The effect of plasmin-mediated degradation on fibrinolysis and tissue plasminogen activator diffusion.

We modify a three-dimensional multiscale model of fibrinolysis to study the effect of plasmin-mediated degradation of fibrin on tissue plasminogen activator (tPA) diffusion and fibrinolysis. We propose that tPA is released from a fibrin fiber by simple kinetic unbinding, as well as by "forced unbinding," which occurs when plasmin degrades fibrin to which tPA is bound. We show that, if tPA is bound to a small-enough piece of fibrin that it can diffuse into the clot, then plasmin can increase the effective diffusion of tPA. If tPA is bound to larger fibrin degradation products (FDPs) that can only diffuse along the clot, then plasmin can decrease the effective diffusion of tPA. We find that lysis rates are fastest when tPA is bound to fibrin that can diffuse into the clot, and slowest when tPA is bound to FDPs that can only diffuse along the clot. Laboratory experiments confirm that FDPs can diffuse into a clot, and they support the model hypothesis that forced unbinding of tPA results in a mix of FDPs, such that tPA bound to FDPs can diffuse both into and along the clot. Regardless of how tPA is released from a fiber, a tPA mutant with a smaller dissociation constant results in slower lysis (because tPA binds strongly to fibrin), and a tPA mutant with a larger dissociation constant results in faster lysis.

Internal fibrinolysis of fibrin clots is driven by pore expansion.

Blood clots, which are composed of blood cells and a stabilizing mesh of fibrin fibers, are critical in cessation of bleeding following injury. However, their action is transient and after performing their physiological function they must be resolved through a process known as fibrinolysis. Internal fibrinolysis is the degradation of fibrin by the endogenous or innate presence of lytic enzymes in the bloodstream; under healthy conditions, this process regulates hemostasis and prevents bleeding or clotting. Fibrin-bound tissue plasminogen activator (tPA) converts nearby plasminogen into active plasmin, which is bound to the fibrin network, breaking it down into fibrin degradation products and releasing the entrapped blood cells. It is poorly understood how changes in the fibrin structure and lytic protein ratios influence the biochemical regulation and behavior of internal fibrinolysis. We used turbidity kinetic tracking and microscopy paired with mathematical modeling to study fibrin structure and lytic protein ratios that restrict internal fibrinolysis. Analysis of simulations and experiments indicate that fibrinolysis is driven by pore expansion of the fibrin network. We show that this effect is strongly influenced by the ratio of fibrin:tPAwhen compared to absolute tPA concentration. Thus, it is essential to consider relative protein concentrations when studying internal fibrinolysis both experimentally and in the clinic. An improved understanding of effective internal lysis can aid in development of better therapeutics for the treatment of bleeding and thrombosis.

Inferring local molecular dynamics from the global actin network structure: A case study of 2D synthetic branching actin networks.

Cells rely on their cytoskeleton for key processes including division and directed motility. Actin filaments are a primary constituent of the cytoskeleton. Although actin filaments can create a variety of network architectures linked to distinct cell functions, the microscale molecular interactions that give rise to these macroscale structures are not well understood. In this work, we investigate the microscale mechanisms that produce different branched actin network structures using an iterative classification approach. First, we employ a simple yet comprehensive agent-based model that produces synthetic actin networks with precise control over the microscale dynamics. Then we apply machine learning techniques to classify actin networks based on measurable network density and geometry, identifying key mechanistic processes that lead to particular branched actin network architectures. Extensive computational experiments reveal that the most accurate method uses a combination of supervised learning based on network density and unsupervised learning based on network symmetry. This framework can potentially serve as a powerful tool to discover the molecular interactions that produce the wide variety of actin network configurations associated with normal development as well as pathological conditions such as cancer.

Fluorescent microspheres can affect in vitro fibrinolytic outcomes.

Hemostasis is the cessation of bleeding due to the formation of a blood clot. After the completion of wound healing, the blood clot is typically dissolved through the natural process of fibrinolysis, the enzymatic digestion by plasmin of the fibrin fibers that make up its structural scaffold. In vitro studies of fibrinolysis reveal mechanisms regulating these processes and often employ fluorescent microscopy to observe protein colocalization and fibrin digestion. In this study, we investigate the effects of labeling a fibrin network with 20 nm diameter fluorescent beads (fluorospheres) for the purpose of studying fibrinolysis. We observed fibers and 2-D fibrin networks labeled with fluorospheres during fibrinolysis. We found that the labeling of fibrin with fluorospheres can alter fibrinolytic mechanisms. In previous work, we showed that, during lysis, fibrin fibers are cleaved into two segments at a single location. Herein we demonstrate that fibrinolysis can be altered by the concentration of fluorospheres used to label the fibers, with high concentrations of fluorospheres leading to very minimal cleaving. Furthermore, fibers that are left uncleaved after the addition of plasmin often elongate, losing their inherent tension throughout the imaging process. Elongation was especially prominent among fibers that had bundled together due to other cleavage events and was dependent on the concentration of fluorophores used to label fibers. Of the fibers that do cleave, the site at which they cleave also shows a predictable trend dependent on fluorosphere concentration; low concentrations heavily favor cleavage locations at either end of fibrin fiber and high concentrations show no disparity between the fiber ends and other locations along the fiber. After the initial cleavage event bead concentration also affects further digestion, as higher bead concentrations exhibited a larger population of fibers that did not digest further. The results described in this paper indicate that fluorescent labeling strategies can impact fibrinolysis results.

