Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Complete resolution of the solid-state NMR spectrum of a uniformly 15N-labeled membrane protein in phospholipid bilayers

Complete resolution of the amide resonances in a three-dimensional solid-state NMR correlation spectrum of a uniformly 15N-labeled membrane protein in oriented phospholipid bilayers is demonstrated. The three orientationally dependent frequencies, 1H chemical shift, 1H–15N dipolar coupling, and 15N chemical shift, associated with each amide resonance are responsible for resolution among resonances and provide sufficient angular restrictions for protein structure determination. Because the protein is completely immobilized by the phospholipids on the relevant NMR time scales (10 kHz), the linewidths will not degrade in the spectra of larger proteins. Therefore, these results demonstrate that solid-state NMR experiments can overcome the correlation time problem and extend the range of proteins that can have their structures determined by NMR spectroscopy to include uniformly 15N-labeled membrane proteins in phospholipid bilayers.

Control of time-dependent biological processes by temporally patterned input

Temporal patterning of biological variables, in the form of oscillations and rhythms on many time scales, is ubiquitous. Altering the temporal pattern of an input variable greatly affects the output of many biological processes. We develop here a conceptual framework for a quantitative understanding of such pattern dependence, focusing particularly on nonlinear, saturable, time-dependent processes that abound in biophysics, biochemistry, and physiology. We show theoretically that pattern dependence is governed by the nonlinearity of the input–output transformation as well as its time constant. As a result, only patterns on certain time scales permit the expression of pattern dependence, and processes with different time constants can respond preferentially to different patterns. This has implications for temporal coding and decoding, and allows differential control of processes through pattern. We show how pattern dependence can be quantitatively predicted using only information from steady, unpatterned input. To apply our ideas, we analyze, in an experimental example, how muscle contraction depends on the pattern of motorneuron firing.

Separation of the arterial wall from blood contact using hydrogel barriers reduces intimal thickening after balloon injury in the rat: The roles of medial and luminal factors in arterial healing

The objective of this study was to clarify the relative roles of medial versus luminal factors in the induction of thickening of the arterial intima after balloon angioplasty injury. Platelet-derived growth factor (PDGF) and thrombin, both associated with thrombosis, and basic fibroblast growth factor (bFGF), stored in the arterial wall, have been implicated in this process. To unequivocally isolate the media from luminally derived factors, we used a 20-μm thick hydrogel barrier that adhered firmly to the arterial wall to block thrombus deposition after balloon-induced injury of the carotid artery of the rat. Thrombosis, bFGF mobilization, medial repopulation, and intimal thickening were measured. Blockade of postinjury arterial contact with blood prevented thrombosis and dramatically inhibited both intimal thickening and endogenous bFGF mobilization. By blocking blood contact on the two time scales of thrombosis and of intimal thickening, and by using local protein release to probe, by reconstitution, the individual roles of PDGF-BB and thrombin, we were able to conclude that a luminally derived factor other than PDGF or thrombin is required for the initiation of cellular events leading to intimal thickening after balloon injury in the rat. We further conclude that a luminally derived factor is required for mobilization of medial bFGF.

Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Dynamical principles in biological processes: A model of charge migration in proteins and DNA

The generalized master equations (GMEs) that contain multiple time scales have been derived quantum mechanically. The GME method has then been applied to a model of charge migration in proteins that invokes the hole hopping between local amino acid sites driven by the torsional motions of the floppy backbones. This model is then applied to analyze the experimental results for sequence-dependent long-range hole transport in DNA reported by Meggers et al. [Meggers, E., Michel-Beyerle, M. E., & Giese, B. (1998) J. Am. Chem. Soc. 120, 12950–12955]. The model has also been applied to analyze the experimental results of femtosecond dynamics of DNA-mediated electron transfer reported by Zewail and co-workers [Wan, C., Fiebig, T., Kelley, S. O., Treadway, C. R., Barton, J. K. & Zewail, A. H. (1999) Proc. Natl. Acad. Sci. USA 96, 6014–6019]. The initial events in the dynamics of protein folding have begun to attract attention. The GME obtained in this paper will be applicable to this problem.

