Conformational Statistics Research Articles

Calibrated Langevin-dynamics simulations of intrinsically disordered proteins.

We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: α-, β-, and γ-synuclein, the microtubule-associated protein τ, and prothymosin α. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein.

Conformational problem of alkanes in liquid crystals by NMR spectroscopy: a mini-review.

Recent discoveries of the role of alkane flexibility in determining liquid-crystal behaviour are surveyed. With the impetus for understanding the alkane conformational problem established, recent model dependent (1)H NMR work on the topic will be reviewed where progress is made but the need to circumvent models eventually becomes evident. A closer look at the rigid basic units of alkanes will provide the way forward where it is shown that the orientational ordering and anisotropic potentials of these molecules dissolved in liquid crystals scale with each other. Once this relationship is established, a series of works using anisotropic and isotropic (1)H NMR spectroscopy to study alkane conformational statistics will be covered, wherein the influence of the gas, isotropic condensed and anisotropic condensed phases will be described.

Ring Polymers in the Melt State: The Physics of Crumpling

The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for nonconcatenated unknotted rings, which are known to crumple and segregate and which have been implicated as models for the generic behavior of interphase chromosomes. Here we use a computationally efficient multiscale approach to show that melts of rings of total contour length Lr can be quantitatively mapped onto melts of interacting lattice trees with gyration radii ⟨R(g)(2)(Lr)⟩ ∝ L(r)(2ν) and ν = 0.32 ± 0.01.

环形DNA分子构象统计 Conformations of DNA Loop

DNA环的形成和性质是生物物理以及软物质物理关注的基本问题。本文以蠕虫状链为模型，应用蒙特卡洛方法模拟了锚定在蛋白质上的DNA环的构象统计。给出了DNA环在不同长度序列情况下的择优构象状态，讨论了不同构象情况下DNA分子对锚定点的作用力。 The formation and property of DNA loop are the basic problems of biophysics and soft matter physics. In present work, the conformational statistics is studied by Monte Carlo method based on the wormlike chain model. The priority conformational state for the different length of DNA loop is predicted and the force acting on the grafting point is also discussed.

Conformational Properties of Semiflexible Chains at Nematic Ordering Transitions in Thin Films: A Monte Carlo Simulation

Athermal solutions of semiflexible macromolecules with excluded volume interactions and with varying concentration (dilute, semidilute, and concentrated solutions) in a film of thickness D between two hard walls have been studied by means of grand canonical Monte Carlo simulation using the bond fluctuation lattice model. In earlier work, we have reported on the phase diagram of this model system, which exhibits a continuous quasi-two-dimensional order–disorder transition at rather small concentration and (for thick enough films) a “capillary nematization”-type first-order phase transition. In the “semi-infinite” case (i.e., macroscopically thick films) the onset of nematic order is triggered by the walls (surface-induced ordering). While the focus of this previous work was on the order parameters of these phase transitions and associated surface effects, in the present paper we focus on the interplay between the conformational statistics of the semiflexible chains and these orientational ordering phenomena. In particular, we study how characteristic lengths of the chains (persistence length, end-to-end distance) depend on the local and global orientational order in the system. We show that there is a strong coupling between single-chain properties and long-range orientational order. The relation between mean-square end-to-end distance of short semiflexible chains and their persistence length predicted by the Kratky–Porod model is found to be applicable (within 10% errors) in the dilute limit, while it fails as soon as nematic short- or long-range order is present.

Molecular Simulations of the Dynamics of Disordered Proteins

Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDPs α-, β-, and γ-synuclein and microtubule-associated protein tau (MAPT) that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent smFRET experiments. We find that all four proteins are disordered with conformational statistics that are intermediate between random walk and collapsed globule behavior and demonstrate close resemblance to the known experimental data. We find that the hydrophobic interactions strongly influence the dynamics of these proteins, and electrostatics only play a role when charges fluctuate over more than several residues as for MAPT. We also investigate the propensity of α-synuclein and MAPT to aggregate and form oligomers, and compare to our previous results with α-synuclein monomers.

