The logical repertoire of ligand-binding proteins

Proteins whose conformation can be altered by the equilibrium binding of a regulatory ligand are one of the main building blocks of signal-processing networks in cells. Typically, such proteins switch between an 'inactive' and an 'active' state, as the concentration of the regulator varies. We investigate the properties of proteins that can bind two different ligands and show that these proteins can individually act as logical elements: their 'output', quantified by their average level of activity, depends on the two 'inputs', the concentrations of both regulators. In the case where the two ligands can bind simultaneously, we show that all of the elementary logical functions can be implemented by appropriate tuning of the ligand-binding energies. If the ligands bind exclusively, the logical repertoire is more limited. When such proteins cluster together, cooperative interactions can greatly enhance the sharpness of the response. Protein clusters can therefore act as digital logical elements whose activity can be abruptly switched from fully inactive to fully active, as the concentrations of the regulators pass threshold values. We discuss a particular instance in which this type of protein logic appears to be used in signal transduction-the chemotaxis receptors of E. coli.     

The logical structure of dreams and their relation to reality.

The contradictions and non sequiturs often found in dreams (or, equivalently, dream-narratives) are not in fact logical errors, but express and work with a type of logic that characterizes the deepest dimensions of our waking reality. These are the dimensions in which we deal with ourselves as a whole, our lives as a whole, or with the sense of reality as a whole. We do so, for example, in situations of deep personal transformation, or of recognition of deep difference of outlook. The paper argues that the logic of these situations is validly one of contradiction and non sequitur, that dreams sometimes express and work with these kinds of situations, and that these kinds of dreams therefore validly involve the same kind of logic. These kinds of dreams consequently also express insight into the sense that our lives or existence as a whole has for us. In achieving that insight, they actively orient, situate, or resituate us in our relation to our lives or existence as a whole. In this respect they are in themselves a practice of philosophy. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Corvidae are able to understand the logical structure in string-pulling tasks

The ability of the Corvidae to understand the logical structure in string-pulling tasks was studied in a set of experiments with varied position of strings. It was demonstrated that some hooded crows (Corvus cornix L.) and common ravens (Corvus corax L.) successfully completed the tasks where the strings were not intersected but placed so that the bait was positioned opposite the forepart of the empty string. Hooded crows also solved the task where the baits were attached to both strings, but one of the strings was disrupted. The task with two intersected strings where the bait was positioned opposite the forepart of the empty string was not solved by the crows. The results suggest the ability of both examined species to grasp the logical structure of such kind of tasks.     

The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling

In this paper simple models for tumour growth incorporating age-structured cell cycle dynamics are considered in the presence of two non-cross-resistant S-phase specific chemotherapeutic drugs. According to the seminal work of Goldie and Coldman, if one cannot deliver two cell cycle phase non-specific, non-cross-resistant drugs simultaneously, for example due to toxicity, and both drugs are identical apart from resistance, one should alternate their delivery as rapidly as possible. However consider S-phase specific drugs. One might speculate that, for example, alternating the two drugs at intervals of T, where T is the mean cell cycle time, is better than alternating the drugs at intervals of T/2, as the latter strategy allows the possibility of a cell cycle sanctuary. Such speculation implicitly requires a sufficiently low variance of the cell cycle time, and hence it is not clear if such reasoning prevents a generalisation of the results of Goldie and Coldman. This question is addressed in this paper via a detailed modelling investigation, as motivated by suggestions for future colorectal adjuvant chemotherapy trials and developments in hepatic arterial infusion technology. It is shown that the cell cycle distribution of the resistant cell populations is strongly influenced by the chemotherapy schedule. The consequences of this can be dramatic, and can lead to chemotherapy failure at resonant chemotherapy timings, especially for a small standard deviation of the cell cycle time. The novel aspects of this observation are highlighted compared to other models in the literature exhibiting resonant behaviour in the timing of a periodic chemotherapy protocol. The above investigation also results in the principal prediction of this paper that reducing the drug alternation time to approximately a few hours, if possible, can result in substantial improvements in predicted chemotherapy outcomes. Critically, such improvements are not predicted by the Goldie Coldman model or other chemotherapy scheduling models in the literature.     

Molecular dynamics study of secondary structure motions in proteins: application to myohemerythrin

The concept of secondary structure motions is examined in a molecular dynamics simulation of the protein myohemerythrin. We extracted from the simulation a corresponding trajectory of helices and demonstrated that the fluctuations of the protein are dominated by a rigid shift of these secondary structure elements. The relative motions of the helices are irregular, with no clear periodicity. They are bounded by approximately 2 A for the center of mass motions and by 20 degrees for the relative orientations. The potential of mean force for the interactions of the helices was calculated, and the correlations between the different extended motions were investigated. It is shown that the one-dimensional mean force potentials are close to quadratic for most of the helices coordinates. The anharmonicity is reflected by changes in the direction of the normal modes as a function of the energy and by the existence of multiple free energy minima for the helices packing. The multiple conformations are associated with a single type of secondary structure coordinate: the angle that describes the relative orientation of the helices in a plane perpendicular to the line connecting their center of mass.     

