Computer simulation studies of self-assembling macromolecules

Coarse-grained (CG) molecular models are now widely used to understand the structure and functionality of macromolecular self-assembling systems. In the last few years, significant efforts have been devoted to construct quantitative CG models based on data from molecular dynamics (MD) simulations with more detailed all-atom (AA) intermolecular force fields as well as experimental thermodynamic data. We review some of the recent progress pertaining to the MD simulation of self-assembling macromolecular systems, using as illustrations the application of CG models to probe surfactant and lipid self-assembly including liposome and dendrimersome formation as well as the interaction of biomembranes with nanoparticles.     

Transport properties of rigid bent-rod macromolecules and of semiflexible broken rods in the rigid-body treatment. Analysis of the flexibility of myosin rod.

The translational diffusion coefficients, rotational relaxation times and intrinsic viscosities of rigid bent rods, composed by two rodlike arms joined rigidly at an angle alpha, have been evaluated for varying conformation using the latest advances in hydrodynamic theory. We have considered semiflexible rods in which the joint is an elastic hinge or swivel, with a potential V(alpha) = 1/2Q alpha 2 with constant Q. Accepting the rigid-body treatment, we calculate properties of broken rods by averaging alpha-dependent values for rigid rods. The results are finally used to interpret literature values of the properties of myosin rod. Q is regarded as an adjustable parameter, and the value fitted is such that the average bending angle of myosin rod is approximately 60 degrees.     

Transport properties and hydrodynamic centers of rigid macromolecules with arbitrary shapes

A general formalism, which includes translation–rotation coupling, is proposed for calculating translational and rotational transport properties, as well as intrinsic viscosities, of rigid macromolecules with an arbitrary shape. This formalism is based on Brenner's theory of translational–rotational dynamics and on methods for the calculation of hydrodynamic properties that have been already presented, and can be regarded as a generalization of the one proposed by Nakajima and Wada. The calculated transport properties depend on the origin as predicted by Brenner's theory, but in a disagreement with him, the center of resistance and the center of diffusion do not coincide. As one can define several hydrodynamic centers, which in practice turn out to be located at different points, the influence of the choice of the center on the calculated transport properties is discussed. An analysis of the translation–rotation coupling effects in translational diffusion reveals that they arise exclusively from hydrodynamic interactions and are rather small in some cases of interest. Finally, we present a study of the rotational diffusion of rigid bent rods with a fixed length-to-diameter ratio. The diffusion coefficients obtained can be useful to estimate changes with respect to a straight rod.     

Sedimentation coefficient and intrinsic viscosity of semiflexible chains

Published theoretical equations for the sedimentation coefficient and intrinsic viscosity of a semiflexible chain are compared, neglecting the excluded volume effect. The theories are extended to the case of a small excluded volume, by applying the perturbation theory, established for flexible chains, to a semiflexible chain. Using the derived equation, the experimental results for the sedimentation coefficient and intrinsic viscosity of DNA and cellulose trinitrate are analyzed.     

HYDRO: a computer program for the prediction of hydrodynamic properties of macromolecules.

HYDRO is a program for the calculation of sedimentation and diffusion coefficients, rotational relaxation times, and intrinsic viscosities of rigid macromolecules of arbitrary shape that are represented by bead models. Actually, HYDRO contains various FORTRAN callable subroutines that can be linked to the user's own programs to account for variability of shape or flexibility. Some hints are given for the use of HYDRO in various situations.     

Multi-scale calculation and global-fit analysis of hydrodynamic properties of biological macromolecules: determination of the overall conformation of antibody IgG molecules

We present a scheme, based on existing and newly developed computational tools, for the determination of the overall conformation of biological macromolecules composed by domains or subunits, using from such structural determination easily available solution properties. In a multi-scale approach, atomic-level structures are used to provide simple shapes for the subunits, which are put together in a coarse grained model, with a few parameters that determine the overall shape of the macromolecule. Computer programs, like those in the HYDRO suite that evaluate the properties of either atomic or coarse-grained models. In this paper we present a new scheme for a global fit of multiple properties, implemented in a new computer program, HYDROFIT, which interfaces with the programs of the HYDRO suite to find an optimum, best-fitting structure in a robust but simple way. The determination of the overall structure of the native antibody IgG3, bearing a long hinge, and that of the hingeless mutant m15 is presented to test and confirm the validity of this simple, systematic and efficient scheme.     

