Protein-protein association in polymer solutions: from dilute to semidilute to concentrated

In a typical cell, proteins function in the crowded cytoplasmic environment where 30% of the space is occupied by macromolecules of varying size and nature. This environment may be simulated in vitro using synthetic polymers. Here, we followed the association and diffusion rates of TEM1-beta-lactamase (TEM) and the beta-lactamase inhibitor protein (BLIP) in the presence of crowding agents of varying molecular mass, from monomers (ethylene glycol, glycerol, or sucrose) to polymeric agents such as different polyethylene glycols (PEGs, 0.2-8 kDa) and Ficoll. An inverse linear relation was found between translational diffusion of the proteins and viscosity in all solutions tested, in accordance with the Stokes-Einstein (SE) relation. Conversely, no simple relation was found between either rotational diffusion rates or association rates (k(on)) and viscosity. To assess the translational diffusion-independent steps along the association pathway, we introduced a new factor, alpha, which corrects the relative change in k(on) by the relative change in solution viscosity, thus measuring the deviations of the association rates from SE behavior. We found that these deviations were related to the three regimes of polymer solutions: dilute, semidilute, and concentrated. In the dilute regime PEGs interfere with TEM-BLIP association by introducing a repulsive force due to solvophobic preferential hydration, which results in slower association than predicted by the SE relation. Crossing over from the dilute to the semidilute regime results in positive deviations from SE behavior, i.e., relatively faster association rates. These can be attributed to the depletion interaction, which results in an effective attraction between the two proteins, winning over the repulsive force. In the concentrated regime, PEGs again dramatically slow down the association between TEM and BLIP, an effect that does not depend on the physical dimensions of PEGs, but rather on their mass concentration. This is probably a manifestation of the monomer-like repulsive depletion effect known to occur in concentrated polymer solutions. As a transition from moderate to high crowding agent concentration can occur in the cellular milieu, this behavior may modulate protein association in vivo, thereby modulating biological function.     

Supercoiled DNA is interwound in liquid crystalline solutions.

Two structures have been proposed for supercoiled DNA: it is idealized either as a toroidal ring or as a rod of two interwound duplex chains. The latter model is the most widely depicted but the evidence remains controversial. We have worked with monomers and dimers of two plasmids, pUC8 and pKS414, of similar size and natural superhelical density. pKS414 contains a bend promoting sequence whereas pUC8 does not. In concentrated solutions these plasmids form a partially ordered liquid crystalline phase which is found, using neutron diffraction, to consist of a hexagonally packed assembly of parallel rod-like particles. This shape strongly suggests an interwound conformation for which some structural parameters are deduced. The mass/unit length obtained by combining the area of the hexagonal lattice and the concentration is approximately 3.6 times that of linear DNA. This implies a shallow superhelical pitch angle approximately 36 degrees which, when combined with the known number of supercoil turns, yields the pitch approximately 360 A and radius approximately 80 A for the supercoil. Oriented X-ray fibre diffraction patterns at 92% relative humidity indicate a B type duplex structure. Nicked circular plasmids also form liquid crystals but their behaviour, as a function of concentration, differs from that of the superhelical plasmids.     

Oxygen transfer in a stirred loop fermentor with dilute polymer solutions

Oxygen transfer in a 0.35 m diameter stirred loop fermentor (a stirred tank with a concentric draft tube) has been studied with water containing a small amount of polymer(polyethylene oxide) as a drag-reducing additive.Power consumption was measured. It was found that the addition of polyethylene oxide causes an increase of power consumption. This is contrary to the results reported in the literature.Volumetric mass transfer coefficients (K _La) were measured. In water the introduction of the draft tube increased the K _La coefficient. The increase in K _La became larger with impeller speed. On the other hand, mass transfer in dilute polymer solutions decreased due to the presence of the draft tube. An empirical correlation has been proposed for the volumetric mass transfer coefficient in stirred loop fermentors. It has a general applicability.List of Symbols a 1/m specific surface area - C constant in Eq. (6) - g m/s² gravitational acceleration - K _L m/s overall liquid-phase mass transfer coefficient - n 1/s impeller speed - P W aerated power input by mechanical agitation - P _g W power input by sparged air - Q m³/min volumetric gas flow rate - U _sg m/s superficial gas velocity - V m³ liquid volume Greek Symbols exponents in Eq. (3) - exponent in Eq. (6) - kg/m³ density     

A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibrium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurement of the persistence length of single-stranded DNA, which is found to be approximately 1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of > or = 7, much larger than the exponent of approximately 1.5-1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of approximately -11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.     

