Aspects of Protein Reaction Dynamics: Deviations from Simple Behavior

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Increasing the accuracy of exchange parameters reporting on slow dynamics by performing CEST experiments with 'high' B1 fields

Over the last decade chemical exchange saturation transfer (CEST) NMR methods have emerged as powerful tools to characterize biomolecular conformational dynamics occurring between a visible major state and 'invisible' minor states. The ability of the CEST experiment to detect these minor states, and provide precise exchange parameters, hinges on using appropriate B1 field strengths during the saturation period. Typically, a pair of B1 fields with ω1 (=2πB1) values around the exchange rate kex are chosen. Here we show that the transverse relaxation rate of the minor state resonance (R2,B) also plays a crucial role in determining the B1 fields that lead to the most informative datasets. Using [Formula: see text]  ≥ kex, to guide the choice of B1, instead of kex, leads to data wherefrom substantially more accurate exchange parameters can be derived. The need for higher B1 fields, guided by K, is demonstrated by studying the conformational exchange in two mutants of the 71 residue FF domain with kex ∼ 11 s-1 and ∼ 72 s-1, respectively. In both cases analysis of CEST datasets recorded using B1 field values guided by kex lead to imprecise exchange parameters, whereas using B1 values guided by K resulted in precise site-specific exchange parameters. The conclusions presented here will be valuable while using CEST to study slow processes at sites with large intrinsic relaxation rates, including carbonyl sites in small to medium sized proteins, amide 15N sites in large proteins and when the minor state dips are broadened due to exchange among the minor states.

Advancing protein therapeutics through proximity-induced chemistry

Recent years have seen a remarkable growth in the field of protein-based medical treatments. Nevertheless, concerns have arisen regarding the cytotoxicity limitations, low affinity, potential immunogenicity, low stability, and challenges to modify these proteins. To overcome these obstacles, proximity-induced chemistry has emerged as a next-generation strategy for advancing protein therapeutics. This method allows site-specific modification of proteins with therapeutic agents, improving their effectiveness without extensive engineering. In addition, this innovative approach enables spatial control of the reaction based on proximity, facilitating the formation of irreversible covalent bonds between therapeutic proteins and their targets. This capability becomes particularly valuable in addressing challenges such as the low affinity frequently encountered between therapeutic proteins and their targets, as well as the limited availability of small molecules for specific protein targets. As a result, proximity-induced chemistry is reshaping the field of protein drug preparation and propelling the revolution in novel protein therapeutics.

Free-Energy Landscape and Rate Estimation of the Aromatic Ring Flips in Basic Pancreatic Trypsin Inhibitors Using Metadynamics

Aromatic side chains (phenylalanine and tyrosine) of a protein flip by 180° around the Cβ-Cγ axis (χ2 dihedral of the side chain), producing two symmetry-equivalent states. The study of ring flip dynamics with nuclear magnetic resonance (NMR) experiments helps to understand local conformational fluctuations. Ring flips are categorized as slow (milliseconds and onward) or fast (nanoseconds to near milliseconds) based on timescales accessible to NMR experiments. In this study, we investigated the ability of the infrequent metadynamics approach to estimate the flip rate and discriminate between slow and fast ring flips for eight individual aromatic side chains (F4, Y10, Y21, F22, Y23, F33, Y35, and F45) of the basic pancreatic trypsin inhibitor. Well-tempered metadynamics simulations were performed to estimate the ring-flipping free-energy surfaces for all eight aromatic residues. The results indicate that χ2 as a standalone collective variable (CV) is not sufficient to obtain computationally consistent results. Inclusion of a complementary CV, such as χ1(Cα-Cβ), solved the problem for most residues and enabled us to classify fast and slow ring flips. This indicates the importance of librational motions in ring flips. Multiple pathways and mechanisms were observed for residues F4, Y10, and F22. Recrossing events were observed for residues F22 and F33, indicating a possible role of friction effects in ring flipping. The results demonstrate the successful application of infrequent metadynamics to estimate ring flip rates and identify certain limitations of the approach.

Studying micro to millisecond protein dynamics using simple amide 15N CEST experiments supplemented with major-state R2 and visible peak-position constraints

Over the last decade amide 15N CEST experiments have emerged as a popular tool to study protein dynamics that involves exchange between a 'visible' major state and sparsely populated 'invisible' minor states. Although initially introduced to study exchange between states that are in slow exchange with each other (typical exchange rates of, 10 to 400 s-1), they are now used to study interconversion between states on the intermediate to fast exchange timescale while still using low to moderate (5 to 350 Hz) 'saturating' B1 fields. The 15N CEST experiment is very sensitive to exchange as the exchange delay TEX can be quite long (~0.5 s) allowing for a large number of exchange events to occur making it a very powerful tool to detect minor sates populated ([Formula: see text]) to as low as 1%. When systems are in fast exchange and the 15N CEST data has to be described using a model that contains exchange, the exchange parameters are often poorly defined because the [Formula: see text] versus [Formula: see text] and [Formula: see text] versus exchange rate ([Formula: see text]) plots can be quite flat with shallow or no minima and the analysis of such 15N CEST data can lead to wrong estimates of the exchange parameters due to the presence of 'spurious' minima. Here we show that the inclusion of experimentally derived constraints on the intrinsic transverse relaxation rates and the inclusion of visible state peak-positions during the analysis of amide 15N CEST data acquired with moderate B1 values (~50 to ~350 Hz) results in convincing minima in the [Formula: see text] versus [Formula: see text] and the [Formula: see text] versus [Formula: see text] plots even when exchange occurs on the 100 μs timescale. The utility of this strategy is demonstrated on the fast-folding Bacillus stearothermophilus peripheral subunit binding domain that folds with a rate constant ~104 s-1. Here the analysis of 15N CEST data alone results in [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] plots that contain shallow minima, but the inclusion of visible-state peak positions and restraints on the intrinsic transverse relaxation rates of both states during the analysis of the 15N CEST data results in pronounced minima in the [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] plots and precise exchange parameters even in the fast exchange regime ([Formula: see text]~5). Using this strategy we find that the folding rate constant of PSBD is invariant (~10,500 s-1) from 33.2 to 42.9 °C while the unfolding rates (~70 to ~500 s-1) and unfolded state populations (~0.7 to ~4.3%) increase with temperature. The results presented here show that protein dynamics occurring on the 10 to 104 s-1 timescale can be studied using amide 15N CEST experiments.

