121 research outputs found
Random walks in the space of conformations of toy proteins
Monte Carlo dynamics of the lattice 48 monomers toy protein is interpreted as
a random walk in an abstract (discrete) space of conformations. To test the
geometry of this space, we examine the return probability , which is the
probability to find the polymer in the native state after Monte Carlo
steps, provided that it starts from the native state at the initial moment.
Comparing computational data with the theoretical expressions for for
random walks in a variety of different spaces, we show that conformational
spaces of polymer loops may have non-trivial dimensions and exhibit negative
curvature characteristic of Lobachevskii (hyperbolic) geometry.Comment: 4 pages, 3 figure
Protein folding rates correlate with heterogeneity of folding mechanism
By observing trends in the folding kinetics of experimental 2-state proteins
at their transition midpoints, and by observing trends in the barrier heights
of numerous simulations of coarse grained, C-alpha model, Go proteins, we show
that folding rates correlate with the degree of heterogeneity in the formation
of native contacts. Statistically significant correlations are observed between
folding rates and measures of heterogeneity inherent in the native topology, as
well as between rates and the variance in the distribution of either
experimentally measured or simulated phi-values.Comment: 11 pages, 3 figures, 1 tabl
Thermodynamically Important Contacts in Folding of Model Proteins
We introduce a quantity, the entropic susceptibility, that measures the
thermodynamic importance-for the folding transition-of the contacts between
amino acids in model proteins. Using this quantity, we find that only one
equilibrium run of a computer simulation of a model protein is sufficient to
select a subset of contacts that give rise to the peak in the specific heat
observed at the folding transition. To illustrate the method, we identify
thermodynamically important contacts in a model 46-mer. We show that only about
50% of all contacts present in the protein native state are responsible for the
sharp peak in the specific heat at the folding transition temperature, while
the remaining 50% of contacts do not affect the specific heat.Comment: 5 pages, 5 figures; to be published in PR
Geometrically Reduced Number of Protein Ground State Candidates
Geometrical properties of protein ground states are studied using an
algebraic approach. It is shown that independent from inter-monomer
interactions, the collection of ground state candidates for any folded protein
is unexpectedly small: For the case of a two-parameter Hydrophobic-Polar
lattice model for -mers, the number of these candidates grows only as .
Moreover, the space of the interaction parameters of the model breaks up into
well-defined domains, each corresponding to one ground state candidate, which
are separated by sharp boundaries. In addition, by exact enumeration, we show
there are some sequences which have one absolute unique native state. These
absolute ground states have perfect stability against change of inter-monomer
interaction potential.Comment: 9 page, 4 ps figures are include
Nucleation phenomena in protein folding: The modulating role of protein sequence
For the vast majority of naturally occurring, small, single domain proteins
folding is often described as a two-state process that lacks detectable
intermediates. This observation has often been rationalized on the basis of a
nucleation mechanism for protein folding whose basic premise is the idea that
after completion of a specific set of contacts forming the so-called folding
nucleus the native state is achieved promptly. Here we propose a methodology to
identify folding nuclei in small lattice polymers and apply it to the study of
protein molecules with chain length N=48. To investigate the extent to which
protein topology is a robust determinant of the nucleation mechanism we compare
the nucleation scenario of a native-centric model with that of a sequence
specific model sharing the same native fold. To evaluate the impact of the
sequence's finner details in the nucleation mechanism we consider the folding
of two non- homologous sequences. We conclude that in a sequence-specific model
the folding nucleus is, to some extent, formed by the most stable contacts in
the protein and that the less stable linkages in the folding nucleus are solely
determined by the fold's topology. We have also found that independently of
protein sequence the folding nucleus performs the same `topological' function.
This unifying feature of the nucleation mechanism results from the residues
forming the folding nucleus being distributed along the protein chain in a
similar and well-defined manner that is determined by the fold's topological
features.Comment: 10 Figures. J. Physics: Condensed Matter (to appear
Entropic Barriers, Frustration and Order: Basic Ingredients in Protein Folding
We solve a model that takes into account entropic barriers, frustration, and
the organization of a protein-like molecule. For a chain of size , there is
an effective folding transition to an ordered structure. Without frustration,
this state is reached in a time that scales as , with
. This scaling is limited by the amount of frustration which
leads to the dynamical selectivity of proteins: foldable proteins are limited
to monomers; and they are stable in {\it one} range of temperatures,
independent of size and structure. These predictions explain generic properties
of {\it in vivo} proteins.Comment: 4 pages, 4 Figures appended as postscript fil
Statics, metastable states and barriers in protein folding: A replica variational approach
Protein folding is analyzed using a replica variational formalism to
investigate some free energy landscape characteristics relevant for dynamics. A
random contact interaction model that satisfies the minimum frustration
principle is used to describe the coil-globule transition (characterized by
T_CG), glass transitions (by T_A and T_K) and folding transition (by T_F).
Trapping on the free energy landscape is characterized by two characteristic
temperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which are
similar to those found in mean field theories of the Potts glass. 1)Above T_A,
the free energy landscape is monotonous and polymer is melted both dynamically
and statically. 2)Between T_A and T_K, the melted phase is still dominant
thermodynamically, but frozen metastable states, exponentially large in number,
appear. 3)A few lowest minima become thermodynamically dominant below T_K,
where the polymer is totally frozen. In the temperature range between T_A and
T_K, barriers between metastable states are shown to grow with decreasing
temperature suggesting super-Arrhenius behavior in a sufficiently large system.
Due to evolutionary constraints on fast folding, the folding temperature T_F is
expected to be higher than T_K, but may or may not be higher than T_A. Diverse
scenarios of the folding kinetics are discussed based on phase diagrams that
take into account the dynamical transition, as well as the static ones.Comment: 41 pages, LaTeX, 9 EPS figure
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