Microscopic viscosity and rotational diffusion of proteins in a macromolecular environment

The Stokes-Einstein-Debye equation is currently used to obtain information on protein size or on local viscosity from the measurement of the rotational correlation time. However, the implicit assumptions of a continuous and homogeneous solvent do not hold either in vivo, because of the high density of macromolecules, or in vitro, where viscosity is adjusted by adding viscous cosolvents of various size. To quantify the consequence of nonhomogeneity, we have measured the rotational Brownian motion of three globular proteins with molecular mass from 66 to 4000 kD in presence of 1.5 to 2000 kD dextrans as viscous cosolvents. Our results indicate that the linear viscosity dependence of the Stokes-Einstein relation must be replaced by a power law to describe the rotational Brownian motion of proteins in a macromolecular environment. The exponent of the power law expresses the fact that the protein experiences only a fraction of the hydrodynamic interactions of macromolecular cosolvents. An explicit expression of the exponent in terms of protein size and cosolvent's mass is obtained, permitting definition of a microscopic viscosity. Experimental data suggest that a similar effective microviscosity should be introduced in Kramers' equation describing protein reaction rates.     

Large-scale rotational motions of proteins detected by electron paramagnetic resonance and fluorescence.

Direct spectroscopic measurements of rotational motions of proteins and large protein segments are crucial to understanding the molecular dynamics of protein function. Fluorescent probes and spin labels attached to proteins have proved to be powerful tools in the study of large-scale protein motions. Fluorescence depolarization and conventional electron paramagnetic resonance (EPR) are applicable to the study of rotational motions in the nanosecond-to-microsecond time range, and have been used to demonstrate segmental flexibility in an antibody and in myosin. Very slow rotational motions, occurring in the microsecond-to-millisecond time range, are particularly important in supramolecular assemblies, where protein motions are restricted by association with other molecules. Saturation transfer spectroscopy (ST-EPR), a recently developed electron paramagnetic resonance (EPR) technique that permits the detection of rotational correlation times as long as 1 ms, has been used to detect large-scale rotational motions of spin-labeled proteins in muscle filaments and in membranes, providing valuable insights into energy transduction mechanisms in these assemblies.     

Time-dependent phosphorescence anisotropy measurements of the slow rotational motions of proteins in viscous solution

A method of monitoring slow rotational motions of proteins from the decay of the intrinsic phosphorescence is described. The phosphorescence is excited with a 10-μsec pulse of vertically polarized light from an air gap lamp, and the anisotropy was computed as a function of time from the simultaneously detected vertically and horizontally polarized components of the emission. The approach is illustrated with time-dependent measurements of the anisotropy of the tryptophan phosphorescence of Staphylococcus aureus nuclease, bovine carbonic anhydrase, and liver alcohol dehydrogenase in glycerol-phosphate buffer between ?90 and ?70°C. The temperature- and molecular-weight dependence of the exponential decays in the anisotropy indicate that overall rotation of the proteins is at the origin of the depolarization. The potential of the approach as a probe of the slow rotational motions of proteins in membranes and other macromolecular complexes is stressed.     

Domain motions in proteins

Although proteins require and possess well defined spatial structures, ever more cases are emerging where parts of proteins have moved relative to each other. These parts can be as small as single side chains or as large as domains of 50–150 residues. Analysis of these motions yields valuable data on the functions of the respective proteins.     

Fluorescence recovery spectroscopy as a probe of slow rotational motions.

Pump-and-probe techniques can be used to follow the slow rotational motions of fluorescent labels bound to macromolecules in solution. A strong pulse of polarized light initially anisotropically depletes the ground-state population. A continuous low-intensity beam of variable polarization then probes the anisotropic ground-state distribution. Using an additional emission polarizer, the generated fluorescence can be recorded as it rises towards its prepump value. A general theory of fluorescence recovery spectroscopy (FRS) is presented that allows for irreversible depletion processes like photobleaching as well as slowly reversible processes like triplet formation. In either case, rotational motions modulate recovery through cosine-squared laws for dipolar absorption and emission processes. Certain pump, probe, and emission polarization directions eliminate the directional dependence of either dipole and simplify the resulting expressions. Two anisotropy functions can then be constructed to independently monitor the rotations of either dipole. These functions are identical in form to the anisotropy used in fluorescence depolarization measurements and all rotational models developed there apply here with minor modifications. Several setups are discussed that achieve the necessary polarization alignments. These include right-angle detection equipment that is commonly available in laboratories using fluorescence methods.     

