Analytical expressions for the homotropic binding of ligand to protein dimers and trimers

Cooperative binding of a ligand to multiple subsites on a protein is a common theme among enzymes and receptors. The analysis of cooperative binding data (either positive or negative) often relies on the assumption that free ligand concentration, L, can be approximated by the total ligand concentration, L(T). When this approximation does not hold, such analyses result in inaccurate estimates of dissociation constants. Presented here are exact analytical expressions for equilibrium concentrations of all enzyme and ligand species (in terms of K(d) values and total concentrations of protein and ligand) for homotropic dimeric and trimeric protein-ligand systems. These equations circumvent the need to approximate L and are provided in Excel worksheets suitable for simulation and least-squares fitting. The equations and worksheets are expanded to treat cases where binding signals vary with distinct site occupancy.     

Trimers, dimers of trimers, and trimers of trimers are common building blocks of annexin a5 two-dimensional crystals

Annexin A5 is a member of a family of homologous proteins sharing the ability to bind to negatively charged phospholipid membranes in a Ca(2+)-dependent manner. Annexin A5, as well as other annexins, self-assembles into two-dimensional (2D) ordered arrays upon binding to membranes, a property that has been proposed to have functional implications. Electron microscopy and atomic force microscopy experiments have revealed that annexin A5 forms two types of 2D crystals-with either p6 or p3 symmetry-that are both based on annexin trimers. In this study, we describe three other crystal forms that coexist with the p6 crystals. All crystal forms are made of the same building blocks, namely, dimers of trimers and trimers of trimers. A mechanistic model of the formation of the annexin A5 2D crystals is proposed.     

Low-resolution structures of thyroid hormone receptor dimers and tetramers in solution

High-resolution X-ray structures of thyroid hormone (TH) receptor (TR) DNA and ligand binding domains (DBD and LBD) have yielded significant insights into TR action. Nevertheless, the TR DBD and LBD act in concert to mediate TH effects upon gene expression, and TRs form multiple oligomers; however, structures of full-length TRs or DBD-LBD constructs that would clarify these influences are not available. Here, we report low-resolution X-ray structures of the TRbeta DBD-LBD construct in solution which define the shape of dimers and tetramers and likely positions of the DBDs and LBDs. The holo TRbeta DBD-LBD construct forms a homodimer with LBD-DBD pairs in close contact and DBDs protruding from the base in the same direction. The DBDs are connected to the LBDs by crossed extended D domains. The apo hTRbeta DBD-LBD construct forms tetramers that resemble bulged cylinders with pairs of LBD dimers in a head-to-head arrangement with DBD pairs packed tightly against the LBD core. Overall, there are similarities with our previous low-resolution structures of retinoid X receptors, but TRs exhibit two unique features. First, TR DBDs are closely juxtaposed in the dimer and tetramer forms. Second, TR DBDs are closely packed against LBDs in the tetramer, but not the dimer. These findings suggest that TRs may be able to engage in hitherto unknown interdomain interactions and that the D domain must rearrange in different oligomeric forms. Finally, the data corroborate our suggestion that apo TRs form tetramers in solution which dissociate into dimers upon hormone binding.     

Aggregation of bacteriochlorophyll c homologs to dimers,tetramers, and polymers in water-saturated carbon tetrachloride

Three homologs of BChl c, 2-(R)-(1-hydroxyethyl)-4-n-propyl-5-ethyl-farnesyl BChl c (PEF-BChl c), 2-(R)-(1-hydroxyethyl)-4-ethyl-5-ethyl-farnesyl BChl c (EEF-BChl c), and 2-(S)-(1-hydroxyethyl)-4-isobutyl-5-methyl/ethyl-farnesyl BChl c (iBM/EF-BChl c), formed aggregates in water-saturated carbon tetrachloride (H₂O-satd CCl₄). The water content was about 100 times higher than that of the dried CCl₄ previously used. Absorption spectra were recorded for 8 concentrations for the three homologs of BChl c and were deconvoluted in terms of standard spectra of monomer, dimer, tetramer and polymer (747-nm aggregate, Olson and Pedersen (1990) Photosynthe Res 25: 25). PEF- and EEF-BChl c formed dimers (680 nm maximum) and tetramers (705–710 nm maximum), but iBM/EF-BChl c formed polymers. Inhibition of dimer formation by water faciliated the study of the initial stages of the polymerization of BChl c. When the logarithm of polymer concentration was plotted versus the logarithm of the monomer concentration for iBM/EF-BChl c, the initial slope was 30±10 and indicated the cooperation of 20–40 BChl c molecules to form a polymer from a seed. Circular dichroism spectra of the polymers with positive and negative bands at 743 and 760 nm, respectively, were similar to those for chlorosomes (Brune et al. (1990) Photosynth Res 24: 253).Abbreviations BChl bacteriochlorophyll - CD circular dichroism - EEF 4-ethyl-5-ethyl farnesyl - iBM/EF 4-isobutyl-5-methyl/ethyl farnesyl - H₂O-satd CCl₄ water saturated carbon tetrachloride - PEF 4-n-propyl-5-ethyl farnesyl     

