
KE8mE9mP
S10
ke−m :em
KE8mE9mMI
S10
ke+m :em
KE5mE10mP
S10
ke−m :em
KE5mE10mMI
S10
+ ktf pia:e10 − ktf pia:e10 + ktf pia:em
KTFPI_E10_P KTFPI_E10_M KTFPIa_E7m_P
S11 S11 S11
Rates of inhibition of fVa by APC on plt. surface
− ktf pia:em 7 KM kecat m :AP C
KTFPIa_E7m_M KE5mAPCM KE5mAPCCAT
S11 S11 S11
Rates of inhibition of fVIIIa by APC on plt. surface
ke−m :AP C 5 KM cat kem :AP C
KE5mAPCMI KE8mAPCM KE8mAPCCAT
S11 S11 S11
Rates of inhibition of fIIa by TM on plt. surface
ke−m :AP C 8 on kT M of f kT M
KE8mAPCMI KTMP KTMM
S11 S11 S12
Rates of activation of fV by fIIa on plt. surface
2
Rates of activation of fVIII by fXa on plt. surface
kz− :em 5 2 KM kzcat m 8 :e
10
Rates of activation of fVIII by fIIa on plt. surface
kz− :em 8 10 KM cat kz8 :em 2
Rates of activation of fX by TEN on plt. surface Rates of activation of fII by PRO on plt. surface
2
Rates of activation of fXI by fIIa on plt. surfaces
11
Rates of activation of fIX by fXIa-fXIa on plt. surface
Rates of formation of TEN on plt. surface
9
11
9
2
8 8
Rates of formation of PRO on plt. surface
5 5
Rates of inhibition of fXa by TFPI Rates of inhibition of TF:VIIa by TFPIa
2
9 9
10 10
7
5
8
PLOS
13/23
Kinetic and Physical Parameter Values: S5 Table. DIFFUSION COEFFICIENTS FOR PLATELETS AND FLUID-PHASE CHEMICAL SPECIES (a) From [3]. (b) From [4]. Platelets Proteins
2.5×10−7 cm2 /s 5×10−7 cm2 /s
a b
S6 Table. NORMAL CONCENTRATIONS AND SURFACE BINDING SITE NUMBERS (a) From [5]. (b) From [6]. (c) [7] suggests that normal plasma concentration of fVIIa is about 1% of the normal fVII concentration. (d) From [8]. (e) (f) From [9]. (g) Estimated as described in the text of the Supplementary Information. (h) From [10]. (i) From [11]. (j) From [12]. (k) From [13]. (l) From [14, 15]. (m) Number of fV molecules released per activated platelet [16]. (n) Maximum concentration of platelets in a 2 µm high reaction zone assuming that 20 platelets can cover a 10µm-by-10µm injured surface [17]. Prothrombin Factor V Factor VII Factor VIIa Factor VIII Factor IX Factor X Factor XI TFPI Protein C Platelet count N2 N2∗ N5 N8 N9 N9∗ N10 N11 ∗ N11 n5 pP LAS
PLOS
1.4 µM 0.01 µM 0.01 µM 0.1 nM 1.0 nM 0.09 µM 0.17 µM 30.0 nM 2.5 nM 65 nM 2.5(10)5 /µl 1000/plt 1000/plt 3000/plt 450/plt 250/plt 250/plt 2700/plt 1500/plt 250/plt 3000/plt 0.167 nM
a b a c a a a a d e f g g h i j j k l l m n
14/23
PLOS S7 Table. REACTIONS ON SUBENDOTHELIUM (a) kzcat = 5.0 sec−1 and KM = 1.2 · 10−6 M [18]. (b) kzcat = 6.1 · 10−2 m m 7 :e10 7 :e2 −1 −6 cat −1 −7 cat −1 sec and KM = 2.7 · 10 M [18]. (d) kz10 :em = 1.15 sec and KM = 4.5 · 10 M [5]. (d) kz9 :em = 1.15 sec and KM = 2.4 · 10−7 M [19]. (e) 7 7 −10 Kd = 1.0 · 10 M [20].