Conformational Changes in Surface-Immobilized Proteins Measured Using Combined Atomic Force and Fluorescence Microscopy

Biological organisms rely on proteins to perform the majority of their functions. Most protein functions are based on their physical motions (conformational changes), which can be described as transitions between different conformational states in a multidimensional free-energy landscape. A comprehensive understanding of this free-energy landscape is therefore of paramount importance for understanding the biological functions of proteins. Protein dynamics includes both equilibrium and nonequilibrium motions, which typically exhibit a wide range of characteristic length and time scales. The relative probabilities of various conformational states in the energy landscape, the energy barriers between them, their dependence on external parameters such as force and temperature, and their connection to the protein function remain largely unknown for most proteins. In this paper, we present a multimolecule approach in which the proteins are immobilized at well-defined locations on Au substrates using an atomic force microscope (AFM)-based patterning method called nanografting. This method enables precise control over the protein location and orientation on the substrate, as well as the creation of biologically active protein ensembles that self-assemble into well-defined nanoscale regions (protein patches) on the gold substrate. We performed AFM-force compression and fluorescence experiments on these protein patches and measured the fundamental dynamical parameters such as protein stiffness, elastic modulus, and transition energies between distinct conformational states. Our results provide new insights into the processes that govern protein dynamics and its connection to protein function.

Ruthenium hydrides encapsulated in sol–gel glasses exhibit new ultrafast vibrational dynamics

Vibrational dynamics were measured by IR pump–probe spectroscopy and two-dimensional IR spectroscopy for triruthenium dodecacarbonyl and the undecacarbonyl hydride that forms when it is encapsulated in an alumina sol–gel glass. For comparison, a triruthenium undecacarbonyl hydride salt was also synthesized and studied in neat solution to identify the potential influence of the confined solvent environment on the dynamics experienced by carbon monoxide ligands. The vibrational lifetime was found to be significantly decreased for both hydride species relative to the dodecacarbonyl compound. Conversely, spectral diffusion of the CO vibrations was measured to be faster for the parent compound. The most significant dynamic changes occurred upon transformation from the starting compound to the hydride, while only minor differences were observed between the dynamics of the freely dissolved and sol–gel encapsulated hydrides. The results suggest that the structural change to the hydride has the largest impact on the dynamics and that its improved catalytic properties likely do not originate from confined solvent effects.

The A39G FF domain folds on a volcano-shaped free energy surface via separate pathways

Conformational dynamics play critical roles in protein folding, misfolding, function, misfunction, and aggregation. While detecting and studying the different conformational states populated by protein molecules on their free energy surfaces (FESs) remain a challenge, NMR spectroscopy has emerged as an invaluable experimental tool to explore the FES of a protein, as conformational dynamics can be probed at atomic resolution over a wide range of timescales. Here, we use chemical exchange saturation transfer (CEST) to detect "invisible" minor states on the energy landscape of the A39G mutant FF domain that exhibited "two-state" folding kinetics in traditional experiments. Although CEST has mostly been limited to studies of processes with rates between ∼5 to 300 s^-1 involving sparse states with populations as low as ∼1%, we show that the line broadening that is often associated with minor state dips in CEST profiles can be exploited to inform on additional conformers, with lifetimes an order of magnitude shorter and populations close to 10-fold smaller than what typically is characterized. Our analysis of CEST profiles that exploits the minor state linewidths of the 71-residue A39G FF domain establishes a folding mechanism that can be described in terms of a four-state exchange process between interconverting states spanning over two orders of magnitude in timescale from ∼100 to ∼15,000 μs. A similar folding scheme is established for the wild-type domain as well. The study shows that the folding of this small domain proceeds through a pair of sparse, partially structured intermediates via two discrete pathways on a volcano-shaped FES.

Modelling single-molecule kinetics of helicase translocation using high-resolution nanopore tweezers (SPRNT)

Single-molecule picometer resolution nanopore tweezers (SPRNT) is a technique for monitoring the motion of individual enzymes along a nucleic acid template at unprecedented spatiotemporal resolution. We review the development of SPRNT and the application of single-molecule kinetics theory to SPRNT data to develop a detailed model of helicase motion along a single-stranded DNA substrate. In this review, we present three examples of questions SPRNT can answer in the context of the Superfamily 2 helicase Hel308. With Hel308, SPRNT's spatiotemporal resolution enables resolution of two distinct enzymatic substates, one which is dependent upon ATP concentration and one which is ATP independent. By analyzing dwell-time distributions and helicase back-stepping, we show, in detail, how SPRNT can be used to determine the nature of these observed steps. We use dwell-time distributions to discern between three different possible models of helicase backstepping. We conclude by using SPRNT's ability to discern an enzyme's nucleotide-specific location along a DNA strand to understand the nature of sequence-specific enzyme kinetics and show that the sequence within the helicase itself affects both step dwell-time and backstepping probability while translocating on single-stranded DNA.