Heme-heme interactions in tetramers and dimers of hemoglobin subunits: DeVoe theory calculations

Detectable exciton couplets arising from heme-heme interactions in the hemoglobin (Hb) tetramers of HbO(2) and deoxyHb were predicted by DeVoe theory. This prediction was supported by the observation of an exciton couplet in the CD difference spectrum between the Hb tetramer and the alphabeta dimer of HbCO. In this paper, DeVoe theory is used to calculate the heme-heme interactions in the CO complex of the Hb tetramer (alpha(2)beta(2)) and dimer (alphabeta), the systems studied by Goldbeck et al. The couplet strength of the resulting theoretical CD difference spectrum agrees well with experiment, thus confirming that heme-heme interactions contribute significantly to the CD of HbCO. Given that the heme-heme distances in HbCO are 25 A and more, it is highly likely that heme-heme interactions also contribute significantly to the CD of other multi-heme proteins, e.g., cytochrome c(3), cytochrome oxidase, cytochrome bc(1), etc., where the hemes are in closer proximity.     

Tsp36, a tapeworm small heat-shock protein with a duplicated alpha-crystallin domain, forms dimers and tetramers with good chaperone-like activity

Small heat shock proteins (sHSPs), which range in monomer size between 12 and 42 kDa, are characterized by a conserved C-terminal alpha-crystallin domain of 80-100 residues. They generally form large homo- or heteromeric complexes, and typically have in vitro chaperone-like activity, keeping unfolding proteins in solution. A special type of sHSP, with a duplicated alpha-crystallin domain, is present in parasitic flatworms (Platyhelminthes). Considering that an alpha-crystallin domain is essential for the oligomerization and chaperone-like properties of sHSPs, we characterized Tsp36 from the tapeworm Taenia saginata. Both wild-type Tsp36 and a mutant (Tsp36C-->R) in which the single cysteine has been replaced by arginine were expressed and purified. Far-UV CD measurements of Tsp36 were in agreement with secondary structure predictions, which indicated alpha-helical structure in the N-terminal region and the expected beta-sandwich structure for the two alpha-crystallin domains. Gel permeation chromatography and nano-ESI-MS showed that wild type Tsp36 forms dimers in a reducing environment, and tetramers in a non-reducing environment. The tetramers are stabilized by disulfide bridges involving a large proportion of the Tsp36 monomers. Tsp36C-->R exclusively occurs as dimers according to gel permeation chromatography, while the nondisulfide bonded fraction of wild type Tsp36 dissociates from tetramers into dimers under nonreducing conditions at increased temperature (43 degrees C). The tetrameric form of Tsp36 has a greater chaperone-like activity than the dimeric form.     

Evidence for covalently cross-linked dimers and trimers of enzyme I of the Escherichia coli phosphotransferase system

Enzyme I of the bacterial phosphotransferase system catalyzes transfer of the phosphoryl moiety from phosphoenolpyruvate to both of the heat-stable phosphoryl carrier proteins of the phosphotransferase system, HPr and FPr. Using sodium dodecyl sulfate-polyacrylamide gel electrophoresis and high-pressure liquid chromatography, we demonstrated the existence of covalently cross-linked enzyme I dimers and trimers. Enzyme I exchange assays and phosphorylation experiments with [32P]phosphoenolpyruvate showed that covalent dimers and trimers are catalytically active. Inhibitors of the enzyme I-catalyzed phosphoenolpyruvate-pyruvate exchange block the phosphorylation of enzyme I dimers and trimers. Inhibition of the activity of enzyme I by N-ethylmaleimide, but not that by p-chloromercuriphenylsulfonate, could be overcome by high concentrations of enzyme, suggesting that N-ethylmaleimide modification changes the associative properties of enzyme I. We present evidence for two distinct classes of sulfhydryl groups in enzyme I.     

