Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape

The size and shape of macromolecules such as proteins and nucleic acids play an important role in their functions. Prior efforts to quantify these properties have been based on various discretization or tessellation procedures involving analytical or numerical computations. In this article, we present an analytically exact method for computing the metric properties of macromolecules based on the alpha shape theory. This method uses the duality between alpha complex and the weighted Voronoi decomposition of a molecule. We describe the intuitive ideas and concepts behind the alpha shape theory and the algorithm for computing areas and volumes of macromolecules. We apply our method to compute areas and volumes of a number of protein systems. We also discuss several difficulties commonly encountered in molecular shape computations and outline methods to overcome these problems. Proteins 33:1–17, 1998. © 1998 Wiley-Liss, Inc.     

The MIDAS database system

The Molecular Interactive Display and Simulation (MIDAS) database system is a hierarchical database specifically designed for complex macromolecular models, such as proteins and nucleic acids. Each molecular model consists of one or more molecules made up of a linear sequence of smaller units that we refer to loosely as “residues.” Each of these residue units, in turn, is composed of one or more even smaller units called “atoms.” The complete model might consist of a single component molecule, as in the case of a water molecule, or it might be a long chain of more complex residue components, such as in the case of amino acid and nucleic acid sequences. Complex functional groups, such as heme and NADH, can also be specified as single subunit components, and the user can then incorporate these groups into a larger model to form a single complex.The various model component types are defined as arbitrary graphs of atoms with defined starting and ending points. The component type thus defines the connectivity of atoms for that component, as well as the linkage atoms to adjacent model components. Molecular “data” are stored in the “leaves” of the database hierarchy and are therefore directly associated with the atoms of a particular residue component, the component having been specified by type and position in the sequence of residues making up the chain. Individual atom data, however, are not restricted to a specific format or quantity, thereby allowing both flexibility and future extensions to easily be made to the database.     

Design of interacting multi-stable nucleic acids for molecular information processing

Despite an exponential increase in computing power over the past decades, present information technology falls far short of expectations in areas such as cognitive systems and micro robotics. Organisms demonstrate that it is possible to implement information processing in a radically different way from what we have available in present technology, and that there are clear advantages from the perspective of power consumption, integration density, and real-time processing of ambiguous data. Accordingly, the question whether the current silicon substrate and associated computing paradigm is the most suitable approach to all types of computation has come to the fore. Macromolecular materials, so successfully employed by nature, possess uniquely promising properties as an alternate substrate for information processing. The two key features of macromolecules are their conformational dynamics and their self-assembly capabilities. The purposeful design of macromolecules capable of exploiting these features has proven to be a challenge, however, for some groups of molecules it is increasingly practicable. We here introduce an algorithm capable of designing groups self-assembling of nucleic acid molecules with multiple conformational states. Evaluation using natural and artificially designed nucleic acid molecules favours this algorithm significantly, as compared to the probabilistic approach. Furthermore, the thermodynamic properties of the generated candidates are within the same approximation as the customised trans-acting switching molecules reported in the laboratory.     

Diffusional anisotropy in collagenous tissues: fluorescence imaging of continuous point photobleaching

Molecular transport in avascular collagenous tissues such as articular cartilage occurs primarily via diffusion. The presence of ordered structures in the extracellular matrix may influence the local transport of macromolecules, leading to anisotropic diffusion depending on the relative size of the molecule and that of extracellular matrix structures. Here we present what we believe is a novel photobleaching technique for measuring the anisotropic diffusivity of macromolecules in collagenous tissues. We hypothesized that macromolecular diffusion is anisotropic in collagenous tissues, depending on molecular size and the local organization of the collagen structure. A theoretical model and experimental protocol for fluorescence imaging of continuous point photobleaching was developed to measure diffusional anisotropy. Significant anisotropy was observed in highly ordered collagenous tissues such as ligament, with diffusivity ratios >2 along the fiber direction compared to the perpendicular direction. In less-ordered tissues such as articular cartilage, diffusional anisotropy was dependent on site in the tissue and size of the diffusing molecule. Anisotropic diffusion was also dependent on the size of the diffusing molecule, with greatest anisotropy observed for larger molecules. These findings suggest that diffusional transport of macromolecules is anisotropic in collagenous tissues, with higher rates of diffusion along primary orientation of collagen fibers.     

