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.

Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

The vibrational energy relaxation of carbon monoxide in the heme pocket of sperm whale myoglobin was studied by using molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300 K for both the δ- and ɛ-tautomers of the distal His-64. Vibrational population relaxation times of 335 ± 115 ps for the δ-tautomer and 640 ± 185 ps for the ɛ-tautomer were estimated by using the Landau–Teller model. Normal mode analysis was used to identify those protein residues that act as the primary “doorway” modes in the vibrational relaxation of the oscillator. Although the CO relaxation rates in both the ɛ- and δ-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the δ-tautomer with the distal His playing an important role in the energy relaxation mechanism. Time-resolved mid-IR absorbance measurements were performed on photolyzed carbonmonoxy hemoglobin (Hb13CO). From these measurements, a T1 time of 600 ± 150 ps was determined. The simulation and experimental estimates are compared and discussed.

Dynamics of contacts between lamellae of fibroblasts: Essential role of the actin cytoskeleton

We investigated actin cytoskeletal and adhesion molecule dynamics during collisions of leading lamellae of nontransformed and oncogene-transformed fibroblasts. By using real-time video microscopy, it was found that during lamellar collision there was considerable overlapping of leading lamellae followed by subsequent retraction. Overlapping of nontransformed fibroblasts was accompanied by formation of β-catenin-positive contact structures organized into strands oriented parallel to the long axis of the cell that were associated with bundles of actin filaments. Maintenance of such cell–cell contact structures critically depended on the contractility of actin cytoskeleton, as inhibition of contractility with serum-free medium or 2,3-butanedione 2-monoxime (BDM) resulted in loss of strand formation. Strand formation was recovered when cells in serum-free medium were incubated with the microtubule inhibitor nocodazole, which is known to increase contractility. Oncogene-transformed fibroblasts reacted to collisions with responses similar to nontransformed fibroblasts but did not develop well-organized cell–cell contacts. A model is presented to describe how differences in the organization of the actin cytoskeleton could account for the structurally distinct responses to cell–cell contact by polarized fibroblastic cells versus nonpolarized epithelial cells.

Region-dependent dynamics of cAMP response element-binding protein phosphorylation in the basal ganglia

The cAMP response element-binding protein (CREB) is an activity-dependent transcription factor that is involved in neural plasticity. The kinetics of CREB phosphorylation have been suggested to be important for gene activation, with sustained phosphorylation being associated with downstream gene expression. If so, the duration of CREB phosphorylation might serve as an indicator for time-sensitive plastic changes in neurons. To screen for regions potentially involved in dopamine-mediated plasticity in the basal ganglia, we used organotypic slice cultures to study the patterns of dopamine- and calcium-mediated CREB phosphorylation in the major subdivisions of the striatum. Different durations of CREB phosphorylation were evoked in the dorsal and ventral striatum by activation of dopamine D1-class receptors. The same D1 stimulus elicited (i) transient phosphorylation (≤15 min) in the matrix of the dorsal striatum; (ii) sustained phosphorylation (≤2 hr) in limbic-related structures including striosomes, the nucleus accumbens, the fundus striati, and the bed nucleus of the stria terminalis; and (iii) prolonged phosphorylation (up to 4 hr or more) in cellular islands in the olfactory tubercle. Elevation of Ca2+ influx by stimulation of L-type Ca2+ channels, NMDA, or KCl induced strong CREB phosphorylation in the dorsal striatum but not in the olfactory tubercle. These findings differentiate the response of CREB to dopamine and calcium signals in different striatal regions and suggest that dopamine-mediated CREB phosphorylation is persistent in limbic-related regions of the neonatal basal ganglia. The downstream effects activated by persistent CREB phosphorylation may include time-sensitive neuroplasticity modulated by dopamine.

Stabilization of microtubule dynamics by estramustine by binding to a novel site in tubulin: A possible mechanistic basis for its antitumor action

The cellular targets for estramustine, an antitumor drug used in the treatment of hormone-refractory prostate cancer, are believed to be the spindle microtubules responsible for chromosome separation at mitosis. Estramustine only weakly inhibits polymerization of purified tubulin into microtubules by binding to tubulin (Kd, ≈30 μM) at a site distinct from the colchicine or the vinblastine binding sites. However, by video microscopy, we find that estramustine strongly stabilizes growing and shortening dynamics at plus ends of bovine brain microtubules devoid of microtubule-associated proteins at concentrations substantially below those required to inhibit polymerization of the microtubules. Estramustine strongly reduced the rate and extent both of shortening and growing, increased the percentage of time the microtubules spent in an attenuated state, neither growing nor shortening detectably, and reduced the overall dynamicity of the microtubules. Significantly, the combined suppressive effects of vinblastine and estramustine on the rate and extent of shortening and dynamicity were additive. Thus, like the antimitotic mechanisms of action of the antitumor drugs vinblastine and taxol, the antimitotic mechanism of action of estramustine may be due to kinetic stabilization of spindle microtubule dynamics. The results may explain the mechanistic basis for the benefit derived from combined use of estramustine with vinblastine or taxol, two other drugs that target microtubules, in the treatment of hormone-refractory prostate cancer.