Activation (of -, by -)
E10 , Z7m
Z7m : E10
E7m
kz+m :e =5.0 · 106
kz−m :e =1.0
(TF:VII, fIIa)
E2 , Z7m
Z7m : E2
E7m
kz+m :e =3.92 · 105
kz−m :e =1.0
(fX, TF:VIIa)
E7m , Z10
Z10 : E7m
E10
kz+
kz−
(fIX, TF:VIIa)
E7m , Z9
Z9 : E7m
E9
kz+ :em =9.4 · 106
kz− :em =1.0
Z7m E7m
k7on =5.0 · 107 k7on =5.0 · 107
k7off =5.0 · 10−3 k7off =5.0 · 10−3
(TF:VII,fXa)
7
7
10 2
m 10 :e7 9
=5.0 · 106
7
7 7
10
kzcat =5.0 m :e 10
a
2
−2 kzcat m :e =6.1 · 10 2
b
m 10 :e7 9
=1.0
7
7 7
kzcat m =1.15 10 :e
c
kzcat m =1.15 9 :e
d
7
7
Binding (of -, with -)
(fVII, TF) (fVIIa, TF)
Z7 , T F E7 , T F
e e
15/23
PLOS = 6.1 · 10−2 sec−1 and = 5.0 sec−1 and KM = 1.2 · 10−6 M [18]. (b) kzcat S8 Table. REACTIONS IN THE PLASMA (a) kzcat 7 :e2 7 :e10 −1 −1 −8 cat = 0.9 sec [22] and K = 2 · 10−7 M [23]. (e) = 0.23 sec and K = 7.17 · 10 M [21]. (d) k KM = 2.7 · 10−6 M [18] (c) kzcat M M z8 :e2 5 :e2 −4 cat kzcat = 1.3 · 10 , K = 50nM [24]. Rate constants apply also for thrombin-activation of XIa-XI. (f) k = 0.21, KM = 0.2µM [25, 26]. Rate M 11 :e2 z9 :eh 11 constants apply also for activation of IX by XIa-XIa. Reaction
Reactants
Complex
Product
M−1 sec−1
sec−1
sec−1
Z7 , E10 Z7 , E2 Z5 , E2 Z8 , E2 Z11 , E2 h Z9 , E11
Z7 : E10 Z7 : E2 Z5 : E2 Z8 : E2 Z11 : E2 h Z9 : E11
E7 E7 E5 E8 h E11 E9
kz+7 :e10 =5 · 106 kz+7 :e2 =3.92 · 105 kz+5 :e2 = 1.73 · 107 kz+8 :e2 =2.64 · 107 kz+11 :e2 = 2.0 · 107 k+ h = 0.6 · (10)7
kz−7 :e10 =1.0 kz−7 :e2 =1.0 kz−5 :e2 =1.0 kz−8 :e2 =1.0 kz−11 :e2 = 1.0 k− h = 1.0
kzcat =5.0 7 :e10 kzcat =6.1 · 10−2 :e 7 2 kzcat =0.23 5 :e2 kzcat =0.9 8 :e2 kzcat = 1.3 · 10−4 11 :e2 kcat h = 0.21
Note
Activation (of -, by -)
(fVII, fXa) (fVII, fIIa) (fV, fIIa) (fVIII, fIIa) (fXI-fXI, fIIa) (fIX, fXIa)
z9 :e11
z9 :e11
z9 :e11
a b c d e f
16/23
PLOS S9 Table. BINDING TO PLATELET SURFACES (a) For fIX binding to platelets, Kd = 2.5 · 10−9 M [12], and for fX binding to platelets, Kd has approximately the same value [10]. For fX binding to PCPS vesicles, the on-rate is about 107 M−1 sec−1 and the off-rate is about 1.0 sec−1 [27] giving a dissociation constant of about 10−7 M. To estimate on- and off-rates for the higher-affinity binding of fX to platelets, we keep the on-rate the same as for vesicles and adjust the off-rate to give the correct dissociation constant. The rates for fIX binding with platelets are taken to be the same as for fX binding. (b) We assume binding constants for fIXa binding to the specific fIXa binding sites are the same as for shared sites. (c) fV binds with high-affinity