Analysis of the unfolding process of green fluorescent protein by molecular dynamics simulation

Molecular dynamics simulation of the enforced stretching of circularly permuted green fluorescent protein (cpGFP) was performed to observe the detailed process of unfolding of beta-sheets in cpGFP and to clarify the structural change arising from the force. The simulation using the generalized Born method with original force field parameters enabled us to observe the unfolding process of the entire region of the protein and to clarify atom motion of the individual domain during the stretching. The force required for the stretching of cpGFP was estimated from the differential of the computed potential energy. A prominent rise in force appeared three times during the stretching. The amplitude and the position of these three peaks were consistent with the observation in atomic force microscopy (AFM) experiments. Further, the movements of atoms involved in each peak were shown to be closely related to the dissociation of hydrogen bonds. Additional simulations for the unfolding process of titin and spectrin also gave satisfactory interpretation of the results of previous AFM experiments. The difference in the enforced stretching process between cpGFP and wild-type GFP was further discussed through the MD simulation.     

Mechanical unfolding of segment-swapped protein G dimer: results from replica exchange molecular dynamics simulations

The protein G dimer (pdb code 1Q10) is a mutated dimeric form of the immunoglobulin-binding domain B1 of streptococcal protein G, in which the two monomeric units have swapped elements of their secondary structure. We have used replica exchange molecular dynamics simulations to study how this dimer responds to a mechanical force that pulls the N-terminus of one unit and the C-terminus of the other apart. We have further compared the mechanical response of the dimer to that of the protein G monomer. When the pulling force is low enough, the mechanical unfolding can be viewed as a thermally activated barrier crossing process. For each protein, we have computed the corresponding free energy barrier and its dependence on the pulling force. While the dimer is found to be less resistant to mechanical unfolding than its monomeric counterpart, the two proteins exhibit essentially the same mechanical unfolding mechanism involving separation of the terminal parallel strands. On the basis of our results, we speculate that the mechanical properties of natural adhesives, composites, fibers, and other materials may be optimized not only at a single molecule level but also at the mesoscopic level through the interactions among individual chains.     

Transient violations of the second law of thermodynamics in protein unfolding examined using synthetic atomic force microscopy and the fluctuation theorem

The synthetic atomic force microscopy (AFM) method is developed to simulate a periodically replicated atomistic system subject to force and length fluctuations characteristic of an AFM experiment. This new method is used to examine the forced-extension and subsequent rupture of the alpha-helical linker connecting periodic images of a spectrin protein repeat unit. A two-dimensional potential of mean force (PMF) along the length and a reaction coordinate describing the state of the linker was calculated. This PMF reveals that the basic material properties of the spectrin repeat unit are sensitive to the state of linker, an important feature that cannot be accounted for in a one-dimensional PMF. Furthermore, nonequilibrium simulations were generated to examine the rupture event in the context of the fluctuation theorem. These atomistic simulations demonstrate that trajectories which are in apparent violation of the second law can overcome unfolding barriers at significantly reduced rupture forces.     

Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin. Unfolding rates calculated from simulations over a broad range of stretching forces, for different pulling directions, reveal a remarkable "turnover" from a force-independent process at low force to a force-dependent process at high force, akin to the "roll-over" in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrate that it can occur for dynamics in just two dimensions. We relate the turnover to the quality of the pulling direction as a reaction coordinate for the intrinsic folding mechanism. A novel pulling direction, designed to be the most relevant to the intrinsic folding pathway, results in the smallest turnover. Our results are in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.     

Topography of the free-energy landscape probed via mechanical unfolding of proteins

Single-molecule experiments in which proteins are unfolded by applying mechanical stretching forces generally force unfolding to proceed along a reaction coordinate that is different from that in chemical or thermal denaturation. Here we simulate the mechanical unfolding and refolding of a minimalist off-lattice model of the protein ubiquitin to explore in detail the slice of the multidimensional free-energy landscape that is accessible via mechanical pulling experiments. We find that while the free-energy profile along typical "chemical" reaction coordinates may exhibit two minima, corresponding to the native and denatured states, the free energy G(z) is typically a monotonic function of the mechanical coordinate z equal to the protein extension. Application of a stretching force along z tilts the free-energy landscape resulting in a bistable (or multistable) free energy G(z)-fz probed in mechanical unfolding experiments. We construct a two-dimensional free-energy surface as a function of both chemical and mechanical reaction coordinates and examine the coupling between the two. We further study the refolding trajectories after the protein has been prestretched by a large force, as well as the mechanical unfolding trajectories in the presence of a large stretching force. We demonstrate that the stretching forces required to destabilize the native state thermodynamically are larger than those expected on the basis of previous experimental estimates of G(z). This finding is consistent with the recent experimental studies, indicating that proteins may refold even in the presence of a substantial stretching force. Finally, we show that for certain temperatures the free energy of a polyprotein chain consisting of multiple domains is a linear function of the chain extension. We propose that the recently observed "slow phase" in the refolding of proteins under mechanical tension may be viewed as downhill diffusion in such a linear potential.     

