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Bleeding frequency and severity within clinical categories of hemophilia A are highly variable and the origin of this variation is unknown. Solving this mystery in coagulation requires the generation and analysis of large data sets comprised of experimental outputs or patient samples, both of which are subject to limited availability. In this review, we describe how a computationally driven approach bypasses such limitations by generating large synthetic patient data sets. These data sets were created with a mechanistic mathematical model, by varying the model inputs, clotting factor, and inhibitor concentrations, within normal physiological ranges. Specific mathematical metrics were chosen from the model output, used as a surrogate measure for bleeding severity, and statistically analyzed for further exploration and hypothesis generation. We highlight results from our recent study that employed this computationally driven approach to identify FV (factor V) as a key modifier of thrombin generation in mild to moderate hemophilia A, which was confirmed with complementary experimental assays. The mathematical model was used further to propose a potential mechanism for these observations whereby thrombin generation is rescued in FVIII-deficient plasma due to reduced substrate competition between FV and FVIII for FXa (activated factor X).

Amyloid appearance is a rare event that is promoted in the presence of other aggregated proteins. These aggregates were thought to act by templating the formation of an assembly-competent nucleation seed, but we find an unanticipated role for them in enhancing the persistence of amyloid after it arises. Specifically, Saccharomyces cerevisiaeRnq1 amyloid reduces chaperone-mediated disassembly of Sup35 amyloid, promoting its persistence in yeast. Mathematical modeling and corresponding in vivo experiments link amyloid persistence to the conformationally defined size of the Sup35 nucleation seed and suggest that amyloid is actively cleared by disassembly below this threshold to suppress appearance of the [PSI+] prion in vivo. Remarkably, this framework resolves multiple known inconsistencies in the appearance and curing of yeast prions. Thus, our observations establish the size of the nucleation seed as a previously unappreciated characteristic of prion variants that is key to understanding transitions between prion states.

The variability in bleeding patterns among individuals with hemophilia A, who have similar factor VIII (FVIII) levels, is significant and the origins are unknown.

The yeast Saccharomyces cerevisiaehas emerged as an ideal model system to study the dynamics of prion proteins which are responsible for a number of fatal neurodegenerative diseases in humans. Within an infected cell, prion proteins aggregate in complexes which may increase in size or be fragmented and are transmitted upon cell division. Recent work in yeast suggests that only aggregates below a critical size are transmitted efficiently. We formulate a continuous-time branching process model of a yeast colony under conditions of prion curing. We generalize previous approaches by providing an explicit formula approximating prion loss as influenced by both aggregate growth and size-dependent transmission.

Blood coagulation is a network of biochemical reactions wherein dozens of proteins act collectively to initiate a rapid clotting response. Coagulation reactions are lipid-surface dependent, and this dependence is thought to help localize coagulation to the site of injury and enhance the association between reactants. Current mathematical models of coagulation either do not consider lipid as a variable or do not agree with experiments where lipid concentrations were varied. Since there is no analytic rate law that depends on lipid, only apparent rate constants can be derived from enzyme kinetic experiments. We developed a new mathematical framework for modeling enzymes reactions in the presence of lipid vesicles. Here the concentrations are such that only a fraction of the vesicles harbor bound enzymes and the rest remain empty. We call the lipid vesicles with and without enzyme TF:VIIa + and TF:VIIa − lipid, respectively. Since substrate binds to both TF:VIIa + and TF:VIIa − lipid, our model shows that excess empty lipid acts as a strong sink for substrate. We used our framework to derive an analytic rate equation and performed constrained optimization to estimate a single, global set of intrinsic rates for the enzyme–substrate pair. Results agree with experiments and reveal a critical lipid concentration where the conversion rate of the substrate is maximized, a phenomenon known as the template effect. Next, we included product inhibition of the enzyme and derived the corresponding rate equations, which enables kinetic studies of more complex reactions. Our combined experimental and mathematical study provides a general framework for uncovering the mechanisms by which lipid mediated reactions impact coagulation processes. • We developed a new mathematical framework for lipid-dependent reactions • We formulated an analytic rate law for lipid-dependent enzyme kinetics • We estimated a single set of rate constants from experimental data with varied lipid • Our model is applicable to a diverse set of enzyme reactions • Our framework serves as a foundation for advanced coagulation models [ABSTRACT FROM AUTHOR]