Short-Term Temperature Response of Leaf Respiration in Different Subtropical Urban Tree Species

Plant leaf respiration is one of the critical components of the carbon cycle in terrestrial ecosystems. To predict changes of carbon emissions from leaves to the atmosphere under a warming climate, it is, therefore, important to understand the thermodynamics of the temperature response of leaf respiration. In this study, we measured the short-term temperature response of leaf respiration from five different urban tree species in a subtropical region of southern China. We applied two models, including an empirical model (the Kavanau model) and a mechanistic model (Macromolecular Rate Theory, MMRT), to investigate the thermodynamic properties in different plant species. Both models are equivalent in fitting measurements of the temperature response of leaf respiration with no significant difference (p = 0.67) in model efficiency, while MMRT provides an easy way to determine the thermodynamic properties, i.e., enthalpy, entropy, and Gibbs free energy of activation, for plant respiration. We found a conserved temperature response in the five studied plant species, showing no difference in thermodynamic properties and the relative temperature sensitivity for different species at low temperatures (<42°C). However, divergent temperature response among species happened at high temperatures over 42°C, showing more than two-fold differences in relative respiration rate compared to that below 42°C, although the causes of the divergent temperature response remain unclear. Notably, the convergent temperature response at low temperatures could provide useful information for land surface models to improve predictions of climate change effects on plant respiration.

A CEST NMR experiment to obtain glycine 1Hα chemical shifts in 'invisible' minor states of proteins

Chemical exchange saturation transfer (CEST) experiments are routinely used to study protein conformational exchange between a 'visible' major state and 'invisible' minor states because they can detect minor states with lifetimes varying from ~ 3 to ~ 100 ms populated to just ~ 0.5%. Consequently several ¹H, ¹⁵N and ¹³C CEST experiments have been developed to study exchange and obtain minor state chemical shifts at almost all backbone and sidechain sites in proteins. Conspicuously missing from this extensive set of CEST experiments is a ¹H CEST experiment to study exchange at glycine (Gly) ¹H^α sites as the existing ¹H CEST experiments that have been designed to study dynamics in amide ¹H-¹⁵N spin systems and methyl ¹³CH₃ groups with three equivalent protons while suppressing ¹H-¹H NOE induced dips are not suitable for studying exchange in methylene ¹³CH₂ groups with inequivalent protons. Here a Gly ¹H^α CEST experiment to obtain the minor state Gly ¹H^α chemical shifts is presented. The utility of this experiment is demonstrated on the L99A cavity mutant of T4 Lysozyme (T4L L99A) that undergoes conformational exchange between two compact conformers. The CEST derived minor state Gly ¹H^α chemical shifts of T4L L99A are in agreement with those obtained previously using CPMG techniques. The experimental strategy presented here can also be used to obtain methylene proton minor state chemical shifts from protein sidechain and nucleic acid backbone sites.

Non-Arrhenius Reaction-Diffusion Kinetics for Protein Inactivation over a Large Temperature Range

Understanding protein folding and unfolding has been a long-standing fundamental question and has important applications in manipulating protein activity in biological systems. Experimental investigations of protein unfolding have been predominately conducted by small temperature perturbations (e.g., temperature jump), while molecular simulations are limited to small time scales (microseconds) and high temperatures to observe unfolding. Thus, it remains unclear how fast a protein unfolds irreversibly and loses function (i.e., inactivation) across a large temperature range. In this work, using nanosecond pulsed heating of individual plasmonic nanoparticles to create precise localized heating, we examine the protein inactivation kinetics at extremely high temperatures. Connecting this with protein inactivation measurements at low temperatures, we observe that the kinetics of protein unfolding is less sensitive to temperature change at the higher temperatures, which significantly departs from the Arrhenius behavior extrapolated from low temperatures. To account for this effect, we propose a reaction-diffusion model that modifies the temperature-dependence of protein inactivation by introducing a diffusion limit. Analysis of the reaction-diffusion model provides general guidelines in the behavior of protein inactivation (reaction-limited, transition, diffusion-limited) across a large temperature range from physiological temperature to extremely high temperatures. We further demonstrate that the reaction-diffusion model is particularly useful for designing optimal operating conditions for protein photoinactivation. The experimentally validated reaction-diffusion kinetics of protein unfolding is an important step toward understanding protein-inactivation kinetics over a large temperature range. It has important applications including molecular hyperthermia and calls for future studies to examine this model for other protein molecules.

High-speed AFM reveals accelerated binding of agitoxin-2 to a K+ channel by induced fit

Agitoxin-2 (AgTx2) from scorpion venom is a potent blocker of K⁺ channels. The docking model has been elucidated, but it remains unclear whether binding dynamics are described by a two-state model (AgTx2-bound and AgTx2-unbound) or a more complicated mechanism, such as induced fit or conformational selection. Here, we observed the binding dynamics of AgTx2 to the KcsA channel using high-speed atomic force microscopy. From images of repeated binding and dissociation of AgTx2 to the channel, single-molecule kinetic analyses revealed that the affinity of the channel for AgTx2 increased during persistent binding and decreased during persistent dissociation. We propose a four-state model, including high- and low-affinity states of the channel, with relevant rate constants. An induced-fit pathway was dominant and accelerated binding by 400 times. This is the first analytical imaging of scorpion toxin binding in real time, which is applicable to various biological dynamics including channel ligands, DNA-modifier proteins, and antigen-antibody complexes.

