Stochastic treatment of cooperative specific adsorption

A stochastic treatment of cooperative specific adsorption of ions at a linear chain of discrete sites leads to a set of differential equations for the various probabilities involved in which the coefficients are determined by nearest neighbor interactions and relative adsorption specificities of the ions for the sites. It is shown that the cooperative specific adsorption isotherm derived earlier on the basis of statistical mechanics for essentially a very large number of sites can be obtained with maximum deviations of only three per cent with this approach by considering only five sites.     

Determination of binding constants for cooperative site-specific protein-DNA interactions using the gel mobility-shift assay

We have investigated the question of whether the gel mobility-shift assay can provide data that are useful to the demonstration of cooperativity in the site-specific binding of proteins to DNA. Three common patterns of protein-DNA interaction were considered: (i) the cooperative binding of a protein to two sites (illustrated by the Escherichia coli Gal repressor); (ii) the cooperative binding of a bidentate protein to two sites (illustrated by the E. coli Lac repressor); and (iii) the cooperative binding of a protein to three sites (illustrated by the lambda cI repressor). A simple, rigorous, and easily extendable statistical mechanical approach to the derivation of the binding equations for the different patterns is presented. Both simulated and experimental data for each case are analyzed. The mobility-shift assay provides estimates of the macroscopic binding constants for each step of ligation based on its separation of liganded species by the number of ligands bound. Resolution of the binding constants depends on the precision with which the equilibrium distribution of liganded species is determined over the entire range of titration of each of the sites. However, the evaluation of cooperativity from the macroscopic binding constants is meaningful only for data that are also accurate. Some criteria that are useful in evaluating accuracy are introduced and illustrated. Resolution of cooperative effects is robust only for the simplest case, in which there are two identical protein binding sites. In this case, cooperative effects of up to 1,000-fold are precisely determined. For heterogeneous sites, cooperative effects of greater than 1,000-fold are resolvable, but weak cooperativity is masked by the heterogeneity. For three-site systems, only averaged pair-wise cooperative effects are resolvable.     

Phase partition studies of actinomycin-nucleotide complexes.

A method is reported for measuring the stoichiometry of complex formation between actinomycin and a series of deoxynucleotides. The amount of bound actinomycin is measured by distribution of the drug between two liquid phases, a buffer phase containing deoxynucleotide and an organic phase in which the nucleotide is insoluble. Using simple statistical mechanical analysis, the equilibrium equations for several models of actinomycin-deoxynucleotide complexes have been derived: actinomycin with one binding site, with two equivalent independent binding sites, and with two sites which must be occupied together. The binding of actinomycin C3 with dpG, dpApG, dpA, and dpGpC has been examined compared with these models. It is found that binding to dpG and dpApG involves two independent binding sites of nearly equal affinity for nucleotides, whereas binding of dpGpC to the two binding sites on actinomycin is a cooperative process. Binding of dpA tp actinomycin is partially cooperative and weaker than binding of dpG. The dimerization constant of actinomycin was also determined by the phase separation technique, and found in agreement with other values, including the results of kinetic measurements reported here.     

On the oscillatory phenomenon in an oil/water interface

A simple theoretical model is presented for simulating the self-sustained oscillations of electric potential and pH at an oil/water interface appearing in a two-phase system composed of 2-nitropropane solution containing picrate acid and an aqueous solution of cetyltrimethylammonium bromide. In the present model, a well-known condition necessary for the occurrence of self-sustained oscillations, i.e., the presence of a positive feedback process far from equilibrium, is taken into account in a set of kinetic equations to describe simplified characters of the following two processes: (i) a cooperative formation of ion pair complexes at the interface, and (ii) supply of picrate anions and cetyltrimethylammonium cations to the interface accompanied by release of ion pair complexes to the organic phase. The numerical solutions of the present equations are shown to reproduce fairly well the characteristic properties of the oscillation of electric potential and pH such as wave forms and frequencies.     

