Graph theory and stability analysis of protein complex interaction networks

Protein complexes play an essential role in many biological processes. Complexes can interact with other complexes to form protein complex interaction network (PCIN) that involves in important cellular processes. There are relatively few studies on examining the interaction topology among protein complexes; and little is known about the stability of PCIN under perturbations. We employed graph theoretical approach to reveal hidden properties and features of four species PCINs. Two main issues are addressed, (i) the global and local network topological properties, and (ii) the stability of the networks under 12 types of perturbations. According to the topological parameter classification, we identified some critical protein complexes and validated that the topological analysis approach could provide meaningful biological interpretations of the protein complex systems. Through the Kolmogorov–Smimov test, we showed that local topological parameters are good indicators to characterise the structure of PCINs. We further demonstrated the effectiveness of the current approach by performing the scalability and data normalization tests. To measure the robustness of PCINs, we proposed to consider eight topological‐based perturbations, which are specifically applicable in scenarios of targeted, sustained attacks. We found that the degree‐based, betweenness‐based and brokering‐coefficient‐based perturbations have the largest effect on network stability.Inspec keywords: graph theory, perturbation theory, proteins, molecular configurations, molecular biophysics, pattern clustering, pattern classification, cellular biophysics, biology computingOther keywords: stability analysis, protein complex interaction networks, biological processes, protein complex interaction network, cellular processes, interaction topology, graph theoretical approach, local network topological properties, topological parameter classification, Kolmogorov‐Smirnov test, network structures, data normalisation tests, topological‐based perturbations, highly clustered protein complexes, brokering‐coefficient‐based perturbations, betweenness‐based perturbations     

Reliability and robustness of thin film composite resistor networks

Reliability of composite NiCr–tantalum nitride resistors was tested according to MIL STD 883 procedures. It was shown analytically and experimentally that these resistors are robust and stable, and they can thus be recommended for use in precise and reliable integrated circuits.     

The relationship between modularity and robustness in signalling networks

Many biological networks tend to have a high modularity structural property and the dynamic characteristic of high robustness against perturbations. However, the relationship between modularity and robustness is not well understood. To investigate this relationship, we examined real signalling networks and conducted simulations using a random Boolean network model. As a result, we first observed that the network robustness is negatively correlated with the network modularity. In particular, this negative correlation becomes more apparent as the network density becomes sparser. Even more interesting is that, the negative relationship between the network robustness and the network modularity occurs mainly because nodes in the same module with the perturbed node tend to be more sensitive to the perturbation than those in other modules. This result implies that dynamically similar nodes tend to be located in the same module of a network. To support this, we show that a pair of genes associated with the same disease or a pair of functionally similar genes is likely to belong to the same module in a human signalling network.     

Graphics processing unit‐based alignment of protein interaction networks

Network alignment is an important bridge to understanding human protein–protein interactions (PPIs) and functions through model organisms. However, the underlying subgraph isomorphism problem complicates and increases the time required to align protein interaction networks (PINs). Parallel computing technology is an effective solution to the challenge of aligning large‐scale networks via sequential computing. In this study, the typical Hungarian‐Greedy Algorithm (HGA) is used as an example for PIN alignment. The authors propose a HGA with 2‐nearest neighbours (HGA‐2N) and implement its graphics processing unit (GPU) acceleration. Numerical experiments demonstrate that HGA‐2N can find alignments that are close to those found by HGA while dramatically reducing computing time. The GPU implementation of HGA‐2N optimises the parallel pattern, computing mode and storage mode and it improves the computing time ratio between the CPU and GPU compared with HGA when large‐scale networks are considered. By using HGA‐2N in GPUs, conserved PPIs can be observed, and potential PPIs can be predicted. Among the predictions based on 25 common Gene Ontology terms, 42.8% can be found in the Human Protein Reference Database. Furthermore, a new method of reconstructing phylogenetic trees is introduced, which shows the same relationships among five herpes viruses that are obtained using other methods.Inspec keywords: graphics processing units, proteins, molecular biophysics, genetics, microorganisms, medical computing, bioinformaticsOther keywords: graphics processing unit‐based alignment, protein interaction networks, network alignment, human protein–protein interactions, Hungarian‐Greedy algorithm, GPU acceleration, gene ontology terms, phylogenetic trees reconstruction, herpes viruses     

Stochastic analysis of biochemical reaction networks with absolute concentration robustness

It has recently been shown that structural conditions on the reaction network, rather than a ‘fine-tuning’ of system parameters, often suffice to impart ‘absolute concentration robustness’ (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.     

A new tool to assess water pipe networks vulnerability and robustness

The safety of a population also relies on the safety of the water pipe network systems. Good quality water supplying is required. A failure of these types of systems may have a huge social impact. The theory of vulnerability of water pipe networks intends to give a contribution in this context by tracing the vulnerable parts of the system and, consequently, giving guidance to increase its robustness. This theory is described in brief and supported on three water pipe networks examples.     

A study of the robustness of pseudorandom binary-array-basedsurface characterization

In this paper me report on aspects of the use of color-coded pseudorandom binary arrays (PRBA's) to model three-dimensional scenes. We evaluate the accuracy and the robustness of the pattern recognition phase in the process. Emphasis is on the added value of the use of PRBA's as a tool to make the image processing robust and highly noise insensitive     

Topology and static response of interaction networks in molecular biology.

