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Bacteriophage T4 is a virus that attacks bacteria by a unique mechanism. It
lands on the surface of the bacterium and attaches its baseplate to the cell
wall. Aided by Brownian motion and chemical bonding, its tail fibres stick to
the cell wall, producing a large moment on the baseplate. This triggers an
amazing phase transformation in the tail sheath, of martensitic type, that
causes it to shorten and fatten. The transformation strain is about 50%. With a
thrusting and twisting motion, this transformation drives the stiff inner tail
core through the cell wall of the bacterium. The DNA of the virus then enters
the cell through the hollow tail core, leading to the invasion of the host.
This is a natural machine. As we ponder the possibility of making man-made
machines that can have intimate interactions with natural ones, on the scale of
biochemical processes, it is an interesting prototype. We present a mathematical
theory of the martensitic transformation that occurs in T4 tail sheath.
Following a suggestion of Pauling, we propose a theory of an active protein
sheet with certain local interactions between molecules. The free energy is
found to have a double-well structure. Using the explicit geometry of T4 tail
sheath we introduce constraints to simplify the theory. Configurations
corresponding to the two phases are found and an approximate formula for the
force generated by contraction is given. The predicted behaviour of the sheet is
completely unlike macroscopic sheets. To understand the position of this
bioactuator relative to nonbiological actuators, the forces and energies are
compared with those generated by inorganic actuators, including nonbiological
martensitic transformations. Joint work with Wayne Falk, @email
Wayne Falk and R. D. James, An elasticity theory for self-assembled protein
lattices with application to the martensitic transformation in Bacteriophage T4
tail sheath, preprint.
K. Bhattacharya and R. D. James, The material is the machine, Science 307
(2005), pp. 53-54.