On the cooperative binding of large ligands to a one-dimensional homogeneous lattice: the generalized three-state lattice model

We present the general secular equation for three-state lattice models for the cooperative binding of large ligands to a one-dimensional lattice. In addition, a closed-form expression for the isotherm is also obtained, that can be used with all values of the cooperativity parameter omega(0 less than omega less than infinity) thus eliminating the need for multiple equations.     

Kinetic model for the interaction of myosin subfragment 1 with regulated actin

A one-dimensional kinetic Ising model is developed to describe the binding of myosin subfragment 1 (SF-1) to regulated actin. The model allows for cooperative interactions between individual actin sites with bound SF-1 ligands rather than assuming that groups of actin monomer sites change their state in a cooperative fashion. With the triplet closure approximation, the model yields a set of 16 independent differential (master) equations which may be solved numerically to yield the extent of binding as a function of time. The predictions of the model are compared with experiments on the transient binding of SF-1 to regulated actin in the presence of Ca2+ and in the absence of Ca2+ with varying amounts of SF-1 prebound to the actin filament and on the equilibrium binding of SF-1 X ADP to regulated actin in the absence of Ca2+. In all cases, the calculations fit the data to within the experimental errors. In the case of SF-1 X ADP, the results suggest that a repulsive interaction exists between adjacently bound SF-1 at the ends of two neighboring seven-site actin units.     

Cooperative effects during the binding of large ligands with DNA. Non-contact interaction between adsorbed ligands

Equations are derived to describe the cooperative binding of large ligands to DNA. A mathematical approach is developed which enables one to give a simple probabilistic interpretation of binding equations and to solve them in the general case when long-range interactions are allowed between bound ligands. These interactions can be mediated by conformation changes induced in the DNA in the course of binding process and transformed over some distances beyond the DNA region immediately covered by a bound ligand molecule (allosteric effect of DNA). Interactions between ligand molecules can be formally described in terms of model potential characterizing pairwise interactions between bound ligands. A procedure is developed which allows one to determined the form of such potential from experimentally measured binding isotherms. It is based on a comparison of experimental binding isotherms with the appropriate curves calculated for the case of non-interacting ligands.     

THE CHARACTERISTICS AND OCCURRENCE OF COOPERATIVE POLYANDRY

This paper discusses the relative position of cooperative polyandry among models for the evolution of both polyandry and cooperative breeding. Cooperative polyandry is described as the situation where more than one male and one female breed as a group with males sharing equally in copulations and the care of one set of young. Sequential and simultaneous polyandry are defined to show how they differ from cooperative polyandry. These systems generally are characterized by the care of only one parent for each set of young, a trait which is in sharp contrast to cooperative polyandry. An argument is made that the present models for the evolution of polyandry cannot be expanded to include the cooperatively polyandrous species. Instead, the cooperative traits of cooperative polyandry fit within the array of characteristics of cooperative (communal) breeding. General characteristics of all cooperative species (monogamous, promiscuous and polyandrous) are reviewed and possible reasons for the evolution of equal-status males are discussed. A plea is made for the unification of evolutionary models dealing with mating systems and cooperative systems.     

Kinetics of the two-sited enzyme. II. A method of distinguishing between anticooperative and independent active sites based on competitive inhibition

The presence of two active sites on an enzyme leads to downwardly curving Lineweaver-Burk plots if (A) the sites are independent, but have different Michaelis constants, or (B) if the sites interact anticooperatively to impair binding, but not catalysis, at the second site filled. Cases A and B are kinetically indistinguishable when only enzyme and substrate are present. However, equations derived by the rapid-equilibrium treatment show that the two cases have different patterns of competitive inhibition and become distinguishable in the presence of a suitable inhibitor. The inhibitor may decrease or increase the curvature of Lineweaver-Burk plots, but certain patterns have diagnostic value because they can occur only in case (B).In one type of diagnostic pattern, high concentrations of inhibitor cause the Lineweaver-Burk plots to curve upward, and cause the corresponding saturation curves to become sigmoid. The effect of the inhibitor is thus to make sites which are anticooperative appear to be cooperative. This suggests that the mere occurrence of sigmoid saturation curves is not necessarily evidence of cooperative binding effects, and may have uncertain significance in considerations of enzyme regulation.     

