Transitions Of Biomolecules Research Articles

Identifying mechanistically distinct pathways in kinetic transition networks.

We present an implementation of a scalable path deviation algorithm to find the k most kinetically relevant paths in a transition network, where each path is distinguished on the basis of having a distinct rate-limiting edge. The potential of the algorithm to identify distinct pathways that exist in separate regions of the configuration space is demonstrated for two benchmark systems with double-funnel energy landscapes, namely a model "three-hole" network embedded on a 2D potential energy surface and the cluster of 38 Lennard-Jones atoms (LJ38). The path cost profiles for the interbasin transitions of the two systems reflect the contrasting nature of the landscapes. There are multiple well-defined pathway ensembles for the three-hole system, whereas the transition in LJ38 effectively involves a single ensemble of pathways via disordered structures. A by-product of the algorithm is a set of edges that constitute a cut of the network, which is related to the discrete analog of a transition dividing surface. The algorithm ought to be useful for determining the existence, or otherwise, of competing mechanisms in large stochastic network models of dynamical processes and for assessing the kinetic relevance of distinguishable ensembles of pathways. This capability will provide insight into conformational transitions in biomolecules and other complex slow processes.

Protocols of IATC, DSC, and PPC: The Multistate Structural Transition of Cytochrome c.

The recent development of high-precision calorimeters allows us to monitor the structural transition of biomolecules by calorimetry and thereby characterize the thermodynamic property changes accompanying three-dimensional structure changes. We developed isothermal acid-titration calorimetry (IATC) to evaluate the pH dependence of protein enthalpy. Using the double deconvolution method with precise differential scanning calorimetry (DSC), we revealed that the MG state is an equilibrium intermediate state of the reversible thermal three-state transition of the protein, and we successfully determined its volumetric properties by pressure perturbation calorimetry (PPC). Our findings underscore the importance of a precise calorimetry and analysis model for protein research.

A probabilistic network model for structural transitions in biomolecules.

Biological macromolecules often undergo large conformational rearrangements during a functional cycle. To simulate these structural transitions with full atomic detail typically demands extensive computational resources. Moreover, it is unclear how to incorporate, in a principled way, additional experimental information that could guide the structural transition. This article develops a probabilistic model for conformational transitions in biomolecules. The model can be viewed as a network of anharmonic springs that break, if the experimental data support the rupture of bonds. Hamiltonian Monte Carlo in internal coordinates is used to infer structural transitions from experimental data, thereby sampling large conformational transitions without distorting the structure. The model is benchmarked on a large set of conformational transitions. Moreover, we demonstrate the use of the probabilistic network model for integrative modeling of macromolecular complexes based on data from crosslinking followed by mass spectrometry.

Metadynamics Enhanced Markov Modeling of Protein Dynamics.

Enhanced sampling techniques represent a versatile approach to account for rare conformational transitions in biomolecules. A particularly promising strategy is to combine massive parallel computing of short molecular dynamics (MD) trajectories (to sample the free energy landscape of the system) with Markov state modeling (to rebuild the kinetics from the sampled data). To obtain well-distributed initial structures for the short trajectories, it is proposed to employ metadynamics MD, which quickly sweeps through the entire free energy landscape of interest. Being only used to generate initial conformations, the implementation of metadynamics can be simple and fast. The conformational dynamics of helical peptide Aib9 is adopted to discuss various technical issues of the approach, including metadynamics settings, minimal number and length of short MD trajectories, and the validation of the resulting Markov models. Using metadynamics to launch some thousands of nanosecond trajectories, several Markov state models are constructed that reveal that previous unbiased MD simulations of in total 16 μs length cannot provide correct equilibrium populations or qualitative features of the pathway distribution of the short peptide.