Monomers,dimers, and tetramers of 4-n-propyl-5-ethyl farnesyl bacteriochlorophyll c in dichloromethane and carbon tetrachloride

Absorption (ABS) and circular dichroism (CD) spectra were recorded for 6 concentrations (2.0–290 M) of bacteriochlorophyll (BChl) c in each solvent. Monomer spectra were obtained by adding methanol (1:200) to each sample. The monomer showed an ABS peak and a CD trough at 664 nm in CH₂Cl₂ (ABS peak at 665 nm in CCl₄). Dimer-plus-monomer spectra were obtained by subtracting high concentration (e.g., 290 M) spectra appropriately scaled from lower concentration (e.g., 26 M) spectra. Pure dimer spectra were then obtained by subtracting monomer spectra appropriately scaled from dimer-plus-monomer spectra. The dimer showed an ABS peak at 679 nm in both CH₂Cl₂ and CCl₄ and a CD trough at ca. 670 nm in CH₂Cl₂. The optical properties of the dimer do not agree with the model for bacteriochlorophyllide d [Smith KM, Bobe FW, Goff DA and Abraham RJ (1986) J Am Chem Soc 108: 1111–1120]. Higher aggregate spectra were obtained by subtracting appropriately scaled monomer and dimer spectra from high concentration (e.g., 290 M) spectra. The aggregate showed ABS shoulders at ca. 636 and 678 nm with a peak at 702 nm in CH₂Cl₂ and at 708 nm in CCl₄; the CD spectrum in either solvent showed peaks at 638 and 679 nm with troughs at 658 and ca. 710 nm. These spectra are consistent with an excitonic interaction between 4 chromophores in the aggregate. Each of the 12 original ABS spectra was deconvoluted in terms of the appropriate monomer, dimer and aggregate spectra, and the concentrations of each component were determined. Plots of log aggregate concentration vs. log dimer concentration lay on or near a line of slope 1.9 for CH₂Cl₂ and on or near a line of slope 2.1 for CCl₄. The aggregate was thus shown to be a tetramer. The theoretical relationship between dimers and monomers (slope 2.0) was not observed in all cases.Abbreviations ABS absorbance - BChl bacteriochlorophyll - CD circular dichroism - Chl chlorophyll - DNS data not shown - PEF 4-n-propyl-5-ethyl farnesyl     

ScFv multimers of the anti-neuraminidase antibody NC10: shortening of the linker in single-chain Fv fragment assembled in V(L) to V(H) orientation drives the formation of dimers, trimers, tetramers and higher molecular mass multimers

Synthetic genes encoding single-chain variable fragments (scFvs) of NC10 anti-neuraminidase antibody were constructed by joining the V(L) and V(H) domains with linkers of fifteen, five, four, three, two, one and zero residues. These V(L)-V(H) constructs were expressed in Escherichia coli and the resulting proteins were characterized and compared with the previously characterized NC10 scFv proteins assembled in V(H)-V(L) orientation. Size-exclusion chromatography and electron microscope images of complexes formed between various NC10 scFvs and anti-idiotype Fab' were used to analyse the oligomeric status of these scFvs. The result showed that as the linker length between V(L) and V(H) was reduced, different patterns of oligomerization were observed compared with those with V(H)-V(L) isomers. As was the case for V(H)-V(L) orientation, the scFv-15 V(L)-V(H) protein existed mainly as a monomer whereas dimer (diabody) was a predominant conformation for the scFv-5, scFv-4 and scFv-3 V(L)-V(H) proteins. In contrast to the V(H)-V(L) isomer, direct ligation of V(L) to V(H) led to the formation of predominantly a tetramer (tetrabody) rather than to an expected trimer (triabody). Furthermore, the transition between dimers and higher order oligomers was not as distinct as for V(H)-V(L). Thus reducing the linker length in V(L)-V(H) from three to two residues did not precisely dictate a transition between dimers and tetramers. Instead, two-residue as well as one-residue linked scFvs formed a mixture of dimers, trimers and tetramers.     

Preparation of trimers and tetramers of mixed sequence oligodeoxynucleoside methylphosphonates and assignment of configurations at the chiral phosphorus.

Synthesis of stereoregular DNA methylphosphonates has been accomplished for homo-oligomers, but remains a formidable problem for oligomers of a defined antisense target sequence. In this work, four trimer and tetramer deoxynucleoside methylphosphonates of mixed sequence (dACA, dCCAA, dAGGG, and dGCAT) were prepared by block coupling of diastereomerically pure dimers with either monomers or other diastereomerically pure dimers. These oligomers were separated chromatographically into individual diastereomers, and the configurations of the chiral methylphosphonate linkages were assigned. Three types of methods were used to assign configuration of a new methylphosphonate linkage: preparation of the same diastereomer through multiple synthetic pathways, base hydrolysis, and acid hydrolysis. Hydrolysis of the diastereomerically pure oligomers into component dimers and monomers was followed by chromatographic comparison with control dimers of known configuration. In all cases studied, oligomers with R configurations displayed faster elution from silica gel than did oligomers with the respective S configuration. NMR spectra of individual diastereomers of dACA were studied, revealing characteristic differences in chemical shifts which may prove useful in configurational assignments of longer oligomers. Thus, these data provide a methodological basis for synthesis and configurational assignment of longer methylphosphonate oligomers to use as antisense probes.     

