Nanosecond Motions in Proteins Impose Bounds on the Timescale Distributions of Local Dynamics

We elucidate the physics of protein dynamical transition via 10-100-ns molecular dynamics simulations at temperatures spanning 160-300 K. By tracking the energy fluctuations, we show that the protein dynamical transition is marked by a crossover from nonstationary to stationary processes that underlie the dynamics of protein motions. A two-timescale function captures the nonexponential character of backbone structural relaxations. One timescale is attributed to the collective segmental motions and the other to local relaxations. The former is well defined by a single-exponential, nanosecond decay, operative at all temperatures. The latter is described by a set of processes that display a distribution of timescales. Although their average remains on the picosecond timescale, the distribution is markedly contracted at the onset of the transition. It is shown that the collective motions impose bounds on timescales spanned by local dynamical processes. The nonstationary character below the transition implicates the presence of a collection of substates whose interactions are restricted. At these temperatures, a wide distribution of local-motion timescales, extending beyond that of nanoseconds, is observed. At physiological temperatures, local motions are confined to timescales faster than nanoseconds. This relatively narrow window makes possible the appearance of multiple channels for the backbone dynamics to operate.     

Functional Dynamics of Hexameric Helicase Probed by Hydrogen Exchange and Simulation

The biological function of large macromolecular assemblies depends on their structure and their dynamics over a broad range of timescales; for this reason, it is a significant challenge to investigate these assemblies using conventional experimental techniques. One of the most promising experimental techniques is hydrogen-deuterium exchange detected by mass spectrometry. Here, we describe to our knowledge a new computational method for quantitative interpretation of deuterium exchange kinetics and apply it to a hexameric viral helicase P4 that unwinds and translocates RNA into a virus capsid at the expense of ATP hydrolysis. Room-temperature dynamics probed by a hundred nanoseconds of all-atom molecular dynamics simulations is sufficient to predict the exchange kinetics of most sequence fragments and provide a residue-level interpretation of the low-resolution experimental results. The strategy presented here is also a valuable tool to validate experimental data, e.g., assignments, and to probe mechanisms that cannot be observed by x-ray crystallography, or that occur over timescales longer than those that can be realistically simulated, such as the opening of the hexameric ring.     

Functional Dynamics of Hexameric Helicase Probed by Hydrogen Exchange and Simulation

The biological function of large macromolecular assemblies depends on their structure and their dynamics over a broad range of timescales; for this reason, it is a significant challenge to investigate these assemblies using conventional experimental techniques. One of the most promising experimental techniques is hydrogen-deuterium exchange detected by mass spectrometry. Here, we describe to our knowledge a new computational method for quantitative interpretation of deuterium exchange kinetics and apply it to a hexameric viral helicase P4 that unwinds and translocates RNA into a virus capsid at the expense of ATP hydrolysis. Room-temperature dynamics probed by a hundred nanoseconds of all-atom molecular dynamics simulations is sufficient to predict the exchange kinetics of most sequence fragments and provide a residue-level interpretation of the low-resolution experimental results. The strategy presented here is also a valuable tool to validate experimental data, e.g., assignments, and to probe mechanisms that cannot be observed by x-ray crystallography, or that occur over timescales longer than those that can be realistically simulated, such as the opening of the hexameric ring.     

How does it really move? Recent progress in the investigation of protein nanosecond dynamics by NMR and simulation

Nuclear magnetic resonance (NMR) spin relaxation experiments currently probe molecular motions on timescales from picoseconds to nanoseconds. The detailed interpretation of these motions in atomic detail benefits from complementarity with the results from molecular dynamics (MD) simulations. In this mini-review, we describe the recent developments in experimental techniques to study the backbone dynamics from ¹⁵N relaxation and side-chain dynamics from ¹³C relaxation, discuss the different analysis approaches from model-free to dynamics detectors, and highlight the many ways that NMR relaxation experiments and MD simulations can be used together to improve the interpretation and gain insights into protein dynamics.     

