Supplemental Digital Content

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Supplemental Digital Content

Controlled multifactorial coagulopathy: effects of dilution, hypothermia, and acidosis on thrombin generation in vitro

Alexander Y. Mitrophanov, PhD, Fania Szlam, MMSc, Roman M. Sniecinski, MD, Jerrold H. Levy, MD, and Jaques Reifman, PhD

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2 Blood Coagulation Protein Measurement in Plasma

Plasma testing for factor (F) II, FV, FVII, FVIII, FIX, FX, protein C (PC), antithrombin (AT), tissue factor pathway inhibitor (TFPI), and fibrinogen (Fg) was performed in undiluted plasma samples without thrombomodulin (Tm) supplementation or pH adjustment. All measurements (except TFPI) were performed on a STA Compact Analyzer (Diagnostica Stago, Parsippany, NJ) using the manufacturer’s kits and reagents. Coagulation factor activities were determined using one-stage clotting assays in individual-factor-deficient plasma, according to prothrombin time (PT) for FII, FV, FVII, and FX, and according to activated partial thromboplastin time (aPTT) for FVIII and FIX. The activity of each factor in a plasma sample was determined from a factor- specific standard curve established by serial dilution of a commercially available unicalibrator (Diagnostica Stago, Parsippany, NJ). AT measurements were conducted using a thrombin-based amidolytic assay and a synthetic chromogenic substrate. Functional PC levels were measured based on prolongation of aPTT according to the assay manufacturer’s protocol. Fibrinogen concentration was measured based on the clotting method of Clauss¹ using an excess of thrombin.

The intra-day coefficient of variation (CV, %) was determined by analyzing the same sample for PT and for aPTT 10 times. The inter-day CV was determined by analyzing the normal control plasma on five separate days. For normal control plasma, the intraday CV was 0.94% for PT, 1.03% for aPTT, and less than 5% for FII, FV, FVII, FVIII, FIX, FX, PC, and AT. The inter-day CV for the evaluated parameters was less than 10%. All coagulation testing was performed at 37 C.

Tissue factor pathway inhibitor (TFPI) analyses were performed using the Diagnostica Stago Asserachrom Free TFPI ELISA (enzyme-linked immunoassay) kit according to the

manufacturer’s directions. The test is based on a “sandwich” technique and, in the final reaction, the intensity of the produced color is directly dependent on the concentration of free TFPI

present in the plasma sample. The absorbance was measured at 492 nm using a Spectramax plate reader (Spectramax 340 PC; Molecular Devices, Sunnyvale, CA) equipped with SoftMax Pro software. The concentrations of free TFPI were based on an assay calibration curve generated with the standards provided in the kit.

Subject Group Characteristics

We analyzed standard hematological indices in the samples from each of the 10 subjects. The blood counts were as follows [mean ± 1 standard deviation (SD), range]: white blood cells (5.9 ± 2.2, 2.6–9.8 × 10³ 1/µL), hemoglobin (14.3 ± 1.2, 12.6–15.7 g/dL), hematocrit (41.6 ± 3.3, 36.9–

46.7 %), and platelets (227.3 ± 66.6, 124.0–347.0 × 10³ 1/µL). All values for each subject were within normal ranges. The concentration of platelets in the PPP samples was 0.0 to the limit of detection for each subject.

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3 Computational Kinetic Model

Thrombin generation in the model was triggered by the presence of TF, whose initial

concentration (5 pM) matched the experimental setup. The model outputs were thrombin time courses generated over a time interval of 90 min. For each model-simulated thrombin time course, we calculated five quantitative parameters according to their definitions for the CAT assay.

During model development, the kinetic constants in the model were adjusted using an algorithm similar to the one developed in our recent work² (to train the “averaged-parameter model” introduced there). For this model training, we used the coagulation-protein-level

measurements also taken from that work. As a result, we obtained the model parameter set given in Table S1, which we used to model thrombin generation in each of the subjects in the present study without any further kinetic-parameter adjustments (“pure validation”). The intersubject differences in this study were captured in the model by using individual coagulation protein levels (Table S3). Specifically, we used these measurements to adjust the default initial values of the coagulation proteins (Table S2) in our kinetic model to simulate thrombin generation for each of the subjects, as described.² The initial protein concentrations in the model were reduced 1.5- fold to reflect plasma dilution in the CAT assay. When necessary, the initial protein

concentrations were further reduced 3- or 5-fold to reflect 3- or 5-fold dilution, respectively.

We reflected hypothermia and acidosis in our kinetic model via temperature- and pH-

dependent adjustments to the default values of the reaction rate constants. For both hypothermia and acidosis, we used our previously developed “reduced” strategy of modeling, which (in contrast with the corresponding “full” strategies) does not rely on extensive randomization of the reaction rate constants.^3,4 Indeed, the reduced approaches have demonstrated sufficient accuracy combined with a substantially smaller computational cost of modeling. Following these

strategies, we modeled the influence of temperature changes on a rate constant via a

multiplicative factor termed the temperature coefficient, which in our case was equal to 2.5 (and was raised to a certain temperature-dependent power). We modified this way all rate constants but not equilibrium constants (see Table S1 below for the list of model constants and their values).³ Analogously, we modeled the influence of pH via multiplicative, pH-dependent pH factors.⁴ The rate constants affected by acidosis were the following: k5, k6, k7, k10, k15, k16, k17, k22, k26, k31, k32, k43, k44, k47, k49, k53, k59, k59_t, k60, k65, k69, k70, k73, k74, k75, k76, k77, k80, k84, k89, k93, k94, k108, and k111 (see Table S1). Hypothermia and acidosis were assumed to influence the target rate constants independently.⁵ Accordingly, we modeled the effects of simultaneous hypothermia and acidosis as the corresponding temperature coefficient and pH factor acting multiplicatively on each affected rate constant.