Fluorescence anisotropy as a probe to study tracer proteins in crowded solutions

Fluorescence anisotropy has been widely used to study the dynamics and interactions of biomolecules in diluted solutions. Comparable studies on single tracer macromolecules at the cellular level are now feasible because of the recent development of non-invasive fluorescence markers, like the growing family of the green fluorescence proteins (GFPs), and the advances in time-resolved fluorescence microscopy instrumentation. The interpretation of fluorescence polarization data in terms of dynamics and biological function of the macromolecular complexes in these physiological environments requires a deep understanding of the tracer rotational diffusion in such complex media. In this work we have studied the rotational diffusion of a tracer protein, apomyoglobin labeled with 1-anilino-8-naphthalene sulfonate, in crowded solutions of an unrelated protein, ribonuclease A. We have evaluated the deviation of the different tracer rotational motions from the Stokes-Einstein-Debye diffusion behavior, and its relation to the properties of the transient molecular cavities where the tracer is rotating in the fluorescence lifetime window. Finally, we have analyzed the application of fluorescence polarization methods to determine the apparent equilibrium constants of homo and hetero-associations of macromolecules in crowded conditions.     

Charge transport in DNA model with vibrational and rotational coupling motions

The dynamics of the Peyrard-Bishop model for vibrational motion of DNA dynamics, which has been extended by taking into account the rotational motion for the nucleotides (Silva et al., J. Biol. Phys. 34, 511–519, 2018) is studied. We report on the presence of the modulational instability (MI) of a plane wave for charge migration in DNA and the generation of soliton-like excitations in DNA nucleotides. We show that the original differential-difference equation for the DNA dynamics can be reduced in the continuum approximation to a set of three coupled nonlinear equations. The linear stability analysis of continuous wave solutions of the coupled systems is performed and the growth rate of instability is found numerically. Numerical simulations show the validity of the analytical approach with the generation of wave packets provided that the wave numbers fall in the instability domain.     

Contribution of translational and rotational motions to molecular association in aqueous solution

Much uncertainty and controversy exist regarding the estimation of the enthalpy, entropy, and free energy of overall translational and rotational motions of solute molecules in aqueous solutions, quantities that are crucial to the understanding of molecular association/recognition processes and structure-based drug design. A critique of the literature on this topic is given that leads to a classification of the various views. The major stumbling block to experimentally determining the translational/rotational enthalpy and entropy is the elimination of vibrational perturbations from the measured effects. A solution to this problem, based on a combination of energy equi-partition and enthalpy-entropy compensation, is proposed and subjected to verification. This method is then applied to analyze experimental data on the dissociation/unfolding of dimeric proteins. For one translational/rotational unit at 1 M standard state in aqueous solution, the results for enthalpy (H degrees (tr)), entropy (S degrees (tr)), and free energy (G degrees (tr)) are H (degrees) (tr) = 4.5 +/- 1.5RT, S (degrees) (tr) = 5 +/- 4R, and G (degrees) (tr) = 0 +/- 5RT. Therefore, the overall translational and rotational motions make negligible contribution to binding affinity (free energy) in aqueous solutions at 1 M standard state.     

