Ammoniacal nitrogen recovery from swine slurry using a gas-permeable membrane: pH control strategies and feed-to-trapping volume ratio

Gas-permeable membrane (GPM) technology is gaining interest to recover nitrogen from residual effluents due to its effectiveness, simple operation and capacity of producing a nutrient rich product with fertilising value. In this study, a GPM contactor was used at 25 °C to recover total ammoniacal nitrogen (TAN) from swine slurry as a concentrated (NH4)2SO4 solution. Firstly, a synthetic solution was tested on a wide pH range (6-12). Results showed that the ammonia mass transfer constants (Km) increased from 7.9·10-9 to 1.2·10-6 m/s as the pH increased. The reagent consumption to control the pH per mole nitrogen recovered had a minimum at pH 9, which showed a Km value of 3.0·10-7 m/s. Secondly, various pH control strategies were tested using swine slurry, including (i) no pH control, (ii) pH control at 8.5, 9.0 and 10.0, and (iii) an initial spike of the NaOH equivalent to the required to control the pH at 9. The test without pH control reached a TAN recovery of around 60%, which could be an interesting strategy when high nitrogen recoveries or short operating times are not required. The pH control at 9 stood out as the most favourable operating condition due to its high Km and lower reagent consumption. Thirdly, several feed-to-trapping volume ratios ranging from 1:1 to 15:1 were tested using swine slurry at pH 9. These assays revealed that a GPM process with a high feed-to-trapping volume ratio fastens the recovery of 99% of TAN as a high purity (NH4)2SO4 solution containing 40 g N/L.

Immunometabolic actions of trabectedin and lurbinectedin on human macrophages: relevance for their anti-tumor activity

In recent years, the central role of cell bioenergetics in regulating immune cell function and fate has been recognized, giving rise to the interest in immunometabolism, an area of research focused on the interaction between metabolic regulation and immune function. Thus, early metabolic changes associated with the polarization of macrophages into pro-inflammatory or pro-resolving cells under different stimuli have been characterized. Tumor-associated macrophages are among the most abundant cells in the tumor microenvironment; however, it exists an unmet need to study the effect of chemotherapeutics on macrophage immunometabolism. Here, we use a systems biology approach that integrates transcriptomics and metabolomics to unveil the immunometabolic effects of trabectedin (TRB) and lurbinectedin (LUR), two DNA-binding agents with proven antitumor activity. Our results show that TRB and LUR activate human macrophages toward a pro-inflammatory phenotype by inducing a specific metabolic rewiring program that includes ROS production, changes in the mitochondrial inner membrane potential, increased pentose phosphate pathway, lactate release, tricarboxylic acids (TCA) cycle, serine and methylglyoxal pathways in human macrophages. Glutamine, aspartate, histidine, and proline intracellular levels are also decreased, whereas oxygen consumption is reduced. The observed immunometabolic changes explain additional antitumor activities of these compounds and open new avenues to design therapeutic interventions that specifically target the immunometabolic landscape in the treatment of cancer.

Collection of Partition Coefficients in Hexadecyltrimethylammonium Bromide, Sodium Cholate, and Lithium Perfluorooctanesulfonate Micellar Solutions: Experimental Determination and Computational Predictions

This study focuses on determining the partition coefficients (logP) of a diverse set of 63 molecules in three distinct micellar systems: hexadecyltrimethylammonium bromide (HTAB), sodium cholate (SC), and lithium perfluorooctanesulfonate (LPFOS). The experimental log p values were obtained through micellar electrokinetic chromatography (MEKC) experiments, conducted under controlled pH conditions. Then, Quantum Mechanics (QM) and machine learning approaches are proposed for the prediction of the partition coefficients in these three micellar systems. In the applied QM approach, the experimentally obtained partition coefficients were correlated with the calculated values for the case of the 15 solvent mixtures. Using Density Function Theory (DFT) with the B3LYP functional, we calculated the solvation free energies of 63 molecules in these 16 solvents. The combined data from the experimental partition coefficients in the three micellar formulations showed that the 1-propanol/water combination demonstrated the best agreement with the experimental partition coefficients for the SC and HTAB micelles. Moreover, we employed the SVM approach and k-means clustering based on the generation of the chemical descriptor space. The analysis revealed distinct partitioning patterns associated with specific characteristic features within each identified class. These results indicate the utility of the combined techniques when we want an efficient and quicker model for predicting partition coefficients in diverse micelles.

