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.     

Explicit formulation of titration models for isothermal titration calorimetry

Isothermal titration calorimetry (ITC) produces a differential heat signal with respect to the total titrant concentration. This feature gives ITC excellent sensitivity for studying the thermodynamics of complex biomolecular interactions in solution. Currently, numerical methods for data fitting are based primarily on indirect approaches rooted in the usual practice of formulating biochemical models in terms of integrated variables. Here, a direct approach is presented wherein ITC models are formulated and solved as numerical initial value problems for data fitting and simulation purposes. To do so, the ITC signal is cast explicitly as a first-order ordinary differential equation (ODE) with total titrant concentration as independent variable and the concentration of a bound or free ligand species as dependent variable. This approach was applied to four ligand-receptor binding and homotropic dissociation models. Qualitative analysis of the explicit ODEs offers insights into the behavior of the models that would be inaccessible to indirect methods of analysis. Numerical ODEs are also highly compatible with regression analysis. Since solutions to numerical initial value problems are straightforward to implement on common computing platforms in the biochemical laboratory, this method is expected to facilitate the development of ITC models tailored to any experimental system of interest.     

A graphical user interface for BIOEQS: a program for simulating and analyzing complex biomolecular interactions

BIOEQS is a global analysis and simulation program for complex biomolecular interaction data developed during the 1990s. Its continued usefulness derives from the fact that it is based on a numerical solver for complex coupled biological equilibria rather than on closed-form analytical equations for the binding isotherms. Therefore, it is quite versatile, allowing easy testing of multiple binding models and analysis of systems too complex for closed-form solutions. However, a major drawback to a generalized use of this program has been the lack of a graphical user interface (GUI) for setting up the binding models and experimental conditions as well as for visualizing the results. We present here a new GUI for BIOEQS that should be useful in both research and teaching applications.     

Perturbation-based Markovian Transmission Model for Probing Allosteric Dynamics of Large Macromolecular Assembling: A Study of GroEL-GroES

Large macromolecular assemblies are often important for biological processes in cells. Allosteric communications between different parts of these molecular machines play critical roles in cellular signaling. Although studies of the topology and fluctuation dynamics of coarse-grained residue networks can yield important insights, they do not provide characterization of the time-dependent dynamic behavior of these macromolecular assemblies. Here we develop a novel approach called Perturbation-based Markovian Transmission (PMT) model to study globally the dynamic responses of the macromolecular assemblies. By monitoring simultaneous responses of all residues (>8,000) across many (>6) decades of time spanning from the initial perturbation until reaching equilibrium using a Krylov subspace projection method, we show that this approach can yield rich information. With criteria based on quantitative measurements of relaxation half-time, flow amplitude change, and oscillation dynamics, this approach can identify pivot residues that are important for macromolecular movement, messenger residues that are key to signal mediating, and anchor residues important for binding interactions. Based on a detailed analysis of the GroEL-GroES chaperone system, we found that our predictions have an accuracy of 71–84% judged by independent experimental studies reported in the literature. This approach is general and can be applied to other large macromolecular machineries such as the virus capsid and ribosomal complex.     

MIAX: a new paradigm for modeling biomacromolecular interactions and complex formation in condensed phases

A new paradigm is proposed for modeling biomacromolecular interactions and complex formation in solution (protein-protein interactions so far in this report) that constitutes the scaffold of the automatic system MIAX (acronym for Macromolecular Interaction Assessment X). It combines in a rational way a series of computational methodologies, the goal being the prediction of the most native-like protein complex that may be formed when two isolated (unbound) protein monomers interact in a liquid environment. The overall strategy consists of first inferring putative precomplex structures by identification of binding sites or epitopes on the proteins surfaces and a simultaneous rigid-body docking process using geometric instances alone. Precomplex configurations are defined here as all those decoys the interfaces of which comply substantially with the inferred binding sites and whose free energy values are lower. Retaining all those precomplex configurations with low energies leads to a reasonable number of decoys for which a flexible treatment is amenable. A novel algorithm is introduced here for automatically inferring binding sites in proteins given their 3-D structure. The procedure combines an unsupervised learning algorithm based on the self-organizing map or Kohonen network with a 2-D Fourier spectral analysis. To model interaction, the potential function proposed here plays a central role in the system and is constituted by empirical terms expressing well-characterized factors influencing biomacromolecular interaction processes, essentially electrostatic, van der Waals, and hydrophobic. Each of these procedures is validated by comparing results with observed instances. Finally, the more demanding process of flexible docking is performed in MIAX embedding the potential function in a simulated annealing optimization procedure. Whereas search of the entire configuration hyperspace is a major factor precluding hitherto systems from efficiently modeling macromolecular interaction modes and complex structures, the paradigm presented here may constitute a step forward in the field because it is shown that a rational treatment of the information available from the 3-D structure of the interacting monomers combined with conveniently selected computational techniques can assist to elude search of regions of low probability in configuration space and indeed lead to a highly efficient system oriented to solve this intriguing and fundamental biologic problem.     

