Slow Conformational Fluctuations Research Articles

Theoretical study of the conditional non-monotonic off rate dependence of catalytic reaction rates in single enzymes in the presence of conformational fluctuations

In ordinary Michaelis–Menten kinetics of enzyme-catalyzed reactions, the enzymatic velocity decreases with the increase in the off dissociation rate constant of the enzyme-substrate complex. In this work, we study the role of the off dissociation rate constants in single-molecule enzymatic reactions in which both the free enzyme and the enzyme-substrate complex undergo slow conformational fluctuations. By applying our theoretical formalism, we calculate the enzymatic velocity and show that there can be an increase in the reaction velocity with the off rate constant dependence which is not very intuitive. From our analytical calculations, we can establish a region of the parameter space and subsequently explore a range of substrate concentration where the enzymatic velocity is accelerated with an increase in the off rate constant. Further, we study the role of the substrate unbinding rate constants on the randomness parameter, which is a measure of the dynamic disorder present in the system.

Statistical properties of fluctuating enzymes with dynamic cooperativity using a first passage time distribution formalism.

We study the temporal fluctuations in catalytic rates for single enzyme reactions undergoing slow transitions between two active states. We use a first passage time distribution formalism to obtain the closed-form analytical expressions of the mean reaction time and the randomness parameter for reaction schemes where conformational fluctuations are present between two free enzyme conformers. Our studies confirm that the sole presence of free enzyme fluctuations yields a non Michaelis-Menten equation and can lead to dynamic cooperativity. The randomness parameter, which is a measure of the dynamic disorder in the system, converges to unity at a high substrate concentration. If slow fluctuations are present between the enzyme-substrate conformers (off-pathway mechanism), dynamic disorder is present at a high substrate concentration. Our results confirm that the dynamic disorder at a high substrate concentration is determined only by the slow fluctuations between the enzyme-substrate conformers and the randomness parameter is greater than unity. Slow conformational fluctuations between free enzymes are responsible for the emergence of dynamic cooperativity in single enzymes. Our theoretical findings are well supported by comparison with experimental data on the single enzyme beta-galactosidase.

单分子拉伸力实验中DNA解链动力学无序效应的介观统计研究

Recent single molecule pulling experiments on DNA unzipping have revealed a heavy-tailed rupture force distribution, indicating dynamic disorder. Here we present a theoretical framework based on a generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and power-law memory kernel to study the kinetics of DNA unzipping to address the effects of dynamic disorder on barrier-crossing kinetics under external pulling force. Such a GLE-fGn strategy is associated with the slow conformational fluctuations of macromolecules. By using the Kramers rate theory, we have obtained analytical formulae for the time-dependent rate coefficient k ( t , F ), and the distribution of rupture force p ( F ) which demonstrates a fat tail at high force as functions of time t and force F . In addition, through fitting our results to data from single molecule pulling experiments on DNA unzipping, we estimate the kinetic parameters and qualify the extent of disorder. Our work provides a plausible interpretation for the evidence of dynamic disorder in force-induced DNA unzipping, compared to two other models based on Bell model and Langevin equation (LE) approach.

How Reliable are Molecular Dynamics Simulations of Membrane Active Antimicrobial Peptides

Membrane-active antimicrobial peptides (AMPs) are challenging to study experimentally, but relatively easy to investigate using molecular dynamics (MD) computer simulations. For this reason, a large number of MD studies of AMPs have been reported over the recent years. Yet relatively little effort has focused on the validity of such simulations. Are these results reliable, and do they agree with what is known experimentally? And how much meaningful information can be obtained? To answer these questions, we demonstrate here some of the requirements and limitations of running MD simulations for several common AMPs: PGLa, melittin, maculatin and BP100. The two most important findings are: (a) Simulation results depend strongly on force field parameters, making experimental verification of the simulations obligatory, and (b) slow orientational and conformational fluctuations mean that much longer sampling timescales (multi-μs) are needed if quantitative agreement between simulation averages and experimental data is to be achieved.

Possible dynamically gated conductance along heme wires in bacterial multiheme cytochromes.

