Specific interactions versus counterion condensation. 1. Nongelling ions/polyuronate systems

The characteristics of the interaction between nongelling divalent cations (typically Mg(2+)) and polyuronates have been explored by means of isothermal calorimetry. In particular, three polyuronates mimicking separately guluronan (polyguluronate, polyG), mannuronan (polymannuronate, polyM), and polyalternating (polyMG), the three block-components of natural alginate samples, have been treated with divalent ions, and the enthalpy of mixing was determined for different values of the [M(2+)]/[Polym](rep.unit) ratio. Despite the absence of a site-specific chemical bonding between the two, as confirmed by circular dichroism spectroscopy, a substantial deviation of the experimental enthalpy of mixing from the theoretical behavior, as predicted by the classical counterion condensation (CC) theory, was observed. Such deviation has been interpreted in terms of a "generic" nonbonding affinity of the condensed divalent counterion for the polyelectrolytes. The mathematical formalism of the CC theory was extended to include a contribution to the (reduced) free energy and enthalpy arising from the counterion affinity, g(aff,0) and h(aff,0), and allowed the parametrical calculation of the fraction of divalent counterions condensed as function of the reduced thermodynamic quantity g(aff,0). A best fit procedure of the experimental enthalpy of mixing allowed the g(aff,0) and h(aff,0) pair to be estimated for each of the different polyuronates considered, revealing differences in the three samples. In qualitative terms, the results obtained seem to suggest a notable contribution of the desolvation process (i.e., release of structured water as a consequence of the interaction between the divalent counterion and the uronate group) to the enthalpy of affinity for polyM which is counterbalanced and overcome by an ion pairing term (i.e., partial formation of ion-ion and/or ion-dipole bonds) for polyG and polyMG, respectively.     

Evaluation of the counterion condensation theory of polyelectrolytes.

We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.     

A new model of counterion condensation in polyelectrolyte solutions. III. Theoretical predictions of competitive condensation between counterions of different valences

Our model has been extended for theoretical estimation of competitive condensation of counterions of different valences onto polyelectrolytes in solution. The estimations are compared with those obtained from Manning theory and with experimental data on counterion activity coefficients. The agreement with the data for sodium polystyrenesulfonate/MgCl2, CaCl2 is satisfactory.     

Approach to the limit of counterion condensation

According to counterion condensation theory, one of the contributions to the polyelectrolyte free energy is a pairwise sum of Debye-Hückel potentials between polymer charges that are reduced by condensed counterions. When the polyion model is taken as an infinitely long and uniformly spaced line of charges, a simple closed expression for the summation, combined with entropy-derived mixing contributions, leads to the central result of the theory, a condensed fraction of counterions dependent only on the linear charge density of the polyion and the valence of the counterion, stable against increases of salt up to concentrations in excess of 0.1 M. Here we evaluate the sum numerically for B-DNA models other than the infinite line of B-DNA charges. For a finite-length line there are end effects at low salt. The condensation limit is reached as a flat plateau by increasing the salt concentration. At a fixed salt concentration the condensation limit is reached by increasing the length of the line. At moderate salt even very short B-DNA line-model oligomers have condensed fractions not far from the infinite polymer limit. For a long double-helical array with charge coordinates at the phosphates of B-DNA, the limiting condensed fraction appears to be approached at low salt. In contrast to the results for the line of charges, however, the computed condensed fraction varies strongly with salt in the range of experimentally typical concentrations. Salt invariance is restored, in agreement with both the line model and experimental data, when dielectric saturation is considered by means of a distance-dependent dielectric function. For sufficiently long B-DNA line and helical models, as typical salt concentrations, the counterion binding fraction approaches the polymer limit as a linear function of 1/P, where P is the number of phosphate groups of B-DNA.     

Examination of the limiting laws of polyelectrolytes and counterion condensation II

The two phase model of polyelectrolyte solutions, which has been developed recently, is examined in a further detail. The binding free energy, which was introduced in the previous paper (J. Chem. Phys. 81 (1977) 1929), is replaced by the entropy of the condensed phase. This replacement leads to a detailed picture of the condensed phase. In a mixed system of mono- and divalent counterions, a couple of possibilities are examined in interpreting the condensation volume, which corresponds to the condensation entropy.     