Fluorescence and photobleaching dynamics of single light-harvesting complexes

Single light-harvesting complexes LH-2 from Rhodopseudomonas acidophila were immobilized on various charged surfaces under physiological conditions. Polarized light experiments showed that the complexes were situated on the surface as nearly upright cylinders. Their fluorescence lifetimes and photobleaching properties were obtained by using a confocal fluorescence microscope with picosecond time resolution. Initially all molecules fluoresced with a lifetime of 1 ± 0.2 ns, similar to the bulk value. The photobleaching of one bacteriochlorophyll molecule from the 18-member assembly caused the fluorescence to switch off completely, because of trapping of the mobile excitations by energy transfer. This process was linear in light intensity. On continued irradiation the fluorescence often reappeared, but all molecules did not show the same behavior. Some LH-2 complexes displayed a variation of their quantum yields that was attributed to photoinduced confinement of the excited states and thereby a diminution of the superradiance. Others showed much shorter lifetimes caused by excitation energy traps that are only ≈3% efficient. On repeated excitation some molecules entered a noisy state where the fluorescence switched on and off with a correlation time of ≈0.1 s. About 490 molecules were examined.

Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy

We have investigated the pH dependence of the dynamics of conformational fluctuations of green fluorescent protein mutants EGFP (F64L/S65T) and GFP-S65T in small ensembles of molecules in solution by using fluorescence correlation spectroscopy (FCS). FCS utilizes time-resolved measurements of fluctuations in the molecular fluorescence emission for determination of the intrinsic dynamics and thermodynamics of all processes that affect the fluorescence. Fluorescence excitation of a bulk solution of EGFP decreases to zero at low pH (pKa = 5.8) paralleled by a decrease of the absorption at 488 nm and an increase at 400 nm. Protonation of the hydroxyl group of Tyr-66, which is part of the chromophore, induces these changes. When FCS is used the fluctuations in the protonation state of the chromophore are time resolved. The autocorrelation function of fluorescence emission shows contributions from two chemical relaxation processes as well as diffusional concentration fluctuations. The time constant of the fast, pH-dependent chemical process decreases with pH from 300 μs at pH 7 to 45 μs at pH 5, while the time-average fraction of molecules in a nonfluorescent state increases to 80% in the same range. A second, pH-independent, process with a time constant of 340 μs and an associated fraction of 13% nonfluorescent molecules is observed between pH 8 and 11, possibly representing an internal proton transfer process and associated conformational rearrangements. The FCS data provide direct measures of the dynamics and the equilibrium properties of the protonation processes. Thus FCS is a convenient, intrinsically calibrated method for pH measurements in subfemtoliter volumes with nanomolar concentrations of EGFP.

Birefringence Imaging Directly Reveals Architectural Dynamics of Filamentous Actin in Living Growth ConesV⃞

We have investigated the dynamic behavior of cytoskeletal fine structure in the lamellipodium of nerve growth cones using a new type of polarized light microscope (the Pol-Scope). Pol-Scope images display with exquisite resolution and definition birefringent fine structures, such as filaments and membranes, without having to treat the cell with exogenous dyes or fluorescent labels. Furthermore, the measured birefringence of protein fibers in the thin lamellipodial region can be interpreted in terms of the number of filaments in the bundles. We confirmed that birefringent fibers are actin-based using conventional fluorescence-labeling methods. By recording movies of time-lapsed Pol-Scope images, we analyzed the creation and dynamic composition of radial fibers, filopodia, and intrapodia in advancing growth cones. The strictly quantitative information available in time-lapsed Pol-Scope images confirms previously deduced behavior and provides new insight into the architectural dynamics of filamentous actin.