Translational and rotational joint power terms in a six degree-of-freedom model of the normal ankle complex

We hypothesized that defining joint power (JP) merely on the basis of joint rotations ignores important translational power terms, and may not adequately represent the energy flow profile for a given muscle group. A novel six degree-of-freedom (6 DOF) model of the ankle complex was implemented, accounting for previously ignored joint translations as well as traditional rotations. Foot and shank kinematic and kinetic data were collected over a stride cycle on five male and five female adults, walking five trials each at 0.69 statures s⁻¹. During intra-subject analyses, ensemble averages were calculated (n=5) for JP associated with each DOF, and for related velocity and force/moment data. Translational joint velocities typically peaked below 10% of the mean walking velocity. The largest peak in JP occurred for the rotational DOF associated with dorsi/planter flexion (360 W). The next largest peak in JP was for the vertical translational DOF, and was nearly 10% of the predominant peak. Positive work during push-off was significantly less p≤0.05) for the 6 DOF model (27.9 J) than for either 1 or 3 DOF rotational models (30.3 and 29.9 J, respectively). Negative work during early stance was significantly less for the 6 DOF model (−10.3 J) than for either the 1 or 3 DOF models (−13.1 and −12.6 J, respectively). Inter-subject analyses (n=50) were conducted for JP data only, with similar results. We conclude that translational JP terms are of practical importance in mechanical energy studies, and may be of particular concern when evaluating energy storing prostheses, when summing total power at several joints, and when studying pathologies that disturb joint geometry.     

Membrane proteins in reverse micelles: myelin basic protein in a membrane-mimetic environment

The solubility, reactivity, and conformational dynamics of myelin basic protein (MBP) from bovine brain were studied in reverse micelles of sodium bis(2-ethylhexyl) sulfosuccinate (AOT)-isooctane and water. Such a membrane-mimetic system resembles the aqueous spaces of native myelin sheath in terms of physicochemical properties as reflected in the high affinity of MBP for interfacial bound water. This is marked by the unusual profile of the solubility curve of the protein in reverse micelles, which shows optimal solubility at a much lower molar ratio of water to surfactant ([ H2O]/[AOT] = w0) than that reported for other water-soluble proteins. The role of counterions and/or charged polar head groups in the solubilization process is revealed by comparison of the solubility of MBP in nonionic surfactant micellar solutions. Whereas MBP is unfolded in aqueous solutions, insertion into reverse micelles generates a more folded structure, characterized by the presence of 20% alpha-helix. This conformation is unaffected by variations in the water content of the system (in the 2.0-22.4 w0 range). The reactivity of epsilon-amino groups of lysine residues with aqueous solutions of o-phthalaldehyde demonstrates that segments of the peptide chain are accessible to water. Similar results were obtained with the sequence involved in heme binding. In contrast, the sole tryptophan residue, Trp-117, is shielded from the aqueous solvent, as indicated by lack of reaction with N-bromosuccinimide. The invariance of the wavelength maximum emission in the fluorescence spectra as a function of w0 is consistent with this result.(ABSTRACT TRUNCATED AT 250 WORDS)     

The microsecond rotational motions of eosin-labelled fatty acids in multilamellar vesicles

The rotational properties of two eosin-labelled fatty acids of different alkyl chain length have been studied in large multilamellar dimyristoylphosphatidylcholine vesicles. The location of the probes at the surface region were ascertained by quenching experiments using a hydrophilic divalent cation solubilized in the aqueous phase (Cu2+) and a hydrophobic aromatic aniline (N,N-dimethylaniline) associated with the lipid. Phosphorescence anisotropy measurements reveal that above the phospholipid phase transition the polarization of eosin luminescence decays monoexponentially in the micro-to-millisecond time range, while below the phase transition a biexponential decay is observed. A model is proposed which attributes the time constants to two separate motions, discrete jumps or 'flipping' of the eosin moiety within restricted boundaries and long-axis rotation. The value of the time-independent term changes with probe position and temperature and reflects orientational constraints imposed by lipid-chromophore interactions. The implications of these results for the study of protein rotations in membranes are discussed.     

