Dynamic information from protein crystallography. An analysis of temperature factors from refinement of the hen egg-white lysozyme structure.

A preliminary analysis is presented of whether the isotropic temperature factors derived from refinement of the tetragonal crystal structure of hen egg-white lysozyme at 2 Å resolution can be interpreted in terms of molecular motion. If the contributions to the temperature factors from experimental errors, crystal disorder and imperfections of the molecular model are neglected, the apparent thermal motion is found to be compatible with the pair of molecules that have the strongest interactions in the crystal either moving as a rigid-body with libration about a common axis, or vibrating in an intramolecular mode with the principal amplitudes radial to this axis. There is only weak evidence for hingebending, i.e. that the two lobes of lysozyme vibrate so that their separation varies. Side-chains that are exposed to the solvent and some segments of the main polypeptide chain (including residues 70–73, 82–84, 101–103) have greater apparent thermal motion than the remainder of the molecule.Although this analysis at a single temperature cannot establish whether thermal motion or static disorder (including conformational variability) underlies the observed effects, it suggests that the accurate determination of temperature factors will be useful in detailed studies of the dynamic properties of macromolecules.     

The structure of percolated polymer systems: a computer simulation study

We studied the percolation process in a system consisting of long flexible polymer chains and solvent molecules. The polymer chains were approximated by linear sequences of beads on a two-dimensional triangular lattice. The system was athermal and the excluded volume was the only potential. The properties of the model system across the entire range of polymer concentrations were determined by Monte Carlo simulations employing a cooperative motion algorithm (CMA). The scaling behavior and the structure of the percolation clusters are presented and discussed.     

Cardinal directions for visual optic flow.

As we move through our environment, the flow of deforming images on the retinae provides a rich source of information about the three-dimensional structure of the external world and how to navigate through it. Recent evidence from psychophysical [1] [2] [3] [4], electrophysiological [5] [6] [7] [8] [9] and imaging [10] [11] studies suggests that there are neurons in the primate visual system - in the medial superior temporal cortex - that are specialised to respond to this type of complex 'optic flow' motion. In principle, optic flow could be encoded by a small number of neural mechanisms tuned to 'cardinal directions', including radial and circular motion [12] [13]. There is little support for this idea at present, however, from either physiological [6] [7] or psychophysical [14] research. We have measured the sensitivity of human subjects for detection of motion and for discrimination of motion direction over a wide and densely sampled range of complex motions. Average sensitivity was higher for inward and outward radial movement and for both directions of rotation, consistent with the existence of detectors tuned to these four types of motion. Principle component analysis revealed two clear components, one for radial stimuli (outward and inward) and the other for circular stimuli (clockwise and counter-clock-wise). The results imply that the mechanisms that analyse optic flow in humans tend to be tuned to the cardinal axes of radial and rotational motion.     

Molecular blending by polymerization of intercalated solvent. Poly(gamma-benzyl-L-glutamate)/benzyl methacrylate as a model system

The aim of the present research is to obtain blending between a polymer and a (polymerized) solvent on the molecular level. Because of its rigid rod structure, poly(gamma-benzyl-L-glutamate) (PBLG) is chosen as the polymer. Benzyl methacrylate (BzMA) has been chosen as the solvent for two reasons. First, the structure of the solvent is very similar to the structure of the side chain of PBLG, favoring interactions between the two materials. Second, the solvent can be polymerized, because of the presence of a C=C bond. In cast films of PBLG and BzMA separate zones of the polymer and solvent are present. Wide-angle X-ray diffraction and Raman results show that upon heating the cast films homogenization occurs and solvent molecules intercalate between the helices of PBLG. At 150 degrees C a hexagonal packing is obtained. The dimensions of the obtained packing depend on the solvent concentration, which confirms that solvent molecules are indeed present within the crystalline lattice. DSC experiments imply that the observed changes upon heating correspond to thermodynamic processes. On cooling the homogeneous samples, disordering of the hexagonal packing occurs. Polymerization of the homogeneous samples results in a disordering of the hexagonal packing and in a contraction of the unit cell. The latter once more confirms that solvent molecules are indeed present within the crystalline lattice. The applied principle of polymerization of a solvent in a molecular homogeneous system can be favorable for many applications, for which morphology control at the molecular level is required.     