A Double-Resonance CEST Experiment To Study Multistate Protein Conformational Exchange: An Application to Protein Folding

Despite the importance of protein dynamics to function, studying exchange between multiple conformational states remains a challenge because sparsely populated states are invisible to conventional techniques. CEST NMR experiments can detect minor states with lifetimes between 5 and 200 ms populated to a level of just ∼1%. However, CEST often cannot provide the exchange mechanism for processes involving three or more states, leaving the role of the detected minor states unknown. Here a double-resonance CEST experiment to determine the kinetics of multistate exchange is presented. The approach that involves irradiating resonances from two minor states simultaneously is used to study the exchange of T4 lysozyme (T4L) between the dominant native state and two minor states, the unfolded state and a second minor state (B), each populated to only ∼4%. Regular CEST does not provide the folding mechanism, but double-resonance CEST clearly shows that T4L can fold directly without going through B.

Exchangeable deuterons introduce artifacts in amide 15N CEST experiments used to study protein conformational exchange

Protein molecules sample different conformations in solution and characterizing these conformations is crucial to understanding protein function. ¹⁵N CEST experiments are now routinely used to study slow conformational exchange of protein molecules between a 'visible' major state and 'invisible' minor states. These experiments have also been adapted to measure the solvent exchange rates of amide protons by exploiting the one bond deuterium isotope effect on the amide ¹⁵N chemical shifts. However at moderately high temperatures (~ 50 °C) that are sometimes required to populate protein minor conformers to levels (~ 1%) that can be detected by CEST experiments solvent H/D exchange can lead to 'dips' in low B₁¹⁵N CEST profiles that can be wrongly assigned to the conformational exchange process being characterized. This is demonstrated in the case of ~ 18 kDa T4 Lysozyme (T4L) at 50 °C and the ~ 11 kDa E. coli hibernation promoting factor (HPF) at 52 °C. This problem is trivially solved by eliminating the exchangeable deuterons in the solvent by using either an external D₂O lock or by using a small amount (~ 1-3%) of a molecule like d6-DMSO that does not contain exchangeable deuterons to lock the spectrometer.

CPMG Experiments for Protein Minor Conformer Structure Determination

CPMG relaxation dispersion NMR experiments have emerged as a powerful method to characterize protein minor states that are in exchange with a visible dominant conformation, and have lifetimes between ~0.5 and 5 milliseconds (ms) and populations greater than 0.5%. The structure of the minor state can, in favorable cases, be determined from the parameters provided by the CPMG relaxation dispersion experiments. Here, we go through the intricacies of setting up these powerful CPMG experiments.

Effects of non-equilibrium angle fluctuation on F1-ATPase kinetics induced by temperature increase

F₁-ATPase (F₁) is an efficient rotary protein motor, whose reactivity is modulated by the rotary angle to utilize thermal fluctuation. In order to elucidate how its kinetics are affected by the change in the fluctuation, we have extended the reaction-diffusion formalism [R. Watanabe et al., Biophys. J., 2013, 105, 2385] applicable to a wider range of temperatures based on experimental data analysis of F₁ derived from thermophilic Bacillus under high ATP concentration conditions. Our simulation shows that the rotary angle distribution manifests a stronger non-equilibrium feature as the temperature increases, because ATP hydrolysis and P_i release are more accelerated compared with the timescale of rotary angle relaxation. This effect causes the rate coefficient obtained from dwell time fitting to deviate from the Arrhenius relation in P_i release, which has been assumed in the previous activation thermodynamic quantities estimation using linear Arrhenius fitting. Larger negative correlation is also found between hydrolysis and P_i release waiting time in a catalytic dwell with the increase in temperature. This loss of independence between the two successive reactions at the catalytic dwell sheds doubt on the conventional dwell time fitting to obtain rate coefficients with a double exponential function at temperatures higher than 65 °C, which is close to the physiological temperature of the thermophilic Bacillus.

Enhanced vibrational solvatochromism and spectral diffusion by electron rich substituents on small molecule silanes

Fourier transform infrared and two-dimensional IR (2D-IR) spectroscopies were applied to two different silanes in three different solvents. The selected solutes exhibit different degrees of vibrational solvatochromism for the Si-H vibration. Density functional theory calculations confirm that this difference in sensitivity is the result of higher mode polarization with more electron withdrawing ligands. This mode sensitivity also affects the extent of spectral diffusion experienced by the silane vibration, offering a potential route to simultaneously optimize the sensitivity of vibrational probes in both steady-state and time-resolved measurements. Frequency-frequency correlation functions obtained by 2D-IR show that both solutes experience dynamics on similar time scales and are consistent with a picture in which weakly interacting solvents produce faster, more homogeneous fluctuations. Molecular dynamics simulations confirm that the frequency-frequency correlation function obtained by 2D-IR is sensitive to the presence of hydrogen bonding dynamics in the surrounding solvation shell.