Gases in ice cores

Air trapped in glacial ice offers a means of reconstructing variations in the concentrations of atmospheric gases over time scales ranging from anthropogenic (last 200 yr) to glacial/interglacial (hundreds of thousands of years). In this paper, we review the glaciological processes by which air is trapped in the ice and discuss processes that fractionate gases in ice cores relative to the contemporaneous atmosphere. We then summarize concentration–time records for CO2 and CH4 over the last 200 yr. Finally, we summarize concentration–time records for CO2 and CH4 during the last two glacial–interglacial cycles, and their relation to records of global climate change.

Two mechanisms for transducer adaptation in vertebrate hair cells

Deflection of the hair bundle atop a sensory hair cell modulates the open probability of mechanosensitive ion channels. In response to sustained deflections, hair cells adapt. Two fundamentally distinct models have been proposed to explain transducer adaptation. Both models support the notion that channel open probability is modulated by calcium that enters via the transduction channels. Both also suggest that the primary effect of adaptation is to shift the deflection-response [I(X)] relationship in the direction of the applied stimulus, thus maintaining hair bundle sensitivity. The models differ in several respects. They operate on different time scales: the faster on the order of a few milliseconds or less and the slower on the order of 10 ms or more. The model proposed to explain fast adaptation suggests that calcium enters and binds at or near the transduction channels to stabilize a closed conformation. The model proposed to explain the slower adaptation suggests that adaptation is mediated by an active, force-generating process that regulates the effective stimulus applied to the transduction channels. Here we discuss the evidence in support of each model and consider the possibility that both may function to varying degrees in hair cells of different species and sensory organs.

The resource consumption principle: attention and memory in volumes of neural tissue.

In the cerebral cortex, the small volume of the extracellular space in relation to the volume enclosed by synapses suggests an important functional role for this relationship. It is well known that there are atoms and molecules in the extracellular space that are absolutely necessary for synapses to function (e.g., calcium). I propose here the hypothesis that the rapid shift of these atoms and molecules from extracellular to intrasynaptic compartments represents the consumption of a shared, limited resource available to local volumes of neural tissue. Such consumption results in a dramatic competition among synapses for resources necessary for their function. In this paper, I explore a theory in which this resource consumption plays a critical role in the way local volumes of neural tissue operate. On short time scales, this principle of resource consumption permits a tissue volume to choose those synapses that function in a particular context and thereby helps to integrate the many neural signals that impinge on a tissue volume at any given moment. On longer time scales, the same principle aids in the stable storage and recall of information. The theory provides one framework for understanding how cerebral cortical tissue volumes integrate, attend to, store, and recall information. In this account, the capacity of neural tissue to attend to stimuli is intimately tied to the way tissue volumes are organized at fine spatial scales.

Proton transport by a bacteriorhodopsin mutant, aspartic acid-85-->asparagine, initiated in the unprotonated Schiff base state.

At alkaline pH the bacteriorhodopsin mutant D85N, with aspartic acid-85 replaced by asparagine, is in a yellow form (lambda max approximately 405 nm) with a deprotonated Schiff base. This state resembles the M intermediate of the wild-type photocycle. We used time-resolved methods to show that this yellow form of D85N, which has an initially unprotonated Schiff base and which lacks the proton acceptor Asp-85, transports protons in the same direction as wild type when excited by 400-nm flashes. Photoexcitation leads in several milliseconds to the formation of blue (630 nm) and purple (580 nm) intermediates with a protonated Schiff base, which decay in tens of seconds to the initial state (400 nm). Experiments with pH indicator dyes show that at pH 7, 8, and 9, proton uptake occurs in about 5-10 ms and precedes the slow release (seconds). Photovoltage measurements reveal that the direction of proton movement is from the cytoplasmic to the extracellular side with major components on the millisecond and second time scales. The slowest electrical component could be observed in the presence of azide, which accelerates the return of the blue intermediate to the initial yellow state. Transport thus occurs in two steps. In the first step (milliseconds), the Schiff base is protonated by proton uptake from the cytoplasmic side, thereby forming the blue state. From the pH dependence of the amplitudes of the electrical and photocycle signals, we conclude that this reaction proceeds in a similar way as in wild type--i.e., via the internal proton donor Asp-96. In the second step (seconds) the Schiff base deprotonates, releasing the proton to the extracellular side.

