Concentration of protein in fibrin fibers and fibrinogen polymers determined by refractive index matching

Voter, William A.; Lucaveche, Carmen; Erickson, Harold P.

doi:10.1002/bip.360251214

Cited by 32 publications

(29 citation statements)

References 10 publications

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“…First, our single fibre fibrin concentration may be too small. The fibrin concentration per fibre has been estimated to be about 824 µM (Carr & Hermans, 1978;Voter et al, 1986), significantly higher than the 29 µM we use. Secondly, the definition of lysis is likely different experimentally than it is in the model.…”

Section: Experiments)mentioning

confidence: 55%

Modelling fibrinolysis: 1D continuum models

Bannish

Keener

Woodbury

et al. 2012

Mathematical Medicine and Biology

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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.Keywords: fibrin; enzymatic degradation; lysis front. B. E. BANNISH ET AL. Fig. 1. Cartoon of fibrinolysis (not to scale): PLG and tPA diffuse in the plasma and can bind to fibrin. If tPA and PLG bind in close proximity to one another, the tPA can convert the plasminogen to plasmin (PLi). PLi then degrades the fibrin by cutting across the fibre. New binding sites for tPA and PLG are exposed as plasmin cleaves fibrin. Plasma concentration of PLG ≈2 µM, and plasma concentration of tPA ≈70 pM.

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Section: Experiments)mentioning

confidence: 55%

Modelling fibrinolysis: 1D continuum models

Bannish

Keener

Woodbury

et al. 2012

Mathematical Medicine and Biology

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“…We think of this slice as running between edge midpoints, so the 1-fibre depth is actually composed of two halves of two separate fibres. To obtain the lattice dimensions, we fix the fibrin concentration per fibre at 824 µM (Carr & Hermans, 1978;Voter et al, 1986), the fibrin concentration in the clot at 8.8 µM (Diamond & Anand, 1993) and the height and width of the chamber at 100 µm (to assure the system is big enough to avoid boundary effects). Then using the radii of the fibres, we calculate the pore size and the number of fibres required to keep the concentrations at their fixed values.…”

Section: Macroscale Modelmentioning

confidence: 99%

“…Despite the seemingly tight packing of protofibrils into fibres, fibrin fibres contain about 20% protein and 80% water (Carr & Hermans, 1978;Voter et al, 1986). Hence, on the scale of a single fibre, it is believed that there are pores through which small molecules can diffuse (Weisel & Litvinov, 2008).…”

Section: Introductionmentioning

confidence: 99%

Modelling fibrinolysis: a 3D stochastic multiscale model

Bannish¹,

Keener²,

Fogelson³

2012

Mathematical Medicine and Biology

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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.

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“…In these models the discrete steps are mechanistically substantiated, but due to the complex nature of the examined phenomenon a high number of independently gained parameters are necessary, which inevitably leads to simplifications to account for the variability of the conditions, under which these are derived, and thus some essential mechanistic aspects can be overlooked. For example, although 80 % of the fibrin fiber volume is occupied by water (11,12), this space is highly compartmented by the protofibrils aligned in parallel within the fibers and by the higher ordering of the fibers encompassing three-dimensional pores. However, in environments with similar fixed geometric obstacles within cells, or in the extracellular matrix, anomalous diffusion is observed (13,14).…”

Section: Introductionmentioning

confidence: 99%

Fractal Kinetic Behavior of Plasmin on the Surface of Fibrin Meshwork

et al. 2014

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Intravascular fibrin clots are resolved by plasmin acting at the interface of gelphase substrate and fluid-borne enzyme. The classic Michaelis−Menten kinetic scheme cannot describe satisfactorily this heterogeneous-phase proteolysis because it assumes homogeneous well-mixed conditions. A more suitable model for these spatial constraints, known as fractal kinetics, includes a time-dependence of the Michaelis coefficient K m F = K m0 F (1 + t) h , where h is a fractal exponent of time, t. The aim of the present study was to build up and experimentally validate a mathematical model for surface-acting plasmin that can contribute to a better understanding of the factors that influence fibrinolytic rates. The kinetic model was fitted to turbidimetric data for fibrinolysis under various conditions. The model predicted K m0 F = 1.98 μM and h = 0.25 for fibrin composed of thin fibers and K m0 F = 5.01 μM and h = 0.16 for thick fibers in line with a slower macroscale lytic rate (due to a stronger clustering trend reflected in the h value) despite faster cleavage of individual thin fibers (seen as lower K m0 F ). ε-Aminocaproic acid at 1 mM or 8 U/mL carboxypeptidase-B eliminated the time-dependence of K m F and increased the lysis rate suggesting a role of C-terminal lysines in the progressive clustering of plasmin. This fractal kinetic concept gained structural support from imaging techniques. Atomic force microscopy revealed significant changes in plasmin distribution on a patterned fibrinogen surface in line with the time-dependent clustering of fluorescent plasminogen in confocal laser microscopy. These data from complementary approaches support a mechanism for loss of plasmin activity resulting from C-terminal lysine-dependent redistribution of enzyme molecules on the fibrin surface.

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Concentration of protein in fibrin fibers and fibrinogen polymers determined by refractive index matching

Cited by 32 publications

References 10 publications

Modelling fibrinolysis: 1D continuum models

Modelling fibrinolysis: 1D continuum models

Modelling fibrinolysis: a 3D stochastic multiscale model

Fractal Kinetic Behavior of Plasmin on the Surface of Fibrin Meshwork

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