Direct measurement of sequence-dependent transition path times and conformational diffusion in DNA duplex formation

The conformational diffusion coefficient, D, sets the timescale for microscopic structural changes during folding transitions in biomolecules like nucleic acids and proteins. D encodes significant information about the folding dynamics such as the roughness of the energy landscape governing the folding and the level of internal friction in the molecule, but it is challenging to measure. The most sensitive measure of D is the time required to cross the energy barrier that dominates folding kinetics, known as the transition path time. To investigate the sequence dependence of D in DNA duplex formation, we measured individual transition paths from equilibrium folding trajectories of single DNA hairpins held under tension in high-resolution optical tweezers. Studying hairpins with the same helix length but with G:C base-pair content varying from 0 to 100%, we determined both the average time to cross the transition paths, τtp, and the distribution of individual transit times, PTP(t). We then estimated D from both τtp and PTP(t) from theories assuming one-dimensional diffusive motion over a harmonic barrier. τtp decreased roughly linearly with the G:C content of the hairpin helix, being 50% longer for hairpins with only A:T base pairs than for those with only G:C base pairs. Conversely, D increased linearly with helix G:C content, roughly doubling as the G:C content increased from 0 to 100%. These results reveal that G:C base pairs form faster than A:T base pairs because of faster conformational diffusion, possibly reflecting lower torsional barriers, and demonstrate the power of transition path measurements for elucidating the microscopic determinants of folding.

Protein-Style Dynamical Transition in a Non-Biological Polymer and a Non-Aqueous Solvent.

Temperature-dependent onset of apparent anharmonicity in the microscopic dynamics of hydrated proteins and other biomolecules has been known as protein dynamical transition for the last quarter of a century. Using neutron scattering and molecular dynamics simulation, techniques most often associated with protein dynamical transition studies, we have investigated the microscopic dynamics of one of the most common polymers, polystyrene, which was exposed to toluene vapor, mimicking the process of protein hydration from water vapor. Polystyrene with adsorbed toluene is an example of a solvent-solute system, which, unlike biopolymers, is anhydrous and lacks hydrogen bonding. Nevertheless, it exhibits the essential traits of the dynamical transition in biomolecules, such as a specific dependence of the microscopic dynamics of both solvent and host on the temperature and the amount of solvent adsorbed. We conclude that the protein dynamical transition is a manifestation of a universal solvent-solute dynamical relationship, which is not specific to either biomolecules as solute, or aqueous media as solvent, or even a particular type of interactions between solvent and solute.

Water and lysozyme: Some results from the bending and stretching vibrational modes

The dynamic or glass transition in biomolecules is important to their functioning. Also essential is the transition between the protein native state and the unfolding process. To better understand these transitions, we use Fourier transform infrared spectroscopy to study the vibrational bending and stretching modes of hydrated lysozymes across a wide temperature range. We find that these transitions are triggered by the strong hydrogen bond coupling between the protein and hydration water. More precisely, we demonstrate that in both cases the water properties dominate the evolution of the system. We find that two characteristic temperatures are relevant: in the supercooled regime of confined water, the fragile-to-strong dynamic transition occurs at T L , and in the stable liquid phase, T* ≈ 315 ± 5 K characterizes the behavior of both isothermal compressibility K T (T,P) and the coefficient of thermal expansion a P (T,P).

Molecular Dynamics and NMR Shed Light on Motions Underpinning Dynamical Transitions in Biomolecules

The intrinsic dynamics of biological macromolecules covers a wide range of timescales, which may be adjusted to adapt to a range of temperatures. In the 1980s, several biophysical investigations showed a change in the dynamical behavior of myoglobin at a temperature at ∼220–230 K (1–3). This dynamical transition, which manifests itself in a drastic change of the temperature dependence of signals related to the amplitude of atomic motions within the protein and of thermodynamic properties, has since then attracted much attention, and it has been observed in many other proteins, as well as in both DNA and RNA, in the same temperature range (4,5).

The influence of water on protein properties.

The "dynamic" or "glass" transition in biomolecules is as important to their functioning as the folding process. This transition occurs in the low temperature regime and has been related to the onset of biochemical activity that is dependent on the hydration level. This protein transition is believed to be triggered by the strong hydrogen bond coupling in the hydration water. We study the vibrational bending mode and measure it using Fourier Transform Infrared spectroscopy. We demonstrate that at the molecular level the hydration water bending mode bonds the C=O and N-H peptide groups, and find that the temperature of the "dynamic" protein transition is the same as the fragile-to-strong dynamic transition in confined water. The fragile-to-strong dynamic transition in water governs the nature of the H bonds between water and peptides and appears to be universal in supercooled glass-forming liquids.

