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.

An approach to probe some neural systems interaction by functional MRI at neural time scale down to milliseconds

In this paper, we demonstrate an approach by which some evoked neuronal events can be probed by functional MRI (fMRI) signal with temporal resolution at the time scale of tens of milliseconds. The approach is based on the close relationship between neuronal electrical events and fMRI signal that is experimentally demonstrated in concurrent fMRI and electroencephalographic (EEG) studies conducted in a rat model with forepaw electrical stimulation. We observed a refractory period of neuronal origin in a two-stimuli paradigm: the first stimulation pulse suppressed the evoked activity in both EEG and fMRI signal responding to the subsequent stimulus for a period of several hundred milliseconds. When there was an apparent site–site interaction detected in the evoked EEG signal induced by two stimuli that were primarily targeted to activate two different sites in the brain, fMRI also displayed signal amplitude modulation because of the interactive event. With visual stimulation using two short pulses in the human brain, a similar refractory phenomenon was observed in activated fMRI signals in the primary visual cortex. In addition, for interstimulus intervals shorter than the known latency time of the evoked potential induced by the first stimulus (≈100 ms) in the primary visual cortex of the human brain, the suppression was not present. Thus, by controlling the temporal relation of input tasks, it is possible to study temporal evolution of certain neural events at the time scale of their evoked electrical activity by noninvasive fMRI methodology.

Multiple pathways for ultrafast transduction of light energy in the photosynthetic reaction center of Rhodobacter sphaeroides

A pathway of electron transfer is described that operates in the wild-type reaction center (RC) of the photosynthetic bacterium Rhodobacter sphaeroides. The pathway does not involve the excited state of the special pair dimer of bacteriochlorophylls (P*), but instead is driven by the excited state of the monomeric bacteriochlorophyll (BA*) present in the active branch of pigments along which electron transfer occurs. Pump-probe experiments were performed at 77 K on membrane-bound RCs by using different excitation wavelengths, to investigate the formation of the charge separated state P+HA−. In experiments in which P or BA was selectively excited at 880 nm or 796 nm, respectively, the formation of P+HA− was associated with similar time constants of 1.5 ps and 1.7 ps. However, the spectral changes associated with the two time constants are very different. Global analysis of the transient spectra shows that a mixture of P+BA− and P* is formed in parallel from BA* on a subpicosecond time scale. In contrast, excitation of the inactive branch monomeric bacteriochlorophyll (BB) and the high exciton component of P (P+) resulted in electron transfer only after relaxation to P*. The multiple pathways for primary electron transfer in the bacterial RC are discussed with regard to the mechanism of charge separation in the RC of photosystem II from higher plants.

The old problems of glass and the glass transition, and the many new twists.

In this paper I review the ways in which the glassy state is obtained both in nature and in materials science and highlight a "new twist"--the recent recognition of polymorphism within the glassy state. The formation of glass by continuous cooling (viscous slowdown) is then examined, the strong/fragile liquids classification is reviewed, and a new twist-the possibility that the slowdown is a result of an avoided critical point-is noted. The three canonical characteristics of relaxing liquids are correlated through the fragility. As a further new twist, the conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is demonstrated. It is then shown that, for comparable systems, it is possible to have the same conversion accomplished via a first-order transition within the liquid state during quenching. This occurs in the systems in which "polyamorphism" (polymorphism in the glassy state) is observed, and the whole phenomenology is accounted for by Poole's bond-modified van der Waals model. The sudden loss of some liquid degrees of freedom through such weak first-order transitions is then related to the polyamorphic transition between native and denatured hydrated proteins, since the latter are also glass-forming systems--water-plasticized, hydrogen bond-cross-linked chain polymers (and single molecule glass formers). The circle is closed with a final new twist by noting that a short time scale phenomenon much studied by protein physicists-namely, the onset of a sharp change in d/dT ( is the Debye-Waller factor)--is general for glass-forming liquids, including computer-simulated strong and fragile ionic liquids, and is closely correlated with the experimental glass transition temperature. The latter thus originates in strong anharmonicity in certain components of the vibrational density of states, which permits the system to access the multiple minima of its configuration space. The connection between the anharmonicity in these modes, vibrational localization, the Kauzmann temperature, and the fragility of the liquid is proposed as the key problem in glass science.

Context-sensitive synaptic plasticity and temporal-to-spatial transformations in hippocampal slices

Hippocampal slices are used to show that, as a temporal input pattern of activity flows through a neuronal layer, a temporal-to-spatial transformation takes place. That is, neurons can respond selectively to the first or second of a pair of input pulses, thus transforming different temporal patterns of activity into the activity of different neurons. This is demonstrated using associative long-term potentiation of polysynaptic CA1 responses as an activity-dependent marker: by depolarizing a postsynaptic CA1 neuron exclusively with the first or second of a pair of pulses from the dentate gyrus, it is possible to “tag” different subpopulations of CA3 neurons. This technique allows sampling of a population of neurons without recording simultaneously from multiple neurons. Furthermore, it reflects a biologically plausible mechanism by which single neurons may develop selective responses to time-varying stimuli and permits the induction of context-sensitive synaptic plasticity. These experimental results support the view that networks of neurons are intrinsically able to process temporal information and that it is not necessary to invoke the existence of internal clocks or delay lines for temporal processing on the time scale of tens to hundreds of milliseconds.