Exploring biomolecular recognition using optical biosensors.

Understanding the basic forces that determine molecular recognition helps to elucidate mechanisms of biological processes and facilitates discovery of innovative biotechnological methods and materials for therapeutics, diagnostics, and separation science. The ability to measure interaction properties of biological macromolecules quantitatively across a wide range of affinity, size, and purity is a growing need of studies aimed at characterizing biomolecular interactions and the structural elements that drive them. Optical biosensors have provided an increasingly impactful technology for such biomolecular interaction analyses. These biosensors record the binding and dissociation of macromolecules in real time by transducing the accumulation of mass of an analyte molecule at the sensor surface coated with ligand molecule into an optical signal. Interactions of analytes and ligands can be analyzed at a microscale and without the need to label either interactant. Sensors enable the detection of bimolecular interaction as well as multimolecular assembly. Most notably, the method is quantitative and kinetic, enabling determination of both steady-state and dynamic parameters of interaction. This article describes the basic methodology of optical biosensors and presents several examples of its use to investigate such biomolecular systems as cytokine growth factor-receptor recognition, coagulation factor assembly, and virus-cell docking.     

Electrophoresis with continuous scanning densitometry: separation of cells in a density gradient.

An instrument and procedure for electrophoresis with continuous optical scanping densitometry, automated data processing, and related methodology are described for the continuous analysis of electrophoresis and unity gravity sedimentation of macromolecules or cells in a static density gradient system. The instrument consists of a dual-beam spectrophotometer, a scanning stage and scanner control unit, an electrophoresis cell cassette, a filling/purging/cooling module, an analog-to-digital converter, and a digital data-logger. The distribution of cells is monitored repetitively during migration by absorbance measurements at any wavelength in the 200–800-nm range. A computer program provides the statistical analysis of each peak (baseline correction, smoothing, area, mean, standard deviation, skewness, and kurtosis) which can be further utilized for computing additional parameters, such as resolution and heterogeneity. A mixture of human and rabbit erythrocytes were used as a model system to evaluate the performance of the instrument and demonstrate some of its capabilities.     

Protein heat capacity reflects the dynamics of enthalpy exchange between the single macromolecule and the surroundings

Heat capacity has played a prominent role in relating macroscopic and microscopic properties of small molecules and crystals. However, its diagnostic power can also be used for macromolecules such as proteins. It is shown in the present study that the macroscopically observed protein heat capacity provides direct access to the thermodynamic state of the single protein molecule. The new model of the physical basis of protein heat capacity emphasizes the dynamic nature of protein molecules. It incorporates equilibrium fluctuations as an integral constituent and shows that the increase in the magnitude of equilibrium fluctuations is coupled to an increase in the enthalpy flux between the individual protein molecule and its surroundings. Proteins 2000;41:86–92. © 2000 Wiley‐Liss, Inc.     

Stable coordination of the inhibitory Ca2+ ion at the metal ion-dependent adhesion site in integrin CD11b/CD18 by an antibody-derived ligand aspartate: implications for integrin regulation and structure-based drug design

