End-to-end Distance Research Articles

Computational modeling suggests binding-induced expansion of Epsin disordered regions upon association with AP2.

Intrinsically disordered regions (IDRs) are prevalent in the eukaryotic proteome. Common functional roles of IDRs include forming flexible linkers or undergoing allosteric folding-upon-binding. Recent studies have suggested an additional functional role for IDRs: generating steric pressure on the plasma membrane during endocytosis, via molecular crowding. However, in order to accomplish useful functions, such crowding needs to be regulated in space (e.g., endocytic hotspots) and time (e.g., during vesicle formation). In this work, we explore binding-induced regulation of IDR steric volume. We simulate the IDRs of two proteins from Clathrin-mediated endocytosis (CME) to see if their conformational spaces are regulated via binding-induced expansion. Using Monte-Carlo computational modeling of excluded volumes, we generate large conformational ensembles (3 million) for the IDRs of Epsin and Eps15 and dock the conformers to the alpha subunit of Adaptor Protein 2 (AP2α), their CME binding partner. Our results show that as more molecules of AP2α are bound, the Epsin-derived ensemble shows a significant increase in global dimensions, measured as the radius of Gyration (RG) and the end-to-end distance (EED). Unlike Epsin, Eps15-derived conformers that permit AP2α binding at one motif were found to be more likely to accommodate binding of AP2α at other motifs, suggesting a tendency toward co-accessibility of binding motifs. Co-accessibility was not observed for any pair of binding motifs in Epsin. Thus, we speculate that the disordered regions of Epsin and Eps15 perform different roles during CME, with accessibility in Eps15 allowing it to act as a recruiter of AP2α molecules, while binding-induced expansion of the Epsin disordered region could impose steric pressure and remodel the plasma membrane during vesicle formation.

Fret Studies of Conformational Changes in Heparin-Binding Peptides

FRET (Förster Resonance Energy Transfer) was applied to study structural properties of heparin-binding peptides containing the sequence XBBBXXBX where 'X' represents hydropathic or uncharged and 'B' represents basic amino acids. Internally quenched fluorogenic peptides were synthesized containing the fluorescent donor oaminobenzoic acid (o-Abz) and the acceptor dinitrophenyl ethylenediamine (Eddnp) group. Using the CONTIN computational package, distance distributions were recovered from time resolved fluorescence data, associated to end-to-end distances of the peptides. The peptides containing three or four repeat units have random structure in aqueous medium, and the interaction with low molecular weight heparin stabilized short end-to end distances. Experiments in water/trifluoroethanol (TFE) mixtures showed changes in distance distributions compatible with compact conformations stabilized above 40% volume content of TFE in the mixture. Similar changes in distance distributions were also observed for the peptides in interaction with SDS micelles in aqueous suspensions and circular dichroism data revealed alpha-helix formation in the peptides in interaction with heparin, SDS micelles or the co-solvent TFE. The process is dependent on electrostatic and hydrogen bond interactions and the end-to-end distances obtained are smaller than expected for the peptides in linear α-helix conformation, indicating the occurrence of structural arrangements leading to additional decrease in the distances.

Free volume in PEP-silica nanocomposites with varying molecular weight

The influence of confinement in polymer-nanocomposites on free volume and glass transition of the polymer chains was studied. The molecular weight (Mw) of poly(ethylene-alt-propylene) (PEP) was varied from 3k to 200k and so the end-to end distance of the chains at fixed diameter (∼15 nm) and concentration (15%) of the silica nanoparticles increased. Thus the topological confinement increases with increasing Mw. Using hydrophobic PEP and particles functionalized with short organic molecules, we can rule out contributions of permanent adsorption of the chains. DSC showed no change in glass transition temperature. The decrease in the specific heat capacity could be explained by a simple mixing rule. By positron annihilation lifetime spectroscopy, taking properly into account contributions of the silica particles, we rule out an influence of the geometrical confinement on the free volume in the PEP nanocomposites studied here.

Nonlinear Elasticity of DNA Bending

Double stranded (ds) DNA has been used as a “molecular spring” to mechanically control the conformation of proteins, ribozymes and peptides [1]. It is thus interesting to characterize quantitatively the mechanics of DNA springs in the relevant regime of sharp bending (x<<2L<<ld, where x is the end-to-end distance (EED), 2L the contour length of the DNA, ld ∼50 nm the persistence length). This nonlinear elasticity regime is also relevant to several cell biology mechanisms, such as DNA packaging and transcription regulation.We address the problem with the stressed molecules consisting of a bent ds DNA part and a stretched ss part: essentially a system of two coupled nonlinear springs. We measured the elastic energy of these molecules with two different equilibrium methods, based on dimer formation [2, 3] and melting curve analysis [4] respectively. We deduce the bending energy of the ds part as a function of EED x. The finding is that the DNA kinks at a critical bending torque τc ∼30 pN x nm, entering a nonlinear regime where the maximum torque is constant (= τc). We derive an analytic expression for the bending energy valid in the linear and nonlinear regimes [3].The critical torque τc introduces a universal energy scale ∼12 kT in the physics of DNA bending.[1] G. Zocchi, “Controlling proteins through molecular springs”, Ann. Rev. Biophys. 38, 75-88 (2009).[2] H. Qu, C.-Y. Tseng, Y. Wang, A. J. Levine, and G. Zocchi, “The elastic energy of sharply bent nicked DNA”, Europhys. Lett. 90, 18003 (2010).[3] H. Qu and G. Zocchi, “The complete bending energy function for nicked DNA”, Europhys. Lett. 94, 18003 (2011).[4] H. Qu, Y. Wang, C.-Y. Tseng, and G. Zocchi, “Critical torque for kink formation in double stranded DNA”, accepted by Phys. Rev. X (2011).

