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Research Papers

A First Model of the Dynamics of the Bacteriophage T4 Injection Machinery

[+] Author and Article Information
Ameneh Maghsoodi

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: maghsudi@umich.edu

Anupam Chatterjee

Department of Chemistry,
University of California,
Irvine, CA 92697
e-mail: anupamc@uci.edu

Ioan Andricioaei

Department of Chemistry,
University of California,
Irvine, CA 92697
e-mail: andricio@uci.edu

N. C. Perkins

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: ncp@umich.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 17, 2015; final manuscript received May 1, 2016; published online May 23, 2016. Assoc. Editor: Brian Feeny.

J. Comput. Nonlinear Dynam 11(4), 041026 (May 23, 2016) (8 pages) Paper No: CND-15-1295; doi: 10.1115/1.4033554 History: Received September 17, 2015; Revised May 01, 2016

Bacteriophage T4 is one of the most common and complex of the tailed viruses that infect host bacteria using an intriguing contractile tail assembly. Despite extensive progress in resolving the structure of T4, the dynamics of the injection machinery remains largely unknown. This paper contributes a first model of the injection machinery that is driven by elastic energy stored in a structure known as the sheath. The sheath is composed of helical strands of protein that suddenly collapse from an energetic, extended conformation prior to infection to a relaxed, contracted conformation during infection. We employ Kirchhoff rod theory to simulate the nonlinear dynamics of a single protein strand coupled to a model for the remainder of the virus, including the coupled translation and rotation of the head (capsid), neck, and tail tube. Doing so provides an important building block toward the future goal of modeling the entire sheath structure which is composed of six interacting helical protein strands. The resulting numerical model exposes fundamental features of the injection machinery including the time scale and energetics of the infection process, the nonlinear conformational change experienced by the sheath, and the contribution of hydrodynamic drag on the head (capsid).

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Figures

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Fig. 1

Image of bacteriophage T4 in the extended conformation (prior to infection) showing major structural components including the head (capsid) and the tail assembly with an elastic sheath surrounding a hollow tail tube. Image with permission modified from the Molecular Expressions website.1

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Fig. 2

Injection process for bacteriophage T4: (a) the long tail fibers recognize the host cell, (b) the baseplate undergoes a conformational change that signals sheath contraction, and (c) sheath contracts and viral DNA is injected into the host cell through the hollow tail tube

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Fig. 5

(a) A first model of the phage injection machinery as represented by a single helical protein strand that drives the motion of the attached capsid/neck/tail tube assembly. (b) Free-body diagram of capsid/neck/tail tube assembly during contraction.

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Fig. 6

(a) Strain, kinetic, and total mechanical energies of a nanoscale protein spring. Phase 1: Stretching phase with prescribed velocity of free end. Phase 2: Free vibration phase following the release of the free end. Energy is reported in the units of kT, where k is the Boltzmann constant and T is the temperature (Kelvin), and time is reported in the units of nanoseconds. (b) Power spectrum of the strain energy of the nanoscale protein spring. Illustrated peak locates natural frequency of fundamental vibration mode.

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Fig. 9

Translational velocity, νe3, and rotational velocity, ωe3, of capsid/neck/tail tube assembly during the injection process

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Fig. 10

Snapshots of the helical strand during the rapid collapse in the injection process: (a) extended conformation, (b) intermediate conformation, and (c) contracted (stress-free) conformation

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Fig. 8

(a) Energetics of rapid collapse from extended conformation to contracted conformation. Increased drag coefficients yield the expected overdamped response. (b) Comparison of kinetic energies for helical strand and capsid/neck/tail tube assembly.

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Fig. 7

Energetics of rapid collapse from extended conformation to contracted conformation. Kinetic, strain, and total energy (kT) are plotted versus time (ns). Unrealistically small drag coefficients yield the underdamped response.

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Fig. 4

(a) A helical strand of gene product 18 (gp18) in extended (green) and contracted (orange) conformations. Image with permission adapted from Refs. [17] and [26]. (b) Infinitesimal element of a Kirchhoff rod as a nonlinear rod model of the helical strand of gp18.

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Fig. 3

Cryo-electron microscopy-resolved structure of bacteriophage T4 showing major components including: the large icosahedral head (a) (adapted with permission from Ref. [26], Copyright (2004) National Academy of Sciences, U.S.A.) and the tail assembly in the extended (b) and contracted (c) conformations (adapted with permission from Ref. [16]). Also, visible are the sheath, tail tube, neck, and baseplate in both conformations.

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