Comment on "Chain Length Scaling of Protein Folding Time", PRL 77, 5433 (1996)

In a recent Letter, Gutin, Abkevich, and Shakhnovich (GAS) reported on a series of dynamical Monte Carlo simulations on lattice models of proteins. Based on these highly simplified models, they found that four different potential energies lead to four different folding time scales tau_f, where tau_f scales with chain length as N^lambda (see, also, Refs. [2-4]), with lambda varying from 2.7 to 6.0. However, due to the lack of microscopic models of protein folding dynamics, the interpretation and origin of the data have remained somewhat speculative. It is the purpose of this Comment to point out that the application of a simple "mesoscopic" model (cond-mat/9512019, PRL 77, 2324, 1996) of protein folding provides a full account of the data presented in their paper. Moreover, we find a major qualitative disagreement with the argumentative interpretation of GAS. Including, the origin of the dynamics, and size of the critical folding nucleus.Comment: 1 page Revtex, 1 fig. upon request. Submitted to PR

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 ($T_\theta$) and the folding ($T_f$) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as $\tau_f\sim F(M)\exp(\sigma/\sigma_0)$, where $\sigma=1-T_f/T_\theta$, $M$ is the number of residues, and $F(M)$ scales algebraically with $M$. We argue that $T_f$ scales linearly with the inverse of entropy of low energy non-native states, whereas $T_\theta$ is almost independent of it. As $\sigma\rightarrow 0$, 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, $\sigma$ can be used to predict sequences that fold rapidly.Comment: 10 pages, latex, figures upon reques

From Collapse to Freezing in Random Heteropolymers

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N_H (out ofN) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction rho_H=N_H/N. The average chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H --> 0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H < 1, entropy approaches zero as N --> infty (being finite for a homopolymer). An abrupt decrease in entropy occurs at the phase boundary between the swollen (R ~ N^nu) and collapsed region. Scaling arguments predict different regimes depending on the ensemble of crosslinks. Some implications to the protein folding problem are discussed.Comment: 4 pages, Revtex, figs upon request. New interpretation and emphasis. Submitted to Europhys.Let

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 $M$, there is an effective folding transition to an ordered structure. Without frustration, this state is reached in a time that scales as $M^{\lambda}$, with $\lambda\simeq 3$. This scaling is limited by the amount of frustration which leads to the dynamical selectivity of proteins: foldable proteins are limited to $\sim 300$ 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

Long-range correlations and trends in Colombian seismic time series

We study long-range correlations and trends in time series extracted from the data of seismic events occurred from 1973 to 2011 in a rectangular region that contains mainly all the continental part of Colombia. The long-range correlations are detected by the calculation of the Hurst exponents for the time series of interevent intervals, separation distances, depth differences and magnitude differences. By using a modification of the classical $R/S$ method that has been developed to detect short-range correlations in time series, we find the existence of persistence for all the time series considered except for magnitude differences. We find also, by using the $DFA$ until the third order, that the studied time series are not influenced by trends. Additionally, an analysis of the Hurst exponent as a function of the number of events in the time and the maximum window size is presented.Comment: 21 pages, 6 figures, 2 figures added, types corrected, accepted to be published in Physica

Ultra--cold gases and the detection of the Earth's rotation: Bogoliubov space and gravitomagnetism

The present work analyzes the consequences of the gravitomagnetic effect of the Earth upon a bosonic gas in which the corresponding atoms have a non--vanishing orbital angular momentum. Concerning the ground state of the Bogoliubov space of this system we deduce the consequences, on the pressure and on the speed of sound, of the gravitomagnetic effect. We prove that the effect on a single atom is very small, but we also show that for some thermodynamical properties the consequences scale as a non--trivial function of the number of particles.Comment: 4 page

White dwarfs as test objects of Lorentz violations

In the present work the thermodynamical properties of bosonic and fermionic gases are analyzed under the condition that a modified dispersion relation is present. This last condition implies a breakdown of Lorentz symmetry. The implications upon the condensation temperature will be studied, as well, as upon other thermodynamical variables such as specific heat, entropy, etc. Moreover, it will be argued that those cases entailing a violation of time reversal symmetry of the motion equations could lead to problems with the concept of entropy. Concerning the fermionic case it will be shown that Fermi temperature suffers a modification due to the breakdown of Lorentz symmetry. The results will be applied to white dwarfs and the consequences upon the Chandrasekhar mass--radius relation will be shown. The possibility of resorting to white dwarfs for the testing of modified dispersion relations is also addressed. It will be shown that the comparison of the current observations against the predictions of our model allows us to discard some values of one of the parameters appearing in the modifications of the dispersion relation.Comment: Accepted in Classical and Quantum Gravitatio

The scalar sector in the Myers-Pospelov model

We construct a perturbative expansion of the scalar sector in the Myers-Pospelov model, up to second order in the Lorentz violating parameter and taking into account its higher-order time derivative character. This expansion allows us to construct an hermitian positive-definite Hamiltonian which provides a correct basis for quantization. Demanding that the modified normal frequencies remain real requires the introduction of an upper bound in the magnitude |k| of the momentum, which is a manifestation of the effective character of the model. The free scalar propagator, including the corresponding modified dispersion relations, is also calculated to the given order, thus providing the starting point to consider radiative corrections when interactions are introduced.Comment: Published in AIP Conf.Proc.977:214-223,200

Improved image quality with new ultrasound imaging techniques

AbstractThis work addresses three key subjects to the image quality with phased arrays: timing accuracy, beamforming strategy and post-processing for increased resolution and suppression of grating and side lobes.Timing accuracy is achieved by defining a modular and scalable architecture which guarantees timing errors of a few tens of picoseconds, whatever is the system size. The proposed beamforming methodology follows the progressive focusing correction technique, which keeps low focusing errors, provides a high information density and has a simple implementation for real-time imaging. Then, phase coherence imaging is defined to suppress grating and sidelobe indications and increasing the lateral resolution