Unusual Aspects of Charge Regulation in Flexible Weak Polyelectrolytes

This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called "wrong side" of the isoelectric point); (v) the influence of macromolecular crowding on CR.

Adsorption of flexible proteins in the 'wrong side' of the isoelectric point: Casein macropeptide as a model system

We analyze the conditions of the adsorption of a flexible peptide onto a charged substrate in the 'wrong side' of the isoelectric point (WSIP), i.e. when surface and peptide charges have the same sign. As a model system, we focus on the casein macropeptide (CMP), both in the aglycosylated (aCMP) and fully glycosydated (gCMP) forms. We model the substrate as a uniformly charged plane while CMP is treated as a bead-and-spring model including electrostatic interactions, excluded volume effects and acid/base equilibria. Adsorption coverage, aminoacid charges and concentration profiles are computed by means of Monte Carlo simulations at fixed pH and salt concentration. We conclude that for different reasons the CMP can be adsorbed to both positively and negatively charged surfaces in the WSIP. For negatively charged surfaces, WSIP adsorption is due to the patchy distribution of charges: the peptide is attached to the surface by the positively charged end of the chain, while the repulsion of the surface for the negatively charged tail is screened by the small ions of the added salt. This effect increases with salt concentration. Conversely, a positively charged substrate induces strong charge regulation of the peptide: the acidic groups are deprotonated, and the peptide becomes negatively charged. This effect is stronger at low salt concentrations and it is more intense for gCMP than for aCMP, due to the presence of the additional sialic groups in gCMP.

Molecular dynamics simulations of an α-synuclein NAC domain fragment with a ff14IDPSFF IDP-specific force field suggest β-sheet intermediate states of fibrillation

For the discovery of treatments against synucleinopathies, it is necessary to unravel and fully understand the mechanism of fibrillation of proteins involved. Among them, α-synuclein (αS) plays a key role in the development of these diseases through its aggregation into oligomers found in Lewy bodies. However, its structural disorder as an intrinsically disordered protein (IDP) makes its characterization by experimental techniques arduously difficult. Atomistic simulations aim to provide insights into this blank canvas and, fortunately, some studies have already suggested promising mechanisms. Still, it is urgent to consider the IDP features in simulations, so recently a lot of force fields designed to deal with IDPs have been developed. In this study, we have carried out a total of 12 μs simulations of an αS core fragment using a popular ff14SB AMBER force field and the ff14IDPSFF variation that includes a grid-based energy correction map (CMAP) method. The predicted chemical shifts from the simulations and those measured from the αS protein in the NMR solution indicate that ff14IDPSFF reproduces the experimental data more accurately. Moreover, structural analysis exhibits opposite trends between secondary structure propensities. The ff14SB force field preserves the α-helices found in the micelle-bound αS structure, which is used as an initial conformation, while ff14IDPSFF stands out with increased structural disorder and the formation of β-sheets, which suggests that the IDP-specific force field can capture more suitable conformations representing the possible intermediate states of the fibrillation process.

Ammonia recovery from acidogenic fermentation effluents using a gas-permeable membrane contactor

A gas-permeable membrane (GPM) contactor was used to recover ammoniacal nitrogen from a synthetic and a biowaste fermentation broth under different pH (from 6 to 11) and temperatures (35 and 55 °C). Ammonia mass transfer constant (K_m) increased as pH and temperature increased. For synthetic broth, pH 10 provided the best results, when considering the K_m (9.2·10^-7 m·s^-1) and the reagents consumption (1.0 mol NaOH·mol^-1 TAN and 0.6 mol H₂SO₄·mol^-1 TAN). Biowaste fermentation generated a broth with a high concentration of ammoniacal nitrogen (4.9 g N·L^-1) and volatile fatty acids (VFA) (41.1 g COD·L^-1). Experiments using the biowaste broth showed a lower K_m (5.0·10^-7 m·s^-1 at pH 10) than the synthetic broth, related to the solution matrix and other species interference. VFAs were not detected in the trapping solution. Overall, these results show that GPM is a suitable technology to efficiently separate ammoniacal nitrogen and VFA from fermentation broths.