We implemented our kinetic model in the SimBiology toolbox of the MATLAB (MathWorks, Inc., Natick, MA) software suite. The biochemical reactions (Table S1) were automatically converted by the toolbox software into a system of differential equations, and solved using the “sundials” solver. The computations were performed in MATLAB R2017b.

The two main outputs of our model are the concentrations of free thrombin and fibrin. The concentration of free thrombin was calculated simply as [FIIa], following our recent thrombin- generation analysis.² By contrast, in our earlier modeling studies, the thrombin output was the

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concentration of active thrombin, which takes into account the effects of thrombin’s

enzymatically active precursor, meizothrombin.^6-8 This is because our previous efforts followed the thrombin modeling strategy of Hockin and Mann, which had been calibrated for a particular in vitro experimental system that uses a chromogenic thrombin substrate.^9,10 However, our current computational model reflects the widely used Calibrated Automated Thrombogram (CAT) thrombin-generation assay, which uses a fluorogenic thrombin substrate.¹¹ While the influence of meizothrombin on the output of this assay is currently unknown, our modeling approach follows the representation of the thrombin signal suggested by CAT experts.¹²

The fibrin output, F, in our model simulations is calculated according to the formula F = [FnII] + [FnII_t] + 2[(FnII)2] + 2[(FnII_t)2],

Where the brackets designate concentrations (for the biochemical species designations, see Table S1). This formula for the fibrin output represents the concentration of fibrin protomers and extends our earlier approach⁸ to include the activated thrombin-activatable fibrinolysis inhibitor (TAFIa)-cleaved fibrin species, FnII_t and (FnII_t)2.

The majority of the default initial concentration values in our model (Table S2) were taken from Mitrophanov et al.⁸ The initial concentrations for α2-macroglobulin and the fluorogenic thrombin substrate were taken from Kremers et al.¹² The “Serpins” model variable, together with its initial value, was introduced in our previous work to ascertain thrombin time course decay in diluted plasma supplemented with several coagulation proteins.² It represents the plasma concentration of unspecified serpins. The initial vitronectin concentration was estimated based on the data in Preissner et al.¹³ and Declerck et al.¹⁴

The model was solved with the integration parameters used in our previous work (“sundials”

ODE solver: absolute tolerance, 1.0×10^-18 M; relative tolerance, 1.0×10^-12; maximal step size, 0.05 s).^2,6,8

Model Construction

The majority of the thrombin generation, fibrin formation, and fibrinolysis reactions in our extended integrated model (see Table S1) were taken from the works of Mitrophanov et al.^2,8 The TAFI activation and TAFIa deactivation reactions in our model were based on the work of

Bajzar et al.¹⁵ The biochemical interactions between vitronectin (VN), plasminogen activator inhibitor 1 (PAI), FIIa, and Tm were represented following the work of Dekker et al.^16,17 and others.^18-20 The interactions between activated protein C (APC), PAI, and VN were represented based on the work of Rezaie.²¹ (The complex formation rate was assumed to be similar in magnitude to that for the analogous reaction involving FIIa instead of APC.) The reaction PAI:VN + tPA  PAI:tPA + VN was assumed to have the same rate as the PAI-tPA binding reaction in the absence of VN.²² Whenever the published kinetic constants for the reactions were measured for a temperature other than 37 C, we rescaled them to 37 C assuming a temperature coefficient of 2.5.³ When only equilibrium constants were available for reversible reactions, we made the assumption of fast protein-protein binding (e.g., for the binding of PAI with VN¹⁸) and used the published kinetic data (e.g., Fig. 2 in Bajzar et al.¹⁵ for TAFI activation kinetics) to

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estimate the mass-action rate constants involved. In certain cases, the rate constant values derived from published quantities needed to be re-tuned based on published kinetic data (for example, modifying the rate constants for the FIIa-PAI-VN interactions to capture the kinetics shown in Fig. 1D from Dekker et al.¹⁷). Consistent with our recent work,² the initial value for the k41 model parameter (i.e., the rate of FIIa inhibition by antithrombin), was taken from the

original Hockin-Mann model,¹⁰ rather than from the Naski-Shafer model as in our earlier work.⁸ These literature-based rate constants served as the initial parameter values for our model

calibration process (see the next section).

The cleavage of fibrin by TAFIa was represented in the model in a parsimonious way to reflect the fact that TAFIa-cleaved fibrin is less efficient than is uncleaved fibrin as a cofactor of plasminogen activation. This was reflected in our model by selecting parameter values so that k59_t < k59 (Table S1, footnote). Furthermore, to reproduce the expected TAFIa effect (i.e., a ~3- fold fibrinolysis slowdown at saturation with TAFIa^15,23,24), we fine-tuned the following

parameters by trial and adjustment: k84, k86,k59_t, K1_t, K2_t, and K3_t (their final values are given in Table S1).

Model Calibration

The model calibration (i.e., parameter adjustment) strategy followed our recent work on

thrombin-generation modeling.² In the present work, the parameters whose values were adjusted during calibration were the rate constants of the reactions that could affect the thrombin-

generation output (in the absence of Tm). These rate constants were k1‒k56, k78, k79, k91‒k100, and k105‒k112 (Table S1).