Langevin dynamics simulations reveal biologically relevant folds arising from the incorporation of a torsional potential

The conformational behaviour of polymer chains has been examined using Langevin dynamics simulation techniques. Polymer chains were modelled as “beads” undergoing Brownian motion in a defined potential that accounted for stretching, bending and solvation energies. As expected, the competition between chain stiffness and solvent interactions was found to yield standard swollen or collapsed configurations in good or poor solvents, respectively. However, when a torsional term was introduced into the model, additional biologically relevant conformations such as helices, sheets, turns and hairpins naturally arose.     

Cooperative effects in the transport of small molecules through an amorphous polymer matrix

The transport of small molecules (penetrants) through polymer materials proceeds by a hopping mechanism: A peneprant typically dwells in a cavity of the polymer for a while and then performs a quick jump into an adjacent cavity. In this article we investigate a jump event in detail. Molecular graphics is used to identify if and how the motion of the penetrant is aided by the fluctuations of the polymer matrix. We employ both traditional molecular graphics techniques to show atomic motion and surface rendering methods to display the redistribution of penetrant-accessible volume in the polymer.     

Solid-state conjugation of proteins with hydrophobic compounds in non-denaturing conditions. I. Acylation of proteins by dansyl proline using a polymeric N-hydroxysuccinimide ester

A method of conjugating protein molecules under native conditions with water-insoluble hydrophobic compounds is developed. It permits very water-insoluble acids to be gently coupled to the primary amines on proteins or other biopolymers. For this purpose we synthesized a polymer (co-polymer of N-hydroxymaleimide and N-vinylpyrrolidone cross-linked by benzidine) which swells equally well in water and in organic solvents. Hydrophobic substances are first activated by esterification to this polymer in organic solvent and then conjugated to protein by acylation in aqueous medium at pH 8.0-8.5. Thus, the contact of native protein with organic co-solvent may be completely avoided. The application of this approach is demonstrated by labeling trypsinogen and plasminogen with dansyl proline.     

Structure of bacteriophage T4 lysozyme refined at 1.7 A resolution

The structure of the lysozyme from bacteriophage T4 has been refined at 1.7 A resolution to a crystallographic residual of 19.3%. The final model has bond lengths and bond angles that differ from "ideal" values by 0.019 A and 2.7 degrees, respectively. The crystals are grown from electron-dense phosphate solutions and the use of an appropriate solvent continuum substantially improved the agreement between the observed and calculated structure factors at low resolution. Apart from changes in the conformations of some side-chains, the refinement confirms the structure of the molecule as initially derived from a 2.4 A resolution electron density map. There are 118 well-ordered solvent molecules that are associated with the T4 lysozyme molecule in the crystal. Four of these are more-or-less buried. There is a clustering of water molecules within the active site cleft but, other than this, the solvent molecules are dispersed around the surface of the molecule and do not aggregate into ice-like structures or pentagonal or hexagonal clusters. The apparent motion of T4 lysozyme in the crystal can be interpreted in terms of significant interdomain motion corresponding to an opening and closing of the active site cleft. For the amino-terminal domain the motion can be described equally well (correlation coefficients approx. 0.87) as quasi-rigid-body motion either about a point or about an axis of rotation. The motion in the crystals of the carboxy-terminal domain is best described as rotation about an axis (correlation coefficient 0.80) although in this case the apparent motion seems to be influenced in part by crystal contacts and may be of questionable relevance to dynamics in solution.     

Magnetic cross-relaxation among protons in protein solutions.

