Biomedical subjects

Dmitrii E Makarov

Publications and source records attributed to Dmitrii E Makarov.

14 recordsLinked to original sources

PubMed2006

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.

Bacterial Proteins↗

PubMed2006

On the calculation of absolute free energies from molecular-dynamics or Monte Carlo data.

We propose a method for calculating absolute free energies from Monte Carlo or molecular-dynamics data. The method is based on the identity that expresses the partition function Q as a Boltzmann average: 1Q=w(p,x)exp[betaH(p,x)], where w(p,x) is an arbitrary weight function such that its integral over the phase space is equal to 1. In practice, to minimize statistical errors the weight function is chosen such that the regions of the phase space where sampling statistics are poor are excluded from the average. The "ideal" weight function would be the equilibrium phase-space density exp[-betaH(p,x)]Q itself. We consider two methods for constructing the weight function based on different estimates of the equilibrium phase-space density from simulation data. In the first method, it is chosen to be a Gaussian function, whose parameters are obtained from the covariance matrix of the atomic coordinates. In the second, a clustering algorithm is used to attempt partitioning the data into clusters corresponding to different basins of attraction visited by the system. The weight function is then constructed as a superposition of Gaussians calculated for each cluster separately. We show that these strategies can be used to improve upon previous methods of estimating absolute entropies from covariance matrices.

Algorithms↗

PubMed2006

Evidence for non-two-state kinetics in the nucleocapsid protein chaperoned opening of DNA hairpins.

In HIV-1 reverse transcription, the nucleocapsid protein, NC, induces secondary structure fluctuations in specific DNA and RNA hairpins. Time-resolved single-molecule fluorescence resonance energy transfer was used to study NC chaperoned opening of DNA hairpins over a broader range of conditions and in more depth than in previous studies. The experiments reveal a complex mechanism for secondary structure fluctuations with dynamic processes occurring over a wide time range, i.e., approximately 5 to >250 ms and with the involvement of long-lived intermediates. The dynamic role of DNA loop regions and NC binding/dissociation events are discussed.

Base Sequence↗

PubMed2005

Site-specific dimensions across a highly denatured protein; a single molecule study.

Do highly denatured proteins adopt random coil configurations? Here, we address this question by measuring residue-to-residue separations across the denatured FynSH3 domain. Using single-molecule Forster resonance energy transfer techniques, we have collected transfer efficiency probability distributions for dye-labeled, denatured protein. Applying maximum likelihood analysis to the interpretation of these distributions, we have determined the through-space distance between five residue pairs in the protein's guanidine hydrochloride-unfolded and trifluoroethanol-unfolded states. We find that, while the dimensions of the guanidine hydrochloride -unfolded molecule generally coincide with the dimensions predicted for a random coil ensemble, potentially statistically significant deviations from random coil behavior are also evident. These small, site-specific deviations may provide a means of reconciling earlier, scattering-based evidence for the random coil nature of the unfolded state with more site-specific spectroscopic evidence suggesting residual structure. We have also studied the unfolded ensemble populated in 50% trifluoroethanol, a denaturant that induces a highly helical unfolded state. We find that the size and shape of the unfolded ensemble under these conditions is effectively indistinguishable from that populated in guanidinium hydrochloride solutions, suggesting that the gross structure of the denatured state is, perhaps surprisingly, independent of the chemistry of the cosolvent.

Escherichia coli Proteins↗

PubMed2005

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.

Adenosine Triphosphate↗

PubMed2005

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.

Computer Simulation↗

PubMed2005

Theoretical studies of the kinetics of mechanical unfolding of cross-linked polymer chains and their implications for single-molecule pulling experiments.

We have used kinetic Monte Carlo simulations to study the kinetics of unfolding of cross-linked polymer chains under mechanical loading. As the ends of a chain are pulled apart, the force transmitted by each cross-link increases until it ruptures. The stochastic cross-link rupture process is assumed to be governed by first order kinetics with a rate that depends exponentially on the transmitted force. We have performed random searches to identify optimal cross-link configurations whose unfolding requires a large applied force (measure of strength) and/or large dissipated energy (measure of toughness). We found that such optimal chains always involve cross-links arranged to form parallel strands. The location of those optimal strands generally depends on the loading rate. Optimal chains with a small number of cross-links were found to be almost as strong and tough as optimal chains with a large number of cross-links. Furthermore, optimality of chains with a small number of cross-links can be easily destroyed by adding cross-links at random. The present findings are relevant for the interpretation of single molecule force probe spectroscopy studies of the mechanical unfolding of "load-bearing" proteins, whose native topology often involves parallel strand arrangements similar to the optimal configurations identified in the study.

Biomechanical Phenomena↗

PubMed2004

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.

Computer Simulation↗

PubMed2004

Simulation of the mechanical unfolding of ubiquitin: probing different unfolding reaction coordinates by changing the pulling geometry.