Fibrinolysis: an illustrated review.

In response to vessel injury (or other pathological conditions), the hemostatic process is activated, resulting in a fibrous, cellular-rich structure commonly referred to as a blood clot. Succeeding the clot's function in wound healing, it must be resolved. This illustrated review focuses on fibrinolysis-the degradation of blood clots or thrombi. Fibrin is the main mechanical and structural component of a blood clot, which encases the cellular components of the clot, including platelets and red blood cells. Fibrinolysis is the proteolytic degradation of the fibrin network that results in the release of the cellular components into the bloodstream. In the case of thrombosis, fibrinolysis is required for restoration of blood flow, which is accomplished clinically through exogenously delivered lytic factors in a process called external lysis. Fibrinolysis is regulated by plasminogen activators (tissue-type and urokinase-type) that convert plasminogen into plasmin to initiate fiber lysis and lytic inhibitors that impede this lysis (plasminogen activator inhibitors, alpha 2-antiplasmin, and thrombin activatable fibrinolysis inhibitor). Furthermore, the network structure has been shown to regulate lysis: thinner fibers and coarser clots lyse faster than thicker fibers and finer clots. Clot contraction, a result of platelets pulling on fibers, results in densely packed red blood cells (polyhedrocytes), reduced permeability to fibrinolytic factors, and increased fiber tension. Extensive research in the field has allowed for critical advancements leading to improved thrombolytic agents. In this review, we summarize the state of the field, highlight gaps in knowledge, and propose future research questions.

Effects of clot contraction on clot degradation: A mathematical and experimental approach.

Thrombosis, resulting in occlusive blood clots, blocks blood flow to downstream organs and causes life-threatening conditions such as heart attacks and strokes. The administration of tissue plasminogen activator (t-PA), which drives the enzymatic degradation (fibrinolysis) of these blood clots, is a treatment for thrombotic conditions, but the use of these therapeutics is often limited due to the time-dependent nature of treatment and their limited success. We have shown that clot contraction, which is altered in prothrombotic conditions, influences the efficacy of fibrinolysis. Clot contraction results in the volume shrinkage of blood clots, with the redistribution and densification of fibrin and platelets on the exterior of the clot and red blood cells in the interior. Understanding how these key structural changes influence fibrinolysis can lead to improved diagnostics and patient care. We used a combination of mathematical modeling and experimental methodologies to characterize the process of exogenous delivery of t-PA (external fibrinolysis). A three-dimensional (3D) stochastic, multiscale model of external fibrinolysis was used to determine how the structural changes that occur during the process of clot contraction influence the mechanism(s) of fibrinolysis. Experiments were performed based on modeling predictions using pooled human plasma and the external delivery of t-PA to initiate lysis. Analysis of fibrinolysis simulations and experiments indicate that fibrin densification makes the most significant contribution to the rate of fibrinolysis compared with the distribution of components and degree of compaction (p < 0.0001). This result suggests the possibility of a certain fibrin density threshold above which t-PA effective diffusion is limited. From a clinical perspective, this information can be used to improve on current therapeutics by optimizing timing and delivery of lysis agents.

Microscale structural changes of individual fibrin fibers during fibrinolysis.

Fibrinolysis is the enzymatic digestion of fibrin, the primary structural component in blood clots. Mechanisms of fibrin fiber digestion during lysis have long been debated and obtaining detailed structural knowledge of these processes is important for developing effective clinical approaches to treat ischemic stroke and pulmonary embolism. Using dynamic fluorescence microscopy, we studied the time-resolved digestion of individual fibrin fibers by the fibrinolytic enzyme plasmin. We found that plasmin molecules digest fibers along their entire lengths, but that the rates of digestion are non-uniform, resulting in cleavage at a single location along the fiber. Using mathematical modeling we estimated the rate of plasmin arrival at the fiber surface and the number of digestion sites on a fiber. We also investigated correlations between local fiber digestion rates, cleavage sites, and fiber properties such as initial thickness. Finally, we uncovered a previously unknown tension-dependent mechanism that pulls fibers apart during digestion. Taken together these results promote a paradigm shift in understanding mechanisms of fibrinolysis and underscore the need to consider fibrin tension when assessing fibrinolytic approaches. STATEMENT OF SIGNIFICANCE: We developed a method for interrogating lysis of individual fibrin fibers, enabling the time-resolved observation of individual fiber digestion for the first time. Our results resolve longstanding disagreements about fibrinolytic processes and reveal previously unknown mechanisms that also play a role. Also, we developed the first microscale mathematical model of plasmin-fibrin interaction, which predicts the number of plasmin molecules on each fiber and can serve as a framework for investigating novel therapeutics.