Probing conformational dynamics in biomolecules via chemical exchange saturation transfer: a primer

Although Chemical Exchange Saturation Transfer (CEST) type NMR experiments have been used to study chemical exchange processes in molecules since the early 1960s, there has been renewed interest in the past several years in using this approach to study biomolecular conformational dynamics. The methodology is particularly powerful for the study of sparsely populated, transiently formed conformers that are recalcitrant to investigation using traditional biophysical tools, and it is complementary to relaxation dispersion and magnetization transfer experiments that have traditionally been used to study chemical exchange processes. Here we discuss the concepts behind the CEST experiment, focusing on practical aspects as well, we review some of the pulse sequences that have been developed to characterize protein and RNA conformational dynamics, and we discuss a number of examples where the CEST methodology has provided important insights into the role of dynamics in biomolecular function.

On the indirect relationship between protein dynamics and enzyme activity

The behaviors of simple thermal systems have been well studied in physical chemistry and the principles obtained from such studies have been applied to complex thermal systems, such as proteins and enzymes. But the simple application of such principles is questionable and may lead to mistakes under some circumstances. In enzymology, the transition state theory of chemical reactions has been accepted as a fundamental theory, but the role of protein dynamics in enzyme catalysis is controversial in the context of transition state theory. By studying behaviors of complex thermal systems, we have revised the Arrhenius equation and transition state theory and our model is validated in enzymology. Formally speaking, the revised Arrhenius equation is apparently similar to a conventional Arrhenius equation, but the physical meanings of its parameters differ from that of traditional forms in principle. Within this model, the role of protein dynamics in enzyme catalysis is well defined and quantified.

Intrinsic Base-Pair Rearrangement in the Hairpin Ribozyme Directs RNA Conformational Sampling and Tertiary Interface Formation

Dynamic fluctuations in RNA structure enable conformational changes that are required for catalysis and recognition. In the hairpin ribozyme, the catalytically active structure is formed as an intricate tertiary interface between two RNA internal loops. Substantial alterations in the structure of each loop are observed upon interface formation, or docking. The very slow on-rate for this relatively tight interaction has led us to hypothesize a double conformational capture mechanism for RNA-RNA recognition. We used extensive molecular dynamics simulations to assess conformational sampling in the undocked form of the loop domain containing the scissile phosphate (loop A). We observed several major accessible conformations with distinctive patterns of hydrogen bonding and base stacking interactions in the active-site internal loop. Several important conformational features characteristic of the docked state were observed in well-populated substates, consistent with the kinetic sampling of docking-competent states by isolated loop A. Our observations suggest a hybrid or multistage binding mechanism, in which initial conformational selection of a docking-competent state is followed by induced-fit adjustment to an in-line, chemically reactive state only after formation of the initial complex with loop B.

Atomistic picture of conformational exchange in a T4 lysozyme cavity mutant: an experiment-guided molecular dynamics study

Despite the importance of dynamics to protein function there is little information about the states that are formed as the protein explores its conformational landscape or about the mechanism by which transitions between the different states occur. Here we used a combined NMR spin relaxation and unbiased molecular dynamics (MD) approach to investigate the exchange process by which a cavity in an L99A mutant of T4 lysozyme (T4L 99A) interconverts between an empty and occupied form that involves repositioning of an aromatic residue, Phe114. Although structures of the end-states of the exchange process are available, insight into the mechanism by which the transition takes place cannot be obtained from experiment and the timescales involved are too slow to address using brute force MD. Using spin relaxation NMR methods, we have identified a triple-mutant of T4L that undergoes the same exchange process as T4L L99A but where the minor state lifetime has decreased significantly so that the spontaneous conformational transition to the major state can be studied using all-atom MD simulations. The simulation trajectories were analyzed using Markov state models and the energy landscape so obtained is in good agreement with expectations based on NMR studies. Notably there is no large-scale perturbation of the structure during the transition, multiple intermediates are formed between the two similar exchanging conformations and the free energy barrier between these two well-folded, compact forms is small (6kBT), only slightly larger than for processes considered to be barrierless.

Enhancing pairwise state-transition weights: A new weighting scheme in simulated tempering that can minimize transition time between a pair of conformational states

Simulated tempering (ST) is a widely used enhancing sampling method for Molecular Dynamics simulations. As one expanded ensemble method, ST is a combination of canonical ensembles at different temperatures and the acceptance probability of cross-temperature transitions is determined by both the temperature difference and the weights of each temperature. One popular way to obtain the weights is to adopt the free energy of each canonical ensemble, which achieves uniform sampling among temperature space. However, this uniform distribution in temperature space may not be optimal since high temperatures do not always speed up the conformational transitions of interest, as anti-Arrhenius kinetics are prevalent in protein and RNA folding. Here, we propose a new method: Enhancing Pairwise State-transition Weights (EPSW), to obtain the optimal weights by minimizing the round-trip time for transitions among different metastable states at the temperature of interest in ST. The novelty of the EPSW algorithm lies in explicitly considering the kinetics of conformation transitions when optimizing the weights of different temperatures. We further demonstrate the power of EPSW in three different systems: a simple two-temperature model, a two-dimensional model for protein folding with anti-Arrhenius kinetics, and the alanine dipeptide. The results from these three systems showed that the new algorithm can substantially accelerate the transitions between conformational states of interest in the ST expanded ensemble and further facilitate the convergence of thermodynamics compared to the widely used free energy weights. We anticipate that this algorithm is particularly useful for studying functional conformational changes of biological systems where the initial and final states are often known from structural biology experiments.