A Simple Coarse-Grained Model to Map the Transition Pathway Between Two Stable Conformations using the Anisotropic Elastic Network Model

Conformational transitions in biomolecules, especially proteins, play an important role in signaling and regulation of various biological processes. Here we propose a fast and simple method for constructing a transition pathway between two stable conformations of a protein. The protein is represented as a simplified coarse-grained (CG) model with a single site located at the C-alpha atom of each residue. The energy function of the two-state CG model is approximated by the anisotropic network model (ANM) harmonic energy surfaces of the end-states. The simple two-state energy surface comprises two local minima centered on the positions of the stable states and the system resides in one of these minima. There is a cusp with discontinuous first derivative in the multi-dimensional configuration space of the system, which acts as the transition state surface for the two-state potential. Given this simple prescription, two structures constrained to remain similar to one another but each residing on the opposite sides of the cusp, are optimized using energy minimization. This virtual “dumbbell” of two structures is then used as a crude approximation to the transition state. The pathway in the multi-dimensional space is constructed by letting these two structures slide down on their ANM surface using steepest descent energy minimization until the stable end-points are reached. This simple two-state ANM model was applied to explore the multi-dimensional and collective character of the conformational transition pathways in several systems of biological significance, including adenylate kinase, leucine transporter, sarcoplasmic reticulum Ca-ATPase and the glutamate transporter.

Efficient Simulation of Complex Transition Pathways using a Weighted Ensemble Based String Method

Large-scale conformational transitions in biomolecules occur on complex, high-dimensional free energy surfaces. Simulating these transitions is often challenging due to the mismatch between the timescales required to traverse the energetic landscape and those accessible by conventional simulation techniques. The “weighted ensemble” (WE) path sampling method is a rigorous technique for simulating this class of rare transitions. We extend the WE method by combining it with a string method to adaptively refine the set of order parameters used to enhance sampling along the transition pathway. This permits sampling transitions in the space of many order parameters for a wide range of equilibrium and non-equilibrium processes. From these simulations, accurate estimates of steady state conformational distributions and reaction rates can be obtained, even for systems with complex transition pathways that may involve metastable intermediates. We demonstrate the application of this method using two simple models of driven Brownian motion, protein conformational change with a coarse-grained model, and fully-atomistic models.

Эффективные генераторы псевдослучайных чисел при молекулярном моделировании на видеокартах

Динамика Ланжевена, метод Монте-Карло и моделирование молекулярной динамики в неявном растворителе требуют больших массивов случайных чисел на каждом шаге расчета. Мы исследовали два подхода в реализации генераторов на графических процессорах. Первый реализует последовательный алгоритм генератора на каждом потоке в отдельности. Второй основан на возможности взаимодействия между потоками и реализует общий алгоритм на всех потоках в целом. Мы покажем использование этих подходов на примере алгоритмов Ran 2, Hybrid Taus и Lagged Fibonacci. Для проверки случайности полученных чисел мы использовали разработанные генераторы при моделировании динамики Ланжевена N независимых гармонических осцилляторов в термостате. Это позволило нам оценить статистические характеристики генераторов. Мы также исследовали производительность, использование памяти и ускорение, получаемое при переносе алгоритма с центрального на графический процессор.

Crowding Induced Conformational Switch

In this talk I will describe a general theoretical framework for describing conformational transitions in biomolecules and biomolecular complexes. The theory is based on the concept of depletion attraction well known in colloid science. The predictions of theory and simulations using coarse-grained models will be compared to specific experiments.

Accommodating Drift in Hidden Markov Analysis of Single-Molecule Data

Single-molecule techniques are increasingly used to measure state transitions in biomolecules. These data are typically a noisy time series with discrete transitions that reflect underlying distinct states; examples include the opening and closing of DNA hairpins, and the folding and unfolding of proteins. Hidden Markov models (HMMs) have been successfully used to infer transitions between the underlying states from noisy data. However, HMMs are typically applied to ratiometric data (e.g., FRET studies of RNA folding) and do not perform well on data that include drift. Yet, drift is common in real-space records from optical traps and atomic force microscopes. We developed a HMM that accommodates experimental drift using low-order Fourier modes. We use simulated traces to demonstrate the improved performance of our method and illustrate its use on measurements of single TATA-box binding proteins bending and unbending DNA.

