Contact Matrix Research Articles

Spectral properties of contact matrix: Application to proteins

A protein can be modelled by a set of points representing its amino acids. Topologically, this set of points is entirely defined by its contact matrix (adjacency matrix in graph theory). The contact matrix characterizing the relation between neighboring amino acids is deduced from Voronoi or Laguerre decomposition. This method allows contact matrices to be defined without any arbitrary cut-off that could induce arbitrary effects. Eigenvalues of these matrices are related with elementary excitations in proteins. We present some spectral properties of these matrices that reflect global properties of proteins. The eigenvectors indicate participation of each amino acids to the excitation modes of the proteins. It is interesting to compare the protein modelled as a close packing of amino acids, with a random close packing of spheres. The main features of the protein are those of a packing, a result that confirms the importance of the dense packing model for proteins. Nevertheless there are some properties, specific to the hierarchical organization of the protein: the primary chain order, the secondary structures and the domain structures.

Experimental performance analysis and modelling of liquid desiccant cooling systems for air conditioning in residential buildings

The paper presents a new desiccant cooling cycle to be integrated in residential mechanical ventilation systems. The process shifts the air treatment completely to the return air side, so that the supply air can be cooled by a heat exchanger. Purely sensible cooling is an essential requirement for residential buildings with no maintenance guarantee for supply air humidifiers. As the cooling power is generated on the exhaust air side, the dehumidification process needs to be highly efficient to provide low supply air temperatures. Solid rotating desiccant wheels have been experimentally compared with liquid sorption systems using contact matrix absorbers and cross flow heat exchangers. The best dehumidification performance at no temperature increase was obtained in an evaporatively cooled heat exchanger with sprayed lithium chloride solution. Up to 7 g kg −1 dehumidification could be reached in an isothermal process, although the surface wetting of the first prototype was low. The process then provides inlet air conditions below 20 °C for the summer design conditions of 32 °C, 40% relative humidity. With air volume flow rates of 200 m 3 h −1 the system can provide 886 W of cooling power. A theoretical model for both the contact absorber and the cross flow system has been developed and validated against experimental data for a wide range of operating conditions. A simulation study identified the optimisation potential of the system, if for example the surface wetting of the liquid desiccant can be improved.

Perceptron learning of pairwise contact energies for proteins incorporating the amino acid environment

Although a coarse-grained description of proteins is a simple and convenient way to attack the protein folding problem, the construction of a global pairwise energy function which can simultaneously recognize the native folds of many proteins has resulted in partial success. We have sought the possibility of a systematic improvement of this pairwise-contact energy function as we extended the parameter space of amino acids, incorporating local environments of amino acids, beyond a 20 x 20 matrix. We have studied the pairwise contact energy functions of 20 x 20, 60 x 60, and 180 x 180 matrices depending on the extent of parameter space, and compared their effect on the learnability of energy parameters in the context of a gapless threading, bearing in mind that a 20 x 20 pairwise contact matrix has been shown to be too simple to recognize the native folds of many proteins. In this paper, we show that the construction of a global pairwise energy function was achieved using 1006 training proteins of a homology of less than 30%, which include all representatives of different protein classes. After parametrizing the local environments of the amino acids into nine categories depending on three secondary structures and three kinds of hydrophobicity (desolvation), the 16290 pairwise contact energies (scores) of the amino acids could be determined by perceptron learning and protein threading. These could simultaneously recognize all the native folds of the 1006 training proteins. When these energy parameters were tested on the 382 test proteins of a homology of less than 90%, 370 (96.9%) proteins could recognize their native folds. We set up a simple thermodynamic framework in the conformational space of decoys to calculate the unfolded fraction and the specific heat of real proteins. The different thermodynamic stabilities of E.coli ribonuclease H (RNase H) and its mutants were well described in our calculation, agreeing with the experiment.

Reaction coordinates and rates from transition paths.

The molecular mechanism of a reaction in solution is reflected in its transition-state ensemble and transition paths. We use a Bayesian formula relating the equilibrium and transition-path ensembles to identify transition states, rank reaction coordinates, and estimate rate coefficients. We also introduce a variational procedure to optimize reaction coordinates. The theory is illustrated with applications to protein folding and the dipole reorientation of an ordered water chain inside a carbon nanotube. To describe the folding of a simple model of a three-helix bundle protein, we variationally optimize the weights of a projection onto the matrix of native and nonnative amino acid contacts. The resulting one-dimensional reaction coordinate captures the folding transition state, with formation and packing of helix 2 and 3 constituting the bottleneck for folding.