Unveiling the Effect of Low pH on the SARS-CoV-2 Main Protease by Molecular Dynamics Simulations

(1) Background: Main Protease (Mpro) is an attractive therapeutic target that acts in the replication and transcription of the SARS-CoV-2 coronavirus. Mpro is rich in residues exposed to protonation/deprotonation changes which could affect its enzymatic function. This work aimed to explore the effect of the protonation/deprotonation states of Mpro at different pHs using computational techniques. (2) Methods: The different distribution charges were obtained in all the evaluated pHs by the Semi-Grand Canonical Monte Carlo (SGCMC) method. A set of Molecular Dynamics (MD) simulations was performed to consider the different protonation/deprotonation during 250 ns, verifying the structural stability of Mpro at different pHs. (3) Results: The present findings demonstrate that active site residues and residues that allow Mpro dimerisation was not affected by pH changes. However, Mpro substrate-binding residues were altered at low pHs, allowing the increased pocket volume. Additionally, the results of the solvent distribution around Sγ, Hγ, Nδ1 and Hδ1 atoms of the catalytic residues Cys145 and His41 showed a low and high-water affinity at acidic pH, respectively. It which could be crucial in the catalytic mechanism of SARS-CoV-2 Mpro at low pHs. Moreover, we analysed the docking interactions of PF-00835231 from Pfizer in the preclinical phase, which shows excellent affinity with the Mpro at different pHs. (4) Conclusion: Overall, these findings indicate that SARS-CoV-2 Mpro is highly stable at acidic pH conditions, and this inhibitor could have a desirable function at this condition.

Unravelling Constant pH Molecular Dynamics in Oligopeptides with Explicit Solvation Model

An accurate description of the protonation state of amino acids is essential to correctly simulate the conformational space and the mechanisms of action of proteins or other biochemical systems. The pH and the electrochemical environments are decisive factors to define the effective pKa of amino acids and, therefore, the protonation state. However, they are poorly considered in Molecular Dynamics (MD) simulations. To deal with this problem, constant pH Molecular Dynamics (cpHMD) methods have been developed in recent decades, demonstrating a great ability to consider the effective pKa of amino acids within complex structures. Nonetheless, there are very few studies that assess the effect of these approaches in the conformational sampling. In a previous work of our research group, we detected strengths and weaknesses of the discrete cpHMD method implemented in AMBER when simulating capped tripeptides in implicit solvent. Now, we progressed this assessment by including explicit solvation in these peptides. To analyze more in depth the scope of the reported limitations, we also carried out simulations of oligopeptides with distinct positions of the titratable amino acids. Our study showed that the explicit solvation model does not improve the previously noted weaknesses and, furthermore, the separation of the titratable amino acids in oligopeptides can minimize them, thus providing guidelines to improve the conformational sampling in the cpHMD simulations.

Influence of macromolecular crowding on the charge regulation of intrinsically disordered proteins

In this work we study the coupling between ionization and conformational properties of two IDPs, histatin-5 and β-amyloid 42, in the presence of neutral and charged crowders. The latter is modeled to resemble bovine serum albumin (BSA). With this aim, semi-grand canonical Monte Carlo simulations are performed, so that the IDP charge is a dynamic property, undergoing protonation/deprotonation processes. Both ionization properties (global and specific amino acid charge and binding capacitance) and radius of gyration are analyzed in a large range of pH values and salt concentrations. Without crowder agents, the titration curve of histatin-5, a polycation, is salt-dependent while that of β-amyloid 42, a polyampholyte, is almost unaffected. The salt concentration is found to be particularly relevant at pH values where the protein binding capacitance (directly linked with charge fluctuation) is larger. Upon addition of neutral crowders, charge regulation is observed in histatin-5, while for β-amyloid 42 this effect is very small. The main mechanism for charge regulation is found to be the effective increase in the ionic strength due to the excluded volume. In the presence of charged crowders, a significant increase in the charge of both IDPs is observed in almost all the pH range. In this case, the IDP charge is altered not only by the increase in the effective ionic strength but also by its direct electrostatic interaction with the charged crowders.