Specific Reaction Parametrization of the AM1/d Hamiltonian for Phosphoryl Transfer Reactions: H, O, and P Atoms

A semiempirical AM1/d Hamiltonian is developed to model phosphoryl transfer reactions catalyzed by enzymes and ribozymes for use in linear-scaling calculations and combined quantum mechanical/molecular mechanical simulations. The model, designated AM1/d-PhoT, is parametrized for H, O, and P atoms to reproduce high-level density-functional results from a recently constructed database of quantum calculations for RNA catalysis ( http://theory.chem.umn.edu/Database/QCRNA ), including geometries and relative energies of minima, transition states and reactive intermediates, dipole moments, proton affinities, and other relevant properties. The model is tested in the gas phase and in solution using a QM/MM potential. The results indicate that the method provides significantly higher accuracy than MNDO/d, AM1, and PM3 methods and, for the transphosphorylation reactions, is in close agreement with the density-functional calculations at the B3LYP/6-311++G(3df,2p) level with a reduction in computational cost of 3-4 orders of magnitude. The model is expected to have considerable impact on the application of semiempirical QM/MM methods to transphosphorylation reactions in solution, enzymes, and ribozymes and to ultimately facilitate the design of improved next-generation multiscale quantum models.

Quantification and modification of the equilibrium dynamics and mechanics of a viral capsid lattice self-assembled as a protein nanocoating

Self-assembling, protein-based bidimensional lattices are being developed as functionalizable, highly ordered biocoatings for multiple applications in nanotechnology and nanomedicine. Unfortunately, protein assemblies are soft materials that may be too sensitive to mechanical disruption, and their intrinsic conformational dynamism may also influence their applicability. Thus, it may be critically important to characterize, understand and manipulate the mechanical features and dynamic behavior of protein assemblies in order to improve their suitability as nanomaterials. In this study, the capsid protein of the human immunodeficiency virus was induced to self-assemble as a continuous, single layered, ordered nanocoating onto an inorganic substrate. Atomic force microscopy (AFM) was used to quantify the mechanical behavior and the equilibrium dynamics ("breathing") of this virus-based, self-assembled protein lattice in close to physiological conditions. The results uniquely provided: (i) evidence that AFM can be used to directly visualize in real time and quantify slow breathing motions leading to dynamic disorder in protein nanocoatings and viral capsid lattices; (ii) characterization of the dynamics and mechanics of a viral capsid lattice and protein-based nanocoating, including flexibility, mechanical strength and remarkable self-repair capacity after mechanical damage; (iii) proof of principle that chemical additives can modify the dynamics and mechanics of a viral capsid lattice or protein-based nanocoating, and improve their applied potential by increasing their mechanical strength and elasticity. We discuss the implications for the development of mechanically resistant and compliant biocoatings precisely organized at the nanoscale, and of novel antiviral agents acting on fundamental physical properties of viruses.

Circadian rhythms. Atomic-scale origins of slowness in the cyanobacterial circadian clock

Circadian clocks generate slow and ordered cellular dynamics but consist of fast-moving bio-macromolecules; consequently, the origins of the overall slowness remain unclear. We identified the adenosine triphosphate (ATP) catalytic region [adenosine triphosphatase (ATPase)] in the amino-terminal half of the clock protein KaiC as the minimal pacemaker that controls the in vivo frequency of the cyanobacterial clock. Crystal structures of the ATPase revealed that the slowness of this ATPase arises from sequestration of a lytic water molecule in an unfavorable position and coupling of ATP hydrolysis to a peptide isomerization with high activation energy. The slow ATPase is coupled with another ATPase catalyzing autodephosphorylation in the carboxyl-terminal half of KaiC, yielding the circadian response frequency of intermolecular interactions with other clock-related proteins that influences the transcription and translation cycle.

Dynamics of solvent response in methanol-chloroform binary solvent mixture: a case of synergistic solvation

Steady-state absorption, emission, and femtosecond transient absorption spectroscopies were used to ascertain the static and dynamic nature of the solvent response of methanol-chloroform binary solvent mixtures of different stoichiometric ratios using 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) as the probe molecule. The appearance of synergistic solvation behavior in the steady-state absorption measurements can be explained in terms of solvent-solvent interactions through an extended hydrogen-bonding network. The disappearance of such synergistic behavior in the excited state of the DCM dye was recently proposed by us to be due to the weak nature of the intermolecular interactions present in binary solvent mixtures (J. Phys. Chem. B 2012, 116, 1345). It was anticipated and subsequently confirmed by the dynamics of the solvent response that the disruption of the weak interactive solvent network is the main reason for the absence of the synergism in the excited state. As expected, we observed the slowest dynamics for the mixture with X(MeOH) = 0.45, with an average solvation time of 12.03 ps, which is much higher than the values for the pure bulk counterparts (⟨τ(s)⟩(Methanol) = 4.32 ps and ⟨τ(s)⟩(Chloroform) = 1.32 ps). The unprecedented slowing of solvation for DCM is probably due to the rigid interactive methanol-chloroform solvent system in the first solvation shell, followed by solvent rearrangements around the solute dipole. Overall interactions present within the methanol-chloroform binary solvent mixture furnish clear evidence of solvent association through weak hydrogen bonding.

The roughness of the protein energy landscape results in anomalous diffusion of the polypeptide backbone

Recombination of photolysed protein disulfide bonds confirms subdiffusional backbone motion and measures the roughness of the protein's energy landscape.