As in the original version of the calibration algorithm, the calibrated parameter values were allowed to increase or decrease no more than 3-fold from their initial values,² which is on the same order of magnitude as experimental variability in rate constant measurements.²⁵ The initial parameter values were either based on our previous work^2,8 or taken from the literature, as described above. In contrast to the original version of the calibration strategy,² here we limited the number of model-training epochs to 4, to expedite the calibration process. In the fitting steps, we ran the fmincon optimization function with the maximal number of function evaluations set to 200, and both the TolX and TolFun parameters set to 10^-8.

Regression Analysis

In our regression analysis, we used the following predictor variables: degree of dilution (values:

1, 1/3, 1/5), temperature (values: 31, 34, 37), pH (values: 6.9, 7.1, 7.4), and Tm level (values: 0, 15). Each of these variables was rescaled as follows (min-max scaling): if X is the variable, then A = (max X + min X)/2, B = (max X – min X)/2, and Scaled X = (X – A)/B. This scaled the interval of variation for the predictor variables to [‒1, 1]. These variables were used in the initial (i.e., full) regression equations for the five thrombin-generation parameters, as well as for PT and aPTT (note that for PT and aPTT temperature was not used as a predictor variable, because the

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assays were performed at a constant temperature). We also introduced an additional categorical variable “Subject number” (#1 to #10), which we used to indicate the measurements in plasma samples from the same subject.

We chose not to include the quadratic terms for temperature and pH so as to minimize the chance of overfitting. Moreover, while restricting flexibility, this contributed to the

interpretability of the resultant models.²⁶ Our data had largely linear structure, and the regression plots against the data showed that the resultant (reduced) regression equations captured the main trends in the data reasonably well (Figures 5, 6, and S3).

We fitted the initial regression equations to our experimental data using the MATLAB function stepwiselm, which implements stepwise linear regression. The corresponding outputs—i.e., reduced regression equations used in our data analysis—are shown below. In these outputs, the Wilkinson notation is used. Accordingly, “X:Y” designates the product of X and Y, whereas “X*Y” designates X + Y + X:Y; “1” designates a constant term (intercept).

Reduced regression equation for PT

f =

Linear regression model:

output ~ 1 + Dilution*pH + Dilution^2

Estimated Coefficients:

Estimate SE tStat pValue ________ _______ _______ ___________

(Intercept) 6.995 0.85163 8.2137 4.5773e-14 Dilution -15.338 0.29184 -52.558 4.0989e-109 pH -1.3947 0.29826 -4.6761 5.8228e-06 Dilution:pH 0.66286 0.33042 2.0061 0.046387 Dilution^2 22.67 0.97214 23.319 1.4228e-55 Number of observations: 180, Error degrees of freedom: 175 Root Mean Squared Error: 3.19

R-squared: 0.942, Adjusted R-Squared 0.941

F-statistic vs. constant model: 712, p-value = 4.43e-107

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7 Reduced regression equation for aPTT

f =

output ~ 1 + pH + Dilution*Tm_level + Dilution^2 Estimated Coefficients:

Estimate SE tStat pValue ________ _______ _______ __________

(Intercept) 14.86 1.4089 10.547 2.0266e-20 Dilution -34.274 0.48144 -71.191 1.315e-130 pH -1.2376 0.47826 -2.5877 0.010478 Tm_level 6.1367 0.40558 15.131 1.4929e-33 Dilution:Tm_level -4.7625 0.44931 -10.6 1.4385e-20 Dilution^2 52.983 1.6083 32.943 1.0738e-76 Number of observations: 180, Error degrees of freedom: 174

Root Mean Squared Error: 5.27

F-statistic vs. constant model: 1.12e+03, p-value = 3.59e-130

Reduced regression equation for LT

f =

output ~ 1 + Temperature + Dilution*pH + Dilution*Tm_level Estimated Coefficients:

Estimate SE tStat pValue _________ ________ ________ __________

(Intercept) 3.6776 0.027755 132.5 0 Dilution -0.22046 0.030748 -7.1698 2.5205e-12 Temperature -0.46344 0.032839 -14.113 1.1834e-38 pH -0.14699 0.033658 -4.3671 1.5133e-05 Tm_level -0.011332 0.027664 -0.40961 0.68226 Dilution:pH 0.073686 0.037287 1.9762 0.048649 Dilution:Tm_level -0.25549 0.030647 -8.3366 6.5453e-16

Number of observations: 540, Error degrees of freedom: 533 Root Mean Squared Error: 0.623

F-statistic vs. constant model: 59.1, p-value = 5.45e-56

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8 Reduced regression equation for ttP

f =

output ~ 1 + Temperature + pH + Dilution*Tm_level Estimated Coefficients:

Estimate SE tStat pValue _________ ________ _______ __________

(Intercept) 6.7197 0.037221 180.53 0 Dilution -0.078183 0.041108 -1.9019 0.057721 Temperature -0.76844 0.044047 -17.446 2.8484e-54 pH -0.20582 0.043757 -4.7037 3.2576e-06 Tm_level -0.21359 0.037107 -5.7561 1.4527e-08 Dilution:Tm_level -0.39274 0.041108 -9.5539 4.5029e-20 Number of observations: 540, Error degrees of freedom: 534

F-statistic vs. constant model: 86.7, p-value = 1.14e-66

Reduced regression equation for VI

f =

output ~ 1 + pH + Dilution*Temperature + Dilution*Tm_level + Dilution^2 Estimated Coefficients:

