The potential for signal integration and processing in interacting MAP kinase cascades

The cellular response to environmental stimuli requires biochemical information processing through which sensory inputs and cellular status are integrated and translated into appropriate responses by way of interacting networks of enzymes. One such network, the mitogen-activated protein (MAP) kinase cascade is a highly conserved signal transduction module that propagates signals from cell surface receptors to various cytosolic and nuclear targets by way of a phosphorylation cascade. We have investigated the potential for signal processing within a network of interacting feed-forward kinase cascades typified by the MAP kinase cascade. A genetic algorithm was used to search for sets of kinetic parameters demonstrating representative key input-output patterns of interest. We discuss two of the networks identified in our study, one implementing the exclusive-or function (XOR) and another implementing what we refer to as an in-band detector (IBD) or two-sided threshold. These examples confirm the potential for logic and amplitude-dependent signal processing in interacting MAP kinase cascades demonstrating limited cross-talk. Specifically, the XOR function allows the network to respond to either one, but not both signals simultaneously, while the IBD permits the network to respond exclusively to signals within a given range of strength, and to suppress signals below as well as above this range. The solution to the XOR problem is interesting in that it requires only two interacting pathways, crosstalk at only one layer, and no feedback or explicit inhibition. These types of responses are not only biologically relevant but constitute signal processing modules that can be combined to create other logical functions and that, in contrast to amplification, cannot be achieved with a single cascade or with two non-interacting cascades. Our computational results revealed surprising similarities between experimental data describing the JNK/MKK4/MKK7 pathway and the solution for the IBD that evolved from the genetic algorithm. The evolved IBD not only exhibited the required non-monotonic signal strength-response, but also demonstrated transient and sustained responses that properly reflected the input signal strength, dependence on both of the MAPKKs for signaling, phosphorylation site preferences by each of the MAPKKs, and both activation and inhibition resulting from the overexpression of one of the MAPKKs.     

A systems biology view of cancer

In order to understand how a cancer cell is functionally different from a normal cell it is necessary to assess the complex network of pathways involving gene regulation, signaling, and cell metabolism, and the alterations in its dynamics caused by the several different types of mutations leading to malignancy. Since the network is typically complex, with multiple connections between pathways and important feedback loops, it is crucial to represent it in the form of a computational model that can be used for a rigorous analysis. This is the approach of systems biology, made possible by new -omics data generation technologies. The goal of this review is to illustrate this approach and its utility for our understanding of cancer. After a discussion of recent progress using a network-centric approach, three case studies related to diagnostics, therapy, and drug development are presented in detail. They focus on breast cancer, B-cell lymphomas, and colorectal cancer. The discussion is centered on key mathematical and computational tools common to a systems biology approach.     

Dynamical analysis of cellular networks based on the Green's function matrix

The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green's function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line.     

Computation and analysis of time-dependent sensitivities in Generalized Mass Action systems

Understanding biochemical system dynamics is becoming increasingly important for insights into the functioning of organisms and for biotechnological manipulations, and additional techniques and methods are needed to facilitate investigations of dynamical properties of systems. Extensions to the method of Ingalls and Sauro, addressing time-dependent sensitivity analysis, provide a new tool for executing such investigations. We present here the results of sample analyses using time-dependent sensitivities for three model systems taken from the literature, namely an anaerobic fermentation pathway in yeast, a negative feedback oscillator modeling cell-cycle phenomena, and the Mitogen Activated Protein (MAP) kinase cascade. The power of time-dependent sensitivities is particularly evident in the case of the MAPK cascade. In this example it is possible to identify the emergence of a concentration of MAPKK that provides the best response with respect to rapid and efficient activation of the cascade, while over- and under-expression of MAPKK relative to this concentration have qualitatively different effects on the transient response of the cascade. Also of interest is the quite general observation that phase-plane representations of sensitivities in oscillating systems provide insights into the manner with which perturbations in the envelope of the oscillation result from small changes in initial concentrations of components of the oscillator. In addition to these applied analyses, we present an algorithm for the efficient computation of time-dependent sensitivities for Generalized Mass Action (GMA) systems, the most general of the canonical system representations of Biochemical Systems Theory (BST). The algorithm is shown to be comparable to, or better than, other methods of solution, as exemplified with three biochemical systems taken from the literature.     