Radially softening diffusive motions in a globular protein

Molecular dynamics simulation, quasielastic neutron scattering and analytical theory are combined to characterize diffusive motions in a hydrated protein, C-phycocyanin. The simulation-derived scattering function is in approximate agreement with experiment and is decomposed to determine the essential contributions. It is found that the geometry of the atomic motions can be modeled as diffusion in spheres with a distribution of radii. The time dependence of the dynamics follows stretched exponential behavior, reflecting a distribution of relaxation times. The average side chain and backbone dynamics are quantified and compared. The dynamical parameters are shown to present a smooth variation with distance from the core of the protein. Moving outward from the center of the protein there is a progressive increase of the mean sphere size, accompanied by a narrowing and shifting to shorter times of the relaxation time distribution. This smooth, "radially softening" dynamics may have important consequences for protein function. It also raises the possibility that the dynamical or "glass" transition with temperature observed experimentally in proteins might be depth dependent, involving, as the temperature decreases, progressive freezing out of the anharmonic dynamics with increasing distance from the center of the protein.     

Na+ shows a markedly higher potential than K+ in DNA compaction in a crowded environment

Whereas many physicochemical investigations have shown that among monovalent cations Na(+) ion possesses minimal potential for DNA binding, biological assays have shown that Na(+) ion (in contrast to K(+) ion) plays a primary role in chromatin compaction and related processes. It is difficult to explain this inverse relationship between the compaction potentials of Na(+) and K(+) and their binding abilities. In this study we sought to resolve this contradiction and emphasize the phenomenological distinction between DNA compaction and DNA binding processes in the case of DNA compaction by monocations. Using polyethylene glycol solutions as a model of a crowded cell environment, we studied DNA compaction by alkali metal salts LiCl, NaCl, KCl, RbCl, and CsCl, and found that all of these monocations promote DNA compaction. Among these monovalent cations Na(+) produces the greatest compaction and the ratio of K(+) cand Na(+) oncentrations for DNA compaction is approximately 1.5-2. A comparative analysis of recent experimental results indicates that a higher binding activity of monocation generally corresponds to a low compaction potential of the corresponding monovalent ion. This inverse relation is explained as a result of partial dehydration of monocations in the compact state.     

Sodium-23 and potassium-39 nuclear magnetic resonance relaxation in eye lens. Examples of quadrupole ion magnetic relaxation in a crowded protein environment.

Single and multiple quantum nuclear magnetic resonance (NMR) spectroscopic techniques were used to investigate the motional dynamics of sodium and potassium ions in concentrated protein solution, represented in this study by cortical and nuclear bovine lens tissue homogenates. Both ions displayed homogeneous biexponential magnetic relaxation behavior. Furthermore, the NMR relaxation behavior of these ions in lens homogenates was consistent either with a model that assumed the occurrence of two predominant ionic populations, "free" and "bound," in fast exchange with each other or with a model that assumed an asymmetric Gaussian distribution of correlation times. Regardless of the model employed, both ions were found to occur in a predominantly "free" or "unbound" rapidly reorienting state. The fraction of "bound" 23Na+, assuming a discrete two-site model, was approximately 0.006 and 0.017 for cortical and nuclear homogenates, respectively. Corresponding values for 39K+ were 0.003 and 0.007, respectively. Estimated values for the fraction of "bound" 23Na+ or 39K+ obtained from the distribution model (tau C greater than omega L-1) were less than or equal to 0.05 for all cases examined. The correlation times of the "bound" ions, derived using either a two-site or distribution model, yielded values that were at least one order of magnitude smaller than the reorientational motion of the constituent lens proteins. This observation implies that the apparent correlation time for ion binding is dominated by processes other than protein reorientational motion, most likely fast exchange between "free" and "bound" environments. The results of NMR visibility studies were consistent with the above findings, in agreement with other studies performed by non-NMR methods. These studies, in combination with those presented in the literature, suggest that the most likely role for sodium and potassium ions in the lens appears to be the regulation of cell volume by affecting the intralenticular water chemical potential.     