A central feature of integrin interaction with physiologic ligands is the monodentate binding of a ligand carboxylate to a Mg(2+) ion hexacoordinated at the metal ion-dependent adhesion site (MIDAS) in the integrin A domain. This interaction stabilizes the A domain in the high-affinity state, which is distinguished from the default low-affinity state by tertiary changes in the domain that culminate in cell adhesion. Small molecule ligand-mimetic integrin antagonists act as partial agonists, eliciting similar activating conformational changes in the A domain, which has contributed to paradoxical adhesion and increased patient mortality in large clinical trials. As with other ligand-mimetic integrin antagonists, the function-blocking mAb 107 binds MIDAS of integrin CD11b/CD18 A domain (CD11bA), but in contrast, it favors the inhibitory Ca(2+) ion over the Mg(2+) ion at MIDAS. We determined the crystal structures of the Fab fragment of mAb 107 complexed to the low- and high-affinity states of CD11bA. Favored binding of the Ca(2+) ion at MIDAS is caused by the unusual symmetric bidentate ligation of a Fab-derived ligand Asp to a heptacoordinated MIDAS Ca(2+) ion. Binding of the Fab fragment of mAb 107 to CD11bA did not trigger the activating tertiary changes in the domain or in the full-length integrin. These data show that the denticity of the ligand Asp/Glu can modify the divalent cation selectivity at MIDAS and hence integrin function. Stabilizing the Ca(2+) ion at MIDAS by bidentate ligation to a ligand Asp/Glu may provide one approach for designing pure integrin antagonists.     

Distinct roles of beta1 metal ion-dependent adhesion site (MIDAS), adjacent to MIDAS (ADMIDAS), and ligand-associated metal-binding site (LIMBS) cation-binding sites in ligand recognition by integrin alpha2beta1

Integrin-ligand interactions are regulated in a complex manner by divalent cations, and previous studies have identified ligand-competent, stimulatory, and inhibitory cation-binding sites. In collagen-binding integrins, such as alpha2beta1, ligand recognition takes place exclusively at the alpha subunit I domain. However, activation of the alphaI domain depends on its interaction with a structurally similar domain in the beta subunit known as the I-like or betaI domain. The top face of the betaI domain contains three cation-binding sites: the metal-ion dependent adhesion site (MIDAS), the ADMIDAS (adjacent to MIDAS), and LIMBS (ligand-associated metal-binding site). The role of these sites in controlling ligand binding to the alphaI domain has yet to be elucidated. Mutation of the MIDAS or LIMBS completely blocked collagen binding to alpha2beta1; in contrast mutation of the ADMIDAS reduced ligand recognition but this effect could be overcome by the activating monoclonal antibody TS2/16. Hence, the MIDAS and LIMBS appear to be essential for the interaction between alphaI and betaI, whereas occupancy of the ADMIDAS has an allosteric effect on the conformation of betaI. An activating mutation in the alpha2 I domain partially restored ligand binding to the MIDAS and LIMBS mutants. Analysis of the effects of Ca(2+), Mg(2+), and Mn(2+) on ligand binding to these mutants showed that the MIDAS is a ligand-competent site through which Mn(2+) stimulates ligand binding, whereas the LIMBS is a stimulatory Ca(2+)-binding site, occupancy of which increases the affinity of Mg(2+) for the MIDAS.     

FGO: a novel ontology for identification of ligand functional group

Small molecules play crucial role in the modulation of biological functions by interacting with specific macromolecules. Hence small molecule interactions are captured by a variety of experimental methods to estimate and propose correlations between molecular structures to their biological activities. The tremendous expanse in publicly available small molecules is also driving new efforts to better understand interactions involving small molecules particularly in area of drug docking and pharmacogenomics. We have studied and designed a functional group identification system with the associated ontology for it. The functional group identification system can detect the functional group components from given ligand structure with specific coordinate information. Functional group ontology (FGO) proposed by us is a structured classification of chemical functional group which acts as an important source of prior knowledge that may be automatically integrated to support identification, categorization and predictive data analysis tasks. We have used a new annotation method which can be used to construct the original structure from given ontological expression using exact coordinate information. Here, we also discuss about ontology-driven similarity measure of functional groups and uses of such novel ontology for pharmacophore searching and de-novo ligand designing.     