Role of Charge Regulation and Fluctuations in the Conformational and Mechanical Properties of Weak Flexible Polyelectrolytes

This work addresses the role of charge regulation (CR) and the associated fluctuations in the conformational and mechanical properties of weak polyelectrolytes. Due to CR, changes in the pH-value modifies the average macromolecular charge and conformational equilibria. A second effect is that, for a given average charge per site, fluctuations can alter the intensity of the interactions by means of correlation between binding sites. We investigate both effects by means of Monte Carlo simulations at constant pH-value, so that the charge is a fluctuating quantity. Once the average charge per site is available, we turn off the fluctuations by assigning the same average charge to every site. A constant charge MC simulation is then performed. We make use of a model which accounts for the main fundamental aspects of a linear flexible polyelectrolyte that is, proton binding, angle internal rotation, bond stretching and bending. Steric excluded volume and differentiated treatment for short-range and long-range interactions are also included. This model can be regarded as a kind of “minimal” in the sense that it contains a minimum number of parameters but still preserving the atomistic detail. It is shown that, if fluctuations are activated, gauche state bond probabilities increase and the persistence length decreases, so that the polymer becomes more folded. Macromolecular stretching is also analyzed in presence of CR (the charge depends on the applied force) and without CR (the charge is fixed to the value at zero force). The analysis of the low force scaling behavior concludes that Pincus exponent becomes pH-dependent. Both, with and without CR, a transition from 1/2 at high pH-values (phantom chain) to 3/5 at low pH-values (Pincus regime) is observed. Finally, the intermediate force stretching regime is investigated. It is found that CR induces a moderate influence in the force-extension curves and persistence length (which in this force regime becomes force-dependent). It is thus concluded that the effect of CR on the stretching curves is mainly due to the changes in the average charge at zero force. It is also found that, for the cases studied, the effect of steric excluded volume is almost irrelevant compared to electrostatic interactions.

Coupling of Charge Regulation and Conformational Equilibria in Linear Weak Polyelectrolytes: Treatment of Long-Range Interactions via Effective Short-Ranged and pH-Dependent Interaction Parameters

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows for analyzing ionization and conformational equilibria on the same foot. In the present work, this approach is extended to include pH-dependent electrostatic Long-Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim, the original LR interactions are taken into account by defining effective Short-Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, which we will refer to as the Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bond. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are explicitly taken into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

Macromolecular diffusion in crowded media beyond the hard-sphere model

The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlongversus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (α) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and α are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient.

Ionization and Conformational Equilibria of Citric Acid: Delocalized Proton Binding in Solution

The microspeciation of citric acid is studied by analyzing NMR titration data. When the site binding (SB) model, which assumes fully localized proton binding to the carboxylic groups, is used to obtain microscopic energy parameters (dissociation constants, pair and triplet interaction energies between charged carboxylate groups), contradictory results are obtained. The resulting macroscopic constants are in very good agreement with the values reported in the literature using potentiometry. However, the found pair interaction energy between the terminal carboxylates and the triplet interaction energy are physically meaningless. To solve this apparent contradiction, we consider the possibility of delocalized proton binding, so that the proton can be exchanged at high velocity in the NMR time scale through short, strong, low-barrier (SSLB) hydrogen bonds. With this aim, ab initio MP2 calculations using the SMD polarizable continuum model for the solvent were performed and the fully roto-microspeciation elucidated. First, fully localized proton binding was assumed, and the resulting microstate probabilities are in reasonable agreement with those reported in previous works that use selective blocking of the carboxylic groups. They are, however, in clear disagreement with the microstate probabilities derived from the NMR titration data, which predict, within a very narrow confidence interval, a unique microspecies for the symmetric di-ionized form. Moreover, counterintuitively, the interaction between terminal charged groups is much larger than that between central and terminal groups. As a consequence, we have explored the possibility of delocalized proton binding by calculating the energy of intermediate proton positions between two carbolxylic groups. The results reveal that the exchange of the proton through the hydrogen bonds is in some cases produced without energetic barrier. This effect is specially relevant in the di-ionized form, with all the most stable conformations forming a SSLB, which together would constitute the only microstate detected by NMR. An alternative reaction scheme for the ionization process, based on proton delocalization, is proposed.

