Cooperative interactions in the binding of ethidium ion to the self-complementary ribodinucleoside monophosphates CpG and GpC

Complexes exhibiting the characteristics of cooperative interactions are formed by ethidium ion and the self-complementary dinucleoside monophosphates CpG and GpC. Complex formation, observed with an ethidium ion selective electrode, can be described by an equilibrium binding model in which complexes are formed with dinucleoside:ethidium combining ratios of 2:1, 2:2, and 2:3. The total amount of ethidium bound in 2:2 and 2:3 complexes, as calculated from the model, is proportional to a circular dichroism band in CpG-ethidium spectra near 305 nm. Van't Hoff analysis of the model equilibrium constants reveals that the addition of ethidium ion to the 2:1 and 2:2 species is exothermic and that the corresponding entropy changes are large and negative. Cooperative interactions in the binding of ethidium ion and of other ligands to some natural and synthetic polymeric nucleic acids have now been observed in several laboratories, but the present work shows that the effect can arise even with nucleic acid fragments as small as dinucleosides. Apparently, a macromolecular nucleic acid is not essential for cooperative interactions.     

Geometric cooperativity and anticooperativity of three-body interactions in native proteins

Characterizing multibody interactions of hydrophobic, polar, and ionizable residues in protein is important for understanding the stability of protein structures. We introduce a geometric model for quantifying 3-body interactions in native proteins. With this model, empirical propensity values for many types of 3-body interactions can be reliably estimated from a database of native protein structures, despite the overwhelming presence of pairwise contacts. In addition, we define a nonadditive coefficient that characterizes cooperativity and anticooperativity of residue interactions in native proteins by measuring the deviation of 3-body interactions from 3 independent pairwise interactions. It compares the 3-body propensity value from what would be expected if only pairwise interactions were considered, and highlights the distinction of propensity and cooperativity of 3-body interaction. Based on the geometric model, and what can be inferred from statistical analysis of such a model, we find that hydrophobic interactions and hydrogen-bonding interactions make nonadditive contributions to protein stability, but the nonadditive nature depends on whether such interactions are located in the protein interior or on the protein surface. When located in the interior, many hydrophobic interactions such as those involving alkyl residues are anticooperative. Salt-bridge and regular hydrogen-bonding interactions, such as those involving ionizable residues and polar residues, are cooperative. When located on the protein surface, these salt-bridge and regular hydrogen-bonding interactions are anticooperative, and hydrophobic interactions involving alkyl residues become cooperative. We show with examples that incorporating 3-body interactions improves discrimination of protein native structures against decoy conformations. In addition, analysis of cooperative 3-body interaction may reveal spatial motifs that can suggest specific protein functions.     

Competitive cooperative bindings of a small ligand to a linear homopolymer. I. Extension of the ising model to the case of two competitive interactions.

The theoretical study of the cooperative binding of a small ligand to a linear homopolymer is extended to systems in which two different complexes can form. The binding isotherms are derived under the assumption that the cooperative interactions exist only between molecules belonging to the same type of binding mode and are limited to nearest neighbors (Ising model). The binding to a single-stranded chain is first considered and two extreme cases are studied: (1) the two complexes can form independently from each other (model of independent classes of binding sites); (2) only one class of binding site exists, each possessing two different states of complexation (three-state model). Binding to a double-helical chain is also considered. Three simple types of competition between the different modes of binding are distinguished. The corresponding models are defined as: (1) the model of independent classes of binding sites; (2) the model of monoexclusive interactions between the different kinds of complexes (the symmetric and asymmetric cases are both considered); (3) the model of biexclusive interactions. The comparative study of the different cases shows that the binding isotherms are very similar at large polymer-to-ligand concentration ratios, while they can be very different at low polymer-to-ligand ratios. This can be used to obtain information on the mechanism of dye binding to nucleic acids by equilibrium studies as shown in a subsequent paper.     

Cooperativity in nucleosomes assembly on supercoiled pBR322 DNA.