Estimate SE tStat pValue ________ _______ ________ ___________

(Intercept) 72.686 2.136 34.029 1.2467e-135 Dilution 4.1368 0.72988 5.6677 2.374e-08 Temperature -0.15155 0.75306 -0.20124 0.84059 pH 1.7062 0.72506 2.3531 0.018979 Tm_level -18.033 0.61487 -29.329 3.2512e-113 Dilution:Temperature -2.0297 0.83425 -2.433 0.015305 Dilution:Tm_level -19.812 0.68117 -29.085 5.0329e-112 Dilution^2 -20.811 2.4383 -8.5351 1.4695e-16 Number of observations: 540, Error degrees of freedom: 532

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9 Reduced regression equation for PH

f =

output ~ [Linear formula with 9 terms in 3 predictors]

Estimate SE tStat pValue ________ ______ _______ ___________

(Intercept) 226.15 5.0202 45.047 1.604e-183 Dilution 25.167 1.7159 14.667 3.8792e-41 Temperature -16.662 1.7704 -9.4116 1.4723e-19 Tm_level -65.428 1.4455 -45.263 2.1286e-184 Dilution:Temperature -4.2746 1.9613 -2.1795 0.02973 Dilution:Tm_level -67.907 1.6014 -42.406 1.2895e-172 Temperature:Tm_level 4.4583 1.7704 2.5183 0.012086 Dilution^2 -66.975 5.7322 -11.684 3.1543e-28 Dilution:Temperature:Tm_level 6.5753 1.9613 3.3526 0.00085764

Number of observations: 540, Error degrees of freedom: 531 Root Mean Squared Error: 32.6

Reduced regression equation for ETP

f =

output ~ [Linear formula with 9 terms in 3 predictors]

Estimate SE tStat pValue ________ ______ _______ ___________

(Intercept) 2112.4 50.14 42.131 1.8607e-171 Dilution -262.72 17.138 -15.33 3.4833e-44 Temperature -355.15 17.682 -20.086 3.5653e-67 Tm_level -482.82 14.437 -33.443 8.544e-133 Dilution:Temperature 24.835 19.588 1.2678 0.20541 Dilution:Tm_level -523.64 15.994 -32.74 1.7124e-129 Temperature:Tm_level 90.965 17.682 5.1446 3.7795e-07 Dilution^2 -490.22 57.251 -8.5627 1.1958e-16 Dilution:Temperature:Tm_level 123.88 19.588 6.3244 5.4011e-10 Number of observations: 540, Error degrees of freedom: 531

Root Mean Squared Error: 325

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Table S1. Biochemical reactions and their parameters represented in the kinetic model.The notation –kx> designates a forward reaction with rate constant kx, when the rate of the reaction is defined by the mass action law. The notation <kx–ky> designates a reversible mass-action reaction, where the forward and reverse half-reactions have the rate constants ky and kx, respectively. The values of the rate constants for forward and reverse reactions are designated as k+ and k‒, respectively. The symbol “:” in this table denotes molecular complex formation. For reactions involving intermediate complex formation, the second forward rate constant is designated as kcat. The notation –rx> indicates a non-mass-action forward reaction with rate rx whose expression is given in the footnote. For monomolecular and bimolecular reactions, the rate constants are given in units of s^-1 and M^-1×s^-1, respectively. For presentation purposes, the parameter values were rounded to two digits in the mantissa (for unrounded values, see the SimBiology representation of the model).

# Chemical reaction k+ k− kcat

1 TF + FVII <k1–k2> TF:FVII 4.6×10⁶ 6.0×10^-3 2 TF + FVIIa <k3–k4> TF:FVIIa 5.2×10⁷ 5.6×10^-3 3 TF:FVIIa + FVII –k5> TF:FVIIa + FVIIa 8.0×10⁵

4 FXa + FVII –k6> FXa + FVIIa 1.9×10⁷ 5 FIIa + FVII –k7> FIIa + FVIIa 2.5×10⁴ 6 TF:FVIIa + FX <k8–k9> TF:FVIIa:FX

–k10> TF:FVIIa:FXa

2.3×10⁷ 1.5 1.3×10¹ 7 TF:FVIIa + FXa <k11–k12> TF:FVIIa:FXa 4.2×10⁷ 3.7×10¹

8 TF:FVIIa + FIX <k13–k14> TF:FVIIa:FIX –k15> TF:FVIIa + FIXa

1.6×10⁷ 3.3 2.6

9 FXa + FII –k16> FXa + FIIa 1.4×10⁴ 10 FIIa + FVIII –k17> FIIa + FVIIIa 4.3×10⁷

11 FVIIIa + FIXa <k18–k19> FIXa:FVIIIa 1.5×10⁷ 5.8×10^-3 12 FIXa:FVIIIa + FX <k20–k21> FIXa:FVIIIa:FX

–k22> FIXa:FVIIIa + FXa

1.5×10⁸ 2.2×10^-3 1.0×10¹ 13 FVIIIa <k23–k24> FVIIIa1-L + FVIIIa2 1.0×10^-2 4.1×10⁴