Forces between a rigid probe particle and a liquid interface. II. The general case

The semianalytic theory developed previously (Chan, D. Y. C., Dagastine, R. R., and White, L. R., J. Colloid Interface Sci. 236, 141 (2001)) to predict the force curve of an AFM measurement at a liquid interface using a colloidal probe has been expanded to incorporate a general force law with both attractive and repulsive forces. Expressions for the gradient of the force curve are developed to calculate the point at which the probe particle on the cantilever will spontaneously jump in toward the liquid interface. The calculation of the jump instability is reduced to a straightforward embroidery of the simple algorithms presented in Chan et al. In a variety of sample calculations using force laws including van der Waals, electrostatic, and hydrophobic forces for both oil/water and bubble/water interfaces, we have duplicated the general behaviors observed in several AFM investigations at liquid interfaces. The behavior of the drop as a Hookean spring and the numerical difficulties of a full numerical calculation of F(deltaX) are also discussed.     

New force replica exchange method and protein folding pathways probed by force-clamp technique

We have developed a new extended replica exchange method to study thermodynamics of a system in the presence of external force. Our idea is based on the exchange between different force replicas to accelerate the equilibrium process. This new approach was applied to obtain the force-temperature phase diagram and other thermodynamical quantities of the three-domain ubiquitin. Using the C(alpha)-Go model and the Langevin dynamics, we have shown that the refolding pathways of single ubiquitin depend on which terminus is fixed. If the N end is fixed then the folding pathways are different compared to the case when both termini are free, but fixing the C terminal does not change them. Surprisingly, we have found that the anchoring terminal does not affect the pathways of individual secondary structures of three-domain ubiquitin, indicating the important role of the multidomain construction. Therefore, force-clamp experiments, in which one end of a protein is kept fixed, can probe the refolding pathways of a single free-end ubiquitin if one uses either the polyubiquitin or a single domain with the C terminus anchored. However, it is shown that anchoring one end does not affect refolding pathways of the titin domain I27, and the force-clamp spectroscopy is always capable to predict folding sequencing of this protein. We have obtained the reasonable estimate for unfolding barrier of ubiquitin, using the microscopic theory for the dependence of unfolding time on the external force. The linkage between residue Lys48 and the C terminal of ubiquitin is found to have the dramatic effect on the location of the transition state along the end-to-end distance reaction coordinate, but the multidomain construction leaves the transition state almost unchanged. We have found that the maximum force in the force-extension profile from constant velocity force pulling simulations depends on temperature nonlinearly. However, for some narrow temperature interval this dependence becomes linear, as have been observed in recent experiments.     

Mechanical unfolding of the beet western yellow virus -1 frameshift signal

Using mechanical unfolding by optical tweezers (OT) and steered molecular dynamics (SMD) simulations, we have demonstrated the critical role of Mg(2+) ions for the resistance of the Beet Western Yellow Virus (BWYV) pseudoknot (PK) to unfolding. The two techniques were found to be complementary, providing information at different levels of molecular scale. Findings from the OT experiments indicated a critical role of stem 1 for unfolding of the PK, which was confirmed in the SMD simulations. The unfolding pathways of wild type and mutant appeared to depend upon pH and nucleotide sequence. SMD simulations support the notion that the stability of stem 1 is critical for -1 frameshifting. The all-atom scale nature of the SMD enabled clarification of the precise role of two Mg(2+) ions, Mg45 and Mg52, as identified in the BWYV X-ray crystallography structure, in -1 frameshifting. On the basis of simulations with "partially" and "fully" hydrated Mg(2+) ions, two possible mechanisms of stabilizing stem 1 are proposed. In both these cases Mg(2+) ions play a critical role in stabilizing stem 1, either by directly forming a salt bridge between the strands of stem 1 or by stabilizing parallel orientation of the strands in stem 1, respectively. These findings explain the unexpected drop in frameshifting efficiency to null levels of the C8U mutant in a manner consistent with experimental observations.     