The staggered cross decaheme configuration of electron transfer cofactors in the outer-membrane cytochrome MtrF serves as a prototype for conformationally gated multiheme electron transport. Derived from the bacterium Shewanella oneidensis, the staggered cross configuration reveals intersecting c-type octaheme and tetraheme "wires" containing thermodynamic "hills" and "valleys" (Proc. Natl. Acad. Sci. U. S. A. 2014, 11, 611-616), suggesting that the protein structure may include a dynamical mechanism for conductance and pathway switching depending on enzymatic functional need. Here, we applied classical molecular and statistical mechanics calculations of large-amplitude protein dynamics in MtrF, to address its potential to modulate pathway conductance, including assessment of the effect of the total charge state. Explicit solvent molecular dynamics simulations of fully oxidized and fully reduced MtrF showed that the slowest mode of collective decaheme motion is 90% similar between the oxidized and reduced states and consists primarily of interheme separation with minor rotational contributions. The frequency of this motion is 1.7 × 10(7) s(-1), both for fully oxidized and fully reduced MtrF, slower than the downhill electron transfer rates between stacked heme pairs at the octaheme termini and faster than the electron transfer rates between parallel hemes in the tetraheme chain. This implies that MtrF uses slow conformational fluctuations to modulate electron flow along the octaheme pathway, apparently for the purpose of increasing the residence time of electrons on lowest potential hemes 4 and 9. This apparent gating mechanism should increase the success rate of electron transfer from MtrF to low potential environmental acceptors via these two solvent-exposed hemes.

How reliable are molecular dynamics simulations of membrane active antimicrobial peptides?

Membrane-active antimicrobial peptides (AMPs) are challenging to study experimentally, but relatively easy to investigate using molecular dynamics (MD) computer simulations. For this reason, a large number of MD studies of AMPs have been reported over recent years. Yet relatively little effort has focused on the validity of such simulations. Are these results reliable, and do they agree with what is known experimentally? And how much meaningful information can be obtained? To answer these questions, we demonstrate here some of the requirements and limitations of running MD simulations for several common AMPs: PGLa, melittin, maculatin and BP100. The two most important findings are: (a) simulation results depend strongly on force field parameters, making experimental verification of the simulations obligatory, and (b) slow orientational and conformational fluctuations mean that much longer sampling timescales (multi-μs) are needed if quantitative agreement between simulation averages and experimental data is to be achieved. This article is part of a Special Issue entitled: Interfacially Active Peptides and Proteins. Guest Editors: William C. Wimley and Kalina Hristova.

Dynamic regulation on energy landscape evolution of single-molecule protein by conformational fluctuation

We formalize a theory to help explore the effect of conformational fluctuation on the energy landscape evolution of single-molecule protein. Using this formalization, we investigate the photon emission from single photoactivated fluorescent protein. A bimodal regulation on the energy landscape evolution was discovered, and its origin was attributed to slow conformational fluctuations of the protein matrix.

Connecting Rare DNA Conformations and Surface Dynamics Using Single-Molecule Resonance Energy Transfer

A mechanistic understanding of single-stranded DNA (ssDNA) behavior in the near-surface environment is critical to advancing DNA-directed self-assembled nanomaterials. A new approach is described that uses total internal reflection fluorescence microscopy to measure resonance energy transfer at the single-molecule level, providing a mechanistic understanding of the connection between molecular conformation and interfacial dynamics near amine-modified surfaces. Large numbers (>10(5)) of ssDNA trajectories were observed, permitting dynamic correlation of molecular conformation with desorption and surface mobility. On the basis of dynamic behavior, molecules could be designated as members of the more common coiled population or a rare, weakly bound conformation. Molecules in the coiled state generally exhibited slow diffusion and conformational fluctuations that decreased with increasing average end-to-end distance. Lattice simulations of adsorbed self-avoiding polymers successfully predicted these trends. In contrast, the weakly bound conformation, observed in about 5% of molecules, had a large end-to-end distance but demonstrated conformational fluctuations that were much higher than predicted by simulations for adsorbed flexible chains. This conformation correlated positively with desorption events and led to fast diffusion, indicating weak surface associations. Understanding the role of the weakly bound conformation in DNA hybridization, and how solution conditions and surface properties may favor it, could lead to improved self-assembled nanomaterials.

Dynamics of Nucleosome Invasion by DNA Binding Proteins

Nucleosomes sterically occlude their wrapped DNA from interacting with many large protein complexes. How proteins gain access to nucleosomal DNA target sites in vivo is not known. Outer stretches of nucleosomal DNA spontaneously unwrap and rewrap with high frequency, providing rapid and efficient access to regulatory DNA target sites located there; however, rates for access to the nucleosome interior have not been measured. Here we show that for a selected high-affinity nucleosome positioning sequence, the spontaneous DNA unwrapping rate decreases dramatically with distance inside the nucleosome. The rewrapping rate also decreases, but only slightly. Our results explain the previously known strong position dependence on the equilibrium accessibility of nucleosomal DNA, which is characteristic of both selected and natural sequences. Our results point to slow nucleosome conformational fluctuations as a potential source of cell–cell variability in gene activation dynamics, and they reveal the dominant kinetic path by which multiple DNA binding proteins cooperatively invade a nucleosome.

