34 research outputs found
Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions
In this paper we prove inversion formulas for the Dunkl intertwining operator
and for its dual and we deduce the expression of the
representing distributions of the inverse operators and
, and we give some applications.Comment: This is a contribution to the Special Issue on Dunkl Operators and
Related Topics, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Designability of lattice model heteropolymers
Protein folds are highly designable, in the sense that many sequences fold to
the same conformation. In the present work we derive an expression for the
designability in a 20 letter lattice model of proteins which, relying only on
the Central Limit Theorem, has a generality which goes beyond the simple model
used in its derivation. This expression displays an exponential dependence on
the energy of the optimal sequence folding on the given conformation measured
with respect to the lowest energy of the conformational dissimilar structures,
energy difference which constitutes the only parameter controlling
designability. Accordingly, the designability of a native conformation is
intimately connected to the stability of the sequences folding to them.Comment: in press on Phys. Rev.
Dynamics of polymer chain collapse into compact states
Molecular dynamics simulation methods are used to study the folding of
polymer chains into packed cubic states. The polymer model, based on a chain of
linked sites moving in the continuum, includes both excluded volume and
torsional interactions. Different native-state packing arrangements and chain
lengths are explored; the organization of the native state is found to affect
both the ability of the chain to fold successfully and the nature of the
folding pathway as the system is gradually cooled. An order parameter based on
contact counts is used to provide information about the folding process, with
contacts additionally classified according to criteria such as core and surface
sites or local and distant site pairs. Fully detailed contact maps and their
evolution are also examined.Comment: 11 pages, 11 figures (some low resolution
Role of bulk and of interface contacts in the behaviour of model dimeric proteins
Some dimeric proteins first fold and then dimerize (three--state dimers)
while others first dimerize and then fold (two--state dimers). Within the
framework of a minimal lattice model, we can distinguish between sequences
obeying to one or to the other mechanism on the basis of the partition of the
ground state energy between bulk than for interface contacts. The topology of
contacts is very different for the bulk than for the interface: while the bulk
displays a rich network of interactions, the dimer interface is built up a set
of essentially independent contacts. Consequently, the two sets of interactions
play very different roles both in the the folding and in the evolutionary
history of the protein. Three--state dimers, where a large fraction of the
energy is concentrated in few contacts buried in the bulk, and where the
relative contact energy of interface contacts is considerably smaller than that
associated with bulk contacts, fold according to a hierarchycal pathway
controlled by local elementary structures, as also happens in the folding of
single--domain monomeric proteins. On the other hand, two--state dimers display
a relative contact energy of interface contacts which is larger than the
corresponding quantity associated with the bulk. In this case, the assembly of
the interface stabilizes the system and lead the two chains to fold. The
specific properties of three--state dimers acquired through evolution are
expected to be more robust than those of two--state dimers, a fact which has
consequences on proteins connected with viral diseases
Reversible stretching of homopolymers and random heteropolymers
We have analyzed the equilibrium response of chain molecules to stretching.
For a homogeneous sequence of monomers, the induced transition from compact
globule to extended coil below the -temperature is predicted to be
sharp. For random sequences, however, the transition may be smoothed by a
prevalence of necklace-like structures, in which globular regions and coil
regions coexist in a single chain. As we show in the context of a random
copolymer, preferential solvation of one monomer type lends stability to such
structures. The range of stretching forces over which necklaces are stable is
sensitive to chain length as well as sequence statistics.Comment: 14 pages, 4 figure
Elastic Theory of pinned flux lattices
The pinning of flux lattices by weak impurity disorder is studied in the
absence of free dislocations using both the gaussian variational method and, to
, the functional renormalization group. We find universal
logarithmic growth of displacements for : and persistence of algebraic quasi-long range
translational order. When the two methods can be compared they agree within
on the value of . We compute the function describing the crossover
between the ``random manifold'' regime and the logarithmic regime. This
crossover should be observable in present decoration experiments.Comment: 12 pages, Revtex 3.
Embedding a Native State into a Random Heteropolymer Model: The Dynamic Approach
We study a random heteropolymer model with Langevin dynamics, in the
supersymmetric formulation. Employing a procedure similar to one that has been
used in static calculations, we construct an ensemble in which the affinity of
the system for a native state is controlled by a "selection temperature" T0. In
the limit of high T0, the model reduces to a random heteropolymer, while for
T0-->0 the system is forced into the native state. Within the Gaussian
variational approach that we employed previously for the random heteropolymer,
we explore the phases of the system for large and small T0. For large T0, the
system exhibits a (dynamical) spin glass phase, like that found for the random
heteropolymer, below a temperature Tg. For small T0, we find an ordered phase,
characterized by a nonzero overlap with the native state, below a temperature
Tn \propto 1/T0 > Tg. However, the random-globule phase remains locally stable
below Tn, down to the dynamical glass transition at Tg. Thus, in this model,
folding is rapid for temperatures between Tg and Tn, but below Tg the system
can get trapped in conformations uncorrelated with the native state. At a lower
temperature, the ordered phase can also undergo a dynamical glass transition,
splitting into substates separated by large barriers.Comment: 19 pages, revtex, 6 figure
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
Aging without disorder on long time scales
We study the Metropolis dynamics of a simple spin system without disorder,
which exhibits glassy dynamics at low temperatures. We use an implementation of
the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out
to be very efficient for the study of glassy systems, which get trapped in
local minima on many different time scales. We find strong evidence of aging
effects at low temperatures. We relate these effects to the distribution
function of the trapping times of single configurations.Comment: 8 pages Revtex, 7 figures uuencoded (Revised version: the figures are
now present
Protein sequence and structure: Is one more fundamental than the other?
We argue that protein native state structures reside in a novel "phase" of
matter which confers on proteins their many amazing characteristics. This phase
arises from the common features of all globular proteins and is characterized
by a sequence-independent free energy landscape with relatively few low energy
minima with funnel-like character. The choice of a sequence that fits well into
one of these predetermined structures facilitates rapid and cooperative
folding. Our model calculations show that this novel phase facilitates the
formation of an efficient route for sequence design starting from random
peptides.Comment: 7 pages, 4 figures, to appear in J. Stat. Phy