Hydraulic conductivity of polymer matrices

We demonstrate that the chondroitin sulfate proteoglycan exhibits enhanced sensitivity to the flow of water compared to other macromolecules which is in accord with their functional role in conferring compressive resistance to cartilage. In order to understand factors that may contribute to its low hydraulic conductivity, a comparative study of hydraulic conductivity, as measured by the sedimentation velocity technique is made of various macromolecules representing variations in charge density, chemical composition, thermodynamic nonideality, size and flexibility. The polymers examined were dextran, poly(ethylene glycol), poly(vinyl alcohol), albumin, and dextran sulfate. The differences in hydraulic conductivity between the various macromolecules could not be explained by conventional theories which included prediction of hydraulic conductivity related to the radius of the molecule regarded as a uniform cylinder, nor the absolute charge density of the molecule and nor to the steric hindrance offered by the macromolecule to the diffusion of tritiated water. A qualitative relationship is established, however, between the noncounterion polymer contribution to osmotic activity and the resistance to water flow for polymers with high osmotic activity.     

A novel class of ion displacement ligands as antagonists of the αIIbβ3 receptor that limit conformational reorganization of the receptor

A collection of αIIbβ3 integrin receptor antagonists possessing a unique MIDAS metal ion displacement mechanism of action is presented. Insight into these agents’ structure–activity relationships, binding modality, and pharmacokinetic and pharmacodynamic profiles highlight the potential of these small molecule ion displacement ligands as attractive candidates for clinical development.     

Structural insights into how the MIDAS ion stabilizes integrin binding to an RGD peptide under force

Integrin alpha(V)beta(3) binds to extracellular matrix proteins through the tripeptide Arg-Gly-Asp (RGD), forming a shallow crevice rather than a deep binding pocket. A dynamic picture of how the RGD-alpha(V)beta(3) complex resists dissociation by mechanical force is derived here from steered molecular dynamic (SMD) simulations in which the major force peak correlates with the breaking of the contact between Asp(RGD) and the MIDAS ion. SMD predicts that the RGD-alpha(V)beta(3) complex is stabilized from dissociation by a single water molecule tightly coordinated to the divalent MIDAS ion, thereby blocking access of free water molecules to the most critical force-bearing interaction. The MIDAS motif is common to many other proteins that contain the phylogenetically ancient von Willebrand A (vWA) domain. The functional role of single water molecules tightly coordinated to the MIDAS ion might reflect a general strategy for the stabilization of protein-protein adhesion against cell-derived forces through divalent cations.     

A rapid method for determining dynamic binding capacity of resins for the purification of proteins

Biolayer interferometry is a novel method for quantifying macromolecules, such as proteins, in solution. The presence of other, non-binding molecules does not interfere with quantification, which allows one to measure the concentration of the molecule of interest in a crude mixture. Here we apply this method to determining the dynamic binding capacity of affinity resins.     

Diffusion Regulation in the Vitreous Humor

The efficient treatment of many ocular diseases depends on the rapid diffusive distribution of solutes such as drugs or drug delivery vehicles through the vitreous humor. However, this multicomponent hydrogel possesses selective permeability properties, which allow for the diffusion of certain molecules and particles, whereas others are immobilized. In this study, we perform an interspecies comparison showing that the selective permeability properties of the vitreous are conserved across several mammalian species. We identify the polyanionic glycosaminoglycans hyaluronic acid and heparan sulfate as two key macromolecules that establish this selective permeability. We show that electrostatic interactions between the polyanionic macromolecules and diffusing solutes can be weakened by charge screening or enzymatic glycosaminoglycan digestion. Furthermore, molecule penetration into the vitreous is also charge-dependent and only efficient as long as the net charge of the molecule does not exceed a certain threshold.     

A molecular semiotic view of biology. Interferon and 'homeokine' as symbols.

A term "homeokine" was introduced as a generic name covering cytokines and protein hormones which serve the purpose of intercellular communication within the animal body for homeostasis and ontogenetic development. The homeokine system, in its complex way of functioning, seems to be analogous to another communication system, human language. Individual homeokine molecules are likened to words; they have meanings and are viewed as symbols, representing those conditions or events inside and outside the body which are relevant to homeostasis. Extending this view, any protein and other molecule can be considered to take on the character of sign, when integrated into a purposive system of higher hierarchy, because the molecule then represents a meaning relative to the system as a whole that is lacking in the isolated state. Living systems with their biological macromolecules as semantic units are constructed upon the principle of double articulation, just like human languages with words as the semantic units. The structure and function of a molecule (of protein and any other substance) are associated with each other, with various degrees of arbitrariness, as are the expression and the content of a sign in general. Namely the activities or the sign functions of biological molecules are determined by the organized system they belong to, and not vice versa.     

