Double-site enzymes and squatting. A study of the regulation by one or several ligands binding at two different classes of site

The existence of two (generally different) binding sites per protomer for the same ligand has already been observed (“double-site enzymes”). Furthermore, in some instances, the two sites appear to be shared in common by two or more ligands (“squatting”). The theoretical implications of such cases have been emphasized here using a generalization of an allosteric V model. This model, by taking into account the competition between ligands which occurs in vivo, evidences various, or even peculiar regulatory patterns, and could be of general physiological interest. It has been illustrated here by some real systems.     

(Na+ + K+)-adenosine triphosphatase of mammalian brain. Catalytic and regulatory K+ sites distinguishable by selectivity for Li+.

Li+, K+, and Rb+ are compared as activators of the hydrolysis of p-nitrophenylphosphate by beef brain (Na+ + K+)-ATPase. Previous experiments have established two classes of K+ binding sites that are involved in this reaction: "catalytic sites" have the higher affinity, their occupation is essential for catalytic activity, and they appear to correspond to the extracellular binding sites for active K+ transport; regulatory sites appear to have an allosteric function to "unmask" the catalytic sites. A separate set of Na+-binding regulatory sites bring about a similar unmasking of catalytic sites under phosphorylating conditions. Rb+ can activate p-nitrophenylphosphate hydrolysis both in the presence and absence of Na+ and, thus, can interact effectively with both K+ regulatory and catalytic sites. Li+ does not activate p-nitrophenylphosphate hydrolysis at 25 degrees C in the absence of other monovalent ligands. Li+ does activate when the catalytic sites are exposed by Na+ + ATP. Thus, K+ regulatory and catalytic sites differ in their cation selectivity. At temperatures less than 25 degrees C Li+ is able to activate the phosphatase reaction in the absence of other monovalent ligands: maximum activity occurs at 10-12 degrees C. A plot of the ratio, Li+ activation/K+ activation, as a function of temperature shows that the allosteric transition that unmasks catalytic sites occurs spontaneously with decreasing temperatures.     

Statistical fluctuations in processes of gene expression regulation: consideration of the problem from point of view of statistical mechanics

The regulation of gene expression is a basic problem of biology. In some cases, the gene activity is regulated by specific binding of regulatory proteins to DNA. In terms of statistical mechanics, this binding is described as the process of adsorption of ligands on the one-dimensional lattice and has a probability nature. As a random physical process, the adsorption of regulatory proteins on DNA introduces a noise to the regulation of gene activity. We derived equations, which make it possible to estimate this noise in the case of the binding of the lac repressor to the operator and showed that these estimates correspond to experimental data. Many ligands are able to bind nonspecifically to DNA. Nonspecific binding is characterized by a lesser equilibrium constant but a greater number of binding sites on the DNA, as compared with specific binding. Relations are presented, which enable one to estimate the probability of the binding of a ligand on a specific site and on nonspecific sites on DNA. The competition between specific and nonspecific binding of regulatory proteins plays a great role in the regulation of gene activity. Similar to the one-dimensional "lattice gas" of particles, ligands adsorbed on DNA produce "one-dimensional" pressure on proteins located at the termini of free regions of DNA. This pressure, an analog of osmotic pressure, may be of importance in processes leading to changes in chromatin structure and activation of gene expression.     

Dynamics of Intraguild Predation Systems with Intraspecific Competition

This paper considers intraguild predation (IGP) systems where species in the same community kill and eat each other and there is intraspecific competition in each species. The IGP systems are characterized by a lattice gas model, in which reaction between sites on the lattice occurs in a random and independent way. Global dynamics of the model with two species demonstrate mechanisms by which IGP leads to survival/extinction of species. It is shown that an intermediary level of predation promotes survival of species, while over-predation or under-predation could result in species extinction. An interesting result is that increasing intraspecific competition of one species can lead to extinction of one or both species, while increasing intraspecific competitions of both species would result in coexistence of species in facultative predation. Initial population densities of the species are also shown to play a role in persistence of the system. Then the analysis is extended to IGP systems with one species. Numerical simulations confirm and extend our results.     

