An Adequate Account of Excluded Volume Is Necessary To Infer Compactness and Asphericity of Disordered Proteins by Förster Resonance Energy Transfer

Single-molecule Förster resonance energy transfer (smFRET) is an important tool for studying disordered proteins. It is commonly utilized to infer structural properties of conformational ensembles by matching experimental average energy transfer ⟨<i>E</i>⟩_exp with simulated ⟨<i>E</i>⟩_sim computed from the distribution of end-to-end distances in polymer models. Toward delineating the physical basis of such interpretative approaches, we conduct extensive sampling of coarse-grained protein chains with excluded volume to determine the distribution of end-to-end distances conditioned upon given values of radius of gyration <i>R</i>_g and asphericity <i>A</i>. Accordingly, we infer the most probable <i>R</i>_g and <i>A</i> of a protein disordered state by seeking the best fit between ⟨<i>E</i>⟩_exp and ⟨<i>E</i>⟩_sim among various (<i>R</i>_g,<i>A</i>) subensembles. Application of our method to residues 1–90 of the intrinsically disordered cyclin-dependent kinase (Cdk) inhibitor Sic1 results in inferred ensembles with more compact conformations than those inferred by conventional procedures that presume either a Gaussian chain model or the mean-field Sanchez polymer theory. The Sic1 compactness we infer is in good agreement with small-angle X-ray scattering data for <i>R</i>_g and NMR measurement of hydrodynamic radius <i>R</i>_h. In contrast, owing to neglect or underappreciation of excluded volume, conventional procedures can significantly overestimate the probabilities of short end-to-end distances, leading to unphysically large smFRET-inferred <i>R</i>_g at high [GdmCl]. It follows that smFRET Sic1 data are incompatible with the presumed homogeneously expanded or contracted conformational ensembles in conventional procedures but are consistent with heterogeneous ensembles allowed by our subensemble method of inference. General ramifications of these findings for smFRET data interpretation are discussed

Extraordinary Reinforcement Effect of Three-Dimensionally Nanoporous Cellulose Gels in Poly(ε-caprolactone) Bionanocomposites

Three-dimensionally nanoporous cellulose gels (NCG) were prepared by dissolution and coagulation of cellulose from aqueous alkali hydroxide-urea solution, and used to fabricate NCG/poly­(ε-caprolactone) (PCL) nanocomposites by in situ ring-opening polymerization of ε-CL monomer in the NCG. The NCG content of the NCG/PCL nanocomposite could be controlled between 7 and 38% v/v by changing water content of starting hydrogel by compression dewatering. FT-IR and solid-state ¹³C NMR showed that the grafting of PCL onto cellulose are most likely occurred at the C6-OH groups and the grafting percentage of PCL is 25 wt % for the nanocomposite with 7% v/v NCG. ¹H NMR, XRD, and DSC results indicate that the number-average molecular weight and crystal formation of PCL in the nanocomposites are remarkably restricted by the presence of NCG. AFM images confirm that the interconnected nanofibrillar cellulose network structure of NCG are finely distributed and preserved well in the PCL matrix after polymerization. DMA results show remarkable increase in tensile storage modulus of the nanocomposites above glass transition and melting temperatures of the PCL matrix. The percolation model was used to evaluate the mechanical properties of the nanocomposites, in which stress transfer among the interconnected nanofibrillar network is facilitated through strong intermolecular hydrogen bonding and entanglement of cellulose nanofibers

Effect of Y density and distribution on EAD activity.

<p>(A, B) The EAD peptides (left) were tested for relative transactivation (black) and simulated (grey), shown in the same style as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi-1003239-g003" target="_blank">Fig. 3</a>. (A) 7Yn (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi-1003239-g001" target="_blank">Fig. 1A</a>) with Y density denoted normal (n or <i>k</i> = 6) was compared with 7Yn/2 (Y density ∼1/2 of 7Yn, <i>k</i> = 12) and 7Yn/4 (Y density ∼1/4 that of 7Yn, <i>k</i> = 24). The actual simulated for 7Yn is 0.11. (B) 10Yn (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi-1003239-g001" target="_blank">Fig. 1A</a>; <i>k</i> = 6) was compared with 5Y (<i>k</i> = 12) and the sequence 5YP which has 5 pairs of sequentially adjacent Ys. The asterisk indicates that 5Y activity is overstated due to relatively higher expression of 5Y protein. (C) Analysis using our analytical model. All were for  = 32, <i>C</i> = 1, and  = −3.5 except the data point plotted as open circle ( = −2.6) was for  = −5.1. The solid line shows results for <i>k</i> = 6 and <i>n</i> = 66. The upper and lower dashed lines provide results for <i>k</i> = 12 with chain lengths <i>n</i> = 66 and <i>n</i> = 71 respectively. The diamonds show results (from bottom to top) for 7Yn, 7Yn/2, and 7Yn/4 in (A), which have chain lengths <i>n</i> = 66, 86, and 156 respectively. To facilitate comparison with the  = 7 data in (A),  = 7 is marked by the vertical dotted line. The squares show results for 5Y ( = 5;  = 4.0) and 10Yn ( = 10;  = −3.2) in (B), both with <i>n</i> = 66. As discussed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi.1003239.s012" target="_blank">Text S1</a>, the model represented by the open circle may be applied to 5YP in (B) with −5.1 as the interaction energy between a cation and two adjacent aromatic residues.</p

Further testing of the polycation-π model.