Direct Observation of the Reversible Two‐State Unfolding and Refolding of an α/β Protein by Single‐Molecule Atomic Force Microscopy

Directly observing protein folding in real time using atomic force microscopy (AFM) is challenging. Here the use of AFM to directly monitor the folding of an α/β protein, NuG2, by using low‐drift AFM cantilevers is demonstrated. At slow pulling speeds (<50 nm s^?1), the refolding of NuG2 can be clearly observed. Lowering the pulling speed reduces the difference between the unfolding and refolding forces, bringing the non‐equilibrium unfolding–refolding reactions towards equilibrium. At very low pulling speeds (ca. 2 nm s^?1), unfolding and refolding were observed to occur in near equilibrium. Based on the Crooks fluctuation theorem, we then measured the equilibrium free energy change between folded and unfolded states of NuG2. The improved long‐term stability of AFM achieved using gold‐free cantilevers allows folding–unfolding reactions of α/β proteins to be directly monitored near equilibrium, opening the avenue towards probing the folding reactions of other mechanically important α/β and all‐β elastomeric proteins.     

Modeling force-induced bio-polymer unfolding

We study the conformations of polymer chains in a poor solvent, with and without bending rigidity, by means of a simple statistical mechanics model. This model can be exactly solved for chains of length up to N = 55 using exact enumeration techniques. We analyze in detail the differences between the constant force and constant distance ensembles for large but finite N. At low temperatures, and in the constant force ensemble, the force–extension curve shows multiple plateaus (intermediate states), in contrast with the abrupt transition to an extended state prevailing in the N → ∞ limit. In the constant distance ensemble, the same curve provides a unified response to pulling and compressing forces, and agrees qualitatively with recent experimental results. We identify a cross-over length, proportional to N, below which the critical force of unfolding decreases with temperature, while above, it increases with temperature. Finally, the force–extension curve for stiff chains exhibits “saw-tooth” like behavior, as observed in protein unfolding experiments.     

Diffusion in linear porous media with periodic entropy barriers: A tube formed by contacting spheres

The problem of transport in quasi-one-dimensional periodic structures has been studied recently by several groups [D. Reguera et al., Phys. Rev. Lett.96, 130603 (2006); P. S. Burada et al., Phys. Rev. E75, 051111 (2007); B. Q. Ai and L. G. Liu, ibid.74, 051114 (2006); B. Q. Ai et al., ibid.75, 061126 (2007); B. Q. Ai and L. G. Liu, J. Chem. Phys.126, 204706 (2007); 128, 024706 (2008); E. Yariv and K. D. Dorfman, Phys. Fluids19, 037101 (2007); N. Laachi et al., Europhys. Lett.80, 50009 (2007); A. M. Berezhkovskii et al., J. Chem. Phys.118, 7146 (2003); 119, 6991 (2003)]. Using the concept of "entropy barrier" [R. Zwanzig, J. Phys. Chem.96, 3926 (1992)] one can classify such structures based on the height of the entropy barrier. Structures with high barriers are formed by chambers, which are weakly connected with each other because they are connected by small apertures. To escape from such a chamber a diffusing particle has to climb a high entropy barrier to find an exit that takes a lot of time [I. V. Grigoriev et al., J. Chem. Phys.116, 9574 (2002)]. As a consequence, the particle intrachamber lifetime tau(esc) is much larger than its intrachamber equilibration time, tau(rel), tau(esc)>tau(rel). When the aperture is not small enough, the intrachamber escape and relaxation times are of the same order and the hierarchy fails. This is the case of low entropy barriers. Transport in this case is analyzed in the works of Schmid and co-workers, Liu and co-workers, and Dorfman and co-workers, while the work of Berezhkovskii et al. is devoted to diffusion in the case of high entropy barriers.     