The magnetic spin-lattice relaxation rates of solvent water nuclei are known to increase upon addition of diamagnetic solute protein. This enhancement of the relaxation rate is a function of magnetic field, and the orientational relaxation time of the protein molecules can be deduced from analysis of the field-dependent relaxation rates. Although the nature of the interactions that convey information about the dynamics of protein motion to the solvent molecules is not established, it is known that there is a contribution to the relaxation rates of solvent protons that plays no role in the relaxation of solvent deuterons and 17O nuclei. We show here that the additional interaction arises from a cross-relaxation process between solvent and solute protons. We introduce a heuristic three-parameter model in which protein protons and solvent protons are considered as two separate thermodynamic systems that interact across the protein-solvent interface. The three parameters are the intrinsic relaxation rates of each system and a cross-relaxation term. The sign of the latter term must always be positive, for all values of magnetic field, in order for magnetization energy to flow from the hotter to the cooler system. We find that the magnetic field-dependence of the cross-relaxation contribution is much like that of the remaining solvent proton relaxation, i.e., about the same as the deuteron relaxation field dependence. This finding is not compatible with the predictions of expressions for the cross-relaxation that have been used by other authors, but not applied to data over a wide range of magnetic field strength. The model predicts that the relaxation behavior of both the protein protons and the solvent protons is the sum of two exponentials, the relative contributions of which would vary with protein concentration and solvent isotopic composition in a fashion suggestive of the presence of two classes of protein protons, when there is in reality only one. This finding has immediate implications for the interpretation of published proton relaxation rates in complex systems such as tissues; these data should be reexamined with cross-relaxation taken into account.     

The B-Z transition of a polynucleotide with a 10-base pair repeating sequence

In this communication we report the synthesis and characterization of a defined-sequence, alternating purine-pyrimidine polymer with a 10-base pair repeating unit: poly[d(CGCGCGTGCA)]. It is seen that the polymer can undergo a right-left-hand helical transition, but the conformational transition requires much higher salt concentration than with poly[d(G-C)]. The results are interpreted in terms of interaction of the polymer with solvent molecules.     

Intermolecular interactions of oxygenated sickle hemoglobin molecules in cells and cell-free solutions.

We have measured the intermolecular interactions of oxygenated sickle hemoglobin molecules in cells and in cell-free solutions, and have compared the results with similar data for liganded normal adult hemoglobin. The experiments involve the measurement of the spin-lattice relaxation time T1 of protons of solvent water molecules, as a function of an externally applied static magnetic field. From such data, one can derive a correlation time tauc, for each sample, which is a measure of the time taken for a hemoglobin molecule to randomize its orientation due to Brownian motion. Thus tauc is a measure of the freedom of rotational motion, on a molecular or microscopic level, of hemoglobin molecules. Intermolecular interactions will reduce this freedom of motion and lengthen tauc. We find that oxygenated sickle hemoglobin molecules have an additional intermolecular interaction not found for normal hemoglobin. This extra interaction is increased by the presence of either inorganic phosphate or diphosphoglycerate, and is greater for sickle hemoglobin within cells than in cell-free solutions. By comparing the present results with published data on the viscosity of oxygenated sickle and normal hemoglobin, we conclude that, at concentrations comparable to intracellular values, oxygenated sickle hemoglobin molecules form aggregates several tetramers in size. The possibility exists that these aggregates are the earliest stage of fiber formation itself, the physical basis of the sickling phenomena.     

Radial migration of DNA molecules in cylindrical flow. II. The non-draining model and possible application to fractionation

The radial-migration calculation of the preceding paper is extended to the non-draining polymer. The results show an inward radial velocity that depends on the 5/2 power of the molecular weight, assuming gaussian statistics for the chain. This sensitivity to size serves as the basis for a method of separating DNA molecules in solution according to their size. Normal stress (Weissenberg) effects are also discussed.     

Radial migration of DNA molecules in cylindrical flow. III. Circles and the effect of non-gaussian polymer statistics.

We have previously shown that DNA will migrate radially inward in a concentric-cylinder shear flow apparatus. We assumed gaussian chain statistics, and we considered only linear molecules. In this paper, we extend the analysis to closed circular molecules, and we consider non-gaussian statistics for both linears and circles. We find that, in good solvents, the inward radial migration velocity is more sensitive to the molecular weight than M5/2, which we previously reported for gaussian chains. Furthermore, linears migrate radially inward 8 times faster than do circles of the same molecular weight. This suggests the possibility of separating linear from circular DNA in solution.     