Evidence of molecular alignment fluctuations in aqueous dilute liquid crystalline media

Protein dynamics can be studied by NMR measurements of aqueous dilute liquid crystalline samples. However, the measured residual dipolar couplings are sensitive not only to internal fluctuations but to all changes in internuclear vectors relative to the laboratory frame. We show that side-chain fluctuations and bond librations in the ps–ns time scale perturb the molecular shape and charge distribution of a small globular protein sufficiently to cause a noticeable variation in the molecular alignment. The alignment variation disperses the bond vectors of a conformational ensemble even further from the dispersion already caused by internal fluctuations of a protein. Consequently RDC-probed order parameters are lower than those obtained by laboratory frame relaxation measurements.     

The inactivation of dilute solutions of crystalline trypsin by x-radiation. I. Kinetics and characteristics

The activity of dilute solutions of crystalline trypsin is destroyed by x-rays. The inactivation is an exponential function of the radiation dose. The reaction yield of inactivation is independent of the intensity at which the radiation is delivered or the quality of the x-rays. The reaction yield increases with increasing concentration of trypsin, varying from 0.06 to 0.7 micromoles per liter per 1000 r for trypsin solutions ranging from 1 x 10(-7) to 2 x 10(-4)M.     

Tracer diffusion in F-actin and Ficoll mixtures. Toward a model for cytoplasm.

We have previously reported that self-diffusion of inert tracer particles in the cytoplasm of living Swiss 3T3 cells is hindered in a size-dependent manner (Luby-Phelps, K., D.L. Taylor, and F. Lanni. 1986. J. Cell Biol. 102:2015-2022; Luby-Phelps, K., P.E. Castle, D.L. Taylor, and F. Lanni. 1987. Proc Natl. Acad. Sci. USA. 84:4910-4913). Lacking a theory that completely explains our data, we are attempting to understand the molecular architecture responsible for this phenomenon by studying tracer diffusion in simple, reconstituted model systems. This report contains our findings on tracer diffusion in concentrated solutions of Ficoll 70 or Ficoll 400, in solutions of entangled F-actin filaments, and in solutions of entangled F-actin containing a background of concentrated Ficoll particles or concentrated bovine serum albumin (BSA). A series of size-fractionated fluorescein-Ficolls were used as tracer particles. By fluorescence recovery after photobleaching (FRAP), we obtained the mean diffusion coefficients in a dilute, aqueous reference phase (Do), the mean diffusion coefficients in the model matrices (D), and the mean hydrodynamic radii (RH) for selected tracer fractions. For each model matrix, the results were compared with similar data obtained from living cells. As in concentrated solutions of globular proteins (Luby-Phelps et al., 1987), D/Do was not significantly size-dependent in concentrated solutions of Ficoll 400 or Ficoll 70. In contrast, D/Do decreased monotonically with increasing RH in solutions of F-actin ranging in concentration from 1 to 12 mg/ml. This size dependence was most pronounced at higher F-actin concentrations. However, the shape of the curve and the extrapolated value of D/Do in the limit, RH----O did not closely resemble the cellular data for tracers in the same size range (3 less than RH less than 30 nm). In mixtures of F-actin and Ficoll or F-actin and BSA, D/Do was well approximated by D/Do for the same concentration of F-actin alone multiplied by D/Do for the same concentrations of Ficoll or BSA alone. Based on these results, it is possible to model the submicroscopic architecture of cytoplasm in living cells as a densely entangled filament network (perhaps made up of F-actin and other filamentous structures) interpenetrated by a fluid phase crowded with globular macromolecules, which in cytoplasm would be primarily proteins.     

