TY - JOUR

T1 - Method for the simulation of blood platelet shape and its evolution during activation

AU - Moskalensky, Alexander E.

AU - Yurkin, Maxim A.

AU - Muliukov, Artem R.

AU - Litvinenko, Alena L.

AU - Nekrasov, Vyacheslav M.

AU - Chernyshev, Andrei V.

AU - Maltsev, Valeri P.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

KW - Algorithms

KW - Blood Platelets/cytology

KW - Cell Shape/physiology

KW - Computational Biology/methods

KW - Computer Simulation

KW - Humans

KW - Platelet Activation/physiology

KW - CELLS

KW - CONSTANT-CURVATURE

KW - MICROTUBULES

KW - DEPOLYMERIZATION

KW - MODEL

KW - ADHESION

KW - MARGINAL BAND COILING

KW - SURFACE

KW - FLOW-CYTOMETRY

KW - AGGREGATION

UR - http://www.scopus.com/inward/record.url?scp=85044734908&partnerID=8YFLogxK

U2 - 10.1371/journal.pcbi.1005899

DO - 10.1371/journal.pcbi.1005899

M3 - Article

C2 - 29518073

AN - SCOPUS:85044734908

VL - 14

SP - e1005899

JO - PLoS Computational Biology

JF - PLoS Computational Biology

SN - 1553-734X

IS - 3

M1 - 1005899

ER -