Complex systems biology approach to understanding coordination of JAK-STAT signaling

In this work, we search for coordination as an organizing principle in a complex signaling system using a multilevel hierarchical paradigm. The objective is to explain the underlying mechanism of Interferon (IFN_γ) induced JAK-STAT (specifically JAK1/JAK2-STAT1) pathway behavior. Starting with a mathematical model of the pathway from the literature, we modularize the system using biological knowledge via principles of biochemical cohesion, biological significance, and functionality. The modularized system is then used as a basis for in silico inhibition, knockdown/deletion and perturbation experiments to discover a coordination mechanism. Our analysis shows that a module representing the SOCS1 complex can be identified as the coordinator. Analysis of the coordinator can then be used for the selection of biological experiments for the discovery of ‘soft’ molecular drug targets, that could lead to the development of improved therapeutics. The coordinator identified is also being investigated to determine its relationship to pathological conditions.     

simBio: a Java package for the development of detailed cell models

Quantitative dynamic computer models, which integrate a variety of molecular functions into a cell model, provide a powerful tool to create and test working hypotheses. We have developed a new modeling tool, the simBio package (freely available from http://www.sim-bio.org/), which can be used for constructing cell models, such as cardiac cells (the Kyoto model from Matsuoka et al., 2003, 2004a, b, the LRd model from Faber and Rudy, 2000, and the Noble 98 model from Noble et al., 1998), epithelial cells (Strieter et al., 1990) and pancreatic β cells (Magnus and Keizer, 1998). The simBio package is written in Java, uses XML and can solve ordinary differential equations. In an attempt to mimic biological functional structures, a cell model is, in simBio, composed of independent functional modules called Reactors, such as ion channels and the sarcoplasmic reticulum, and dynamic variables called Nodes, such as ion concentrations. The interactions between Reactors and Nodes are described by the graph theory and the resulting graph represents a blueprint of an intricate cellular system. Reactors are prepared in a hierarchical order, in analogy to the biological classification. Each Reactor can be composed or improved independently, and can easily be reused for different models. This way of building models, through the combination of various modules, is enabled through the use of object-oriented programming concepts. Thus, simBio is a straightforward system for the creation of a variety of cell models on a common database of functional modules.     

Transmembrane signal transduction of the alpha(IIb)beta(3) integrin

Integrins are composed of noncovalently bound dimers of an alpha- and a beta-subunit. They play an important role in cell-matrix adhesion and signal transduction through the cell membrane. Signal transduction can be initiated by the binding of intracellular proteins to the integrin. Binding leads to a major conformational change. The change is passed on to the extracellular domain through the membrane. The affinity of the extracellular domain to certain ligands increases; thus at least two states exist, a low-affinity and a high-affinity state. The conformations and conformational changes of the transmembrane (TM) domain are the focus of our interest. We show by a global search of helix-helix interactions that the TM section of the family of integrins are capable of adopting a structure similar to the structure of the homodimeric TM protein Glycophorin A. For the alpha(IIb)beta(3) integrin, this structural motif represents the high-affinity state. A second conformation of the TM domain of alpha(IIb)beta(3) is identified as the low-affinity state by known mutational and nuclear magnetic resonance (NMR) studies. A transition between these two states was determined by molecular dynamics (MD) calculations. On the basis of these calculations, we propose a three-state mechanism.     