The inactivation of dilute solutions of crystalline trypsin by x-radiation. II. Effects of enzyme concentration,medium, pH,and temperature

The proteolytic activity of dilute solutions of clystalline trypsin is destroyed by x-rays, the amount of inactivation being an exponential function of the radiation dose. The reaction yield increases steadily with increasing concentration of trypsin, varying, as the concentration of enzyme is increased from 1 to 300 microM, from 0.068 to 0.958 micromole of trypsin per liter inactivated per 1000 r with 0.005 N hydrochloric acid as the solvent, from 0.273 to 0.866 with 0.005 N sulfuric acid as the solvent, and from 0.343 to 0.844 with 0.005 N nitric acid as the solvent. When the reaction yields are plotted as a function of the initial concentration of trypsin, they fall on a curve given by the expression Y alpha X(K), in which Y is the reaction yield, X is the concentration of trypsin, and K is a constant equal to 0.46, 0.20, and 0.16, respectively, with 0.005 N hydrochloric, sulfuric, and nitric acids as solvents. The differences between the reaction yields found with chloride and sulfate ions in I to 10 microM trypsin solutions are significant only in the pH range from 2 to 4. The amount of inactivation obtained with a given dose of x-rays depends on the pH of the solution being irradiated and the nature of the solvent. The reaction yield-pH curve is a symmetrical one, with minimum yields at about pH 7. Buffers such as acetate, citrate, borate and barbiturate, and other organic molecules such as ethanol and glucose, in concentrations as low as 20 microM, inhibit the inactivation of trypsin by x-radiation. Sigmoid inactivation-dose curves instead of exponential ones are obtained in the presence of ethanol. The reaction yields for the inactivation of trypsin solutions by x-rays are approximately 1.5 times greater when the irradiation is done at 26 degrees C. than when it is done at 5 degrees C., when 0.005 N hydrochloric acid is the solvent. The dependence on temperature is less when 0.005 N sulfuric acid is used, and is negligible with 0.005 N nitric acid. The difficulties involved in interpreting radiation effects in aqueous systems, and in comparing the results obtained under different experimental conditions, are discussed.     

Highly efficient reinforcement of poly-L-lactide materials by polymer blending of a thermotropic liquid crystalline polymer

A novel polymer blend system consisting of poly(l-lactide) (PLLA) and a thermotropic liquid crystalline polymer (LCP: an aromatic polyester comprising poly(4-hydroxybenzoate) sequences) was investigated in the presence and absence of a polycabodiimide (PCD). Scanning electron micrographs of the injection-molded polymer blends revealed the formation of fibrous structure of LCP in the PLLA matrix, supporting the efficient toughening. In particular, the LCP fibrils became semimicrometer in diameter in the presence of PCD with which both PLLA and LCP had reacted during the melt blending to form their block and graft copolymers working as compatibilizer. The blend specimens containing LCP in 20-30 wt % were found to hold high dynamic storage-moduli (E') at high temperature. In addition, the E' value of the specimens containing 30 wt % of LCP reached 10.7 GPa at room temperature, being significantly higher than that of PLLA.     

Quantitation of liquid-crystalline ordering in F-actin solutions.

Actin filaments (F-actin) are important determinants of cellular shape and motility. These functions depend on the collective organization of numerous filaments with respect to both position and orientation in the cytoplasm. Much of the orientational organization arises spontaneously through liquid crystal formation in concentrated F-actin solutions. In studying this phenomenon, we found that solutions of purified F-actin undergo a continuous phase transition, from the isotropic state to a liquid crystalline state, when either the mean filament length or the actin concentration is increased above its respective threshold value. The phase diagram representing the threshold filament lengths and concentrations at which the phase transition occurs is consistent with that predicted by Flory's theory on solutions of noninteracting, rigid cylinders (Flory, 1956b). However, in contrast to other predictions based on this model, we found no evidence for the coexistence of isotropic and anisotropic phases. Furthermore, the phase transition proved to be temperature dependent, which suggests the existence of orientation-dependent interfilament interactions or of a temperature-dependent filament flexibility. We developed a simple method for growing undistorted fluorescent acrylodan-labeled F-actin liquid crystals; and we derived a simple theoretical treatment by which polarization-of-fluorescence measurements could be used to quantitate, for the first time, the degree of spontaneous filament ordering (nematic order parameter) in these F-actin liquid crystals. This order parameter was found to increase monotonically with both filament length and concentration. Actin liquid crystals can readily become distorted by a process known as "texturing." Zigzaging and helicoidal liquid crystalline textures which persisted in the absence of ATP were observed through the polarizing microscope. Possible texturing mechanisms are discussed.     