A simple clustering algorithm can be accurate enough for use in calculations of pKs in macromolecules

Structure and function of macromolecules depend critically on the ionization states of their acidic and basic groups. Most current structure-based theoretical methods that predict pK of ionizable groups in macromolecules include, as one of the key steps, a computation of the partition sum (Boltzmann average) over all possible protonation microstates. As the number of these microstates depends exponentially on the number of ionizable groups present in the molecule, direct computation of the sum is not realistically feasible for many typical proteins that may have tens or even hundreds of ionizable groups. We have tested a simple and robust approximate algorithm for computing these partition sums for macromolecules. The method subdivides the interacting sites into independent clusters, based upon the strength of site-site electrostatic interaction. The resulting partition function is factorizable into computationally manageable components. Two variants of the approach are presented and validated on a representative test set of 602 proteins, by comparing the pK(1/2) values computed by the proposed method with those obtained by the standard Monte Carlo approach used as a reference. With 95% confidence, the relative error introduced by the more accurate of the two methods is less than 0.25 pK units. The algorithms are one to two orders of magnitude faster than the Monte Carlo method, with the typical settings. A graphical representation is introduced that visualizes the clusters of strong site-site interactions in the context of the three-dimensional (3D) structure of the macromolecule, facilitating identification of functionally important clusters of ionizable groups; the approach is exemplified on two proteins, bacteriorhodopsin and myoglobin.     

AURELIA,a program for computer-aided analysis of multidimensional NMR spectra

Summary AURELIA is an advanced program for the computer-aided evaluation of two-, three- and four-dimensional NMR spectra of any type of molecule. It can be used for the analysis of spectra of small molecules as well as for evaluation of complicated spectra of biological macromolecules such as proteins. AURELIA is highly interactive and offers a large number of tools, such as artefact reduction, cluster and multiplet analysis, spin system searches, resonance assignments, automated calculation of volumes in multidimensional spectra, calculation of distances with different approaches, including the full relaxation matrix approach, Bayesian analysis of peak features, correlation of molecular structures with NMR data, comparison of spectra via spectral algebra and pattern match techniques, automated sequential assignments on the basis of triple resonance spectra, and automatic strip calculation. In contrast to most other programs, many tasks are performed automatically.     

Membrane molecule reorientation in an electric field recorded by attenuated total reflection Fourier-transform infrared spectroscopy

Electric fields play an important role in the physiological function of macromolecules. Much is known about the role that electric fields play in biological systems, but membrane molecule structure and orientation induced by electric fields remain essentially unknown. In this paper, we present a polarized attenuated total reflection (ATR) experiment we designed to study the effect of electric fields on membrane molecule structure and orientation by Fourier-transform infrared (FTIR) spectroscopy. Two germanium crystals used as the internal reflection element for ATR-FTIR experiments were coated with a thin layer of polystyrene as insulator and used as electrodes to apply an electric field on an oriented stack of membranes made of dioleylphosphatidylcholine (DOPC) and melittin. This experimental set up allowed us for the first time to show fully reversible orientational changes in the lipid headgroups specifically induced by the electric potential difference.     

A Functional Group Database: A Charge Density – DARC Approach

The principle of the DARC approach of hierarchical organization is applied to a molecular electron density representation of functional groups, designed to represent some of the large-scale features of biomolecules, especially macromolecules important in biotechnology and bioinformatics. The proposed representation of the hierarchical structure of the interrelations among functional groups and other, chemically identifiable molecular moieties within a molecule, and a weighting scheme assigned to these local molecular components are justified by the internal structures of the actual fuzzy electron density distributions associated with these molecular moieties. These hierarchical relations serve as a basis for the organization of a functional group database, providing a tool for synthesis design and molecular engineering.