Effects of Host Interspecific Interaction in the <Emphasis Type="Italic">Maculinea</Emphasis>–<Emphasis Type="Italic">Myrmica</Emphasis> Parasite–Host System

A model of interspecific host competition in a system with one parasite (butterfly—Maculinea) and multiple potential hosts (ants—Myrmica) is presented. Results indicate that host interspecific competition increases the occurrence of multiple host behaviour in Maculinea natural populations but decreases the ability of the parasite populations to adapt to the most abundant host species. These qualitative predictions were compared with data on host specificity, with good agreement. Analysis of the data also indicates that Maculinea teleius and Maculinea arion respond differently to changes in relative host abundances. Maculinea teleius shows a larger fraction of sites where it displays multiple host behaviour and a larger fraction of sites where the niches of the hosts overlap. In some instances, Maculinea teleius is adapted to Myrmica hosts that are present in lower frequencies. Maculinea arion is locally more host-specific and occurs at sites where host interspecific competition is unlikely and is more frequently adapted to the most abundant host species.     

A two-channel hypothesis for regulation of cell division and differentiation

We propose the hypothesis that extracellular regulation of cell division and differentiation acts through just two communications channels. These channels consist of a series of redundant components: extracellular messenger hormones; these hormones' receptors; cytoplasmic proteins activated by the hormone-receptor complex; and trans-activating nuclear regulatory proteins. One channel, here labeled "D" ("differentiate"), includes transforming growth factor-beta as one of its hormones; the other, labeled "G" ("growth") includes epidermal growth factor. We postulate that signal reception occurs as a result of competition between different actuating proteins for equilibrium-controlled binding to critical DNA sites. Stem cells commit to mitosis when some high proportion of critical sites is occupied by actuating proteins of the G class, and to terminal differentiation when a high proportion is occupied by "D" actuators. Intermediate occupancy can either lead to division into one differentiated and one stem cell, or to maintenance of cells in the reference state, quiescence. Equilibrium control of binding implies that critical site occupancy will be proportional to the relative concentrations of "D" and "G" actuating proteins in the nuclear fluid. These concentrations depend on the external hormone concentrations, the numbers of receptors on the cell membrane, and the coefficients of the rate-determining steps between internalization of the hormone-receptor complexes and activation of the actuating proteins. All of these quantities can be affected by various factors, including endocrine hormones. This model is consistent with most reported behavior of various growth factors, interferons, etc, toward a variety of cells in culture. It predicts that under otherwise constant conditions, high relative concentrations of a D-hormone (e.g. transforming growth factor-beta) will induce commitment to terminal differentiation, while high relative concentrations of a "G" hormone (e.g. epidermal growth factor) will induce mitosis. We have seen no report of an experiment which adequately tests this prediction. The model implies that cancer causing mutations are those which increase the relative intensity of the "G" signal; this can occur via changes in components of either channel. Such mutant cells should be both more likely to divide and less likely to differentiate than normal stem cells. Conversely, mutations which increase relative sensitivity to the "D" signal during embryonal development can lead to premature differentiation, cessation of growth, and structural abnormalities (terata).     

Competition between unit-restricted fungi: a metapopulation model

We aimed to provide a theoretical framework for dynamic studies of competition between fungi living on divided and ephemeral resources. We previously adapted the seminal Skellam's patch-occupancy model (Skellam, 1951) to describe the population dynamics of one species of unit-restricted fungus whose mycelial growth occurs within resource units and which colonizes new resource units by spore dispersal (Gourbiere et al., 1999). In this study, we extended this model to describe the competition between a pair of unit-restricted fungal species that interact with each other inside units by decreasing their spore production. Accordingly, we designed a discrete-time metapopulation model where all patches go extinct at each generation and species interact by lowering their propagule production in jointly occupied patches. We showed that the two species easily coexist although there is no trade-off between their competitive and colonization abilities. Furthermore, the outcome of the competition process can depend on a founder effect. Founder effect determines either which species is excluded or the relative densities of each species when they coexist. We investigated the implications of these results on the distribution and abundance of fungal species along environmental gradients. This work bridges the gap between the mycological theory of "Resource Units" and the metapopulation theory, showing the specificity of fungal exploitation competition. We suggest that unit-restricted fungal species are appropriate biological models to test the theoretical results of the metapopulation theory, such as the appearance of alternative stable equilibria.     

A Model of Binocular Rivalry and Cross-orientation Suppression

Binocular rivalry and cross-orientation suppression are well-studied forms of competition in visual cortex, but models of these two types of competition are in tension with one another. Binocular rivalry occurs during the presentation of dichoptic grating stimuli, where two orthogonal gratings presented separately to the two eyes evoke strong alternations in perceptual dominance. Cross-orientation suppression occurs during the presentation of plaid stimuli, where the responses to a component grating presented to both eyes is weakened by the presence of a superimposed orthogonal grating. Conventional models of rivalry that rely on strong competition between orientation-selective neurons incorrectly predict rivalry between the components of plaids. Lowering the inhibitory weights in such models reduces rivalry for plaids, but also reduces it for dichoptic gratings. Using an exhaustive grid search, we show that this problem cannot be solved simply by adjusting the parameters of the model. Instead, we propose a robust class of models that rely on ocular opponency neurons, previously proposed as a mechanism for efficient stereo coding, to yield rivalry only for dichoptic gratings, not for plaids. This class of models reconciles models of binocular rivalry with the divisive normalization framework that has been used to explain cross-orientation. Our model makes novel predictions that we confirmed with psychophysical tests.     