Analysis of red-fluorescent proteins provides insight into dark-state conversion and photodegradation

Fluorescent proteins (FPs) are powerful tools that permit real-time visualization of cellular processes. The utility of a given FP for a specific experiment depends strongly on its effective brightness and overall photostability. However, the brightness of FPs is limited by dark-state conversion (DSC) and irreversible photobleaching, which occur on different timescales. Here, we present in vivo ensemble assays for measuring DSC and irreversible photobleaching under continuous and pulsed illumination. An analysis of closely related red FPs reveals that DSC and irreversible photobleaching are not always connected by the same mechanistic pathway. DSC occurs out of the first-excited singlet state, and its magnitude depends predominantly on the kinetics for recovery out of the dark state. The experimental results can be replicated through kinetic simulations of a four-state model of the electronic states. The methodology presented here allows light-driven dynamics to be studied at the ensemble level over six orders of magnitude in time (microsecond to second timescales).     

Numerical studies of the membrane fluorescent dyes dynamics in ground and excited states

Fluorescence methods are widely used in studies of biological and model membranes. The dynamics of membrane fluorescent markers in their ground and excited electronic states and correlations with their molecular surrounding within the fully hydrated phospholipid bilayer are still not well understood. In the present work, Quantum Mechanical (QM) calculations and Molecular Dynamics (MD) simulations are used to characterize location and interactions of two membrane polarity probes (Prodan; 6-propionyl-2-dimethylaminonaphthalene and its derivative Laurdan; 2-dimethylamino-6-lauroylnaphthalene) with the dioleoylphosphatidylcholine (DOPC) lipid bilayer model. MD simulations with fluorophores in ground and excited states are found to be a useful tool to analyze the fluorescent dye dynamics and their immediate vicinity. The results of QM calculations and MD simulations are in excellent agreement with available experimental data. The calculation shows that the two amphiphilic dyes initially placed in bulk water diffuse within 10 ns towards their final location in the lipid bilayer. Analysis of solvent relaxation process in the aqueous phase occurs on the picoseconds timescale whereas it takes nanoseconds at the lipid/water interface. Four different relaxation time constants, corresponding to different relaxation processes, where observed when the dyes were embedded into the membrane.     

Plant propagation fronts and wind dispersal: an analytical model to upscale from seconds to decades using superstatistics

Scale separation crossing many orders of magnitude is a consistent challenge in the ecological sciences. Wind dispersal of seed that generates plant propagation fronts is a typical case where timescales range from less than a second for fast turbulent processes to interannual timescales governing plant growth and climatic forcing. We show that the scale separation can be overcome by developing mechanistic and statistical links between processes at the different timescales. A mechanistic model is used to scale up from the turbulent regime to hourly timescales, while a superstatistical approach is used to relate the half-hourly timescales to annual vegetation migration speeds. We derive a semianalytical model to predict vegetation front movement as a function of wind-forcing statistics and characteristics of the species being dispersed. This model achieves better than order-of-magnitude agreement in a case study of tree dispersal from the early Holocene, a marked improvement over diffusion models. Plant migration is shown to depend nonlinearly on the wind environment forcing the movement but linearly on most physiological parameters. Applications of these analytical results to parameterizing models of plant dispersion and the implications of the superstatistical approach for addressing other ecological problems plagued by similar "dimensionality curses" are outlined.     

