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.     

Single-molecule electrophoresis of beta-hairpin peptides by electrical recordings and Langevin dynamics simulations

We used single-channel electrical recordings and Langevin molecular dynamics simulations to explore the electrophoretic translocation of various beta-hairpin peptides across the staphylococcal alpha-hemolysin (alphaHL) protein pore at single-molecule resolution. The beta-hairpin peptides, which varied in their folding properties, corresponded to the C terminal residues of the B1 domain of protein G. The translocation time was strongly dependent on the electric force and was correlated with the folding features of the beta-hairpin peptides. Highly unfolded peptides entered the pore in an extended conformation, resulting in fast single-file translocation events. In contrast, the translocation of the folded beta-hairpin peptides occurred more slowly. In this case, the beta-hairpin peptides traversed the alphaHL pore in a misfolded or fully folded conformation. This study demonstrates that the interaction between a polypeptide and a beta-barrel protein pore is dependent on the folding features of the polypeptide.     

A New Expression for Higher Order Accelerations and Poles Under the One Parameter Planar Hyperbolic Homothetic Motions

The one parameter planar hyperbolic homothetic motion was introduced in Ersoy and Akyigit (Adv Appl Clifford Algebras 21:297–313, 2011). We give a formula for higher order accelerations and poles under this motion. In the case of the homothetic rate \({h\equiv 1}\) we obtain the higher order accelerations and poles under one parameter planar hyperbolic motion which was given by Sahin and Yüce (Math Probl Eng 2014, 2014). Also, the higher order velocities and accelerations are analyzed by taking the angle of the rotation instead of the parameter of the motion.     

A DFT‐based mechanistic study on the formation of oximes

Oxime chemistry has been proven to be a reliable bioconjugation method for biomedical applications. Because of its stable and bio‐orthogonal nature, a number of materials have been devised for in vitro and in vivo applications such as drug delivery, imaging, and biochemical assays. Polymers, synthetic molecules, nanoparticles, and biomolecules carrying alkoxyamine and aldehyde/ketone functional groups could be linked to each other through oxime bond, and a variety of modular platforms could be produced. Formation of oximes is catalyzed in acidic medium, and the proposed reaction mechanism follows classical imine formation pathways. Aniline has been found to accelerate the rate of oxime formation several orders of magnitude. In this computational study, we analyzed the proposed mechanism on model systems using DFT calculations including a solvation model. The energetics of the reaction steps in neutral and acidic conditions as well as in the presence of aniline was performed. Explicit water molecules were included in the calculations to study the energetics of solvent assisted proton transfer steps.     

A new synthon for the synthesis of aminoinositol derivatives

The regio- and stereoselective synthesis of a new synthon, trans-3,8-dioxatricyclo[3.2.1.0^2,4]octane-6,7-diamine, from 7-oxabicyclo[2.2.1]hept-5-ene-2,3-dicarboxylate is reported. Transformation of the acid functionalities to acyl azides followed by Curtius rearrangement gave the corresponding trans-diisocyanate, which was reacted with HCl to produce a trans-diamino compound that is a potentially important synthon for the versatile synthesis of aminocyclitols.     

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.     

Simulations of the untying of molecular friction knots between individual polymer strands

The dynamics of molecular knots is implicated in a broad range of phenomena, from DNA replication to relaxation of polymer melts. Motivated by the recent experiments, in which biopolymer knots have been observed and manipulated at a single-molecule level, we have used computer simulations to study the dynamics of "friction knots" joining individual polymer strands. A friction knot splicing two ropes becomes jammed when the ropes are pulled apart. In contrast, molecular friction knots eventually become undone by thermal motion. We show that depending on the knot type and on the polymer structure, a microscopic friction knot can be strong (the time tau the knot stays tied increases with the force F applied to separate the strands) or weak (tau decreases with increasing F). The strong knot behavior is a microscopic analog of macroscopic knot jamming. We further describe a simple model explaining these behaviors.     

Translocation of a beta-hairpin-forming peptide through a cylindrical tunnel

We use Langevin dynamics simulations of a minimalist off-lattice model to study the translocation of a beta hairpin forming peptide through a tunnel that mimics the exit tunnel in a ribosome. We have computed the free energy of the peptide as a function of its position relative to the tunnel exit and also studied the properties of the conformational ensemble, when the peptide's position is restricted at different points along the tunnel. Confining the peptide within a sufficiently wide tunnel stabilizes the folded state. The protein then remains folded as it moves towards the tunnel exit. However, when the diameter D of the tunnel is below a certain critical value D(c), confinement destabilizes the folded state and forces the peptide to assume an extended configuration. In this case, as the peptide progresses towards the tunnel exit and eventually leaves the tunnel, it goes through a series of compact, misfolded conformations and eventually folds when it gets close to the exit. The critical tunnel diameter D(c) is comparable to the width of ribosomal tunnels. Our results suggest that co-translational folding is probably not universal, but rather a protein-specific phenomenon.     

Revisiting and computing reaction coordinates with Directional Milestoning

The method of Directional Milestoning is revisited. We start from an exact and more general expression and state the conditions and validity of the memory-loss approximation. An algorithm to compute a reaction coordinate from Directional Milestoning data is presented. The reaction coordinate is calculated as a set of discrete jumps between Milestones that maximizes the flux between two stable states. As an application we consider a conformational transition in solvated adenosine. We compare a long molecular dynamic trajectory with Directional Milestoning and discuss the differences between the maximum flux path and minimum energy coordinates.