Theoretical Perspectives on Protein Folding

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense.Comment: 48 pages, 9 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

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

Comprehensive review of various corrosion behaviours on 316 stainless steel

Corrosion is a destructive process that converts the pure metal into a chemically stabled form by hydroxide or sulphide and it is a slow process of destruction on the material by the chemical or electrochemical reaction in the environmental space. This kind of destruction has been typically produced from oxides or salt content on the material and it results in distinctive orange coloration. The classifications of corrosion act on atmospheric air and liquids as well as on contact of two solids. To resist the corrosion rate, stainless steel 316 has been chosen because of the presence of 2-3% molybdenum content and the presence of molybdenum plays a vital role in corrosion resistance. In this study, literature related to various works has been reviewed to explain the corrosion behaviour on cavitation, crevice, electrochemical, erosion, fatigue, galvanic, uniform, pitting, and stress corrosion which act on 316 stainless steel. In the present work, several coating processes and the additives, that have been added to SS 316 to enhance the outcomes according to various corrosion causes, are discussed

High-rate, high-fidelity entanglement of qubits across an elementary quantum network

We demonstrate remote entanglement of trapped-ion qubits via a quantum-optical fiber link with fidelity and rate approaching those of local operations. Two ${}^{88}$Sr${}^{+}$ qubits are entangled via the polarization degree of freedom of two photons which are coupled by high-numerical-aperture lenses into single-mode optical fibers and interfere on a beamsplitter. A novel geometry allows high-efficiency photon collection while maintaining unit fidelity for ion-photon entanglement. We generate remote Bell pairs with fidelity $F=0.940(5)$ at an average rate $182\,\mathrm{s}^{-1}$ (success probability $2.18\times10^{-4}$).Comment: v2 updated to include responses to reviewers, as published in PR

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure

Semiflexible chains in confined spaces

We develop an analytical method for studying the properties of a noninteracting wormlike chain (WLC) in confined geometries. The mean-field-like theory replaces the rigid constraints of confinement with average constraints, thus allowing us to develop a tractable method for treating a WLC wrapped on the surface of a sphere, and fully encapsulated within it. The efficacy of the theory is established by reproducing the exact correlation functions for a WLC confined to the surface of a sphere. In addition, the coefficients in the free energy are exactly calculated. We also describe the behavior of a surface-confined chain under external tension that is relevant for single molecule experiments on histone-DNA complexes. The force-extension curves display spatial oscillations, and the extension of the chain, whose maximum value is bounded by the sphere diameter, scales as f−1 at large forces, in contrast to the unconfined chain that approaches the contour length as f−1∕2. A WLC encapsulated in a sphere, that is relevant for the study of the viral encapsulation of DNA, can also be treated using the mean-field approach. The predictions of the theory for various correlation functions are in excellent agreement with Langevin simulations. We find that strongly confined chains are highly structured by examining the correlations using a local winding axis. The predicted pressure of the system is in excellent agreement with simulations but, as is known, is significantly lower than the pressures seen for DNA packaged in viral capsids

Relaxational behavior of the infinite-range Ising spin-glass in a transverse field

We study the zero-temperature behavior of the infinite-ranged Ising spin glass in a transverse field. Using spin summation techniques and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well compatible with a value $\nu=\frac{1}{4}$ for the correlation length exponent, $z=4$ for the dynamical exponent and an algebraic decay $t^{-1}$ for the imaginary-time correlation function. The zero-temperature relaxation of the energy in the presence of the transverse field shows that the system monotonically reaches the ground state energy due to tunneling processes and displays strong glassy effects.Comment: 15 pages + 5 Figures, Revte