Change of handedness in cholesteric liquid crystalline phase for N-phthaloylchitosan solutions in organic solvents

The influence of concentration on the helicoidal change of N-phthaloylchitosan (PhCh) solutions in Me2SO, DMAc and DMF was investigated by means of circular dichroism (CD). The critical concentrations to form liquid crystal phase in these three solvents were 43, 45 and 48 wt.%, respectively as measured with polarized optical microscope. There were two kinds of CD peaks, sharp peaks with absorption maximum at about 330 nm induced by the helical conformation of molecular chain, and very broad peaks covering almost whole visible region induced by the cholesteric helix of mesophase. The later only appeared in concentrated solutions with the concentration higher than the critical concentration. The handedness of both levels of helicoidal structures changed from left- to right-handed with the increase of concentration for PhCh/Me2SO solutions. The chirality transfer occurred between these two chiral levels. For PhCh/DMAc and PhCh/DMF systems, only the handedness of helical conformation reversed, but the cholesteric helix did not change. As a method to measure critical concentration, CD is more sensitive than polarized optical microscopy (POM).     

Dynamics of phosphatidylcholine-cholesterol mixed model membranes in the liquid crystalline state.

The effects of cholesterol on the dynamics of cholestane spin probe (CSL) in various phosphatidylcholine-cholesterol mixed model membranes are examined. The lateral diffusion, D of CSL in DMPC/POPC/cholesterol ternary mixtures, is measured utilizing an improved dynamic imaging electron spin resonance method. It shows a factor of two decrease at 10 mol % and 25 degrees C, whereas it shows only a 40% decrease at 50 mol % and 50 degrees C. A comparison with results in POPC/cholesterol mixtures, which show a stronger effect of cholesterol on D, indicates that acyl chain unsaturation leads to stronger self association of cholesterol in PC model membranes. An S2CSL dependence of the activation energy for D, has been confirmed for the DMPC/POPC/cholesterol mixtures. Here SCSL is the order parameter for CSL. A similar correlation of R perpendicular, the perpendicular component of the rotational diffusion coefficient, with SCSL, which is true for all three mixtures (DMPC/cholesterol, POPC/cholesterol, and DMPC/POPC/cholesterol) we have studied, is also found. These are associated with the effects of enhanced local ordering on the free volume needed for translation and reorientation. Such correlations of dynamic properties D and R perpendicular with the thermodynamic quantity S, as well as the consistent interpretations of the effect of acyl chain unsaturation on the dynamics in terms of the activity coefficients, strongly emphasize the interrelation between the dynamic structure and the thermodynamics of the PC/cholesterol mixtures.     

p-NN''-phenylenebismaleimide, a specific cross-linking agent for F-actin.

Covalent cross-links can be inserted between the subunits of F-actin by using p-NN'-phenylenebismaleimide. Cross-linking reaches its maximum value when one molecule of reagent has reacted with each actin subunit. p-NN'-Phenylenebismaleimide reacts initially with a cysteine residue on one subunit, the slower cross-linking reaction involving a lysine residue on a neighbouring subunit. Hydrolysis of the actin-bound reagent limits the extent of cross-linking. Quantitative analysis of the amounts of cross-linked oligomers seen on polyacrylamide gels containing sodium dodecyl sulphate suggests that neither the binding of the reagent to actin nor the formation of cross-links introduces strain into the structure. The cross-links do not join together different F-actin filaments, and evidence is presented that suggests that the cross-links join subunits of the same long-pitched helix.     

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.     

