Hopping around an entropic barrier created by force

We use Langevin dynamics to investigate the role played by the recently discovered force-induced entropic energy barrier on the two-state hopping phenomena that has been observed in single RNA, DNA and protein molecules placed under a stretching force. Simple considerations about the free energy of a molecule readily show that the application of force introduces an entropic barrier separating the collapsed state of the molecule, from a force-driven extended conformation. A notable characteristic of the force induced barrier is its long distances to transition state, up to tens of nanometers, which renders the kinetics of crossing this barrier highly sensitive to an applied force. Langevin dynamics across such force induced barriers readily demonstrates the hopping behavior observed for a variety of single molecules placed under force. Such hopping is frequently interpreted as a manifestation of two-state folding/unfolding reactions observed in bulk experiments. However, given that such barriers do not exist at zero force these reactions do not take place at all in bulk.     

丁香油酚和乙酸香茅酯对蜂王信息素活性的影响:量子化学研究

植物次生代谢物质可影响昆虫信息素的功能,但有关影响机制尚不清楚。本文利用量子化学理论分析了广泛存在于花粉或花蜜中的挥发性丁香油酚和乙酸香茅酯能否与蜜蜂蜂王信息素挥发性成分4-羟基-3-甲氧苯乙醇(HVA)反应。使用Gaussian 09软件来完成几何优化、过渡态搜索、频率分析,并计算了反应能垒和速率常数。结果表明,丁香油酚和HVA分别与OH自由基反应生成有机自由基后,通过自由基-自由基途径发生聚合反应(反应能垒为0.613077 kcal/mol,反应速率常数为9.559953×1011cm3/molecule/s),而不易通过自由基-分子途径发生反应(反应能垒为31.792769 kcal/mol,反应速率常数为4.268854×10-13cm3/molecule/s)。相似地,乙酸香茅酯和HVA分别与OH自由基反应后,也可通过自由基-自由基途径发生反应(反应能垒为2.086469 kcal/mol,反应速率常数为2.328216×1011cm3/molecule/s),但不易通过自由基-分子途径发生反应(反应能垒为25.881002 kcal/mol,反应速率常数为1.513828×10-8cm3/molecule/s)。由于全球环境变化可能导致大气中OH自由基浓度升高,使得花蜜或花粉中挥发性不饱和化合物有可能影响蜂王信息素的功能,从而干扰蜂群的化学通讯。     

A quantum chemical study of the water-assisted mechanism in one-carbon unit transfer reaction catalyzed by glycinamide ribonucleotide transformylase

A theoretical study for the water-assisted mechanism in one-carbon unit transfer reaction catalyzed by glycinamide ribonucleotide transformylase (GAR Tfase) is investigated in which the proton transfers in an indirect way and the energy barrier for each transition state has been lowered about 80–100 kJ/mol when compared with the corresponding one in a no-water-involved mechanism. There are two possible pathways in each mechanism: one is concerted and the other is stepwise. Our results have verified the presumption from experiments that one water molecule can assist to achieve the whole reaction. Because the addition of this water molecule in the transition states can relax the strong strain in the unstable system and greatly lowered the energy barrier. The water-assisted paths are preferable to the no-water-involved ones and the bulk solvent effect of water is also discussed.     

Direct Quantification of the Attempt Frequency Determining the Mechanical Unfolding of Ubiquitin Protein

Understanding protein dynamics requires a comprehensive knowledge of the underlying potential energy surface that governs the motion of each individual protein molecule. Single molecule mechanical studies have provided the unprecedented opportunity to study the individual unfolding pathways along a well defined coordinate, the end-to-end length of the protein. In these experiments, unfolding requires surmounting an energy barrier that separates the native from the extended state. The calculation of the absolute value of the barrier height has traditionally relied on the assumption of an attempt frequency, υ^‡. Here we used single molecule force-clamp spectroscopy to directly determine the value of υ^‡ for mechanical unfolding by measuring the unfolding rate of the small protein ubiquitin at varying temperatures. Our experiments demonstrate a significant effect of the temperature on the mechanical rate of unfolding. By extrapolating the unfolding rate in the absence of force for different temperatures, varying within the range spanning from 5 to 45 °C, we measured a value for the activation barrier of ΔG^‡ = 71 ± 5 kJ/mol and an exponential prefactor υ^‡ ∼4 × 10⁹ s⁻¹. Although the measured prefactor value is 3 orders of magnitude smaller than the value predicted by the transition state theory (∼6 × 10¹² s⁻¹), it is 400-fold higher than that encountered in analogous experiments studying the effect of temperature on the reactivity of a protein-embedded disulfide bond (∼10⁷ m⁻¹ s⁻¹). This approach will allow quantitative characterization of the complete energy landscape of a folding polypeptide from highly extended states, of capital importance for proteins with elastic function.     

