Petri net-based method for the analysis of the dynamics of signal propagation in signaling pathways

MOTIVATION: Cellular signaling networks are dynamic systems that propagate and process information, and, ultimately, cause phenotypical responses. Understanding the circuitry of the information flow in cells is one of the keys to understanding complex cellular processes. The development of computational quantitative models is a promising avenue for attaining this goal. Not only does the analysis of the simulation data based on the concentration variations of biological compounds yields information about systemic state changes, but it is also very helpful for obtaining information about the dynamics of signal propagation. RESULTS: This article introduces a new method for analyzing the dynamics of signal propagation in signaling pathways using Petri net theory. The method is demonstrated with the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) regulation network. The results constitute temporal information about signal propagation in the network, a simplified graphical representation of the network and of the signal propagation dynamics and a characterization of some signaling routes as regulation motifs.     

Testing for predator dependence in predator-prey dynamics: a non-parametric approach

The functional response is a key element in all predator-prey interactions. Although functional responses are traditionally modelled as being a function of prey density only, evidence is accumulating that predator density also has an important effect. However, much of the evidence comes from artificial experimental arenas under conditions not necessarily representative of the natural system, and neglecting the temporal dynamics of the organism (in particular the effects of prey depletion on the estimated functional response). Here we present a method that removes these limitations by reconstructing the functional response non-parametrically from predator-prey time-series data. This method is applied to data on a protozoan predator-prey interaction, and we obtain significant evidence of predator dependence in the functional response. A crucial element in this analysis is to include time-lags in the prey and predator reproduction rates, and we show that these delays improve the fit of the model significantly. Finally, we compare the non-parametrically reconstructed functional response to parametric forms, and suggest that a modified version of the Hassell-Varley predator interference model provides a simple and flexible function for theoretical investigation and applied modelling.     

Zinc networks: the cell-specific compartmentalization of zinc for specialized functions

Abstract Zinc (Zn2+) is the most abundant trace element in cells and is essential for a vast number of catalytic, structural, and regulatory processes. Mounting evidence indicates that like calcium (Ca2+), intracellular Zn2+ pools are redistributed for specific cellular functions. This occurs through the regulation of 24 Zn2+ transporters whose localization and expression is tissue and cell specific. We propose that the complement and regulation of Zn2+ transporters expressed within a given cell type reflects the function of the cell itself and comprises a 'Zn2+ network.' Importantly, increasing information implicates perturbations in the Zn2+ network with metabolic consequences and disease. Herein, we discuss our current understanding of Zn2+ transporters from the perspective of a Zn2+ network in four specific tissues with unique Zn2+ requirements (mammary gland, prostate, pancreas, and brain). Delineating the entire Zn2+ transporting network within the context of unique cellular Zn2+ needs is important in identifying critical gaps in our knowledge and improving our understanding of the consequences of Zn2+ dysregulation in human health and disease.     

Mitochondrial dynamics: a strategy for avoiding autophagy

Cells normally respond to a lack of nutrients by activating autophagy, a prominent pro-survival pathway that involves the catabolism and recycling of cytoplasmic material. Recent results indicate that mitochondria actively elongate during autophagy, thereby avoiding their degradation and sustaining cell viability.     

STEPP--Search Tool for Exploration of Petri net Paths: a new tool for Petri net-based path analysis in biochemical networks

To understand biochemical processes caused by, e. g., mutations or deletions in the genome, the knowledge of possible alternative paths between two arbitrary chemical compounds is of increasing interest for biotechnology, pharmacology, medicine, and drug design. With the steadily increasing amount of data from high-throughput experiments new biochemical networks can be constructed and existing ones can be extended, which results in many large metabolic, signal transduction, and gene regulatory networks. The search for alternative paths within these complex and large networks can provide a huge amount of solutions, which can not be handled manually. Moreover, not all of the alternative paths are generally of interest. Therefore, we have developed and implemented a method, which allows us to define constraints to reduce the set of all structurally possible paths to the truly interesting path set. The paper describes the search algorithm and the constraints definition language. We give examples for path searches using this dedicated special language for a Petri net model of the sucrose-to-starch breakdown in the potato tuber.     

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.     

nucleR: a package for non-parametric nucleosome positioning

SUMMARY: nucleR is an R/Bioconductor package for a flexible and fast recognition of nucleosome positioning from next generation sequencing and tiling arrays experiments. The software is integrated with standard high-throughput genomics R packages and allows for in situ visualization as well as to export results to common genome browser formats. AVAILABILITY: Additional information and methodological details can be found at http://mmb.pcb.ub.es/nucleR     

The statistical mechanics of complex signaling networks: nerve growth factor signaling

The inherent complexity of cellular signaling networks and their importance to a wide range of cellular functions necessitates the development of modeling methods that can be applied toward making predictions and highlighting the appropriate experiments to test our understanding of how these systems are designed and function. We use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. A key difficulty with signaling models is that, while significant effort is being made to experimentally measure the rate constants for individual steps in these networks, many of the parameters required to describe their behavior remain unknown or at best represent estimates. To establish the usefulness of our approach, we have applied our methods toward modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. In particular, we study the actions of NGF and mitogenic epidermal growth factor (EGF) in rat pheochromocytoma (PC12) cells. Through a network of intermediate signaling proteins, each of these growth factors stimulates extracellular regulated kinase (Erk) phosphorylation with distinct dynamical profiles. Using our modeling approach, we are able to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems that we call 'sloppiness.'     

