98,946 research outputs found
Design of Toy Proteins Capable to Rearrange Conformations in a Mechanical Fashion
We design toy protein mimicking a machine-like function of an enzyme. Using
an insight gained by the study of conformation space of compact lattice
polymers, we demonstrate the possibility of a large scale conformational
rearrangement which occurs (i) without opening a compact state, and (ii) along
a linear (one-dimensional) path. We also demonstrate the possibility to extend
sequence design method such that it yields a "collective funnel" landscape in
which the toy protein (computationally) folds into the valley with
rearrangement path at its bottom. Energies of the states along the path can be
designed to be about equal, allowing for diffusion along the path. They can
also be designed to provide for a significant bias in one certain direction.
Together with a toy ligand molecule, our "enzimatic" machine can perform the
entire cycle, including conformational relaxation in one direction upon ligand
binding and conformational relaxation in the opposite direction upon ligand
release. This model, however schematic, should be useful as a test ground for
phenomenological theories of machine-like properties of enzymes.Comment: 13 pages, 12 figure
Initial Value Problems for Integrable Systems on a Semi-Strip
Two important cases, where boundary conditions and solutions of the
well-known integrable equations on a semi-strip are uniquely determined by the
initial conditions, are rigorously studied in detail. First, the case of
rectangular matrix solutions of the defocusing nonlinear Schr\"odinger equation
with quasi-analytic boundary conditions is dealt with. (The result is new even
for a scalar nonlinear Schr\"odinger equation.) Next, a special case of the
nonlinear optics (-wave) equation is considered.Comment: Boundary conditions are recovered from the initial ones. The paper
supplements in this respect our previous article arXiv:1403.8111, where
initial conditions are recovered from the boundary condition
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