Extending the diffuse layer model of surface acidity behaviour: III. Estimating bound site activity coefficients

Abstract

Although detailed thermodynamic analyses of the 2-pK diffuse layer surface complexation model generally specify bound site activity coefficients for the purpose of accounting for those non-ideal excess free energies contributing to bound site electrochemical potentials, in application these terms are ignored based on one or more of the following assumptions: (1) bound site activity coefficients cancel out in the mass action quotients; (2) bound sites display ideal behaviour; and/or (3) these energies are already included in the exponential Boltzmann terms. In this work it is demonstrated that the bound site charging energy terms discussed in the two previous papers in this series have both conceptual and computational analogies to the charging energy contribution to the activity coefficients obtained from the Debye–Huckel Limiting Law. On high charge density colloidal particles at constant counterion condensation (τ), these charging energies can be related to the surface potential (ψ) by: ΔG_charging = (1 – τ)Fψ (where F is the Faraday constant). If one assumes a maximum practical accuracy of ± 10% in experimental estimates of ψ, then it is suggested that charging energies are likely to be experimentally indiscernible under conditions where τ > 0.9. These findings support the historical practice of ignoring bound site activity coefficients with the 2-pK diffuse layer surface complexation model in the following situations: for spherical particles with a radius ≥ 0.1 μm at ionic strengths ≥ 0.001 M (1 : 1), and for spherical particles with a radius >0.01 μm at an ionic strength >0.1 M (1 : 1). In contrast, charging energies (and non-ideal behaviour) are predicted to be significant at all charge densities and ionic strengths for spherical particles with a radius of 0.001 μm.     

Extending the diffuse layer model of surface acidity constant behaviour: IV. Diffuse layer charge/potential relationships

Abstract

Most current electrostatic surface complexation models describing ionic binding at the particle/water interface rely on the use of Poisson–Boltzmann (PB) theory for relating diffuse layer charge densities to diffuse layer electrostatic potentials. PB theory is known to contain a number of implicit assumptions whose significance in environmental applications is largely unknown. This study seeks to better quantify the impact of these assumptions by: (1) comparing potentials obtained from planar analytical solutions to the PB with those obtained from Hypernetted Chain (HNC) theory (Attard, 2006), (2) assessing the accuracy of the Ohshima et al. (1982) spherical approximate analytical solution to the PB equation by comparison with published numerical values (Loeb et al., 1961), and (3) comparing interfacial potential estimates obtained from the spherical approximate analytical solution to the PB equation at and adjacent to the particle surface with potential estimates obtained from the Entropic Balanced Surface Potential (EB) model (Loux, 1985; Loux and Anderson, 2001) and published potential estimates obtained from the Hypernetted Chain/Mean Spherical Approximation procedure (HNC/MSA; Gonzalez-Tovar and Lozada-Cassou, 1989). EB potential estimates were obtained assuming a surface volume thickness equal to the Bjerrum length (0.357 nm in a room temperature monovalent electrolyte solution). Findings from the study included: (1) the planar, surficial HNC estimates compared favourably with planar surficial PB relationships at charge densities equal to or less than 0.05 C m^?2, (2) the Ohshima et al. (1982) approximate spherical analytical solution to the PB equation replicated the numerical charge density estimates required to obtain 72 datapoints over an e<img>/kT range of one to four with a maximum error of 3.37% and a coefficient of variation of 0.92%, (3) for a 0.1 μm radius particle in a room temperature 0.01 M (1 : 1) ionic strength solution, potential estimates over a surface charge density range of 0 to 0.3C m^?2 occurred in the following order: ψ_HNC/MSA,R >ψ_PB,R >_{ψHNC/MSA,R+0.2125nm} >ψ_PB,R+0.2nm ~ ψ_EB >ψ_{HNC/MSA,R+0.425nm} ~ _ψPB,R+0.4nm and (4) with 45 datapoints including both 1 μm and 10 nm radius particles over an ionic strength range of 1.0 to 0.001 M, the PB potential estimates 0.2 nm from the particle surface (ψ_PBR+02nm) closely tracked the corresponding EB estimates (ψ_EB) with a 5.3% coefficient of variation. If one assumes that interfacial potential values adjacent to the particle surface are most relevant for describing environmental phenomena and that a 10% coefficient of variation in potential estimates is acceptable, then presumably any of the non-surficial charge/potential relationships would be useful below an absolute charge density of 0.125 C m ^?2 (with monovalent electrolyte solutions).     