Many studies have shown that in reconstituted chromatin model systems, containing only purified DNA and histone octamer, nucleosomes can adopt well defined locations with respect to DNA nucleotide sequence. Recently, nucleosome-nucleosome interactions were suggested as one of the factors underlying preferential nucleosomes positioning. In the present paper this aspect has been studied by topological analysis and electron microscopy visualization of minichromosomes reconstituted at different histone/DNA ratios. Both methods suggest that cooperativity plays a role in nucleosomes formation. A linear cooperative model in which nucleosomes are formed on discrete sites with cooperative interactions occurring only between nearest neighbours allows to calculate the cooperative constant. The reported results show that basic interactions, which are of relevance in the process of chromatin folding, are present also in very simple model system.     

Generalization of the Lotka-Volterra equation]

A complete qualitative study of Lotka--Volterra model with cooperative interactions in the system predator-prey is carried out. The model is as follows: (see abstract). The character of all possible stationary states is investigated in the first quadrant of the phase plane of the model variables depending on the system parameters. It is shown that for the generalized model considered unstable and stable limit cycles only of the infinite amplitude are possible in the first quadrant.     

The Kinetics of Cooperative Cofilin Binding Reveals Two States of the Cofilin-Actin Filament

The interaction of cofilin with actin filaments displays positive cooperativity. The equilibrium binding and associated thermodynamic properties of this interaction are well described by a simple, one-dimensional Ising model with nearest neighbor interactions. Here we evaluate the kinetic contributions to cooperative binding and the ability of this model to account for binding across a wide range of cofilin concentrations. A Monte Carlo-based simulation protocol that allows for nearest-neighbor interactions between adjacent binding sites was used to globally fit time courses of human cofilin binding to human nonmuscle (β-, γ-) actin filaments. Several extensions of the one-dimensional Ising model were tested, and a mechanism that includes isomerization of the actin filament was found to best account for time courses of association as well as irreversible dissociation from a saturated filament. This model predicts two equilibrium states of the cofilin-actin, or cofilactin, filament, and the resulting set of binding parameters are in agreement with equilibrium thermodynamic parameters. We conclude that despite its simplicity, this one-dimensional Ising model is a reliable model for analyzing and interpreting the energetics and kinetics of cooperative cofilin-actin filament interactions. The model predicts that severing activity associated with boundaries between bare and decorated segments will not be linear, but display a transient burst at short times on cofilin activation then dissipate due to a kinetic competition between severing activity and cofilin binding. A second peak of severing activity is predicted to arise from irreversible cofilin dissociation on inactivation. These behaviors predict what we believe to be novel mechanisms of cofilin severing and spatial regulation of actin filament turnover in cells. The methods developed for this system are generally applicable to the kinetic analysis of cooperative ligand binding to linear polymers.     

Evolution of cooperative cross-feeding could be less challenging than originally thought

The act of cross-feeding whereby unrelated species exchange nutrients is a common feature of microbial interactions and could be considered a form of reciprocal altruism or reciprocal cooperation. Past theoretical work suggests that the evolution of cooperative cross-feeding in nature may be more challenging than for other types of cooperation. Here we re-evaluate a mathematical model used previously to study persistence of cross-feeding and conclude that the maintenance of cross-feeding interactions could be favoured for a larger parameter ranges than formerly observed. Strikingly, we also find that large populations of cross-feeders are not necessarily vulnerable to extinction from an initially small number of cheats who receive the benefit of cross-feeding but do not reciprocate in this cooperative interaction. This could explain the widespread cooperative cross-feeding observed in natural populations.     