<p>Designed mutant EADs (left) were tested for transcriptional activity and simulated binding. Full peptide sequences are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi.1003239.s001" target="_blank">Fig. S1</a>. Y residues for all peptides are shown in magenta as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi-1003239-g001" target="_blank">Fig. 1</a> and the key residues are similarly depicted. Protein expression levels were determined by Western blot analysis of epitope-tagged activator proteins in extracts from transfected cells using KT3 antibody (right). The histograms show percentage experimental activities (black) and simulated (grey) relative to that of the first sequence (100%) in each experiment. Estimated errors for simulated are standard deviations from ten independent simulations. (A) Efficacy of different aromatic moieties. All Ys in 5Yn (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi-1003239-g001" target="_blank">Fig. 1A</a>) were replaced by W (yellow) or F (orange). The variation of well depth for cation-F (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi-1003239-g001" target="_blank">Fig. 1B</a>) entails a range of relative from 24% to 80% and the latter is plotted here. (B) Effect of adding anions (Asp, shown in blue). (C) Effect of adding cations (Arg, shown in green).</p

IDP-target binding in the analytical model.

<p>To match the chain simulation model, we used  = 438.0 ų, where <i>b</i> = 3.8 Å is the – virtual bond length and  = 6 Å is the capture radius for a cation-π contact in the chain model. (A) The IDP's chain length <i>n</i> = 66, with <i>k</i> = 6 (corresponding to the sequences in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi-1003239-g001" target="_blank">Fig. 1</a>). was computed for different values.  = 32 for the target and <i>V</i> = (600 Å)³ as in the simulations [hence  = 13.1]. Inset: The energy () and entropy () components of for  = −3.5. Results in (B–D) are also for  = −3.5. (B) Effects of <i>k</i> and <i>V</i> on binding;  = 32;  = 1/(600 Å)³ is used as a reference IDP concentration. The black curves show at for hypothetical sequences with <i>k</i> = 9, 8, 7, 6, 5, 4, and 3 (from top to bottom), <i>n</i> = 66 for <i>k</i>≤6 and <i>n</i> =  for <i>k</i>≥7. The blue curves are for the <i>k</i> = 6 sequences for three IDP concentrations with <i>C</i> = 0.25, 3.0, and 10.0 (from top to bottom). (C) for <i>k</i> = 6 sequences at <i>C</i> = 1 on different targets of the same size with different  = 8, 16, 32, 48, 64, and 80 (from left to right; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi.1003239.s012" target="_blank">Text S1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi.1003239.s005" target="_blank">Fig. S5B</a>). (D) of the <i>k</i> = 6 sequences at different IDP concentrations <i>C</i> = 10.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.5, 0.33, and 0.25 (from top to bottom).</p

Model for molecular recognition by EAD.

<p>The EAD peptide is depicted here as a string of beads with aromatic (Y) residues in magenta and other residues in grey (see also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003239#pcbi.1003239.s002" target="_blank">Fig. S2</a>). The target protein (Target) is generic and the number/distribution of surface positively charged (R) residues for real targets are unknown. Rs are chosen over Ks simply because Rs are more commonly paired with Ys in cation-π interactions. Binding is driven predominantly by cation-π interactions between Ys and Rs. A key postulate of the model is that the EAD remains disordered irrespective of binding and exists as a dynamic ensemble. Two general, high-probability states are depicted: (A) At low Y number the probability of EAD rebinding is low; dissociation is favored. (B) At higher Y number the probability of rebinding is sufficient to counteract dissociation and maintain binding.</p

Tough and Cell-Compatible Chitosan Physical Hydrogels for Mouse Bone Mesenchymal Stem Cells in Vitro

Most hydrogels involve synthetic polymers and organic cross-linkers that cannot simultaneously fulfill the mechanical and cell-compatibility requirements of biomedical applications. We prepared a new type of chitosan physical hydrogel with various degrees of deacetylation (<i>DD</i>s) via the heterogeneous deacetylation of nanoporous chitin hydrogels under mild conditions. The <i>DD</i> of the chitosan physical hydrogels ranged from 56 to 99%, and the hydrogels were transparent and mechanically strong because of the extra intra- and intermolecular hydrogen bonding interactions between the amino and hydroxyl groups on the nearby chitosan nanofibrils. The tensile strength and Young’s modulus of the chitosan physical hydrogels were 3.6 and 7.9 MPa, respectively, for a <i>DD</i> of 56% and increased to 12.1 and 92.0 MPa for a <i>DD</i> of 99% in a swelling equilibrium state. In vitro studies demonstrated that mouse bone mesenchymal stem cells (mBMSCs) cultured on chitosan physical hydrogels had better adhesion and proliferation than those cultured on chitin hydrogels. In particular, the chitosan physical hydrogels promoted the differentiation of the mBMSCs into epidermal cells in vitro. These materials are promising candidates for applications such as stem cell research, cell therapy, and tissue engineering

Interfacial Synthesis of Conjugated Two-Dimensional N‑Graphdiyne

We explored the interfacial synthesis of 2D N-graphdiyne films at the gas/liquid and liquid/liquid interfaces. Triazine- or pyrazine-based monomers containing ethynyl group were polymerized through the Glaser coupling reactions at interfaces. Several layered, highly ordered and conjugated 2D N-graphdiyne were obtained. Their structures were characterized by TEM, SEM, AFM, XPS, and Raman spectra. Thin films with minimum thickness of 4 nm could be prepared