Is the tiger shark Galeocerdo cuvier a coastal species? Expanding its distribution range in the Atlantic Ocean using at-sea observer data

The occurrence of tiger shark Galeocerdo cuvier in the Atlantic Ocean was assessed using at-sea observer data from multiple pelagic longline fisheries. Geographic positions of 2764 G. cuvier recorded between 1992 and 2013 and covering a wide area of the Atlantic Ocean were compared with the currently accepted distribution ranges of the species. Most records fell outside those ranges in both the Southern and Northern Hemispheres, which strongly suggests that the distribution range of G. cuvier in the open ocean is considerably larger than previously described.

Macromolecular crowding effect upon in vitro enzyme kinetics: mixed activation-diffusion control of the oxidation of NADH by pyruvate catalyzed by lactate dehydrogenase

Enzyme kinetics studies have been usually designed as dilute solution experiments, which differ substantially from in vivo conditions. However, cell cytosol is crowded with a high concentration of molecules having different shapes and sizes. The consequences of such crowding in enzymatic reactions remain unclear. The aim of the present study is to understand the effect of macromolecular crowding produced by dextran of different sizes and at diverse concentrations in the well-known reaction of oxidation of NADH by pyruvate catalyzed by L-lactate dehydrogenase (LDH). Our results indicate that the reaction rate is determined by both the occupied volume and the relative size of dextran obstacles with respect to the enzyme present in the reaction. Moreover, we analyzed the influence of macromolecular crowding on the Michaelis-Menten constants, vmax and Km. The obtained results show that only high concentrations and large sizes of dextran reduce both constants suggesting a mixed activation-diffusion control of this enzymatic reaction due to the dextran crowding action. From our knowledge, this is the first experimental study that depicts mixed activation-diffusion control in an enzymatic reaction due to the effect of crowding.

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in a three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media. These results underline that the pattern of the spatial partitioning of the obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.

Effective affinity distribution for the binding of metal ions to a generic fulvic acid in natural waters

The effective distribution of affinities (Conditional Affinity Spectrum, CAS) seen by a metal ion binding to a humic substance under natural water conditions is derived and discussed within the NICA-Donnan model. Analytical expressions for the average affinity of these distributions in general multi-ion mixtures are reported here for the first time. These expressions enable a simple evaluation of the effect of all interfering cations on the affinity distribution of a given one. We illustrate this methodology by plotting the affinity spectra of a generic fulvic acid for 14 different cations in the presence of major inorganic ions and trace metals at pH and concentration values representative of a river water. The distribution of occupied sites and their average affinity at the typical freshwater conditions are also reported for each ion. The CAS allows usto distinguish three groups of cations: (a) Al, H, Pb, Hg, and Cr, which are preferentially bound to the phenolic sites of the fulvic ligand; (b) Ca, Mg, Cd, Fe(II), and Mn, which display a greater effective affinity for carboxylic sites, in contrast to what would be expected from their individual complexation parameters; and (c) Fe(III), Cu, Zn, and Ni, for which phenolic and carboxylic distributions are overlapped.

Conditional affinity spectra of Pb2+-humic acid complexation from data obtained with AGNES

The new electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) has been applied to follow Pb2+ complexation to Purified Aldrich Humic Acid. A refined methodology of AGNES, allowing considerably larger gains, reached free metal ion concentrations down to subnanomolar values in a reasonable deposition time due to the lability and mobility of these complexes. Further insights into the meaning of the binding data, fitted to a NICA (Non Ideal Competitive Adsorption) isotherm, can be obtained with the concept of conditional affinity spectrum (CAS). For this purpose, we present the analytical expression for the CAS of NICA isotherm and show the CAS distributions for the Pb binding at fixed pH. Results reveal that the underlying spectra of each elementary distribution of the bimodal NICA evolve with pH yielding different overlapping and nonsymmetrical distributions. A non-negligible occupation of phenolic and carboxylic sites by Pb2+ takes place in the range of 4 < pH < 9.