Thermodynamics of intersubunit interactions in cholera toxin upon binding to the oligosaccharide portion of its cell surface receptor, ganglioside GM1

The binding and the energetics of the interaction of cholera toxin with the oligosaccharide portion of ganglioside GM1 (oligo-GM1), the toxin cell surface receptor, have been studied by high-sensitivity isothermal titration calorimetry and differential scanning calorimetry. Previously, we have shown that the association of cholera toxin to ganglioside GM1 enhances the cooperative interactions between subunits in the B-subunit pentamer [Goins, B., & Freire, E. (1988) Biochemistry 27, 2046-2052]. New experiments presented in this paper reveal that the oligosaccharide portion of the receptor is by itself able to enhance the intersubunit cooperative interactions within the B pentamer. This effect is seen in the protein unfolding transition as a shift from independent unfolding of the B promoters toward a cooperative unfolding. To identify the origin of this effect, the binding of cholera toxin to oligo-GM1 has been measured calorimetrically under isothermal conditions. The binding curve at 37 degrees C is sigmoidal, indicating cooperative binding. The binding data can be described in terms of a nearest-neighbor cooperative interaction binding model. In terms of this model, the association of a oligo-GM1 molecule to a B protomer affects the association to adjacent B promoters within the pentameric ring. The measured intrinsic binding enthalpy per protomer is -22 kcal/mol and the cooperative interaction enthalpy -11 kcal/mol. The intrinsic binding constant determined calorimetrically is 1.05 x 10(6) M-1 at 37 degrees C and the cooperative Gibbs free energy equal to -850 cal/mol.(ABSTRACT TRUNCATED AT 250 WORDS)     

Understanding the cooperative interaction between myosin II and actin cross-linkers mediated by actin filaments during mechanosensation

Myosin II is a central mechanoenzyme in a wide range of cellular morphogenic processes. Its cellular localization is dependent not only on signal transduction pathways, but also on mechanical stress. We suggest that this stress-dependent distribution is the result of both the force-dependent binding to actin filaments and cooperative interactions between bound myosin heads. By assuming that the binding of myosin heads induces and/or stabilizes local conformational changes in the actin filaments that enhances myosin II binding locally, we successfully simulate the cooperative binding of myosin to actin observed experimentally. In addition, we can interpret the cooperative interactions between myosin and actin cross-linking proteins observed in cellular mechanosensation, provided that a similar mechanism operates among different proteins. Finally, we present a model that couples cooperative interactions to the assembly dynamics of myosin bipolar thick filaments and that accounts for the transient behaviors of the myosin II accumulation during mechanosensation. This mechanism is likely to be general for a range of myosin II-dependent cellular mechanosensory processes.     

Individual-site binding data and the energetics of protein–DNA interactions

Individual-site isotherms for the binding of bacteriophage λ repressor to the left and right λ operators have been determined [D. F. Senear, M. Brenowitz, M. A. Shea, and G. K. Ackers (1986) Biochemistry, Vol. 25, pp. 7344–7354.] using the DNAse protection technique [ footprinting; D. J. Galas and A. Schmitz (1978) Nucleic Acids Research, Vol. 5, pp. 3157–3170]. These extensive data have been interpreted with a quantitative model that emphasized cooperative interactions between adjacently bound ligands [occupied ? occupied interactions; G. K. Ackers, A. D. Johnson, and M. A. Shea (1982) Proceedings of the National Academy of Science, USA, Vol. 79, pp. 1129–1133]. Overlooked in this model are the effects of cooperative interactions between a site containing a bound ligand and its neighboring unoccupied site (occupied ? unoccupied interactions). This paper reinterprets the existing data with a model that considers occupied ? unoccupied as well as occupied ? occupied interactions. The results yield parameters that differ substantially from those already reported. A discussion on the advisability of ignoring occupied ? unoccupied interactions is included. © 1993 John Wiley & Sons, Inc.     

Structural model for the cooperative assembly of HIV-1 Rev multimers on the RRE as deduced from analysis of assembly-defective mutants.