Real-Time Imaging of the Axonal Transport of Granules Containing a Tissue Plasminogen Activator/Green Fluorescent Protein Hybrid

A hybrid protein, tPA/GFP, consisting of rat tissue plasminogen activator (tPA) and green fluorescent protein (GFP) was expressed in PC12 cells and used to study the distribution, secretory behavior, and dynamics of secretory granules containing tPA in living cells with a neuronal phenotype. High-resolution images demonstrate that tPA/GFP has a growth cone-biased distribution in differentiated cells and that tPA/GFP is transported in granules of the regulated secretory pathway that colocalize with granules containing secretogranin II. Time-lapse images of secretion reveal that secretagogues induce substantial loss of cellular tPA/GFP fluorescence, most importantly from growth cones. Time-lapse images of the axonal transport of granules containing tPA/GFP reveal a surprising complexity to granule dynamics. Some granules undergo canonical fast axonal transport; others move somewhat more slowly, especially in highly fluorescent neurites. Most strikingly, granules traffic bidirectionally along neurites to an extent that depends on granule accumulation, and individual granules can reverse their direction of motion. The retrograde component of this bidirectional transport may help to maintain cellular homeostasis by transporting excess tPA/GFP back toward the cell body. The results presented here provide a novel view of the axonal transport of secretory granules. In addition, the results suggest that tPA is targeted for regulated secretion from growth cones of differentiated cells, strategically positioning tPA to degrade extracellular barriers or to activate other barrier-degrading proteases during axonal elongation.

The Dynamics of Golgi Protein Traffic Visualized in Living Yeast Cells

We describe for the first time the visualization of Golgi membranes in living yeast cells, using green fluorescent protein (GFP) chimeras. Late and early Golgi markers are present in distinct sets of scattered, moving cisternae. The immediate effects of temperature-sensitive mutations on the distribution of these markers give clues to the transport processes occurring. We show that the late Golgi marker GFP-Sft2p and the glycosyltransferases, Anp1p and Mnn1p, disperse into vesicle-like structures within minutes of a temperature shift in sec18, sft1, and sed5 cells, but not in sec14 cells. This is consistent with retrograde vesicular traffic, mediated by the vesicle SNARE Sft1p, to early cisternae containing the target SNARE Sed5p. Strikingly, Sed5p itself moves rapidly to the endoplasmic reticulum (ER) in sec12 cells, implying that it cycles through the ER. Electron microscopy shows that Golgi membranes vesiculate in sec18 cells within 10 min of a temperature shift. These results emphasize the dynamic nature of Golgi cisternae and satisfy the kinetic requirements of a cisternal maturation model in which all resident proteins must undergo retrograde vesicular transport, either within the Golgi complex or from there to the ER, as anterograde cargo advances.

Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins

Fast excitation-driven fluctuations in the fluorescence emission of yellow-shifted green fluorescent protein mutants T203Y and T203F, with S65G/S72A, are discovered in the 10−6–10−3-s time range, by using fluorescence correlation spectroscopy at 10−8 M. This intensity-dependent flickering is conspicuous at high pH, with rate constants independent of pH and viscosity with a minor temperature effect. The mean flicker rate increases linearly with excitation intensity for at least three decades, but the mean dark fraction of the molecules undergoing these dynamics is independent of illumination intensity over ≈6 × 102 to 5 × 106 W/cm2. These results suggest that optical excitation establishes an equilibration between two molecular states of different spectroscopic properties that are coupled only via the excited state as a gateway. This reversible excitation-driven transition has a quantum efficiency of ≈10−3. Dynamics of external protonation, reversibly quenching the fluorescence, are also observed at low pH in the 10- to 100-μs time range. The independence of these two bright–dark flicker processes implies the existence of at least two separate dark states of these green fluorescent protein mutants. Time-resolved fluorescence measurements reveal a single exponential decay of the excited state population with 3.8-ns lifetime, after 500-nm excitation, that is pH independent. Our fluorescence correlation spectroscopy results are discussed in terms of recent theoretical studies that invoke isomerization of the chromophore as a nonradiative channel of the excited state relaxation.

Coalescent estimates of HIV-1 generation time in vivo

The generation time of HIV Type 1 (HIV-1) in vivo has previously been estimated using a mathematical model of viral dynamics and was found to be on the order of one to two days per generation. Here, we describe a new method based on coalescence theory that allows the estimate of generation times to be derived by using nucleotide sequence data and a reconstructed genealogy of sequences obtained over time. The method is applied to sequences obtained from a long-term nonprogressing individual at five sampling occasions. The estimate of viral generation time using the coalescent method is 1.2 days per generation and is close to that obtained by mathematical modeling (1.8 days per generation), thus strengthening confidence in estimates of a short viral generation time. Apart from the estimation of relevant parameters relating to viral dynamics, coalescent modeling also allows us to simulate the evolutionary behavior of samples of sequences obtained over time.