Stochastic modeling of the phase-variable pap operon regulation in uropathogenic Escherichia coli

Regulation of the pap operon in uropathogenic Escherichia coli is phase variable. This phase variation arises from competition between regulatory proteins at two sites within the regulatory region, GATC(dist) and GATC(prox). We have used the available literature data to design a stochastic model of the molecular interactions of pap regulation and expression during growth in a non-glucose environment at 37 degrees C. The resulting wild-type model is consistent with reported data. The wild-type model served as a basis for two "in silico" mutant models for investigating the role of key regulatory components, the GATC(dist) binding site and the PapI interaction with Lrp at the GATC(prox) site. Our results show that competition at GATC(dist) is required for phase variation, as previously reported. However, our results suggest that removal of competition at GATC(dist) does not affect initial state dependence. Additionally, the PapI involvement in Lrp translocation from GATC(prox) to GATC(dist) is required for the initial state dependence but not for phase variation. Our results also predict that pap expression is maximized at low growth rates and minimized at high growth rates. These predictions provide a basis for further experimental investigation.     

A model of calcium dynamics in cardiac myocytes based on the kinetics of ryanodine-sensitive calcium channels.

The ryanodine-sensitive calcium channels are pivotal to signal transduction and cell function in many cell types, including cardiac myocytes. In this paper a kinetic model is proposed for these channels. In the model there are two Ca regulatory sites on the channel protein, one positive and the other negative. Cytoplasmic Ca binds to these regulatory sites independently It is assumed that the binding of Ca to the positive site is a much faster process than binding to the negative site. At steady state, the channel opening as a function of the Ca concentration is a bell-shaped curve. The model predicts the adaptation of channels to constant Ca stimulus. When this model is applied to cardiac myocytes, it predicts excitability with respect to Ca perturbations, smoothly graded responses, and Ca oscillations in certain pathological circumstances. In a spatially distributed system, traveling Ca waves in individual myocytes exist under certain conditions. This model can also be applied to other systems where the ryanodine-sensitive channels have been identified.     

The exponential model for a regulatory enzyme: Its extension to describe the binding of two ligands

The exponential model for a regulatory enzyme (Ainsworth, 1977a) is extended to deal explicitly with the presence in solution of a second ligand. This is achieved by introducing exponential interaction coefficients which respectively describe how the affinity of the free and bound forms of the protein for the ligand depend on its fractional saturation by the second ligand. The basic equations, so derived, are applied to binding experiments where the ligands bind independently or competitively and to rate experiments where the ligands represent two substrates or one substrate and a modifier which may be either competitive or non-competitive in type. The conditions required to display linkage between the binding of the two ligands are established and it is also shown that rate data may display a maximum as one ligand concentration is varied at a fixed concentration of the other. The equations that are derived are tested by application to experimental data and the conditions that have to be met to justify such an application are discussed.     

Two affinity states of M1 muscarine receptors

1. The binding of oxotremorine-M to M1 muscarine receptors was examined by measuring competition between the agonist and 3H-pirenzepine, using rabbit hippocampal membranes suspended in 20 mM Tris buffer containing 1 mM Mn2+. 2. Both ligands interacted with a single class of receptors. The receptors could assume two affinity states for oxotremorine-M, with equal numbers of high-affinity (KH) and low-affinity (KL) sites. 3. KH interconverted reversibly to KL in the absence of divalent cations and interconverted reversibly to a state similar to KL in the presence of guanyl 5'-yl imidodiphosphate. 4. The results are compatible with a model in which a pair of receptor molecules can be stabilized by a guanine nucleotide-binding "G protein" and have one site each of KH and KL affinity.     

