Amyloid fibril bending and ring formation at liquid interfaces
Sophia Jordens, Emily E. Riley, Ivan Usov, Lucio Isa, Peter D. Olmsted, and Raffaele Mezzenga, ACS Nano 8 (2014) 11071-11079.

fancy picture The Protein fibril accumulation at interfaces is an important step in many physiological processes and neurodegenerative diseases as well as in designing materials. Here we show, using beta-lactoglobulin fibrils as a model, that semiflexible fibrils exposed to a surface do not possess the Gaussian distribution of curvatures characteristic for wormlike chains, but instead exhibit a spontaneous curvature, which can even lead to ring-like conformations. The long-lived presence of such rings is confirmed by atomic force microscopy, cryogenic scanning electron microscopy, and passive probe particle tracking at air! and oil!water interfaces. We reason that this spontaneous curvature is governed by structural characteristics on the molecular level and is to be expected when a chiral and polar fibril is placed in an inhomogeneous environment such as an interface. By testing β-lactoglobulin fibrils with varying average thicknesses, we conclude that fibril thickness plays a determining role in the propensity to form rings.

Free energy landscapes of proteins: insights from mechanical probes
Zu Thur Yew, Peter D Olmsted, and Emanuele Paci, Advances in Chemical Physics: "Single-Molecule Biophysics: Experiment and Theory" 146 (2012) 394-417.

Introduction; One-Dimensional Models of Mechanical Strength; Multidimensionality of Energy Landscapes; Use of the Jarzynski Relation to Directly Determine Free Energies; Conclusion.

Internal protein dynamics shifts the distance to the mechanical transition state
DK West, E Paci, and PD Olmsted, Physical Review E 74 (2006) 061912.

Mechanical unfolding of polyproteins by force spectroscopy provides valuable insight into their free energy landscapes. Most experiments of the unfolding process have been fit to two-state and/or one dimensional models, with the details of the protein and its dynamics often subsumed into a zero-force unfolding rate and a distance x_u(1D) to the transition state. We consider the entire phase space of a model protein under a constant force, and show that x_u(1D) contains a sizeable contribution from exploring the full multidimensional energy landscape. This effect is greater for proteins with many degrees of freedom that are affected by force; and surprisingly, we predict that externally attached flexible linkers also contribute to the measured unfolding characteristics.

Free energy of protein folding using the Jarzynski equality
DK West, PD Olmsted, and E Paci, Journal of Chemical Physics 125 (2006) 204910.

The equilibrium free energy difference between two long-lived molecular species or "conformational states" of a protein (or any other molecule) can in principle be estimated by measuring the work needed to shuttle the system between them, independent of the irreversibility of the process. This is the meaning of the Jarzynski equality (JE), which we test in this paper by performing simulations that unfold a protein by pulling two atoms apart. Pulling is performed fast relative to the relaxation time of the molecule and is thus far from equilibrium. Choosing a simple protein model for which we can independently compute its equilibrium properties, we show that the free energy can be exactly and effectively estimated from nonequilibrium simulations. To do so, one must carefully and correctly determine the ensemble of states that are pulled, which is more important the farther from equilibrium one performs simulations; this highlights a potential problem in using the JE to extract the free energy from forced unfolding experiments. The results presented here also demonstrate that the free energy difference between the native and denatured states of a protein measured in solution is not always equal to the free energy profile that can be estimated from forced unfolding simulations (or experiments) using the JE.

Mechanical unfolding revisited through a simple but realistic model
DK West, PD Olmsted, and E Paci, Journal of Chemical Physics 124 (2006) 154909.

Single-molecule experiments and their application to probe the mechanical resistance and related properties of proteins provide a new dimension in our knowledge of these important and complex biological molecules. Single-molecule techniques may not have yet overridden solution experiments as a method of choice to characterize biophysical and biological properties of proteins, but have stimulated a debate and contributed considerably to bridge theory and experiment. Here we demonstrate this latter contribution by illustrating the reach of some theoretical findings using a solvable but nontrivial molecular model whose properties are analogous to those of the corresponding experimental systems. In particular, we show the relationship between the thermodynamic and the mechanical properties of a protein. The simulations presented here also illustrate how forced and spontaneous unfolding occur through different pathways and that folding and unfolding rates at equilibrium cannot in general be obtained from forced unfolding experiments or simulations. We also study the relationship between the energy surface and the mechanical resistance of a protein and show how a simple analysis of the native state can predict much of the mechanical properties of a protein.

Mechanical resistance of proteins explained using simple molecular models
Daniel K. West, David J. Brockwell, Peter D. Olmsted, Sheena E. Radford, and Emanuele Paci, Biophysical Journal 90 (2006) 287-297.

Recent experiments have demonstrated that proteins unfold when two atoms are mechanically pulled apart, and that this process is different to when heated or when a chemical denaturant is added to the solution. Experiments have also shown that the response of proteins to external forces is very diverse, some of them being "hard", and others "soft". Mechanical resistance originates from the presence of barriers on the energy landscape; together, experiment and simulation have demonstrated that unfolding occurs through alternative pathways when different pairs of atoms undergo mechanical extension. Here we use simulation to probe the mechanical resistance of six structurally diverse proteins when pulled in different directions. For this, we use two very different models: a detailed, transferable one, and a coarse-grained, structure-based one. The coarse-grained model gives results that are surprisingly similar to the detailed one and qualitatively agree with experiment; i.e., the mechanical resistance of different proteins or of a single protein pulled in different directions can be predicted by simulation. The results demonstrate the importance of pulling direction relative to the local topology in determining mechanical stability, and rationalize the effect of the location of importation/degradation tags on the rates of mitochondrial import or protein degradation in vivo.

