1,802 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
Dependence of folding rates on protein length
Using three-dimensional Go lattice models with side chains for proteins, we
investigate the dependence of folding times on protein length. In agreement
with previous theoretical predictions, we find that the folding time grows as a
power law with the chain length N with exponent for the
Go model, in which all native interactions (i.e., between all side chains and
backbone atoms) are uniform. If the interactions between side chains are given
by pairwise statistical potentials, which introduce heterogeneity in the
contact energies, then the power law fits yield large values that
typically signifies a crossover to an underlying activated process.
Accordingly, the dependence of folding time is best described by the stretched
exponential \exp(\sqrt{N}). The study also shows that the incorporation of side
chains considerably slows down folding by introducing energetic and topological
frustration.Comment: 6 pages, 5 eps figure
Probing the Mechanisms of Fibril Formation Using Lattice Models
Using exhaustive Monte Carlo simulations we study the kinetics and mechanism
of fibril formation using lattice models as a function of temperature and the
number of chains. While these models are, at best, caricatures of peptides, we
show that a number of generic features thought to govern fibril assembly are
present in the toy model. The monomer, which contains eight beads made from
three letters (hydrophobic, polar, and charged), adopts a compact conformation
in the native state. The kinetics of fibril assembly occurs in three distinct
stages. In each stage there is a cascade of events that transforms the monomers
and oligomers to ordered structures. In the first "burst" stage highly mobile
oligomers of varying sizes form. The conversion to the aggregation-prone
conformation occurs within the oligomers during the second stage. As time
progresses, a dominant cluster emerges that contains a majority of the chains.
In the final stage, the aggregation-prone conformation particles serve as a
template onto which smaller oligomers or monomers can dock and undergo
conversion to fibril structures. The overall time for growth in the latter
stages is well described by the Lifshitz-Slyazov growth kinetics for
crystallization from super-saturated solutions.Comment: 27 pages, 6 figure
Resonant Relaxation in Electroweak Baryogenesis
We compute the leading, chiral charge-changing relaxation term in the quantum
transport equations that govern electroweak baryogenesis using the closed time
path formulation of non-equilibrium quantum field theory. We show that the
relaxation transport coefficients may be resonantly enhanced under appropriate
conditions on electroweak model parameters and that such enhancements can
mitigate the impact of similar enhancements in the CP-violating source terms.
We also develop a power counting in the time and energy scales entering
electroweak baryogenesis and include effects through second order in ratios
of the small and large scales. We illustrate the implications of the
resonantly enhanced terms using the Minimal
Supersymmetric Standard Model, focusing on the interplay between the
requirements of baryogenesis and constraints obtained from collider studies,
precision electroweak data, and electric dipole moment searches.Comment: 30 pages plus appendices, 7 figure
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