The ligand binding site of the synaptosomal choline transporter: A provisional model based on inhibition studies

A topographic model of the ligand binding site of the choline transporter was deduced from inhibition studies with the help of CPK molecular models. It is posited that there are two identical or closely similar hydrophilic anionic sites separated from each other by an hinged, essentially planar but conformationally flexible cationic hydrophobic domain. Subsequently to attachment of external choline to either one of the anionic sites, both sites cooperate in enveloping the ligand by a Venus fly-trap mechanism. This leads to rapid configurational changes by which the closed-liganded form of the transporter opens up to the interior to release the bound choline. Intracellular K⁺, a ligand for the choline-binding site, is proposed to be countertransported by a reversal of the above mechanism.Special issue dedicated to Dr. Morris H. Aprison.     

Oxidation of apolipoprotein(a) inhibits kringle-associated lysine binding: the loss of intrinsic protein fluorescence suggests a role for tryptophan residues in the lysine binding site.

Lipoprotein(a) [Lp(a)] is a low-density lipoprotein complex consisting of apolipoprotein(a) [apo(a)] disulfide-linked to apolipoprotein B-100. Lp(a) has been implicated in atherogenesis and thrombosis through the lysine binding site (LBS) affinity of its kringle domains. We have examined the oxidative effect of 2,2'-azobis-(amidinopropane) HCl (AAPH), a mild hydrophilic free radical initiator, upon the ability of Lp(a) and recombinant apo(a), r-apo(a), to bind through their LBS domains. AAPH treatment caused a time-dependent decrease in the number of functional Lp(a) or r-apo(a) molecules capable of binding to fibrin or lysine-Sepharose and in the intrinsic protein fluorescence of both Lp(a) and r-apo(a). The presence of a lysine analogue during the reaction prevented the loss of lysine binding and provided a partial protection from the loss of tryptophan fluorescence. The partial protection of fluorescence by lysine analogues was observed in other kringle-containing proteins, but not in proteins lacking kringles. No significant aggregation, fragmentation, or change in conformation of Lp(a) or r-apo(a) was observed as assessed by native or SDS-PAGE, light scattering, retention of antigenicity, and protein fluorescence emission spectra. Our results suggest that AAPH destroys amino acids in the kringles of apo(a) that are essential for lysine binding, including one or more tryptophan residues. The present study, therefore, raises the possibility that the biological roles of Lp(a) may be mediated by its state of oxidation, especially in light of our previous study showing that the reductive properties of sulfhydryl-containing compounds increase the LBS affinity of Lp(a) for fibrin.     

Sarcolemmal calcium binding sites in heart: II. Mathematical model for diffusion of calcium released from the sarcoplasmic reticulum into the diadic region

Summary We present a model for predicting the temporal and spatial dependence of [Ca] in the cardiac subsarcolemmal diadic region (cleft), following Ca release from the feet of the sarcoplasmic reticulum. This region is modeled as a disc 10 nm thick, 430 nm in radius, with or without Ca binding sites and open at its periphery to the cytosol. [Ca] is computed for three diffusion coefficients (100, 20 and 4% of aqueous diffusion), following release of a 20-msec square pulse sufficient to produce 50% maximal contractile force, or repetitive release (400/min) of such pulses. Numerical solutions are obtained for the general diffusion/binding problem and analytic solutions for the case of no binding sites. For the middle value of diffusion coefficient, and in the absence of binding sites, [Ca] rises to 1.5 mm in 20-msec and then falls to 0.1 m in < 3 msec. Adding binding sites reduces peak [Ca] to 0.6 mm but prolongs its decline, requiring 200 msec to reach 20 m. For repetitive release [Ca] is > 100 m for roughly half of each cycle. Two major implications of the predicted [Ca] are: (i) The effect of Ca binding sites on [Ca] will cause Ca efflux from the cleft via the NaCa exchanger (K _m (Ca) 20 m) to continue at a significant level for > 200 msec, (ii) The time constant for inactivation of release from the feet must be much greater than for activation if Cainduced Ca release is to continue for > 1–2 msec.     

A test of the relationship between sequence and structure in proteins: excision of the heme binding site in apocytochrome b5.