Use of quantitative affinity chromatography for characterizing high-affinity interactions: binding of heparin to antithrombin III

The versatility of quantitative affinity chromatography (QAC) for evaluating the binding of macromolecular ligands to macromolecular acceptors has been increased substantially as a result of the derivation of the equations which describe the partitioning of acceptor between matrix-bound and soluble forms in terms of total, rather than free, ligand concentrations. In addition to simplifying the performance of the binding experiments, this development makes possible the application of the technique to systems characterized by affinities higher than those previously amenable to investigation by QAC. Addition of an on-line data acquisition system to monitor the concentration of partitioning solute in the liquid phase as a function of time has permitted the adoption of an empirical approach for determining the liquid-phase concentration of acceptor in the system at partition equilibrium, a development which decreases significantly the time required to obtain a complete binding curve by QAC. The application of these new QAC developments is illustrated by the determination of binding constants for the interactions of high-affinity heparin (Mr 20,300) with antithrombin III at three temperatures. Association constants of 8.0 +/- 2.2 x 10(7), 3.4 +/- 0.3 x 10(7), and 1.0 +/- 0.2 x 10(7) M-1 were observed at 15, 25, and 35 degrees C, respectively. The standard enthalpy change of -4.2 +/- 0.6 kcal/mol that is calculated from these data is in good agreement with a reported value obtained from fluorescence quenching measurements.     

Simultaneous Determination of Protein Structure and Dynamics Using Cryo-Electron Microscopy

Cryo-electron microscopy is rapidly emerging as a powerful technique to determine the structures of complex macromolecular systems elusive to other techniques. Because many of these systems are highly dynamical, characterizing their movements is also a crucial step to unravel their biological functions. To achieve this goal, we report an integrative modeling approach to simultaneously determine structure and dynamics of macromolecular systems from cryo-electron microscopy density maps. By quantifying the level of noise in the data and dealing with their ensemble-averaged nature, this approach enables the integration of multiple sources of information to model ensembles of structures and infer their populations. We illustrate the method by characterizing structure and dynamics of the integral membrane receptor STRA6, thus providing insights into the mechanisms by which it interacts with retinol binding protein and translocates retinol across the membrane.     

Biosensor analysis of the interleukin-2 receptor complex

Surface plasmon resonance (SPR) biosensor technology has been a significant addition to the evolution and refinement of methods to study macromolecular interactions. Prior to the advent of SPR, we employed a variety of biochemical and biological techniques to study the interleukin-2/interleukin-2 receptor system (IL-2/IL-2R). By combining site-directed mutagenesis, equilibrium and kinetic radioligand binding, and competitive biological assays, we and others had begun to understand many aspects of the structure-activity relationships of the IL-2/IL-2R system. Due to the complexity of the IL-2R, cell-based assays proved limited in their ability to provide quantitative information on the binding characteristics of subclasses of the IL-2 receptor. SPR technology promised to be a new and powerful approach to the quantitative analysis of complex receptor systems. To demonstrate the feasibility of this technology, we employed Biacore analysis to investigate the ligand binding characteristics of novel, pre-assembled, IL-2R coiled-coil complexes. The results of these studies, although limited by instrumentation and data analysis, clearly established the utility of this method. Subsequently, by incorporating advancements in both of these areas, we have been able to carry out detailed kinetic analyses of the binding properties of individual IL-2R subunits as well as heteromeric complexes on the surface of a biosensor. Therefore, SPR biosensor analysis combined with other established analytical methods has proven to be a powerful tool for the analysis of complex hematopoietic receptor systems. Published in 1999 by John Wiley & Sons, Ltd.     