Femtosecond dynamics of DNA-mediated electron transfer

Diverse biophysical and biochemical studies have sought to understand electron transfer (ET) in DNA in part because of its importance to DNA damage and its repair. However, the dynamics and mechanisms of the elementary processes of ET in this medium are not fully understood and have been heavily debated. Two fundamental issues are the distance over which charge is transported and the time-scale on which the transport through the π-stack of the DNA base pairs may occur. With femtosecond resolution, we report direct observation in DNA of ultrafast ET, initiated by excitation of tethered ethidium (E), the intercalated electron acceptor (A); the electron donor (D) is 7-deazaguanine (Z), a modified base, placed at different, fixed distances from A. The ultrafast ET between these reactants in DNA has been observed with time constants of 5 ps and 75 ps and was found to be essentially independent of the D–A separation (10–17 Å). However, the ET efficiency does depend on the D–A distance. The 5-ps decay corresponds to direct ET observed from 7-deazaguanine but not guanine to E. From measurements of orientation anisotropies, we conclude that the slower 75-ps process requires the reorientation of E before ET, similar to E/nucleotide complexes in water. These results reveal the nature of ultrafast ET and its mechanism: in DNA, ET cannot be described as in proteins simply by a phenomenological parameter, β. Instead, the involvement of the base pairs controls the time scale and the degree of coherent transport.

Modeling the dynamics of human hair cycles by a follicular automaton

The hair follicle cycle successively goes through the anagen, catagen, telogen, and latency phases, which correspond, respectively, to hair growth, arrest, shedding, and absence before a new anagen phase is initiated. Experimental observations collected over a period of 14 years in a group of 10 male volunteers, alopecic and nonalopecic, allowed us to determine the characteristics of scalp hair follicle cycles. On the basis of these observations, we propose a follicular automaton model to simulate the dynamics of human hair cycles. The automaton model is defined by a set of rules that govern the stochastic transitions of each follicle between the successive states anagen, telogen, and latency, and the subsequent return to anagen. The transitions occur independently for each follicle, after time intervals given stochastically by a distribution characterized by a mean and a variance. The follicular automaton model accounts both for the dynamical transitions observed in a single follicle and for the behavior of an ensemble of independently cycling follicles. Thus, the model successfully reproduces the evolution of the fractions of follicle populations in each of the three phases, which fluctuate around steady-state or slowly drifting values. We apply the follicular automaton model to the study of spatial patterns of follicular growth that result from a spatially heterogeneous distribution of parameters such as the mean duration of anagen phase. When considering that follicles die or miniaturize after going through a critical number of successive cycles, the model can reproduce the evolution to hair patterns similar to well known types of diffuse or androgenetic alopecia.

Femtosecond dynamics of the forbidden carotenoid S1 state in light-harvesting complexes of purple bacteria observed after two-photon excitation

Time-resolved excited-state absorption intensities after direct two-photon excitation of the carotenoid S1 state are reported for light-harvesting complexes of purple bacteria. Direct excitation of the carotenoid S1 state enables the measurement of subsequent dynamics on a fs time scale without interference from higher excited states, such as the optically allowed S2 state or the recently discovered dark state situated between S1 and S2. The lifetimes of the carotenoid S1 states in the B800-B850 complex and B800-B820 complex of Rhodopseudomonas acidophila are 7 ± 0.5 ps and 6 ± 0.5 ps, respectively, and in the light-harvesting complex 2 of Rhodobacter sphaeroides ≈1.9 ± 0.5 ps. These results explain the differences in the carotenoid to bacteriochlorophyll energy transfer efficiency after S2 excitation. In Rps. acidophila the carotenoid S1 to bacteriochlorophyll energy transfer is found to be quite inefficient (φET1 <28%) whereas in Rb. sphaeroides this energy transfer is very efficient (φET1 ≈80%). The results are rationalized by calculations of the ensemble averaged time constants. We find that the Car S1 → B800 electronic energy transfer (EET) pathway (≈85%) dominates over Car S1 → B850 EET (≈15%) in Rb. sphaeroides, whereas in Rps. acidophila the Car S1 → B850 EET (≈60%) is more efficient than the Car S1 → B800 EET (≈40%). The individual electronic couplings for the Car S1 → BChl energy transfer are estimated to be approximately 5–26 cm−1. A major contribution to the difference between the energy transfer efficiencies can be explained by different Car S1 energy gaps in the two species.