Comment on “Glass Transition in Biomolecules and the Liquid-Liquid Critical Point of Water”

Comment on “Glass Transition in Biomolecules and the Liquid-Liquid Critical Point of Water”

Optimizing the Performance of Bias-Exchange Metadynamics: Folding a 48-Residue LysM Domain Using a Coarse-Grained Model

Computer simulation of complex conformational transitions in biomolecules, such as protein folding, is considered one of the main goals of computational chemistry. A recently developed methodology, bias-exchange metadynamics, was successfully used to reversibly fold some small globular proteins. The objective of this work is to further improve this promising technique. This is accomplished by searching for the optimal set of parameters that enable folding a 48 amino acid protein, 1E0G , in the shortest possible time, using a coarse-grained force field UNRES. It is shown that bias-exchange metadynamics, if appropriately optimized, allows finding the folded state of 1E0G significantly faster than normal replica exchange.

Conformational Changes of Lipids in Bilayers at the Dynamical Transition Near 200 K Seen by Raman Scattering

Dynamical transition in biomolecules (proteins, membranes, etc.) is the phenomenon of increase of mean square atomic displacements, when temperature increases above 180-230 K. This increase is seen in neutron scattering and is ascribed to the increase of anharmonical motion of hydrogen atoms in biomolecules. In this work, Raman scattering study was performed for model synthetic membranes of dipalmitoylphosphatidylcholine in the spectral range of C-C vibrations (1050-1150 cm(-1)). It was demonstrated that dynamical transition is accompanied by appearance of newly achievable conformations of the lipid tails. In particular, the portion of the all-trans conformations decreases above the temperature of the dynamical transition. The data are compared with simple theoretical models.

Molecular simulation of conformational transitions in biomolecules using a combination of structure-based potential and empirical valence bond theory

The functions of biological macromolecules are inherently linked to their complex conformational behaviour. As a consequence of this complexity, the corresponding potential energy landscapes encompass multiple minima. Some of the intermediate structures between initial and final states can be characterized by experimental techniques. Computer simulations can explore the dynamics of individual states and bring these together to rationalize the overall process. Here, we show that the experimental structures can be exploited to define simple yet accurate atomistic structure-based potentials (SBP) that describe individual conformational states. These individual states can then be coupled by using the empirical valence bond (EVB) model. The overall energy landscape can easily be parameterised to reproduce available kinetic and thermodynamic data. We illustrate the procedure by applying the EVB-SBP method to study base flipping in B-DNA. Simple SBP is shown to reproduce structural ensembles obtained by using more refined force field simulations. Umbrella sampling in conjunction with the general energy gap reaction coordinate enables us to study alternative molecular pathways efficiently. We find that base rotation takes place via both grooves of the B-DNA with a marked preference for the major groove pathway. We also identify an unusual high-energy off-pathway intermediate that may appear if the base closing process is initiated from a syn base.

Calorimetry and Thermodynamics in Drug Design

Modern instrumentation for calorimetry permits direct determination of enthalpy values for binding reactions and conformational transitions in biomolecules. Complete thermodynamic profiles consisting of free energy, enthalpy, and entropy may be obtained for reactions of interest in a relatively straightforward manner. Such profiles are of enormous value in drug design because they provide information about the balance of driving forces that cannot be obtained from structural or computational methods alone. This perspective shows several examples of the insight provided by thermodynamic data in drug design.

Coarse-grained models reveal functional dynamics--I. Elastic network models--theories, comparisons and perspectives.

In this review, we summarize the progress on coarse-grained elastic network models (CG-ENMs) in the past decade. Theories were formulated to allow study of conformational dynamics in time/space frames of biological interest. Several highlighted models and their underlined hypotheses are introduced in physical depth. Important ENM offshoots, motivated to reproduce experimental data as well as to address the slow-mode-encoded configurational transitions, are also introduced. With the theoretical developments, computational cost is significantly reduced due to simplified potentials and coarse-grained schemes. Accumulating wealth of data suggest that ENMs agree equally well with experiment in describing equilibrium dynamics despite their distinct potentials and levels of coarse-graining. They however do differ in the slowest motional components that are essential to address large conformational changes of functional significance. The difference stems from the dissimilar curvatures of the harmonic energy wells described for each model. We also provide our views on the predictability of 'open to close' (open-->close) transitions of biomolecules on the basis of conformational selection theory. Lastly, we address the limitations of the ENM formalism which are partially alleviated by the complementary CG-MD approach, to be introduced in the second paper of this two-part series.