End-to-End Distances in Four-Junction Polymers

The various end-to-end distances of four-junction polymers are investigated. The sizes of the different kinds of equal length branches and the backbone of two different polymers, with either nine or eleven branches, are estimated by means of both renormalization-group and MC calculations. The comparisons of first-order ε = 4 − d predictions with the MC results are satisfactory. The same trends are present in both techniques. The excluded-volume interactions from additional branches further expand the various parts of the chains so that internal branches are larger than external ones. The branch ratios in the eleven-branch case are expanded even more than the corresponding ratios of the nine-branch polymer.

Dielectric Normal and Segmental Modes in Undiluted Poly(butylene oxide)

Dielectric measurements were carried out on undiluted poly(butylene oxide) (PBO) with various molecular weights. The dielectric normal mode relaxation due to fluctuation of the end-to-end vector and the segmental relaxation due to local motions were observed. The relaxation time τn for the normal mode and τs for the segmental mode conformed to the Vogel−Fulcher equation, and the ratio of τn/τs did not depend on temperature. From the relaxation strengths for the normal and segmental modes, the parallel and perpendicular components of the dipole moment were determined. With the aid of the literature data of the end-to end distance, the dipole moment per unit contour length of PBO chains was also determined. It was found that the M dependence of τn changed around the characteristic molecular weight Mc (=6000), i.e., in the range of M Mc τn is proportional to M3.4. The relationship between the segmental dynamics and chain dynamics is discussed.

Viscoelastic Properties of Polymer Melts from Equilibrium Molecular Dynamics Simulations

Viscoelastic Properties of Polymer Melts from Equilibrium Molecular Dynamics Simulations

Model for the Binding of the Inactivation N−Terminal to the Ion Pore of Shaker Potassium Channel: Both Electrostatic Attraction and Covalent Linkage Are Required for Rapid Inactivation

A model is presented for relating the binding of the inactivation N-terminal to the ion pore of the Shaker potassium channel (ShB) to the bimolecular binding of the N-terminal peptide with the deletion mutant ShB¢646. The binding site is modeled as a small patch on the surface of the channel protein, to which the N-terminal “inactivation ball” is tethered by a flexible linker. The potential energy due to electrostatic interactions between the channel and the N-terminal is ‚U(r) )- Qexp[-(r - a)/I]/(1 + a/I)r, where a is the closest approach distance and I is the screening length determined by the ionic strength. The probability density for the endto-end vector of the flexible linker (with L residues) is taken from a previous study [Zhou, J. Phys. Chem. B 2001, 105, 6763] as p(r) ) (3/4﷿lpbL) 3/2 exp(-3r 2 /4lpbL)(1-5lp/4bL + ...). The intramolecular binding rate constant kon in of the intact ShB is related to the bimolecular binding rate constant kon bi via kon in ) kon bi p(a)/ sexp[-‚U(r)]p(r)dV. The model rationalizes a number of important experimental observations. (1) The weaker ionic strength dependence of kon in is quantitatively reproduced by the relation between kon in and kon bi . (2) The linker length dependence of kon in (observed when the linker length is reduced by deletion and extended by insertion) is qualitatively predicted by the L dependence of p(r). (3) The fact that koff in ) koff bi and both are insensitive to the change in ionic strength is due to the stereospecificity of the binding site. If the binding of the activation N-terminal were to occur in a bimolecular fashion, the millisecond inactivation time would have required the presence of the N-terminal at a concentration of 0.2 mM, even after considering the binding rate enhancement by the electrostatic attraction of the channel pore. The difficult task of maintaining such a high concentration underscores the importance of covalently linking the inactivation peptide to the ion channel.

Conformational elasticity theory of chain molecules

This paper develops a conformational elasticity theory of chain molecules, which is based on three key points: (i) the molecular model is the rotational isomeric state (RIS) model; (ii) the conformational distribution function of a chain molecule is described by a function of two variables, the end-to-end distance of a chain conformation and the energy of the conformation; (iii) the rule of changes in the chain conformational states during deformation is that a number of chain conformations would vanish. The ideal deformation behavior calculated by the theory shows that the change in chain conformations is physically able to make the upward curvature of the stress-strain curve at the large-scale deformation of natural rubber. With the theory, different deformation behaviors between polymers with different chemical structures can be described, the energy term of the stress in the deformations can be predicted, and for natural rubber the fraction of the energy term is around 13%, coinciding with the experimental results.