Prediction of Site-Specific Amino Acid Distributions and Limits of Divergent Evolutionary Changes in Protein Sequences

We derive an analytic expression for site-specific stationary distributions of amino acids from the Structurally Constrained Neutral (SCN) model of protein evolution with conservation of folding stability. The stationary distributions that we obtain have a Boltzmann-like shape, and their effective temperature parameter, measuring the limit of divergent evolutionary changes at a given site, can be predicted from a site-specific topological property, the principal eigenvector of the contact matrix of the native conformation of the protein. These analytic results, obtained without free parameters, are compared with simulations of the SCN model and with the site-specific amino acid distributions obtained from the Protein Data Bank. These results also provide new insights into how the topology of a protein fold influences its designability, i.e. the number of sequences compatible with that fold. The dependence of the effective temperature on the principal eigenvector decreases for longer proteins, a possible consequence of the fact that selection for thermodynamic stability becomes weaker in this case.

Equations of motion for polymer chains in a thermostat

A constrained dynamics method suitable for molecular dynamics simulations is considered to study the long-time dynamics of polymer chains. The method is initially discussed on the basis of the Lagrangian and Hamiltonian formalisms for isolated polymer chains with fixed monomer–monomer links. Subsequently, the corresponding equations of motion are obtained for describing the dynamics of such polymer chains in the presence of a thermostat. The approach is applied to a few typical cases to illustrate how the formalism is implemented numerically and to elucidate its convergence properties when studying such systems in equilibrium. As an example, we consider the problem of reconstructing the backbone structure (chain of Cα atoms) of protein Rubredoxin from its contact matrix. It is shown that the target structure is succesfully reached after a long transient regime (typically in the range from 106 to 108 integration steps). A particular attractive extension of the algorithm presented here is to environment-dependent couplings, which could allow the study of the long-time polymer dynamics in realistic environments. The present method is thus expected to have useful applications in the modelling of the complex dynamics of bio-polymers such as proteins, and also in the context of nanoscale polymer materials.

Homogenization of a viscoelastic matrix in linear frictional contact

AbstractThe paper is devoted to study of acoustic wave propagation in a partially consolidated composite material containing loose particles. Friction of particles against the consolidated part of the material causes mechanical energy dissipation. This situation is modelled by assuming that the medium has a periodic microstructure changing rapidly on the small scale ε. Each of the periodic microscopic cells is composed of a viscoelastic matrix containing a rigid particle in frictional contact with the matrix. We use the methods of two‐scale convergence to obtain effective acoustic equations for the homogenized material. The effective equations are history‐dependent and contain the body force term, reminiscent of the well‐known Stokes drag force. Copyright © 2004 John Wiley & Sons, Ltd.

Prediction of Site-Specific Amino Acid Distributions and Limits of Divergent Evolutionary Changes in Protein Sequences

We derive an analytic expression for site-specific stationary distributions of amino acids from the structurally constrained neutral (SCN) model of protein evolution with conservation of folding stability. The stationary distributions that we obtain have a Boltzmann-like shape, and their effective temperature parameter, measuring the limit of divergent evolutionary changes at a given site, can be predicted from a site-specific topological property, the principal eigenvector of the contact matrix of the native conformation of the protein. These analytic results, obtained without free parameters, are compared with simulations of the SCN model and with the site-specific amino acid distributions obtained from the Protein Data Bank. These results also provide new insights into how the topology of a protein fold influences its designability, i.e., the number of sequences compatible with that fold. The dependence of the effective temperature on the principal eigenvector decreases for longer proteins, as a possible consequence of the fact that selection for thermodynamic stability becomes weaker in this case.

