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

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

Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing

We show that Kramers rate theory gives a straightforward, accurate estimate of the closing time $\tau_c$ of a semiflexible polymer that is valid in cases of physical interest. The calculation also reveals how the time scales of chain relaxation and closing are intertwined, illuminating an apparent conflict between two ways of calculating $\tau_c$ in the flexible limit.Comment: Europhys. Lett., 2003 (in press). 8 pages, 3 figures. See also, physics/0101087 for physicist's approach to and the importance of semiflexible polymer looping, in DNA replicatio

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

Viscosity Dependence of the Folding Rates of Proteins

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn \alpha-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical Review Letter

Magnetic field stabilization system for atomic physics experiments

Atomic physics experiments commonly use millitesla-scale magnetic fields to provide a quantization axis. As atomic transition frequencies depend on the amplitude of this field, many experiments require a stable absolute field. Most setups use electromagnets, which require a power supply stability not usually met by commercially available units. We demonstrate stabilization of a field of 14.6 mT to 4.3 nT rms noise (0.29 ppm), compared to noise of $\gtrsim$ 100 nT without any stabilization. The rms noise is measured using a field-dependent hyperfine transition in a single $^{43}$Ca$^+$ ion held in a Paul trap at the centre of the magnetic field coils. For the $^{43}$Ca$^+$ "atomic clock" qubit transition at 14.6 mT, which depends on the field only in second order, this would yield a projected coherence time of many hours. Our system consists of a feedback loop and a feedforward circuit that control the current through the field coils and could easily be adapted to other field amplitudes, making it suitable for other applications such as neutral atom traps.Comment: 6 pages, 5 figure