Figure 2

<p>(a) As for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002509#pcbi-1002509-g001" target="_blank">Fig. 1c</a>, but with only main-chain atoms (N, O, C, C, H) included in the force calculation. (b) Mean inter-residue forces (main-chain only) for beta strands 1 and 5. (c) & (d) Distributions of main-chain–main-chain force vs C separation for the residue pairs Gln2-Glu64 (c) and Ile3-Ser65 (c). Each dot corresponds to a single frame from the MD trajectory. The vertical red line shows the mean separation, and the blue curve is a local polynomial fit to the data using the Loess method. The inset highlights the relevant residue pair in the beta sheet structure.</p

A New Transferable Forcefield for Simulating the Mechanics of CaCO₃ Crystals

Many sets of forcefield parameters for calcium carbonate (CaCO3) and CaCO3–water interactions have been developed for thermodynamic calculations, but growing interest in modeling the molecular-scale mechanics of biomineral nanocomposite materials such as nacre has led to a need for interaction parameters that accurately model the anisotropic mechanical properties of CaCO3. A novel forcefield for aragonite, one polymorph of CaCO3, has been fitted to the structure and elastic constants of the mineral, and the validation of these interaction parameters demonstrates that the forcefield can well capture the shear and elastic moduli of aragonite and also performs well when transferred to other CaCO3 polymorphs. The corresponding aragonite–water and aragonite–protein parameters are also obtained and utilized in force probe molecular dynamics (FPMD) simulations of the forced desorption of an acidic polypeptide from an aragonite crystal surface, resulting in a rupture force of roughly 60 pN per amino acid residue at pulling speeds characteristic of Atomic Force Microscope experiments. Our forcefield for CaCO3 and CaCO3–protein interactions can be applied to study the physical and mechanical properties of organic–inorganic composite systems, especially for the next generation of bionanocomposite materials

Figure 5

<p>(a) Left: Effective force profile for the side-chains of Asp52 and Arg72. Right: Snapshots of various hydrogen binding states observed for the trio of Asp39, Asp52, and Arg72. Sometimes two of the amides in the Asp side-chain are simultaneously hydrogen bonded to the two oxygens in the Asp side-chain (upper left); sometimes an amide is bound to a side-chain oxygen, and another to the backbone carbonyl oxygen (upper right); sometimes only a single bond is formed, to the backbone oxygen (lower left); and sometimes the Asp39-Arg72 salt bridge breaks entirely, and Arg72 instead forms a short-lived salt bridge with Asp52, which is simultaneously bound to Lys27 (lower right). (b) As for (a), but for the residues Leu8 and Val70. In one state (the ‘out’ state), the side-chain of Leu8 is oriented outwards, above that of Val70. In the other (the ‘in’ state), the Leu8 side-chain is buried underneath Val70. Superimposed on the scatterplot are two density plots, which show the density of points belonging to each of the ‘in’ (red) and ‘out’ (blue) states. The classification of points into two states is described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002509#pcbi.1002509.s004" target="_blank">Fig. S4</a>.</p

Average forces for each of the cross-strand hydrogen bonds in beta sheet 1–5.

<p>Error bars show the standard error in the mean.</p

Dynamic Prestress in a Globular Protein

<div><p>A protein at equilibrium is commonly thought of as a fully relaxed structure, with the intra-molecular interactions showing fluctuations around their energy minimum. In contrast, here we find direct evidence for a protein as a molecular tensegrity structure, comprising a balance of tensed and compressed interactions, a concept that has been put forward for macroscopic structures. We quantified the distribution of inter-residue prestress in ubiquitin and immunoglobulin from all-atom molecular dynamics simulations. The network of highly fluctuating yet significant inter-residue forces in proteins is a consequence of the intrinsic frustration of a protein when sampling its rugged energy landscape. In beta sheets, this balance of forces is found to compress the intra-strand hydrogen bonds. We estimate that the observed magnitude of this pre-compression is enough to induce significant changes in the hydrogen bond lifetimes; thus, prestress, which can be as high as a few 100 pN, can be considered a key factor in determining the unfolding kinetics and pathway of proteins under force. Strong pre-tension in certain salt bridges on the other hand is connected to the thermodynamic stability of ubiquitin. Effective force profiles between some side-chains reveal the signature of multiple, distinct conformational states, and such static disorder could be one factor explaining the growing body of experiments revealing non-exponential unfolding kinetics of proteins. The design of prestress distributions in engineering proteins promises to be a new tool for tailoring the mechanical properties of made-to-order nanomaterials.</p> </div

Force-Extension curve of the (Ala) chain (<i>grey dots</i>).

