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Mathematical Medicine and Biology Advance Access originally published online on March 22, 2007
Mathematical Medicine and Biology 2007 24(3):251-270; doi:10.1093/imammb/dqm002
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Modelling HA protein-mediated interaction between an influenza virus and a healthy cell: pre-fusion membrane deformation

Naveen K. Vaidya{dagger} and Huaxiong Huang{ddagger}

Department of Mathematics and Statistics, York University, Toronto, Canada M3J 1P3

Shu Takagi§

Department of Mechanical Engineering, The University of Tokyo, Tokyo, Japan

{dagger} Email: nvaidya{at}mathstat.yorku.ca

{ddagger} Corresponding author. Email: hhuang{at}mathstat.yorku.ca

§ Email: takagi{at}mech.t.u-tokyo.ac.jp

Received on August 29, 2006. Revised on January 23, 2007. Accepted on February 15, 2007.

We present a mathematical model for pre-fusion interaction between an influenza virus and a healthy cell. Our model describes the role played by hemagglutinin (HA) protein clusters in bringing the viral membrane into close contact with the host cell membrane as a first step of the fusion process between the two membranes. The viral membrane is modelled as a lipid bilayer with bending rigidity. Using the calculus of variations, we compute the deformation of the viral membrane under the influence of HA protein clusters. Our numerical results support the hypothesis of dimple formation in the fusion site proposed in the literature. The asymmetric nature of the protein molecules due to various reasons such as tilting is the primary cause for the dimple formation. We discuss the effects of spontaneous curvature, the protein cluster radius, fusion-site size and the bending moment exerted by the protein cluster. We also examine the effects of membrane tension and the presence of a host cell on the dimple shape. Our results support previous experimental observations.

Keywords: bending rigidity; equilibrium membrane shape; Euler–Lagrange equations; HA protein; influenza virus; lipid bilayer; membrane pre-fusion


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