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Molecular recognition plays a central role in many biological processes. For enzymatic reactions and slow protein-protein recognition events, turn-over rates and on-rates in the millisecond-to-second time scale have been connected to internal protein dynamics detected with atomic resolution by NMR spectroscopy, and in particular conformational sampling could be established as a mechanism for enzyme-substrate and protein-protein recognition. [1][2][3][4][5] Recent theoretical studies indicate that faster rates of conformational interconversion in the microsecond time scale might limit on-rates for protein-protein recognition. [6,7] However experimental proofs were lacking so far, mainly because such rates could not be determined accurately enough and kinetic experiments in the microsecond time range are difficult to perform.Nevertheless, for proteins and TAR-RNA, [8][9][10] recent studies based on residual dipolar couplings (RDCs) and other NMR spectroscopy techniques [11,12] have detected substantial internal dynamics in a time window from the rotational correlation time t c (one-digit nanoseconds) to approximately 50 ms, [8,[13][14][15] called the supra-t c window in the following. However, the exact rates of internal dynamics within this four orders of magnitude wide time window could not be determined.Supra-t c dynamics in ubiquitin [9] and TAR-RNA [16] could be connected to the conformational sampling required for molecular recognition. While the amplitudes of motions have been indirectly detected by RDCs and characterized in great detail, it has so far been impossible to directly observe these motions and to determine the exact rate of these supra-t c motions. In contrast, conformational sampling in enzymes occurs on a time scale that is 100 to 1000 times slower than supra-t c dynamics and therefore NMR relaxation dispersion (RD) techniques have been able to establish the functional link to enzyme kinetics with atomic resolution at physiological conditions.[1, 2, 5] However, for technical reasons, RD is not sensitive to motion faster than approximately 50 ms (RD window) and therefore does not access motion in the supra-t c window at room temperature.Here we determine the rate of interconversion between conformers of free ubiquitin by a combination of NMR RD experiments in super-cooled solution and dielectric relaxation spectroscopy (DR). Furthermore, we corroborate the motional amplitudes in the RDC-derived ensembles quantitatively with the observed amplitudes of RD and DR. The methods utilized herein can be used to directly study protein dynamics in a time range that was previously inaccessible.Significant motional amplitude in the supra-t c window has been observed using RDC measurements, and was connected to the conformational sampling for a protein in the ground

Periodic ripples generated from the off-normal-incidence ion-beam bombardment of solid surfaces have been observed to propagate with a dispersion in the velocity. We investigate this ripple behavior by means of a Monte Carlo model of the erosion process, in conjuction with one of two different surface-diffusion mechanisms, representative of two different classes of materials; one is a Arrhenius-type Monte Carlo method including a term ͑possibly zero͒ that accounts for the Schwoebel effect, while the other is a thermodynamic mechanism without the Schwoebel effect. We find that the behavior of the ripple velocity and wavelength depends on the sputtering time scale, which is qualitatively consistent with experiments. Futhermore, we observe a strong temperature dependance of the ripple velocity, calling for experiments at different temperatures. Also, we observe that the ripple velocity vanishes ahead of the periodic ripple pattern.

A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories. Due to its simple structure, simulations of the model can be performed on time scales, where effects beyond the linearized theory become important. Whereas for short times we observe the formation of ripple structures in accordance with the linearized theory, we find a roughening surface for intermediate times. The long time behavior of the model strongly depends on the surface relaxation mechanism.Keywords (PACS-codes): 68.35. 79.20.Rf, 82.20.Wt Introduction During the last years, two features of surface morphologies created by ion beam sputtering attracted particular attention: ripple structures on sub-micrometer length scales and self-affine, rough surfaces [1].The formation of periodic ripple structures has been observed experimentally in amorphous materials [2], metallic crystals [3,4] and semiconductors amorphized by the ion beam [5,6]. Ripples are typically oriented perpendicular to the projection of the ion beam in the surface plane for small angles of incidence Θ (relative to the surface normal), whereas for larger angles Θ, the observed ripple pattern is rotated by 90• . Surfaces eroded by ion bombardment may also exhibit self-affine properties [7]. With increasing ion fluence, a crossover from ripple structures to self-affine, rough surfaces has recently been observed experimentally [4].Our present understanding of these features is based upon the work of Bradley and Harper (BH) [8], who found that Sigmund's sputtering theory [9] implies a curvature dependence of the sputtering yield. Based on BH a continuum theory of surface evolution by sputter erosion was formulated as an anisotropic Kuramoto-Sivashinsky (KS) equation [10] with additive noise [11,12,13]. However, there are strong indications from experiment [3,14] that surface relaxation processes, are also important during pattern formation. Such processes have not yet been adequately included in existing theories. Our results will show that the long-time behavior of patterns depends crucially on details of surface relaxation.To investigate the analytic theory beyond the linearized regime, numerical integrations of the KS equation have been performed [15] [16], which uncovered two markedly different long-time regimes, depending on the signs of the non-linear couplings.Computer simulations may be helpful in clarifying both the role of surface relaxation and of non-linear effects. Two types of simulations have been performed