Nanopore detachment kinetics of poly(A) binding proteins from RNA molecules reveals the critical role of C-terminus interactions

The ubiquitous and abundant cytoplasmic poly(A) binding protein (PABP) is a highly conserved multifunctional protein, many copies of which bind to the poly(A) tail of eukaryotic mRNAs to promote translation initiation. The N-terminus of PABP is responsible for the high binding specificity and affinity to poly(A), whereas the C-terminus is known to stimulate PABP multimerization on poly(A). Here, we use single-molecule nanopore force spectroscopy to directly measure interactions between poly(A) and PABPs. Both electrical and biochemical results show that the C-C domain interaction between two consecutive PABPs promotes cooperative binding. Up to now, investigators have not been able to probe the detailed polarity configuration (i.e., the internal arrangement of two PABPs on a poly(A) streak in which the C-termini face toward or away from each other). Our nanopore force spectroscopy system is able to distinguish the cooperative binding conformation from the noncooperative one. The ～50% cooperative binding conformation of wild-type PABPs indicates that the C-C domain interaction doubles the cooperative binding probability. Moreover, the longer dissociation time of a cooperatively bound poly(A)/PABP complex as compared with a noncooperatively bound one indicates that the cooperative mode is the most stable conformation for PABPs binding onto the poly(A). However, ～50% of the poly(A)/PABP complexes exhibit a noncooperative binding conformation, which is in line with previous studies showing that the PABP C-terminal domain also interacts with additional protein cofactors.     

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.     

The Fokker-Planck approach for the cooperative molecular motor model with finite number of motors

We provide the methodology for the analysis of the cooperative molecular motor model with finite number of motors, which are linearly and rigidly coupled, based on the Fokker-Planck approach. The probability density functions for the position of motors are solved numerically from the stationary Fokker-Planck equations. By using these probability density functions, we provide the analytical expressions, such as the velocity, the rate of the ATP consumption, the energetic efficiency, and the dissipation energy rates. Furthermore, we investigate three specific examples, such as single motor model, 2-motor model, and infinitely coupled motor model. Numerical algorithm to solve the Fokker-Planck equations is also provided.     

Transmembrane modulation of the concanavalin A inhibition of 5'-nucleotidase is not due to a direct association of the enzyme with the cytoskeleton

The inhibition of the cell surface enzyme 5'-nucleotidase by concanavalin A is being studied as a model for understanding transmembrane modulation of cell surface functions. Nucleotidase of 13762 MAT-C1 ascites rat mammary adenocarcinoma cells is inhibited by concanavalin A in a noncooperative process. When cells are treated with the cytoplasmic effectors cytochalasins, colchicine, energy poisons, calcium plus ionophore or hypotonic buffers, the concanavalin A inhibition of the enzyme becomes cooperative. 5'-Nucleotidase of isolated MAT-C1 microvilli is also inhibited by concanavalin A in a noncooperative process; however, treatment of the microvilli with the same cytoplasmic effectors does not induce cooperativity. Since previous studies in several systems have suggested an association of nucleotidase with actin-containing microfilaments or the cell cytoskeleton, one explanation for the cooperativity changes is that they result from a change in the association of the enzyme with the cytoskeleton. However, Triton X-100 extractability of nucleotidase is the same for MAT-C1 cells exhibiting cooperative or noncooperative concanavalin A inhibition. Moreover, enzyme from cells exhibiting cooperative inhibition can be extracted into the zwitterionic detergent Zwittergent in a cooperative form, while enzyme exhibiting noncooperative behavior can be extracted into Zwittergent in a noncooperative form. Gel filtration and rate-zonal sucrose density gradient centrifugation showed little discernible size or sedimentation difference between enzyme samples exhibiting noncooperative and cooperative inhibition. These results indicate that changes in the cooperativity of the concanavalin A inhibition of nucleotidase are not a result of changes in the association of the enzyme with the cytoskeleton. These studies emphasize the caution which must be exercised in interpreting the effects of cytoskeletal perturbants on cell surface functions.     

