The normal range variation in plasma concentration that characterizes the 8 model species with initial non-zero values is presented in Table S2
. In order to assess the consequences of this variation, computationally simulated thrombin generation profiles (cTGPs) were produced by assigning a specific normal range value to each of these factors and a constant concentration (5 pM) for tissue factor. In this analysis, the term “individual” refers to a unique ensemble of these 8 factors from which a cTGP, representing the model integrated effect of this ensemble, is generated. The ensemble having all factors at their mean physiologic level serves as a reference cTGP for assessing the relative intensity of thrombin generation characterizing other ensembles. To capture the maximum potential distribution (scope) of cTGPs resulting from normal range variation in these factors, a theoretical population of “normal” individuals, each with a unique ensemble of initial factor concentrations, was generated by allowing each factor to have 3 possible values spanning its normal range (38
or 6561 individuals). To quantify differences between these cTGPs, thrombin parameters were extracted from each cTGP (see ).
Factor composition and thrombin generation phenotypes
presents cTGPs of groups of individuals in the theoretical population selected because their cTGPs showed significant overlap despite their disparate factor composition. Factor ensembles (presented in the figure insets) with ~50% or greater differences in 4 to 8 factor concentrations characterize these individuals. Such individuals, representing disparate factor ensembles but with similar cTGPs, are defined to have the same thrombin generation phenotype. Thus three thrombin generation phenotypes are represented in .
Thrombin generation time courses from selected individuals from an hypothetical population defined by normal range variation in factors.
In panel A, individuals with cTGPs that overlap the reference cTGP are shown. Panels B and C show individuals with similarly disparate factor composition but overlapping cTGPs that display more or less robust thrombin generation respectively. In panel B, normal range factor variation produces ensembles resulting in cTGPs displaying a 2–3 fold shortening of the clot time parameter and 2 to 3 fold increases in the parameters max rate, max level and total thrombin compared to the reference cTGP. Panel C displays distinct ensembles that produce overlapping cTGPs characterized by a relatively attenuated response: a 2–3 fold prolongation of the clot time parameter and 2 to 3 fold decreases in the parameters max rate, max level and total thrombin compared to the reference cTGP.
The results of these limited comparisons highlight a consequence of normal range variation in factor levels on thrombin generation: factor variation per se (analyzing factor concentrations and not their integrated effect) is not a sufficient discriminator for predicting differences in thrombin generation between individuals. Ensembles, when integrated mechanistically, can effectively compensate for apparently procoagulant or anticoagulant variations in individual factor levels 
, yielding similar thrombin outputs.
The possible range of “normal” thrombin generation phenotypes
compares all individuals in the theoretical population in terms of their relative ability to generate thrombin by creating a graphic representation of each individual that reflects the magnitude their thrombin parameters. Individuals (model integrated factor ensembles) are depicted by a positioned, colored ball of specific size, a collective representation of the four thrombin parameters extracted from their respective cTGPs. Time to clot (y axis) and max rate parameters (x axis) position each individual, while color indicates the max level and size defines the total thrombin parameter. To relate the differences between cTGPs observed in to this form of presentation, three individuals are highlighted: an individual with all factors at mean physiologic concentrations and individuals from . The levels of variation for the thrombin parameters in this population are as follows: 6.5 fold for the clot time (2.3 to 14.97 min); 33.4 fold for max level (23.7 to 792.4 nM); 120 fold for max rate (0.1 to 12.4 nM/s); and 17 fold for total thrombin (8,179 to 134,338 nM•s) (see Table S4
). Thrombin parameters for the individual with all factors at mean physiologic values are: clot time—4.4 min; max rate—2.21 nM/s; max level—271.4 nM; and total thrombin—56,458 nM•s.
Thrombin generation phenotypes in an hypothetical population defined by normal range variation in factor levels.
This population is designed to set the outer boundaries for the types of thrombin generation phenotypes possible because of normal range variations in coagulation factor levels. As is evident from and visual inspection of , significant overlap of individuals occurs, and thus the number of thrombin generation phenotypes is less than the number of individuals (factor ensembles). The question that presents itself is whether all potential phenotypes derived from ensembles with normal factor levels are representative of a normal or healthy hemostatic response?