Principal eigenvector of contact matrices and hydrophobicity profiles in proteins

With the aim of studying the relationship between protein sequences and their native structures, we adopted vectorial representations for both sequence and structure. The structural representation was based on the principal eigenvector of the fold's contact matrix (PE). As has been recently shown, the latter encodes sufficient information for reconstructing the whole contact matrix. The sequence was represented through a hydrophobicity profile (HP), using a generalized hydrophobicity scale that we obtained from the principal eigenvector of a residue-residue interaction matrix, and denoted as interactivity scale. Using this novel scale, we defined the optimal HP of a protein fold, and, by means of stability arguments, predicted to be strongly correlated with the PE of the fold's contact matrix. This prediction was confirmed through an evolutionary analysis, which showed that the PE correlates with the HP of each individual sequence adopting the same fold and, even more strongly, with the average HP of this set of sequences. Thus, protein sequences evolve in such a way that their average HP is close to the optimal one, implying that neutral evolution can be viewed as a kind of motion in sequence space around the optimal HP. Our results indicate that the correlation coefficient between N-dimensional vectors constitutes a natural metric in the vectorial space in which we represent both protein sequences and protein structures, which we call vectorial protein space. In this way, we define a unified framework for sequence-to-sequence, sequence-to-structure and structure-to-structure alignments. We show that the interactivity scale is nearly optimal both for the comparison of sequences to sequences and sequences to structures.

Gastrulation in the sea urchin embryo: a model system for analyzing the morphogenesis of a monolayered epithelium.

Processes of gastrulation in the sea urchin embryo have been intensively studied to reveal the mechanisms involved in the invagination of a monolayered epithelium. It is widely accepted that the invagination proceeds in two steps (primary and secondary invagination) until the archenteron reaches the apical plate, and that the constituent cells of the resulting archenteron are exclusively derived from the veg2 tier of blastomeres formed at the 60-cell stage. However, recent studies have shown that the recruitment of the archenteron cells lasts as late as the late prism stage, and some descendants of veg1 blastomeres are also recruited into the archenteron. In this review, we first illustrate the current outline of sea urchin gastrulation. Second, several factors, such as cytoskeletons, cell contact and extracellular matrix, will be discussed in relation to the cellular and mechanical basis of gastrulation. Third, differences in the manner of gastrulation among sea urchin species will be described; in some species, the archenteron does not elongate stepwise but continuously. In those embryos, bottle cells are scarcely observed, and the archenteron cells are not rearranged during invagination unlike in typical sea urchins. Attention will be also paid to some other factors, such as the turgor pressure of blastocoele and the force generated by blastocoele wall. These factors, in spite of their significance, have been neglected in the analysis of sea urchin gastrulation. Lastly, we will discuss how behavior of pigment cells defines the manner of gastrulation, because pigment cells recently turned out to be the bottle cells that trigger the initial inward bending of the vegetal plate.

Photoionization pathways and free electrons in UV-MALDI.

The recently developed model for primary and secondary UV-MALDI ion formation (Knochenmuss, R. J. Mass Spectrom. 2002, 37, 867-877. Knochenmuss, R. Anal. Chem. 2003, 75, 2199.) is applied to questions regarding photoionization pathways and electron versus negative ion production. Two-photon ionization of the matrix in direct contact with analyte is possible under some circumstances (Kinsel, G.; Knochenmuss, R.; Setz, P.; Land, C. M.; Goh, S.-K.; Archibong, E. F.; Hardesty, J. H.; Marynik, D. J. Mass Spectrom. 2002, 37, 1131-1140.), and is added to the model. When analyte is present in large mole ratios (such as when matrix suppression is desired), this effect contributes modestly to the ion yield. Generally, matrix exciton pooling remains dominant. The interfacial layer of thin samples on a metal substrate may also be ionizable in a 2-photon process. A mechanism is proposed, and the correspondingly modified model gives excellent agreement with electron emission versus laser intensity data. Capture in, or escape of low-energy electrons from a thick sample (or on a nonmetallic substrate) is also examined. Because the mean free path for MALDI electrons in a solid matrix is on the order of 10 nm, below such depths, any electrons generated are captured to form negative ions. Only a surface layer can emit free electrons. This surface emission effect is also well reproduced by the model, up to a laser intensity limit caused by surface charging. This charging phenomenon is investigated and illustrated by molecular dynamics calculations.