Solution structure and fluctuation of the Mg2+‐bound form of calmodulin C‐terminal domain

Calmodulin (CaM) is a Ca(2+)-binding protein that functions as a ubiquitous Ca(2+)-signaling molecule, through conformational changes from the "closed" apo conformation to the "open" Ca(2+)-bound conformation. Mg(2+) also binds to CaM and stabilizes its folded structure, but the NMR signals are broadened by slow conformational fluctuations. Using the E104D/E140D mutant, designed to decrease the signal broadening in the presence of Mg(2+) with minimal perturbations of the overall structure, the solution structure of the Mg(2+)-bound form of the CaM C-terminal domain was determined by multidimensional NMR spectroscopy. The Mg(2+)-induced conformational change mainly occurred in EF hand IV, while EF-hand III retained the apo structure. The helix G and helix H sides of the binding sequence undergo conformational changes needed for the Mg(2+) coordination, and thus the helices tilt slightly. The aromatic rings on helix H move to form a new cluster of aromatic rings in the hydrophobic core. Although helix G tilts slightly to the open orientation, the closed conformation is maintained. The fact that the Mg(2+)-induced conformational changes in EF-hand IV and the hydrophobic core are also seen upon Ca(2+) binding suggests that the Ca(2+)-induced conformational changes can be divided into two categories, those specific to Ca(2+) and those common to Ca(2+) and Mg(2+).

Structural plasticity of staphylococcal nuclease probed by perturbation with pressure and pH

The ionization of internal groups in proteins can trigger conformational change. Despite this being the structural basis of most biological energy transduction, these processes are poorly understood. Small angle X-ray scattering (SAXS) and nuclear magnetic resonance (NMR) spectroscopy experiments at ambient and high hydrostatic pressure were used to examine how the presence and ionization of Lys-66, buried in the hydrophobic core of a stabilized variant of staphylococcal nuclease, affect conformation and dynamics. NMR spectroscopy at atmospheric pressure showed previously that the neutral Lys-66 affects slow conformational fluctuations globally, whereas the effects of the charged form are localized to the region immediately surrounding position 66. Ab initio models from SAXS data suggest that when Lys-66 is charged the protein expands, which is consistent with results from NMR spectroscopy. The application of moderate pressure (<2 kbar) at pH values where Lys-66 is normally neutral at ambient pressure left most of the structure unperturbed but produced significant nonlinear changes in chemical shifts in the helix where Lys-66 is located. Above 2 kbar pressure at these pH values the protein with Lys-66 unfolded cooperatively adopting a relatively compact, albeit random structure according to Kratky analysis of the SAXS data. In contrast, at low pH and high pressure the unfolded state of the variant with Lys-66 is more expanded than that of the reference protein. The combined global and local view of the structural reorganization triggered by ionization of the internal Lys-66 reveals more detectable changes than were previously suggested by NMR spectroscopy at ambient pressure.

Slow conformational motions that favor sub-picosecond motions important for catalysis.

It has been accepted for many years that functionally important motions are crucial to binding properties of ligands in such molecules as hemoglobin and myoglobin. In enzymatic reactions, theory and now experiment are beginning to confirm the importance of motions on a fast (ps) time scale in the chemical step of the catalytic process. What is missing is a clear physical picture of how slow conformational fluctuations are related to the fast motions that have been identified as crucial. This paper presents a theoretical analysis of this issue for human heart lactate dehydrogenase. We will examine how slow conformational motions bring the system to conformations that are distinguished as catalytically competent because they favor specific fast motions.

Dynamic disorder in quasi-equilibrium enzymatic systems.

Conformations and catalytic rates of enzymes fluctuate over a wide range of timescales. Despite these fluctuations, there exist some limiting cases in which the enzymatic catalytic rate follows the macroscopic rate equation such as the Michaelis-Menten law. In this paper we investigate the applicability of macroscopic rate laws for fluctuating enzyme systems in which catalytic transitions are slower than ligand binding-dissociation reactions. In this quasi-equilibrium limit, for an arbitrary reaction scheme we show that the catalytic rate has the same dependence on ligand concentrations as obtained from mass-action kinetics even in the presence of slow conformational fluctuations. These results indicate that the timescale of conformational dynamics – no matter how slow – will not affect the enzymatic rate in quasi-equilibrium limit. Our numerical results for two enzyme-catalyzed reaction schemes involving multiple substrates and inhibitors further support our general theory.