Normal thrombin generation phenotypes; possible range vs actual
Computationally analyzed thrombin generation using factor composition data from an apparently healthy control group of 473 individuals from the Leiden Thrombophilia Study has been reported 
. Factor level variation in this population was similar to or exceeded the ranges used to generate the theoretical population presented in (Table S2
). In this population of Dutch individuals (272 women, 201 men) the range in thrombin parameters was: 3.3 fold for the clot time; 3.9 fold for maximum level thrombin; 4.8 fold for maximum rate; and 4.5 fold for total thrombin. The 2 to 20 fold larger ranges predicted for the thrombin parameters of the theoretical population reflect factor ensembles that were possible in the LETS population (given the factor composition ranges) but that did not occur.
The wider ranges of thrombin parameters characterizing the theoretical population have two potential origins: a methodologic one due to its larger size, emphasis on the extremes of each factor range and its treatment of all possible ensembles as of equal probability; or a biological one reflecting the fact that some ensembles, perhaps those resulting in individuals with the more extreme characteristics in , are consistent with coagulopathic states and thus would not be found in a healthy population.
Relevant coagulation factor composition data from comparably sized populations of apparently healthy individuals are not available currently. However, factor composition data for smaller populations, including those with coagulopathies resulting from inherited or pharmacologically induced deficiency states, are available. A comparative analysis of individuals with defined, composition-based hemostatic defects resulting in a diminished coagulant response was performed to determine whether their thrombin generation phenotypes fall within the theoretical normal range population distribution.
presents the graphic representation of the thrombin parameters characterizing a population of apparently healthy individuals (N
32), with the boundary of the theoretical population (from ) also shown. Factor level variation in this population is presented in Table S2
and the mean factor levels in Table S3
. The max level and max rate parameters vary ~3 fold in this population, the total thrombin parameter ~4 fold and the clot time parameter ~1.4 fold. The parameter ranges for max level, max rate and total thrombin are similar to those reported for the larger LETS population (N
while the range of clot time values in this population is ~40% that of LETS. Thus both populations appear confined to a relatively small region of the potential distribution of thrombin generation phenotypes available because of normal range variation in coagulation factor levels.
Thrombin generation phenotypes in a population of apparently healthy individuals.
“Abnormal” thrombin generation phenotypes
presents a comparison of thrombin generation between a group of severe hemophilia A individuals (N
16; factor VIII<1%; panel A), a cohort of individuals anticoagulated with warfarin (N
65; panel B) and the relevant subset of the theoretical population (panel C). Plasma composition data for the hemophilia and warfarin treated populations are presented in Table S3
. To facilitate the comparison, the max rate (x axis) parameter extends only to 1.5 nM/s and the size of each individual's symbol (total thrombin parameter) has been increased by a factor of 5 relative to to improve its visibility. The boundaries for the hemophilia and warfarin-treated groups are indicated in panel C.
Thrombin generation phenotypes in hemophilia A individuals and individuals undergoing warfarin therapy.
In general, individuals with severe hemophilia A, in the absence of replacement therapy with rfVIII or other agents, experience prolonged and potentially life threatening bleeding in response to a hemostatic challenge as well as episodes of “spontaneous bleeding” 
. In this hemophilia population, all factors other than fVIII are within the normal range (Table S3
). FVIII concentrations vary from 0.07% to 1% mean physiologic. For the overall population the parameter ranges were: time to 2 nM thrombin—y axis, range (8.2→14 min); maximum rate of thrombin generation—x axis, range (0.02→97 nM/s); maximum thrombin level—color, range (16→50 nM); and total thrombin—size, range (17,300→40,845 sec•nM).
As can be seen by comparing the distribution of phenotypes in panel C with that of panel A, the hemophilia population is positioned outside the most extreme phenotypes in the theoretical normal population. These individuals are characterized by lower max rates but substantially higher total thrombin values across their distribution than their nearest neighbors in the theoretical population. The defect in thrombin generation occasioned by severe fVIII deficiency also segregates these individuals from the warfarin-treated group, again drive by differences in max rate and total thrombin parameters.
The warfarin-treated individuals represented in , were initially considered, in terms of their clinical history, to be stably anticoagulated, as assessed by a 2 to 3 fold prolongation of their plasma clotting time in a standardized assay (INR: 2 to 3.3). In this population, the non-VKD protein concentrations are all within the normal range, while the VKD proteins (fII, fX, fIX, fVII/fVIIa) are suppressed 50 to 90%, with the level of suppression of each VKD protein varying between individuals. For the overall population the parameter ranges were: time to 2 nM thrombin, range (5.3→17 min); maximum rate of thrombin generation, range (0.08→1 nM/s); maximum thrombin level, range (13→100 nM); and total thrombin, range (6,048→18,978 sec•nM).