Transmembrane modulation of the concanavalin A inhibition of 5′-nucleotidase is not due to a direct association of the enzyme with the cytoskeleton

The inhibition of the cell surface enzyme 5′-nucleotidase by concanavalin A is being studied as a model for understanding transmembrane modulation of cell surface functions. Nucleotidase of 13762 MAT-C1 ascites rat mammary adenocarcinoma cells is inhibited by concanavalin A in a noncooperative process. When cells are treated with the cytoplasmic effectors cytochalasins, colchicine, energy poisons, calcium plus ionophore or hypotonic buffers, the concanavalin A inhibition of the enzyme becomes cooperative. 5′-Nucleotidase of isolated MAT-C1 microvilli is also inhibited by concanavalin A in a noncooperative process; however, treatment of the microvilli with the same cytoplasmic effectors does not induce cooperativity. Since previous studies in several systems have suggested an association of nucleotidase with actin-containing microfilaments or the cell cytoskeleton, one explanation for the cooperativity changes is that they result from a change in the association of the enzyme with the cytoskeleton. However, Triton X-100 extractability of nucleotidase is the same for MAT-C1 cells exhibiting cooperative or noncooperative concanavalin A inhibition. Moreover, enzyme from cells exhibiting cooperative inhibition can be extracted into the zwitterionic detergent Zwittergent in a cooperative form, while enzyme exhibiting noncooperative behavior can be extracted into Zwittergent in a noncooperative form. Gel filtration and rate-zonal sucrose density gradient centrifugation showed little discernible size or sedimentation difference between enzyme samples exhibiting noncooperative and cooperative inhibition. These results indicate that changes in the cooperativity of the concanavalin A inhibition of nucleotidase are not a result of changes in the association of the enzyme with the cytoskeleton. These studies emphasize the caution which must be exercised in interpreting the effects of cytoskeletal perturbants on cell surface functions.     

Kinetic analysis of multisite phosphorylation using analytic solutions to Michaelis-Menten equations

Phosphorylation-induced expression or modulation of a functional protein is a common signal in living cells. Many functional proteins are phosphorylated at multiple sites and it is frequently observed that phosphorylation at one site enhances or suppresses phosphorylation at another site. Therefore, characterizing such cooperative phosphorylation is important. In this study, we determine a temporal progress curve of multisite phosphorylation by analytically integrating the Michaelis-Menten equations in time. Using this theoretical progress curve, we derive the useful criterion that an intersection of two progress curves implies the presence of cooperativity. Experiments generally yield noisy progress curves. We fit the theoretical progress curves to noisy progress curves containing 4% Gaussian noise in order to determine the kinetics of the phosphorylation. This fitting correctly identifies the sites involved in cooperative phosphorylation.     

The dependence of flux,sensitivity and response of the flux on the concentrations of substrate and modifiers for cooperative enzymes

The sensitivity (change of flux per unit change in the concentration of substrate) and response (change of flux per unit change in the concentration of modifier) are studied for a two-site Adair model in which cooperativity arises from both binding and catalytic interactions. For positive cooperativity, the sensitivity is weakly dependent on the Hill coefficient for the binding case, but can increase without limit for the catalytic case. Negatively cooperative enzymes (binding only) give very large sensitivities compared with positively or non-interacting systems, but the sensitivity rapidly decreases as the saturation increases above 25%. Modifiers greatly enhance the sensitivity; large changes in flux can be obtained for small changes in the concentrations of substrates and modifiers. In general, increasing the degree of kinetic cooperativity decreases the degree of binding cooperativity; selective pressure to maximize the sensitivity and response of allosteric enzymes may act to optimize cooperativity of binding modifiers and kinetic cooperativity of substrate turnover. The initial velocity equations including modifiers can be extended to bi-substrate, cooperative kinetics. The kinetics of methanol dehydrogenase are discussed.     