Organization of ligand binding sites at the acetylcholine receptor: a study with monoclonal antibodies

We have studied 20 monoclonal antibodies directed against both the solubilized and the membrane-bound receptor from Torpedo marmorata. We find the following: (i) Six of the antibodies compete with cholinergic ligands for receptor binding and, hence, are directed against the ligand binding regions. (ii) Of these six antibodies, two cross-react with receptor from Electrophorus electricus, rat myotubes, and chicken sympathetic ganglia. These two antibodies therefore define a preserved structure within the ligand binding regions. The other four antibodies bind to structures not common between the receptor preparations tested. (iii) From competition binding studies using internally 3H-labeled antibodies, nine nonoverlapping antigenic regions were defined at the surface of the receptor. Three of these regions overlap with the ligand binding regions. Since two of these three regions do not overlap with each other, two structurally distinct ligand binding regions must exist at the receptor. (iv) From competition binding studies with representative cholinergic ligands, the antibodies directed against the ligand binding regions can be subdivided into three groups: one group competes with all ligands tested; the second group competes with all ligands except the bismethonium compounds; the third group competes with all ligands except the bismethonium compounds and tubocurarine. The results are summarized in a model of the organization of ligand binding sites at the receptor: There are two ligand binding regions differing in their antigenic properties. Furthermore, either there exists separate sites for distinct groups of ligands within each of these binding regions or some ligands produce conformational changes of the receptor that reversibly abolish some antigenic sites. In any case, the cholinergic ligands must interact with the receptor by more and/or other structural determinants than are provided by the structure of acetylcholine.     

Discrete time models for two-species competition.

A discrete (difference) single age-class model for two-species competition is presented and its stability properties discussed. It resembles the Lotka-Volterra model in having linear zero growth isoclines, and thus, also in its general requirements for the coexistence of competing species. It differs in allowing the populations to show damped oscillations, stable cycles or even apparent “chaos” if competition is sufficiently severe. A similar two age-class model is discussed where there is both intra- and interspecific competition in one of the developmental stages, but only intraspecific competition in the other. Even this slight increase in complexity leads to markedly different properties. The zero growth curves become nonlinear and up to three equilibria between two competing species are possible.     

The regulatory control of β-receptor dependent adenylate cyclase

The characteristics of the β-receptor in turkey erythrocyte adenylate cyclase were studied using both kinetics of enzyme activation and direct binding measurement of the β-agonists and antagonists to the β-receptor. The regulatory ligands Gpp(NH)p and Ca²⁺ do not have any direct effect on the β-receptor, but modulate the enzyme activity through the interaction with specific regulatory sites. It was found that the role of the catecholamine hormone is to facilitate the activation of the enzyme by the guanyl nucleotide. The regulatory guanyl nucleotide binds to its allosteric site in the absence of hormone, but the activation of the enzyme is slow in the absence of hormone. This role of the hormone can be described by the scheme: Where R is the receptor, E the enzyme, G the guanyl nucleotide, H the hormone, and E′ the activated form of the enzyme. The binding steps are fast and reversible but the conversion of the inactive enzyme E to its active form occurs with a k～1.0 min^?1 In the absence of the β-agonist (l-catecholamine) at the β-receptor and at physiological free Mg²⁺ concentrations, the activation of the enzyme is insignificant. Thus the presence of a guanyl nucleotide at the allosteric site is obligatory but not sufficient to induce the conversion of the inactive enzyme to its active form. At high (nonphysiological) Mg²⁺ concentration the conversion of E to E′ occurs slowly in the absence of hormone probably by another pathway. There are two classes of Gpp(NH)p regulatory sites: tight sites and loose sites, both of which can be identified kinetically. We have also identified the tight sites by direct binding studies using ³H-Gpp(NH)p. It is not clear, however, whether these are two distinct classes of sites or whether their existence reflects the presence of negative cooperativity among the guanyl nucleotide regulatory sites. Calcium was found to be a negative allosteric inhibitor of adenylate cyclase. The inhibitory effect of Ca²⁺ is exerted on the nonactivated enzyme as well as on the Gpp(NH)p preactivated enzyme.     

A Mathematical Model for Timing the Release from Sequestration and the Resultant Brownian Migration of SeqA Clusters in <Emphasis Type="Italic">E. coli</Emphasis>

DNA replication in Escherichia coli is initiated by DnaA binding to oriC, the replication origin. During the process of assembly of the replication factory, the DnaA is released back into the cytoplasm, where it is competent to reinitiate replication. Premature reinitiation is prevented by binding SeqA to newly formed GATC sites near the replication origin. Resolution of the resulting SeqA cluster is one aspect of timing for reinitiation. A Markov model accounting for the competition between SeqA binding and methylation for one or several GATC sites relates the timing to reaction rates, and consequently to the concentrations of SeqA and methylase. A model is proposed for segregation, the motion of the two daughter DNAs into opposite poles of the cell before septation. This model assumes that the binding of SeqA and its subsequent clustering results in loops from both daughter nucleoids attached to the SeqA cluster at the GATC sites. As desequestration occurs, the cluster is divided in two, one associated with each daughter. As the loops of DNA uncoil, the two subclusters migrate apart due to the Brownian ratchet effect of the DNA loop.     

