On the energy density of helical proteins

We solve the problem of determining the energy actions whose moduli space of extremals contains the class of Lancret helices with a prescribed slope. We first see that the energy density should be linear both in the total bending and in the total twisting, such that the ratio between the weights of them is the prescribed slope. This will give an affirmative answer to the conjecture stated in Barros and Ferrández (J Math Phys 50:103529, 2009). Then, we normalize to get the best choice for the helical energy. It allows us to show that the energy, for instance of a protein chain, does not depend on the slope and is invariant under homotopic changes of the cross section which determines the cylinder where the helix is lying. In particular, the energy of a helix is not arbitrary, but it is given as natural multiples of some basic quantity of energy.     

Minimum energy configurations of the 2-dimensional HP-model of proteins by self-organizing networks.

We use self-organizing maps (SOM) as an efficient tool to find the minimum energy configurations of the 2-dimensional HP-models of proteins. The usage of the SOM for the protein folding problem is similar to that for the Traveling Salesman Problem. The lattice nodes represent the cities whereas the neurons in the network represent the amino acids moving towards the closest cities, subject to the HH interactions. The valid path that maximizes the HH contacts corresponds to the minimum energy configuration of the protein. We report promising results for the cases when the protein completely fills a lattice and discuss the current problems and possible extensions. In all the test sequences up to 36 amino acids, the algorithm was able to find the global minimum and its degeneracies.     

Bioanalytical characterization of proteins

Allergens from the view of a protein chemist are quite normal proteins, not to distinguish from non allergenic proteins. The first task is therefore to recognize and identify the proteins responsible for the allergenic reaction. This is usually only possible if the allergenic structure is conserved during the purification procedures. For a detailed analysis of the allergenic protein modern protein chemical methods for characterization, identification, determination of posttranslational modifications and epitope characterization have to be applied. Such techniques are briefly described in this article.     

Computational characterization of proteins

Computational characterization of proteins is a necessary first step in understanding the biologic role of a protein. The composite architecture of mammalian proteins makes the prediction of the biologic role rather difficult. Nevertheless, integration of many different prediction methods allows for a more accurate representation. Information on the 3D structure of a protein improves the reliability of predictions of many features. This article reviews existing methods used to characterize proteins and several tools that provide an integrated access to different types of information. The authors point out the increasing importance of structural constraints and an increasing need to integrate different approaches.     

On the excited-state energy transfer between tryptophan residues in proteins: the case of penicillin acylase

The problem, whether excited-state energy transfer occurs between Trp residues in a multi-tryptophan proteins and if it does, what kind of changes it induces in different parameters of protein fluorescence, is currently under active investigation. In our previous paper [Biophys. Chem. 72 (1998) 265], the energy transfer was found and studied in detail for Na,K-ATPase. It was shown that this transfer influences all parameters of fluorescence emission, which is detected at site-selective conditions (red-edge of excitation, blue and red edges of emission). Present experiments were performed on unusually tryptophan-rich protein, bacterial penicillin acylase (28 Trp per dimer of 82 kDa) and were aimed to extend these observations. They demonstrate substantial heterogeneity in the environments of tryptophan residues within the protein structure. This suggests, that in the present case, if the energy transfer exists, it should be directed from short-wavelength-emitting to long-wavelength-emitting tryptophan residues and thus could be easily observed by a number of time-resolved and steady-state fluorescence techniques. Unexpectedly, no signature of inter-tryptophan energy transfer was found.     

Computational characterization of proteins

Computational characterization of proteins is a necessary first step in understanding the biologic role of a protein. The composite architecture of mammalian proteins makes the prediction of the biologic role rather difficult. Nevertheless, integration of many different prediction methods allows for a more accurate representation. Information on the 3D structure of a protein improves the reliability of predictions of many features. This article reviews existing methods used to characterize proteins and several tools that provide an integrated access to different types of information. The authors point out the increasing importance of structural constraints and an increasing need to integrate different approaches.     

Interaction energy based protein structure networks

The three-dimensional structure of a protein is formed and maintained by the noncovalent interactions among the amino-acid residues of the polypeptide chain. These interactions can be represented collectively in the form of a network. So far, such networks have been investigated by considering the connections based on distances between the amino-acid residues. Here we present a method of constructing the structure network based on interaction energies among the amino-acid residues in the protein. We have investigated the properties of such protein energy-based networks (PENs) and have shown correlations to protein structural features such as the clusters of residues involved in stability, formation of secondary and super-secondary structural units. Further we demonstrate that the analysis of PENs in terms of parameters such as hubs and shortest paths can provide a variety of biologically important information, such as the residues crucial for stabilizing the folded units and the paths of communication between distal residues in the protein. Finally, the energy regimes for different levels of stabilization in the protein structure have clearly emerged from the PEN analysis.     

Mapping and characterization of LCA networks

Purpose

The aims of this study were to provide an up-to-date overview of global, regional and local networks supporting life cycle thinking and to characterize them according to their structure and activities.

Methods

Following a tentative life cycle assessment (LCA) network definition, a mapping was performed based on (1) a literature search, (2) a web search and (3) an inquiry to stakeholders distributed via the two largest LCA fora. Networks were characterized based on responses from a survey.