Glutamate transporter currents in Bergmann glial cells follow the time course of extrasynaptic glutamate

Glutamate transporters in the central nervous system are expressed in both neurons and glia, they mediate high affinity, electrogenic uptake of glutamate, and they are associated with an anion conductance that is stoichiometrically uncoupled from glutamate flux. Although a complete cycle of transport may require 50–100 ms, previous studies suggest that transporters can alter synaptic currents on a much faster time scale. We find that application of l-glutamate to outside-out patches from cerebellar Bergmann glia activates anion-potentiated glutamate transporter currents that activate in <1 ms, suggesting an efficient mechanism for the capture of extrasynaptic glutamate. Stimulation in the granule cell layer in cerebellar slices elicits all or none α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor and glutamate transporter currents in Bergmann glia that have a rapid onset, suggesting that glutamate released from climbing fiber terminals escapes synaptic clefts and reaches glial membranes shortly after release. Comparison of the concentration dependence of both α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor and glutamate transporter kinetics in patches with the time course of climbing fiber-evoked responses indicates that the glutamate transient at Bergmann glial membranes reaches a lower concentration than attained in the synaptic cleft and remains elevated in the extrasynaptic space for many milliseconds.

Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes

Two-dimensional infrared spectra of peptides are introduced that are the direct analogues of two- and three-pulse multiple quantum NMR. Phase matching and heterodyning are used to isolate the phase and amplitudes of the electric fields of vibrational photon echoes as a function of multiple pulse delays. Structural information is made available on the time scale of a few picoseconds. Line narrowed spectra of acyl-proline-NH2 and cross peaks implying the coupling between its amide-I modes are obtained, as are the phases of the various contributions to the signals. Solvent-sensitive structural differences are seen for the dipeptide. The methods show great promise to measure structure changes in biology on a wide range of time scales.

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.

Real-time quantitative measurement of autocrine ligand binding indicates that autocrine loops are spatially localized

Autocrine ligands are important regulators of many normal tissues and have been implicated in a number of disease states, including cancer. However, because by definition autocrine ligands are synthesized, secreted, and bound to cell receptors within an intrinsically self-contained “loop,” standard pharmacological approaches cannot be used to investigate relationships between ligand/receptor binding and consequent cellular responses. We demonstrate here a new approach for measurement of autocrine ligand binding to cells, using a microphysiometer assay originally developed for investigating cell responses to exogenous ligands. This technique permits quantitative measurements of autocrine responses on the time scale of receptor binding and internalization, thus allowing investigation of the role of receptor trafficking and dynamics in cellular responses. We used this technique to investigate autocrine signaling through the epidermal growth factor receptor by transforming growth factor alpha (TGFα) and found that anti-receptor antibodies are far more effective than anti-ligand antibodies in inhibiting autocrine signaling. This result indicates that autocrine-based signals can operate in a spatially restricted, local manner and thus provide cells with information on their local microenvironment.

A joint hazard and time scaling model to compare survival curves.

To provide a more general method for comparing survival experience, we propose a model that independently scales both hazard and time dimensions. To test the curve shape similarity of two time-dependent hazards, h1(t) and h2(t), we apply the proposed hazard relationship, h12(tKt)/ h1(t) = Kh, to h1. This relationship doubly scales h1 by the constant hazard and time scale factors, Kh and Kt, producing a transformed hazard, h12, with the same underlying curve shape as h1. We optimize the match of h12 to h2 by adjusting Kh and Kt. The corresponding survival relationship S12(tKt) = [S1(t)]KtKh transforms S1 into a new curve S12 of the same underlying shape that can be matched to the original S2. We apply this model to the curves for regional and local breast cancer contained in the National Cancer Institute's End Results Registry (1950-1973). Scaling the original regional curves, h1 and S1 with Kt = 1.769 and Kh = 0.263 produces transformed curves h12 and S12 that display congruence with the respective local curves, h2 and S2. This similarity of curve shapes suggests the application of the more complete curve shapes for regional disease as templates to predict the long-term survival pattern for local disease. By extension, this similarity raises the possibility of scaling early data for clinical trial curves according to templates of registry or previous trial curves, projecting long-term outcomes and reducing costs. The proposed model includes as special cases the widely used proportional hazards (Kt = 1) and accelerated life (KtKh = 1) models.