A hierarchical approach to cooperativity in macromolecular and self-assembling binding systems

The study of complex macromolecular binding systems reveals that a high number of states and processes are involved in their mechanism of action, as has become more apparent with the sophistication of the experimental techniques used. The resulting information is often difficult to interpret because of the complexity of the scheme (large size and profuse interactions, including cooperative and self-assembling interactions) and the lack of transparency that this complexity introduces into the interpretation of the indexes traditionally used to describe the binding properties. In particular, cooperative behaviour can be attributed to very different causes, such as direct chemical modification of the binding sites, conformational changes in the whole structure of the macromolecule, aggregation processes between different subunits, etc. In this paper, we propose a novel approach for the analysis of the binding properties of complex macromolecular and self-assembling systems. To quantify the binding behaviour, we use the global association quotient defined as K(c) = [occupied sites]/([free sites] L), L being the free ligand concentration. K(c) can be easily related to other measures of cooperativity (such as the Hill number or the Scatchard plot) and to the free energies involved in the binding processes at each ligand concentration. In a previous work, it was shown that K(c) could be decomposed as an average of equilibrium constants in two ways: intrinsic constants for Adair binding systems and elementary constants for the general case. In this study, we show that these two decompositions are particular cases of a more general expression, where the average is over partial association quotients, associated with subsystems from which the system is composed. We also show that if the system is split into different subsystems according to a binding hierarchy that starts from the lower, microscopic level and ends at the higher, aggregation level, the global association quotient can be decomposed following the hierarchical levels of macromolecular organisation. In this process, the partial association quotients of one level are expressed, in a recursive way, as a function of the partial quotients of the level that is immediately below, until the microscopic level is reached. As a result, the binding properties of very complex macromolecular systems can be analysed in detail, making the mechanistic explanation of their behaviour transparent. In addition, our approach provides a model-independent interpretation of the intrinsic equilibrium constants in terms of the elementary ones.

Competitive ion complexation to polyelectrolytes: determination of the stepwise stability constants. The Ca2+/H+/polyacrylate system

This work presents a new methodology aimed at obtaining the stepwise stability constants corresponding to the binding of ions (or other small molecules) to macromolecular ligands having a large number of sites. For complexing agents with a large number of sites, very simple expressions for the stepwise stability constants arise. Such expressions are model-independent; that is, they allow the determination of the stepwise stability constants without making any previous assumption of the detailed complexation mechanism. The formalism is first presented for a single complexing ion and further extended to competitive systems where the competing ions can display, in general, different stoichiometric relationships. These ideas are applied to the analysis of experimental titrations corresponding to competitive binding of calcium ions to poly(acrylic acid) for different pH values and ionic strengths. Intrinsic stability constants were estimated from the stepwise stability constants (by removing the corresponding statistical factor), and split into specific and electrostatic contributions (by means of the Poisson-Boltzmann equation). After this treatment, the specific proton binding energies showed almost no dependence on the coverage and ionic strength. Likewise, for the range of concentrations studied, the specific component of the intrinsic stability constants of the calcium ions, calculated assuming bidentate binding of Ca to neighboring groups of a linear chain, is almost independent of the calcium and proton coverage and ionic strength.

Effect of the surface charge discretization on electric double layers: A Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.

Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements

Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero-order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.

Conditional equilibrium constants in multicomponent heterogeneous adsorption: The conditional affinity spectrum

The concept of conditional stability constant is extended to the competitive binding of small molecules to heterogeneous surfaces or macromolecules via the introduction of the conditional affinity spectrum (CAS). The CAS describes the distribution of effective binding energies experienced by one complexing agent at a fixed concentration of the rest. We show that, when the multicomponent system can be described in terms of an underlying affinity spectrum [integral equation (IE) approach], the system can always be characterized by means of a CAS. The thermodynamic properties of the CAS and its dependence on the concentration of the rest of components are discussed. In the context of metal/proton competition, analytical expressions for the mean (conditional average affinity) and the variance (conditional heterogeneity) of the CAS as functions of pH are reported and their physical interpretation discussed. Furthermore, we show that the dependence of the CAS variance on pH allows for the analytical determination of the correlation coefficient between the binding energies of the metal and the proton. Nonideal competitive adsorption isotherm and Frumkin isotherms are used to illustrate the results of this work. Finally, the possibility of using CAS when the IE approach does not apply (for instance, when multidentate binding is present) is explored.