Role of counterion condensation in folding of the Tetrahymena ribozyme. II. Counterion-dependence of folding kinetics

Condensed counterions contribute to the stability of compact structures in RNA, largely by reducing electrostatic repulsion among phosphate groups. Varieties of cations induce a collapsed state in the Tetrahymena ribozyme that is readily transformed to the catalytically active structure in the presence of Mg2+. Native gel electrophoresis was used to compare the effects of the valence and size of the counterion on the kinetics of this transition. The rate of folding was found to decrease with the charge of the counterion. Transitions in monovalent ions occur 20- to 40-fold faster than transitions induced by multivalent metal ions. These results suggest that multivalent cations yield stable compact structures, which are slower to reorganize to the native conformation than those induced by monovalent ions. The folding kinetics are 12-fold faster in the presence of spermidine3+ than [Co(NH3)6]3+, consistent with less effective stabilization of long-range RNA interactions by polyamines. Under most conditions, the observed folding rate decreases with increasing counterion concentration. In saturating amounts of counterion, folding is accelerated by addition of urea. These observations indicate that reorganization of compact intermediates involves partial unfolding of the RNA. We find that folding of the ribozyme is most efficient in a mixture of monovalent salt and Mg2+. This is attributed to competition among counterions for binding to the RNA. The counterion dependence of the folding kinetics is discussed in terms of the ability of condensed ions to stabilize compact structures in RNA.     

Role of counterion condensation in folding of the Tetrahymena ribozyme. I. Equilibrium stabilization by cations

Folding of RNA into an ordered, compact structure requires substantial neutralization of the negatively charged backbone by positively charged counterions. Using a native gel electrophoresis assay, we have examined the effects of counterion condensation upon the equilibrium folding of the Tetrahymena ribozyme. Incubation of the ribozyme in the presence of mono-, di- and trivalent ions induces a conformational state that is capable of rapidly forming the native structure upon brief exposure to Mg2+. The cation concentration dependence of this transition is directly correlated with the charge of the counterion used to induce folding. Substrate cleavage assays confirm the rapid onset of catalytic activity under these conditions. These results are discussed in terms of classical counterion condensation theory. A model for folding is proposed which predicts effects of charge, ionic radius and temperature on counterion-induced RNA folding transitions.     

Dielectric behavior of polyelectrolytes. III. The role of counterion interactions

The role of the Coulomb forces between the counterions on the surface of polyelectrolytes on the dielectric response is analyzed. An estimate of the maximum dielectric increment (as a function of the number of counterions) is found as a function of the molecular length. The minimum-energy configuration of the counterions on a cylinder is found to be a double helix, suggesting the fundamental importance of electrostatic interactions in determining structure. Solutions of the dynamical equations for a few counterions indicate that a single mode dominates the relaxation which is enhanced by the inter-ion repulsions. A lower bound is found for this mode based on analysis of the system response for short lengths. Sum rules for the rates and amplitudes of the dipolar correlation function are derived and lead to an upper bound for the rate of the dominant mode. These bounds approach one another for the parameters characteristic of restriction fragments of DNA. This permits a prediction of the magnitude and time scale of the dielectric response.     

Analysis of potentiometric titrations of heterogeneous natural polyelectrolytes in terms of counterion condensation theory: application to humic acid

A model, developed within the framework of the counterion condensation theory of linear polyelectrolytes, is presented in this paper to describe the acid-base properties of linear polyelectrolytes, consisting of several types of functional ionizable groups. This formalism has been successfully applied to Fluka humic acid under salt-free conditions, as well as in the presence of supporting simple 1:1 salt (KNO3) at three different concentrations. As part of this approach, the charge density of the humic acid is obtained from the activity coefficient measurements of potassium counterions at different humic acid concentrations at a constant degree of dissociation of the polyelectrolyte. The humic acid average charge density was found to be 0.80 +/- 0.05. Using the present model, we are able to satisfactorily describe the experimental data obtained from acid-base potentiometric titrations. Four main functional groups making up the polymer are determined through their fractional abundances (Xi) and intrinsic pK (pK0i) values. The fractional abundances remained constant and independent of the ionic strength, indicating that the humic acid constitution does not depend on the concentration of excess salts. The pK0i values show a small change with ionic strength, which can be explained by the polyelectrolytic behavior of the solution.     