Mechanically unfolding the small, topologically simple protein L
David J Brockwell Godfrey S Beddard, Emanuele Paci, Dan K West, Peter D Olmsted, D Alastair Smith, and Sheena E Radford, Biophysical Journal 89 (2005) 506-513.

Beta-sheet proteins are generally more able to resist mechanical deformation than a-helical proteins. Experiments measuring the mechanical resistance of b-sheet proteins extended by their termini led to the hypothesis that parallel, directly hydrogen-bonded terminal b-strands provide the greatest mechanical strength. Here we test this hypothesis by measuring the mechanical properties of protein L, a domain with a topology predicted to be mechanically strong, but with no known mechanical function. A pentamer of this small, topologically simple protein is resistant to mechanical deformation over a wide range of extension rates. Molecular dynamics simulations show the energy landscape for protein L is highly restricted for mechanical unfolding and that this protein unfolds by the shearing apart of two structural units in a mechanism similar to that proposed for ubiquitin, which belongs to the same structural class as protein L, but unfolds at a significantly higher force. These data suggest that the mechanism of mechanical unfolding is conserved in proteins within the same fold family and demonstrate that although the topology and presence of a hydrogen-bonded clamp are of central importance in determining mechanical strength, hydrophobic interactions also play an important role in modulating the mechanical resistance of these similar proteins.

Pulling geometry defines the mechanical resistance of a beta-sheet protein
DJ Brockwell, E Paci, RC Zinober, GS Beddard, PD Olmsted, DA Smith, RN Perham, and SE Radford, Nature Structural Biology 10 (2003) 731. Reviewed in Nature Structural Biology 10 (2003) 674-676 (News and Views), Science 301 (2003) 1291.

Proteins show diverse responses when placed under mechanical stress. The molecular origins of their differing mechanical resistance are still unclear, although the orientation of secondary structural elements relative to the applied force vector is thought to have an important function. Here, by using a method of protein immobilization that allows force to be applied to the same all- protein, E2lip3, in two different directions, we show that the energy landscape for mechanical unfolding is markedly anisotropic. These results, in combination with molecular dynamics (MD) simulations, reveal that the unfolding pathway depends on the pulling geometry and is associated with unfolding forces that differ by an order of magnitude. Thus, the mechanical resistance of a protein is not dictated solely by amino acid sequence, topology or unfolding rate constant, but depends critically on the direction of the applied extension.

Unfolding Dynamics of Proteins Under Applied Force
DA Smith, DJ Brockwell, RC Zinober, AW Blake, GS Beddard, PD Olmsted, and SE Radford, Philosophical Transactions of the Royal Society A 361 (2003) 713-730. From the Royal Society Discussion Meeting, "Slow Dynamics in Complex Systems", 25-26 September 2002.

Mechanically unfolding proteins: the effect of unfolding history and the supramolecular scaffold
RC Zinober, DJ Brockwell, GS Beddard, AW Blake, PD Olmsted, SE Radford, and DA Smith, Protein Science 11 (2002) 2759-2765.

The mechanical resistance of a folded domain in a polyprotein of five mutant I27 domains (C47S, C63S I27)5is shown to depend on the unfolding history of the protein. This observation can be understood on the basis of competition between two effects, that of the changing number of domains attempting to unfold, and the progressive increase in the compliance of the polyprotein as domains unfold. We present Monte Carlo simulations that show the effect and experimental data that verify these observations. The results are confirmed using an analytical model based on transition state theory. The model and simulations also predict that the mechanical resistance of a domain depends on the stiffness of the surrounding scaffold that holds the domain in vivo, and on the length of the unfolded domain. Together, these additional factors that influence the mechanical resistance of proteins have important consequences for our understanding of natural proteins that have evolved to withstand force.

The Effect of Core Destabilisation on the Mechanical Resistance of I27
DJ Brockwell, GS Beddard, J Clarkson, RC Zinober, AW Blake, J Trinick, PD Olmsted, DA Smith, and SE Radford, Biophysical Journal, 83 (2002) 458-472.

It is still unclear whether mechanical unfolding probes the same pathways as chemical denaturation. To address this point, we have constructed a concatamer of five mutant I27 domains (denoted (I27)5*) and used it for mechanical unfolding studies. This protein consists of four copies of the mutant C47S, C63S I27 and a single copy of C63S I27. These mutations severely destabilize I27 (GUN = 8.7 and 17.9 kJ mol1 for C63S I27 and C47S, C63S I27, respectively). Both mutations maintain the hydrogen bond network between the A' and G strands postulated to be the major region of mechanical resistance for I27. Measuring the speed dependence of the force required to unfold (I27)5* in triplicate using the atomic force microscope allowed a reliable assessment of the intrinsic unfolding rate constant of the protein to be obtained (2.0 × 103 s1). The rate constant of unfolding measured by chemical denaturation is over fivefold faster (1.1 × 102 s1), suggesting that these techniques probe different unfolding pathways. Also, by comparing the parameters obtained from the mechanical unfolding of a wild-type I27 concatamer with that of (I27)5*, we show that although the observed forces are considerably lower, core destabilization has little effect on determining the mechanical sensitivity of this domain.

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