Iterative approach to model identification of biological networks

Background  

Recent advances in molecular biology techniques provide an opportunity for developing detailed mathematical models of biological processes. An iterative scheme is introduced for model identification using available system knowledge and experimental measurements.     

EXAMINE: a computational approach to reconstructing gene regulatory networks

Reverse-engineering of gene networks using linear models often results in an underdetermined system because of excessive unknown parameters. In addition, the practical utility of linear models has remained unclear. We address these problems by developing an improved method, EXpression Array MINing Engine (EXAMINE), to infer gene regulatory networks from time-series gene expression data sets. EXAMINE takes advantage of sparse graph theory to overcome the excessive-parameter problem with an adaptive-connectivity model and fitting algorithm. EXAMINE also guarantees that the most parsimonious network structure will be found with its incremental adaptive fitting process. Compared to previous linear models, where a fully connected model is used, EXAMINE reduces the number of parameters by O(N), thereby increasing the chance of recovering the underlying regulatory network. The fitting algorithm increments the connectivity during the fitting process until a satisfactory fit is obtained. We performed a systematic study to explore the data mining ability of linear models. A guideline for using linear models is provided: If the system is small (3-20 elements), more than 90% of the regulation pathways can be determined correctly. For a large-scale system, either clustering is needed or it is necessary to integrate information in addition to expression profile. Coupled with the clustering method, we applied EXAMINE to rat central nervous system development (CNS) data with 112 genes. We were able to efficiently generate regulatory networks with statistically significant pathways that have been predicted previously.     

Theoretical and computational models of biological ion channels

The goal of this review is to establish a broad and rigorous theoretical framework to describe ion permeation through biological channels. This framework is developed in the context of atomic models on the basis of the statistical mechanical projection-operator formalism of Mori and Zwanzig. The review is divided into two main parts. The first part introduces the fundamental concepts needed to construct a hierarchy of dynamical models at different level of approximation. In particular, the potential of mean force (PMF) as a configuration-dependent free energy is introduced, and its significance concerning equilibrium and non-equilibrium phenomena is discussed. In addition, fundamental aspects of membrane electrostatics, with a particular emphasis on the influence of the transmembrane potential, as well as important computational techniques for extracting essential information from all-atom molecular dynamics (MD) simulations are described and discussed. The first part of the review provides a theoretical formalism to 'translate' the information from the atomic structure into the familiar language of phenomenological models of ion permeation. The second part is aimed at reviewing and contrasting results obtained in recent computational studies of three very different channels: the gramicidin A (gA) channel, which is a narrow one-ion pore (at moderate concentration), the KcsA channel from Streptomyces lividans, which is a narrow multi-ion pore, and the outer membrane matrix porin F (OmpF) from Escherichia coli, which is a trimer of three beta-barrel subunits each forming wide aqueous multi-ion pores. Comparison with experiments demonstrates that current computational models are approaching semi-quantitative accuracy and are able to provide significant insight into the microscopic mechanisms of ion conduction and selectivity. We conclude that all-atom MD with explicit water molecules can represent important structural features of complex biological channels accurately, including such features as the location of ion-binding sites along the permeation pathway. We finally discuss the broader issue of the validity of ion permeation models and an outlook to the future.     

Qualitative networks: a symbolic approach to analyze biological signaling networks

Background  

A central goal of Systems Biology is to model and analyze biological signaling pathways that interact with one another to form complex networks. Here we introduce Qualitative networks, an extension of Boolean networks. With this framework, we use formal verification methods to check whether a model is consistent with the laboratory experimental observations on which it is based. If the model does not conform to the data, we suggest a revised model and the new hypotheses are tested in-silico.     

A proteomic approach to neuropeptide function elucidation

Many of the diverse functions of neuropeptides are still elusive. As they are ideally suited to modulate traditional signaling, their added actions are not always detectable under standard laboratory conditions. The search for function assignment to peptide encoding genes can therefore greatly benefit from molecular information. Specific molecular changes resulting from neuropeptide signaling may direct researchers to yet unknown processes or conditions, for which studying these signaling systems may eventually lead to phenotypic confirmation. Here, we applied gel-based proteomics after pdf-1 neuropeptide gene knockout in the model organism Caenorhabditis elegans. It has previously been described that pdf-1 null mutants display a locomotion defect, being slower and making more turns and reversals than wild type worms. The vertebrate functional homolog of PDF-1, vasocative intestinal peptide (VIP), is known to influence a plethora of processes, which have so far not been investigated for pdf-1. Because proteins represent the actual effectors inside an organism, proteomic analysis can guide our view to novel pdf-1 actions in the nematode worm. Our data show that knocking out pdf-1 results in alteration of levels of proteins involved in fat metabolism, stress resistance and development. This indicates a possible conservation of VIP-like actions for pdf-1 in C. elegans.     