Calculated sedimentation ratios for assemblies of two, three, four, and five spatially equivalent protomers

Sedimentation ratios of oligomeric structures containing from two to five protomers in spatially equivalent positions are calculated on the basis of equations derived by Kirkwood. A range of oblate and prolate protomers and a systematic set of assembly modes is considered for each type of oligomer. The results are presented graphically. Dimensions in three mutually perpendicular directions are also given for each structure considered, in a format which allows calculation in A of the dimensions of appropriate models for actual molecules. Together with the results for hexameric aggregates presented previously these data allow sedimentation velocity measurements with any oligomer, up to and including the hexamer, to be analysed readily and systematically in terms of quaternary structure.     

The use of sedimentation coefficients to distinguish between models for protein oligomers.

The sedimentation coefficients of proteins are dependent on their sizes, shapes and densities and on the density and viscosity of the solvent. However, when the sedimentation coefficients of an oligomeric protein and its protomer are measured under the same experimental conditions, the ratio of the two coefficients depends only on the protomer shape and the mode of aggregation. This property, which we shall call the sedimentation ratio, therefore provides a way of distinguishing between models for oligomeric proteins. To allow examination of the behaviour of the sedimentation ratio, sedimentation coefficients are calculated for a comprehensive range of protomer shapes and modes of aggregation in hexameric systems using equations derived by Kirkwood. As illustrations of the method the resulting sedimentation ratios are compared with experimental values for insulin and arthroped hemocyanin, which eliminates many of the possible structures for these proteins. When experimental estimates of degree of hydration and molecular dimensions are also considered, all but a group of virtually identical structures are eliminated for the insulin hexamer and a single most likely structure remains for arthropod hemocyanin. The insulin structure is in good agreement with that determined by X-ray crystallography while the hemocyanin hexameric structure is a hexagonal prism formed by the cyclic aggregation of prolate ellipsoids of axial ratio about 2.5 : 1.     

The two coiled coils in the isolated rod domain of the intermediate filament protein desmin are staggered. A hydrodynamic analysis of tetramers and dimers

Desmin protofilaments and the proteolytically derived alpha-helical rod domain have been characterized by high-resolution gel permeation chromatography (GPC) using columns calibrated for the determination of viscosity radii. Additional characterization by chemical cross-linking and the determination of sedimentation values allowed the calculation of the molecular dimensions of the molecular species isolated. In dilute buffers GPC separated desmin rod preparations into two complexes: a dimer species (single coiled coil) with a length of 50 +/- 5 nm and a tetramer species (two coiled coils) with a length of 65 +/- 5 nm. Thus the two coiled coils in the tetramer are staggered by approximately 15 nm. The hydrodynamically derived lengths of the rod dimer and tetramer are supported by electron microscopy after metal shadowing. The hydrodynamic properties of desmin protofilaments follow that of the rod tetramer. The data on the hydrodynamic analysis of the rod tetramer of desmin in solution are in full agreement with the structural information recently deduced from paracrystals of the rod of glial fibrillary acid protein [Stewart, M., Quinlan, R.A. & Moir, R.D. (1989) J. Cell Biol. 109, 225-234]. Our results explain the inhomogeneity of molecules encountered in previous electron microscopical analyses.     

ProML--the protein markup language for specification of protein sequences,structures and families

We propose a specification language ProML for protein sequences, structures, and families based on the open XML standard. The language allows for portable, system-independent, machine-parsable and human-readable representation of essential features of proteins. The language is of immediate use for several bioinformatics applications: we discuss clustering of proteins into families and the representation of the specific shared features of the respective clusters. Moreover, we use ProML for specification of data used in fold recognition bench-marks exploiting experimentally derived distance constraints.     

Differences in the electric birefringence of spectrin dimers and tetramers as shown by the fast reversing electric pulse method

The electric birefringence of purified Spectrin has been examined in medium of low ionic strength ai 20°C and for electric fields smaller than 4 × 10⁴ V m^?1. using the reversing electric pulse method. This technique allows study of the permanent and induced dipole electric moment of macromolecules more easily than in measurements using only rectangular pulses. We show that spectrin heterodimers and heterotetramers have different electro-optical properties. The relaxation time of the tetramer (7 μs) is significantly longer than that of the dimer (4.5 μs). Tetramers and dimers have also different polarizability parameters.     