Monte Carlo approach to the analysis of the rotational diffusion of wormlike chains

A Monte Carlo analysis is presented which establishes a relationship between the rotational diffusion coefficients and the flexibility (persistence length, P) of short, wormlike chains. The results of this analysis are presented in terms of experimentally observable quantities; namely, the rotational relaxation times for the field-free decay of optical anisotropy. The pertinent theoretical quantity is R, defined as the ratio of the longest rotational relaxation time of a wormlike chain to the transverse rotational relaxation time of a rigid cylinder having the same axial length (L) and segmental volume. R, so defined, is essentially independent of the axial ratio of the cylinder for any value of L/P within the range of validity of the present analysis (axial ratio > 20; 0.1 < L/P < 5). It is pointed out that P can be determined with reasonable accuracy even in the absence of a precise knowledge of the local hydrodynamic radius of the chain.     

Computer simulation of DNA supercoiling

We treat supercoiled DNA within a wormlike model with excluded volume. A modified Monte Carlo approach has been used, which allowed computer statistical-mechanical simulations of moderately and highly supercoiled DNA molecules. Even highly supercoiled molecules do not have a regular shape, though with an increase in writhing the chains look more and more like branched interwound helixes. The averaged writhing (Wr) approximately 0.7 delta Lk. The superhelical free energy F is calculated as a function of the linking number. Lk. The calculations have shown that the generally accepted quadratic dependence of F on Lk is valid for a variety of conditions, though it is by no means universal. Significant deviations from the quadratic dependence are expected at high superhelical density under ionic conditions where the effective diameter of DNA is small. The results are compared with the available experimental data.     

Transport properties of rigid and flexible macromolecules by brownian dynamics simulation

The method of Ermak and McCammon [Ermak, D. L. & McCammon, J. A. (1978) J. Chem. Phys. 69 , 1352–1360] is used to simulate the Brownian dynamics of a system of identical, interacting beads. In the present study, we use the method to obtain transport coefficients for a variety of rigid and flexible structures modeled as arrays of spherical subunits. Constraints are enforced using the SHAKE algorithm or a modification, SHAKE-HI, that is described for the first time. In SHAKE-HI, hydrodynamic interactions between subunits are taken into account when the constraints are enforced. Use of SHAKE-HI yields transport coefficients that are in perfect agreement with those obtained by other methods. The primary advantage of the present method is its generality. We also propose that multistep Brownian dynamics may be important in simulating actual experiments (such as fluorescence depolarization) on well-defined model systems that possess an arbitrary degree of internal flexibility.     

In vitro polyoma DNA synthesis: self-annealing properties of short DNA chains.

Short DNA chains, isolated from in vitro pulse-labeled replicating polyoma DNA, exhibit some degree of self-complementarity (28% resistance to S1 nuclease after self-annealing to plateau levels). This level of self-annealing is not increased if short DNA chains present as free single-stranded DNA after extraction are included in the hybridization, excluding a selective loss of chains from one side of the growing fork and supporting a semi-discontinuous mode of chain growth. This mode also applies to restricted synthesis conditions under which a relative excess of short chains is made, since no increase in the self-annealing of such short chains is observed. The self-annealing that can be measured is higher for the faster sedimenting portion (46%) of the short DNA chains than for the slower sedimenting portion (18.5%), indicating that it is most likely due to contaminating continuously growing strands from the other side of the fork. High self-annealing values (up to 60%) are obtained if virus stocks generating defective DNA are used for infection. Restriction endonuclease (Hpall) characterization of such DNA shows evidence for the presence of multiple origins of replication. One of several possible mechanisms is discussed by which replicating defective DNA can generate self-complementary short chains despite a semi-discontinuous mode of replication.     

Hemolysis, toxicity, and randomly amplified polymorphic DNA analysis of Stachybotrys chartarum strains.