Mechanistic models of seed dispersal by wind

Over the past century, various mechanistic models have been developed to estimate the magnitude of seed dispersal by wind, and to elucidate the relative importance of physical and biological factors affecting this passive transport process. The conceptual development has progressed from ballistic models, through models incorporating vertically variable mean horizontal windspeed and turbulent excursions, to models accounting for discrepancies between airflow and seed motion. Over hourly timescales, accounting for turbulent fluctuations in the vertical velocity component generally leads to a power-law dispersal kernel that is censored by an exponential cutoff far from the seed source. The parameters of this kernel vary with the flow field inside the canopy and the seed terminal velocity. Over the timescale of a dispersal season, with mean wind statistics derived from an “extreme-value” distribution, these distribution-tail effects are compounded by turbulent diffusion to yield seed dispersal distances that are two to three orders of magnitude longer than the corresponding ballistic models. These findings from analytic models engendered explicit simulations of the effects of turbulence on seed dispersal using computationally intensive fluid dynamics tools. This development marks a bifurcation in the approaches to wind dispersal, seeking either finer resolution of the dispersal mechanism at the scale of a single dispersal event, or mechanistically derived analytical dispersal kernels needed to resolve long-term and large-scale processes such as meta-population dynamics and range expansion. Because seed dispersal by wind is molded by processes operating over multiple scales, new insights will require novel theoretical tactics that blend these two approaches while preserving the key interactions across scales.     

Out of the Randomness: Correlating Noise in Biological Systems

The study of the dynamics of biological systems requires one to follow relaxation processes in time with micron-size spatial resolution. This need has led to the development of different fluorescence correlation techniques with high spatial resolution and a tremendous (from nanoseconds to seconds) temporal dynamic range. Spatiotemporal information can be obtained even on complex dynamic processes whose time evolution is not forecast by simple Brownian diffusion. Our discussion of the most recent applications of image correlation spectroscopy to the study of anomalous sub- or superdiffusion suggests that this field still requires the development of multidimensional image analyses based on analytical models or numerical simulations. We focus in particular on the framework of spatiotemporal image correlation spectroscopy and examine the critical steps in getting information on anomalous diffusive processes from the correlation maps. We point out how a dual space-time correlative analysis, in both the direct and the Fourier space, can provide quantitative information on superdiffusional processes when these are analyzed through an empirical model based on intermittent active dynamics. We believe that this dual space-time analysis, potentially amenable to mathematical treatment and to the exact fit of experimental data, could be extended to include the rich phenomenology of subdiffusive processes, thereby quantifying relevant parameters for the various motivating biological problems of interest.     

Single Pair Förster Resonance Energy Transfer: A Versatile Tool To Investigate Protein Conformational Dynamics

Conformational changes of proteins and other biomolecules play a fundamental role in their functional mechanism. Single pair Förster resonance energy transfer (spFRET) offers the possibility to detect these conformational changes and dynamics, and to characterize their underlying kinetics. Using spFRET on microscopes with different modes of detection, dynamic timescales ranging from nanoseconds to seconds can be quantified. Confocal microscopy can be used as a means to analyze dynamics in the range of nanoseconds to milliseconds, while total internal reflection fluorescence (TIRF) microscopy offers information about conformational changes on timescales of milliseconds to seconds. While the existence of dynamics can be directly inferred from the FRET efficiency time trace or the correlation of FRET efficiency and fluorescence lifetime, additional computational approaches are required to extract the kinetic rates of these dynamics, a short overview of which is given in this review.

     

The fractal nature of nature: power laws,ecological complexity and biodiversity

Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science.     

Local and long range potentials for heparin-protein systems for coarse-grained simulations

Heparin belongs to glycosaminoglycans (GAGs), a class of periodic linear anionic polysaccharides, which are functionally important components of the extracellular matrix owing to their interactions with various protein targets. Heparin is known to be involved in many cell signaling processes, while the experimental data available for heparin are significantly more abundant than for other GAGs. At the same time, the length and conformational flexibility of the heparin represent major challenges for its theoretical analysis. Coarse-grained (CG) approaches, which enable us to extend the size- and time-scale by orders of magnitude owing to reduction of system representation, appear, therefore, to be useful in simulating these systems. In this work, by using umbrella-sampling molecular dynamics simulations, we derived and parameterized the CG backbone-local potentials of heparin chains and the orientational potentials for the interactions of heparin with amino acid side chains to be further included in the physics-based Unified Coarse-Grained Model of biological macromolecules. With these potentials, simulations of extracellular matrix processes where both heparin and multiple proteins participate will be possible.     