Multisyringe flow injection analysis of stable and radioactive strontium in samples of environmental interest

A multisyringe flow injection (MSFIA) method for the determination of stable and radioactive strontium, using a solid phase resin (Sr-Resin), has been developed. Strontium concentrations are determined by atomic emission spectroscopy and by a low background proportional counter. The method has been applied to different samples (water, milk and soil) of environmental interest. The LLD of the stable and radioactive Sr were 10 microg/l and 0.01 Bq, respectively. The standard deviation of the separation procedure is 2% (n=10).

Affinity distribution functions in multicomponent heterogeneous adsorption. Analytical inversion of isotherms to obtain affinity spectra

An analytical approach for the interpretation of multicomponent heterogeneous adsorption or complexation isotherms in terms of multidimensional affinity spectra is presented. Fourier transform, applied to analyze the corresponding integral equation, leads to an inversion formula which allows the computation of the multicomponent affinity spectrum underlying a given competitive isotherm. Although a different mathematical methodology is used, this procedure can be seen as the extension to multicomponent systems of the classical Sips's work devoted to monocomponent systems. Furthermore, a methodology which yields analytical expressions for the main statistical properties (mean free energies of binding and covariance matrix) of multidimensional affinity spectra is reported. Thus, the level of binding correlation between the different components can be quantified. It has to be highlighted that the reported methodology does not require the knowledge of the affinity spectrum to calculate the means, variances, and covariance of the binding energies of the different components. Nonideal competitive consistent adsorption isotherm, widely used in metal/proton competitive complexation to environmental macromolecules, and Frumkin competitive isotherms are selected to illustrate the application of the reported results. Explicit analytical expressions for the affinity spectrum as well as for the matrix correlation are obtained for the NICCA case.

Sensitivity analysis of metabolic cascades catalyzed by bifunctional enzymes

Covalent modification/demodification cycles are common in metabolism. When the modification and demodification steps are carried out by two independent enzymes, the degree of modification can be ultrasensitive to the total concentration of either catalyst. We recently showed that the degree of modification of a target molecule cannot exhibit ultrasensitivity to the free concentrations of effectors that decide whether a bifunctional enzyme acts as modifier or demodifier. However, here we can now demonstrate that the degree of modification of a target molecule can display ultrasensitivity to the total, rather than free, concentrations of such effectors. Our results clarify some general aspects of ultrasensitive responses to effectors, including competitive inhibitors, in mono-cyclic cascades.

Product dependence and bifunctionality compromise the ultrasensitivity of signal transduction cascades

Covalent modification cycles are ubiquitous. Theoretical studies have suggested that they serve to increase sensitivity. However, this suggestion has not been corroborated experimentally in vivo. Here, we demonstrate that the assumptions of the theoretical studies, i.e., irreversibility and absence of product inhibition, were not trivial: when the conversion reactions are close to equilibrium or saturated by their product, "zero-order" ultrasensitivity disappears. For high sensitivities to arise, not only substrate saturation (zero-order) but also high equilibrium constants and low product saturation are required. Many covalent modification cycles are catalyzed by one bifunctional 'ambiguous' enzyme rather than by two independent proteins. This makes high substrate concentration and low product concentration for both reactions of the cycle inconsistent; such modification cycles cannot have high responses. Defining signal strength as ratios of modified (e.g., phosphorylated) over unmodified protein, signal-to-signal response sensitivity equals 1: signal strength should remain constant along a cascade of ambiguous modification cycles. We also show that the total concentration of a signalling effector protein cannot affect the signal emanating from a modification cycle catalyzed by an ambiguous enzyme if the ratio of the two forms of the effector protein is not altered. This finding may explain the experimental result that the pivotal signal transduction protein PII plus its paralogue GlnK do not control steady-state N-signal transduction in Escherichia coli. It also rationalizes the absence of strong phenotypes for many signal-transduction proteins. Emphasis on extent of modification of these proteins is perhaps more urgent than transcriptome analysis.