Stachybotrys chartarum is an indoor air, toxigenic fungus that has been associated with a number of human and veterinary health problems. Most notable among these has been a cluster of idiopathic pulmonary hemorrhage cases that were observed in the Cleveland, Ohio, area. In this study, 16 strains of S. chartarum isolated from case (n = 8) or control (n = 8) homes in Cleveland and 12 non-Cleveland strains from diverse geographic locations were analyzed for hemolytic activity, conidial toxicity, and randomly amplified polymorphic DNA banding patterns. In tests for hemolytic activity, strains were grown at 23 degrees C on wet wallboard pieces for an 8-week test period. Conidia from these wallboard pieces were subcultured on sheep's blood agar once a week over this period and examined for growth and clearing of the medium at 37 or 23 degrees C. Five of the Cleveland strains (all from case homes) showed hemolytic activity at 37 degrees C throughout the 8-week test compared to 3 of the non-Cleveland strains. Five of the Cleveland strains, compared to two of the non-Cleveland strains, produced highly toxic conidia (>90 microgram of T2 toxin equivalents per g [wet weight] of conidia) after 10 and 30 days of growth on wet wallboard. Only 3 of the 28 strains examined both were consistently hemolytic and produced highly toxic conidia. Each of these strains was isolated from a house in Cleveland where an infant had idiopathic pulmonary hemorrhage.     

F-actin, a model polymer for semiflexible chains in dilute, semidilute, and liquid crystalline solutions.

Single actin filaments were analyzed in solutions ranging from dilute (0.2 microgram/ml), where filaments interact only with solvent, to concentrations (4.0 mg/ml) at which F-actin forms a nematic phase. A persistence length of approximately 1.8 microns and an average length of approximately 22 microns (Kaufmann et al., 1992) identify actin as a model for studying the dynamics of semiflexible polymers. In dilute solutions the filaments exhibit thermal bending undulations in addition to diffusive motion. At higher semidilute concentrations (1.4 mg/ml) three-dimensional reconstructions of confocal images of fluorescently labeled filaments in a matrix of unlabeled F-actin reveal steric interactions between filaments, which account for the viscoelastic behavior of these solutions. The restricted undulations of these labeled chains reveal the virtual tube formed around a filament by the surrounding actin. The average tube diameter <a> scales with monomer concentration c as <a> varies; is directly proportional to c-(0.5 +/- 0.15). The diffusion of filaments in semidilute solutions (c = (0.1-2.0) mg/ml) is dominated by diffusion along the filament contour (reptation), and constraint release by remodeling of the surrounding filaments is rare. The self-diffusion coefficient D parallel along the tube decreases linearly with the chain length for semidilute solutions. For concentrations > 2.5 mg/ml a transition occurs from an isotropic entangled phase to a coexistence between isotropic and nematic domains. Analysis of the molecular motions of filaments suggests that the filaments in the aligned domains are in thermal equilibrium and that the diffusion coefficient parallel to the director D parallel is nearly independent of filament length. We also report the novel direct observation of u-shaped defects, called hairpins, in the nematic domains.     

Sedimentation coefficients of DNA topoisomers: the helical wormlike chain

The sedimentation coefficient s_N of the DNA topoisomer with the linking number N is evaluated as a function of N and chain length on the basis of a (circular) twisted wormlike chain, i.e., a special case of the helical wormlike chain. Evaluation is carried out by an application of the Oseen–Burgers procedure of hydrodynamics to the cylinder model with the preaveraged Oseen tensor. The necessary mean reciprocal distance between two contour points is obtained by a Monte Carlo method. It is shown that s_N increases as |ΔN| is increased from 0 in the range of small |ΔN|, where ΔN = N ? N , with N the number of helix turns in the linear DNA chain in the undeformed state. It is found that there is semiquantitative agreement between the Monte Carlo values and the experimental data obtained by Wang for s_N.     

Viscometry and sedimentation equilibrium of partially hydrolyzed hyaluronate: Comparison with theoretical models of wormlike chains

Fractionated samples of sodium hyaluronate of low molecular weight were used to calibrate the carbazole method for glucuronyl analsis and to determine the density increment (based on dry weight) of 0.444 (±0.003) mL/g in water and 0.386 (±0.003) mL/g for samples dialyzed against 0.2M NaCl. Weight-average molecular weights obtained by high-speed sedimentation equilibrium were used to calibrate the limiting viscosity number [η] in 0.2M NaCl, which gave [η]/M_w = 0.0028 (±0.0002) mL/g, valid to M_w = 0.0028 (±0.0002) mL/g, valid to M_w = 10⁵. Experimental data from this work and the literature, including viscosity and light- and small-angle x-ray scattering measurements, were compared to theoretical chain models of the Kratky-Porod (KP) wormlike and the helical wormlike (HW) chain, as treated by Yamakawa and collaborators. Although either model could be fitted to experimental data about equally well with consistent parameters, provided those for the HW chain were of weakly helical nature, calculation of the unperturbed meansquare end-to-end distance as a function of chain length from a conformational model favored the KP chain alternative. The parameters that provide the best fit to experimental data for the KP wormlike model are a persistence length of 4.5–5 nm and a diameter of 1.1 nm. The latter is resonable for a hydrated hydrodynamic cylinder in view of the approximate unhydrated value of 0.7 nm estimated from the density increment.     