The 65 individuals of the warfarin-treated population distribute within the region of the theoretical population characterized by low max rates and prolonged clot times (). This is demonstrated more clearly in , where the boundaries of the warfarin treated population are indicated by the orange line. Their overall characteristics, i.e. their 4 thrombin parameters, do not distinguish them from their nearest neighbors in the theoretical population, suggesting that this region of the theoretical population is characterized by thrombin generation phenotypes reflecting a compromised coagulant response.
Three of the warfarin-treated individuals (circled in ) were subsequently reported to have suffered a thrombotic event. The graphical method employed separates these individuals from the remainder of the warfarin-treated group, primarily because of their max rate parameter, consistent with the idea that they were under anticoagulated despite clinical INR values between 2.1 and 2.5. Inspection of the plasma factor composition data for these three individuals shows at most minor differences between their VKD protein levels (fII 30±3%; fVII 35±6%; fIX 42±2%; fX 32±13%; mean±SD) and the overall warfarin-treated population (Table S3
); however, within the non VKD proteins, their TFPI values (74±3%, mean±SD) are at the low end of the range characterizing this population while their fVIII values (212±7%, mean±SD) are at the high end (Table S3
). These compositional data are consistent with the graphical characterization of these individuals as being under anticoagulated compared to the whole group in two ways: the pattern of high fVIII and low TFPI levels is computationally consistent with more robust thrombin generation; and the prothrombin time assay, which is the basis for INR metric, is relatively insensitive to variations in TFPI and FVIII levels and thus would not identify these individuals as insufficiently anticoagulated.
To further test the “normalcy” of our theoretical population of thrombin phenotypes, additional populations representing “bleeding” phenotypes (fIX deficiency, prothrombin deficiency) or prothrombotic phenotypes (antithrombin deficiency) were analyzed. These populations were generated using the group (N
32) of apparently healthy individuals for which factor composition data was available (Tables S2
& S3). In each case, all factors were left at their individual specific values except fIX or prothrombin or antithrombin, which were set to an average value characterizing their clinical deficiency state.
presents the distributions of the individuals in the artificial fIX and prothrombin deficient groups. The outer boundaries of the theoretical population are depicted by the yellow line, with each group representing a one factor deficiency state circumscribed to define its limits. As with , the size of each individual's symbol (total thrombin parameter) has been increased by a factor of five to improve its visibility and the x axis is truncated relative to .
Thrombin generation phenotypes for hypothetical fIX deficiency, fII deficiency and AT deficiency.
The fIX deficient population was modeled to represent a severe hemophilia B state, with fIX levels set to 0.01%. In general the bleeding problems associated with severe fIX deficiency (fIX<1%) are similar to those characterizing hemophilia A 
. The distribution of this artificial hemophilia B population lies outside the hypothetical population and appears roughly equivalent to the one characterizing actual hemophilia individuals (). Differences in the total thrombin parameter between the actual hemophilia A individuals () and the artificial fIX deficient individuals reflect the fact that most of the hemophilia A individuals have higher fVIII levels than the fIX level selected for the “hemophilia B” population.
Two levels of prothrombin deficiency are also represented in , with the prothrombin concentration set to 10% or 40% of its mean physiologic value in each of the 32 control individuals. Clinically, prothrombin deficiency is a rare coagulation disorder with homozygous individuals displaying prothrombin levels less than 10% mean physiologic; it is characterized by severe, often life threatening bleeding episodes 
. Heterozygous individuals with prothombin levels 40 to 60% mean physiologic are usually asymptomatic, with excess bleeding occurring occasionally after surgical procedures.
The model representation of homozygous prothrombin deficiency () places these individuals along the edge of the theoretical population, overlapping, with respect to three of the thrombin parameters, the more highly anticoagulated individuals in the warfarin population (). However, the total thrombin parameter for individuals with this level of PT deficiency is suppressed relative to the total thrombin values typifying the nearest neighbors in the theoretical population and the warfarin-treated population. The distinction between stably anticoagulated individuals on warfarin and severe prothombin deficiency is consistent with the more extreme hemorrhagic phenotype seen in severe prothrombin deficiency.