Essential cell division protein FtsZ assembles into one monomer-thick ribbons under conditions resembling the crowded intracellular environment

Experimental conditions that simulate the crowded bacterial cytoplasmic environment have been used to study the assembly of the essential cell division protein FtsZ from Escherichia coli. In solutions containing a suitable concentration of physiological osmolytes, macromolecular crowding promotes the GTP-dependent assembly of FtsZ into dynamic two-dimensional polymers that disassemble upon GTP depletion. Atomic force microscopy reveals that these FtsZ polymers adopt the shape of ribbons that are one subunit thick. When compared with the FtsZ filaments observed in vitro in the absence of crowding, the ribbons show a lag in the GTPase activity and a decrease in the GTPase rate and in the rate of GTP exchange within the polymer. We propose that, in the crowded bacterial cytoplasm under assembly-promoting conditions, the FtsZ filaments tend to align forming dynamic ribbon polymers. In vivo these ribbons would fit into the Z-ring even in the absence of other interactions. Therefore, the presence of mechanisms to prevent the spontaneous assembly of the Z-ring in non-dividing cells must be invoked.     

The effects of pressure and cholesterol on rotational motions of perylene in lipid bilayers

Using steady-state fluorescence polarization measurements, an isothermal pressure-induced phase transition was observed in dimyristoyl-L-alpha-phosphatidylcholine multilamellar vesicles containing perylene. The temperature-to-pressure equivalence, dT/dP, estimated from the phase transition pressure, P1/2, is about 22 K X kbar-1, which is comparable to values determined from diphenylhexatriene polarization (Chong, P.L.-G. and Weber, G. (1983) Biochemistry 22, 5544-5550). In addition, we have employed a new method, introduced in this paper, to calculate the rate of in-plane rotation (Rip) and the rate of out-of-plane rotation (Rop) of perylene in lipid bilayers. The effects of pressure and cholesterol on the rotational rates of perylene in two lipid bilayer systems have been examined. They are 1-palmitoyl-2-oleoyl-L-alpha-phosphatidylcholine (POPC) multilamellar vesicles (MLV) and 50 mol% cholesterol in POPC (MLV). Rop is smaller than Rip due to the fact that the out-of-plane rotation requires a larger volume change than the in-plane rotation. Cholesterol seems not to affect Rop significantly, but pressure causes a decrease in Rop by about a factor of three. In contrast, the effects of pressure and cholesterol on Rip are less straightforward. At 1 atm cholesterol increases Rip by a factor of about two. Similarly, in the absence of cholesterol 1.5 kbar pressure essentially triples Rip. However, if both cholesterol is added and pressure is applied, Rip decreases sharply. The possible interactions between cholesterol and perylene are discussed.     

Translational control of exported proteins in Escherichia coli

We recently described the suppression of export of a class of periplasmic proteins of Escherichia coli caused by overproduction of a C-terminal truncated periplasmic enzyme (GlpQ'). This truncated protein was not released into the periplasm but remained attached to the inner membrane and was accessible from the periplasm. The presence of GlpQ' in the membrane strongly reduced the appearance in the periplasm of some periplasmic proteins, including the maltose-binding protein (MBP), but did not affect outer membrane proteins, including the lambda receptor (LamB) (R. Hengge and W. Boos, J. Bacteriol., 162:972-978, 1985). To investigate this phenomenon further we examined the fate of MBP in comparison with the outer membrane protein LamB. We found that not only localization but also synthesis of MBP was impaired, indicating a coupling of translation and export. Synthesis and secretion of LamB were not affected. The possibility that this influence was exerted via the level of cyclic AMP could be excluded. Synthesis of MBP with altered signal sequences was also reduced, demonstrating that export-defective MBP which ultimately remains in the cytoplasm abortively enters the export pathway. When GlpQ' was expressed in a secA51(Ts) strain, the inhibition of MBP synthesis caused by GlpQ' was dominant over the precursor accumulation usually caused by secA51(Ts) at 41 degrees C. Therefore, GlpQ' acts before or at the level of recognition by SecA. For LamB the usual secA51(Ts) phenotype was observed. We propose a mechanism by which GlpQ' blocks an yet unknown membrane protein, the function of which is to couple translation and export of a subclass of periplasmic proteins.