14 FIXa:FVIIIa:FX –k25> FVIIIa1-L + FVIIIa2 + FX + FIXa

1.2×10^-3 15 FIXa:FVIIIa –k25> FVIIIa1-L + FVIIIa2 +

FIXa

1.2×10^-3 16 FIIa + FV –k26> FIIa + FVa 2.8×10⁷

17 FXa + FVa <k27–k28> FXa:FVa 7.9×10⁸ 2.4×10^-1 18 FXa:FVa + FII <k29–k30> FXa:FVa:FII

–k31> FXa:FVa + mIIa

9.0×10⁷ 2.3×10² 7.8×10¹ 19 mIIa + FXa:FVa –k32> FIIa + FXa:FVa 6.0×10⁸

20 FXa + TFPI <k33–k34> FXa:TFPI 1.3×10⁶ 6.3×10^-4 21 TF:FVIIa:FXa + TFPI <k35–k36>

TF:FVIIa:FXa:TFPI

3.6×10⁸ 2.0×10^-4 22 TF:FVIIa + FXa:TFPI

–k37> TF:FVIIa:FXa:TFPI

7.1×10⁷

23 FXa + AT –k38> FXa:AT 3.2×10³

24 mIIa + AT –k39> mIIa:AT 6.3×10³

25 FIXa + AT –k40> FIXa:AT 7.4×10²

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26 FIIa + AT –k41> FIIa:AT 2.7×10³

27 TF:FVIIa + AT –k42> TF:FVIIa:AT 4.2×10² 28 FIXa + FX –k43> FIXa + FXa 1.1×10⁴ 29 mIIa + FV –k44> mIIa + FVa 6.6×10⁶ 30 Fg + FIIa <k45–k46> Fg:FIIa –k47> FnI + FIIa +

FPA

8.2×10⁷ 8.2×10² 1.8×10² 31 FnI + FIIa <k48–k46> FnI:FIIa –k49> FnII +

FIIa + FPB

8.2×10⁷ 1.7×10³ 7.7 32 2FnI <k50–k51> (FnI)2 2.1×10⁶ 8.2×10^-2

33 (FnI)2 + FIIa <k52–k46> (FnI)2:FIIa –k53>

(FnII)2 + FIIa + 2FPB

8.2×10⁷ 9.6×10² 9.0×10¹ 34 FnII+ FIIa <k54–k46> FnII:FIIa 8.2×10⁷ 2.2×10³

35 (FnI)2:FIIa + AT –k55> (FnI)2:FIIa:AT 2.0×10⁴ 36 FnI:FIIa + AT –k55> FnI:FIIa:AT 2.0×10⁴ 37 FnII:FIIa + AT –k56> FnII:FIIa:AT 1.4×10⁴

38 Pn + AP –k57> Pn:AP 3.0×10⁶

39 tPA + PAI –k58> tPA:PAI 4.0×10⁷

40 Pg –r1> Pn (see footnote) --- 41 FnII –r2> FDP (see footnote) --- 42 (FnII)2 –r3> 2FDP (see footnote) ---

43 Tm + FIIa <k61–k62> Tm:FIIa 8.0×10⁷ 4.6×10^-1 44 Tm:FIIa + PC <k63−k64> Tm:FIIa:PC

–k65> Tm:FIIa + APC

3.4×10⁷ 2.0×10² 2.5×10^-1 45 Tm:FIIa + AT –k66> FIIa:AT + Tm 1. 5×10⁴

46 APC + FVa <k67−k68> APC:FVa 3.4×10⁷ 2.0

47 APC:FVa –k69> APC + FVa5 4.4×10^-1

48 APC:FVa –k70> APC + FVa3 1.4×10^-1

49 APC + FVa5 <k67−k68> APC:FVa5 –k70> APC + FVa53

3.4×10⁷ 2.0 1.4×10^-1 50 APC + FVa3 <k67−k68> APC:FVa3 –k69> APC

+ FVa53

3.4×10⁷ 2.0 4.4×10^-1

51 FVa3 –k71> HCF + LCA1 1.3×10^-2

52 FVa53 –k71> HCF + LCA1 1.3×10^-2

53 APC + LCA1 <k67−k68> APC:LCA1 3.4×10⁷ 2.0 54 APC + Tm:FIIa <k63−k64> Tm:FIIa:APC 3.4×10⁷ 2.0×10² 55 FXa + FVa5 <k72−k28> FXa:FVa5 7.9×10⁸ 2.9×10^-1 56 FXa + FVa3 <k72−k28> FXa:FVa3 7.9×10⁸ 2.9×10^-1 57 FXa:FVa5 + FII <k29−k30> FXa:FVa5:FII

–k73> FXa:FVa5 + mIIa

9.0×10⁷ 2.3×10² 2.4×10¹ 58 FXa:FVa3 + FII <k29−k30> FXa:FVa3:FII

9.0×10⁷ 2.3×10² 6.0 59 FXa:FVa5 + mIIa –k75> FXa:FVa5 + FIIa 1.3×10⁸

60 FXa:FVa3 + mIIa –k76> FXa:FVa3 + FIIa 1.0×10⁸ 61 FXa:FVa3 –k77> HCF + LCA1 + FXa 2.9×10^-3 62 FXa:FVa3:FII –k77> HCF + LCA1 + FXa +

FII

2.9×10^-3

63 Tm + mIIa <k61−k62> Tm:mIIa 8.0×10⁷ 4.6×10^-1

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12 64 Tm:mIIa + PC <k63−k64> Tm:mIIa:PC