In contrast, thrombin parameter analysis of individuals modeled to be heterozygous in their prothombin deficiency (40% mean physiologic, ) indicates that this population is embedded within the boundaries of the theoretical population. An individual from is also graphed to provide a comparison to a conventional representation of thrombin generation for this region of the theoretical population. Neither max level nor total thrombin parameters distinguish these individuals from their nearest neighbor in the theoretical population. If one excludes the three warfarin-treated individuals who proved to be insufficiently anticoagulated, these individuals are situated outside the warfarin-treated population, displaying shorter clot times and larger max rates, parameter differences consistent with their overall lack of bleeding incidents. An individual from is also graphed to provide a comparison to a conventional representation of thrombin generation for this region of the theoretical population.
Heterozygous AT deficiency, with an incidence rate of 1 in 500 to 1 in 5000 in the general population, is characterized by AT concentrations 40 to 60% mean physiologic, below the normal range variation of ~80 to 170% mean physiologic 
). These lower levels of AT induce a prothrombotic phenotype associated with a 5 to 50 fold increased risk for venous embolism 
The results of altering AT levels in the 32 control individuals to 40% mean physiologic are presented in . The scaling is the same as the theoretical population displayed in . As can be seen by visual inspection of and , this level of AT deficiency yields individuals with extreme thrombin generation phenotypes with respect to the parameters max level and total thrombin. Comparison with the model representation () of the same individuals prior to the induction of AT deficiency also shows a systematic increase (~2 fold) in the max rate parameter. None of the nearest neighbors in the theoretical population () display similar max level and total thrombin parameters. In fact, no individual in the theoretical population displays total thrombin levels of the magnitude characterizing the AT deficient population. The mean total thrombin parameter in the AT deficient group (392,776 nM•s) exceeds that of the matching 32 controls (71,000 nM•s) by ~5.5 fold.
Single factor contribution to overall variation in thrombin generation
presents the results of an analysis testing the sensitivity of model outputs to normal range variation in the 8 initial nonzero factor levels. Each factor was set sequentially to 11 values spanning its normal range, the other 7 factors held at their mean physiologic values and the time courses for all 34 model output species collected. Analysis (Figure S2
) resulted in the generation of time averaged coefficients of variation for all 34 output species which were manipulated ultimately to rank each factor by the magnitude of the contribution its normal range variation makes to variation in all model species or variation in thrombin generation (Figure S3
). It is this ranking, the explained variance, which is presented in .
Ranking factors by the effect that normal range variation in their initial values has on model output.
These analyses indicate that two factors account for ~50% of the observed sensitivity of model output, whether the generation of thrombin is considered or all output species are assessed. Variation in the initial TFPI concentration has the greatest impact on both outputs while variation in the fII level is the second most effective contributor to overall differences in thrombin generation. In general this analysis suggests that TFPI alone or coordinated normal range variation of a few factors may account for the extreme thrombin generation phenotypes in the “normal” theoretical population.
Factor pair induced variation in thrombin parameters
To further explore the relationship between outlying thrombin generation phenotypes and initial factor composition, a comparison focusing on the effect of normal range variation of pairs of factors was conducted. The effects of factor pair variation were quantified in terms of the magnitude of the range of potential thrombin parameter values induced by the coordinated variation in the concentrations of each pair of factors. Unlike the sensitivity analysis ranking the global effects of single factor variation (), this approach quantifies the effects of variation on each thrombin parameter, facilitating direct comparisons to the distributions of individuals observed in graphical representations of the various populations.
presents the results of this analysis, with the color scale reflecting the normalized range values. Each thrombin parameter box displays 64 range comparisons as colored squares: 28 factor pair effects are ranked (in duplicate); and the intensity of each single factor (8 total) contribution to variation in the indicated thrombin parameter is represented in the reverse diagonal: bottom right to upper left. presents a summary of the most potent single and factor pair contributors to variation in each thrombin parameter.
Factor pair induced variation in thrombin parameters.
Most potent inducers of alteration in thrombin parameters: single versus factor pair variation.
Visual inspection of highlights the differences between each thrombin parameter's sensitivity to every single factor and factor pair induced variation. Maximum parameter ranges induced by single factor variation are approximately half that induced by the most effective pair for each parameter. Variations in the parameters clot time and total thrombin are dominated by coordinate variation of AT and TFPI and AT and fII respectively, with more than one half the other factors pairs showing relatively minimal effects (<20% of the most effective pair). In contrast, the analysis shows the parameters max rate and max level to have a more complex dependency: strong sensitivity (induced ranges at least 80% of that for the most effective pair) is observed with coordinate variation in 8 factor pairs for the max rate parameter and for 6 factor pairs with the max level parameter.