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

Ultrasound mapping of lymph node and subcutaneous metastases in patients with cutaneous melanoma: Results of a prospective multicenter study

Background: Ultrasound (sonography, B-mode sonography, ultrasonography) examination improves the sensitivity in more than 25% compared to the clinical palpation, especially after surgery on the regional lymph node area. Objective: To evaluate the distribution of metastases during follow-up in the draining lymph node areas from the scar of primary to regional lymph nodes ( head and neck, supraclavicular, axilla, infraclavicular, groin) in patients with cutaneous melanoma with or without sentinel lymph node biopsy (SLNB) or former elective or consecutive complete lymph node dissection in case of positive sentinel lymph node (CLND). Methods: Prospective multicenter study of the Departments of Dermatology of the Universities of Homburg/Saar, Tubingen and Munich (Germany) in which the distribution of lymph node and subcutaneous metastases were mapped from the scar of primary to the lymphatic drainage region in 53 melanoma patients ( 23 women, 30 men; median age: 64 years; median tumor thickness: 1.99 mm) with known primary, visible lymph nodes or subcutaneous metastases proven by ultrasound and histopathology during the follow-up. Results: Especially in the axilla, infraclavicular region and groin the metastases were not limited to the anatomic lymph node regions. In 5 patients (9.4%) ( 4 of them were in stage IV) lymph node metastases were not located in the corresponding lymph node area. 32 patients without former SLNB had a time range between melanoma excision and lymph node metastases of 31 months ( median), 21 patients with SLNB had 18 months ( p < 0.005). In 11 patients with positive SLNB the time range was 17 months, in 10 patients with negative SLNB 21 months ( p < 0.005); in 32 patients with CLND the time range was 31 m< 0.005). In thinner melanomas lymph node metastases occurred later ( p < 0.05). Conclusions: After surgery of cutaneous melanoma, SLNB and CLND the lymphatic drainage can show significant changes which should be considered in clinical and ultrasound follow-up examinations. Especially for high-risk melanoma patients follow-up examinations should be performed at intervals of 3 months in the first years. Patients at stage IV should be examined in all regional lymph node areas clinically and by ultrasound. Copyright (c) 2006 S. Karger AG, Basel

A lattice model of hydrophobic interactions

Hydrogen bonding is modeled in terms of virtual exchange of protons between water molecules. A simple lattice model is analyzed, using ideas and techniques from the theory of correlated electrons in metals. Reasonable parameters reproduce observed magnitudes and temperature dependence of the hydrophobic interaction between substitutional impurities and water within this lattice.Comment: 7 pages, 3 figures. To appear in Europhysics Letter

A test generation framework for quiescent real-time systems

We present an extension of Tretmans theory and algorithm for test generation for input-output transition systems to real-time systems. Our treatment is based on an operational interpretation of the notion of quiescence in the context of real-time behaviour. This gives rise to a family of implementation relations parameterized by observation durations for quiescence. We define a nondeterministic (parameterized) test generation algorithm that generates test cases that are sound with respect to the corresponding implementation relation. Also, the test generation is exhaustive in the sense that for each non-conforming implementation a test case can be generated that detects the non-conformance

Kramers rate theory of ionization and dissociation of bound states

Calculating the microscopic dissociation rate of a bound state, such as a classical diatomic molecule, has been difficult so far. The problem was that standard theories require an energy barrier over which the bound particle (or state) escapes into the preferred low-energy state. This is not the case when the long-range repulsion responsible for the barrier is either absent or screened (as in Cooper pairs, ionized plasma, or biomolecular complexes). We solve this classical problem by accounting for entropic memory at the microscopic level. The theory predicts dissociation rates for arbitrary potentials and is successfully tested on the example of plasma, where it yields an estimate of ionization in the core of Sun in excellent agreement with experiments. In biology, the new theory accounts for crowding in receptor-ligand kinetics and protein aggregation