Motivated by the recent experimental atomic force microscopy (AFM) measurements of the mechanical unfolding of proteins pulled in different directions [D. J. Brockwell et al., Nat. Struct. Biol. 10, 731 (2003); M. Carrion-Vazquez et al., ibid 10, 738 (2003)] we have computed the unfolding free energy profiles for the ubiquitin domain when it is stretched between its (A) N and C termini, (B) Lys48 and C terminus, (C) Lys11 and C terminus, and (D) N terminus and Lys63. Our results for cases (A) and (B) are in good agreement with the experimental unfolding forces measured for the N-C and Lys48-C linked polyubiquitin, in particular, indicating a considerably lower unfolding force in the latter case. Mechanical unfolding in case (A) involves longitudinal shearing of the terminal parallel strands while in case (C) the same strands are "unzipped" by the force. The computed unfolding forces in case (C) are found to be very low, less than 50 pN for pulling rates typical of AFM experiments. The unfolding free energy barrier found in case (C) is approximately 13 kcal/mol, which corresponds to a zero-force unfolding rate constant that is comparable to the rate of chemical unfolding extrapolated to zero denaturant concentration. The unfolding barrier calculated in case (A) in the limit of zero force is much higher, suggesting that mechanical unfolding in this case follows a pathway that is different from that of thermal/chemical denaturation.

Computer Simulation↗

PubMed2003

Molecular nanosprings in spider capture-silk threads.

Spider capture silk is a natural material that outperforms almost any synthetic material in its combination of strength and elasticity. The structure of this remarkable material is still largely unknown, because spider-silk proteins have not been crystallized. Capture silk is the sticky spiral in the webs of orb-weaving spiders. Here we are investigating specifically the capture spiral threads from Araneus, an ecribellate orb-weaving spider. The major protein of these threads is flagelliform protein, a variety of silk fibroin. We present models for molecular and supramolecular structures of flagelliform protein, derived from amino acid sequences, force spectroscopy (molecular pulling) and stretching of bulk capture web. Pulling on molecules in capture-silk fibres from Araneus has revealed rupture peaks due to sacrificial bonds, characteristic of other self-healing biomaterials. The overall force changes are exponential for both capture-silk molecules and intact strands of capture silk.

Animals↗

PubMed2003

The topomer search model: A simple, quantitative theory of two-state protein folding kinetics.

Most small, single-domain proteins fold with the uncomplicated, single-exponential kinetics expected for diffusion on a smooth energy landscape. Despite this energetic smoothness, the folding rates of these two-state proteins span a remarkable million-fold range. Here, we review the evidence in favor of a simple, mechanistic description, the topomer search model, which quantitatively accounts for the broad scope of observed two-state folding rates. The model, which stipulates that the search for those unfolded conformations with a grossly correct topology is the rate-limiting step in folding, fits observed rates with a correlation coefficient of approximately 0.9 using just two free parameters. The fitted values of these parameters, the pre-exponential attempt frequency and a measure of the difficulty of ordering an unfolded chain, are consistent with previously reported experimental constraints. These results suggest that the topomer search process may dominate the relative barrier heights of two-state protein-folding reactions.

Amino Acids↗

PubMed2002

Configurational entropy and mechanical properties of cross-linked polymer chains: implications for protein and RNA folding.

We discuss the statistical mechanical properties of a single polymer chain that forms cross links among its monomers. Models of this type have served as prototypes in theories of RNA and protein folding. The chain is allowed to form pseudoknots and its monomers can each participate in multiple cross links. We demonstrate that the conformational free energy of such a chain can be estimated by using an algorithm that scales as a power of the number of cross links N(N1-N3, depending on the problem). Straightforward exact evaluation of the chain partition function via multidimensional integration scales exponentially with N and often is computationally prohibitive. Our approach can also be used to compute the "entropic force" generated by a cross-linked chain when it is stretched at its ends. Such forces can be directly measured by atomic force microscopy or by laser optical trap experiments performed on single RNA, DNA, and protein molecules.

Biomechanical Phenomena↗

PubMed2002

Observation of single molecule transport at surfaces via scanning microscopies: Monte Carlo wave function study of a model problem.

We discuss experiments where the trajectories of individual molecules or atoms at surfaces are observed by means of scanning microscopy. A scanning probe moves along the surface and excites the molecule so that the molecule's location is deduced from the times at which fluorescence photons are emitted. Operation of other types of scanning microscopes can be described by similar models. The observed trajectories are inherently affected by the interaction between the molecule and the probe such that the measured diffusion coefficient depends on the frequency at which the surface is scanned. The number of photons emitted by the molecule during a scan is affected in a nontrivial way by its mobility. If photoexcitation increases the mobility, we find emission to be suppressed.

Journal Article↗

PubMed2002

How the folding rate constant of simple, single-domain proteins depends on the number of native contacts.

Experiments have shown that the folding rate constants of two dozen structurally unrelated, small, single-domain proteins can be expressed in terms of one quantity (the contact order) that depends exclusively on the topology of the folded state. Such dependence is unique in chemical kinetics. Here we investigate its physical origin and derive the approximate formula ln(k) = ln(N) + a + bN, were N is the number of contacts in the folded state, and a and b are constants whose physical meaning is understood. This formula fits well the experimentally determined folding rate constants of the 24 proteins, with single values for a and b.

Binding Sites↗