<p>The average is shown in <i>blue</i>, and the fitting result of the worm-like-chain model is shown in <i>red</i>. A minimized root mean square residual error of 0.1 nN was obtained by nonlinear least square fitting.</p

(a) and (b) Networks representing the inter-residue forces for ubiquitin, as for <b>Fig. 1c</b>, but accounting for side-chain atoms only; (a) inward-pointing side-chains, (b) outward-facing side-chains.

<p>(a) and (b) Networks representing the inter-residue forces for ubiquitin, as for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002509#pcbi-1002509-g001" target="_blank"><b>Fig. 1c</b></a>, but accounting for side-chain atoms only; (a) inward-pointing side-chains, (b) outward-facing side-chains.</p

(a) X-ray structure of ubiquitin (PDB accession code 1UBI).

<p>The lower view is rotated 90 around the horizontal axis with respect to the upper view. Helices are colored red, and beta strands green. Note that the beta strands 1 and 5 are closest to the N- and C- termini respectively, and thus the interaction between them is the primary determinant of the protein's mechanical stability against stretching from the termini. (b) The network representing the inter-residue forces for ubiquitin, averaged over 100 ns of molecular dynamics simulations, superimposed on the 3D structure of the protein. The color and width of cylinders connecting residue pairs correspond to the direction and magnitude of the mean inter-residue force: blue for repulsive force, red for attractive force, and the maximum width corresponding to a force magnitude of pN. (c) A circle graph representation of the prestress network in (b). Numbers around the circumference are residue indices. Colored arcs correspond to secondary structure: alpha helix (red), beta strand (green), hydrogen-bonded loop (purple) and 3–10 helix (cyan).</p

How Fast Does a Signal Propagate through Proteins?

<div><p>As the molecular basis of signal propagation in the cell, proteins are regulated by perturbations, such as mechanical forces or ligand binding. The question arises how fast such a signal propagates through the protein molecular scaffold. As a first step, we have investigated numerically the dynamics of force propagation through a single (Ala) protein following a sudden increase in the stretching forces applied to its end termini. The force propagates along the backbone into the center of the chain on the picosecond scale. Both conformational and tension dynamics are found in good agreement with a coarse-grained theory of force propagation through semiflexible polymers. The speed of force propagation of 50Å ps⁻¹ derived from these simulations is likely to determine an upper speed limit of mechanical signal transfer in allosteric proteins or molecular machines.</p></div

Tension propagation from MD simulations and comparison to dynamic bead-spring and semiflexible chain models.

<p>(a) Tension evolution as predicted by a bead-spring model (colored curves) fitted to the tension in Ala as obtained from MD simulations (colored diamonds). Coloring red, yellow, green yellow, blue and purple show residue pairs 1–2, 4–5, 7–8, 10–11, 15–16 and 20–21, respectively. A manually reduced friction coefficient was used to map the WLC model and numerical results. We note that here forces were averaged over 100 fs time periods for clarity. (b) Tension evolution from the dynamic WLC model (colored curve) fitted to the tension in Ala as obtained from MD simulations (colored diamonds). Coloring and averaging as in (a). (c) Boundary layer size relative to the contour length obtained from MD simulations shown in <i>blue</i>. Numeric solution to the dynamic WLC model prediction in <i>green</i> and growth law in <i>black</i>. (d) Extension shown as <i>black dots</i> compared to two growth laws, in <i>blue</i> and in <i>red</i>.</p