Structural responsiveness of filamentous bacteriophage Pf1: comparison of virion structure in fibers and solution. The effect of temperature and ionic strength.

X-ray diffraction from fibers and magnetically oriented solutions has been used to study the effect of changes in environment on the helical symmetry and radial structure of the Pf1 virus particle. Detailed analysis of equatorial scattering to a spacing of 8-10 A was used to identify small radial motions of structural elements in the virus particle. R-factor ratios were used to determine the statistical significance of observed changes. Comparison of the structure of virus particles in fibers with those in solution indicated that the helical symmetry of the virions remains unchanged during fiber formation. In most fibers the virions appear to be slightly distorted by the tight packing of virus particles. This distortion results in an apparent increase in the radius of the virus particle of approximately 0.6 A. A change in the radius of the DNA is also observed. Increase in the concentration of solvent molecules during fiber formation results in penetration of the virus interior by some solvent components. NaCl is also able to enter the virus interior. The change in the helical symmetry of the virions at approximately 8 degrees C appears to be the same whether observed by diffraction from fibers or from solutions. Only subtle changes in radial structure are associated with the temperature transition.     

On the structure of molecularly imprinted polymers by modifying charge on functional groups through molecular dynamics simulations

Molecularly imprinted polymers (MIPs) have been widely applied in many fields owing to their advantages. The recognition mechanism between target molecules and MIPs and the influence of dominant factor on the recognition process are still poorly understood. In this paper, a cubic methacrylate-based MIP model was constructed, and the charge on carboxyl group atoms was changed artificially to investigate the recognition process. It is found that the diffusion coefficients of the target molecules (cholesterol) are not affected by polymer network structure. The recognition process is mainly determined by the mesh sizes of the polymer network. In addition, the structure of modified MIP systems was also discussed from the viewpoints of radial distribution function and hydrogen bonds system. These results suggest that the polymer matrix structure would be enhanced with an increase in charge. Thus, it influences the structure of the water molecules in the system a little.     

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to “breathing,” advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.     

Interpretation of the stokes radius of macromolecules determined by gel filtration chromatography

From a comparison of the gel chromatographic properties of large randomly-coiled polypeptides in 6 M guanidine hydrochloride and of large globular proteins, we found that the distribution coefficient was more closely correlated with the intrinsic viscosity-based Stokes radius than with the translational frictional coefficient-based Stokes radius. This means that the effect of the hydrodynamic flow of dissolved molecules during gel chromatography should be considered. The ratio of transport of solute by bulk flow as compared with that by net diffusion (i.e., Brownian motion) is large under some conditions. On the other hand, we consider that the distribution coefficient obtained in static equilibrium experiments should be determined by the translational frictional coefficient-based Stokes radius, since the solvent does not flow. On this basis, we discuss the meaning of the Stokes radius and the separation mechanism of macromolecules by gel filtration.     

Molecular beams of macroions. 3. Zein and polyvinylpyrrolidone

A 95% ethanol solution of the prolamin zein and of the synthetic polymer polyvinyl-pyrrolidone (PVP) can be successfully electrosprayed and a molecular beam, containing ions of these substances in nitrogen carrier gas, formed. Similarly to polystyrene in benzene–acetone solvent, negative beams of zein and PVP have more substructure than beams containing positive ions. The results indicate considerable aggregation in the beam, possibly of six molecular units per aggregate, in addition to the singly charged single molecules.     

The effect of a myelin apoprotein on lipid structure: a spin probe study.

Spin probes, stable free radical derivatives of stearic acid and cholestanone, were used to observe the effects of the "Folch-Lees" protein isolated from the white matter of bovine brain on the organization and motion of lipid molecules. The incorporation of the organic solvent soluble form of this protein decreased the tendency of a variety of lipid molecules with zero, positive or negative net charges to arrange themselves close to the normal to the lipid bilayer. The aqueous form of the protein also had a profound chaotropic effect on the molecular geometry of the lipid, but only if the lipids had a net negative charge (the protein has a net positive charge in the pH range investigated). Examination of the ESR spectra indicated that this protein altered the geometry of the lipid structure without causing major changes in the mobility of the individual lipid molecules.