to phospholipids (PCPS) [27] and we use the same rate constants reported there to describe fV binding to platelets. (d) The Kd for fVIII binding with platelets is taken from [11]. We set the off-rate k8off for fVIII binding to platelets equal to that for fV binding to platelets, and calculate the on-rate k8on . (e) For prothrombin interactions with platelets, Kd is reported to be 5.9 · 10−7 M [28]. We choose k2off and set k2on = k2off /Kd . (f) Estimated as described in the text of the Supplementary Information. (g) Kd = 10 nM [29]. (h) Kd = 1.7 nM [15]. Reaction
Reactants
Products
M−1 sec−1
sec−1
Factor Factor Factor Factor Factor Factor Factor Factor Factor Factor Factor Factor Factor
Z 9 , P9 E9 , P9 E9 , P9∗ Z10 , P10 E10 , P10 Z 5 , P5 E5 , P5 Z 8 , P8 E8 , P8 Z 2 , P2 E2 , P2 Z11 , P11 ∗ E11 , P11
Z9m E9m E9m,∗ m Z10 m E10 Z5m E5m Z8m E8m Z2m E2m m Z11 m E11
k9on =1.0 · 107 k9on =1.0 · 107 k9on =1.0 · 107 on =1.0 · 107 k10 on =1.0 · 107 k10 k5on =5.7 · 107 k5on = 5.7 · 107 k8on = 5.0 · 107 k8on = 5.0 · 107 k2on = 1.0 · 107 k2∗,on = 1.0 · 107 kzon = 1.0 · 107 11 keon = 1.0 · 107 11
k9off =2.5 · 10−2 k9off =2.5 · 10−2 k9off =2.5 · 10−2 off =2.5 · 10−2 k10 off =2.5 · 10−2 k10 k5off =0.17 k5off =0.17 k8off =0.17 k8off =0.17 k2off =5.9 k2∗,off = 0.2 kzoff =0.1 11 keoff =0.017 11
IX IXa IXa X Xa V Va VIII VIIIa II IIa XI XIa
Note
a a b a a c c d d e f g h
17/23
PLOS −1 S10 Table. REACTIONS ON PLATELET SURFACES (a) kzcat and KM = 10.4 · 10−9 M [30]. (b) The rate constants m m = 0.046 sec 5 :e10 cat for thrombin activation of fV on platelets are assumed to be the same as in plasma. (c) kz8m :em = 0.023 sec−1 and KM = 2.0 · 10−8 M [23]. (d) The 10 rate constants for thrombin activation of fVIII on platelets are assumed to be the same as in plasma. (e) The formation of the tenase and prothrombinase complexes is assumed to be very fast with Kd = 1.0 · 10−10 M [31]. (f) kzcat = 20 sec−1 and KM = 1.6 · 10−7 M [32]. (g) m 10 :ten −4 = 30 sec−1 and KM = 3.0 · 10−7 M [33]. (h) kzcat , KM = 50 nM [24]. Rate constants apply also for thrombin-activation of kzcat m m = 1.3 · 10 m 11 :e2 2 :pro cat Plt-XIa-XI. (i) kzm :eh,m = 0.21, KM = 0.2µM [25, 26]. Rate constants apply also for activation of platelet-bound IX by Plt-XIa-XIa. 9
11
Reaction
Reactants
Complex
Product
M−1 sec−1
sec−1
sec−1
E5m
kz+m :em =1.0 · 108
kz−m :em =1.0
−2 kzcat m :em =4.6 · 10
a
kzcat m :em = 0.23
b
Note
Activation (of -, by -)
(V, Xa)
m Z5m , E10
(V, IIa)
Z5m , Z8m , Z8m , m Z10 , m Z10 , Z2m , m Z11 , Z9m ,