A proteomic approach to characterize protein shedding

Shedding (i.e. proteolysis of ectodomains of membrane proteins) plays an important pathophysiological role. In order to study the feasibility of identifying shed proteins, we analyzed serum-free media of human mammary epithelial cells by mass spectrometry following induction of shedding by the phorbol ester, 4 beta-phorbol 12-myristate 13-acetate (PMA). Different means of sample preparation, including biotinylation of cell surface proteins, isolation of glycosylated proteins, and preparation of crude protein fractions, were carried out to develop the optimal method of sample processing. The collected proteins were digested with trypsin and analyzed by reversed-phase capillary liquid chromatography interfaced to an ion-trap mass spectrometer. The resulting peptide spectra were interpreted using the program SEQUEST. Analyzing the sample containing the crude protein mixture without chemical modification or separation resulted in the greatest number of identifications, including putatively shed proteins. Overall, 45 membrane-associated proteins were identified including 22 that contain at least one transmembrane domain and 23 that indirectly associate with the extracellular surface of the plasma membrane. Of the 22 transmembrane proteins, 18 were identified by extracellular peptides providing strong evidence they originate from regulated proteolysis or shedding processes. We combined results from the different experiments and used a peptide count method to estimate changes in protein abundance. Using this approach, we identified two proteins, syndecan-4 and hepatoma-derived growth factor, whose abundances increased in media of cells treated with PMA. We also detected proteins whose abundances decreased after PMA treatment such as 78 kDa glucose-regulated protein and lactate dehydrogenase A. Further analysis using immunoblotting validated the abundance changes for syndecan-4 and 78 kDa glucose-regulated protein as a result of PMA treatment. These results demonstrate that tandem mass spectrometry can be used to identify shed proteins and to estimate changes in protein abundance.     

A proteomic approach to study parathyroid glands

Parathyroid tumours are heterogeneous and in some cases the diagnosis may be difficult using histological features. In this study we used a two-dimensional electrophoresis (2D)/mass spectrometry (MS)-based approach to examine the global changes of parathyroid adenoma tissues protein profile compared to the parathyroid normal tissues. Validation of protein expression was performed by immunoblotting using specific antibodies. Ingenuity software was used to identify the biological processes to which these proteins belong and to construct a potential network. A total of 30 proteins were found to be differentially expressed, of which 22 resulted in being over-expressed. Proteins identified by 2D/MS/MS proteomics were classified into functional categories and a major change (≥ 2-fold) in terms of expression was found in proteins involved in response to biotic stimuli, cell organization and signal transduction. After Ingenuity analysis, 14-3-3 ζ/δ appears to be a key protein in the network of parathyroid adenoma, where it is linked to other proteins such as annexin A2, B box and SPRY domain-containing protein (BSPRY), p53 and epidermal growth factor receptor (EGFR). Our results suggest that the proteomic approach was able to differentiate the protein profiles of normal parathyroid and parathyroid adenoma and identify a panel of proteins which are differentially expressed. The functional role of these proteins in the network of intracellular pathways is discussed.     

A computational approach to animal breeding

We propose a computational model of mating strategies for controlled animal breeding programs. A mating strategy in a controlled breeding program is a heuristic with some optimization criteria as a goal. Thus, it is appropriate to use the computational tools available for analysis of optimization heuristics. In this paper, we propose the first discrete model of the controlled animal breeding problem and analyse heuristics for two possible objectives: (1) breeding for maximum diversity and (2) breeding a target individual. These two goals are representative of conservation biology and agricultural livestock management, respectively. We evaluate several mating strategies and provide upper and lower bounds for the expected number of matings. While the population parameters may vary and can change the actual number of matings for a particular strategy, the order of magnitude of the number of expected matings and the relative competitiveness of the mating heuristics remains the same. Thus, our simple discrete model of the animal breeding problem provides a novel viable and robust approach to designing and comparing breeding strategies in captive populations.     

A computational approach to motion perception

In this paper it is shown that the computation of the optical flow from a sequence of timevarying images is not, in general, an underconstrained problem. A local algorithm for the computation of the optical flow which uses second order derivatives of the image brightness pattern, and that avoids the aperture problem, is presented. The obtained optical flow is very similar to the true motion field — which is the vector field associated with moving features on the image plane — and can be used to recover 3D motion information. Experimental results on sequences of real images, together with estimates of relevant motion parameters, like time-to-crash for translation and angular velocity for rotation, are presented and discussed. Due to the remarkable accuracy which can be achieved in estimating motion parameters, the proposed method is likely to be very useful in a number of computer vision applications.     

Engineering aspects of biological ion channels--from biosensors to computational models for permeation

This paper presents two important engineering aspects of biological ion channels-how to build sensors out of gramicidin channels and how to construct computational models for ion channel permeation. We describe our recent research in these areas, potential challenges and possible solutions.     

Duplication models for biological networks.

Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit power-law graphs (number of nodes with degree k, N(k) approximately k(-beta)), yet the exponents, beta, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce power-law graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.     