The Utility and Potential of Mathematical Models in Predicting Fibrinolytic Outcomes.

The enzymatic degradation of blood clots, fibrinolysis, is an important part of a healthy hemostatic system. If intrinsic fibrinolysis is ineffective, thrombolysis - the clinically-induced enzymatic degradation of blood clots - may be necessary to treat life-threatening conditions. In this review we discuss recent models of fibrinolysis and thrombolysis, and open questions that could be resolved through modeling and modeling-experimental collaboration. In particular, we focus on 2- and 3-dimensional models that can be used to study effects of fibrin network structure and realistic blood vessel geometries on the phenomena underlying lytic outcomes. Significant open questions such as the role of clot contraction, network and inherent fiber tension, and fibrinolytic inhibitors in lysis could benefit from mathematical models aimed at understanding the underlying biological mechanisms.

Molecular and Physical Mechanisms of Fibrinolysis and Thrombolysis from Mathematical Modeling and Experiments.

Despite the common use of thrombolytic drugs, especially in stroke treatment, there are many conflicting studies on factors affecting fibrinolysis. Because of the complexity of the fibrinolytic system, mathematical models closely tied with experiments can be used to understand relationships within the system. When tPA is introduced at the clot or thrombus edge, lysis proceeds as a front. We developed a multiscale model of fibrinolysis that includes the main chemical reactions: the microscale model represents a single fiber cross-section; the macroscale model represents a three-dimensional fibrin clot. The model successfully simulates the spatial and temporal locations of all components and elucidates how lysis rates are determined by the interplay between the number of tPA molecules in the system and clot structure. We used the model to identify kinetic conditions necessary for fibrinolysis to proceed as a front. We found that plasmin regulates the local concentration of tPA through forced unbinding via degradation of fibrin and tPA release. The mechanism of action of tPA is affected by the number of molecules present with respect to fibrin fibers. The physical mechanism of plasmin action (crawling) and avoidance of inhibition is defined. Many of these new findings have significant implications for thrombolytic treatment.

Modelling fibrinolysis: a 3D stochastic multiscale model.

Fibrinolysis, the proteolytic degradation of the fibrin fibres that stabilize blood clots, is initiated when tissue-type plasminogen activator (tPA) activates plasminogen to plasmin, the main fibrinolytic enzyme. Many experiments have shown that coarse clots made of thick fibres lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. The generally accepted explanation for this is that a coarse clot with fewer fibres to transect will be degraded faster than a fine clot with a higher fibre density. Other experiments show the opposite result. The standard mathematical tool for investigating fibrinolysis has been deterministic reaction-diffusion models, but due to low tPA concentrations, stochastic models may be more appropriate. We develop a 3D stochastic multiscale model of fibrinolysis. A microscale model representing a fibre cross section and containing detailed biochemical reactions provides information about single fibre lysis times, the number of plasmin molecules that can be activated by a single tPA molecule and the length of time tPA stays bound to a given fibre cross section. Data from the microscale model are used in a macroscale model of the full fibrin clot, from which we obtain lysis front velocities and tPA distributions. We find that the fibre number impacts lysis speed, but so does the number of tPA molecules relative to the surface area of the clot exposed to those molecules. Depending on the values of these two quantities (tPA number and surface area), for given kinetic parameters, the model predicts coarse clots lyse faster or slower than fine clots, thus providing a possible explanation for the divergent experimental observations.

Modelling fibrinolysis: 1D continuum models.

Fibrinolysis is the enzymatic degradation of the fibrin mesh that stabilizes blood clots. Experiments have shown that coarse clots made of thick fibres sometimes lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. This paper aims at using a 1D continuum reaction-diffusion model of fibrinolysis to elucidate the mechanism by which coarse clots lyse more quickly than fine clots. Reaction-diffusion models have been the standard tool for investigating fibrinolysis, and have been successful in capturing the wave-like behaviour of lysis seen in experiments. These previous models treat the distribution of fibrin within a clot as homogeneous, and therefore cannot be used directly to study the lysis of fine and coarse clots. In our model, we include a spatially heterogeneous fibrin concentration, as well as a more accurate description of the role of fibrin as a cofactor in the activation of the lytic enzyme. Our model predicts spatio-temporal protein distributions in reasonable quantitative agreement with experimental data. The model also predicts observed behaviour such as a front of lysis moving through the clot with an accumulation of lytic proteins at the front. In spite of the model improvements, however, we find that 1D continuum models are unable to accurately describe the observed differences in lysis behaviour between fine and coarse clots. Features of the problems that lead to the inaccuracy of 1D continuum models are discussed. We conclude that higher-dimensional, multiscale models are required to investigate the effect of clot structure on lysis behaviour.