Energy Considerations in a Model of Nematode Sperm Crawling
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1.
Institute of Applied Mathematics and Mechanics, National Academy of Science
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2.
IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120
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3.
Ohio State University, Department of Mathematics, Columbus, OH 43210
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4.
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
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Received:
01 November 2005
Accepted:
29 June 2018
Published:
01 February 2006
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MSC :
92C17, 35B35, 35R35.
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In this paper we propose a mathematical model for nematode sperm
cell crawling. The model takes into account both force and energy
balance in the process of lamellipodium protrusion and cell
nucleus drag. It is shown that by specifying the (possibly
variable) efficiency of the major sperm protein biomotor one
completely determines a self-consistent problem of the
lamellipodium-nucleus motion. The model thus obtained properly
accounts for the feedback of the load on the lamellipodium
protrusion, which in general should not be neglected. We study and
analyze the steady crawling state for a particular efficiency
function and find that all nonzero modes, up to a large magnitude,
are linearly asymptotically stable, thus reproducing the
experimental observations of the long periods of steady crawling
exhibited by the nematode sperm cells.
Citation: Borys V. Bazaliy, Ya. B. Bazaliy, Avner Friedman, Bei Hu. Energy Considerations in a Model of Nematode Sperm Crawling[J]. Mathematical Biosciences and Engineering, 2006, 3(2): 347-370. doi: 10.3934/mbe.2006.3.347
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Abstract
In this paper we propose a mathematical model for nematode sperm
cell crawling. The model takes into account both force and energy
balance in the process of lamellipodium protrusion and cell
nucleus drag. It is shown that by specifying the (possibly
variable) efficiency of the major sperm protein biomotor one
completely determines a self-consistent problem of the
lamellipodium-nucleus motion. The model thus obtained properly
accounts for the feedback of the load on the lamellipodium
protrusion, which in general should not be neglected. We study and
analyze the steady crawling state for a particular efficiency
function and find that all nonzero modes, up to a large magnitude,
are linearly asymptotically stable, thus reproducing the
experimental observations of the long periods of steady crawling
exhibited by the nematode sperm cells.
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