Genomic evolution during a 10,000-generation experiment with bacteria

Molecular methods are used widely to measure genetic diversity within populations and determine relationships among species. However, it is difficult to observe genomic evolution in action because these dynamics are too slow in most organisms. To overcome this limitation, we sampled genomes from populations of Escherichia coli evolving in the laboratory for 10,000 generations. We analyzed the genomes for restriction fragment length polymorphisms (RFLP) using seven insertion sequences (IS) as probes; most polymorphisms detected by this approach reflect rearrangements (including transpositions) rather than point mutations. The evolving genomes became increasingly different from their ancestor over time. Moreover, tremendous diversity accumulated within each population, such that almost every individual had a different genetic fingerprint after 10,000 generations. As has been often suggested, but not previously shown by experiment, the rates of phenotypic and genomic change were discordant, both across replicate populations and over time within a population. Certain pivotal mutations were shared by all descendants in a population, and these are candidates for beneficial mutations, which are rare and difficult to find. More generally, these data show that the genome is highly dynamic even over a time scale that is, from an evolutionary perspective, very brief.

Dynamic mapping at the laminar level of odor-elicited responses in rat olfactory bulb by functional MRI

We have applied functional MRI (fMRI) based on blood oxygenation level-dependent (BOLD) image-contrast to map odor-elicited olfactory responses at the laminar level in the rat olfactory bulb (OB) elicited by iso-amyl acetate (10−2 dilution of saturated vapor) with spatial and temporal resolutions of 220×220×1,000 μm and 36 s. The laminar structure of the OB was clearly depicted by high-resolution in vivo anatomical MRI with spatial resolution of 110×110×1,000 μm. In repeated BOLD fMRI measurements, highly significant (P < 0.001) foci were located in the outer layers of both OBs. The occurrence of focal OB activity within a domain at the level of individual glomeruli or groups of glomeruli was corroborated on an intra- and inter-animal basis under anesthetized conditions with this noninvasive method. The dynamic studies demonstrated that the odor-elicited BOLD activations were highly reproducible on a time scale of minutes, whereas over tens of minutes the activations sometimes varied slowly. We found large BOLD signal (ΔS/S = 10–30%) arising from the olfactory nerve layer, which is devoid of synapses and composed of unmyelinated fibers and glial cells. Our results support previous studies with other methods showing that odors elicit activity within glomerular layer domains in the mammalian OB, and extend the analysis to shorter time periods at the level of individual glomeruli or groups of glomeruli. With further improvement, BOLD fMRI should be ideal for systematic analysis of the functional significance of individual glomeruli in olfactory information encoding and of spatiotemporal processing within the olfactory system.

Calibrating bacterial evolution

Attempts to calibrate bacterial evolution have relied on the assumption that rates of molecular sequence divergence in bacteria are similar to those of higher eukaryotes, or to those of the few bacterial taxa for which ancestors can be reliably dated from ecological or geological evidence. Despite similarities in the substitution rates estimated for some lineages, comparisons of the relative rates of evolution at different classes of nucleotide sites indicate no basis for their universal application to all bacteria. However, there is evidence that bacteria have a constant genome-wide mutation rate on an evolutionary time scale but that this rate differs dramatically from the rate estimated by experimental methods.

Revised geochronology of the Casamayoran South American Land Mammal Age: Climatic and biotic implications

Isotopic age determinations (40Ar/39Ar) and associated magnetic polarity stratigraphy for Casamayoran age fauna at Gran Barranca (Chubut, Argentina) indicate that the Barrancan “subage” of the Casamayoran South American Land Mammal “Age” is late Eocene, 18 to 20 million years younger than hitherto supposed. Correlations of the radioisotopically dated magnetic polarity stratigraphy at Gran Barranca with the Cenozoic geomagnetic polarity time scale indicate that Barrancan faunal levels at the Gran Barranca date to within the magnetochronologic interval from 35.34 to 36.62 megannums (Ma) or 35.69 to 37.60 Ma. This age revision constrains the timing of an adaptive shift in mammalian herbivores toward hypsodonty. Specifically, the appearance of large numbers of hypsodont taxa in South America occurred sometime between 36 and 32 Ma (late Eocene–early Oligocene), at approximately the same time that other biotic and geologic evidence has suggested the Southern high latitudes experienced climatic cooling associated with Antarctic glaciation.

Dissociation of HIV-1 from follicular dendritic cells during HAART: Mathematical analysis

Follicular dendritic cells (FDC) provide a reservoir for HIV type 1 (HIV-1) that may reignite infection if highly active antiretroviral therapy (HAART) is withdrawn before virus on FDC is cleared. To estimate the treatment time required to eliminate HIV-1 on FDC, we develop deterministic and stochastic models for the reversible binding of HIV-1 to FDC via ligand–receptor interactions and examine the consequences of reducing the virus available for binding to FDC. Analysis of these models shows that the rate at which HIV-1 dissociates from FDC during HAART is biphasic, with an initial period of rapid decay followed by a period of slower exponential decay. The speed of the slower second stage of dissociation and the treatment time required to eradicate the FDC reservoir of HIV-1 are insensitive to the number of virions bound and their degree of attachment to FDC before treatment. In contrast, the expected time required for dissociation of an individual virion from FDC varies sensitively with the number of ligands attached to the virion that are available to interact with receptors on FDC. Although most virions may dissociate from FDC on the time scale of days to weeks, virions coupled to a higher-than-average number of ligands may persist on FDC for years. This result suggests that HAART may not be able to clear all HIV-1 trapped on FDC and that, even if clearance is possible, years of treatment will be required.