Results and discussion

We identified 100 networks, of which 29 fulfilled all six criteria composing our tentative network definition (the remaining fulfilled four to five criteria). The networks are mainly located in Europe and the USA, whilst Africa, the Middle East and Central Asia are less covered regions. The survey results (from 25 network responses) indicate that LCA networks appear to be primarily small- to medium-sized (<100 members) and to include a large proportion of academia and industries, including small- and medium-sized enterprises, with much less involvement of authorities and non-governmental organisations. Their major activities relate to knowledge sharing and communication, support of case studies, and development of life cycle inventories and impact assessment methods. Networks in developing economies have different structures and activities than networks in developed economies and, for instance, more frequently have members from non-governmental organisations. Globally, an increasing trend in the formation of LCA networks over time is observed, which tends to correlate with the number of LCA scientific publications over the same time period. Continental distributions of networks also show a correlation with the number of LCA publications from the same region.

Conclusions

The provided list of LCA networks is currently the most comprehensive, publicly available mapping. We believe that the results of this mapping can serve as a basis for deciding where priorities should be set to increase the dissemination and development of LCA worldwide. In this aim, we also advocate the creation of an online, regularly updated database of LCA networks supplemented by an online platform that could facilitate network communication and knowledge sharing.     

Fluorescence characterization of denatured proteins

Characterization of unfolded states, while critical to a complete understanding of protein folding, is inherently difficult due to structural heterogeneity and dynamic interchange between states. The growing body of work focusing on single molecule fluorescence techniques for the study of protein folding, also highlights their potential for studies of unfolded proteins. These methods can obtain conformational information about individual subpopulations of molecules in an ensemble, and measure dynamics without the need for synchronization. The studies highlighted here demonstrate the promise of these techniques for obtaining novel information about unfolded states in vitro and in more physiologically relevant milieu.     

On the crystallization of proteins

We report on theoretical and experimental work aimed at a systematic approach to the crystallization of proteins. Successful crystallization depends on the competition between the growth rates for compact three-dimensional structures and long-chain structures leading to an amorphous precipitate. Quasi-elastic light scattering was used to monitor the size and shape distribution of small aggregates in a model system (lysozyme) during the pre-nucleation stage. With the aid of a simple model, the line-width of the scattered light was used to predict whether crystals or an amorphous precipitate would result. Once visible crystals appeared, the lysozyme concentration near the crystal surface was monitored and the kinetic parameters for growth obtained. A peculiar self-limiting phenomenon causes crystals to stop growing after a certain size has been reached. When these terminal size crystals were cleaved, growth occurred at the surface until the original size was approximately restored.     

An analysis of non-bonded energy of proteins

Non-bonded energy of 16 proteins was calculated using the atomic co-ordinates obtained by X-ray crystallography. The curve of total energy against the number of atoms in proteins is approximately linear with a slight concaved shape. According to a linear equation to fit the curve, the extrapolated length of a polypeptide chain of a globular shape is expected to be 18 residues, which corresponds conceivably to an approximate size of nucleus for a folding of the polypeptide chain. Contributions from short-range and medium-range energies are always much greater than those from long-range energy for all the proteins and there seems to exist a change of each contribution in a range from 1200 to 1700 atoms. The energies with a lag less than four residues are a major part of the total energy and the contribution of energy from main-chain atoms is considerably higher than that from side-chain atoms. Side-chain atoms of a residue have a tendency to interact more strongly with main-chain atoms of N-terminal, than with those of C-terminal side of the residue, indicating asymmetry of the interaction in a protein. Amino acid residues in proteins may be divided into three groups by the order of strength of average energy. The first group exhibiting strong interaction consists mainly of hydrophobic amino acids and the third group consists of hydrophilic ones corresponding to the location in a protein molecule. Cys, val, leu and met are important for medium-range and long-range energies; gly and ala for medium-range energy; ile, trp, phe, tyr and arg for long-range energy. One simple application of the average energy of amino acid residues is illustrated to estimate local energy of a segment of nine residues given by a protein sequence. There is a good correlation between the curve computed by the average energy and the experimental curve for myoglobin.     

On the architecture of cell regulation networks

Background  

With the rapid development of high-throughput experiments, detecting functional modules has become increasingly important in analyzing biological networks. However, the growing size and complexity of these networks preclude structural breaking in terms of simplest units. We propose a novel graph theoretic decomposition scheme combined with dynamics consideration for probing the architecture of complex biological networks.     

On the performance of single-layered neural networks

This paper studies the performance of single-layered neural networks. This study begins with the performance of single-layered neural networks trained using the outer-product rule. The outer-product rule is a suboptimal learning scheme, resulting under certain assumptions from optimal least-squares training of single-layered neural networks with respect to their analog output. Extensive analysis reveals the improvement on the network performance caused by its optimal least-squares training. The effect of the training scheme on the performance of single-layered neural networks with binary output is exhibited by experimentally comparing the performance of single-layered neural networks trained with respect to their analog and binary output.     

On the sparse reconstruction of gene networks

We discuss a heuristic method for the sparse reconstruction of gene networks. The method is based on iterative greedy algorithms, and uses gene expression data from microarray experiments. Also, we show numerically that the greedy algorithms are able to give good approximative solutions to the sparse reconstruction problem even in the presence of significant levels of noise.     

On the elasticity of cytoskeletal networks.

Models relating to the gelation and elasticity of complex cytoskeletal networks are formulated and investigated. Kinetic equations for reversible elongation of nucleated actin filaments are analyzed when the filaments are acted upon by capping proteins and cross-linking factors. Analytical expressions are obtained that relate the low frequency elastic shear modulus of a network, G, to chain growth kinetics, the number of nucleation sites, monomer concentration, and the amount of capping and cross-linking protein. Elasticity curves that relate G to such factors as the association constant for cross-linking are derived and then used to determine solation-gelation phase contours.