Supramolecular polymers of 4,5-bis(bromomethyl)-1,3-dithiole-2-thione-dihalogen adducts

The title compound has been reacted with I2, IBr and ICl to afford the charge-transfer adducts 4·2I2, 4·IBr and 4·ICl·½I2, respectively. The products have been characterised by Raman and IR spectroscopy and X-ray crystallography. The adducts contain linear S⋯I–X (X = I, Br or Cl) units (174–178°) in which the S⋯I contacts range from 2.534–2.597 A. In 4·2I2 and 4·ICl·½I2, the materials contain additional ‘free’ diiodine units which are held within a matrix of intermolecular contacts, predominantly through non-covalent halogen–halogen and sulfur–halogen interactions. Although the functional groups in the parent molecule (4) are inert at the supramolecular level, the bromomethyl groups in the adducts contribute strong interactions through Br⋯Br, Br⋯I, Br⋯S and Br⋯H close contacts. The structures of the complexes are polymeric in nature, providing interactions in two and three dimensions.

Structural determinant of protein designability.

Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structure's contact matrix, and then use a Monte Carlo simulation to test the applicability of this analytical result to cubic lattice proteins. We find that the lattice structures with the most low-energy sequences are the same as those predicted by the theory. We argue that, given sufficiently strict requirements for foldability, these structures are the most designable, and we propose a simple means to test whether the results in this paper hold true for real proteins.

Algorithmic stabilization of FE analyses of 2D frictional contact problems with large slip

This paper is concerned with a regularization method to avoid slip oscillations of contact nodes resulting from lack of C 1-continuity of low-order finite element discretizations. The purpose of this method is to enhance the robustness of contact algorithms for 2D contact analyses. Based on the actual finite element boundary, a virtual (smooth) boundary with C 1-continuity is established to define the normal vector and, in case of frictional contact, also the tangential vector. The proposed regularization method allows using standard low-order elements. The respective algorithm including the consistent contact matrix is derived for frictionless as well as for frictional contact. Selected numerical examples demonstrate the effectiveness of the method.

Cell-to-cell contact and extracellular matrix

A selection of World Wide Web sites relevant to papers published in this issue of Current Opinion in Cell Biology.

PCI at the start of the 21st century

The paper presents a new desiccant cooling cycle to be integrated in residential mechanical ventilation systems. The process shifts the air treatment completely to the return air side, so that the supply air can be cooled by a heat exchanger. Purely sensible cooling is an essential requirement for residential buildings with no maintenance guarantee for supply air humidifiers. As the cooling power is generated on the exhaust air side, the dehumidification process needs to be highly efficient to provide low supply air temperatures. Solid rotating desiccant wheels have been experimentally compared with liquid sorption systems using contact matrix absorbers and cross flow heat exchangers. The best dehumidification performance at no temperature increase was obtained in an evaporatively cooled heat exchanger with sprayed lithium chloride solution. Up to 7 g kg−1 dehumidification could be reached in an isothermal process, although the surface wetting of the first prototype was low. The process then provides inlet air conditions below 20 °C for the summer design conditions of 32 °C, 40% relative humidity. With air volume flow rates of 200 m3 h−1 the system can provide 886 W of cooling power.A theoretical model for both the contact absorber and the cross flow system has been developed and validated against experimental data for a wide range of operating conditions. A simulation study identified the optimisation potential of the system, if for example the surface wetting of the liquid desiccant can be improved.

Contact with fibronectin enhances preservation of normal but not chronic myelogenous leukemia primitive hematopoietic progenitors.

Coculture with stromal cells enhances preservation and self-renewal of primitive progenitor potential in hematopoietic cells during ex vivo culture with growth factors (GF). However, the respective roles of growth factors, stromal contact, and extracellular matrix (ECM) ligands in this effect are not clear. Here we investigated the role of direct contact with stroma and the ECM protein fibronectin (FN) in these effects, and investigated whether abnormal integrin receptor function in chronic myelogenous leukemia (CML) progenitors was associated with perturbation in these responses. Normal bone marrow CD34+ cells were cultured in GF-containing medium with or without contact with stromal layers, glutaraldehyde-fixed stromal layers (stroma-contact), or integrin-binding FN fragments for 7 days. Progeny cells were assayed for primitive progenitors in week-6 long-term culture-initiating cell (LTC-IC) and week-10 extended LTC-IC (ELTC-IC) assays. Increased LTC-IC and ELTC-IC preservation was seen following coculture with stroma, and was also observed after culture in contact with fixed stromal layers and FN. Both alpha4beta1 and alpha5beta1-integrin binding FN fragments enhanced LTC-IC preservation. Analysis of single CD34+CD38- cells showed that coculture with FN resulted in significantly reduced cell division, but enhanced retention of LTC-IC capacity in divided cells. FN also increased LTC-IC frequency in undivided cells. CML progenitors demonstrate deficient integrin-mediated adhesion, migration, and signaling. Coculture of CML CD34+ cells with stroma and FN failed to enhance LTC-IC preservation. We conclude that beta1 integrin-FN interactions enhance normal primitive progenitor preservation with or without cell division, and that these mechanisms are impaired in CML primitive progenitors.