Exponential decay kinetics in "downhill" protein folding

The observation of single-exponential kinetic phases in early stages of protein folding is often interpreted as evidence that these phases are rate limited by significant energy or entropy barriers. However, although the existence of large barriers reliably implies exponential kinetics, the reverse is not necessarily true. A simple model for the hydrophobic collapse of a chain molecule demonstrates that a barrierless or "downhill" diffusional relaxation can give rise to kinetics that are practically indistinguishable from a pure exponential. Within this model, even a highly nonlinear experimental probe such as resonance energy transfer (F?rster transfer) could exhibit a large amplitude decay (greater than 90% in fluorescence) that deviates from a simple exponential by less than 0.5%. Only a detailed analysis of the dynamics is likely to reveal that a free energy barrier is absent.     

Theory of cooperative transitions in protein molecules. I. Why denaturation of globular protein is a first-order phase transition

A theory of equilibrium denaturation of proteins is suggested. According to this theory, a cornerstone of protein denaturation is disruption of tight packing of side chains in protein core. Investigation of this disruption is the object of this paper. It is shown that this disruption is an "all-or-none" transition (independent of how compact is the denatured state of a protein and independent of the protein-solvent interactions) because expansion of a globule must exceed some threshold to release rotational isomerization of side chains. Smaller expansion cannot produce entropy compensation of nonbonded energy loss; this is the origin of a free-energy barrier (transition state) between the native and denatured states. The density of the transition state is so high that the solvent cannot penetrate into protein in this state. The results obtained in this paper make it possible to present in the following paper a general phase diagram of protein molecule in solution.     

Comparing proteins by their unfolding pattern

Single molecule force spectroscopy has evolved into an important and extremely powerful technique for investigating the folding potentials of biomolecules. Mechanical tension is applied to individual molecules, and the subsequent, often stepwise unfolding is recorded in force extension traces. However, because the energy barriers of the folding potentials are often close to the thermal energy, both the extensions and the forces at which these barriers are overcome are subject to marked fluctuations. Therefore, force extension traces are an inadequate representation despite widespread use particularly when large populations of proteins need to be compared and analyzed. We show in this article that contour length, which is independent of fluctuations and alterable experimental parameters, is a more appropriate variable than extension. By transforming force extension traces into contour length space, histograms are obtained that directly represent the energy barriers. In contrast to force extension traces, such barrier position histograms can be averaged to investigate details of the unfolding potential. The cross-superposition of barrier position histograms allows us to detect and visualize the order of unfolding events. We show with this approach that in contrast to the sequential unfolding of bacteriorhodopsin, two main steps in the unfolding of the enzyme titin kinase are independent of each other. The potential of this new method for accurate and automated analysis of force spectroscopy data and for novel automated screening techniques is shown with bacteriorhodopsin and with protein constructs containing GFP and titin kinase.     

ROSETTALIGAND: protein-small molecule docking with full side-chain flexibility

Protein-small molecule docking algorithms provide a means to model the structure of protein-small molecule complexes in structural detail and play an important role in drug development. In recent years the necessity of simulating protein side-chain flexibility for an accurate prediction of the protein-small molecule interfaces has become apparent, and an increasing number of docking algorithms probe different approaches to include protein flexibility. Here we describe a new method for docking small molecules into protein binding sites employing a Monte Carlo minimization procedure in which the rigid body position and orientation of the small molecule and the protein side-chain conformations are optimized simultaneously. The energy function comprises van der Waals (VDW) interactions, an implicit solvation model, an explicit orientation hydrogen bonding potential, and an electrostatics model. In an evaluation of the scoring function the computed energy correlated with experimental small molecule binding energy with a correlation coefficient of 0.63 across a diverse set of 229 protein- small molecule complexes. The docking method produced lowest energy models with a root mean square deviation (RMSD) smaller than 2 A in 71 out of 100 protein-small molecule crystal structure complexes (self-docking). In cross-docking calculations in which both protein side-chain and small molecule internal degrees of freedom were varied the lowest energy predictions had RMSDs less than 2 A in 14 of 20 test cases.     