Elucidating tumor-stromal metabolic crosstalk in colorectal cancer through integration of constraint-based models and LC-MS metabolomics

Colorectal cancer (CRC) is a major cause of morbidity and mortality in the United States. Tumor-stromal metabolic crosstalk in the tumor microenvironment promotes CRC development and progression, but exactly how stromal cells, in particular cancer-associated fibroblasts (CAFs), affect the metabolism of tumor cells remains unknown. Here we take a data-driven approach to investigate the metabolic interactions between CRC cells and CAFs, integrating constraint-based modeling and metabolomic profiling. Using metabolomics data, we perform unsteady-state parsimonious flux balance analysis to infer flux distributions for central carbon metabolism in CRC cells treated with or without CAF-conditioned media. We find that CAFs reprogram CRC metabolism through stimulation of glycolysis, the oxidative arm of the pentose phosphate pathway (PPP), and glutaminolysis, as well as inhibition of the tricarboxylic acid cycle. To identify potential therapeutic targets, we simulate enzyme knockouts and find that CAF-treated CRC cells are especially sensitive to inhibitions of hexokinase and glucose-6-phosphate, the rate limiting steps of glycolysis and oxidative PPP. Our work gives mechanistic insights into the metabolic interactions between CRC cells and CAFs and provides a framework for testing hypotheses towards CRC-targeted therapies.     

Stochastic Petri Net extension of a yeast cell cycle model

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.     

Optimal control strategy of malaria vector using genetically modified mosquitoes

The development of transgenic mosquitoes that are resistant to diseases may provide a new and effective weapon of diseases control. Such an approach relies on transgenic mosquitoes being able to survive and compete with wild-type populations. These transgenic mosquitoes carry a specific code that inhibits the plasmodium evolution in its organism. It is said that this characteristic is hereditary and consequently the disease fades away after some time. Once transgenic mosquitoes are released, interactions between the two populations and inter-specific mating between the two types of mosquitoes take place. We present a mathematical model that considers the generation overlapping and variable environment factors. Based on this continuous model, the malaria vector control is formulated and solved as an optimal control problem, indicating how genetically modified mosquitoes should be introduced in the environment. Numerical simulations show the effectiveness of the proposed control.     

An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases

The parameter identifiability problem for dynamic system ODE models has been extensively studied. Nevertheless, except for linear ODE models, the question of establishing identifiable combinations of parameters when the model is unidentifiable has not received as much attention and the problem is not fully resolved for nonlinear ODEs. Identifiable combinations are useful, for example, for the reparameterization of an unidentifiable ODE model into an identifiable one. We extend an existing algorithm for finding globally identifiable parameters of nonlinear ODE models to generate the ‘simplest’ globally identifiable parameter combinations using Gröbner Bases. We also provide sufficient conditions for the method to work, demonstrate our algorithm and find associated identifiable reparameterizations for several linear and nonlinear unidentifiable biomodels.     

Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function

In this article, four different mathematical models of chemotherapy from the literature are investigated with respect to optimal control of drug treatment schedules. The various models are based on two different sets of ordinary differential equations and contain either chemotherapy, immunotherapy, anti-angiogenic therapy or combinations of these. Optimal control problem formulations based on these models are proposed, discussed and compared. For different parameter sets, scenarios, and objective functions optimal control problems are solved numerically with Bock’s direct multiple shooting method.In particular, we show that an optimally controlled therapy can be the reason for the difference between a growing and a totally vanishing tumor in comparison to standard treatment schemes and untreated or wrongly treated tumors. Furthermore, we compare different objective functions. Eventually, we propose an optimization-driven indicator for the potential gain of optimal controls. Based on this indicator, we show that there is a high potential for optimization of chemotherapy schedules, although the currently available models are not yet appropriate for transferring the optimal therapies into medical practice due to patient-, cancer-, and therapy-specific components.     

Modeling the influence of circadian rhythms on the acute inflammatory response

A wide variety of modeling techniques have been applied towards understanding inflammation. These models have broad potential applications, from optimizing clinical trials to improving clinical care. Models have been developed to study specific systems and diseases, but the effect of circadian rhythms on the inflammatory response has not been modeled. Circadian rhythms are normal biological variations obeying the 24-h light/dark cycle and have been shown to play a critical role in the treatment and progression of many diseases. Several of the key components of the inflammatory response, including cytokines and hormones, have been observed to undergo significant diurnal variations in plasma concentration. It is hypothesized that these diurnal rhythms are entrained by the cyclic production of the hormones cortisol and melatonin, as stimulated by the central clock in the suprachiasmatic nucleus. Based on this hypothesis, a mathematical model of the interplay between inflammation and circadian rhythms is developed. The model is validated by its ability to reproduce diverse sets of experimental data and clinical observations concerning the temporal sensitivity of the inflammatory response.     