Computational identification of slow conformational fluctuations in proteins.

Conformational flexibility of proteins has been linked to their designated functions. Slow conformational fluctuations occurring at the microsecond to millisecond time scale, in particular, have recently attracted considerable interest in connection to the mechanism of enzyme catalysis. Computational methods are providing valuable insights into the connection between protein structure, flexibility, and function. In this report, we present studies on identification and characterization of microsecond flexibility of ubiquitin, based on quasi-harmonic analysis (QHA) and normal-mode analysis (NMA). The results indicate that the slowest 10 QHA modes, computed from the 0.5 mus molecular dynamics ensemble, contribute over 78% of all motions. The identified slow movements show over 75% similarity with the conformational fluctuations observed in nuclear magnetic resonance ensemble and also agree with displacements in the set of X-ray structures. The slowest modes show high flexibility in the beta1-beta2, alpha1-beta3, and beta3-beta4 loop regions, with functional implications in the mechanism of binding other proteins. NMA of ubiquitin structures was not able to reproduce the long time scale fluctuations, as they were found to strongly depend on the reference structures. Further, conformational fluctuations coupled to the cis/trans isomerization reaction catalyzed by the enzyme cyclophilin A (CypA), occurring at the microsecond to millisecond time scale, have also been identified and characterized on the basis of QHA of conformations sampled along the reaction pathway. The results indicate that QHA covers the same conformational landscape as the experimentally observed CypA flexibility. Overall, the identified slow conformational fluctuations in ubiquitin and CypA indicate that the intrinsic flexibility of these proteins is closely linked to their designated functions.

Dynamic Disorder-Driven Substrate Inhibition and Bistability in a Simple Enzymatic Reaction

Conformations and catalytic rates of enzymes (biological catalysts) fluctuate over a wide range of time scales. Recent experimental and theoretical investigations demonstrated case studies where the enzymatic catalysis rate follows the Michaelis-Menten (MM) rate law despite molecular fluctuations. In this paper, we investigate deviations from MM law and their effects on the dynamical behavior of the enzymatic network. We consider a simple kinetic scheme for a single substrate enzymatic reaction in which the product release step is treated explicitly. We examine how conformational fluctuations affect the underlying rate law in the quasi-static limit when conformational dynamics is very slow in one of the states. Our numerical results and analytically solvable model indicate that slow conformational fluctuations of the enzyme-substrate complex lead to non-MM behavior, substrate inhibition, and possible bistability of the reaction network.

Fluctuating Enzyme and Its Biological Functions: Positive Cooperativity without Multiple States

Positive, sigmoidal cooperativity is known to occur to a monomeric single-site enzyme with slow conformational fluctuations in its unbound (E) states when the enzyme undergoes steady-state catalytic turnover (mnemonic enzymes, hysteretic enzyme). We show that positive cooperativity occurs even when the E state is a single thermodynamic state, provided that the fluctuation amplitude of the state is sufficiently greater than that of the enzyme-substrate complex ES and the fluctuation times being comparable. This can occur even without mean structural change between E and ES. Slow conformational fluctuations are widely observed in enzymes. Our result suggests that enzymes with substrate association that reduces conformational fluctuations while maintaining fluctuation temporality can exhibit sigmoidal binding inside of living cells. Implications of this result on drug-target interactions are discussed.

Dynamics of a truncated prion protein, PrP(113–231), from 15N NMR relaxation: Order parameters calculated and slow conformational fluctuations localized to a distinct region

Prion diseases are associated with the misfolding of the prion protein (PrP(C)) from a largely alpha-helical isoform to a beta-sheet rich oligomer (PrP(Sc)). Flexibility of the polypeptide could contribute to the ability of PrP(C) to undergo the conformational rearrangement during PrP(C)-PrP(Sc) interactions, which then leads to the misfolded isoform. We have therefore examined the molecular motions of mouse PrP(C), residues 113-231, in solution, using (15)N NMR relaxation measurements. A truncated fragment has been used to eliminate the effect of the 90-residue unstructured tail of PrP(C) so the dynamics of the structured domain can be studied in isolation. (15)N longitudinal (T(1)) and transverse relaxation (T(2)) times as well as the proton-nitrogen nuclear Overhauser effects have been used to calculate the spectral density at three frequencies, 0, omega(N,) and 0.87omega(H). Spectral densities at each residue indicate various time-scale motions of the main-chain. Even within the structured domain of PrP(C), a diverse range of motions are observed. We find that removal of the tail increases T(2) relaxation times significantly indicating that the tail is responsible for shortening of T(2) times in full-length PrP(C). The truncated fragment of PrP has facilitated the determination of meaningful order parameters (S(2)) from the relaxation data and shows for the first time that all three helices in PrP(C) have similar rigidity. Slow conformational fluctuations of mouse PrP(C) are localized to a distinct region that involves residues 171 and 172. Interestingly, residues 170-175 have been identified as a segment within PrP that will form a steric zipper, believed to be the fundamental amyloid unit. The flexibility within these residues could facilitate the PrP(C)-PrP(Sc) recognition process during fibril elongation.