Reovirus FAST Proteins Drive Pore Formation and Syncytiogenesis Using a Novel Helix-Loop-Helix Fusion-Inducing Lipid Packing Sensor

Pore formation is the most energy-demanding step during virus-induced membrane fusion, where high curvature of the fusion pore rim increases the spacing between lipid headgroups, exposing the hydrophobic interior of the membrane to water. How protein fusogens breach this thermodynamic barrier to pore formation is unclear. We identified a novel fusion-inducing lipid packing sensor (FLiPS) in the cytosolic endodomain of the baboon reovirus p15 fusion-associated small transmembrane (FAST) protein that is essential for pore formation during cell-cell fusion and syncytiogenesis. NMR spectroscopy and mutational studies indicate the dependence of this FLiPS on a hydrophobic helix-loop-helix structure. Biochemical and biophysical assays reveal the p15 FLiPS preferentially partitions into membranes with high positive curvature, and this partitioning is impeded by bis-ANS, a small molecule that inserts into hydrophobic defects in membranes. Most notably, the p15 FLiPS can be functionally replaced by heterologous amphipathic lipid packing sensors (ALPS) but not by other membrane-interactive amphipathic helices. Furthermore, a previously unrecognized amphipathic helix in the cytosolic domain of the reptilian reovirus p14 FAST protein can functionally replace the p15 FLiPS, and is itself replaceable by a heterologous ALPS motif. Anchored near the cytoplasmic leaflet by the FAST protein transmembrane domain, the FLiPS is perfectly positioned to insert into hydrophobic defects that begin to appear in the highly curved rim of nascent fusion pores, thereby lowering the energy barrier to stable pore formation.     

Converting structural changes upon oxidation of cytochrome c to electrostatic reorganization energy

The observed X-ray structural differences between reduced and oxidized cytochrome c are converted to electrostatic energy. This conversion is used to estimate the protein reorganization energy which determines the protein contribution to the activation barrier for the electron transfer reaction. It is shown that the reorganization energy of cytochrome c is much smaller than the corresponding energy for electron transfer in water and that this is consistent with the role for cytochromes as electron transfer catalysts.     

Kinetics of adsorption of globular proteins at an air-water interface.

Adsorption of globular proteins at an air-water interface from an infinite stagnant medium was modeled as one-dimensional diffusion in a potential field. The interaction potential experienced by an adsorbing molecule consisted of contributions from electrostatic interactions, work done against the surface pressure to clear area at the interface in order to anchor the adsorbed segments, and the change in the free energy due to exposure of penetrated surface hydrophobic functional groups to air. The assumption of irreversible adsorption is employed in the present analysis. The energy barrier to adsorption, present at sufficiently large surface pressures, was found to be higher for smaller surface hydrophobicities, larger surface pressures, larger size molecules, and oblate orientation of an ellipsoidal molecule. Consequently, more adsorption occurred at larger surface hydrophobicities, smaller size molecules, and for prolate orientation of ellipsoidal molecules. The subphase concentration has been shown to be zero at short times, increasing with time at larger times, and eventually becoming close to the bulk concentration as a result of increasing energy barrier to adsorption. The predicted evolution of surface concentration with time for adsorption of lysozyme at an air-water interface agreed well with the experimental data of Graham and Phillips (1979a).     