(VIII, Xa) (VIII, IIa) (X, VIIIa:IXa) (X, VIIIa:IXa∗ ) (II, Va:Xa) (XI-XI, IIa) (IX, XIa)
E2m m E10 E2m T EN T EN ∗ P RO E2m hm E11
m Z5m : E10
Z5m : E2m m Z8m : E10 m Z8 : E2m m Z10 : T EN m Z10 : T EN ∗ m Z2 : P RO m Z11 : E2m m hm Z9 : E11
E5m E8m E8m m E10 m E10 E2m hm E11 E9
5 10 kz+m :em =1.73 · 107 5 2 kz+m :em =5.1 · 107 8 10 kz+m :em =2.64 · 107 2 8 kz+m :ten =1.31 · 108 10 kz+m :ten =1.31 · 108 10 kz+m :pro = 1.03 · 108 2 kz+m :em = 2.0 · 107 11 2 kz+m :em = 0.6 · 107 9 11
5 10 kz−m :em =1.0 5 2 kz−m :em =1.0 8 10 kz−m :em =1.0 8 2 kz−m :ten =1.0 10 kz−m :ten =1.0 10 kz−m :pro =1.0 2 kz−m :em = 1.0 11 2 kz−m :em = 1.0 9 11
+ kten =1.0 · 108 + kten =1.0 · 108 + kpro =1.0 · 108
− kten =0.01 − kten =0.01 − kpro =0.01
5 5
10 2
−2 kzcat m :em =2.3 · 10
8 10 kzcat m m = 0.9 8 :e2 kzcat =20.0 m 10 :ten kzcat m :ten =20.0 10 kzcat =30.0 m 2 :pro kzcat m :em = 1.3 · 11 2 kzcat m m = 0.21 9 :e11
c d f f g
10−4
h i
Binding (of -, with -)
(VIIIa, IXa) (VIIIa, IXa∗ ) (Va, Xa)
E8m , E9m E8m , E9m,∗ m E5m , E10
T EN T EN ∗ P RO
e e e
18/23
PLOS S11 Table. INHIBITION REACTIONS (a) We estimate these parameters based on the half-lives of Factors IXa, Xa, IIa in plasma [34] −1 and assume that the rate of fXIa inactivation is the same as that of fXa and thrombin. (b) For inhibition of fVa by APC, kecat and m :AP C = 0.5 sec 5 −9 KM = 12.5 · 10 [35]. We assume the same reaction rates for the inhibition of fVIIIa by APC. (c) From [36]. (d) Kd = 0.5 nM and [P C] = 65 nM [37]. (e) kP C:T M :eec = 0.167 sec−1 , KM = 0.7 · 10−6 M [38]. 2 Reaction
Reactants
Product
(IXa, AT-III) (Xa, AT-III) (IIa, AT-III) (XIa, AT-III) (APC, Va)
E9 E10 E2 E11 AP C, E5m
none none none none none
(APC, VIIIa)
E8m
M−1 sec−1
sec−1
sec−1
ke+m :AP C = 1.2 · 108
in kAT :e9 =0.1 in kAT :e10 =0.1 in kAT :e2 =0.2 in kAT :e11 =0.2 ke−m :AP C = 1.0
kecat m :AP C = 0.5
a a a a b
= 1.0
kecat m :AP C = 0.5
b
Note
Inactivation (of -, by -)
AP C,
none
5 ke+m :AP C 8
8
= 1.2 · 10
5 ke−m :AP C 8
5 8
Binding (of -, with -)
(TFPI, Xa) (TFPIa, TF:VIIa)
T F P I,E10 T F P Ia,E7m
T F P Ia T F P Ia : E7m
+ 7 ktf pia:e10 =1.6 · 10 + 7 =1.0 · 10 ktf pia:em
− −4 ktf pia:e10 =3.3 · 10 − −3 ktf =1.1 · 10 pia:em
c c
(TM, Thrombin)
T M, E2ec
T M : E2ec
on 8 kT M = 1.0 · 10
off −2 kT M = 5.0 · 10
d
T M : E2ec
AP C
+ = 1.7 · 106 kP C:T M :eec
− kP = 1.0 C:T M :eec
7
7
Activation (of -, by -) (PC, TM:Eec 2 )
2
2
cat kP C:T M :eec = 0.16 2
e
19/23
PLOS S12 Table. PLATELET TRANSITIONS described in [1]. SE=subendothelium.