Analysis of anisotropic side-chain packing in proteins and application to high-resolution structure prediction

pi-pi, Cation-pi, and hydrophobic packing interactions contribute specificity to protein folding and stability to the native state. As a step towards developing improved models of these interactions in proteins, we compare the side-chain packing arrangements in native proteins to those found in compact decoys produced by the Rosetta de novo structure prediction method. We find enrichments in the native distributions for T-shaped and parallel offset arrangements of aromatic residue pairs, in parallel stacked arrangements of cation-aromatic pairs, in parallel stacked pairs involving proline residues, and in parallel offset arrangements for aliphatic residue pairs. We then investigate the extent to which the distinctive features of native packing can be explained using Lennard-Jones and electrostatics models. Finally, we derive orientation-dependent pi-pi, cation-pi and hydrophobic interaction potentials based on the differences between the native and compact decoy distributions and investigate their efficacy for high-resolution protein structure prediction. Surprisingly, the orientation-dependent potential derived from the packing arrangements of aliphatic side-chain pairs distinguishes the native structure from compact decoys better than the orientation-dependent potentials describing pi-pi and cation-pi interactions.     

A new strategy for primary structure determination of proteins: application to bovine beta-casein

A new approach has been developed for sequencing proteins. A radioactive label is attached specifically to the C-terminus of the protein. The labelled molecule is subjected to varying proteolysis conditions. From the electrophoretic patterns (SDS-PAGE) of the hydrolysates, appropriate cleavage conditions are selected, giving labelled peptides of different lengths which are purified. The labelled peptides are sequenced in order of increasing size (from 1 to n), peptide (i) being sequenced until the N-terminal sequence of peptide (i-1) is encountered. This approach allows the determination of a complete protein sequence with a minimal number of Edman cycles. The method was successfully applied to bovine beta-casein (209 residues) which was completely resequenced with only 239 Edman cycles.     

An approach to sequential NMR assignments of proteins: application to chemical shift restraint-based structure prediction

A procedure for the simultaneous acquisition of {HNCOCANH & HCCCONH} chemical shift correlation spectra employing sequential \(^{1}\hbox {H}\) data acquisition for moderately sized proteins is presented. The suitability of the approach for obtaining sequential resonance assignments, including complete \(^{15}\hbox {N}{},\, ^{1}\hbox {H}{}^{N},\, ^{13}\hbox {CO}{},\, ^{13}\hbox {C}^{\alpha }{},\, ^{13}\hbox {C}^{\beta }\) and \(^{1}\hbox {H}^{\alpha }\) chemical shift information, is demonstrated experimentally for a \(^{13}\hbox {C}\) and \(^{15}\hbox {N}\) labelled sample of the C-terminal winged helix (WH) domain of the minichromosome maintenance (MCM) complex of Sulfolobus solfataricus. The chemical shift information obtained was used to calculate the global fold of this winged helix domain via CS-Rosetta. This demonstrates that our procedure provides a reliable and straight-forward protocol for a quick global fold determination of moderately-sized proteins.     

The application of bone morphogenetic proteins to dental tissue engineering

Progress in understanding the role of bone morphogenetic proteins (BMPs) in craniofacial and tooth development, the demonstration of stem cells in dental pulp and accumulating knowledge on biomaterial scaffolds have set the stage for tissue engineering and regenerative therapy of the craniofacial complex. Furthermore, the recent approval by the US Food and Drug Administration (FDA; Rockville, MD, USA) of recombinant human BMPs for accelerating bone fusion in slow-healing fractures indicates that this protein family may prove useful in designing regenerative treatments in dental applications. In the near term, these advances are likely to be applied to endodontics and periodontal surgery; ultimately, they may facilitate approaches to regenerating whole teeth for use in tooth replacement.     

Protein sequence and structure relationship ARMA spectral analysis: application to membrane proteins.

If it is assumed that the primary sequence determines the three-dimensional folded structure of a protein, then the regular folding patterns, such as alpha-helix, beta-sheet, and other ordered patterns in the three-dimensional structure must correspond to the periodic distribution of the physical properties of the amino acids along the primary sequence. An AutoRegressive Moving Average (ARMA) model method of spectral analysis is applied to analyze protein sequences represented by the hydrophobicity of their amino acids. The results for several membrane proteins of known structures indicate that the periodic distribution of hydrophobicity of the primary sequence is closely related to the regular folding patterns in a protein's three-dimensional structure. We also applied the method to the transmembrane regions of acetylcholine receptor alpha subunit and Shaker potassium channel for which no atomic resolution structure is available. This work is an extension of our analysis of globular proteins by a similar method.     