–k65> Tm:mIIa + APC

3.4×10⁷ 2.0×10² 2.5×10^-1 65 Tm:mIIa + AT –k66> mIIa:AT + Tm 1.5×10⁴

66 FXa + FVa53 <k72−k28> FXa:FVa53 7.9×10⁸ 2.9×10^-1 67 FXa:FVa53 + FII <k29−k30> FXa:FVa53:FII

9.0×10⁷ 2.3×10² 6.0 68 FXa:FVa53 + mIIa –k76> FXa:FVa53 + FIIa 1.0×10⁸

69 FXa:FVa53 –k77> HCF + LCA1 + FXa 2.9×10^-3 70 FXa:FVa53:FII –k77> HCF + LCA1 + FXa +

FII

2.9×10^-3

71 FII + FVa <k78−k79> FII:FVa 5.5×10⁷ 3.7×10² 72 FXa:FVa5 + APC –k80> FXa:FVa53 + APC 1.7×10⁶

73 TAFIa –k81> TAFIai 6.0×10^-4

74 TAFIa + FnII <k82−k83> TAFIa:FnII –k84> TAFIa + FnII_t

1.0×10⁸ 1.0×10⁴ 1.1×10² 75 TAFIa + (FnII)2 <k82−k83> TAFIa:(FnII_t)2

–k84> TAFIa + (FnII_t)2

1.0×10⁸ 1.0×10⁴ 1.1×10² 76 FnII_t –r4> FDP (see footnote) ---

77 (FnII_t)2 –r5> 2FDP (see footnote) ---

78 FIIa + TAFI <k85−k86> FIIa:TAFI 1.4×10⁷ 4.0 79 Tm:FIIa + TAFI <k85−k86> Tm:FIIa:TAFI 1.4×10⁷ 4.0 80 FIIa:TAFI + Tm <k87−k88> Tm:FIIa:TAFI

−k89> Tm:FIIa + TAFIa

4.0×10⁶ 3.4×10^-2 4.9

81 PAI –k90> PAI_latent 1.3×10^-4

82 FIIa + PAI <k91−k92> FIIa:PAI

−k93> FIIa:PAI_t

6.9×10⁵ 5.9×10^-1 5.8×10^-3 83 FIIa:PAI_t −k94> FIIa + PAI_i 3.3×10^-2

84 FIIa:PAI_t −k95> FIIa:PAI_s 3.1×10^-2

85 PAI + VN <k96−k97> PAI:VN 1.6×10⁴ 5.1×10^-6 86 FIIa + PAI:VN <k98−k99> FIIa:PAI:VN

−k100> FIIa:PAI + VN

7.8×10⁵ 5.1×10^-4 4.8×10^-4 87 APC + PAI:VN <k101−k102> APC:PAI:VN

−k103> APC:PAI + VN

5.0×10⁵ 1.0×10^-2 5.0×10^-4 88 PAI:VN + tPA −k104> tPA:PAI + VN 4.0×10⁷

89 FIIa + α2-M −k105> FIIa:α2-M 4.2×10² 90 FIIa + FS <k106−k107> FIIa:FS

−k108> FIIa + FS_c

1.5×10⁸ 6.1×10⁴ 3.5 91 FIIa:α2-M + FS <k109−k110> FIIa:α2-M:FS

−k111> FIIa:α2-M + FS_c

2.0×10⁸ 5.4×10⁴ 2.8 92 FIIa + Serpins −k112> FIIa:Serpins 4.4×10²

Protein name abbreviations are as in the previous section. The suffix “a” denotes the activated form of a factor. Additional abbreviations: APC, activated protein C; mIIa, meizothrombin; VN,

vitronectin; α2-M, α2-macroglobulin; FPA and FPB, fibrinopeptides A and B, respectively; Pg, plasminogen; Pn, plasmin; AP, α2-antiplasmin; TAFI, thrombin-activatable fibrinolysis inhibitor;

FDP, fibrin degradation products; Fg, fibrinogen; FnI, fibrin I monomers; FnII, fibrin II monomers;

FnII_t, FnII cleaved by TAFIa; FPA, fibrinopeptide A; FPB, fibrinopeptide B; FS, fluorogenic substrate; FIIa:PAI_t, transformed FIIa:PAI; FIIa:PAI_s, stable FIIa:PAI; FVa5, FVa3, and FVa53,

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partially proteolyzed forms of FVa; HCF and LCA1, inactive FVa fragments; mIIa, meizothrombin;

PAI_i, inactivated PAI; PAI_latent, latent PAI; Serpins, unspecified plasma serine protease inhibitors possibly acting in plasma; TAFIai, inactive TAFIa.

The non-mass-action rates r1−r5 were defined as follows:

) /(

) (

] Pg [

) /(

] Pg ][

tPA [ )

/(

) (

] Pg [

) /(

] Pg ][

tPA [

FnII_t t

_ 1 FnII_t t

_ 3 t _ 2

FnII_t t

_ 1 FnII_t t

_ 59 FnII

1 FnII 3 2

FnII 1 FnII 59

1 K K C K C

C K C

k C

K C

K K

C K C r k



 



  ,

where C_FnII[FnII]2[(FnII)₂] and C_{FnII_t} [FnII_t]2[(FnII_t)₂];

] FnII [

] FnII ][

Pn [

4 60

2  

K

r k ;

] FnII) [(

] FnII) ][(

Pn [

2 4

2 60

3  

K

r k ;

] FnII_t [

] FnII_t ][

Pn [

4 60

4  

K

r k ;

] FnII_t) [(

] FnII_t) ][(

Pn [

2 4

2 60

5  

K

r k .

In these expressions, k59 = 0.09 s^-1; k60 = 0.47 s^-1; K1 = 7.7×10^-8 M, K2 = 4.1×10^-7 M, K3 = 3.0×10^-7 M, and K4 = 2.1×10^-6 M; k59_t = 0.027 s^-1; K1_t = 3.85×10^-7 M, K2_t = 2.05×10^-7 M, K3_t = 3.0×10^-6 M.