AFM surface force measurements conducted with silica in CnTACl solutions: Effect of chain length on hydrophobic force

Surface forces were measured using an AFM with silica surfaces immersed in C_nTACl (n = 12–18) solutions in the absence of added salt. The results showed long-range attractive forces that cannot be explained by the DLVO theory. The long-range attractions increased with increasing surfactant concentration, reaching a maximum at the point of charge neutralization (p.c.n.) and then decreased. The long-range forces decayed exponentially, with the decay lengths increasing from 3 to 32 nm as the chain length of the surfactants increased from C-12 to C-18. The measured forces can be fitted to the charged-patch model of Miklavic et al. [S.J. Miklavic, D.Y.C. Chan, L.R. White, T.W. Healy, J. Phys. Chem. 98 (1994) 9022–9032] by assuming patch sizes that are much larger than the values reported in the literature.

It was found that the decay length decreases linearly with the effective concentration of the CH₂/CH₃ groups of the C_nTACl homologues raised to the power of −1/2, which is in line with the Eriksson et al.'s hydrophobic force model derived using a mean-field approach. It appears, therefore, that the long-range attractions observed in the present work are hydrophobic forces originating from changes in water structure across the thin surfactant solution film between the silica surfaces. It is conceivable that hydrocarbon chains in solution disrupt the surface-induced water structure and cause a decrease in hydrophobic force. This observation may also provide an explanation for the very long-range forces observed with silylated, LB-deposited, and thiol-coated surfaces.     

Direct comparison of atomic force microscopic and total internal reflection microscopic measurements in the presence of nonadsorbing polyelectrolytes

We have investigated the structural and depletion forces between silica glass surfaces in aqueous, salt-free solutions of sodium poly(styrene sulfonate). The interaction forces were investigated by two techniques: total internal reflectance microscopy (TIRM) and colloid probe atomic force microscopy (AFM). The TIRM technique measures the potential energy of interaction directly, while the AFM is a force balance. Comparison between the data sets was used to independently calibrate the AFM data since the separation distances cannot be unequivocally determined by this technique. Oscillatory structural forces are excellent for this work since they give multiple reference points against which to analyze. Comparison of the data from the two techniques highlighted significant uncertainties in the AFM data. At low polymer concentrations, a significant uncertainty in the apparent zero separation distance was seen as a result of the AFM cantilever reaching an apparent constant compliance region prior to any real contact between the surfaces. Further complications arising from the number and position of the measured minima were also seen in the dilute polymer concentration regime as a result of hydrodynamic drainage between the approaching surfaces in the AFM perturbing the delicate structural components in the fluid.     

Effects of degassing and ionic strength on AFM force measurements in octadecyltrimethylammonium chloride solutions

Sakamoto et al. (Langmuir 2002, 18, 5713) conducted AFM force measurements between silica sphere and fused-silica plate in aqueous octadecyltrimethylammonium chloride (C18TACl) solutions and concluded that long-range attractive force is not observed in carefully degassed solutions. In the present work, AFM force measurements were conducted by following the procedures described by Sakamoto et al. The results showed the presence of an attractive force that was much stronger than the van der Waals force both in air-saturated and degassed solutions. The force was most attractive at 5 x 10(-6) M C18TACl, where contact angle was maximum. At this concentration, which is close to the charge compensation point (ccp) of the glass sphere, the long-range decay lengths (D) were 34 and 38 nm in air-saturated and degassed solutions, respectively. At 10(-5) M, the decay length decreased from 30 to 4 nm upon degassing. This decrease in decay length can be explained by a pH increase (from 5.7 to 6.6), which in turn causes additional surfactant molecules to adsorb on the surface with inverse orientation. The attractive force was screened by an added electrolyte (NaCl), indicating that the attractive force may be of electrostatic origin. Therefore, the very long decay lengths observed in the absence of electrolyte may be ascribed to the fact that the ccp occurs at a very low surfactant concentration.     

Thermal denaturing of mutant lysozyme with both the OPLSAA and the CHARMM force fields

Biomolecular simulations enabled by massively parallel supercomputers such as BlueGene/L promise to bridge the gap between the currently accessible simulation time scale and the experimental time scale for many important protein folding processes. In this study, molecular dynamics simulations were carried out for both the wild-type and the mutant hen lysozyme (TRP62GLY) to study the single mutation effect on lysozyme stability and misfolding. Our thermal denaturing simulations at 400-500 K with both the OPLSAA and the CHARMM force fields show that the mutant structure is indeed much less stable than the wild-type, which is consistent with the recent urea denaturing experiment (Dobson et al. Science 2002, 295, 1719-1722; Nature 2003, 424, 783-788). Detailed results also reveal that the single mutation TRP62GLY first induces the loss of native contacts in the beta-domain region of the lysozyme protein at high temperatures, and then the unfolding process spreads into the alpha-domain region through Helix C. Even though the OPLSAA force field in general shows a more stable protein structure than does the CHARMM force field at high temperatures, the two force fields examined here display qualitatively similar results for the misfolding process, indicating that the thermal denaturing of the single mutation is robust and reproducible with various modern force fields.     