Separation of dilute aqueous butanol and acetone solutions by pervaporation through liquid membranes

A simultaneous extraction-stripping process is proposed for separating volatile products from fermentation broths, it is based on pervaporation through a liquid membrane supported with a hydrophobic porous membrane. The liquid membrane prepared with oleyl alcohol was selected as the most suitable for separating volatile products resulting from acetone-butanol fermentation. The separation performance and stability of the oleyl alcohol liquid membrane were investigated by using dilute aqueous butanol and acetone solutions. The oleyl alcohol liquid membrane was found to be superior by far in both selectivity and permeability of butanol to the better known silicone rubber membrane in its high selectivity for alcohols. Using the oleyl alcohol liquid membrane, the dilute aqueous butanol solutions of around 4 g/L obtained in acetone-butanol fermentation could be concentrated up to 100 times. The stability of this liquid membrane was also quite good as long as the surface tension of the feed solution was less than the critical surface tension of the support membrane. No change in the separation performance was found after the continuous usage in a long period of 100 h.     

Resonance energy transfer in a model system of membranes: application to gel and liquid crystalline phases.

Resonance energy transfer between octadecyl rhodamine B (donor) and 1,1',3,3,3',3'-hexamethylindotricarbocyanine (acceptor) was studied in a model system of membranes (large unilamellar vesicles of dipalmitoylphosphatidylcholine), using both steady-state and time-resolved techniques. In the fluid phase (temperature = 50 degrees C) the decay law and the steady-state theoretical curve for energy transfer in two dimensions are verified. In the gel phase (temperature = 25 degrees C) an apparent reduction of dimensionality is observed, which is explained on the basis of probe segregation to the defect lines (grain boundaries). An estimation of the domain size from the model recovered linear probe concentrations is approximately 1750-2000 lipid molecules. In both phases, the existence of a fractal geometry was ruled out.     

Screening for synergistic interactions in dilute polysaccharide solutions

A simple viscometric approach has been used to screen for binding interactions between different polysaccharides in very dilute solution where exclusion effects should be negligible. The method involves preparing stock solutions to approximately the same, low, viscosity (η_sp≈1), dialysing to identical ionic conditions, mixing in various proportions, and looking for departures from the initial common viscosity.

Mixtures of xanthan or de-acetylated xanthan with locust bean gum (LBG) or konjac glucomannan (KM) show massive enhancement of viscosity, as anticipated from the formation of synergistic gels at higher concentrations. However, no viscosity changes on mixing with LBG or KM were observed for other conformationally ordered bacterial polysaccharides (welan and rhamsan) or for alginate and pectin with sufficient Ca²⁺ to induce almost complete conversion to the dimeric ‘egg box’ form, demonstrating that conformational rigidity is not, in itself, sufficient for other polysaccharides to form heterotypic junctions with mannan or glucomannan chains.

Interactions of carrageenans with LBG appear to depend on both conformation and the extent of aggregation. Mixtures of LBG with K⁺ kappa carrageenan in 100mM KCl (which is known to promote extensive aggregation of double helices) gave erratic values for rotational viscosity and showed typical gel-like mechanical spectra under low-amplitude oscillation. Disordered carrageenans (K⁺ kappa in water and lambda in 100mM KCl) showed no evidence of interaction with LBG. Negative results were also obtained for iota carrageenan under ionic conditions believed to promote ordering without significant aggregation (100mM KCl). However, under conditions where limited aggregation might be expected (iota carrageenan in 90 mM CaCl₂; Me₄N⁺ kappa carrageenan in 150 mM Me₄NI), significant reductions in viscosity were observed on mixing with LBG, which may indicate some intermolecular association but without the formation of an extended network structure.     

Problem in liquid scintillation counting: adsorption of (14-C)pholyethylene glycol in dilute solutions.

[¹⁴C]polyethylene glycol is the method of choice for quantitating changes in intestinal water flux during drug absorption experiments in animals and man. This study points out some of the problems which can be encountered in using this method and provides ways to minimize these problems. Polyethylene glycol selectively binds to the glass wall of scintillation vials during counting and results in a decrease in counting efficiency as a function of time. The results obtained when using this method are determined by the choice of scintillation vial, scintillation cocktail, concentration of polyethylene glycol and the time period over which the samples are counted.