Photosynthetic rates and vegetative production of Sorghastrum nutans in response to competition at two strip mines and a railroad prairie

The effect of differing environmental conditions on competition for resources was investigated by a comparison of net photosynthetic rate (PN) and vegetative production of Indiangrass [Sorghastrum nutans (L.) Nash.] at two strip mine sites with differing reclamation histories, and a railroad prairie site where this species occurs naturally. The treatment for a competition experiment consisted of tying back all species of neighboring plants around a target plant, and measuring its PN and vegetative performance during the growing season. Environmental variables at each site were also measured during the growing season. Soil bulk density and pH were higher at the two mine sites than at the prairie site, and soil texture, nutrients, and water potential were different at each of the three sites. PN of target plants compared closely among the three sites, and were lowest for plants at the railroad prairie. The competition experiment indicated that lower canopy leaves were most affected by competition for photosynthetically active radiation (PAR) at all sites. Significant differences in PN of upper canopy leaves were found between treatment and control plants at one of the mine sites. This site had higher soil water potentials and higher soil levels of P and K than the other mine site or the railroad prairie. Target plants at the other mine site experienced a low competition for PAR, likely due to lower soil moisture availability and therefore lower aboveground productivity. The largest differences in PN and irradiances between upper and lower canopy leaves occurred in target plants with neighbors at the railroad prairie, likely due to inter-specific competition. Vegetative production of the target plants also reflected the environment at each site, but did not reflect PN differences between treatments. S. nutans is well adapted to the varying environment at these three sites, and aboveground competition for radiant energy was probably not as limiting for this C4 grass as belowground competition.     

Resource competition determines selection of B cell repertoires

Previous experiments with mouse chimeras demonstrated that cellular competition for antigen-specific survival signals plays a crucial role in the maintenance of the naive B cell repertoire. Transgenic (Tg) B cell populations in these chimeras have a shortened lifespan and poor competitive abilities as compared to more diverse non-Tg populations in the same mice. We develop a mathematical model to investigate the mechanism of B cell competition. The model allows for various B cell clones, generated in the bone marrow, to go into the peripheral circulation, where they compete specifically for various ligands providing survival signals. In the model we also find the observed poor competitive abilities of the Tg repertoire. Investigating the nature of the competition in the model, we find that most of the competition is "intraspecific" occurring largely within the clone of truly Tg B cells, and within the repertoire of leaky Tg and non-Tg B cells. This is confirmed by analysing a simplified version of the model, which only allows for intraspecific competition, and resembles a simple ecological model with density-dependent death. The fact that our model accounts for the data, casts doubt on a previous interpretation of the same data arguing that more diverse repertoires outcompete repertoires of lower diversity. Here, we conclude that most of the data can be explained with intraspecific competition, and formulate an experimental prediction that allows one to distinguish between the previous interpretation of inter-specific competition between repertoires, and the current interpretation of intraspecific competition.     

The McrBC endonuclease translocates DNA in a reaction dependent on GTP hydrolysis.

McrBC specifically recognizes and cleaves methylated DNA in a reaction dependent on GTP hydrolysis. DNA cleavage requires at least two recognition sites that are optimally separated by 40-80 bp, but can be spaced as far as 3 kb apart. The nature of the communication between two recognition sites was analyzed on DNA substrates containing one or two recognition sites. DNA cleavage of circular DNA required only one methylated recognition site, whereas the linearized form of this substrate was not cleaved. However, the linearized substrate was cleaved if a Lac repressor was bound adjacent to the recognition site. These results suggest a model in which communication between two remote sites is accomplished by DNA translocation rather than looping. A mutant protein with defective GTPase activity cleaved substrates with closely spaced recognition sites, but not substrates where the sites were further apart. This indicates that McrBC translocates DNA in a reaction dependent on GTP hydrolysis. We suggest that DNA cleavage occurs by the encounter of two DNA-translocating McrBC complexes, or can be triggered by non-specific physical obstacles like the Lac repressor bound on the enzyme's path along DNA. Our results indicate that McrBC belongs to the general class of DNA "motor proteins", which use the free energy associated with nucleoside 5'-triphosphate hydrolysis to translocate along DNA.