A new geometric biclustering algorithm based on the Hough transform for analysis of large-scale microarray data

Biclustering is an important tool in microarray analysis when only a subset of genes co-regulates in a subset of conditions. Different from standard clustering analyses, biclustering performs simultaneous classification in both gene and condition directions in a microarray data matrix. However, the biclustering problem is inherently intractable and computationally complex. In this paper, we present a new biclustering algorithm based on the geometrical viewpoint of coherent gene expression profiles. In this method, we perform pattern identification based on the Hough transform in a column-pair space. The algorithm is especially suitable for the biclustering analysis of large-scale microarray data. Our studies show that the approach can discover significant biclusters with respect to the increased noise level and regulatory complexity. Furthermore, we also test the ability of our method to locate biologically verifiable biclusters within an annotated set of genes.     

OS-FRET: a new one-sample method for improved FRET measurements

Fluorescence resonance energy transfer (FRET) is a powerful tool for studying macromolecular assemblies in vitro under near-physiological conditions. Here we present a new type of one-sample FRET (OS-FRET) method employing a novel, nonfluorescent methanethiosulfonate-linked acceptor that can be reversibly coupled to a target sulfhydryl residue via a disulfide bond. After the quenched donor emission is quantitated, the acceptor is removed by reduction, allowing measurement of unquenched donor emission in the same sample. Previous one-sample methods provide distinct advantages in specific FRET applications. The new OS-FRET method is a generalizable spectrochemical approach that can be applied to macromolecular systems lacking essential disulfide bonds and eliminates the potential systematic errors of some earlier one-sample methods. In addition, OS-FRET enables quantitative FRET measurements in virtually any fluorescence spectrometer or detection device. Compared to conventional multisample FRET methods, OS-FRET conserves sample, increases the precision of data, and shortens the time per measurement. The utility of the method is illustrated by its application to a protein complex of known structure formed by CheW and the P4-P5 fragment of CheA, both from Thermotoga maritima. The findings confirm the practicality and advantages of OS-FRET. Anticipated applications of OS-FRET include analysis of macromolecular structure, binding and conformational dynamics, and high-throughput screening for interactions and inhibitors.     

The fundamental nature of life as a chemical system: the part played by inorganic elements

In this article we show why inorganic metal elements from the environment were an essential part of the origin of living aqueous systems of chemicals in flow. Unavoidably such systems have many closely fixed parameters, related to thermodynamic binding constants, for the interaction of the essential exchangeable inorganic metal elements with both inorganic and organic non-metal materials. The binding constants give rise to fixed free metal ion concentration profiles for different metal ions and ligands in the cytoplasm of all cells closely related to the Irving-Williams series. The amounts of bound elements depend on the organic molecules present as well as these free ion concentrations. This system must have predated coding which is probably only essential for reproductive life. Later evolution in changing chemical environments became based on the development of extra cytoplasmic compartments containing quite different energised free (and bound) element contents but in feed-back communication with the central primitive cytoplasm which changed little. Hence species multiplied late in evolution in large part due to the coupling with the altered inorganic environment.     

Analysis of ligand binding curves in terms of species fractions

The ligand binding curve for a macromolecular system presents the average number or ligand molecules bound per macromolecule as a function of the chemical potential or the logarithm of the ligand concentration. We show that various observable properties of this curve, for example its asymptotes and derivatives, are expressible in terms of linear combinations of the mole fractions α_i of macromolecules binding i molecules of ligand. Whenever enough such properties of the binding curve are known, the linear equations in α_i can be solved to give the mole fractions of each of the various macromolecular species. An application of these results is that a Hill plot for hemoglobin-ligand equilibrium where the asymptotes approach unit slope can be made to yield the four Adair constants by a simple algebraic method. A second use is that a knowledge of the first and second derivatives of the binding curve at points along the curve can yield the species fractions as functions of the degree of saturation without direct knowledge of the ligand binding constants. These methods are illustrated by some numerical examples.     

Transition modes in Ising networks: an approximate theory for macromolecular recognition.