Folding dynamics and pathways of the trp-cage miniproteins

Using alternate measures of fold stability for a wide variety of Trp-cage mutants has raised the possibility that prior dynamics T-jump measures may not be reporting on complete cage formation for some species. NMR relaxation studies using probes that only achieve large chemical shift difference from unfolded values on complete cage formation indicate slower folding in some but not all cases. Fourteen species have been examined, with cage formation time constants (1/kF) ranging from 0.9-7.5 μs at 300 K. The present study does not change the status of the Trp-cage as a fast folding, essentially two-state system, although it does alter the stage at which this description applies. A diversity of prestructuring events, depending on the specific analogue examined, may appear in the folding scenario, but in all cases, formation of the N-terminal helix is complete either at or before the cage-formation transition state. In contrast, the fold-stabilizing H-bonding interactions of the buried Ser14 side chain and the Arg/Asp salt bridge are post-transition state features on the folding pathway. The study has also found instances in which a [P12W] mutation is fold destabilizing but still serves to accelerate the folding process.

Single-molecule enzymatic conformational dynamics: spilling out the product molecules

Product releasing is an essential step of an enzymatic reaction, and a mechanistic understanding primarily depends on the active-site conformational changes and molecular interactions that are involved in this step of the enzymatic reaction. Here we report our work on the enzymatic product releasing dynamics and mechanism of an enzyme, horseradish peroxidase (HRP), using combined single-molecule time-resolved fluorescence intensity, anisotropy, and lifetime measurements. Our results have shown a wide distribution of the multiple conformational states involved in active-site interacting with the product molecules during the product releasing. We have identified that there is a significant pathway in which the product molecules are spilled out from the enzymatic active site, driven by a squeezing effect from a tight active-site conformational state, although the conventional pathway of releasing a product molecule from an open active-site conformational state is still a primary pathway. Our study provides new insight into the enzymatic reaction dynamics and mechanism, and the information is uniquely obtainable from our combined time-resolved single-molecule spectroscopic measurements and analyses.

Kinetics of molecular transitions with dynamic disorder in single-molecule pulling experiments

Macromolecular transitions are subject to large fluctuations of rate constant, termed as dynamic disorder. The individual or intrinsic transition rates and activation free energies can be extracted from single-molecule pulling experiments. Here we present a theoretical framework based on a generalized Langevin equation with fractional Gaussian noise and power-law memory kernel to study the kinetics of macromolecular transitions to address the effects of dynamic disorder on barrier-crossing kinetics under external pulling force. By using the Kramers' rate theory, we have calculated the fluctuating rate constant of molecular transition, as well as the experimentally accessible quantities such as the force-dependent mean lifetime, the rupture force distribution, and the speed-dependent mean rupture force. Particular attention is paid to the discrepancies between the kinetics with and without dynamic disorder. We demonstrate that these discrepancies show strong and nontrivial dependence on the external force or the pulling speed, as well as the barrier height of the potential of mean force. Our results suggest that dynamic disorder is an important factor that should be taken into account properly in accurate interpretations of single-molecule pulling experiments.

The principle of stationary action in biophysics: stability in protein folding

We conceptualize protein folding as motion in a large dimensional dihedral angle space. We use Lagrangian mechanics and introduce an unspecified Lagrangian to study the motion. The fact that we have reliable folding leads us to conjecture the totality of paths forms caustics that can be recognized by the vanishing of the second variation of the action. There are two types of folding processes: stable against modest perturbations and unstable. We also conjecture that natural selection has picked out stable folds. More importantly, the presence of caustics leads naturally to the application of ideas from catastrophe theory and allows us to consider the question of stability for the folding process from that perspective. Powerful stability theorems from mathematics are then applicable to impose more order on the totality of motions. This leads to an immediate explanation for both the insensitivity of folding to solution perturbations and the fact that folding occurs using very little free energy. The theory of folding, based on the above conjectures, can also be used to explain the behavior of energy landscapes, the speed of folding similar to transition state theory, and the fact that random proteins do not fold.

Nucleotide recognition by the initiation factor aIF5B: free energy simulations of a neoclassical GTPase

The GTPase aIF5B is a universally conserved initiation factor that assists ribosome assembly. Crystal structures of its nucleotide complexes, X-ray(GTP) and X-ray(GDP), are similar in the nucleotide vicinity, but differ in the orientation of a distant domain IV. This has led to two, contradictory, mechanistic models. One postulates that X-ray(GTP) and X-ray(GDP) are, respectively, the active, "ON" and the inactive, "OFF" states; the other postulates that both structures are OFF, whereas the ON state is still uncharacterized. We study GTP/GDP binding using molecular dynamics and a continuum electrostatic free energy method. We predict that X-ray(GTP) has a ≈ 3 kcal/mol preference to bind GDP, apparently contradicting its assignment as ON. However, the preference arises mainly from a single, nearby residue from the switch 2 motif: Glu81, which becomes protonated upon GTP binding, with a free energy cost of about 4 kcal/mol. We then propose a different model, where Glu81 protonation/deprotonation defines the ON/OFF states. With this model, the X-ray(GTP):GTP complex, with its protonated Glu81, is ON, whereas X-ray(GTP):GDP is OFF. The model postulates that distant conformational changes such as domain IV rotation are "uncoupled" from GTP/GDP exchange and do not affect the relative GTP/GDP binding affinities. We analyze the model using a general thermodynamic framework for GTPases. It yields rather precise predictions for the nucleotide specificities of each state, and the state specificities of each nucleotide, which are roughly comparable to the homologues IF2 and aIF2, despite the lack of any conformational switching in the model.