The role of growth temperature in the adhesion and mechanics of pathogenic L. monocytogenes: an AFM study

The adhesion strengths of pathogenic L. monocytogenes EGDe to a model surface of silicon nitride were quantified using atomic force microscopy (AFM) in water for cells grown under five different temperatures (10, 20, 30, 37, and 40 °C). The temperature range investigated was chosen to bracket the thermal conditions in which L. monocytogenes survive in the environment. Our results indicated that adhesion force and energy quantified were at their maximum when the bacteria were grown at 30 °C. The higher adhesion observed at 30 °C compared to the adhesion quantified for bacterial cells grown at 37, 40, 20, and 10 °C was associated with longer and denser bacterial surface biopolymer brushes as predicted from fitting a model of steric repulsion to the approach distance-force data as well from the results of protein colorimetric assays. Theoretically predicted adhesion energies based on soft-particle DLVO theory agreed well with the adhesion energies computed from AFM force-distance retraction data (r(2) = 0.94); showing a minimum energy barrier to adhesion at 30 °C.     

Effect of water chemistry and aging on iron-mica interaction forces: implications for iron particle transport

The transport of particles through groundwater systems is governed by a complex interplay of mechanical and chemical forces that are ultimately responsible for binding to geological substrates. To understand these forces in the context of zero valent iron particles used in the remediation of groundwater, atomic force microscopy (AFM)-based force spectroscopy was employed to characterize the interactions between AFM tips modified with either carbonyl iron particles (CIP) or electrodeposited Fe as a function of counterion valency, temperature, particle morphology, and age. The measured interaction forces were always attractive for both fresh and aged CIP and electrodeposited iron, except in 100 mM NaCl, as a consequence of electrostatic attraction between the negatively charged mica and positively charged iron. In 100 mM NaCl, repulsive hydration forces appeared to dominate. Good agreement was found between the experimental data and predictions based on the extended DLVO (XDLVO) theory. The effect of aging on iron particle composition and morphology was assessed by X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), and energy dispersive spectroscopy (EDS) revealing that the aged particles comprising a zero valent iron core passivated by a mixture of iron oxides and hydroxides. Force spectroscopy showed that aging caused variations in the adhesive force due to the changes in particle morphology and contact area.     

基于原子力显微镜的单分子力谱在生物研究中的应用

原子力显微镜被广泛应用于生物研究领域,基于原子力显微镜的单分子力谱可以在单分子、单细胞水平上研究生物分子内和分子间的相互作用。 本文介绍了原子力显微镜单分子力谱在生物分子间相互作用、蛋白质去折叠、细胞表面生物分子、细胞力学性质和基于单分子力谱成像等研究中的最新进展。     

Computer simulations of the translocation and unfolding of a protein pulled mechanically through a pore

Protein degradation by ATP-dependent proteases and protein import into the mitochondrial matrix involve the unfolding of proteins upon their passing through narrow constrictions. It has been hypothesized that the cellular machinery accomplishes protein unfolding by pulling mechanically at one end of the polypeptide chain. Here, we use Langevin dynamics simulations of a minimalist off-lattice model to examine this hypothesis and to study the unfolding of a protein domain pulled mechanically through a long narrow pore. We compute the potential of mean force (PMF) experienced by the domain as a function of its displacement along the pore and identify the unfolding intermediates corresponding to the local minima of the PMF. The observed unfolding mechanism is different from that found when the two termini are pulled apart, as in single-molecule mechanical unfolding experiments. It depends on the pore diameter, the magnitude of the pulling force, and on whether the force is applied at the N- or the C-terminus of the chain. Consequently, the translocation time exhibits a pulling force dependence that is more complex than a simple exponential function expected on the basis of simple phenomenological models of translocation.