For a statistical lattice, or Ising network, composed of N identical units existing in two possible states, 0 and 1, and interacting according to a given geometry, a set of values can be found for the mean free energy of the 0-->1 transition of a single unit. Each value defines a transition mode in an ensemble of nu N = 3N - 2N possible values and reflects the role played by intermediate states in shaping the energetics of the system as a whole. The distribution of transition modes has a number of intriguing properties. Some of them apply quite generally to any Ising network, regardless of its dimension, while others are specific for each interaction geometry and dimensional embedding and bear on fundamental aspects of analytical number theory. The landscape of transition modes encapsulates all of the important thermodynamic properties of the network. The free energy terms defining the partition function of the system can be derived from the modes by simple transformations. Classical mean-field expressions can be obtained from consideration of the properties of transition modes in a rather straightforward way. The results obtained in the analysis of the transition mode distributions have been used to develop an approximate treatment of the problem of macromolecular recognition. This phenomenon is modeled as a cooperative process that involves a number of recognition subsites across an interface generated by the binding of two macromolecular components. The distribution of allowed binding free energies for the system is shown to be a superposition of Gaussian terms with mean and variance determined a priori by the theory. Application to the analysis of the biologically interaction of thrombin with hirudin has provided some useful information on basic aspects of the interaction, such as the number of recognition subsites involved and the energy balance for binding and cooperative coupling among them. Our results agree quite well with information derived independently from analysis of the crystal structure of the thrombin-hirudin complex.     

The interaction of the polyene antibiotic lucensomycin with cholesterol in erythrocyte membranes and in model systems. III. Characterization of spectral parameters.

The variations of optical density and fluorescence of lucensomycin are good indices of the binding of this polyenic antibiotic to membranes. The former parameter reflects more generally the binding to any site present in the membrane, while the latter is more specific for binding to cholesterol. The chromophore of the lucensomycin-cholesterol complex has a relatively long lifetime, is almost immobile in the membrane, and is not accessible to water-soluble fluorescence-quenching agents. The stoichiometry, evaluated fluorometrically, corresponds to about two cholesterol molecules per polyene. In colloidal cholesterol suspensions, the extent of binding as a function of free polyene concentration is described by rectangular hyperbolae, the dissociation constant being, however, dependent on the sterol concentration. In erythrocyte membranes, on the other hand, and even more markedly in model systems containing appropriate solvents, the combination between lucensomycin and the sterol sites is described by sigmoid titration curves, indicative of cooperative effects, and probably due to solvation of cholesterol.     

Predicting oligomeric assemblies: N-mers a primer

Multi-protein complexes play key roles in many biological processes. However, since the structures of these assemblies are hard to resolve experimentally, the detailed mechanism of how they work cooperatively in the cell has remained elusive. Similarly, recent advances on in silico prediction of protein-protein interactions have so far avoided this difficult problem. In this paper, we present a general algorithm to predict molecular assemblies of homo-oligomers. Given the number of N-mers and the 3D structure of one monomer, the method samples all the possible symmetries that N-mers can be assembled. Based on a scoring function that clusters the low free energy structures at each binding interface, the algorithm predicts the complex structure as well as the symmetry of the protein assembly. The method is quite general and does not involve any free parameters. The algorithm has been implemented as a public server and integrated to the protein-protein complex prediction server ClusPro. Using this application, we validated predictions for trimers, tetramers (discriminating between dimer of dimers and 4-fold symmetry structures), pentamers and hexamers (discriminating between trimer of dimers, dimer of trimers, and 6-fold symmetry structures), for a total of 107 assemblies. For 85% of the multimers, the server predicts the complex structure within an average rms deviation of 2A from the full crystal. For complexes that involve more than one binding interface, the cluster size at each surface provides a strong indication as to which interface forms first. With improving scoring functions and computer power, our multimer docking approach could be used as a framework to address the more general problem of multi-protein assemblies.     