Detailed qualitative dynamic knowledge representation using a BioNetGen model of TLR-4 signaling and preconditioning

INTRODUCTION: Intracellular signaling/synthetic pathways are being increasingly extensively characterized. However, while these pathways can be displayed in static diagrams, in reality they exist with a degree of dynamic complexity that is responsible for heterogeneous cellular behavior. Multiple parallel pathways exist and interact concurrently, limiting the ability to integrate the various identified mechanisms into a cohesive whole. Computational methods have been suggested as a means of concatenating this knowledge to aid in the understanding of overall system dynamics. Since the eventual goal of biomedical research is the identification and development of therapeutic modalities, computational representation must have sufficient detail to facilitate this 'engineering' process. Adding to the challenge, this type of representation must occur in a perpetual state of incomplete knowledge. We present a modeling approach to address this challenge that is both detailed and qualitative. This approach is termed 'dynamic knowledge representation,' and is intended to be an integrated component of the iterative cycle of scientific discovery. METHODS: BioNetGen (BNG), a software platform for modeling intracellular signaling pathways, was used to model the toll-like receptor 4 (TLR-4) signal transduction cascade. The informational basis of the model was a series of reference papers on modulation of (TLR-4) signaling, and some specific primary research papers to aid in the characterization of specific mechanistic steps in the pathway. This model was detailed with respect to the components of the pathway represented, but qualitative with respect to the specific reaction coefficients utilized to execute the reactions. Responsiveness to simulated lipopolysaccharide (LPS) administration was measured by tumor necrosis factor (TNF) production. Simulation runs included evaluation of initial dose-dependent response to LPS administration at 10, 100, 1000 and 10,000, and a subsequent examination of preconditioning behavior with increasing LPS at 10, 100, 1000 and 10,000 and a secondary dose of LPS at 10,000 administered at approximately 27h of simulated time. Simulations of 'knockout' versions of the model allowed further examination of the interactions within the signaling cascade. RESULTS: The model demonstrated a dose-dependent TNF response curve to increasing stimulus by LPS. Preconditioning simulations demonstrated a similar dose-dependency of preconditioning doses leading to attenuation of response to subsequent LPS challenge - a 'tolerance' dynamic. These responses match dynamics reported in the literature. Furthermore, the simulated 'knockout' results suggested the existence and need for dual negative feedback control mechanisms, represented by the zinc ring-finger protein A20 and inhibitor kappa B proteins (IkappaB), in order for both effective attenuation of the initial stimulus signal and subsequent preconditioned 'tolerant' behavior. CONCLUSIONS: We present an example of detailed, qualitative dynamic knowledge representation using the TLR-4 signaling pathway, its control mechanisms and overall behavior with respect to preconditioning. The intent of this approach is to demonstrate a method of translating the extensive mechanistic knowledge being generated at the basic science level into an executable framework that can provide a means of 'conceptual model verification.' This allows for both the 'checking' of the dynamic consequences of a mechanistic hypothesis and the creation of a modular component of an overall model directed at the engineering goal of biomedical research. It is hoped that this paper will increase the use of knowledge representation and communication in this fashion, and facilitate the concatenation and integration of community-wide knowledge.     

A model of TLR4 signaling and tolerance using a qualitative, particle-event-based method: introduction of spatially configured stochastic reaction chambers (SCSRC)

Introduction

There have been great advances in the examination and characterization of intracellular signaling and synthetic pathways. However, these pathways are generally represented using static diagrams when in reality they exist with considerable dynamic complexity. In addition to the expansion of existing mathematical pathway representation tools (many utilizing systems biology markup language format), there is a growing recognition that spatially explicit modeling methods may be necessary to capture essential aspects of intracellular dynamics. This paper introduces spatially configured stochastic reaction chambers (SCSRC), an agent-based modeling (ABM) framework that incorporates an abstracted molecular ‘event’ rule system with a spatially explicit representation of the relationship between signaling and synthetic compounds. Presented herein is an example of the SCSRC as applied to Toll-like receptor (TLR) 4 signaling and the inflammatory response.