Gamma-linolenic acid alters the composition of mitochondrial membrane subfractions, decreases outer mitochondrial membrane binding of hexokinase and alters carnitine palmitoyltransferase I properties in the Walker 256 rat tumour

Gamma-linolenic acid (GLA) is known to be an inhibitor of Walker 256 tumour growth in vivo and causes changes in both mitochondrial structure and cellular metabolism. The aim of the present study was to investigate in greater detail the changes in energy metabolism and ultrastructure induced by GLA in this tumour model. A diet containing 5.5% GLA, which is sufficient to cause a 45% decrease in tumour growth, was found to almost double the triacylglycerol (TAG) content of the tumour and to increase the quantity of 20:3 n−6, 20:4 n−6, 22:4 n−6 and 22:5 n−6 in the TAG fraction as determined by gas chromatography–mass spectrometry (GCMS) analysis. Morphometric analysis of the tumour by electron microscopy confirmed this increase in TAG content, identifying a doubling of lipid droplet content in the GLA dietary group. The surface density of mitochondrial cristae was reduced, along with a reduction in the number of contact sites (CS) and matrix granules. These three parameters are likely indicators of a reduction in mitochondrial metabolic activity. Measurement of hexokinase activity identified that much of the total hexokinase activity was in the mitochondrially bound form (66.5%) in the control tumour and that GLA caused a decrease in the amount of enzyme in the bound form (39.3%). The fatty acyl chain composition of the tumour mitochondrial subfractions, outer membranes (OM), CSs and inner membranes (IM) was determined by GCMS. All subfractions showed considerable increases in 20:3 n−6 and decreases in 18:1 n−9, 18:2 n−6 and 22:6 n−3, when exposed to GLA diet. These changes were reflected in a large increase in the n−6/ n−3 ratio in the GLA OM vs. the control OM, 21.299 vs. 6.747, respectively. The maximal activity of OM carnitine palmitoyltransferase I (CPT I) was found to be decreased by 61.6% in the GLA diet group. This was accompanied by a decrease in malonyl CoA sensitivity and a decrease in affinity for 16:0 CoA substrate. Such changes in CPT I may be the cause of cytoplasmic acyl CoA accumulation seen in this tumour model. These effects, together with previously reported increases in lipid peroxidation, lead to the conclusion that GLA may cause inhibition of tumour cell growth through separate but interlinked pathways, all of which eventually lead to apoptosis and a decrease in tumour development. The influence of mitochondrial OM fatty acyl chain composition upon two important enzymes of energy metabolism, hexokinase and CPT I, both of which have been linked to apoptosis, is of considerable importance for future studies on fatty acid-induced cell death.

Web alert: Cell-to-cell contact and extracellular matrix

A selection of World Wide Web sites relevant to papers published in this issue of Current Opinion in Cell Biology.

Effects of the matrix and sample preparation on the determination of fluoroquinolone residues in animal tissues

The effects of aqueous–organic solvent extraction and enzymic digestion sonication procedure on the isolation of spiked fluoroquinolones from poultry tissue have been studied. The highest recovery from spiked tissue was obtained using a mixture of trichloroacetic acid–acetonitrile (8:2) as extractant and an SDB1 cartridge for clean-up purposes. Validation data are presented for enrofloxacin, ciprofloxacin, sarafloxacin and difloxacin. The spiking procedure (spike contact time, spike solvent and matrix) had a small influence on the recovery of fluroquinolones from poultry muscle or liver. The effects of a different extraction on the determination of incurred enrofloxacin and its metabolite, ciprofloxacin, residues in poultry tissues have been investigated. The extraction procedures investigated – aqueous–organic solvent extraction, enzymic digestion or sonication – all gave similar results for incurred fluoroquinolone concentration in poultry muscle after correlation for spike recovery. The highest results were obtained in poultry liver when enzymic digestion has been used.