Incremental mutual information: a new method for characterizing the strength and dynamics of connections in neuronal circuits

Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). By conditioning out the temporal dependencies in the responses of individual neurons before measuring the dependency between them, IMI improves on standard correlation-based measures in several important ways: 1) it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e.g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales, 2) for the study of early sensory systems, it does not require responses to repeated trials of identical stimulation, and 3) it does not assume that the connection between neurons is linear. We describe the theory and implementation of IMI in detail and demonstrate its utility on experimental recordings from the primate visual system.     

Salt-bridge networks within globular and disordered proteins: characterizing trends for designable interactions

There has been considerable debate about the contribution of salt bridges to the stabilization of protein folds, in spite of their participation in crucial protein functions. Salt bridges appear to contribute to the activity–stability trade-off within proteins by bringing high-entropy charged amino acids into close contacts during the course of their functions. The current study analyzes the modes of association of salt bridges (in terms of networks) within globular proteins and at protein–protein interfaces. While the most common and trivial type of salt bridge is the isolated salt bridge, bifurcated salt bridge appears to be a distinct salt-bridge motif having a special topology and geometry. Bifurcated salt bridges are found ubiquitously in proteins and interprotein complexes. Interesting and attractive examples presenting different modes of interaction are highlighted. Bifurcated salt bridges appear to function as molecular clips that are used to stitch together large surface contours at interacting protein interfaces. The present work also emphasizes the key role of salt-bridge-mediated interactions in the partial folding of proteins containing long stretches of disordered regions. Salt-bridge-mediated interactions seem to be pivotal to the promotion of “disorder-to-order” transitions in small disordered protein fragments and their stabilization upon binding. The results obtained in this work should help to guide efforts to elucidate the modus operandi of these partially disordered proteins, and to conceptualize how these proteins manage to maintain the required amount of disorder even in their bound forms. This work could also potentially facilitate explorations of geometrically specific designable salt bridges through the characterization of composite salt-bridge networks.

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The nucleolar detention pathway: A cellular strategy for regulating molecular networks

Molecular dynamics ensures that proteins and other factors reach their site of action in a timely and efficient manner. This is essential to the formation of molecular complexes, as they require an ever-changing framework of specific interactions to facilitate a model of self-assembly. Therefore, the absence or reduced availability of any key component would significantly impair complex formation and disrupt all downstream molecular networks. Recently, we identified a regulatory mechanism that modulates protein mobility through the inducible expression of a novel family of long noncoding RNA. In response to diverse environmental stimuli, the nucleolar detention pathway (NoDP) captures and immobilizes essential cellular factors within the nucleolus away from their effector molecules. The vast array of putative NoDP targets, including DNA (cytosine-5)-methyltransferase 1 (DNMT1) and the delta catalytic subunit of DNA polymerase (POLD1), suggests that this may be a common and significant regulatory mechanism. Here, we discuss the implications of this new posttranslational strategy for regulating molecular networks.     

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction–diffusion system in the inner volume to a reaction–diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction–diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.     

The dynamics of sparse random networks

Recurrent neural networks with full symmetric connectivity have been extensively studied as associative memories and pattern recognition devices. However, there is considerable evidence that sparse, asymmetrically connected, mainly excitatory networks with broadly directed inhibition are more consistent with biological reality. In this paper, we use the technique of return maps to study the dynamics of random networks with sparse, asymmetric connectivity and nonspecific inhibition. These networks show three qualitatively different kinds of behavior: fixed points, cycles of low period, and extremely long cycles verging on aperiodicity. Using statistical arguments, we relate these behaviors to network parameters and present empirical evidence for the accuracy of this statistical model. The model, in turn, leads to methods for controlling the level of activity in networks. Studying random, untrained networks provides an understanding of the intrinsic dynamics of these systems. Such dynamics could provide a substrate for the much more complex behavior shown when synaptic modification is allowed.     

A theoretical framework of ecological phase transitions for characterizing tree-grass dynamics

This paper describes a theoretical framework of ecological phase transitions for modeling tree-grass dynamics and analyzing the shifts or phase transitions from one vegetation structure to another in the southern Texas landscape. This framework implements the integration of percolation theory, fractal geometry and phase transition theory as a method for modeling the spatial patterns of tree-grass dynamics, and nonlinear Markov non-equilibrium thermodynamic stability theory as a method for characterizing temporal tree-grass dynamics and phase transition. An historical sequence of aerial photographs at a Prosopis - thornscrub savanna parkland site in southern Texas was used to determine the parameters of the models. The preliminary analytical result accords well with current understanding and field survey of vegetation dynamics in the southern Texas landscape. The potential of such approaches and other relevant theories such as self-organized criticality and synergetics to vegetation dynamics is also discussed.     

Ektacytometry: a method for characterizing erythrocyte deformability

In principle, the ektacytometer consists of a combination of a Laser-illuminated diffractometer with a circular viscometric fluid flow, analogous to that of a rotation viscometer. In this device erythrocytes are deformed to ellipsoid-like shapes and produce a diffraction pattern which, depending on the flow conditions, is to some degree elliptically distorted. From the shape of this pattern the extent of cell deformation can be deduced. In this survey an introduction into the mode of operation of the ektacytometer as well as an overview on methodical variants are given on the basis of literature. Since its publication in 1974 ektacytometry has found many applications, mainly in basic research. Presumably, it will receive still broader interest also as a routine method in haematological or pharmaceutical laboratories.     

A control theoretic paradigm for cell signaling networks: a simple complexity for a sensitive robustness

The fields of molecular biology and cell biology are being flooded with complex genomic and proteomic datasets of large dimensions. We now recognize that each molecule in the cell and tissue can no longer be viewed as an isolated entity. Instead, each molecule must be considered as one member of an interacting network. Consequently, there is an urgent need for mathematical models to understand the behavior of cell signaling networks in health and in disease.