Recent advances in employing molecular modelling to determine the specificity of glycan-binding proteins

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The use of basis functions in modelling joint articular surfaces: application to the knee joint

This article introduces a new method to represent bone surface geometry for simulations of joint contact. The method uses the inner product of two basis functions to provide a mathematical representation of the joint surfaces. This method guarantees a continuous transition in the direction of the surface normals, an important property for computation of joint contact. Our formulation handles experimental data that are not evenly distributed, a common characteristic of digitized data of musculoskeletal morphologies. The method makes it possible to represent highly curved surfaces, which are encountered in many anatomical structures. The accuracy of this method is demonstrated by modeling the human knee joint. The mean relative percentage error in the representation of the patellar track surface was 0.25% (range 0-1.56%) which corresponded to an absolute error of 0.17mm (range 0-0.16mm).     

Reduced-order modelling of biochemical networks: application to the GTPase-cycle signalling module

Biochemical systems embed complex networks and hence development and analysis of their detailed models pose a challenge for computation. Coarse-grained biochemical models, called reduced-order models (ROMs), consisting of essential biochemical mechanisms are more useful for computational analysis and for studying important features of a biochemical network. The authors present a novel method to model-reduction by identifying potentially important parameters using multidimensional sensitivity analysis. A ROM is generated for the GTPase-cycle module of m1 muscarinic acetylcholine receptor, Gq, and regulator of G-protein signalling 4 (a GTPase-activating protein or GAP) starting from a detailed model of 48 reactions. The resulting ROM has only 17 reactions. The ROM suggested that complexes of G-protein coupled receptor (GPCR) and GAP--which were proposed in the detailed model as a hypothesis--are required to fit the experimental data. Models previously published in the literature are also simulated and compared with the ROM. Through this comparison, a minimal ROM, that also requires complexes of GPCR and GAP, with just 15 parameters is generated. The proposed reduced-order modelling methodology is scalable to larger networks and provides a general framework for the reduction of models of biochemical systems.     

Molecular modelling of the mass density of single proteins

Using molecular dynamics (MD) simulations, the density of single proteins and its temperature dependence was modelled starting from the experimentally determined protein structure and a generic, transferable force field, without the need of prior parameterization. Although all proteins consist of the same 20 amino acids, their density in aqueous solution varies up to 10% and the thermal expansion coefficient up to twofold. To model the protein density, systematic MD simulations were carried out for 10 proteins with a broad range of densities (1.32-1.43 g/cm(3)) and molecular weights (7-97 kDa). The simulated densities deviated by less than 1.4% from their experimental values that were available for four proteins. Further analyses of protein density showed that it can be essentially described as a consequence of amino acid composition. For five proteins, the density was simulated at different temperatures. The simulated thermal expansion coefficients ranged between 4.3 and 7.1 × 10(-4) K(-1) and were similar to the experimentally determined values of ribonuclease-A and lysozyme (deviations of 2.4 and 14.6%, respectively). Further analyses indicated that the thermal expansion coefficient is linked to the temperature dependence of atomic fluctuations: proteins with a high thermal expansion coefficient show a low increase in flexibility at increasing temperature. A low increase in atomic fluctuations with temperature has been previously described as a possible mechanism of thermostability. Thus, a high thermal expansion coefficient might contribute to protein thermostability.     

Two-intermediate model to characterize the structure of fast-folding proteins

This paper introduces a new model that enables researchers to conduct protein folding simulations. A two-step in silico process is used in the course of structural analysis of a set of fast-folding proteins. The model assumes an early stage (ES) that depends solely on the backbone conformation, as described by its geometrical properties—specifically, by the V-angle between two sequential peptide bond planes (which determines the radius of curvature, also called R-radius, according to a second-degree polynomial form). The agreement between the structure under consideration and the assumed model is measured in terms of the magnitude of dispersion of both parameters with respect to idealized values. The second step, called late-stage folding (LS), is based on the “fuzzy oil drop” model, which involves an external hydrophobic force field described by a three-dimensional Gauss function. The degree of conformance between the structure under consideration and its idealized model is expressed quantitatively by means of the Kullback-Leibler entropy, which is a measure of disparity between the observed and expected hydrophobicity distributions. A set of proteins, representative of the fast-folding group - specifically, cold shock proteins - is shown to agree with the proposed model.