A multidimensional proteomic approach to identify hypertrophy-associated proteins

Left ventricular hypertrophy (LVH) is a leading cause of congestive heart failure. The exact mechanisms that control cardiac growth and regulate the transition to failure are not fully understood, in part due to the lack of a complete inventory of proteins associated with LVH. We investigated the proteomic basis of LVH using the transverse aortic constriction model of pressure overload in mice coupled with a multidimensional approach to identify known and novel proteins that may be relevant to the development and maintenance of LVH. We identified 123 proteins that were differentially expressed during LVH, including LIM proteins, thioredoxin, myoglobin, fatty acid binding protein 3, the abnormal spindle-like microcephaly protein (ASPM), and cytoskeletal proteins such as actin and myosin. In addition, proteins with unknown functions were identified, providing new directions for future research in this area. We also discuss common pitfalls and strategies to overcome the limitations of current proteomic technologies. Together, the multidimensional approach provides insight into the proteomic changes that occur in the LV during hypertrophy.     

Evolution of biological interaction networks: from models to real data

We are beginning to uncover common mechanisms leading to the evolution of biological networks. The driving force behind these advances is the increasing availability of comparative data in several species.     

A computational approach to the synthesis of dirithromycin

Dirithromycin is a macrolide antibiotic derived from erythromycin A. Dirithromycin is synthesized by the condensation of 9(S)-erythromycylamine with 2-(2-methoxyethoxy)-acetaldehyde. To gain insight into the synthesis, the condensation mechanism has been analyzed computationally by the AM1 method in the gas phase. First, the formation of the Schiff bases of dirithromycin and epidirithromycin from 9(S)-erythromycylamine and 2-(2-methoxyethoxy)-acetaldehyde were modeled. Then, the tautomerization of the Schiff bases to dirithromycin and epidirithromycin were considered. Finally, the epimerization of the Schiff base of epidirithromycin to the Schiff base of dirithromycin was investigated. Our results show that, even though carbinolamine forms faster for epidirithromycin than the corresponding structure for dirithromycin, dirithromycin is the major product of the synthesis. Figure Synthesis of dirithromycin     

A computational approach to the polymerizabilities of diallylamines

Some selected diallylamine monomers have been studied with the semiempirical PM3 method as model compounds for N,N-dialkyl-N-2-(alkoxycarbonyl)allylammonium salts, in order to build up a quantitative and qualitative relationship between the experimental cyclopolymerizabilities of the monomers and calculated parameters such as charge, energy, geometrical features, bond orders, local softness values and HOMO-LUMO gaps. The charges on nitrogen, vinyl and allyl carbons, the activation barriers, the local softness values and the HOMO-LUMO gaps are found to represent the polymerizability trend of the monomers in general. Three-dimensional structures have been proposed for the reactants and their transition states by geometry optimizations with PM3.     

Supervised reconstruction of biological networks with local models

MOTIVATION: Inference and reconstruction of biological networks from heterogeneous data is currently an active research subject with several important applications in systems biology. The problem has been attacked from many different points of view with varying degrees of success. In particular, predicting new edges with a reasonable false discovery rate is highly demanded for practical applications, but remains extremely challenging due to the sparsity of the networks of interest. RESULTS: While most previous approaches based on the partial knowledge of the network to be inferred build global models to predict new edges over the network, we introduce here a novel method which predicts whether there is an edge from a newly added vertex to each of the vertices of a known network using local models. This involves learning individually a certain subnetwork associated with each vertex of the known network, then using the discovered classification rule associated with only that vertex to predict the edge to the new vertex. Excellent experimental results are shown in the case of metabolic and protein-protein interaction network reconstruction from a variety of genomic data. AVAILABILITY: An implementation of the proposed algorithm is available upon request from the authors.     

A computational approach to design energetic ionic liquids

The present work deals with the theoretical estimation of ion-pair binding energies and the energetic properties of four ion pairs formed by combining the 1-butyl-2,4-dinitro-3-methyl imidazolium ion with nitrate (I), perchlorate (II), dinitramide (III), or 3,5-dinitro-1,2,4-triazolate (IV) anions. The counterpoise-corrected ion-pair binding energies were calculated for each ion pair at the B3LYP/6-311+G(d,p) level of theory. Results show that the cation–anion interaction is strongest for ion pair I and weakest for IV, indicating that the nitrate (I) has a greater tendency to exist as a stable ionic salt whereas the 3,5-dinitro-1,2,4-triazolate (IV) may exist as an ionic liquid. Natural bond orbital (NBO) analysis and electrostatic potential (ESP) mapping revealed that charge transfer occurs in all of the ion pairs, but is greatest (0.25e) for ion pair I and smallest (0.03e) for IV, resulting in ion pair I being the least polarized. A nucleus-independent chemical shift (NICS) study revealed that the aromaticity of the 1-butyl-2,4-dinitro-3-methyl imidazolium ion significantly increases in ion pair IV, indicating that this has the greatest charge delocalization among all of the four ion pairs considered. Studies of thermodynamic and detonation properties showed that ion pair II is the most energetic ion pair in terms of its detonation velocity (D = 7.5 km s^?1) and detonation pressure (P = 23.1 GPa). It is also envisaged that ion pair IV would exist as an energetic azolium azolate type ionic liquid that could be conveniently used as a secondary explosive characterized by detonation parameters D and P of 6.9 km s^?1 and 19.3 GPa, respectively. These values are comparable to those of conventional explosives such as TNT.