NOTE: in the model, we do not represent the proteins FXI and FXII, or other components of the intrinsic pathway of blood coagulation, because they make a significant contribution to in-vitro thrombin

generation primarily under conditions of low TF ([TF] < 2 pM).^27,28

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Table S2. Default initial concentrations of coagulation factors in the kinetic model.* All of the modeled biochemical species not listed in this table have an initial concentration of zero. See the section “Computational Kinetic Model” for literature references. For proteins measured experimentally, these default concentrations were adjusted accordingly in a subject-specific manner² using the data from Table S3.

Protein Concentration (M)

TF 5.0×10^-12

FVII 1.0×10^-8

FVIIa 1.0×10^-10

FX 1.6×10^-7

FIX 9.0×10^-8

FII 1.4×10^-6

FVIII 7.0×10^-10

FV 2.0×10^-8

TFPI 2.5×10^-9

AT 3.4×10^-6

Fg 9.0×10^-6

Pg 2.0×10^-6

PAI 4.0×10^-10

AP 1.0×10^-6

tPA 7.0×10^-11

PC 7.0×10^-8

Tm 0 or 15×10^-9

TAFI 7.5×10^-8

VN 3.0×10^-6

α2-M 3.03×10^-6

FS 4.17×10^-4

Serpins 1.0×10^-5

*These initial concentrations (except those for TF, Tm, Serpins, and FS) represent the average levels of coagulation proteins in normal human plasma.⁸

Specifically, it is known that FVIIa is typically present in plasma at a concentration of ~1% of the FVII

concentration.¹⁰

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Table S3. Individual coagulation-protein levels for the subject group (n = 10).*

Volunteer

#

FII (%)

FV (%)

FVII**

(%)

FVIII (%)

FIX (%)

FX (%)

AT (%)

PC (%)

Fg (mg/dL)

TFPI (ng/mL)

1 90 102 107 81 99 96 102 124 262 8.8

2 134 125 147 117 141 155 114 148 322 9.2

3 104 89 88 135 105 102 94 99 252 5.9

4 85 99 104 96 107 86 101 113 314 4.6

5 102 97 128 199 155 130 96 120 252 8.1

6 89 89 110 188 101 96 98 67 294 7.5

7 88 98 97 167 125 98 98 124 236 9.6

8 93 109 70 137 121 110 112 119 332 8.7

9 102 118 138 92 100 110 109 119 213 7.5

10 119 119 116 119 198 124 126 162 295 11.8

*Of all the proteins reflected in our model (Table S1), we chose to measure the levels of this protein subset, because it represents the core of the biochemical coagulation network.^10,29 We did not measure the levels of fibrinolytic proteins, because fibrinolysis was not induced in our in vitro system.

**Because the average FVIIa concentration is 1% of the average FVII concentration in plasma,¹⁰ we assumed that the same relationship would be a reasonable approximation for the subject-specific levels of these two proteins.

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Figure S1. Thrombin-generation time courses for the subject group (n = 10) at pH 7.1 with 0 supplemented thrombomodulin. A–C, computational model simulations; D–F, experimental results obtained using the CAT assay. Blue, green, and red lines represent no dilution, 3-fold dilution, and 5-fold dilution, respectively. A and D, 37 C; B and E, 34 C; C and F, 31 C.

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Figure S2. Computationally simulated quantitative parameters of thrombin generation under different experimental conditions. A–C, lag time (LT). D–F, velocity index (VI). The

experimental points (circles) and error bars represent mean ±1 SD (n = 10). Blue, green, and red

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lines indicate no dilution, 3-fold dilution, and 5-fold dilution, respectively. The lines connect the circles (means) and are shown to emphasize trends in the data. Solid and dashed lines correspond to 0 and 15 nM supplemented thrombomodulin, respectively. A and D, pH 7.4; B and E, pH 7.1;

C and F, pH 6.9.

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Figure S3. Quantitative parameters of thrombin generation under different experimental conditions. The parameter values were derived from thrombin time courses measured using the CAT assay. A and D, time to thrombin peak (ttP). B and E, thrombin peak height (PH). C and F, endogenous thrombin potential (ETP). The

experimental points (circles) and error bars represent mean ±1 SD (n = 10). Blue, green,

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and red lines show the outputs of our regression models and indicate no dilution, 3-fold dilution, and 5-fold dilution, respectively. Solid and dashed lines correspond to 0 and 15 nM supplemented thrombomodulin, respectively. A‒C, pH 6.9; D‒F, pH 7.1.

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21 REFERENCES

1. Molinaro RJ, Szlam F, Levy JH, Fantz CR, Tanaka KA. Low plasma fibrinogen levels with the Clauss method during anticoagulation with bivalirudin. Anesthesiology 2008;

109: 160-161.

2. Mitrophanov AY, Szlam F, Sniecinski RM, Levy JH, Reifman J. A step toward balance:

thrombin generation improvement via procoagulant factor and antithrombin supplementation. Anesth Analg 2016; 123: 535-546.

3. Mitrophanov AY, Rosendaal FR, Reifman J. Computational analysis of the effects of reduced temperature on thrombin generation: the contributions of hypothermia to coagulopathy. Anesth Analg 2013; 117: 565-574.

4. Mitrophanov AY, Rosendaal FR, Reifman J. Mechanistic modeling of the effects of acidosis on thrombin generation. Anesth Analg 2015; 121: 278-288.

5. Tijskens LM, Greiner R, Biekman ES, Konietzny U. Modeling the effect of temperature and pH on activity of enzymes: the case of phytases. Biotechnol Bioeng 2001; 72: 323- 330.