Limiting laws and counterion condensation in polyelectrolyte solutions: V. Further development of the chemical model

Counterion binding to polyelectrolyte chains is formulated as a chemical reaction M^z(free) → M^z(bound). Expressions for the chemical potentials of free and bound counterions are set equal to obtain the reaction equilibrium. The results are equivalent to those in the previous paper of this series. An additional result obtained here is that a polyion holds its bound counterion layer with a strength on the order of 100 $\text{kcal}\text{(mole cooperative unit)}$. The method is then applied to the calculation of the polarizability along the chain due to the bound (condensed) counterions.     

Specific interactions of chromatin with the nuclear envelope: positional determination within the nucleus in Drosophila melanogaster.

Specific interactions of chromatin with the nuclear envelope (NE) in early embryos of Drosophila melanogaster have been mapped and analyzed. Using fluorescence in situ hybridization, the three-dimensional positions of 42 DNA probes, primarily to chromosome 2L, have been mapped in nuclei of intact Drosophila embryos, revealing five euchromatic and two heterochromatic regions associated with the NE. These results predict that there are approximately 15 NE contacts per chromosome arm, which delimit large chromatin loops of approximately 1-2 Mb. These NE association sites do not strictly correlate with scaffold-attachment regions, heterochromatin, or binding sites of known chromatin proteins. Pairs of neighboring probes surrounding one NE association site were used to delimit the NE association site more precisely, suggesting that peripheral localization of a large stretch of chromatin is likely to result from NE association at a single discrete site. These NE interactions are not established until after telophase, by which time the nuclear envelope has reassembled around the chromosomes, and they are thus unlikely to be involved in binding of NE vesicles to chromosomes following mitosis. Analysis of positions of these probes also reveals that the interphase nucleus is strongly polarized in a Rabl configuration which, together with specific targeting to the NE or to the nuclear interior, results in each locus occupying a highly determined position within the nucleus.     

Base-stacking interactions in double-helical DNA structures: experiment versus theory

Atom-atom potential energy calculations have been undertaken for deriving stacking energies in double-helical structures. A comparison between the energy patterns of A- and B-type double-helical fragments determined by single-crystal X-ray diffraction methods versus idealized uniform models based on fibre diffraction data shows that the van der Waals stacking energy is largely sensitive to local changes in the relative orientation of adjacent base pairs. The sequence-dependent conformational variability observed in the high-resolution structures appears to be a consequence of the equipartitioning of the stacking energy along the double helix. The large energy variations expected for a uniform structure are dampened considerably in the observed structures by means of local changes in conformational features such as helix rotation and roll angles between base pairs.     

Specific nucleoprotein complexes within adenovirus capsids.

Adenoviral DNA was examined within capsids by dimethyl sulfate footprinting. Protein-DNA interactions were visualized through ligation-mediated PCR (LM-PCR). Signals for protein binding were found adjacent to both inverted terminal repeats (ITR). There were no indications of close protein binding at several other loci of the viral genome. Therefore, adenovirus type 5 seems to contain sequence- or locus-specific DNA binding proteins within the virion.     

Intricate interactions within the ccd plasmid addiction system.

The ccd addiction system plays a crucial role in the stable maintenance of the Escherichia coli F plasmid. It codes for a stable toxin (CcdB) and a less stable antidote (CcdA). Both are expressed at low levels during normal cell growth. Upon plasmid loss, CcdB outlives CcdA and kills the cell by poisoning gyrase. The interactions between CcdB, CcdA, and its promoter DNA were analyzed. In solution, the CcdA-CcdB interaction is complex, leading to various complexes with different stoichiometry. CcdA has two binding sites for CcdB and vice versa, permitting soluble hexamer formation but also causing precipitation, especially at CcdA:CcdB ratios close to one. CcdA alone, but not CcdB, binds to promoter DNA with high on and off rates. The presence of CcdB enhances the affinity and the specificity of CcdA-DNA binding and results in a stable CcdA*CcdB*DNA complex with a CcdA:CcdB ratio of one. This (CcdA(2)CcdB(2))(n) complex has multiple DNA-binding sites and spirals around the 120-bp promoter region.     

