Method for the simulation of blood platelet shape and its evolution during activation

Alexander E Moskalensky,Vyacheslav M Nekrasov,Valeri P Maltsev,Alena L Litvinenko,Artem R Muliukov,Maxim A Yurkin,Andrei V Chernyshev,Scott L Diamond

doi:10.1371/journal.pcbi.1005899

Abstract

We present a simple physically based quantitative model of blood platelet shape and its evolution during agonist-induced activation. The model is based on the consideration of two major cytoskeletal elements: the marginal band of microtubules and the submembrane cortex. Mathematically, we consider the problem of minimization of surface area constrained to confine the marginal band and a certain cellular volume. For resting platelets, the marginal band appears as a peripheral ring, allowing for the analytical solution of the minimization problem. Upon activation, the marginal band coils out of plane and forms 3D convoluted structure. We show that its shape is well approximated by an overcurved circle, a mathematical concept of closed curve with constant excessive curvature. Possible mechanisms leading to such marginal band coiling are discussed, resulting in simple parametric expression for the marginal band shape during platelet activation. The excessive curvature of marginal band is a convenient state variable which tracks the progress of activation. The cell surface is determined using numerical optimization. The shapes are strictly mathematically defined by only three parameters and show good agreement with literature data. They can be utilized in simulation of platelets interaction with different physical fields, e.g. for the description of hydrodynamic and mechanical properties of platelets, leading to better understanding of platelets margination and adhesion and thrombus formation in blood flow. It would also facilitate precise characterization of platelets in clinical diagnosis, where a novel optical model is needed for the correct solution of inverse light-scattering problem.

Highlights

Human blood platelets are the paramount element of hemostasis and contribute to a variety of other normal and pathological processes, including thrombosis, inflammation, and tumor development
Blood platelets are the second most numerous component of blood after red blood cells. Their main function is to stop bleeding upon vessel wall injury
The first step in reaction to such stimuli is platelet activation, which comprises a series of prothrombotic events, triggered by the increase of intracellular calcium [2,3,4]

Summary

Introduction

Human blood platelets are the paramount element of hemostasis and contribute to a variety of other normal and pathological processes, including thrombosis, inflammation, and tumor development. These corpuscles attracted attention of early microscopists by the outstanding capacity to change physical properties in response to vessel wall injury or foreign substances [1]. Dramatic shape change of platelet from discoid (resting) to rounded with pseudopodia (activated) occurs within seconds and leads to the alteration of optical, hydrodynamic, and mechanical properties of cells. An oblate spheroid is commonly used to approximate the platelet shape in optical and hydrodynamic simulations This model accurately captures cell properties in a limited number of cases. The model should be simple (controlled by a few tunable parameters) to facilitate the advancements in the above-mentioned fields

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Discussion

Conclusion