2,782 research outputs found
Emergence of stable and fast folding protein structures
The number of protein structures is far less than the number of sequences. By
imposing simple generic features of proteins (low energy and compaction) on all
possible sequences we show that the structure space is sparse compared to the
sequence space. Even though the sequence space grows exponentially with N (the
number of amino acids) we conjecture that the number of low energy compact
structures only scales as ln N. This implies that many sequences must map onto
countable number of basins in the structure space. The number of sequences for
which a given fold emerges as a native structure is further reduced by the dual
requirements of stability and kinetic accessibility. The factor that determines
the dual requirement is related to the sequence dependent temperatures,
T_\theta (collapse transition temperature) and T_F (folding transition
temperature). Sequences, for which \sigma =(T_\theta-T_F)/T_\theta is small,
typically fold fast by generically collapsing to the native-like structures and
then rapidly assembling to the native state. Such sequences satisfy the dual
requirements over a wide temperature range. We also suggest that the functional
requirement may further reduce the number of sequences that are biologically
competent. The scheme developed here for thinning of the sequence space that
leads to foldable structures arises naturally using simple physical
characteristics of proteins. The reduction in sequence space leading to the
emergence of foldable structures is demonstrated using lattice models of
proteins.Comment: latex, 18 pages, 8 figures, to be published in the conference
proceedings "Stochastic Dynamics and Pattern Formation in Biological Systems
Mechanical unfolding of RNA hairpins
Mechanical unfolding trajectories, generated by applying constant force in
optical tweezer experiments, show that RNA hairpins and the P5abc subdomain of
the group I intron unfold reversibly. We use coarse-grained Go-like models for
RNA hairpins to explore forced-unfolding over a broad range of temperatures. A
number of predictions that are amenable to experimental tests are made. At the
critical force the hairpin jumps between folded and unfolded conformations
without populating any discernible intermediates. The phase diagram in the
force-temperature (f,T) plane shows that the hairpin unfolds by an all-or-none
process. The cooperativity of the unfolding transition increases dramatically
at low temperatures. Free energy of stability, obtained from time averages of
mechanical unfolding trajectories, coincide with ensemble averages which
establishes ergodicity. The hopping time between the the native basin of
attraction (NBA) and the unfolded basin increases dramatically along the phase
boundary. Thermal unfolding is stochastic whereas mechanical unfolding occurs
in "quantized steps" with great variations in the step lengths. Refolding
times, upon force quench, from stretched states to the NBA is "at least an
order of magnitude" greater than folding times by temperature quench. Upon
force quench from stretched states the NBA is reached in at least three stages.
In the initial stages the mean end-to-end distance decreases nearly
continuously and only in the last stage there is a sudden transition to the
NBA. Because of the generality of the results we propose that similar behavior
should be observed in force quench refolding of proteins.Comment: 23 pages, 6 Figures. in press (Proc. Natl. Acad. Sci.
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