The water-soluble domain of rat hepatic holocytochrome b5 is an alphabeta protein containing elements of secondary structure in the sequence beta1-alpha1-beta4-beta3-alpha2-alpha3-beta5- alpha4-alpha5-beta2-alpha6. The heme group is enclosed by four helices, a2, a3, a4, and a5. To test the hypothesis that a small b hemoprotein can be constructed in two parts, one forming the heme site, the other an organizing scaffold, a protein fragment corresponding to beta1-alpha1-beta4-beta3-lambda-beta2-alpha6 was prepared, where lambda is a seven-residue linker bypassing the heme binding site. The fragment ("abridged b5") was found to contain alpha and beta secondary structure by circular dichroism spectroscopy and tertiary structure by Trp fluorescence emission spectroscopy. NMR data revealed a species with spectral properties similar to those of the full-length apoprotein. This folded form is in slow equilibrium on the chemical shift time scale with other less folded species. Thermal denaturation, as monitored by circular dichroism, absorption, and fluorescence spectroscopy, as well as size-exclusion chromatography-fast protein liquid chromatography (SEC-FPLC), confirmed the coexistence of at least two distinct conformational ensembles. It was concluded that the protein fragment is capable of adopting a specific fold likely related to that of cytochrome b5, but does not achieve high thermodynamic stability and cooperativity. Abridged b5 demonstrates that the spliced sequence contains the information necessary to fold the protein. It suggests that the dominating influence to restrict the conformational space searched by the chain is structural propensities at a local level rather than internal packing. The sequence also holds the properties necessary to generate a barrier to unfolding.     

Macromolecularization of a tripeptide analogue of the Cu(II) binding site of human serum albumin: 2. Conformational and binding properties towards Cu(II) and Ni(II)ions of Gly-Gly-His derivatives of poly(l-lysine)

The conformational and binding properties towards Cu(II) and Ni(II) ions of Gly-Gly-His derivatives of poly(l-lysine) have been investigated mainly using circular dichroism (c.d.) spectroscopy. These derivatized polymers can be considered macromolecular analogues of the Cu(II) and Ni(II) binding site of human serum albumin. It has been shown that modification up to 53% of the ε-amino groups of lysine side chains by covalent binding of the tripeptide unit Gly-Gly-His does not induce appreciable alteration of the α-helix forming tendency of the polylysine backbone. The derivatized polymers exhibit strong affinity towards Cu(II) and Ni(II) ions. At neutral pH, complexes are formed in which each tripeptide chelating unit is linked to one metal ion. The spectral characteristics in the visible absorption region are consistent with a square planar geometry of the complexes, with deprotonated peptide groups and one imidazole nitrogen in the coordination sphere of the ion. C.d. measurements in the far u.v. indicate that complex formation in the side chains causes an increase of ordered structure of the peptide backbone at neutral pH. This fact is interpreted in terms of a reduced electrostatic repulsion among side chains due to charge neutralization in the tripeptide units linked to metal ions.     

Macromolecularization of a tripeptide analogue of the Cu(II) binding site of human serum albumin: 2. Conformational and binding properties towards Cu(II) and Ni(II)ions of Gly-Gly-His derivatives of poly(l-lysine)

The conformational and binding properties towards Cu(II) and Ni(II) ions of Gly-Gly-His derivatives of poly(l-lysine) have been investigated mainly using circular dichroism (c.d.) spectroscopy. These derivatized polymers can be considered macromolecular analogues of the Cu(II) and Ni(II) binding site of human serum albumin. It has been shown that modification up to 53% of the ε-amino groups of lysine side chains by covalent binding of the tripeptide unit Gly-Gly-His does not induce appreciable alteration of the α-helix forming tendency of the polylysine backbone. The derivatized polymers exhibit strong affinity towards Cu(II) and Ni(II) ions. At neutral pH, complexes are formed in which each tripeptide chelating unit is linked to one metal ion. The spectral characteristics in the visible absorption region are consistent with a square planar geometry of the complexes, with deprotonated peptide groups and one imidazole nitrogen in the coordination sphere of the ion. C.d. measurements in the far u.v. indicate that complex formation in the side chains causes an increase of ordered structure of the peptide backbone at neutral pH. This fact is interpreted in terms of a reduced electrostatic repulsion among side chains due to charge neutralization in the tripeptide units linked to metal ions.