Protein dynamics from solution NMR

Solution nuclear magnetic resonance (NMR) spectroscopy is unique in its ability to elucidate the details of atomic-level structural and dynamical properties of biological macromolecules under native-like conditions. Recent advances in NMR techniques and protein sample preparation now allow comprehensive investigation of protein dynamics over timescales ranging 14 orders of magnitude at nearly every atomic site. Thus, solution NMR is poised to reveal aspects of the physico-chemical properties that govern the ensemble distribution of protein conformers and the dynamics of their interconversion. We review these advances as well as their recent application to the study of proteins.     

Protein dynamics from solution NMR: theory and applications

Solution nuclear magnetic resonance (NMR) spectroscopy is unique in its ability to elucidate the details of atomic-level structural and dynamical properties of biological macromolecules under native-like conditions. Recent advances in NMR techniques and protein sample preparation now allow comprehensive investigation of protein dynamics over timescales ranging 14 orders of magnitude at nearly every atomic site. Thus, solution NMR is poised to reveal aspects of the physico-chemical properties that govern the ensemble distribution of protein conformers and the dynamics of their interconversion. We review these advances as well as their recent application to the study of proteins.     

New techniques in fast time-resolved structure determination.

New techniques in fast time-resolved X-ray crystallography provide a different approach to understanding the structural basis of protein function. Two biological systems have been studied as part of the refinement of these techniques, and have actually spurred new ideas in time-resolved structural studies. The dissociation of carbon monoxide from carbon-monoxy myoglobin has earlier been investigated over a time range spanning 18 orders of magnitude (femtoseconds to hours) using spectroscopic methods. Rapid time-resolved determination of the entire myoglobin structure made it possible to determine both the position of the CO after photodissociation and the entire globin structure, over a time range from nanoseconds to milliseconds, during which the heme and globin relax and the carbon monoxide rebinds. Photoactive yellow protein, a relative newcomer to biophysical research, has a fully-reversible photocycle containing several spectrally distinct intermediates. Identifying and solving the structures of each intermediate is the initial goal in time-resolved studies on this protein and will contribute to a greater understanding of the biological process of light driven signal transduction.     

Periodic Forces Trigger a Complex Mechanical Response in Ubiquitin

Mechanical forces govern physiological processes in all living organisms. Many cellular forces, for example, those generated in cyclic conformational changes of biological machines, have repetitive components. In apparent contrast, little is known about how dynamic protein structures respond to periodic mechanical information. Ubiquitin is a small protein found in all eukaryotes. We developed molecular dynamics simulations to unfold single and multimeric ubiquitins with periodic forces. By using a coarse-grained representation, we were able to model forces with periods about 2 orders of magnitude longer than the protein's relaxation time. We found that even a moderate periodic force weakened the protein and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. A complex dynamic response with secondary structure refolding and an increasing importance of local interactions was revealed. Importantly, repetitive forces with broadly distributed frequencies elicited very similar molecular responses compared to fixed-frequency forces. When testing the influence of pulling geometry on ubiquitin's mechanical stability, it was found that the linkage involved in the mechanical degradation of cellular proteins renders the protein remarkably insensitive to periodic forces. We also devised a complementary kinetic energy landscape model that traces these observations and explains periodic-force, single-molecule measurements. In turn, this analytical model is capable of predicting dynamic protein responses. These results provide new insights into ubiquitin mechanics and a potential mechanical role during protein degradation, as well as first frameworks for dynamic protein stability and the modeling of repetitive mechanical processes.     

Pathway engineering via quorum sensing and sRNA riboregulators-interconnected networks and controllers

