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 Computer Science , 2014, Abstract: Can folding a piece of paper flat make it larger? We explore whether a shape $S$ must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries $S\rightarrow R^2$). The underlying problem is motivated by computational origami, and is related to other covering and fixturing problems, such as Lebesgue's universal cover problem and force closure grasps. In addition to considering special shapes (squares, equilateral triangles, polygons and disks), we give upper and lower bounds on scale factors for single folds of convex objects and arbitrary folds of simply connected objects.
 Physics , 2010, DOI: 10.1103/PhysRevE.82.011916 Abstract: We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by assembling the solitons together, one after another. We present a simple theoretical model that realizes our proposal and apply it to a number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to construct solitons that reproduce secondary structural motifs such as alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall root-mean-square-distance accuracy of around 0.7 Angstrom or less for the central alpha-carbons, i.e. within the limits of current experimental accuracy.
 Brazilian Journal of Medical and Biological Research , 2002, DOI: 10.1590/S0100-879X2002000300015 Abstract: previous studies have demonstrated that some components of the leukocyte cell membrane, cr3 (mac-1, cd11b/cd18) and p150/95, are able to bind to denatured proteins. thus, it is of interest to know which effector functions of these cells can be triggered by these receptors when they interact with particles or surfaces covered with denatured proteins. in the present study we analyzed their possible role as mediators of phagocytosis of red cells covered with denatured bovine serum albumin (bsa) by mouse peritoneal macrophages. we observed that a) macrophages are able to recognize (bind to) these red cells, b) this interaction can be inhibited by denatured bsa in the fluid phase, c) there is no phagocytosis of these particles by normal macrophages, d) phagocytosis mediated by denatured bsa can be, however, effectively triggered in inflammatory macrophages induced by glycogen or in macrophages activated in vivo with lps, and e) this phagocytic capacity is strongly dependent on the activity of tyrosine protein kinases in its signal transduction pathway, as demonstrated by using three kinds of enzyme inhibitors (genistein, quercetin and herbimycin a).
 Brazilian Journal of Medical and Biological Research , 2002, Abstract: Previous studies have demonstrated that some components of the leukocyte cell membrane, CR3 (Mac-1, CD11b/CD18) and p150/95, are able to bind to denatured proteins. Thus, it is of interest to know which effector functions of these cells can be triggered by these receptors when they interact with particles or surfaces covered with denatured proteins. In the present study we analyzed their possible role as mediators of phagocytosis of red cells covered with denatured bovine serum albumin (BSA) by mouse peritoneal macrophages. We observed that a) macrophages are able to recognize (bind to) these red cells, b) this interaction can be inhibited by denatured BSA in the fluid phase, c) there is no phagocytosis of these particles by normal macrophages, d) phagocytosis mediated by denatured BSA can be, however, effectively triggered in inflammatory macrophages induced by glycogen or in macrophages activated in vivo with LPS, and e) this phagocytic capacity is strongly dependent on the activity of tyrosine protein kinases in its signal transduction pathway, as demonstrated by using three kinds of enzyme inhibitors (genistein, quercetin and herbimycin A).
 Physics , 2009, DOI: 10.1103/PhysRevE.82.021910 Abstract: We combine the principle of gauge invariance with extrinsic string geometry to develop a lattice model that can be employed to theoretically describe properties of chiral, unbranched homopolymers. We find that in its low temperature phase the model is in the same universality class with proteins that are deposited in the Protein Data Bank, in the sense of the compactness index. We apply the model to analyze various statistical aspects of folded proteins. Curiously we find that it can produce results that are a very good good match to the data in the Protein Data Bank.
 Bioinformation , 2008, Abstract: Multi-fractal property of heat-denatured protein aggregates (HDPA) is characteristic of its individual form. The visual similarity between digitally generated microscopic images of HDPA with that of surface-image of its individual X-ray structures in protein databank (PDB) displayed using Visual Molecular Dynamics (VMD) viewer is basis of the study. We deigned experiments to view the fractal nature of proteins at different aggregate scales. Intensity based multi-fractal dimensions (ILMFD) extracted from various planes of digital microscopic images of protein aggregates were used to characterize HDPA into different classes. Moreover, the ILMFD parameters extracted from aggregates show similar classification pattern to digital images of protein surface displayed by VMD viewer using PDB entry. We discuss the use of irregular patterns of heat-denatured aggregate proteins to understand various surface properties in native proteins.