The functional efficacy of the HIV-1 Rev protein is highly dependent on its ability to assemble onto its HIV-1 RNA target (the RRE) as a multimeric complex. To elucidate the mechanism of multimeric assembly, we have devised two rapid and broadly applicable strategies for examining cooperative interactions between proteins bound to RNA, one based on cooperative translational repression of a two-site reporter and the other on gel shift analysis with crude E. coli extracts. Using these strategies, we have identified two distinct surfaces of Rev (head and tail) that are critical for different steps in multimeric assembly. Our data indicate that Rev assembles cooperatively on the RRE via a series of symmetrical tail-to-tail and head-to-head protein-protein interactions. The insights into molecular architecture suggested by these findings have enabled us to derive a structural model for Rev and its multimerization on the RRE.     

Cooperation and the evolution of intelligence

The high levels of intelligence seen in humans, other primates, certain cetaceans and birds remain a major puzzle for evolutionary biologists, anthropologists and psychologists. It has long been held that social interactions provide the selection pressures necessary for the evolution of advanced cognitive abilities (the 'social intelligence hypothesis'), and in recent years decision-making in the context of cooperative social interactions has been conjectured to be of particular importance. Here we use an artificial neural network model to show that selection for efficient decision-making in cooperative dilemmas can give rise to selection pressures for greater cognitive abilities, and that intelligent strategies can themselves select for greater intelligence, leading to a Machiavellian arms race. Our results provide mechanistic support for the social intelligence hypothesis, highlight the potential importance of cooperative behaviour in the evolution of intelligence and may help us to explain the distribution of cooperation with intelligence across taxa.     

Thermodynamic model of cooperativity in a dimeric protein: unique and independent parameters formulation.

A model of the cooperative interaction of ligand binding to a dimeric protein is presented based upon the unique and independent parameters (UIP) thermodynamic formulation (Gutheil and McKenna, Biophys. Chem. 45 (1992) 171-179). The analysis is developed from an initial model which includes coupled conformational and ligand binding equilibria. This completely general model is then restricted to focus on conformationally mediated cooperative interactions between the ligands and the expressions for the apparent ligand binding constant and the apparent ligand-ligand interaction constant are derived. The conditions under which there is no cooperative interaction between the ligands are found as roots to a polynomial equation. Consideration of the distribution of species among the various conformational states in this general model leads to a set of inequalities which can be represented as a two dimensional plot of boundaries. By superimposing a contour plot of the value of the apparent ligand-ligand interaction constant over the plot of boundaries a complete graphical representation of this system is achieved similar to a phase diagram. It is found that the parameter space homologous to Koshland-Nemethy-Filmer type of model is most consistent with both positive and negative cooperativity in this model. The maximal amount of positive and negative cooperativity are found to be simple functions of Kc, the equilibrium constant associated with the change of a subunit and ligand from the unligated to ligated conformation. It is shown that under certain limiting conditions the apparent allosteric interaction between ligands is equal to the conformational interaction between subunits. The methods presented are generally applicable to the theoretical analysis of thermodynamic interactions in complex systems.     

Male cleaner wrasses adjust punishment of female partners according to the stakes

Punishment is an important deterrent against cheating in cooperative interactions. In humans, the severity of cheating affects the strength of punishment which, in turn, affects the punished individual's future behaviour. Here, we show such flexible adjustments for the first time in a non-human species, the cleaner wrasse (Labroides dimidiatus), where males are known to punish female partners. We exposed pairs of cleaners to a model client offering two types of food, preferred 'prawn' items and less-preferred 'flake' items. Analogous to interactions with real clients, eating a preferred prawn item ('cheating') led to model client removal. We varied the extent to which female cheating caused pay-off reduction to the male and measured the corresponding severity of male punishment. Males punished females more severely when females cheated during interactions with high value, rather than low value, model clients; and when females were similar in size to the male. This pattern may arise because, in this protogynous hermaphrodite, cheating by similar-sized females may reduce size differences to the extent that females change sex and become reproductive competitors. In response to more severe punishment from males, females behaved more cooperatively. Our results show that punishment can be adjusted to circumstances and that such subtleties can have an important bearing on the outcome of cooperative interactions.     

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.