(a) Estimated from data in [39, 40] as described in [1]. (b) Estimated from data in [41] as
Reactants
Reactants
Products
M−1 sec−1
sec−1
Unactivated platelet adhering to SE Activated platelet adhering to SE Platelet activation by platelet in solution Platelet activation on SE Platelet activation by thrombin
P L, SE P Lva , SE P L, P Lva P L, P Lsa P L, E2
P Lsa P Lva 2P Lva P Lva , P Lsa P Lva
+ kadh =2 · 1010 + kadh =2 · 1010 act kplt = 3 · 108 act = 3 · 108 kplt
− kadh =0 − kadh =0
keact =0.50 2
Note
a a b b b
20/23
References 1. Kuharsky AL, Fogelson AL. Surface-mediated Control of Blood Coagulation: The Role of Binding Site Densities and Platelet Deposition. Biophys J. 2001;80:1050–1074. 2. Fogelson AL, Tania N. Coagulation under flow: The influence of flow-mediated transport on the initiation and inhibition of coagulation. Pathophysiol Haemost Thromb. 2005;34:91–108. 3. Turitto VT, Leonard EF. Platelet adhesion to a spinning surface. Trans Amer Soc Artif Int Organs. 1972;18:348–54. 4. Young M, Carroad P, Bell R. Estimation of diffusion coefficients of proteins. Biotech and Bioeng. 1980;22(5):947–955. 5. Mann KG, Nesheim ME, Church WR, Haley P, Krishnaswamy S. Surface-dependent Reactions of the Vitamin K-dependent enzyme complexes. Blood. 1990;76:1–16. 6. Mann KG, Bovill EG, Krishnaswamy S. Surface-dependent reactions in the propagation phase of blood coagulation. Ann N Y Acad Sci. 1991;614:63–75. 7. Morrissey JH. Tissue Factor Modulation of Factor VIIa Activity: Use in Measuring Trace Levels of Factor VIIa in Plasma,. Thromb Haemost. 1995;74:185–188. 8. Novotny WF, Brown SG, Miletich JP, Rader DJ, Broze GJ. Plasma antigen levels of the lipoprotein-associated coagulation inhibitor in patient samples. Blood. 1991;78:387–93. 9. Weiss HJ. Platelet Physiology and Abnormalities of Platelet Function (Part 1). New Engl J Med. 1975;293:531–541. 10. Walsh PN. Platelet-Coagulant Protein Interactions. In: Colman RW, Hirsh J, Marder VJ, Salzman EW, editors. Hemostasis and Thrombosis: Basic Principles and Clinical Practice. 3rd ed. Philadelphia, PA: J.B. Lippincott Company; 1994. p. 629–651. 11. Nesheim ME, Pittman DD, Wang JH, Slonosky D, Giles AR, Kaufman RJ. The binding of S-labeled recombinant Factor VIII to activated and unactivated human platelets. J Biol Chem. 1988;263:16467. 12. Ahmad SS, Rawala-Sheikh R, Walsh PN. Comparative interactions of Factor IX and Factor IXa with human platelets. Journal of Biological Chemistry. 1989;264:3244–3251. 13. Mann KG, Krishnaswamy S, Lawson JH. Surface-dependent Hemostasis. Semin Hematol. 1992;29:213–26. 14. Baglia FA, Jameson BA, Walsh PN. Identification and Characterization of a Binding Site for Platelets in the Apple 3 domain of coagulation Factor XI. J Biol Chem. 1995;270:6734–40. 15. Miller TN, Sinha D, Baird TR, Walsh PN. A Catalytic Domain Exosite (Cys527 -Cys542 ) in Factor XIa mediates binding to a site on activated platelets. Biochemistry. 2007;46:14450–60.
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