Polyethylenimine: Experimental and Simulation Study of Polymer Biophysics During Ph Buffering

Dynamic Light Scattering (DLS) and all atom molecular dynamics (MD) simulation were used in complementary ways to study the effect of protonation (simulation) and pH changes (experiment) on the polymer chain dynamics of a 2.4kDa linear PEI (∼50mer). Simulations were performed with a modified CHARMM potential for a variety of charge states and ionic strengths to generate conformational statistics. DLS yielded a phase map of PEI aggregation to select for conditions in which PEI was in the dilute and free polymer state. Hydrodynamic radii from the experiments and simulations were within 3A agreement. The results indicate that PEI absorbs protons with minimal change in its elongation length, except at high protonation where the chain elongates and deviates from worm chain distributions. Salt screening introduced changes in the protonation/pH response. Our observations are consistent with PEI studies showing that intra-chain charge repulsion raised the free energy of subsequent protonation.

Recovering the reptation dynamics of polymer melts in dissipative particle dynamics simulations via slip-springs

We report a multi-chain approach for dissipative particle dynamics where the uncrossability constraints of polymer chains are mimicked by temporary cross-links, so-called slip-springs. The conformational statistics of the chains are not affected by the introduction of slip-springs. Dynamical properties such as mean square displacements, diffusion coefficient, and longest relaxation time are in good agreement with the results of reptation theory. According to our analysis, the present formalism is 500 times faster and requires 7 times fewer beads than conventional generic polymer models employing Newtonian dynamics and excluded-volume potentials.

Calculator for conformational statistics of DNA and applications to high-curvature bending

DNA conformation plays an important role in a host of cellular processes. Despite the central importance of DNA conformation, there is not yet a general-purpose calculator for conformational statistics that is designed for the scientific community. Here we describe a public tool we developed for calculating an important class of conformational statistics: the end-to-end probability density of finding a locus of the DNA polymer at a given displacement and orientation relative to a second locus on the same polymer. As a demonstration, we propose a cyclization experiment and use our calculator to show that this experiment could measure the energy of DNA bending as a direct function of bend angle in the poorly understood high-bending regime. Our tool is available as both an online calculator and a downloadable program at http://mtshasta.phys.washington.edu/wormulator/.

Molecular Simulations of the Fluctuating Conformational Dynamics of α-Synuclein

Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP α-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent smFRET experiments. We find that α-synuclein is disordered with conformational statistics that are intermediate between random walk and collapsed globule behavior and demonstrate close resemblance to the known experimental data. We use these simulations to study oligomerization and aggregation of multiple α-synuclein proteins that may precede amyloid formation.

The Conformational Ensembles of α-Synuclein and Tau: Combining Single-Molecule FRET and Simulations

Intrinsically disordered proteins (IDPs) are increasingly recognized for their important roles in a range of biological contexts, both in normal physiological function and in a variety of devastating human diseases. However, their structural characterization by traditional biophysical methods, for the purposes of understanding their function and dysfunction, has proved challenging. Here, we investigate the model IDPs α-Synuclein (αS) and tau, that are involved in major neurodegenerative conditions including Parkinson’s and Alzheimer’s diseases, using excluded volume Monte Carlo simulations constrained by pairwise distance distributions from single-molecule fluorescence measurements. Using this, to our knowledge, novel approach we find that a relatively small number of intermolecular distance constraints are sufficient to accurately determine the dimensions and polymer conformational statistics of αS and tau in solution. Moreover, this method can detect local changes in αS and tau conformations that correlate with enhanced aggregation. Constrained Monte Carlo simulations produce ensembles that are in excellent agreement both with experimental measurements on αS and tau and with all-atom, explicit solvent molecular dynamics simulations of αS, with much lower configurational sampling requirements and computational expense.

Molecular simulations of the fluctuating conformational dynamics of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP α-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent single-molecule fluorescence energy transfer (smFRET) experiments. We find that α-synuclein is disordered, with conformational statistics that are intermediate between random walk and collapsed globule behavior. An advantage of calibrated molecular simulations over constraint methods is that physical forces act on all residues, not only on residue pairs that are monitored experimentally, and these simulations can be used to study oligomerization and aggregation of multiple α-synuclein proteins that may precede amyloid formation.

