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

Refolding dynamics of stretched biopolymers upon force quench

Single molecule force spectroscopy methods can be used to generate folding trajectories of biopolymers from arbitrary regions of the folding landscape. We illustrate the complexity of the folding kinetics and generic aspects of the collapse of RNA and proteins upon force quench, using simulations of an RNA hairpin and theory based on the de Gennes model for homopolymer collapse. The folding time, $\tau_F$, depends asymmetrically on $\delta f_S = f_S - f_m$ and $\delta f_Q = f_m - f_Q$ where $f_S$ ($f_Q$) is the stretch (quench) force, and $f_m$ is the transition mid-force of the RNA hairpin. In accord with experiments, the relaxation kinetics of the molecular extension, $R(t)$, occurs in three stages: a rapid initial decrease in the extension is followed by a plateau, and finally an abrupt reduction in $R(t)$ that occurs as the native state is approached. The duration of the plateau increases as $\lambda =\tau_Q/\tau_F$ decreases (where $\tau_Q$ is the time in which the force is reduced from $f_S$ to $f_Q$). Variations in the mechanisms of force quench relaxation as $\lambda$ is altered are reflected in the experimentally measurable time-dependent entropy, which is computed directly from the folding trajectories. An analytical solution of the de Gennes model under tension reproduces the multistage stage kinetics in $R(t)$. The prediction that the initial stages of collapse should also be a generic feature of polymers is validated by simulation of the kinetics of toroid (globule) formation in semiflexible (flexible) homopolymers in poor solvents upon quenching the force from a fully stretched state. Our findings give a unified explanation for multiple disparate experimental observations of protein folding.Comment: 31 pages 11 figure

A New Approach for Guaranteed State Estimation by Zonotopes

18th World CongressThe International Federation of Automatic ControlMilano (Italy) August 28 - September 2This paper proposes a methodology for guaranteed state estimation of linear discrete-time systems in the presence of bounded disturbances and noises. This aims at computing an outer approximation of the state estimation domain represented by a zonotope. A new criterion is used to reduce the size of the zonotope at each sample time. An illustrative example is analyzed in order to highlight the advantages of the proposed algorithm

A new approach for Guaranteed ellipsoidal state estimation

The 19th World Congress of the International Federation of Automatic Control 2014. Cape Town, SudáfricaThis paper proposes a new ellipsoid-based guaranteed state estimation approach for linear discrete-time systems with bounded perturbations and bounded measurement noise. This approach is based on the minimization of the radius of the ellipsoidal state estimation set. Firstly, the ellipsoidal state estimation is computed by off-line solving a Linear Matrix Inequality optimization problem. Secondly, a new online method is developed in order to improve the accuracy of the estimation but it leads to an increase of the online computation load. A new scaling technique is proposed to reduce the computation time, while keeping a good accuracy of the state estimation. An illustrative example is analyzed in order to show the advantages of the proposed approach

Comparison between two state estimation techniqueds for linear systems

20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse, FranceThis paper presents a comparison in terms of accuracy and complexity between two approaches used for state estimation of linear systems: a classic Kalman filter and a guaranteed set-membership state estimation technique. The main goal of this paper is to analyze the advantages of these techniques and to combine them in the future in a new accurate and simple extension that handles system uncertainties and chance constraints. Two academic examples illustrate the main differences between the compared techniques

Extending the SACOC algorithm through the Nystrom method for dense manifold data analysis

Data analysis has become an important field over the last decades. The growing amount of data demands new analytical methodologies in order to extract relevant knowledge. Clustering is one of the most competitive techniques in this context.Using a dataset as a starting point, these techniques aim to blindly group the data by similarity. Among the different areas, manifold identification is currently gaining importance. Spectral-based methods, which are the mostly used methodologies in this area, are however sensitive to metric parameters and noise. In order to solve these problems, new bio-inspired techniques have been combined with different heuristics to perform the clustering solutions and stability, specially for dense datasets. Ant Colony Optimization (ACO) is one of these new bio-inspired methodologies. This paper presents an extension of a previous algorithm named Spectral-based ACO Clustering (SACOC). SACOC is a spectral-based clustering methodology used for manifold identification. This work is focused on improving this algorithm through the Nystrom extension. The new algorithm, named SACON, is able to deal with Dense Data problems.We have evaluated the performance of this new approach comparing it with online clustering algorithms and the Nystrom extension of the Spectral Clustering algorithm using several datasets