955 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
A Criterion That Determines Fast Folding of Proteins: A Model Study
We consider the statistical mechanics of a full set of two-dimensional
protein-like heteropolymers, whose thermodynamics is characterized by the
coil-to-globular () and the folding () transition temperatures.
For our model, the typical time scale for reaching the unique native
conformation is shown to scale as , where
, is the number of residues, and scales
algebraically with . We argue that scales linearly with the inverse of
entropy of low energy non-native states, whereas is almost
independent of it. As , non-productive intermediates
decrease, and the initial rapid collapse of the protein leads to structures
resembling the native state. Based solely on {\it accessible} information,
can be used to predict sequences that fold rapidly.Comment: 10 pages, latex, figures upon reques
Cellular signaling networks function as generalized Wiener-Kolmogorov filters to suppress noise
Cellular signaling involves the transmission of environmental information
through cascades of stochastic biochemical reactions, inevitably introducing
noise that compromises signal fidelity. Each stage of the cascade often takes
the form of a kinase-phosphatase push-pull network, a basic unit of signaling
pathways whose malfunction is linked with a host of cancers. We show this
ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov
(WK) optimal noise filter. Using concepts from umbral calculus, we generalize
the linear WK theory, originally introduced in the context of communication and
control engineering, to take nonlinear signal transduction and discrete
molecule populations into account. This allows us to derive rigorous
constraints for efficient noise reduction in this biochemical system. Our
mathematical formalism yields bounds on filter performance in cases important
to cellular function---like ultrasensitive response to stimuli. We highlight
features of the system relevant for optimizing filter efficiency, encoded in a
single, measurable, dimensionless parameter. Our theory, which describes noise
control in a large class of signal transduction networks, is also useful both
for the design of synthetic biochemical signaling pathways, and the
manipulation of pathways through experimental probes like oscillatory input.Comment: 15 pages, 5 figures; to appear in Phys. Rev.
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
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