Cooperative disordering of single-stranded polynucleotides through copper crosslinking

The thermal transitions of single-stranded polynucleotides are noncooperative. In contrast, Cu(II) cooperatively disorders the single-stranded helical structures of poly(A) and poly(C), as demonstrated by ORD and UV spectral changes as a function of the Cu²⁺ activity, and by a dramatic chain-length dependence of the spectral changes. Equilibrium dialysis binding studies indicate that the cooperative disordering is paralleled by a somewhat less cooperative binding process. The difference between the thermal- and Cu(II)-induced transition is explained by the following mechanism. (1) Cu(II) initially binds in a noncooperative fashion to phosphate. (2) The Cu(II) so bound forms a second bond to a nonadjacent base site on the same polymer strand or another strand. These intramolecular and intermolecular crosslinks to the bases are responsible for the disordering. (3) The initial crosslinks formed provide nuclei for the cooperative formation of additional crosslinks, producing cooperative spectral changes paralleled by cooperative binding. A comparison of the spectral and binding transitions indicates that there is appreciable noncooperative binding of copper to phosphate, which produces no spectral changes in the presence of added electrolyte. This comparison also indicates that each copper crosslink disorders several bases. The formation of intermolecular crosslinks is demonstrated by a polymer concentration dependence of the disordering. The formation of intramolecular crosslinks can be deduced from the fact that the “cooperative unit” required to explain the differences between the hexamer, which does not readily form intramolecular crosslinks, and the polymer is considerably larger than the cooperative unit determined from the polymer results. The poly(A) disordering transition is less symmetrical than that of poly(C), particularly at low polymer concentrations. These results, together with other phenomena, are explained by a greater flexibility of poly(A), which favors the formation of small intramolecular loops.     

Experimental peripheral administration of oxytocin elevates a suite of cooperative behaviours in a wild social mammal

The evolution and expression of different forms of cooperative behaviour (e.g. feeding, guarding, sentinel duties, etc.) are usually studied independently, with few studies considering them as a single syndrome. However, studies investigating individuals' investment across a suite of different behaviours reveal that they are correlated, suggesting a single mechanism determining the evolution and expression of cooperative behaviours. A hormonal mechanism could achieve this, and one possibility is oxytocin (OT), which affects several prosocial or alloparental behaviours independently. We show, using a double-blind experiment, that peripheral administration of OT to social, free-living meerkats Suricata suricatta elevates a suite of cooperative behaviours. Treated individuals increase their contributions to communal, cooperative activities (digging, guarding, pup-feeding and associating with pups) and decrease initiation of aggressive interactions, compared with a saline control. This suggests that different forms of cooperative behaviour form a single syndrome with a common causal basis. If our peripherally administered OT acts in the same way as the naturally released hormone, then a general tendency to prosociality may be modulated by this hormonal system. Therefore, it may be difficult for an individual to decouple expression of cooperative behaviours that provide the practitioner with benefits from those that provide the recipient with benefits. It may also explain why social species typically exhibit a suite of cooperative behaviours, without having to invoke independent evolution of each.     

Cooperate or speciate: new theory for the distribution of passerine birds

In cooperatively breeding birds, adults often forego reproduction and help care for the offspring of others. A universal explanation for this mode of breeding has eluded evolutionary biologists, who have considered it to be a rare, and largely Australian, phenomenon. In a recent paper, Andrew Cockburn reports that the number of known cooperative breeders among oscine passerine birds has more than doubled since the last substantial review, published 16 years ago. Cooperative breeding is often the ancestral trait, and predominantly cooperative genera are species poor compared with their pair-breeding counterparts. Cockburn argues that speciation is less likely in cooperative clades, because the philopatric tendencies of individuals make them poor dispersers, colonizers and migrants. This new hypothesis helps explain the distribution and composition of migrant and island avifauna. However, a major challenge remains to reconcile the roles of phylogenetic history and current ecology in promoting cooperative behaviour.