The advent of genetic engineering has elevated our level of comprehension of cellular processes and functions. A natural progression of these findings is determining not only how these processes function within individual cells but also within a community. Bacterial cells monitor the conditions and microorganisms in their vicinity by producing, releasing and sensing chemical-signaling molecules. When a specific cell-density threshold is reached, a quorum is perceived, gene expression profiles are altered and the community orchestrates activities that are more effective en masse. This communication mechanism, in the language of autoinducers (AI), is referred to as quorum sensing (QS). It has become increasingly evident that while scientists attempt to decipher the intricacies of cellular communication and quorum sensing networks, we must remain conscious of the broader context of how a cell may identify itself in the environment and how this also impacts QS. Importantly, these phenomena span time and length scales by several orders in magnitude. Though the revelation of small RNAs, as both sensing and regulatory elements participating in the quorum sensing cascade, has connected new pieces of the puzzle, it has also added a new tier of uncertainty. The complexity of quorum sensing networks makes resolution of its diverse mechanisms difficult. The ability to design simpler networks with defined, more predictable or even "modular" elements will help elucidate these actions. Because it embraces innovative concepts of biological design accommodating the many length and time scales at play, synthetic biology serves as one of the most promising platforms for describing QS phenomena as well as enabling novel implementation strategies for biotechnological application.     

Structured modelling of animal cells

Recent advances in computer technology have promoted the design and use of detailed, computer-based models for biological systems. For many non-biological systems, the complexity of such simulations may be considered inappropriate and unwieldy, but in biological systems, and more specifically in animal cell culture, this level of complexity simply mimics what is only beginning to be understood about metabolic processs. With this in mind, we contend that complex, structured models are vital tools in the investigation of fundamental biological processes. An example of such a simulation, which describes the commercial production of therapeutic proteins by animal cell cultures, is considered.     

Biological responses to environmental heterogeneity under future ocean conditions

Organisms are projected to face unprecedented rates of change in future ocean conditions due to anthropogenic climate‐change. At present, marine life encounters a wide range of environmental heterogeneity from natural fluctuations to mean climate change. Manipulation studies suggest that biota from more variable marine environments have more phenotypic plasticity to tolerate environmental heterogeneity. Here, we consider current strategies employed by a range of representative organisms across various habitats – from short‐lived phytoplankton to long‐lived corals – in response to environmental heterogeneity. We then discuss how, if and when organismal responses (acclimate/migrate/adapt) may be altered by shifts in the magnitude of the mean climate‐change signal relative to that for natural fluctuations projected for coming decades. The findings from both novel climate‐change modelling simulations and prior biological manipulation studies, in which natural fluctuations are superimposed on those of mean change, provide valuable insights into organismal responses to environmental heterogeneity. Manipulations reveal that different experimental outcomes are evident between climate‐change treatments which include natural fluctuations vs. those which do not. Modelling simulations project that the magnitude of climate variability, along with mean climate change, will increase in coming decades, and hence environmental heterogeneity will increase, illustrating the need for more realistic biological manipulation experiments that include natural fluctuations. However, simulations also strongly suggest that the timescales over which the mean climate‐change signature will become dominant, relative to natural fluctuations, will vary for individual properties, being most rapid for CO₂ (~10 years from present day) to 4 decades for nutrients. We conclude that the strategies used by biota to respond to shifts in environmental heterogeneity may be complex, as they will have to physiologically straddle wide‐ranging timescales in the alteration of ocean conditions, including the need to adapt to rapidly rising CO₂ and also acclimate to environmental heterogeneity in more slowly changing properties such as warming.     

Sampling efficiency in explicit and implicit membrane environments studied by peptide folding simulations

Efficient exploration of the conformational space of peptides embedded in biological membranes is vital to extract converged thermodynamic and kinetic data from simulation studies. Recently developed implicit membrane models promise vast increases in sampling efficiency compared to explicit membrane simulations, allowing for ab initio structure prediction and functional studies. In this study, a previously developed implicit membrane model, based on the generalized Born method, is compared to an explicit di‐palmitoyl‐phosphatidyl‐choline lipid bilayer and an octane slab membrane mimic. The complete folding process of a synthetic 16‐residue peptide is compared using these three setups. Since the comparison requires the entire folding pathway to be captured, individual simulations ranged up to 3 μs of MD. A quantitative sampling comparison using a wide range of performance metrics reveals that the implicit membrane model is at least 2 orders of magnitude more efficient than the simplest explicit setups. Proteins 2009. © 2008 Wiley‐Liss, Inc.