Regulation of the micromechanical properties of pulmonary endothelium by S1P and thrombin: role of cortactin

Disruption of pulmonary endothelial cell (EC) barrier function is a critical pathophysiologic event in highly morbid inflammatory conditions such as sepsis and acute respiratory disease stress syndrome. Actin cytoskeleton, an essential regulator of endothelial permeability, is a dynamic structure whose stimuli-induced rearrangement is linked to barrier modulation. Here, we used atomic force microscopy to characterize structural and mechanical changes in the F-actin cytoskeleton of cultured human pulmonary artery EC in response to both barrier-enhancing (induced by sphingosine 1-phosphate (S1P)) and barrier-disrupting (induced by thrombin) conditions. Atomic force microscopy elasticity measurements show differential effects: for the barrier protecting molecule S1P, the elastic modulus was elevated significantly on the periphery; for the barrier-disrupting molecule thrombin, on the other hand, it was elevated significantly in the central region of the cell. The force and elasticity maps correlate with F-actin rearrangements as identified by immunofluorescence analysis. Significantly, reduced expression (via siRNA) of cortactin, an actin-binding protein essential to EC barrier regulation, resulted in a shift in the S1P-mediated elasticity pattern to more closely resemble control, unstimulated endothelium.     

A molecular dynamics study of thermodynamic and structural aspects of the hydration of cavities in proteins.

The structure and activity of a protein molecule are strongly influenced by the extent of hydration of its cavities. This is, in turn, related to the free energy change on transfer of a water molecule from bulk solvent into a cavity. Such free energy changes have been calculated for two cavities in a sulfate-binding protein. One of these cavities contains a crystallographically observed water molecule while the other does not. Thermodynamic integration and perturbation methods were used to calculate free energies of hydration for each of the cavities from molecular dynamics simulations of two separate events: the removal of a water molecule from pure water, and the introduction of a water molecule into each protein cavity. From the simulations for the pure water system, the excess chemical potential of water was computed to be -6.4 +/- 0.4 kcal/mol, in accord with experiment and with other recent theoretical calculations. For the protein cavity containing an experimentally observed water molecule, the free energy change on hydrating it with one water molecule was calculated as -10.0 +/- 1.3 kcal/mol, indicating the high probability that this cavity is occupied by a water molecule. By contrast, for the cavity in which no water molecules were experimentally observed, the free energy change on hydrating it with one water molecule was calculated as 0.2 +/- 1.5 kcal/mol, indicating its low occupancy by water. The agreement of these results with experiment suggests that thermodynamic simulation methods may become useful for the prediction and analysis of internal hydration in proteins.     

The effect of viscosity on the accessibility of the single tryptophan in human serum albumin.

When reactions take place with one of the reactants tied to protein matrix, movements along the reaction coordinate towards the transition state can become coupled to structural fluctuations of the protein matrix. This investigation aims to test the assumptions underlying the arguments supporting such a coupling. A coupling is allowed only if the activation barrier is high and broad enough as shown to be the case for the proton catalyzed isotope exchange at Trp-63 of lysozyme. In the present investigation the activation barrier for the same reaction has been lowered radically in an effort to show that the coupling, as measured by the dependence of rate on solution viscosity, will diminish and ideally vanish, despite the unchanged effects of cosolvents on the chemical activities of all the reactants. The isotope exchange rate at the indole nitrogen of the single tryptophan residue of human serum albumin was measured with UV. This residue is rigidly held to the protein surface and the solvent access, although restricted, corresponds to a partially exposed residue. As a consequence, the isotope exchange rates and the bimolecular quenching rate of fluorescence by acrylamide, also measured, are high. The experiments were carried out at pH 5.2 where the molecule is in the N-form and the exchange is catalyzed by OH- ions. The activation energy of the hydroxyl catalyzed reaction is 22 kJ lower than for the proton catalyzed process. Under these conditions the exchange rate is viscosity independent both in the case of glycerol and in ethylene glycol.(ABSTRACT TRUNCATED AT 250 WORDS)     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.     

Light activation of the isomerization and deprotonation of the protonated Schiff base retinal

We perform an ab initio analysis of the photoisomerization of the protonated Schiff base of retinal (PSB-retinal) from 11-cis to 11-trans rotating the C10-C11=C12-C13 dihedral angle from 0° (cis) to -180° (trans). We find that the retinal molecule shows the lowest rotational barrier (0.22 eV) when its charge state is zero as compared to the barrier for the protonated molecule which is ∼0.89 eV. We conclude that rotation most likely takes place in the excited state of the deprotonated retinal. The addition of a proton creates a much larger barrier implying a switching behavior of retinal that might be useful for several applications in molecular electronics. All conformations of the retinal compound absorb in the green region with small shifts following the dihedral angle rotation; however, the Schiff base of retinal (SB-retinal) at trans-conformation absorbs in the violet region. The rotation of the dihedral angle around the C11=C12 π-bond affects the absorption energy of the retinal and the binding energy of the SB-retinal with the proton at the N-Schiff; the binding energy is slightly lower at the trans-SB-retinal than at other conformations of the retinal.     