A sampling problem in molecular dynamics simulations of macromolecules.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.

Stars and brown dwarfs in the σ Orionis cluster (Research Note) III. OSIRIS/GTC low-resolution spectroscopy of variable sources

Context. Although many studies have been performed so far, there are still dozens of low-mass stars and brown dwarfs in the young σ Orionis open cluster without detailed spectroscopic characterisation. Aims. We look for unknown strong accretors and disc hosts that were undetected in previous surveys. Methods. We collected low-resolution spectroscopy (R ~ 700) of ten low-mass stars and brown dwarfs in σ Orionis with OSIRIS at the Gran Telescopio Canarias under very poor weather conditions. These objects display variability in the optical, infrared, Hα, and/or X-rays on time scales of hours to years. We complemented our spectra with optical and near-/mid-infrared photometry. Results. For seven targets, we detected lithium in absorption, identified Hα, the calcium doublet, and forbidden lines in emission, and/or determined spectral types for the first time. We characterise in detail a faint, T Tauri-like brown dwarf with an 18 h-period variability in the optical and a large Hα equivalent width of –125  ±  15 Å, as well as two M1-type, X-ray-flaring, low-mass stars, one with a warm disc and forbidden emission lines, the other with a previously unknown cold disc with a large inner hole. Conclusions. New unrevealed strong accretors and disc hosts, even below the substellar limit, await discovery among the list of known σ Orionis stars and brown dwarfs that are variable in the optical and have no detailed spectroscopic characterisation yet.

The Climate-system Historical Forecast Project: do stratosphere-resolving models make better seasonal climate predictions in boreal winter?

Using an international, multi-model suite of historical forecasts from the World Climate Research Programme (WCRP) Climate-system Historical Forecast Project (CHFP), we compare the seasonal prediction skill in boreal wintertime between models that resolve the stratosphere and its dynamics (high-top') and models that do not (low-top'). We evaluate hindcasts that are initialized in November, and examine the model biases in the stratosphere and how they relate to boreal wintertime (December-March) seasonal forecast skill. We are unable to detect more skill in the high-top ensemble-mean than the low-top ensemble-mean in forecasting the wintertime North Atlantic Oscillation, but model performance varies widely. Increasing the ensemble size clearly increases the skill for a given model. We then examine two major processes involving stratosphere-troposphere interactions (the El Niño/Southern Oscillation (ENSO) and the Quasi-Biennial Oscillation (QBO)) and how they relate to predictive skill on intraseasonal to seasonal time-scales, particularly over the North Atlantic and Eurasia regions. High-top models tend to have a more realistic stratospheric response to El Niño and the QBO compared to low-top models. Enhanced conditional wintertime skill over high latitudes and the North Atlantic region during winters with El Niño conditions suggests a possible role for a stratospheric pathway.

Simulated magnetic field expulsion in neutron star cores

The study of long-term evolution of neutron star (NS) magnetic fields is key to understanding the rich diversity of NS observations, and to unifying their nature despite the different emission mechanisms and observed properties. Such studies in principle permit a deeper understanding of the most important parameters driving their apparent variety, e.g. radio pulsars, magnetars, X-ray dim isolated NSs, gamma-ray pulsars. We describe, for the first time, the results from self-consistent magnetothermal simulations considering not only the effects of the Hall-driven field dissipation in the crust, but also adding a complete set of proposed driving forces in a superconducting core. We emphasize how each of these core-field processes drive magnetic evolution and affect observables, and show that when all forces are considered together in vectorial form, the net expulsion of core magnetic flux is negligible, and will have no observable effect in the crust (consequently in the observed surface emission) on megayear time-scales. Our new simulations suggest that strong magnetic fields in NS cores (and the signatures on the NS surface) will persist long after the crustal magnetic field has evolved and decayed, due to the weak combined effects of dissipation and expulsion in the stellar core.