 Physics , 1997, DOI: 10.1103/PhysRevLett.79.3530 Abstract: By balancing the average energy gap with its typical change due to mutations for protein-like heteropolymers with M residues, we show that native states are unstable to mutations on a scale M* ~ (lambda/sigma_mu)^(1/zeta_s), where lambda is the dispersion in the interaction free energies and sigma_mu their typical change. Theoretical bounds and numerical estimates (based on complete enumeration on four lattices) of the instability exponent zeta_s are given. Our analysis suggests that a limiting size of single-domain proteins should exist, and leads to the prediction that small proteins are insensitive to random mutations.
 Quantitative Biology , 2010, Abstract: The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the different cutoff distances used for constructing the residue networks from the knowledge of the experimental coordinates. In this study, we present a systematical study of network construction, and their effect on the predicted properties. Probing bond orientational order around each residue, we propose a natural partitioning of the interactions into an essential and a residual set. In this picture the robustness originates from the way with which new contacts are added so that an unusual local orientational order builds up. These residual interactions have a vanishingly small effect on the force vectors on each residue. The stability of the overall force balance then translates into the Hessian as small shifts in the slow modes of motion and an invariance of the corresponding eigenvectors. We introduce a rescaled version of the Hessian matrix and point out a link between the matrix Frobenius norm based on spectral stability arguments. A recipe for the optimal choice of partitioning the interactions into essential and residual components is prescribed. Implications for the study of biologically relevant properties of proteins are discussed with specific examples.
 PLOS ONE , 2008, DOI: 10.1371/journal.pone.0003235 Abstract: Recent in vitro and in vivo studies suggest that destabilized proteins with defective folding induce aggregation and toxicity in protein-misfolding diseases. One such unstable protein state is called amyloid oligomer, a precursor of fully aggregated forms of amyloid. Detection of various amyloid oligomers with A11, an anti-amyloid oligomer conformation-specific antibody, revealed that the amyloid oligomer represents a generic conformation and suggested that toxic β-aggregation processes possess a common mechanism. By using A11 antibody as a probe in combination with mass spectrometric analysis, we identified GroEL in bacterial lysates as a protein that may potentially have an amyloid oligomer conformation. Surprisingly, A11 reacted not only with purified GroEL but also with several purified heat shock proteins, including human Hsp27, 40, 70, 90; yeast Hsp104; and bovine Hsc70. The native folds of A11-reactive proteins in purified samples were characterized by their anti-β-aggregation activity in terms of both functionality and in contrast to the β-aggregation promoting activity of misfolded pathogenic amyloid oligomers. The conformation-dependent binding of A11 with natively folded Hsp27 was supported by the concurrent loss of A11 reactivity and anti-β-aggregation activity of heat-treated Hsp27 samples. Moreover, we observed consistent anti-β-aggregation activity not only by chaperones containing an amyloid oligomer conformation but also by several A11-immunoreactive non-chaperone proteins. From these results, we suggest that the amyloid oligomer conformation is present in a group of natively folded proteins. The inhibitory effects of A11 antibody on both GroEL/ES-assisted luciferase refolding and Hsp70-mediated decelerated nucleation of Aβ aggregation suggested that the A11-binding sites on these chaperones might be functionally important. Finally, we employed a computational approach to uncover possible A11-binding sites on these targets. Since the β-sheet edge was a common structural motif having the most similar physicochemical properties in the A11-reactive proteins we analyzed, we propose that the β-sheet edge in some natively folded amyloid oligomers is designed positively to prevent β aggregation.
 Quantitative Biology , 2010, DOI: 10.1103/PhysRevE.83.041907 Abstract: A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a classification scheme that describes a protein starting from its well organized secondary structures and often involves direct human involvement, with an atomary level Physics based approach where a protein is fundamentally nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen and nitrogen atoms. In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced. Here we explain how the geometrical shape of entire folded proteins can be described analytically in terms of a single explicit elementary function that is familiar from nonlinear physical systems where it is known as the kink-soliton. Our approach enables the conversion of hierarchical structural information into a quantitative form that allows for a folded protein to be characterized in terms of a small number of global parameters that are in principle computable from atomary level considerations. As an example we describe in detail how the native fold of the myoglobin 1M6C emerges from a combination of kink-solitons with a very high atomary level accuracy. We also verify that our approach describes longer loops and loops connecting $\alpha$-helices with $\beta$-strands, with same overall accuracy.
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