Structure, force, and energy of a double-stranded DNA oligonucleotide under tensile loads

The end-to-end stretching of a duplex DNA oligonucleotide has been studied using potential of mean force (PMF) calculations based on molecular dynamics (MD) simulations and atomic force microscopy (AFM) experiments. Near quantitative agreement between the calculations and experiments was obtained for both the extension length and forces associated with strand separation. The PMF calculations show that the oligonucleotide extends without a significant energetic barrier from a length shorter than A-DNA to a length 2.4 times the contour length of B-DNA at which the barrier to strand separation is encountered. Calculated forces associated with the barrier are 0.09±0.03 nN, based on assumptions concerning tip and thermal-activated barrier crossing contributions to the forces. Direct AFM measurements show the oligonucleotide strands separating at 2.6±0.8 contour lengths with a force of 0.13±0.05 nN. Analysis of the energies from the MD simulations during extension reveals compensation between increases in the DNA-self energy and decreases in the DNA-solvent interaction energy, allowing for the barrierless extension of DNA beyond the canonical B form. The barrier to strand separation occurs when unfavorable DNA interstrand repulsion cannot be compensated for by favorable DNA-solvent interactions. The present combination of single molecule theoretical and experimental approaches produces a comprehensive picture of the free energy surface of biological macromolecular structural transitions. Received: 2 June 1998 / Revised version: 25 January 1999 / Accepted: 11 February 1999     

A channel mechanism for electrogenic ion pumps.

A model of active ion transport is analyzed in which an essential part of the pumps molecule is an ion channel. Ion translocation in the channel is described as a series of jumps between binding sites which are separated by energy barriers. Pumping action results from a transient energy-dependent modification of the barrier structure of the channel and requires only minor conformational changes of the pump molecule. This model is applied to the light-driven proton pump of Halobacterium and to redox-coupled proton pumps in the mitochondrial respiratory chain. Similar considerations may be used to describe ATP-dependent ion transport.     

A desolvation barrier to hydrophobic cluster formation may contribute to the rate-limiting step in protein folding.

To gain insight into the free energy changes accompanying protein hydrophobic core formation, we have used computer simulations to study the formation of small clusters of nonpolar solutes in water. A barrier to association is observed at the largest solute separation that does not allow substantial solvent penetration. The barrier reflects an effective increase in the size of the cavity occupied by the expanded but water-excluding cluster relative to both the close-packed cluster and the fully solvated separated solutes; a similar effect may contribute to the barrier to protein folding/unfolding. Importantly for the simulation of protein folding without explicit solvent, we find that the interactions between nonpolar solutes of varying size and number can be approximated by a linear function of the molecular surface, but not the solvent-accessible surface of the solutes. Comparison of the free energy of cluster formation to that of dimer formation suggests that the assumption of pair additivity implicit in current protein database derived potentials may be in error.     

Posttransition state desolvation of the hydrophobic core of the src-SH3 protein domain

The folding thermodynamics of the src-SH3 protein domain were characterized under refolding conditions through biased fully atomic molecular dynamics simulations with explicit solvent. The calculated free energy surfaces along several reaction coordinates revealed two barriers. The first, larger barrier was identified as the transition state barrier for folding, associated with the formation of the first hydrophobic sheet of the protein. phi values calculated from structures residing at the transition state barrier agree well with experimental phi values. The microscopic information obtained from our simulations allowed us to unambiguously assign intermediate phi values as the result of multiple folding pathways. The second, smaller barrier occurs later in the folding process and is associated with the cooperative expulsion of water molecules between the hydrophobic sheets of the protein. This posttransition state desolvation barrier cannot be observed through traditional folding experiments, but is found to be critical to the correct packing of the hydrophobic core in the final stages of folding. Hydrogen exchange and NMR experiments are suggested to probe this barrier.