Conformations of random self-avoiding walks (SAWs)

These are SAWs written in PDB format. The compactness is determined by
the parameters (T', C).  The most compact conformations are generated
by (T', C) = (0.1, 0.6), and the least compact conforamtios are
generated by (T', C) = (-2.0, 0.0). "T_infinity" is data for infinity
high temperature, ie, uniform distribution of SAWs.  For detail, see J
Zhang, R Chen, C Tang, and J Liang, J of Chem Phys, Vol. 118,
13:6102-6109, 2003.

There are two files associated with each set of conformations: 1) The
conformation file, and 2) the weight file.

Conformation file is named by the values of T, C parameters, the run
number, and the chain length.  For example, "T1.0_C0_R0_L1000.tar.gz"
is the tarred and compressed file for SAWs of length 1000 generated in
the 0th run with parameters (T', C) = (1.0, 0.0). There are at least
10 runs for each set of T,C, and length.  The tarred and compressed
file contains about 600 conformations.

Each conformation is written as the coordinates of C_alpha atoms of N
glycine residues.  You can subsititute the residue names to any other
residues.

The weight file (eg. "T1.0_C0_R0_L1000_Wt.dat") contains weight
coefficient associated with each conformation.  These conformations
are generated from the target distribution of uniform distribution of
all geometrically feasible SAWs, with the additional criterion that
their alpha coordination number $z_\alpha$ must be within some
intervals (See Zhang et al for detail).  Because these conformations
are generated by importance sampling, each conformation comes with a
weight. To calculate an ensemble properties of a set of conformations,
eg. the mean of end-to-end distance $d_m$, one calculates the
end-to-end distance $d_i$ for each conformation, and multiply it with
the weight:
\[
d_m = \sum_i^N {w_i \times d_i}/ \sum_i^N {w_i}
\]  

To calculate ensemble properties of these conformations under a
different target distribution (e.g. Boltzman distribution), one can
simply re-weight each conformation.



Jinfeng Zhang and Jie Liang

jzhang10@uic.edu and jliang@uic.edu

3/18/2003