Non-Markovian polymer reaction kinetics

Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.

Weak-to-strong confinement transition of semi-flexible macromolecules in slit and in channel

We compare confinement of stiff macromolecule in channel and in slit. Whereas in the channel a distinct and established transition exists, we elucidate here an ongoing controversy reported from previous experiment and simulation on existence of such transition in the slit. Our extensive molecular simulations in both geometries show only a very weak conformational crossover between moderate and strong confinements in slit in the same range of confinements where the distinct transition in channel is observed. In contrast to situation in channels relatively stable hairpin-like structures are not indicated around this weak transition in the slit. Observed difference from the prediction on behavior in blob regime under moderate confinement is explained by a crossover between dimensionalities in the slit and the extent of ideal conformation statistics to which the stiffer chains are prone. The strong confinement regime of stiff chain in slit characterized here has not been interpreted yet and it differs from the respective saturation-like Odijk regime in the channel.

Nuclear magnetic resonance study of alkane conformational statistics

NMR spectra of ethane, propane, and n-butane as solutes in the nematic liquid crystals 4-n-pentyl-4(')-cyanobiphenyl (5CB) and Merck ZLI 1132 (1132) are investigated over a wide temperature range. The ratios of dipolar couplings of ethane to propane are constant over the entire temperature range. Assuming that this constancy applies to the butane conformers facilitates the separation of probability from order parameter. This separation allows the investigation of conformational distribution without the need of invoking any model for the anisotropic intermolecular potential. The results give an order matrix that is consistent with that predicted from model potentials that describe the orientational potential in terms of short-range size and shape effects. The isotropic intermolecular potential contribution to the trans-gauche energy difference E(tg) is found to be temperature dependent with the values and variation in agreement with that found when the same results are analyzed using the chord model for anisotropic interactions [A. C. J. Weber and E. E. Burnell, Chem. Phys. Lett. 506, 196 (2011)]. The fit obtained for 9 spectra in 5CB (63 dipolar couplings) has an RMS difference between experimental and calculated dipolar couplings of 2.7 Hz, while that for the 16 spectra in 1132 (112 couplings) is 6.2 Hz; this excellent fit with nine adjustable parameters suggests that the assumption of equal temperature dependencies of the order parameters for ethane, propane, and each conformer of butane is correct. Also the fit parameters (E(tg) and the methyl angle increase) obtained for 1132 and 5CB agree. The results indicate that the chord model, which was designed to treat hydrocarbon chains, is indeed the model of choice for these chains. The temperature variation of E(tg) provides a challenge for theoreticians. Finally, even better fits to the experimental dipolar couplings are obtained when the energy in the Boltzmann factor is used for scaling ethane to butane results. However, in this case the values obtained for E(tg) differ between 1132 and 5CB.

Pharmacological Characterization of Chemically Synthesized Monomeric phi29 pRNA Nanoparticles for Systemic Delivery

Previous studies have shown that the packaging RNA (pRNA) of bacteriophage phi29 DNA packaging motor folds into a compact structure, constituting a RNA nanoparticle that can be modularized with functional groups as a nanodelivery system. pRNA nanoparticles can also be self-assembled by the bipartite approach without altering folding property. The present study demonstrated that 2'-F-modified pRNA nanoparticles were readily manufactured through this scalable bipartite strategy, featuring total chemical synthesis and permitting diverse functional modularizations. The RNA nanoparticles were chemically and metabolically stable and demonstrated a favorable pharmacokinetic (PK) profile in mice (half-life (T(1/2)): 5-10 hours, clearance (Cl): <0.13 l/kg/hour, volume of distribution (V(d)): 1.2 l/kg). It did not induce an interferon (IFN) response nor did it induce cytokine production in mice. Repeat intravenous administrations in mice up to 30 mg/kg did not result in any toxicity. Fluorescent folate-pRNA nanoparticles efficiently and specifically bound and internalized to folate receptor (FR)-bearing cancer cells in vitro. It also specifically and dose-dependently targeted to FR(+) xenograft tumor in mice with minimal accumulation in normal tissues. This first comprehensive pharmacological study suggests that the pRNA nanoparticle had all the preferred pharmacological features to serve as an efficient nanodelivery platform for broad medical applications.