Light scattering and hydrodynamic properties of linear and circular bacteriophage lambda DNA

Low-angle light scattering, sedimentation velocity, and intrinsic viscosity measurements have been made on circular and linear forms of lambda (λ) bacteriophage DNA. Available equations, used to relate hydrodynamic parameters of both forms to the molecular weight, give relatively consistent values of particle weights which essentially agree with the light-scattering results. An average molecular weight of (34 ± 3) × 10⁶ for λ DNA was obtained in good agreement with literature values of (31–33) × 10⁶. The linear λ DNA has a larger root-mean-square radius than the circular molecule, when determined by light scattering, but the difference does not appear to be us large as expected from hydrodynamic data. The two forms also show significantly different angular distrbutions of scattered light intensities which agree only qualitatively with those derived from existing theory. The light-scattering results suggest that further experiments and modifications of available theories should be undertaken.     

Temperature dependence of conformational properties of natural lipid oligomer chains: computer simulation

The conformational properties of several oligomeric chain molecules at T = 278 and T = 403 K have been studied using Monte Carlo computer simulations. Hydrocarbon oligomers with methylene-interrupted cis double bonds in the main chain were considered. These oligomers are typical constituents of natural lipid molecules. The characteristics of the shape of C-H and C-C bond orientation distribution functions with respect to the principal axis of inertia of the chains and their temperature dependences were studied. It was found that the temperature sensitivity of not only the common geometric characteristics of the polyunsaturated chain is significantly reduced compared with the saturated one, but also that of local characteristics, i. e., the shape of each bond orientation distribution function of the polyunsaturated chain. The relationship between the properties of lipid polyunsaturated hydrocarbon chains and their functions in natural membrane systems, in particular their possible role in the stabilization or optimization of lipid-protein interactions, was discussed.     

Configuration-dependent properties of randomly coiling polynucleotide chains. I. A comparison of theoretical energy estimates

Various theoretical estimates of the conformational energy associated with polynucleotides in solution have been compared with each other and also with the experimentally observed conformations found in X-ray crystallographic investigations of low-molecular-weight nucleic acid analogs. In view of the disparities between these data, certain configuration-dependent properties (i.e., the mean-square unperturbed end-to-end distance 〈r²〉₀ and the average vicinal nmr coupling constant 〈J〉) appropriate to randomly coiling polynucleotides described by either the energy estimates or by the crystallographically preferred conformations have also been calculated and compared with the known solution behavior of polynucleotide chains. Both the theoretical energy surfaces and the X-ray data show good agreement with the nmr coupling constant indications of the preferred rotations about the O-C and C-C bonds of the chain backbone. The principal discrepancies between the theoretical methods and X-ray data arise in their ability to predict successfully the preferred rotations about the two phosphodiester bonds of the chain backbone and the unperturbed dimensions of randomly coiling polynucleotide chains.     

Configuration-dependent properties of randomly coiling polynucleotide chains. II. The role of the phosphodiester linkage

The dependence of the unperturbed dimensions of randomly coiling polynucleotides on the rotations about the phosphodiester linkages of the chain has been examined in order to understand the conformational discrepancies, set forth in paper I, regarding these angles (ω′ and ω). Large values of the characteristic ratio 〈r²〉₀/nl² , which agree with the experimental behavior of the chain, are obtained only if a sizeable proportion of the polymer residues have trans ω′ values. The asymmetric torsional potential that is believed to arise from gauche effects associated with the P-O bonds has been approximated using a hard core model. The calculated characteristic ratio exhibits a strong dependence upon the magnitude of this torsional barrier (separating trans and gauche conformations) and shows agreement with experimental values for polyribonucleotides only if this energy difference is 1 kcal/mol or less.