6. Mitrophanov AY, Rosendaal FR, Reifman J. Therapeutic correction of thrombin

generation in dilution-induced coagulopathy: computational analysis based on a data set of healthy subjects. J Trauma Acute Care Surg 2012; 73: S95-S102.

7. Mitrophanov AY, Rosendaal FR, Reifman J. Computational analysis of intersubject variability and thrombin generation in dilutional coagulopathy. Transfusion 2012; 52:

2475-2486.

8. Mitrophanov AY, Wolberg AS, Reifman J. Kinetic model facilitates analysis of fibrin generation and its modulation by clotting factors: implications for hemostasis-enhancing therapies. Mol BioSyst 2014; 10: 2347-2357.

9. Danforth CM, Orfeo T, Mann KG, Brummel-Ziedins KE, Everse SJ. The impact of uncertainty in a blood coagulation model. Math Med Biol 2009; 26: 323-336.

10. Hockin MF, Jones KC, Everse SJ, Mann KG. A model for the stoichiometric regulation of blood coagulation. J Biol Chem 2002; 277: 18322-18333.

11. Hemker HC, Giesen P, Al Dieri R, Regnault V, de Smedt E, Wagenvoord R, Lecompte T, Béguin S. Calibrated automated thrombin generation measurement in clotting plasma.

Pathophysiol Haemost Thromb 2003; 33: 4-15.

12. Kremers RM, Peters TC, Wagenvoord RJ, Hemker HC. The balance of pro- and anticoagulant processes underlying thrombin generation. J Thromb Haemost 2015; 13:

437-447.

13. Preissner KT, Reuning U. Vitronectin in vascular context: facets of a multitalented matricellular protein. Semin Thromb Hemost 2011; 37: 408-424.

14. Declerck PJ, De Mol M, Alessi MC, Baudner S, Paques EP, Preissner KT, Muller- Berghaus G, Collen D. Purification and characterization of a plasminogen activator inhibitor 1 binding protein from human plasma. Identification as a multimeric form of S protein (vitronectin). J Biol Chem 1988; 263: 15454-15461.

15. Bajzar L, Morser J, Nesheim M. TAFI, or plasma procarboxypeptidase B, couples the coagulation and fibrinolytic cascades through the thrombin-thrombomodulin complex. J Biol Chem 1996; 271: 16603-16608.

16. Dekker RJ, Eichinger A, Stoop AA, Bode W, Pannekoek H, Horrevoets AJ. The variable region-1 from tissue-type plasminogen activator confers specificity for plasminogen

(22)

22

activator inhibitor-1 to thrombin by facilitating catalysis: release of a kinetic block by a heterologous protein surface loop. J Mol Biol 1999; 293: 613-627.

17. Dekker RJ, Pannekoek H, Horrevoets AJ. A steady-state competition model describes the modulating effects of thrombomodulin on thrombin inhibition by plasminogen activator inhibitor-1 in the absence and presence of vitronectin. Eur J Biochem 2003; 270: 1942- 1951.

18. Seiffert D, Loskutoff DJ. Kinetic analysis of the interaction between type 1 plasminogen activator inhibitor and vitronectin and evidence that the bovine inhibitor binds to a thrombin-derived amino-terminal fragment of bovine vitronectin. Biochim Biophys Acta 1991; 1078: 23-30.

19. Naski MC, Lawrence DA, Mosher DF, Podor TJ, Ginsburg D. Kinetics of inactivation of α-thrombin by plasminogen activator inhibitor-1. Comparison of the effects of native and urea-treated forms of vitronectin. J Biol Chem 1993; 268: 12367-12372.

20. Rezaie AR. Elucidation of the structural basis for the slow reactivity of thrombin with plasminogen activator inhibitor-1. Biochemistry 1998; 37: 13138-13142.

21. Rezaie AR. Vitronectin functions as a cofactor for rapid inhibition of activated protein C by plasminogen activator inhibitor-1. Implications for the mechanism of profibrinolytic action of activated protein C. J Biol Chem 2001; 276: 15567-15570.

22. Lawrence DA, Berkenpas MB, Palaniappan S, Ginsburg D. Localization of vitronectin binding domain in plasminogen activator inhibitor-1. J Biol Chem 1994; 269: 15223- 15228.

23. Bajzar L, Nesheim M, Morser J, Tracy PB. Both cellular and soluble forms of

thrombomodulin inhibit fibrinolysis by potentiating the activation of thrombin-activable fibrinolysis inhibitor. J Biol Chem 1998; 273: 2792-2798.

24. Walker JB, Nesheim ME. A kinetic analysis of the tissue plasminogen activator and DSPAalpha1 cofactor activities of untreated and TAFIa-treated soluble fibrin degradation products of varying size. J Biol Chem 2001; 276: 3138-3148.

25. Bravo MC, Orfeo T, Mann KG, Everse SJ. Modeling of human factor Va inactivation by activated protein C. BMC Syst Biol 2012; 6: 45.

26. James G, Witten D, Hastie T, Tibshirani R. An Introduction to Statistical Learning with Applications in R, New York: Springer, 2014.

27. Chatterjee MS, Denney WS, Jing H, Diamond SL. Systems biology of coagulation initiation: kinetics of thrombin generation in resting and activated human blood. PLOS Comput Biol 2010; 6: e1000950.

28. Kravtsov DV, Matafonov A, Tucker EI, Sun MF, Walsh PN, Gruber A, Gailani D. Factor XI contributes to thrombin generation in the absence of factor XII. Blood 2009; 114: 452- 458.

29. Butenas S, van't Veer C, Mann KG. "Normal" thrombin generation. Blood 1999; 94:

2169-2178.