Structural and dynamic aspects of protein clocks: how can they be so slow and stable?

KaiC is a core protein of the cyanobacterial Kai oscillator, which persists without transcription-translation feedback. In the presence of KaiA and KaiB, KaiC reveals rhythmic activation/inactivation of its ATPase and autokinase/autophosphotase activities over approximately 24 h. Since the in vitro reconstruction of the Kai oscillator, the structures and functions of the Kai proteins have been studied extensively. Each protein's crystal structure and low-resolution views of Kai complexes have been reported. In addition, newer data are emerging on dynamic aspects such as assembly/disassembly of the Kai components and a ticking motion of KaiC, which is probably coupled to its slow, temperature-compensated ATPase activity. The accumulated evidence offers an ideal opportunity to revisit a fundamental question regarding biological circadian clocks: what determines the temperature-compensated 24 h period? In this review, I summarize the current understanding of the Kai oscillator's molecular mechanism and discuss emerging ideas on protein clocks.

Dynamics of metastable β-hairpin structures in the folding nucleus of amyloid β-protein

The amyloid β-protein (Aβ), which is present predominately as a 40- or 42-residue peptide, is postulated to play a seminal role in the pathogenesis of Alzheimer's disease (AD). Folding of the Aβ(21-30) decapeptide region is a critical step in the aggregation of Aβ. We report results of constant temperature all-atom molecular dynamics simulations in explicit water of the dynamics of monomeric Aβ(21-30) and its Dutch [Glu22Gln], Arctic [Glu22Gly], and Iowa [Asp23Asn] isoforms that are associated with familial forms of cerebral amyloid angiopathy and AD. The simulations revealed a variety of loop conformers that exhibited a hydrogen bond network involving the Asp23 and Ser26 amino acids. A population of conformers, not part of the loop population, was found to form metastable β-hairpin structures with the highest probability in the Iowa mutant. At least three β-hairpin structures were found that differed in their hydrogen bonding register, average number of backbone hydrogen bonds, and lifetimes. Analysis revealed that the Dutch mutant had the longest β-hairpin lifetime (≥500 ns), closely followed by the Iowa mutant (≈500 ns). Aβ(21-30) and the Arctic mutant had significantly lower lifetimes (≈200 ns). Hydrophobic packing of side chains was responsible for enhanced β-hairpin lifetimes in the Dutch and Iowa mutants, whereas lifetimes in Aβ(21-30) and its Arctic mutant were influenced by the backbone hydrogen bonding. The data suggest that prolonged β-hairpin lifetimes may impact peptide pathogenicity in vivo.

Dissipative electro-elastic network model of protein electrostatics

We propose a dissipative electro-elastic network model to describe the dynamics and statistics of electrostatic fluctuations at active sites of proteins. The model combines the harmonic network of residue beads with overdamped dynamics of the normal modes of the network characterized by two friction coefficients. The electrostatic component is introduced to the model through atomic charges of the protein force field. The overall effect of the electrostatic fluctuations of the network is recorded through the frequency-dependent response functions of the electrostatic potential and electric field at the protein active site. We also consider the dynamics of displacements of individual residues in the network and the dynamics of distances between pairs of residues. The model is tested against loss spectra of residue displacements and the electrostatic potential and electric field at the heme's iron from all-atom molecular dynamics simulations of three hydrated globular proteins.

Density functional calculations on the effect of sulfur substitution for 2'-hydroxypropyl-p-nitrophenyl phosphate: C-O vs. P-O bond cleavage

Density functional theory calculations have been used to investigate the intra-molecular attack of 2'-hydroxypropyl-p-nitrophenyl phosphate (HPpNP) and its analogous compound 2-thiouridyl-p-nitrophenyl phosphate (s-2'pNP). Bulk solvent effect has been tested at the geometry optimization level with the polarized continuum model. It is found that the P-path involving the intra-molecular attack at the phosphorus atom and C-path involving the attack at the beta carbon atom proceed through the S(N)2-type mechanism for HPpNP and s-2'pNP. The calculated results indicate that the P-path with the free energy barrier of about 11 kcal/mol is more accessible than the C-path for the intra-molecular attack of HPpNP, which favors the formation of the five-membered phosphate diester. While for s-2'pNP, the C-path with the free energy barrier of about 21 kcal/mol proceeds more favorably than the P-path. The calculated energy barriers of the favorable pathways for HPpNP and s-2'pNP are both in agreement with the experimental results.

Delineation of folding pathways of a β-sheet miniprotein

Several methods have been developed in the past few years for the analysis of molecular dynamics simulations of biological (macro)molecules whose complexity is difficult to capture by simple projections of the free-energy surface onto one or two geometric variables. The locally scaled diffusion map (LSDMap) method is a nonlinear dimensionality reduction technique for describing the dynamics of complex systems in terms of a few collective coordinates. Here, we compare LSDMap to two previously developed approaches for the characterization of the configurational landscape associated with the folding dynamics of a three-stranded antiparallel β-sheet peptide, termed Beta3s. The analysis is aided by an improved procedure for extracting pathways from the equilibrium transition network, which enables calculation of pathway-specific cut-based free energy profiles. We find that the results from LSDMap are consistent with analysis based on transition networks and allow a coherent interpretation of metastable states and folding pathways in terms of different time scales of transitions between minima on the free energy projections.