Methods

The underlying rationale for the architecture of the SCSRC is described. A SCSRC model of TLR-4 signaling was developed after a review of the literature regarding TLR-4 signaling and downstream synthetic events. The TLR-4 SCSRC was implemented in the free-ware software platform, Netlogo. A series of in silico experiments were performed to evaluate the response of the TLR-4 SCSRC with respect to response to simulated administration of lipopolysaccharide (LPS). The pro-inflammatory response was represented by simulated secretion of tumor necrosis factor (TNF). Subsequent in silico experiments examined the response to of the TLR-4 SCSRC in terms of a simulated preconditioning effect represented as tolerance of pro-inflammatory signaling to a second dose of LPS.

Results

The SCSRC produces simulated dynamics of TLR-4 signaling in response to LPS stimulation that are qualitatively similar to that reported in the literature. The expression of various components of the signaling cascade demonstrated stochastic noise, consistent with molecular expression data reported in the literature. There is a dose dependent pro-inflammatory response effect seen with increasing initial doses of LPS, and there was also a dose dependent response with respect to preconditioning effect and the establishment of tolerance. Both of these dynamics are consistent with published responses to LPS.

Conclusions

The particle-based, spatially oriented SCSRC model of TLR-4 signaling captures the essential dynamics of the TLR-4 signal transduction cascade, including stochastic signal behavior, dose dependent response, negative feedback control, and preconditioning effect. This is accomplished even given a high degree of molecular event abstraction. The component detail of the SCSRC may allow for sequential parsing of various preconditioning effects, something not possible without computational modeling and simulation, and may give insight into the expected consequences and responses resulting from manipulation of one or many of these modulating factors. The SCSRC is admittedly a work in evolution, and future work will sequentially incorporate additional regulatory mechanisms, both intracellular and paracrine/autocrine, and improved mapping between the spatial chamber configuration and molecular event rules, and experimentally define biochemical reaction rate constants. However, the SCSRC has promise as a highly modular and flexible modeling method that is suited to the dynamic knowledge representation of intracellular processes.     

Cumulative exposure assessment for trace-level polycyclic aromatic hydrocarbons (PAHs) using human blood and plasma analysis

Humans experience chronic cumulative trace-level exposure to mixtures of volatile, semi-volatile, and non-volatile polycyclic aromatic hydrocarbons (PAHs) present in the environment as by-products of combustion processes. Certain PAHs are known or suspected human carcinogens and so we have developed methodology for measuring their circulating (blood borne) concentrations as a tool to assess internal dose and health risk. We use liquid/liquid extraction and gas chromatography–mass spectrometry and present analytical parameters including dynamic range (0–250 ng/ml), linearity (>0.99 for all compounds), and instrument sensitivity (range 2–22 pg/ml) for a series of 22 PAHs representing 2–6-rings. The method is shown to be sufficiently sensitive for estimating PAHs baseline levels (typical median range from 1 to 1000 pg/ml) in groups of normal control subjects using 1-ml aliquots of human plasma but we note that some individuals have very low background concentrations for 5- and 6-ring compounds that fall below robust quantitation levels.     

Modeling, simulation, and experimental validation for continuous Cr(VI) removal from aqueous solutions using sawdust as an adsorbent

Continuous adsorption experiments were performed in a fixed-bed adsorption column to evaluate the performance of low-cost adsorbent (sawdust) developed for the removal of Cr(VI) from aqueous solutions. The effects of influencing parameters such as flow rate, mass of adsorbent, initial Cr(VI) concentration were studied and the corresponding breakthrough curves were obtained. The fixed-bed adsorption process parameters such as breakthrough time, total percentage removal of Cr(VI), adsorption exhaustion rate and fraction of unused bed-length were obtained. A mathematical model for fixed-bed adsorption column was proposed by incorporating the effect of velocity variation along the bed-length in the existing model. Pore and solid diffusion models were used to describe the intra-particle mechanism for Cr(VI) adsorption. The proposed mathematical model was validated with the literature data and the experimental data obtained in the present study and the model was found to be good for explaining the behavior of breakthrough curves.