Interaction of phycobilisomes with photosystem II dimers and photosystem I monomers and trimers in the cyanobacterium Spirulina platensis.

Distribution of phycobilisomes between photosystem I (PSI) and photosystem II (PSII) complexes in the cyanobacterium Spirulina platensis has been studied by analysis of the action spectra of H2 and O2 photoevolution and by analysis of the 77 K fluorescence excitation and emission spectra of the photosystems. PSI monomers and trimers were spectrally discriminated in the cell by the unique 760 nm low-temperature fluorescence, emitted by the trimers under reductive conditions. The phycobilisome-specific 625 nm peak was observed in the action spectra of both PSI and PSII, as well as in the 77 K fluorescence excitation spectra for chlorophyll emission at 695 nm (PSII), 730 nm (PSI monomers), and 760 nm (PSI trimers). The contributions of phycobilisomes to the absorption, action, and excitation spectra were derived from the in vivo absorption coefficients of phycobiliproteins and of chlorophyll. Analyzing the sum of PSI and PSII action spectra against the absorption spectrum and estimating the P700:P680 reaction center ratio of 5.7 in Spirulina, we calculated that PSII contained only 5% of the total chlorophyll, while PSI carried the greatest part, about 95%. Quantitative analysis of the obtained data showed that about 20% of phycobilisomes in Spirulina cells are bound to PSII, while 60% of phycobilisomes transfer the energy to PSI trimers, and the remaining 20% are associated with PSI monomers. A relevant model of organization of phycobilisomes and chlorophyll pigment-protein complexes in Spirulina is proposed. It is suggested that phycobilisomes are connected with PSII dimers, PSI trimers, and coupled PSI monomers.     

Kinetic investigations of the quaternary enhancement effect and alpha/beta differences in binding the last oxygen to hemoglobin tetramers and dimers

Analysis of O2 binding equilibria by two independent groups has suggested that the affinity for binding the fourth O2 to Hb tetramers is very high, about 800-1200 cal/mol higher than that of dimers (Chu, A. H., Turner, B. W., and Ackers, G. K. (1984) Biochemistry 23, 604-167; Di Cera, E., Robert, C. H., and Gill, S. J. (1987) Biochemistry 26, 4003-4008). Recently, Gibson and Edelstein challenged the reality of the quaternary enhancement effect, based on kinetic data (Gibson, Q. H., and Edelstein, S. J. (1987) J. Biol. Chem. 262, 516-519). However, these studies failed to directly address the key issue of the relative affinities of dimers and alpha 2 beta 2(O2)3. Furthermore, the extent to which alpha/beta differences influence these results remains an open question. Using partial laser photolysis and O2/CO replacement techniques we have, for the first time, resolved the rates of O2 association and dissociation to both alpha and beta chains within "R state" tetramers and dimers. We find that the beta chains are faster than alpha for both O2 binding (approximately 2-fold) and release (approximately 3-fold). The kinetically determined O2 affinities derived from these data are essentially identical for dimers and alpha 2 beta 2(O2)3. That is, the data do not show significant quaternary enhancement and suggest that the equilibrium data have both overestimated the affinity of alpha 2 beta 2(O2)3 and underestimated the affinity of dimers. The significance of and possible origins for the discrepancy between equilibrium and kinetic data are discussed.     

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometric behavior of succinoglycan monomers, dimers, and trimers isolated from Sinorhizobium meliloti 1021

Low-molecular-weight (LMW) succinoglycans (monomers, dimers, and trimers) were isolated from Sinorhizobium meliloti 1021 and have been firstly investigated by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) using 2,4,6-trihydroxyacetophenone (THAP) as an optimal matrix in the negative ion mode. The main fractions of LMW succinoglycans contain molecules assembled of octasaccharide subunits. MALDI-TOF mass spectra of the LMW succinoglycan monomers, the dimers, and the trimers showed the daughter ions resulting from the losses of the terminal galactose residues at the reducing ends, clearly indicating that the galactosyl linkages are more labile than the other glucosyl linkages. Furthermore, the losses of the acetyl groups as substituents rather than the succinyl and pyruvyl ester linkages by prompt fragmentation primarily occurred during MALDI-TOF analysis, suggesting the greater instability of acetyl linkages compared to pyruvyl and succinyl linkages.