Human dynamics revealed through Web analytics

When the World Wide Web was first conceived as a way to facilitate the sharing of scientific information at the CERN (European Center for Nuclear Research) few could have imagined the role it would come to play in the following decades. Since then, the increasing ubiquity of Internet access and the frequency with which people interact with it raise the possibility of using the Web to better observe, understand, and monitor several aspects of human social behavior. Web sites with large numbers of frequently returning users are ideal for this task. If these sites belong to companies or universities, their usage patterns can furnish information about the working habits of entire populations. In this work, we analyze the properly anonymized logs detailing the access history to Emory University's Web site. Emory is a medium size university located in Atlanta, Georgia. We find interesting structure in the activity patterns of the domain and study in a systematic way the main forces behind the dynamics of the traffic. In particular, we show that both linear preferential linking and priority based queuing are essential ingredients to understand the way users navigate the Web.Comment: 7 pages, 8 figure

One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures

We consider a one-dimensional lattice of Ising-type variables where the ferromagnetic exchange interaction J between neighboring sites is frustrated by a long-ranged anti-ferromagnetic interaction of strength g between the sites i and j, decaying as |i-j|^-alpha, with alpha>1. For alpha smaller than a certain threshold alpha_0, which is larger than 2 and depends on the ratio J/g, the ground state consists of an ordered sequence of segments with equal length and alternating magnetization. The width of the segments depends on both alpha and the ratio J/g. Our Monte Carlo study shows that the on-site magnetization vanishes at finite temperatures and finds no indication of any phase transition. Yet, the modulation present in the ground state is recovered at finite temperatures in the two-point correlation function, which oscillates in space with a characteristic spatial period: The latter depends on alpha and J/g and decreases smoothly from the ground-state value as the temperature is increased. Such an oscillation of the correlation function is exponentially damped over a characteristic spatial scale, the correlation length, which asymptotically diverges roughly as the inverse of the temperature as T=0 is approached. This suggests that the long-range interaction causes the Ising chain to fall into a universality class consistent with an underlying continuous symmetry. The e^(Delta/T)-temperature dependence of the correlation length and the uniform ferromagnetic ground state, characteristic of the g=0 discrete Ising symmetry, are recovered for alpha > alpha_0.Comment: 12 pages, 7 figure

Folding in two-dimenensional off-lattice models of proteins

Model off-lattice sequences in two dimensions are constructed so that their native states are close to an on-lattice target. The Hamiltonian involves the Lennard-Jones and harmonic interactions. The native states of these sequences are determined with a high degree of certainty through Monte Carlo processes. The sequences are characterized thermodynamically and kinetically. It is shown that the rank-ordering-based scheme of the assignment of contact energies typically fails in off-lattice models even though it generates high stability of on-lattice sequences. Similar to the on-lattice case, Go-like modeling, in which the interaction potentials are restricted to the native contacts in a target shape, gives rise to good folding properties. Involving other contacts deteriorates these properties.Comment: REVTeX, 9 pages, 8 EPS figure

A New Monte Carlo Algorithm for Protein Folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (P. Grassberger, Phys. Rev. E 56 (1997) 3682) leads to extremely efficient algorithms for the folding of simple model proteins. We test them on several models for lattice heteropolymers, and compare to published Monte Carlo studies. In all cases our algorithms are faster than all previous ones, and in several cases we find new minimal energy states. In addition to ground states, our algorithms give estimates for the partition sum at finite temperatures.Comment: 4 pages, Latex incl. 3 eps-figs., submitted to Phys. Rev. Lett., revised version with changes in the tex

The Origin of the Designability of Protein Structures

We examined what determines the designability of 2-letter codes (H and P) lattice proteins from three points of view. First, whether the native structure is searched within all possible structures or within maximally compact structures. Second, whether the structure of the used lattice is bipartite or not. Third, the effect of the length of the chain, namely, the number of monomers on the chain. We found that the bipartiteness of the lattice structure is not a main factor which determines the designability. Our results suggest that highly designable structures will be found when the length of the chain is sufficiently long to make the hydrophobic core consisting of enough number of monomers.Comment: 17 pages, 2 figure