Conformational statistics of n-butane in the condensed phase and the effects of temperature

Experimental dipolar couplings are obtained from the 1H NMR spectra of n-butane dissolved in a liquid crystal over an 80° temperature range with Covariance Matrix Adaptation Evolutionary Strategies (CMA-ES). These observables are rationalized using a size-and-shape potential [E.E. Burnell, C.A. de Lange, Chem. Rev. 98 (1998) 2359], CI (2k), and with a modified chord model [D.J. Photinos, E.T. Samulski, H. Toriumi, J. Phys. Chem. 94 (1990) 4694], CCd, for the orientational ordering potential. The trans– gauche energy difference, E tg , is temperature dependent when using the CCd model and temperature independent when using the CI (2k) model for the orientational ordering potential.

Methods and Tools for the Prediction of Hydrodynamic Coefficients and Other Solution Properties of Flexible Macromolecules in Solution. A Tutorial Minireview

The calculation of solution properties of flexible macromolecules and other nanoparticles requires, in addition to the hydrodynamic formalisms needed for the sedimentation coefficient and other transport properties, the consideration of the conformational statistics and internal dynamics. The latter aspects can be handled with simulation methods like Monte Carlo and Brownian dynamics. An example of a Monte Carlo simulation for a model specific of DNA is illustrated with results for the several solution properties over an extremely wide range of molecular weight. The convenience of having computational tools of a quite general applicability has prompted us to implement the simulation and hydrodynamic treatments in software packages, MONTEHYDRO for Monte Carlo, and SIMUFLEX for Brownian dynamics which-with a scope similar to the HYDRO suite for rigid particles-can handle a variety of situations. As an application of the new methodology to a yet unclear problem in analytical ultracentrifugation, in a simple application of the SIMUFLEX software, we present a simulation of the so-called anomalous sedimentation of very long DNA molecules, obtaining results for the experimentally observable rotor-speed-dependence of the sedimentation coefficient.

Effect of intrinsic curvature on semiflexible polymers

Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influences the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C(r)=<t(s).t(s+r)>, both in two and three dimensions. Contrary to expectation, C(r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We also compute the distribution function P(R) of the end to end distance R and show how curved chains can be distinguished from wormlike chains using loop formation probability.

Velocity and conformation statistics based on reduced Karhunen–Loeve projection data from DNS of viscoelastic turbulent channel flow

To investigate the effectiveness of the Karhunen–Loeve (K–L) method as a data reduction approach, we study here its effect on the velocity and conformation statistics in a drag reducing turbulent polymer flow. The K–L method has been used to construct a set of basis velocity eigenfunctions from a large number of independent realizations of the velocity. Those were obtained from direct numerical simulation (DNS) of a viscoelastic turbulent channel flow using the Giesekus model. A subset of the K–L eigenfunctions, large enough to contain more than 90% of the fluctuating kinetic energy of the flow on the average, has then been subsequently used to obtain time series of projection coefficients of the velocity fields generated further from DNS. In a post-processing step, velocity fields were reconstructed using selected subsets of the projection coefficients. Those reconstructed velocity fields were then used to evaluate turbulent statistics as well as to integrate the constitutive equation. The turbulent statistics (r.m.s. velocities, Reynolds stress etc.) thus constructed showed good agreement with the full results from DNS. The Reynolds stress anisotropy was also calculated in this work for the first time. It was found to increase with viscoelasticity that was well reproduced in the reduced K–L data except near the channel centerline where the K–L data showed some loss of anisotropy. The biggest differences however between the K–L reduced data and the full DNS results were seen in the conformation statistics. The average polymer conformation extracted from the K–L reduced data was significantly less than that corresponding to the full DNS results anywhere except in the shear-dominated wall region. A further comparison of the energy and dissipation spectra between the full DNS and the K–L reconstructed data illustrated the impact of the K–L process in resulting to a significant damping of small turbulent scales even those contributing to the maximum in turbulent dissipation. This may also be the principal reason behind the poor quality of the K–L reconstructed conformation data.