Interspecies interactions within oral microbial communities.

While reductionism has greatly advanced microbiology in the past 400 years, assembly of smaller pieces just could not explain the whole! Modern microbiologists are learning "system thinking" and "holism." Such an approach is changing our understanding of microbial physiology and our ability to diagnose/treat microbial infections. This review uses oral microbial communities as a focal point to describe this new trend. With the common name "dental plaque," oral microbial communities are some of the most complex microbial floras in the human body, consisting of more than 700 different bacterial species. For a very long time, oral microbiologists endeavored to use reductionism to identify the key genes or key pathogens responsible for oral microbial pathogenesis. The limitations of reductionism forced scientists to begin adopting new strategies using emerging concepts such as interspecies interaction, microbial community, biofilms, polymicrobial disease, etc. These new research directions indicate that the whole is much more than the simple sum of its parts, since the interactions between different parts resulted in many new physiological functions which cannot be observed with individual components. This review describes some of these interesting interspecies-interaction scenarios.     

Specific Grb2-mediated interactions regulate clathrin-dependent endocytosis of the cMet-tyrosine kinase

Lysosomal degradation of the receptor-tyrosine kinase cMet requires receptor ubiquitination by the E3 ubiquitin ligase Cbl followed by clathrin-dependent internalization. A role for Cbl as an adaptor for cMet internalization has been previously reported. However, the requirement for Cbl ubiquitin ligase activity in this process and its mode of recruitment to cMet has yet to be determined. Cbl can directly bind cMet at phosphotyrosine 1003 or indirectly via Grb2 to phosphotyrosine 1356 in the multisubstrate binding domain of cMet. The direct binding of Cbl with cMet is critical for receptor degradation and not receptor internalization. Here we show a strict requirement for Grb2 and the ubiquitin ligase activity of Cbl for cMet endocytosis. Receptor internalization was impaired by small interfering RNA depletion of Grb2, overexpression of dominant negative Grb2 mutants, and point mutations in the cMet multisubstrate docking site that inhibits the direct association of Grb2 with cMet. The requirement for Grb2 was specific and did not involve the multiadaptor Gab1. cMet internalization was impaired in cells expressing an ubiquitin ligase-deficient Cbl mutant or conjugation-deficient ubiquitin but was unaffected in cells expressing a Cbl mutant that is unable to bind cMet directly. Expression of a Cbl-Grb2 chimera rescued impaired cMet endocytosis in cells depleted of endogenous Grb2. These results indicate that the ubiquitin ligase activity of Cbl is critical for clathrin-dependent cMet internalization and suggest a role for Grb2 as an intermediary linking Cbl ubiquitin ligase activity to this process.     

Specific host-guest interactions in a protein-based artificial transaminase.

Artificial enzymes can be created by covalent attachment of a catalytic active group to a protein scaffold. Recently, we assembled an artificial transaminase by conjugation of intestinal fatty acid binding protein (IFABP) with a pyridoxamine derivative via a disulfide bond; the resulting construct catalyzed a transamination reaction 200-fold faster than free pyridoxamine. To identify the origin of this increased catalytic efficiency computer modeling was first used to identify two putative residues, Y14 and R126, that were in close proximity to the gamma-carboxylate group of the substrate, alpha-ketoglutartate. These positions were mutated to phenylalanine and methionine, respectively, and used to prepare semisynthetic transaminases by conjugation to pyridoxamine (Px) or an N-methylated derivative (MPx). Kinetic analysis of the resulting constructs showed that the R126M mutation reduced substrate affinity 3- to 6-fold while the additional Y14F mutation had a negligible effect. These results are consistent with a model for substrate recognition that involves an electrostatic interaction between the cationic guanidinium group of R126 and the anionic carboxylate from the substrate. Interestingly, one of the conjugates that contains an N-methylated pyridoxamine catalyzes a transamination reaction with a k(cat)' value of 1.1h(-1) which is the fastest value for k(cat) we have thus far obtained and is 34-fold greater than that for the free cofactor in the absence of the protein.