The coupling of chiral chains to mechanical distortions in elastomers

We calculate the joint probability distribution for endtoend and binormal vectors for a random walk of chiral steps, firstly by a simple combinatoric lattice model, and then fully by Raleigh's meth...

Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponenty is calculated at the tricritical points.

Computational analysis of triplex formation of oligonucleotides:protonated and 5-methylated py-pu-py motif

A triple helix composed of three dodecanucleotides, 5′-d(TC)6, 5′-(AG)6 and 3′-d(TC)6 with each containing a methylcytosine or a protonated-cytosine, was examined in terms of various interactions. Computational analysis of the stability of triplex formation was consistent with the experimental observations. The Hoogsteen base pairing interaction was increased through substitution of 5-methylcytosine for cytosine and/or protonation. The interaction between water molecules and DNA triplex was visualized in terms of the end-to-end distance change of each strand. The chain length was reduced by about 7.5 %–16.2 % due to the screening effect. In addition, as the screening effect increases, Hoogsteen base pairs appear to be stable in triplex formation. Our computational results also show that the effect of protonated- and methylated-cytosine on the stability of triplex formation was due to the change of the electrostatic interactions rather than the surface stacking interaction.

Conformational statistics of polymer chain terminally attached to wall (III)——NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface, the polymer chain forms the “loop” conformation. Investigation has been made on the conformational statistics of a model loop chain by the normal random walk (NRW) on a lattice confined in the half-infinite space. Based on the conformational distribution function of the NRW model tail chain, it is easy to deduce an analytical formula expressing the conformational number of the model loop chain. It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power functionN -2/3 when the chain lengthN→οο. The same result -was obtained by means of the recursion equation. The ratio of the mean square end-to-end distanceh 2 for the model loop chain to its mean square bond lengthl 2 is 2N/3. Compared with the free chain with the same lengthN, the mean square end-to-end distance of the model loop chain contracts to a certain extent. The basic relationships deduced were supported by the exact enumeration and Monte Carlo simulations.

Nonlocal interactions stabilize long range loops in the initial folding intermediates of reduced bovine pancreatic trypsin inhibitor.

A search for the topology of the chain folding of reduced bovine pancreatic trypsin inhibitor (BPTI), in unfolded and partially folded states, was done by means of time resolved dynamic nonradiative excitation energy transfer (ET) measurements. Four double labeled BPTI derivatives were used in which the donor was attached to the N-terminal arginine residue and the acceptor was specifically attached to one of the lysine residues. The four derivatives form a series of labeled backbone segments of increasing length spanning the full lengths of the BPTI chain: 15, 26, 41, and 46 residues. The intramolecular segmental end-to-end distance (EED) distributions were determined for all the derivatives by global analysis of the decay curves of both the donor and the acceptor in the reduced state, in low (0.5 M) guanidinium chloride (GuHCl) concentrations at pH 3.6 and 2.1 (R and A states, respectively). The results show that, in the partial folding conditions of low GuHCl concentration, reduced BPTI is in a compact state, but in this state the polypeptide chain is not in a condensed statistical coil conformation. Two distinct subpopulations were found for the four intramolecular EED distributions. One subpopulation was compact, with native-like EED distribution, while the second was unfolded. The pairs of sites, residues 1 and 26 and residues 1 and 46, showed close proximity in the dominant subpopulation. These contacts form two loops (probably collapsed): one consists of the first 26 residues, and the second comprises the full length of the chain from the N- to the C-terminal segments, which is in fact made up to two shorter loops (1-26 and 27-46). The N-terminal 15 residue segment was relaxed into statistical coil-like non-native conformation, in contrast to its extended conformation in the native state. The effect of temperature in the range of 2-60 degrees C was small; the folded subpopulations were stable over this range. These results show that in BPTI the compact conformations found under unfolding and partially folding conditions have native-like chain topology. Under the conditions of transition to partially folding conditions the compact conformation is stabilized, not only by the hydrophobic collapse and the local interaction but also by nonlocal interactions (NLIs). Few specific, very stable NLIs between the three segments which form the main structural elements of the native conformation direct the formation of native-like topology of the chain in the transition.(ABSTRACT TRUNCATED AT 250 WORDS)

Distribution of conformations and chain ends near the surface of a melt of linear flexible macromolecules

In a melt of linear flexible macromolecules the conformations adopted by the chains follow the ideal Kuhn random walk distribution, because of the extremely high, but uniform, local conformational attrition factor. Long-range exclusion effects are overwhelmed and pseudoideal conditions prevail. One may assume that at an interface with a melt all but the uppermost segment layers are still ideal in the above sense. This assumption leads to a method allowing the enumeration of conformations according to their end-to-end distance and the determination of the mean square end-toend distance. The result is that coils in the interfacial layer tend to be compressed. The extent of the surface zone of altered end-to-end distribution is scaled by the root mean square end-to-end distance of the coils in the bulk of the melt.