MeltMan: Optimization,Evaluation, and Universal Application of a qPCR System Integrating the TaqMan qPCR and Melting Analysis into a Single Assay

In the present work, we optimised and evaluated a qPCR system integrating 6-FAM (6-carboxyfluorescein)-labelled TaqMan probes and melting analysis using the SYTO 82 (S82) DNA binding dye in a single reaction. We investigated the influence of the S82 on various TaqMan and melting analysis parameters and defined its optimal concentration. In the next step, the method was evaluated in 36 different TaqMan assays with a total of 729 paired reactions using various DNA and RNA templates, including field specimens. In addition, the melting profiles of interest were correlated with the electrophoretic patterns. We proved that the S82 is fully compatible with the FAM-TaqMan system. Further, the advantages of this approach in routine diagnostic TaqMan qPCR were illustrated with practical examples. These included solving problems with flat or other atypical amplification curves or even false negativity as a result of probe binding failure. Our data clearly show that the integration of the TaqMan qPCR and melting analysis into a single assay provides an additional control option as well as the opportunity to perform more complex analyses, get more data from the reactions, and obtain analysis results with higher confidence.     

Analysis of heterologous interacting systems by sedimentation velocity: curve fitting algorithms for estimation of sedimentation coefficients, equilibrium and kinetic constants

Analytical ultracentrifugation (AUC) has played and will continue to play an important role in the investigation of protein-protein, protein-DNA and protein-ligand interactions. A major advantage of AUC over other methods is that it allows the analysis of systems free in solution in nearly any buffer without worry about spurious interactions with a supporting matrix. Large amounts of high-quality data can be acquired in relatively short times. Advances in software for the treatment of AUC data over the last decade have eliminated many of the tedious aspects of AUC data analysis, allowing relatively rapid analysis of complicated systems that were previously unapproachable. A software package called sedanal is described that can perform global fits to AUC sedimentation velocity data obtained for both interacting and non-interacting, macromolecular multi-species, multi-component systems, by combining data from multiple runs over a range of sample concentrations and component ratios. Interaction parameters include both forward and reverse rate constants, or equilibrium constants, for each reaction, as well as concentration dependence of both sedimentation and diffusion coefficients. sedanal fits to time-difference data to eliminate time-independent systematic errors inherent in AUC data. The sedanal software package is based on the use of finite-element numerical solutions of the Lamm equation.     

A “Fuzzy”-Logic Language for Encoding Multiple Physical Traits in Biomolecules

To carry out their activities, biological macromolecules balance different physical traits, such as stability, interaction affinity, and selectivity. How such often opposing traits are encoded in a macromolecular system is critical to our understanding of evolutionary processes and ability to design new molecules with desired functions. We present a framework for constraining design simulations to balance different physical characteristics. Each trait is represented by the equilibrium fractional occupancy of the desired state relative to its alternatives, ranging from none to full occupancy, and the different traits are combined using Boolean operators to effect a “fuzzy”-logic language for encoding any combination of traits. In another paper, we presented a new combinatorial backbone design algorithm AbDesign where the fuzzy-logic framework was used to optimize protein backbones and sequences for both stability and binding affinity in antibody-design simulation. We now extend this framework and find that fuzzy-logic design simulations reproduce sequence and structure design principles seen in nature to underlie exquisite specificity on the one hand and multispecificity on the other hand. The fuzzy-logic language is broadly applicable and could help define the space of tolerated and beneficial mutations in natural biomolecular systems and design artificial molecules that encode complex characteristics.     

Molecular dynamics and free energy analysis of neuraminidase-ligand interactions

We report molecular dynamics calculations of neuraminidase in complex with an inhibitor, 4-amino-2-deoxy-2,3-didehydro-N-acetylneuraminic acid (N-DANA), with subsequent free energy analysis of binding by using a combined molecular mechanics/continuum solvent model approach. A dynamical model of the complex containing an ionized Glu119 amino acid residue is found to be consistent with experimental data. Computational analysis indicates a major van der Waals component to the inhibitor-neuraminidase binding free energy. Based on the N-DANA/neuraminidase molecular dynamics trajectory, a perturbation methodology was used to predict the binding affinity of related neuraminidase inhibitors by using a force field/Poisson-Boltzmann potential. This approach, incorporating conformational search/local minimization schemes with distance-dependent dielectric or generalized Born solvent models, correctly identifies the most potent neuraminidase inhibitor. Mutation of the key ligand four-substituent to a hydrogen atom indicates no favorable binding free energy contribution of a hydroxyl group; conversely, cationic substituents form favorable electrostatic interactions with neuraminidase. Prospects for further development of the method as an analysis and rational design tool are discussed.