We introduce a mathematical framework describing static response of networks occurring in molecular biology. This formalism has many similarities with the Laplace-Kirchhoff equations for electrical networks. We introduce the concept of graph boundary and we show how the response of the biological networks to external perturbations can be related to the Dirichlet or Neumann problems for the corresponding equations on the interaction graph. Solutions to these two problems are given in terms of path moduli (measuring path rigidity with respect to the propagation of interaction along the graph). Path moduli are related to loop products in the interaction graph via generalized Mason-Coates formulae. We apply our results to two specific biological examples: the lactose operon and the genetic regulation of lipogenesis. Our applications show consistency with experimental results and in the case of lipogenesis check some hypothesis on the behaviour of hepatic fatty acids on fasting.     

Modelling protein-protein interaction networks via a stickiness index.

What type of connectivity structure are we seeing in protein-protein interaction networks? A number of random graph models have been mooted. After fitting model parameters to real data, the models can be judged by their success in reproducing key network properties. Here, we propose a very simple random graph model that inserts a connection according to the degree, or 'stickiness', of the two proteins involved. This model can be regarded as a testable distillation of more sophisticated versions that attempt to account for the presence of interaction surfaces or binding domains. By computing a range of network similarity measures, including relative graphlet frequency distance, we find that our model outperforms other random graph classes. In particular, we show that given the underlying degree information, fitting a stickiness model produces better results than simply choosing a degree-matching graph uniformly at random. Therefore, the results lend support to the basic modelling methodology.     

Anticancer drug-inorganic nanohybrid and its cellular interaction

An anticancer drug, methotrexate (MTX), has been successfully hybridized with layered double hydroxide (LDH) through co-precipitation route to produce MTX-LDH nanohybrids (MTX-LDH). According to the X-ray diffraction and FT-IR spectroscopy, it was confirmed that MTX molecules are stabilized in the interlayer space of LDHs by electrostatic interaction, maintaining their functional groups and structural integrity. According to the drug release study, the total amount of released MTX from the LDH lattice was determined to be larger under a simulated intracellular lysosomal condition (pH = 4.5) than simulated body fluid one (pH = 7.4). It is, therefore, expected that the MTX molecules in MTX-LDH can be effectively released in lysosomes, since the MTX release could be accelerated via ion-exchange reaction and dissolution of LDH in an acidic lysosomal condition. We also examined the anticancer efficacy of MTX-LDH in human breast adenocarcinoma MCF-7 cells. The cellular uptake of MTX was considerably higher in MTX-LDH-treated cells than in free MTX-treated cells, giving a lower IC50 value for the former than the latter. All the results demonstrated that the MTX-LDH nanohybrid allows the efficient drug delivery in cells, and thus enhances drug efficacy.     

Characterization and optimization of an entropic trap for DNA separation.

Recently, a microfabricated entropic trap array was demonstrated to be useful in separating large (5-200 kbp) DNA molecules efficiently (within approximately 30 min), by dc electrophoresis, on a microchip platform without a sieving matrix. This paper reports further development of the technique, with emphasis on optimizing separation selectivity and resolution. The interaction of DNA molecules with regularly spaced entropic barriers was modeled in order to predict the effect of changing various structural parameters. The selectivity (differential mobility) was shown to be dependent on the depth of deep and shallow channel regions, applied electric field, and number of entropic barriers. Experimental data were compared with the prediction of the model. It was expected from the model that, in the low-field (severe trapping) limit, separation resolution should depend only on the number of entropic traps. However, in reality, resolution did depend on the applied field because the relaxation of DNA is not achieved at high fields. The requirement and feasibility of megabase pair DNA separation with the entropic trap array device was discussed.     

Feasibility and robustness of transiently chaotic neural networks applied to the cell formation problem

Cell formation is a key issue in the design of cellular manufacturing systems. Effective grouping of parts and machines can improve considerably the performance of manufacturing cells. The transiently chaotic neural network (TCNN) is a recent methodology in intelligent computation that has the advantages of both the chaotic neural network and the Hopfield neural network. The present paper investigates the dynamics of the TCNN network and studies the feasibility and robustness of final solutions of TCNN when applied to the cell formation problem. The paper provides insight into the feasibility and robustness of TCNN for cell formation problems. It also discusses how to set the initial values of the TCNN parameters in the case of well-structured and ill-structured cell formation problems.     

Spontaneous emergence of modularity in cellular networks

Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the formation of modular structures, which would specialize in different functions. Here we show that, within the context of cellular networks, no such selection pressure is needed to obtain modularity. Instead, the intrinsic dynamics of network growth by duplication and diversification is able to generate it for free and explain the statistical features exhibited by small subgraphs. The implications for the evolution and evolvability of both biological and technological systems are discussed.     

An optimal procedure to extract interaction potentials for protein folding

A formidable challenge in molecular biology is the prediction of the three-dimensional structures of the native state of proteins from their sequence of amino acids. An essential step to solve this problem is the extraction of the coarse-grained interaction potentials between the amino acids. Here we outline preliminary results of a strategy that accomplishes such goal with the search of those potentials which are able to recognize the native state of a protein as a stable local minimum. The method is implemented by exploiting several numerical and analytical tools which have been recently developed by our group. The results are extremely promising: despite the fact that we have used simple forms for Hamiltonians, the extracted potentials are able to stabilize simultaneously at least 10 proteins of different classes to an average distance (per residue) less than 3 Å from the native state.     

Polar Mapper: a computational tool for integrated visualization of protein interaction networks and mRNA expression data

Polar Mapper is a computational application for exposing the architecture of protein interaction networks. It facilitates the system-level analysis of mRNA expression data in the context of the underlying protein interaction network. Preliminary analysis of a human protein interaction network and comparison of the yeast oxidative stress and heat shock gene expression responses are addressed as case studies.