Simultaneous measurement of fluorescence anisotropy and translational fluctuations by polarization-modulated MFICS

A novel, high signal-to-noise strategy is presented for phase-selective, wavevector- and polarization-resolved fluorescence fluctuation spectroscopy. The approach is based on molecular Fourier imaging correlation spectroscopy (MFICS) and combines polarization- and intensity-modulated photoexcitation with phase-synchronous detection to simultaneously monitor centre-of-mass and slow fluorescence anisotropy fluctuations from a relatively large number (∼106) of fluorescent molecules. The method is demonstrated using DsRed, a tetrameric complex of fluorescent protein subunits, to unambiguously separate signal contributions due to slow optical conformational fluctuations from translational diffusion.

Local structural plasticity of the prion protein. Analysis of NMR relaxation dynamics.

A template-assisted conformational change of the cellular prion protein (PrP(C)) from a predominantly helical structure to an amyloid-type structure with a higher proportion of beta-sheet is thought to be the causative factor in prion diseases. Since flexibility of the polypeptide is likely to contribute to the ability of PrP(C) to undergo the conformational change that leads to the infective state, we have undertaken a comprehensive examination of the dynamics of two recombinant Syrian hamster PrP fragments, PrP(29-231) and PrP(90-231), using (15)N NMR relaxation measurements. The molecular motions of these PrP fragments have been studied in solution using (15)N longitudinal (T(1)) and transverse relaxation (T(2)) measurements as well as [(1)H]-(15)N nuclear Overhauser effects (NOE). These data have been analyzed using both reduced spectral density mapping and the Lipari-Szabo model free formalism. The relaxation properties of the common regions of PrP(29-231) and PrP(90-231) are very similar; both have a relatively inflexible globular domain (residues 128-227) with a highly flexible and largely unstructured N-terminal domain. Residues 29-89 of PrP(29-231), which include the copper-binding octarepeat sequences, are also highly flexible. Analysis of the spectral densities at each residue indicates that even within the structured core of PrP(C), a markedly diverse range of motions is observed, consistent with the inherent plasticity of the protein. The central portions of helices B and C form a relatively rigid core, which is stabilized by the presence of an interhelix disulfide bond. Of the remainder of the globular domain, the parts that are not in direct contact with the rigid region, including helix A, are more flexible. Most significantly, slow conformational fluctuations on a millisecond to microsecond time scale are observed for the small beta-sheet. These results are consistent with the hypothesis that the infectious, scrapie form of the protein PrP(Sc) could contain a helical core consisting of helices B and C, similar in structure to the cellular form PrP(C). Our results indicate that residues 90-140, which are required for prion infectivity, are relatively flexible in PrP(C), consistent with a lowered thermodynamic barrier to a template-assisted conformational change to the infectious beta-sheet-rich scrapie isoform.

Backbone dynamics of the c-Myb DNA-binding domain complexed with a specific DNA.

The DNA-binding domain of c-Myb consists of three imperfect tandem repeats, R1, R2, and R3. Each repeat contains three helices. The minimal DNA-binding domain is an R2R3 fragment. Here, we have examined the backbone dynamics of R2R3 in its DNA-bound form by NMR. Upon binding to DNA, the N- and C-termini, and the linker between R2 and R3 become less flexible. In the free form the third helix of R2 exhibits slow conformational exchange fluctuations owing to a cavity in the hydrophobic core of R2. Upon binding to DNA, the conformational exchange contributions in R2 are reduced but remain significant in NMR relaxation measurements. Upon binding to DNA, the third helix of R3 comes to exhibit significant chemical exchange contributions. These findings suggest that the orientations of the third helices of both R2 and R3 as to DNA are being chemically exchanged. In the DNA-bound form both R2 and R3 exhibit similar dynamical characters, except for amino acids Trp 95, Thr 96, and Val 103 of R2, which are located around the cavity of the unbound form. Upon binding to DNA, since Trp 95 moves into the cavity to fill it up, the local conformational exchange contributions seem to be still observable around the filled cavity.